[ { "image_filename": "designv10_9_0001261_s00170-017-1187-z-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001261_s00170-017-1187-z-Figure1-1.png", "caption": "Fig. 1 Laser scanning of stripes with hatching in LPBF", "texts": [ " Thefactorsand thecorresponding three levelsaredefinedas laser power (P = 169, 182, and 195W), laser scan velocity (vs = 725, 800, and 875 mm/s), and hatch distance (h = 0.09, 0.10, and 0.11 mm). Powder layer thickness is fixed as s = 20 \u03bcm with approximately 55% powder packing density. Aminimum and a maximum energy density are obtained as 94.6 and 139.5 J/mm3 respectively, using Eq. 1. E \u00bc P= vshs\u00f0 \u00de: \u00f01\u00de The LPBF process melts the powder and fuses desired locations on a particular layer of the powder bed. Hatching for a single layer is broken up into several \u201cstripes\u201d that are arranged in various patterns covering the surface (Fig. 1). In this work, the stripes are 4 mm wide and alternate direction in a serpentine manner (as indicated with dotted lines). Each stripe consists of multiple tracks, separated by a hatch distance, and each track is processed with the laser beam moving with a constant scan velocity. After a track is completed by the movement of the laser beam in one direction, the laser turns off for approximately 0.042 ms, during which time, scanning mirrors are aligned to scan the next unprocessed track, and turns on again to move the beam in the opposite direction of the previous track" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002833_j.ymssp.2020.106778-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002833_j.ymssp.2020.106778-Figure3-1.png", "caption": "Fig. 3. Configuration of three-phase 12/8 SRM.", "texts": [ " Finally, the electromagnetic force obtained by the FEM is decomposed by the 2D Fourier transform, and all force harmonic amplitudes are absolute values, as shown in Fig. 2. As can be seen from Fig. 2, when the spatial orders are 0 or 12, and the corresponding temporal orders are 0, 3, 6, 9, 12, etc. When the spatial order is 4, the corresponding temporal orders are 1, 2, 4, 5, 7, 8, 10, 11, etc. When the spatial order is 8, the corresponding temporal orders also are 1, 2, 4, 5, 7, 8, 10, 11, etc. Therefore, the above-mentioned theoretical analysis of the spatial\u2013temporal orders is correct. Fig. 3 is the configuration of a three-phase 12/8 SRM, including the end cover, the enclosure, the rotor, the bearing, the spindle, the stator core, the winding, etc. The stator core and the winding constitute the stator, and there is an interference fit between the stator and the enclosure. The enclosure is bolted to the end cover. The spindle is supported on the end cover by the bearing. Fig. 4 shows the electromagnetic vibration and noise prediction process of SRMs, mainly covering the electromagnetic analysis, the modal analysis considering the orthotropy, the vibroacoustic prediction, and the test", " By this time, we know that the orthotropic material parameters of the stator core and the winding have a great effect on the modal frequencies of the motor. Besides, the influence of the contact conditions between parts cannot be ignored. Because the stiffness of the whole machine depends on the contact properties, the contact conditions have to be set reasonably [31]. Therefore, the reasonable selection of the contact conditions is also very significant. Table 6 presents the contact conditions of the whole machine in Fig. 3. For example, owing to the prestress between the enclosure and the stator, the contact is stiff enough to be considered a bonded pair [17,32]. Moreover, the rotor is supported on the end cover by the bearing. In addition, considering that the stiffness of the bearing is larger, the bearing is directly simplified into a hollow cylinder composed of the inner ring and the outer ring according to [17]. The outer ring is fixed in the end cover, and the inner ring is fixed in the spindle, so the contact conditions should also be set as bonded" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001520_j.jsv.2014.09.004-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001520_j.jsv.2014.09.004-Figure1-1.png", "caption": "Fig. 1. Schematic of the electric machine structure: (a) cutaway diagram of a typical rotating electric machine (IPM motor); (b) motor stator fixed at \u0393D and subject to magnetic force on \u0393N .", "texts": [ " Therefore, if one deals with the vibration problem in time-domain, one has to run the time integration for a long time until the system reaches its steady-state. Thus, the treatment of the problem in frequency-domain is inevitable since it directly looks for steady-state solution and faster in general than the time integration method. In this section, a frequency-domain vibration analysis method is presented and its mathematical background is briefly discussed. A schematic of the typical rotating electric machines is shown in Fig. 1(a). The machines consist of the rotating and stationary parts. The rotating parts mainly consist of rotor core, magnets, and shafts, whereas the stationary parts consist of stator core, windings, and the casing that supports the motor core structure. The rotor is forced to rotate by the magnetic force field or the external load torque, whereas the stator stays stationary during the operation of the machine. Not only the rotor, but also the stator is subject to the magnetic force. The schematic of the motor stator subject to the magnetic force is shown in Fig. 1(b). Let us assume that the displacement field of any points on the stator is small, such that any nonlinearity can be neglected. Also, the domain is assumed to be subjected to damping that is modeled as the Rayleigh damping [17], whose two components are proportional to the mass and the stiffness of the system. Designating the vibrating part of the stator in 3D space as \u03a9 R3, let xA\u03a9 be the position vector, and u\u00f0x; t\u00deAR3 be the displacement field, then the governing equation for the displacement field can be written in a strong form as follows: \u03c1 \u20acu\u00fe\u03b1\u03c1 _u \u00bc\u2207 \u03c4 in \u03a9; (1) u\u00bc 0 on \u0393D; (2) \u03c3 n\u00bc f on \u0393N ; (3) where \u03c1 denotes density, \u03b1 denotes the coefficient of the mass-proportional part of the Rayleigh damping, \u0393D denotes a Dirichlet boundary where the displacement is prescribed, f denotes the magnetic force vector acting on the surface of the stator teeth, which are Neumann boundaries designated as \u0393N " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001919_tfuzz.2018.2880695-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001919_tfuzz.2018.2880695-Figure4-1.png", "caption": "Fig. 4. Inverted pendulum system", "texts": [ " Finally, the analytic solutions to this optimal design problem are discussed in (74)-(79). VIII. ILLUSTRATIVE EXAMPLES The system presented in the form of (7) in Section III is actually a general mechanical system, which can be derived by Newton-Euler mechanics or Lagrangian mechanics. All our theories, including the adaptive robust control design and fuzzy optimimal design, are derived based on the model (7). In this section, we will present two examples to validate the proposed control approach. Consider a simple inverted pendulum system whose pivotal point is at O (see Fig. 4). We shall apply the proposed adaptive robust control and optimal design method to control this inverted pendulum system. The specific steps are shown in Fig. 5. Step 1. The equation of motion is expressed as: M\u03b8\u0308(t)\u2212mgl sin \u03b8(t) = \u03c4(t) + f(t), (80) where \u03b8 is the angular displacement, M > 0 is the moment of inertia, m > 0 is the mass, l is the distance between O and the center of gravity, \u03c4 is the control, and f is the external disturbance. Step 2. The system (80) can be cast into the form of (7) with q = \u03b8, q\u0307 = \u03b8\u0307, q\u0308 = \u03b8\u0308, Cq\u0307 = 0, G = \u2212mgl sin \u03b8, F = \u2212f" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000039_978-1-84996-220-9-Figure8.6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000039_978-1-84996-220-9-Figure8.6-1.png", "caption": "Figure 8.6 Walk-through of an autonomous SELECTCONNECT: (a) Problem; (b) RCH; (c) Keyhole solution; (d) Final plan", "texts": [ " Algorithm:SelectConnect(W t ,PrevList, r f ) AvoidList \u2190 /01 if x f \u2208 C acc R (W t) then2 return FIND-PATH(Wt ,x f ))3 end while (O1,C1) \u2190 RCH(W t ,AvoidList,PrevList, r f ) =NIL do4 (W t+2,\u03c4M,c) \u2190 MANIP-SEARCH(Wt ,O1,C1)5 if \u03c4M = NIL then6 FuturePlan \u2190 SELECTCONNECT(Wt+2,PrevList append C1, r f )7 if FuturePlan = NIL then8 \u03c4N \u2190 FIND-PATH(W t ,\u03c4M[0])9 return ((\u03c4N ,\u03c4M) append FuturePlan)10 end end AvoidList append(O1 ,C1)11 end return NIL12 We have implemented the proposed NAMO planner in a dynamic simulation environment. The intuitive nature of SELECTCONNECT is best illustrated by a sample problem solution generated by the planner. In Figure 8.6(a), we see that C f ree R is disjoint\u2013making this a NAMO problem. Line 4 of SC calls RCH, the heuristic subplanner. RCH finds that the least cost Valid(Oi,Cj) path to the goal lies through Oi = Couch. The path is shown in Figure 8.6(b). RCH also determines that the freespace component to be connected contains the goal. Line 6 calls MANIP-SEARCH to find a motion for the couch. Figure 8.6(c) shows the minimum cost manipulation 224 M. Stilman path that opens the goal free-space. Finally, SELECTCONNECT is called recursively. Since r f is accessible, line 3 finds a plan to the goal and completes the procedure (Figure 8.6(d)). The remainder of the pseudo-code iterates this process until the goal is reached and backtracks when a space cannot be connected. Figure 8.6(d) is particularly interesting because it demonstrates our use of C f ree R connectivity. As opposed to the local planner approach employed in PLR [22], MANIP-SEARCH does not directly attempt to connect two neighboring points in C R. MANIP-SEARCH searches all actions in the manipulation space to join the configuration space components occupied by the robot and the subgoal. The procedure finds that it is easiest to pull the couch from one side and then go around the table for access. This decision resembles human reasoning and cannot be reached with existing navigation planners. Figure 8.6(a) also demonstrates a weakness of L1 planning. Suppose the couch was further constrained by the table such that there was no way to move it. Although the table is obstructing the couch, the table does not explicitly disconnect any freespace and would therefore not be considered for motion. Figure 8.7 is a more complex example with backtracking. In the lower frame, we changed the initial configuration of the table. The initial call to RCH still plans through the couch, however, MANIP-SEARCH finds that it cannot be moved. The planner backtracks, calling RCH again and selects an alternative route. 8 Autonomous Manipulation of Movable Obstacles 225 Figures 8.7 and 8.8 show the scalability of our algorithm to problems with more movable objects. While computation time for Figure 8.6(a) is < 1s, the solutions for Figures 8.7 and 8.8 were found in 6.5 and 9s, respectively (on a Pentium 4 3 GHz). Notice that the planning time depends primarily on the number of manipulation plans that need to be generated for a solution. Although the largest example contains 90 movable obstacles, compared with 20 in Figure 8.7, there is no sizable increase in the solution time. Finally, consider the simple examples for which BFS examined tens of thousands of states in Figure 8.2. The solution to (a) is found instantly by the first heuristic search after examining 15 states" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002207_icesi.2019.8863004-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002207_icesi.2019.8863004-Figure5-1.png", "caption": "Figure 5. Experimental setup and welding strategy", "texts": [ " The laser features a wavelength \u03bb of 1030 nm and, in combination with the optics, the laser beam can be focused to a diameter DL of 255 \u00b5m. Since a programmable focusing optics PFO33-2 is used, high feed rates up to 150 m/s can be realized flexibly without moving the workpiece. The sample parts are positioned under the optics by means of a specially designed clamping device. This enables that all lateral and rotational degrees of freedom of the two sample parts to be connected can be changed in relation to each other in a defined way. Figure 5 shows the clamping of the samples and the strategy of the feed movement. At strategies with one welding line, only line 3 is operated, while at strategies with three welding lines, line number 1 and 2 are executed immediately before line number 3. In these cases, line number 1 and 3 may show a lower laser power PL than line 3 and the offset o may be varied. In preliminary tests, suitable process parameters were determined for the investigated application, whereby one welding line was used. The evaluated process parameters listed in Table 1 are used to produce 30 samples under constant surrounding conditions", " In addition to the risk of damaging the insulation, the tests also showed that the welding seam is displaced downwards from the top of the sample as shown in Figure 8. This phenomenon does not occur reproducibly, for that reason the shape of the weld is very irregular. In order to avoid the displacement of the welding seam and to achieve more uniform welding results, a higher amount of material should be molten so that a larger melt pool is formed. For this reason, the feed strategy is extended by the two further welding geometries 1 and 2 shown in Figure 5. Experiments are used to determine the effect of the offset o and the laser power P1 and P2 of the two additional welding lines on the contact resistance that can be achieved. In the experiments the laser power P1 and P2 are varied between 20% and 80% of the power P3 and the influence on the resistance of the joining area is measured. All other settings are used as displayed in Table 1. The resistance RC depending on the power P1 and P2 is shown in Figure 9. The evaluation in Figure 9 shows that the resistance of the joining area RC is significantly reduced at a power of 60% (4", " To further optimize the welding strategy, the distance of the secondary welding geometry from the joint area o is increased step by step from 0.2 mm to 0.8 mm and the change in the measured resistance RC is determined. In the experiments 60% (4.2 kW) are used as power P1 and P2. The analysis of the measurement data shows that at a small distance of 0.2 mm no significant difference to the initial state can be observed. With further increasing o, the resistance RC decreases until it reaches a minimum at 0.6 mm and then increases again. For the optimization of the feed strategy thus two secondary welding geometries as showed in Figure 5 with a power P1 and P2 of 4.2 kW and an offset o of 0.6 mm are used. To compare the initial strategy with the optimized feed movement, Figure 11 compares the resulting geometry of both cases. It can be seen, that the optimized strategy on the right side results in a broader joining area and reduced displacement due to the higher amount of molten material. Properties As the contact points have to resist the mechanical operating forces during vehicle operation, it is also necessary to be able to assess their mechanical properties" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002277_978-3-319-27131-6-Figure9.4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002277_978-3-319-27131-6-Figure9.4-1.png", "caption": "Fig. 9.4 Two-plane balancing of a statically unbalanced electric rotor", "texts": [ " The eccentricity \u03b5 of the static unbalance and the misalignment angle \u03b1 of the couple unbalance are combined together leading to the dynamic unbalance of the electric rotor. Considering the rotor with an unbalance mass mu at a radius ru, as shown in Fig. 9.3, the static unbalance of the rotor is written as U \u00bc muru \u00f09:1\u00de Due to unbalance mass mu, the resulting mass center G of the rotor locates at the unbalance radius \u03b5. The rotor unbalance results as U \u00bc m\u00fe mu\u00f0 \u00de\u03b5 \u00f09:2\u00de Substituting of Eqs. 9.1 and 9.2, one obtains the unbalance radius at mu< 0, neutral steer, if KUS = 0, and oversteer, if KUS < 0. For a linear two-wheel vehicle and tyre model, assuming small slip and steering angles, the understeer gradient KUS can be derived straight forward, e.g. [2]. Therewith the required steering angle for steady-state cornering becomes \u03b4H is = l \u03c1 + KUSay . (1.2) Basic stability analysis reveals a stable steady-state motion for vehicles with understeer characteristics, while for vehicles with oversteer, stability is lost for v > \u221a \u2212l/KUS . *E-mail: johannes.edelmann@tuwien.ac.at **E-mail: manfred.ploechl@tuwien.ac.at 682 By including simple nonlinear tyre characteristics, but assuming still small angles, it turns out in [3], that different steady-state operating points for neutral steer (and the related definitions of over-/understeer) result from Eq. (1.1) dependent on the test conditions, i.e. on a specified constraint on the relationship between v and l/\u03c1. In particular, v = constant or \u03c1 = constant are discussed in [3], and for the later, d(\u03b4 \u2212 l/\u03c1) day \u2223 \u2223\u2223 \u2223 \u03c1=const = \u03c1 2v \u2202\u03b4 \u2202v , (1.3) with steering angle \u03b4 = \u03b4H/is of the front tyre(s), is derived. In accordance with [2], \u2202\u03b4/\u2202v = 0 then defines the boundary between over- and understeer, which is often used from a practical point of view. Also in this context, steady-state cornering test manoeuvres have been performed for various speeds, but constant cornering radius \u03c1. Stable, steady-state cornering requires that \u2202\u03b4 \u2202(l/\u03c1) \u2223\u2223 \u2223\u2223 v=const > 0 (1.4) for most regular driving conditions, see [2]. At regular steady-state cornering manoeuvres both steering angles of the front wheels and all side slip angles will remain small up to moderate lateral accelerations. Only small traction forces are required for constant speed there. However, steady-state cornering can also be performed with a very high side slip angle of the vehicle, considerably large traction forces and also large, negative steering angles of the front wheels, which are directed towards the outside of the curve. As a consequence, the constraint of small angles needs to be abandoned in this paper, and in addition, the mutual influence of the traction force on the lateral tyre force needs to be considered. For obvious reasons this manoeuvre may be called powerslide, and occurs most often in a transient way, e.g. on gravel roads at Rallye sports. In Figs. 1 and 2, the driving conditions for a two-wheel vehicle model with rear wheel-drive at regular and powerslide steady-state cornering are illustrated. Both vehicles perform the same right-hand turn (radius \u03c1) at the same velocity v. Note the negative steering angle \u03b4 and the large side slip angle of the rear tyre and of the vehicle, \u03b1r and \u03b2 respectively, in the powerslide condition, compared with a typical regular cornering condition. Other quantities are mentioned in the subsequent section. While regular steady-state cornering has fundamentally been covered e.g. in [3\u20137], the powerslide motion has hardly been addressed in literature. Early, but rudimentary contributions to the powerslide can be found in [4, 8], more recent ones in [9\u201312]. REGULAR AND CHAOTIC DYNAMICS Vol. 14 No. 6 2009 In section 2 the applied nonlinear vehicle and tyre model is presented and the equations of motion are derived. Handling characteristics are discussed in section 3, and compared with field measurements in section 4. As the equations of motion have been linearized with respect to the trim states, a basic linear stability analysis of the steady-state motion including the powerslide condition is given in section 5. Some remarks on continuing research will conclude the paper." ] }, { "image_filename": "designv10_9_0001745_j.engfailanal.2014.01.016-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001745_j.engfailanal.2014.01.016-Figure2-1.png", "caption": "Fig. 2. Test Rig 3D model and photo.", "texts": [ " The characteristic bearing potential frequencies of each bearing can be calculated with the use of Eqs. (9)\u2013(12). The dimensions of the bearings are required but instead, the manufacturer provides these values according to the operation speed. For the rotational speed of 2400 rpm (40 Hz) and for a contact angle of 0 the characteristic frequencies are given in Table 4. The setup simulates a common industrial arrangement where a shaft is radially loaded on its free end. The schematic of the bearing test rig on which the experiments are carried out is shown in Fig. 2. The rig consists from a concrete platform based on four rubber bumpers and a 30 mm diameter shaft supported by two self-aligning double ball bearings in their housings. The shaft is coupled with a 3-phase AC motor using a donut type coupling arrangement, which can accommodate small axial and angular misalignments and ensures that the shaft is isolated and it is not affected by the motor\u2019s vibrations. The speed of the motor is controlled from a variable speed drive and it can be adjusted between 0 and 3000 rpm" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000546_j.jprocont.2011.06.011-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000546_j.jprocont.2011.06.011-Figure6-1.png", "caption": "Fig. 6. Contour plot of estimation error |x\u0304 \u2212 \u02c6\u0304x| based on the H\u221e modal observer.", "texts": [], "surrounding_texts": [ "rocess Control 21 (2011) 1172\u2013 1182 1177\nt l f\ny\ns\nx\nw d l c c t s p\n\u02c7\nb t\nc\nF n o\nx\nw[\nM\nC\nL t a\ny\n\u02c7 i c\nx\nH.-N. Wu, H.-X. Li / Journal of P\nemperature profile of a catalytic rod [12]. The spatiotemporal evoution of the dimensionless rod temperature is described by the ollowing parabolic PDE:\n\u2202x\u0304 \u2202t = \u22022x\u0304 \u2202z2 + \u02c7T (e\u2212(\u03d1/(1+x\u0304)) \u2212 e\u2212\u03d1) + \u02c7U(b\u0304u(z)u(t) \u2212 x\u0304) + b\u0304w(z)w(t)\n(40)\n(t) = \u222b\n0\n\u0131 ( z \u2212\n2\n) )x\u0304(z, t)dz + v(t) = x\u0304 ( 2 , t ) + v(t) (41)\nubject to the Dirichlet boundary conditions:\n\u00af (0, t) = 0, x\u0304( , t) = 0 (42)\nhere x\u0304 denotes the dimensionless temperature of the rod, \u02c7T\nenotes a dimensionless heat of reaction, \u03d1 denotes a dimensioness activation energy, \u02c7U denotes a dimensionless heat transfer oefficient, u(t) is the manipulated input (temperature of the ooling medium), w(t) is the process disturbance, y(t) is the hermocouple measurement at point z = /2, and v(t) is the meaurement disturbance. The following typical values are given to the rocess parameters:\nT = 50.0, \u02c7U = 2.0, \u03d1 = 4.0.\nThe actuator and disturbance distribution functions are taken to e b\u0304u(z) = \u221a 2\nsin(z), and respectively. The eigenvalue problem for he spatial differential operator of the process:\nAx\u0304 = \u22022 x\u0304 \u2202z2 , x\u0304 \u2208 S(A) = {x\u0304 \u2208 H2,[0, ], x\u0304(0, t) = 0, x\u0304( , t) = 0}\nan be solved analytically and its solution is of the form: j = \u2212j2, j(z) = \u221a 2 sin(jz), j = 1, 2, . . . , \u221e.\nor this system, we consider the first 2 eigenvalues as the domiant ones (and thus, \u03b5 = | 1|/| 3| \u2248 0.1111). Using the procedure f Section 2.2, the following 2-dimensional slow system is derived:\n\u02d9 s(t) = Asxs(t) + f s(xs(t), 0) + Bw,sw(t) + Bu,su(t) (43)\nhere xs(t) = [\nx1(t) x2(t)\n] , As = [ \u22121 0 0 \u22124 ] , Bw,s = [ \u221a 2 2 4 \u221a\n2 3\n] , Bu,s =\n\u02c7U\n0\n] , and\nf s(xs(t), 0)\n= \u23a1 \u23a2\u23a3\u2212\u02c7U x1(t) + \u02c7T \u222b 0 1(z)(e\u2212(\u03d1/(1+x1(t) 1(z)+x2(t) 2(z))) \u2212 e\u2212\u03d1) dz\n\u2212\u02c7U x2(t) + \u02c7T\n\u222b\n0\n2(z)(e\u2212(\u03d1/(1+x1(t) 1(z)+x2(t) 2(z))) \u2212 e\u2212\u03d1) dz\n\u23a4 \u23a5\u23a6\noreover, Cs in (7) can be obtained as s = \u222b\n0\n\u0131 ( z \u2212\n2\n) [ 1(z) 2(z) ] dz = [\u221a 2 0 ] et v\u0303(t) = y(t) \u2212 Csxs(t), where Csxs(t) is the output of the slow sysem (43). Then, the measurement equation (41) can be written s\n(t) = Csxs(t) + v\u0303(t) (44)\nTo illustrate the proposed result, we assume that f (x\u0304) = (e\u2212(\u03d1/(1+x\u0304)) \u2212 e\u2212\u03d1) \u2212 \u02c7 x\u0304 is unknown, and thus, f (x (t), 0) in (43)\nT U s s\ns unknown. In the following simulation, we suppose that the initial ondition of the PDE system is\n\u00af (z, 0) = x\u03040(z) = 0.5 (45)\nthe control input is u(t) = \u22123y(t), the process disturbance is w(t) = 0.8 sin(t), and the measurement disturbance v(t) is uniformly distributed in the interval (\u22120.1, 0.1). From (45), we obtain xs(0) =[\u221a\n2 0 ]T . Fig. 1 shows the contour plot of evolution of the rod temperature x\u0304(z, t) with these settings. To show the effectiveness of the proposed method, two observers are studied for comparison. A suboptimal H\u221e filter based modal observer is first used as follows:\n\u02d9\u0302xs = Asx\u0302s + Bu,su + K inf (y \u2212 Csx\u0302s), x\u0302s(0) = 0 (46)\nwhere K inf = [\n1.1460 0.0885\n] (47)\nRemark 5. Note that in the suboptimal H\u221e modal observer design, we view the function f s(xs, 0) in (43) as a part of the\nprocess disturbance defined by w\u0304 [\nw f T s (xs, 0)\n]T , and assume\nthat d\u0303 [ w\u0304T v\u0303 ]T \u2208 L2[0, \u221e) is a finite energy signal. From [2], it follows that there exists a stable observer (46) such that the system G : d\u0303 \u2192 (xs \u2212 x\u0302s) is stable and satisfies \u222b \u221e 0 ||xs(t) \u2212 x\u0302s(t)||2 dt <\n2 inf \u222b \u221e 0 ||d\u0303(t)||2 dt if and only if the algebraic Riccati equation (ARE)\nQ AT s + AsQ \u2212 Q (CT s Cs \u2212 \u22122 inf I)Q + B\u0304B\u0304 T = 0 (48)\nhas a solution such that As \u2212 Q (CT s Cs \u2212 \u22122 inf I) is asymptotically stable and Q \u2265 0, where B\u0304 = [ Bw,s I ] . In this case, the observer gain matrix in (47) is given by K inf = Q CT s . It is found that ARE (48) has a solution for any inf \u2265 0.8790. With inf = 0.8790, the solution to\n(48) is Q = [\n1.4363 0.1109 0.1109 0.1761\n] , and thus, we have (47).\nThen, a suboptimal robust adaptive neural modal observer (20) proposed in this paper is applied to the catalytic rod. According to Remark 4, in the following design of Gaussian RBF network, the centers and widths of Gaussian RBFs are chosen on a regular lattice in a compact set. Specifically, the network contains 50 nodes and\n(x\u0302s) = [\n1(x\u0302s) 0 0 2(x\u0302s)\n] where i(x\u0302s) is a 25-dimensional vec-\ntor of Gaussian RBFs with centers ji evenly spaced in [\u22124.5, 4.5] \u00d7 [\u22120.9, 0.9] and widths ji = 2.25 (i = 1, 2, j = 1, 2, . . . , 25). By simulation, we obtain \u0304( (x\u0302s)) \u2264 \u0304 = 2.3377 for all x\u03021 \u2208 [\u22124.5, 4.5] and x\u03022 \u2208 [\u22120.9, 0.9]. The design parameters in (35) are chosen to be = 1, max = 5 and = 0.01. The initial weight is simply selected", "1178 H.-N. Wu, H.-X. Li / Journal of Process Control 21 (2011) 1172\u2013 1182\nt [\nP\n\u02c7\nT\ni r\nr t F p s ( T t s\nthe temperature estimation error converge to a small region after a short time.\no be = 0. Selecting \u02c70 = 4.5 and using the Matlab LMI toolbox 26], it is found that the problem (39) has a solution as follows:\ns = [\n168.8420 \u221214.5630 \u221214.5630 690.8985\n] , Z = [ 589.2288 42.9170 ]\n1 = 861.8413, \u02c72 = 857.2543, \u02c73 = 365.9037,\n= 1.1374\nhus, we obtain K = P\u22121 s Z = [ 3.5015 0.1359 ] . Substituting the result-\nng K and Ps into (20) and (35), respectively, yield the suboptimal obust adaptive neural modal observer.\nFigs. 2\u20134 illustrate the simulation results. The actual trajectoies of states x1(t) and x2(t) of the slow system are indicated by he dashed lines in Figs. 2 and 3, respectively. The solid lines in igs. 2 and 3 indicate the estimates of x1(t) and x2(t) using the proosed modal observer, respectively. The dotted lines in Figs. 2 and 3 how the estimates of x1(t) and x2(t) using the H\u221e modal observer 46). The boundedness of the NN weight estimates is shown in Fig. 4. he contour plots of temperature estimation errors |x\u0304 \u2212 \u02c6\u0304x| based on wo observers are shown in Figs. 5 and 6, respectively. It is easily een from Figs. 5 and 6 that after a short time, the proposed modal\nobserver can present a smaller temperature estimation error than the H\u221e modal observer. Moreover, it was observed through simulations that the initial state estimation error is very sensitive to the choice of initial state condition, since the proposed estimation scheme does not require the initial condition to be known. Even so, it is seen from Fig. 5 that the proposed modal observer can make", "rocess\nc a k c w o s t\n5\no u f t u l s M u T o o\nt m i a i\nA\nH e a ( t e\nA\nL a i\n(\n(\nL\nV\ni\nV\nf\n+ \u02c70 ||f\u0303 s||\u221e + \u02c70 + ||\u0303||\u221e\n\u2264 e\u2212\u02c70t \u0304(Ps) ( ||xs(0)|| + \u221a 1\n\u0304(Ps) ||\u0303(0)||\n)2\nH.-N. Wu, H.-X. Li / Journal of P\nTo illustrate the effectiveness of the methodology under signifiant parametric uncertainties for the process described by (40), we ssume 20% uncertainties in the process parameters \u02c7T and \u02c7U , and eep other simulation parameters unchanged. Fig. 7 presents the ontour plot of estimation error |x\u0304 \u2212 \u02c6\u0304x| using the proposed observer hen \u02c7T = 60.0 and \u02c7U = 2.4. We observe that the proposed modal bserver can make the temperature estimation error converge to a mall region after a short time even in the presence of 20% uncerainties in the process parameters.\n. Conclusions\nIn this paper, a robust adaptive neural observer design methodlogy has been proposed for a class of parabolic PDE systems with nknown nonlinearities and bounded disturbances. The condition or the existence of robust adaptive neural modal observers such hat the state estimation error of the slow system is UUB with an ltimate bound, is provided in terms of LMIs. The weight update aw of the network is represented in terms of the available meaurement error signal, while no SPR-like condition is required. oreover, a suboptimal observer in the sense of minimizing the\npper bound of the peak gains in the ultimate bound is proposed. he proposed observer can ensure that the state estimation error f the actual PDE system is also UUB. Finally, the simulation results n a catalytic rod indicate that the proposed method is effective.\nOur future work will investigate the control strategies based on he proposed observer to achieve desirable stability and perfor-\nance properties for the systems under consideration. Moreover, t should be mentioned that the proposed observer involves several djustable parameters. However, how to find suitable parameters s a difficult tuning problem, which still remains open.\ncknowledgments\nThe work is partially supported by GRF projects from RGC of ong Kong SAR (CityU: 117208; 117310), the National Natural Scince Foundation of China under Grants 61074057 and 91016004, nd the Fundamental Research Funds for the Central Universities YWF-10-01-A19), China. The authors also gratefully acknowledge he helpful comments and suggestions of the anonymous reviewrs, which have improved the presentation.\nppendix A.\nThe following results will be used in the proof of Theorem 1.\nemma A1 ([29,30]). Let \u2217 \u2208 D0, and let the parameter (t) evolve ccording to the dynamics \u0307 = Proj( , r), (0) \u2208 D0. Then, the following s true:\n1) (t) \u2208 D { \u2208 R h| T \u2264 2 max + }, \u2200t \u2265 0. 2) ( (t) \u2212 \u2217)T [Proj( (t), r) \u2212 r] \u2264 0, \u2200t \u2265 0.\nemma A2 ([31]). Let V(t) and g(t) be real scalar functions. Then\n\u02d9 (t) \u2264 \u2212\u02c7V(t) + g(t), \u2200t \u2265 0\nmplies that \u222b t\n(t) \u2264 e\u2212\u02c7tV(0) + 0 e\u2212\u02c7(t\u2212 )g( ) d , \u2200t \u2265 0\nor any finite constant \u02c7.\nControl 21 (2011) 1172\u2013 1182 1179\nProof of Theorem 1. From Assumptions 1 and 3, it is obvious that y(t) \u2208 L\u221e which, together with Fact 2, gives v\u0303(t) \u2208 L\u221e. Thus, w\u0303 \u2208 L\u221e. From Fact 3, (19) and Assumption 5, it is easily seen that\n||f\u0303 s|| \u2264 ||f s(xs, 0)|| + \u0304( (x\u0302s))|| \u2217|| \u2264 fs,b + \u0304 max\nfor all xs, x\u0302s \u2208 Xs, i.e., f\u0303 s \u2208 L\u221e. Since (t) evolves according to (35), it follows from Lemma A1 that\n\u0303 T [ \u22121\u0307 \u2212 (x\u0302s)PsE1y\u0303s] < 0 (A1)\nand (t) \u2208 D , \u2200t \u2265 0. Thus, we have ||\u0303|| \u2264 || \u2217|| + || || \u2264 max + \u221a 2 max +\nfor all {t \u2265 0}, i.e., \u0303 \u2208 L\u221e. Substituting Z = PsK into (34) yields\ns < 0 (A2)\nConsider the Lyapunov function candidate (28). From (A1), (A2), and (19), it follows that the time-derivative of V(x\u0303, \u0303) in (33) satisfies\nV\u0307(x\u0303s, \u0303) \u2264 \u2212\u02c70x\u0303T s Psx\u0303s + \u02c71||w\u0303||2 + \u02c72||f\u0303 s||2 + \u02c73|| T (x\u0302s)\u0303||2\n\u2264 \u2212\u02c70V(x\u0303s, \u0303) + \u02c71||w\u0303||2\u221e + \u02c72||f\u0303 s||2\u221e + \u00af\u030c 3||\u0303||2\u221e (A3)\nwhere\n\u00af\u030c 3 = \u02c73\u0304 + \u02c70 \u22121 (A4)\nBy Lemma A2, we obtain\nV(x\u0303s, \u0303) \u2264 e\u2212\u02c70tV(x\u0303s(0), \u0303(0))\n+ (\u02c71||w\u0303||2\u221e + \u02c72||f\u0303 s||2\u221e + \u00af\u030c 3||\u0303||2\u221e)\n\u222b t\n0\ne\u2212\u02c70(t\u2212 ) d\n= e\u2212\u02c70tV(xs(0), \u0303(0))\n+ (\u02c71||w\u0303||2\u221e + \u02c72||f\u0303 s||2\u221e + \u00af\u030c 3||\u0303||2\u221e) 1 \u02c70 (1 \u2212 e\u2212\u02c70t)\nwhich implies\nx\u0303T s Psx\u0303s \u2264 e\u2212\u02c70tV(xs(0), \u0303(0))\n+ ( \u02c71\n\u02c70 ||w\u0303||2\u221e + \u02c72 \u02c70 ||f\u0303 s||2\u221e +\n\u00af\u030c 3 \u02c70 ||\u0303||2\u221e\n) sup\nt \u2208 [0,\u221e) {1 \u2212 e\u2212\u02c70t}\n\u2264 e\u2212\u02c70tV(xs(0), \u0303(0)) + \u02c71 \u02c70 ||w\u0303||2\u221e + \u02c72 \u02c70 ||f\u0303 s||2\u221e\n+ ( \u02c73\u0304\n\u02c70 + \u22121\n) ||\u0303||2\u221e (A5)\nThus, from (A5) we have\n- (Ps)||x\u0303s||2 \u2264 e\u2212\u02c70t( \u0304(Ps)||xs(0)||2 + \u22121||\u0303(0)||2) + \u02c71\n\u02c70 ||w\u0303||2\u221e\n\u02c72 2 ( \u02c73\u0304 \u22121 ) 2\n+ (\u221a \u02c71\n\u02c70 ||w\u0303||\u221e+\n\u221a \u02c72\n\u02c70 ||f\u0303 s||\u221e +\n\u221a \u02c73\u0304\n\u02c70 + 1 ||\u0303||\u221e\n)2" ] }, { "image_filename": "designv10_9_0001202_978-3-319-32552-1_49-Figure49.14-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001202_978-3-319-32552-1_49-Figure49.14-1.png", "caption": "Fig. 49.14 Lateral forces applying to a car-like vehicle", "texts": [ "54) with e the angle between the vehicle\u2019s body axis PRPF and the tangent to the desired path evaluated at the projection of the point PR on this path, c.s/ the path curvature at the projected point, 1 D .tan. C\u02c7F/ tan.\u02c7R//=L and 2 D .c.s/ cos. e C\u02c7R//=.1 d c.s//. Dynamic Model of Sliding Angles The kinematic model (49.53) can be used for control design once it is completed by a model of the dynamics of the sliding angles \u02c7R and \u02c7F. Such a model can be obtained from Newton\u2019s law and a model of tire/ground interactions. A few notation (Fig. 49.14 for details) and assumptions are introduced for this purpose: The vehicle\u2019s mass is denoted as m and its moment of inertia with respect to the (body-fixed) vertical axis is denoted as Iz. The vehicle\u2019s center of mass G is located on the segment joining PR to PF, at a distance LR from PR and LF from PF. The longitudinal dynamics is neglected. More precisely, it is assumed that the traction force applied to the vehicle, in relation to the monitoring of longitudinal tire/ground contact forces, is controlled independently of the vehicle\u2019s lateral dynamics and that, as a result of this control, the longitudinal velocity of the vehicle expressed in body frame, i" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002611_j.optlastec.2019.105719-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002611_j.optlastec.2019.105719-Figure2-1.png", "caption": "Fig. 2. (a) Illustration of the laser scanning strategies, (b) melt track and melt track boundaries.", "texts": [ " The building chamber of the SLM machine is vacuumized prior to the manufacturing process, followed by filling of argon to form an anti-oxidation atmosphere. For the experiments of this paper, the following parameters are applied: (1) Laser beam power of 360W, (2) Laser beam diameter of \u03a6 0.1 mm, (3) Layer thickness of 0.02mm, (4) Laser scanning speed of 600mm/s for Al-15Si and 650mm/s for Al-15Si/TiC, (5) Laser scanline spacing of 0.06mm, The long bidirectional scanning vectors strategy was used for the cubic sample fabricating as shown in Fig. 2a. Melt track and melt track boundaries in top view are depicted in Fig. 2b. The density of the specimens was measured via the Archimedes methods. The morphologies and microstructure of the samples were analyzed by the SEM (JSM-7600F, JEOL, Japan). The element variation was investigated by the energy dispersive X-ray (EDX) spectrometer equipped on the SEM. The phases were identified by XRD analysis (Philips Co. Ltd., X\u2019 Pert diffractometer with Cu K\u03b1 radiation at 40 kV and 50mA). Polished samples were subjected to Vickers micro-hardness testing (Wilson Hardness TM, 432SVD) under a maximum load of 1 kg and a dwell time of 15 s at room temperature" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001514_j.mechmachtheory.2014.04.017-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001514_j.mechmachtheory.2014.04.017-Figure2-1.png", "caption": "Fig. 2. Contact angle of the ball screw mechanism.", "texts": [ " TH S \u00bc \u2212 cos\u03b1 sin\u03b8 \u2212 cos\u03b8 sin\u03b1 sin\u03b8 r cos\u03b8 cos\u03b1 cos\u03b8 \u2212 sin\u03b8 \u2212 sin\u03b1 cos\u03b8 r sin\u03b8 sin\u03b1 0 cos\u03b1 r\u03b8 tan\u03b1 0 0 0 1 2 664 3 775: \u00f014\u00de Thus, the transform relationship between the position vector in the Frenet\u2013Serret coordinates system OHtnb and the position vector in the coordinates system OXYZ can be expressed as PS \u00bc TH S P H : \u00f015\u00de The coordinate transformation matrix from the Frenet\u2013Serret coordinates system OHtnb to the coordinates system ObXbYbZb is Tb H \u00bc 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 2 664 3 775: \u00f016\u00de 4. Contact angle To determine the contact positions of the ball on the raceways of the screw and nut, the contact angle \u03b2A between the ball and the screw and the contact angle \u03b2B between the ball and the nut are defined on the normal plane of the helix path of the center of the ball on the screw, as shown in Fig. 2. Fig. 2 shows the position relationship of the ball, the nut and the screw on the normal plane, in which A is the contact point between the ball and the raceway of the screw, and B is the contact point between the ball and the raceway of the nut. CS is the arc center of the normal section of the raceway of the screw, and CN is the arc center of the normal section of raceway of the nut. The position vector of point A can be written as PH A \u00bc 0 rb cos\u03b2A rb sin\u03b2A 1 2 664 3 775: \u00f017\u00de The position vector of point B can be written as PH B \u00bc 0 \u2212rb cos\u03b2B \u2212rb sin\u03b2B 1 2 664 3 775 \u00f018\u00de the superscript H of P denotes the position vector with respect to the coordinates system OHtnb; and the subscripts A and B where denote the position of contact points. For the right-handed ball screw mechanism, the nut moves linearly along the negative direction of the ZW axis when the screw rotates around the positive direction of the ZW axis, and the contact angles \u03b2A and \u03b2B are positive in Eqs. (17) and (18), as shown in Fig. 2. In the process of changing the rotation direction of the screw, it is difficult to decide the position and motion state of the ball. However, it will not affect the final relative position of the ball on the raceways of the nut and screw on the whole. Thus, it can be inferred that the result of kinematic analysis will not be affected if the ball is assumed not to move along the tangential direction of the helix path in the process of changing the rotational direction of the screw. The contact angles \u03b2A and \u03b2B are negative in Eqs" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002952_tbme.2020.2994152-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002952_tbme.2020.2994152-Figure1-1.png", "caption": "Fig. 1. The TF8 mechatronic system architecture is a reaction force series elastic actuator with an on-board embedded control system.", "texts": [ " The number of circuits for each trial was chosen to ensure at least 20 samples were attained for each terrain. 1) Prosthesis: a) Mechanical subsystem: This study employed a novel ankle-foot prosthesis comprised of a reaction force series elastic actuator. This device was built to achieve biological kinetics and kinematics that enable operation over a range of terrain conditions. The device is a torque controlled powered prosthesis designed around a series elastic actuator that can provide peak torques up to 180 Nm across a 115 degree total operational range of motion. The system, shown in Figure 1, consists of a large gap radius motor (manufactured by TMotor) modified to integrate a ball screw into the rotor. The ball screw transmission applies a linear force to an output moment arm that generates a torque about the ankle joint. b) Electrical subsystem: An axial load cell directly measures the force in the ball screw. This force signal is evaluated along with the joint encoder measurements to determine the effective joint torque with an accuracy of \u00b10.5 Nm. The joint encoder is a 14-bit absolute encoder, AS5048 (manufactured by Austria Microsystems)" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003608_s11665-021-05603-9-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003608_s11665-021-05603-9-Figure5-1.png", "caption": "Fig. 5 Orientation of tensile, small punch, and fracture toughness specimens for AM Ti64, with respect to the build direction (Z)", "texts": [ " Non-standard Ti64 HIP (1050 C, 100 MPa, 2 h, rapid 1600 C/minute cooling in Ar) with an additional HIP (800 C, 30 MPa, 2 h, slow 12 C/minute cooling in Armeant for martensite tempering). e. Scan lengths of: e1. 78 mm and e2. 26 mm. All SP disks were machined from AM Ti64 non-supported blocks (i.e., directly attached to the build plate) by electrodischarge machining (EDM) in accordance with the drawing in Fig. 4. The relationship between the orientation of tensile, small punch, and fracture toughness specimens is illustrated in Fig. 5. Z is the build direction. After machining, some of the specimens were polished to the surface finish required by ASTM 3205-20 (Ref 6), Ra \u00a3 0.25 lm, by means of abrasive paper with an abrasive grit size designation P400 followed by fine grinding (P1200). As a result, polished disks had a thickness ranging from 0.43 mm to 0.48 mm. The rest of the specimens (EDM \u2018\u2018rough\u2019\u2019 disks) had surface roughness in the range Ra = 3 lm to 4 lm. This allowed us to investigate the influence of surface finish on SP test results" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002966_012083-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002966_012083-Figure2-1.png", "caption": "Figure 2. The boundary conditions of the clamping force exerted on the base plate in Y-directions", "texts": [ " In this research, the bead modelling strategy utilizes a much simpler rectangular shape which gives a smaller margin of relative percentage errors and shorter CPU-Time [9]. Hence, this WAAM model applied \u2018element birth technique\u2019 to simulate the weld filler material [10]. This technique works as at the initial status of analysis, all the elements of the weld bead are deactivated and then the elements are activated consecutively following the heat source movements [10, 11]. ICAME 2019 IOP Conf. Series: Materials Science and Engineering 834 (2020) 012083 IOP Publishing doi:10.1088/1757-899X/834/1/012083 For mechanical boundary conditions, Figure 2 shows the 400N clamping force exerted on the base plate in negatively Y-directions. Furthermore, there are three basic equations that shall be considered in mechanical analysis which are the equilibrium equations, constitutive stress\u2013strain relations and geometric compatibility equations [12]. The variations in the temperature distribution contributes to the deformation of the body via thermal strains and influences the material properties. A large strain was activated as the nonlinear procedure for analysis option which large plastic strains and large deformations are accounted for meanwhile the additive decomposition of elastic, plastic and thermal strain contributions is employed for the stress recovery process [13]" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001782_2829948-Figure23-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001782_2829948-Figure23-1.png", "caption": "Fig. 23. Insertion of new edges (rulings) in direction of minimal compression makes a triangle likely to be bent as a conical surface during the next simulation step. Top: triangle without singular point. Bottom: triangle with singular point.", "texts": [ " Second, we divide the region found into the parts which stay planar and the part corresponding to the new curved region and then remesh the region accordingly. This algorithm takes the compressed triangle Tcomp and the direction of minimal compression v\u22a5 as input. It computes and returns the triangle strip composed by all the triangles affected by the compression of Tcomp and the two borders. To initialize the algorithm, we choose the two edges of Tcomp which are the most affected by the compression by selecting the edges which form the largest angle with v\u22a5, as shown in Figure 23 (top). We then iteratively apply to each of the selected edges e one of the following propagation steps with the direction of propagation being respectively dprop = v\u22a5 and then \u2212v\u22a5 until finding the corresponding borders of the region. A particular case arises when the edge e of Tcomp with the largest angle to v\u22a5 is opposite to a singular point s (see Figure 23 (bottom)). In this case, the singular point (i.e., apex of a d-cone) plays the role of a special border imposing that all rulings pass through it. The propagation algorithm iterates for a given edge e and a direction of propagation dprop until a border is found as follows: \u2014if e is common to another triangle T \u2208 TF (the dihedral angle of e being smaller than \u03b80), then we collect T and we selected the edge of T (other than e) which forms the greatest angle with dprop, see Figure 6(a), and continue the propagation with the next iteration" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002966_012083-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002966_012083-Figure4-1.png", "caption": "Figure 4. An illustration of Goldak\u2019s double ellipsoidal heat source model [5]", "texts": [ " Suitable heat source model must be chosen as the welding process accordingly. Hence, double ellipsoidal model was executed to imitate the real heat source of GMAW process. Goldak et al. defined the double ellipsoid model [15]. Nowadays, the Goldak\u2019s double ellipsoidal model is extensively utilized as the heat source model for GMAW welding process in manufacturing background [16]. The double ellipsoidal heat source has been revealed to accurately represent the heat power density from an electric arc penetrating the surface of a flat workpiece of plate. Figure 4 presents Goldak\u2019s double ellipsoid heat source model with the geometrical conditions but the geometrical parameters a, b and c can be modified in values for the front or rear quadrants. ICAME 2019 IOP Conf. Series: Materials Science and Engineering 834 (2020) 012083 IOP Publishing doi:10.1088/1757-899X/834/1/012083 The subsequent equations were applied to characterize the power density distribution inside the front and rear quadrants of the heat source along the welding path (z-axis). The power density of the heat flux in front section (\ud835\udc5e\ud835\udc63\ud835\udc53) of heat source can be modelled with equation (1) and the rear section (\ud835\udc5e\ud835\udc63\ud835\udc5f) with equation (2) [17]" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001123_j.jpowsour.2015.04.089-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001123_j.jpowsour.2015.04.089-Figure2-1.png", "caption": "Fig. 2. (a) Main components in the air-breathing HmFC; (b) Setup for the HmFC fuelled with human blood.", "texts": [ " The microchannel is sandwiched between the bioanode and abiotic-cathode described above. The electrodes share the same silicone film dimensions; however, the active areas (catalytic surface) were 9.5 mm 7 mm. Finally, the micro device was placed between two poly(methylmethacrylate) (PMMA) plates fabricated using a CNC micro milling system and homogeneously tightened. Gold-pins were used to improve the electrical conductivity. Finally, a window in the PMMA tap (9.5 mm 2 mm) was opened as an air intake into the catholyte stream (Fig. 2a) for the air-breathing cathode [18]. 2.5. Performance of the HmFC In this study, the air-breathing HmFC was evaluated under the four operating conditions described in Table 2. In case I, two flows were introduced in the device, in which the catholyte solution consisted of PB at pH 7, and the anolyte solution was 5 mM glucose in PB at pH 7 previously saturated with nitrogen gas. In case II the anolyte was replaced with human serum saturated with nitrogen before to inject it in the device, meanwhile the catholyte was maintained as case I (PB at pH 7). In the cases III and IV was used only a single flow of serum and blood, respectively (Fig. 2b). This single flow simulated blood flux in the human body. In cases I and II fuel cell tests were performed using a pressuredriven fluid rate of 0.5 and 1.5 mL h 1 for the anolyte and catholyte, respectively. For the cases III and IV fuel cell experiments were carried out at 0.5 mL h 1 flow rate. The flows were electronically controlled using a syringe pump (NE-4000, New Era Pump Systems Inc.). The voltage and current were measured using a BioLogic potentiostat/galvanostat (SAS Science Instrument VSP)" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000879_1.4026264-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000879_1.4026264-Figure5-1.png", "caption": "Fig. 5 Pressure distribution in the oil film for the basic values of the machine-tool setting parameters", "texts": [], "surrounding_texts": [ "The optimization problem formulated according to Eq. (5) is a nonlinear constrained optimization problem, belonging to the general framework of nonlinear programming. In addition functions f mp\u00f0 \u00de and C mp\u00f0 \u00de are not available analytically and are only computable, that is, they exist numerically through the EHD lubrication calculation. Therefore, the problem defined by Eq. (5) also falls within the category of simulation-based optimization. In the simulation-based optimization setting [71], the computer simulation of EHD lubrication must be run, repeatedly, in order to compute the various quantities needed by the optimization algorithm. As a consequence, a good deal of numerical noise is introduced into the model, that causes the calculation of partial derivatives for the gradient-based optimization algorithms to be quite impractical. For this reason, a nonderivative method is selected to solve this particular optimization problem. One of the direct search methods described in Ref. [71] can be adopted. Here, the Hooke and Jeeves pattern search method [72] will be used. This method is designed to solve nonlinear optimization problems, even for nonsmooth cases, when function derivatives are unavailable or their calculation would be impractical or unreliable. A computer program was developed to implement the formulation provided above. The program searches for a local minimum, beginning from the starting guess. The program works by taking steps from one estimate of a minimum, to another (hopefully better) estimate. Taking big steps achieves the minimum more quickly, at the risk of stepping right over an excellent point. The step size is controlled by the parameter Dmp. At each iteration, the step size is multiplied by Dmp (0 < Dmp < 1), so the step size is successfully reduced. Small values of Dmp correspond to big step size changes, which make the program run more quickly. However, there is a chance (especially with highly nonlinear functions) that these big changes will accidentally overlook a promising search vector, leading to nonconvergence. Large values of Dmp correspond to small step size changes, which force the program to carefully examine nearby points instead of optimistically forging ahead, This improves the probability of convergence. In this program, parameter Dmp is set to 0.5. The calculations have shown that in this case it is a reliable value." ] }, { "image_filename": "designv10_9_0000411_aim.2011.6027137-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000411_aim.2011.6027137-Figure1-1.png", "caption": "Fig. 1. Kinematics of a planar curve.", "texts": [ " Mathematical representation and mechanical analysis of these objects are complicated. In such cases, the Theory of Cosserat Rod is well applicable. This theory can formulate statics and dynamics of spatial objects [30, 29, 31 and 36]. However, in this paper, this formulation is used for statics of a planar non-extensible rod, as the backbone of a continuum manipulator. In this section, a brief introduction to this formulation is presented. A. Kinematics Each point of a one-dimensional rod can be parameterized by its unstretched length, here represented by the variable s as in Fig. 1. The position vector [ ] 3( ) ( ) ( ) R T s X s Y s= \u2208r and rotational angle ( ) Rs\u03b8 \u2208 are defined as functions of s, to specify the characteristics of a rod at each point (Fig. 1). Therefore, \u03b8(s) is the rotational angle from the reference coordinate XY to the local coordinate x-y that is attached to the rod at r(s). Based on Fig. 1, for non-extensible rods we have ( ) ( )( ) ( ) sin ( ) cos ( ) Td s s s s ds \u03b8 \u03b8\u2032= = \u2212 r r . (1) B. Statics In order to solve the mechanics of a rod, like what is shown in Fig. 2(a), the force and moment balance equations must be considered first. Fig. 2(b) shows a portion of a rod and the forces and moments experienced by that. In Fig. 2(b), body forces or distributed external forces applied to the rod are specified by f(s), which is typically equal to gravity loading. The other two-element variable n(s) specifies the contact forces and is equal to the sum of all the forces acting from the tip of the rod to a point s" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000931_9781118703274.ch2-Figure2.41-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000931_9781118703274.ch2-Figure2.41-1.png", "caption": "Figure 2.41 Frictional moments in blade bearings", "texts": [ " due to the acceleration of inert masses) cancel each other out with respect to the external drive. Propeller moments, on the other hand, can change considerably. Because of the significant influences and the continually changing conditions during the rotation of a blade, these effects cannot be handled as they stand without unacceptable computing effort. The determination of extreme conditions is often sufficient, however, for dimensioning purposes. Frictional moments in the blade bearings alwayswork against blademovement (Figure 2.41). They depend upon the rotor position and speed of revolution, the speed of pitch variation and the wind speed, and have a quasi-damping character. The frictional moment of a bearing can be expressed as the sum of a load-independent component and a load-dependent component. The load-independent component depends on hydrodynamic losses in the lubricant. This depends on lubricant viscosity and quantity, and also on rolling speed, and is dominant in swift-running lightly loaded bearings. The pitch angle varies only very slowly (maximum \ud835\udf0b\u22156 per second) and the load on the bearing is high, so this component can be neglected" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001710_j.cja.2015.03.003-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001710_j.cja.2015.03.003-Figure6-1.png", "caption": "Fig. 6 Selection of choosing grid center points.", "texts": [ " Analysis of the position errors in Section 2 shows that the error surface of the robot is spatially variable. It may lead the error ns of the robot TCP. compensations in different regions to respond differently to the same change in different grids. Therefore, several representative areas in the region to be calibrated are selected to analyze the variation of the compensation effect. Both a peripheral area and a central area in the given region are tested. In addition, the points close to the central points of the marginal area and the central area are used as the central points of the grids (see Fig. 6). To test the error compensation method of different grid sizes, several cubes with the same central point are chosen, and their side lengths increase with a fixed value. Then, the position errors of the grid vertex are obtained through measurement at the selected sampling points for error compensation. To examine the actual accuracy after compensation, the proposed error compensation method is used to correct the errors of the test points in the region. The measured position error is the actual compensation effect value when the grid side length is selected" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002151_j.apm.2015.04.031-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002151_j.apm.2015.04.031-Figure1-1.png", "caption": "Fig. 1. The prototype of VCM.", "texts": [ " Finally, the simulation and experimental results are verified. The structure of this paper is as follows. In Section 2, the mathematical model of the VCM is established. The FOS reference curve is designed in Section 3. In Section 4, the HFPWM modulation method of the HCHB inverter is presented. The modified ADRC positioning control strategy is put forward in Section 4. The simulation and experimental results are verified in Section 5. Finally, the conclusion of the present study is drawn in Section 7. The mechanical structure of the VCM is shown in Fig. 1, the primary winding of the motor is fixed to the base frame by using two cooling plates, its secondary structure is fixed to the base frame by the springs. Therefore, the mathematical model of the VCM is MFK type, the dynamics of VCM can be described by, Please precis u \u00bc ke dx dt \u00fe iR\u00fe L di dt ; F \u00bc m d2x dt2 \u00fe c dx dt \u00fe kx; F \u00bc kmi; 8>>< >: \u00f01\u00de where u, i, x and F are motor voltage, current, position and the developed force, respectively; c is the damping coefficient, k, km and ke are the spring coefficient, the thrust coefficient and the back EMF coefficient, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003169_j.mechmachtheory.2020.103844-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003169_j.mechmachtheory.2020.103844-Figure2-1.png", "caption": "Fig. 2. PMs with closed-loop passive limbs: (a) a planar 2 P 6R PM; (b) a spatial 3-[ PP ]S ( S S ) PM.", "texts": [ " As a result, novel approaches for singularity analysis and closeness measurement to singularities of non-redundant PMs were established. The above works divided the motion/force transmission and constraint performance into two parts. However, in PMs with closed-loop passive limbs, the transmission and constraint wrenches are always strongly coupled. How to separate them is still an open problem. To develop a better understanding of this issue, a 2 P 6R planar PM and a spatial 3-[ PP ]S ( S S ) PM ([ PP ], 2-DOF actuated prismatic joints; R, revolute joint; S, spherical joint), illustrated in Fig. 2 , with closed-loop passive limbs are presented as examples. In the 2 P 6R PM, the closed-loop passive limb consists of two passive chains (bar B 1,1 C 1,1 and bar B 1,2 C 1,2 with two revolute joints, respectively). These two passive chains are connected between the mobile platform and the actuated joint. Here, a closed loop (B1,1-B1,2-C1,2-C1,1-B1,1) exists in the 1st limb, as shown in Fig. 2 (a). In the spatial 3- [ PP ]S ( S S ) PM, the closed-loop passive limb consists of two passive chains (bar B i C i ,1 and bar B i C i ,2 with two spherical joints, respectively). There is also a closed loop (Bi-Ci,1-Ci,2-B i ) in each limb, as shown in Fig. 2 (b). In these two cases, wrenches which strictly belong to the concept of actuation or constraint are ambiguous according to the screw-based identification method [32] . So far, there seems to be no uniform approach to distinguishing actuation and constraint wrenches of these PMs. However, two wrenches are physically available inside the closed-loop passive limb, and these wrenches lie along two passive chains due to the two-force rod. In this paper, the physically available wrenches are adopted to carry out the evaluation of the coupled motion/force transmissibility and constrainability, that is, the motion-force interaction performance, of PMs with closed-loop passive limbs" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000476_1.4007349-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000476_1.4007349-Figure4-1.png", "caption": "Fig. 4 Load coordinate system", "texts": [ " The bearing supporting structure is the cast hub shown in Fig. 3. There are three holes required for the bearing installation, the left hole for the main shaft connection and access holes in the hub to allow for service. The outer diameter of the hub shell is 3450 mm. The shell thickness is 65 mm. The other bearing connection is the hollow blade root made of an anisotropic material. In the static analysis, extreme loads of the pitch bearing are taken into account. The corresponding load coordinate system and bearing circumference angle is defined in Fig. 4. Here z coincides with the bearing\u2019s center axis, x is perpendicular with y and parallel with the bearing plane, y is perpendicular to the x and z axes and parallel with the bearing plane. Table 2 gives the radial force, axial force, and overturning moment about three axes of the Cartesian coordinate system at the pitch bearing center. It is obvious that the overturning moment about the x axis dominates, which is up to 8326000 N m. That is, the pitch bearing should mainly overcome the overturning moment", " 134, OCTOBER 2012 Transactions of the ASME Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use For clarification, the nomenclature of the contact force and angle is defined in Fig. 8, where Q is the contact force. a is the contact angle. The first subscript denotes the row number, the second subscript denotes the raceway, where 1 means the upper raceway of the outer ring and 2 means the lower raceway of the outer ring. The circumference angle is defined as Fig. 4. Figures 9 and 10 give contact forces in the first row and the second row about these three cases, respectively. At first sight, loads in these three cases are very different from each other, which indicates that the stiffness of the bearing supporting structure greatly affects the load distribution in the bearing. When the outer ring is fixed as a rigid body, loads concentrate on few balls in the first raceway due to lack of the outer ring\u2019s compatibility of deformation. The first raceway is loaded more than the second raceway" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002508_j.triboint.2019.03.048-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002508_j.triboint.2019.03.048-Figure2-1.png", "caption": "Fig. 2. Spiral bevel gear box for experiments.", "texts": [ " Some characteristics of the test rig are introduced as follows: firstly, the two spiral bevel gears are cantilever-type mounted and the splash lubrication is applied in the spiral bevel gearbox of test rig, which are the same as those of the real intermediate gearbox; secondly, two side surfaces of the gearbox are fitted with transparent circular windows to ensure that the spiral bevel gears are partly visible; in addition, in order to be able to measure the flow rate of the intermediate gearbox, a circular hole with a diameter of 22mm is located at one of the see-through windows, and the oil which flows through the circular hole will be guided to a measuring cup beside the test gearbox by an oil guide tube, then the average flow rate of the oil through the circular hole can be measured, as shown in Fig. 2. Besides, detailed parameters of validation experiments are shown in Table 1. Number of elements for the entire fluid domain of validation simulations is 54,5189, and total number of nodes is 9, 5162. The experiment process is introduced as follows: firstly, starting power supply to make the spiral bevel gears rotate and stir the oil to move inside the experimental gearbox; after the oil flow field in the gearbox is relatively stable, the circular hole is opened, and then the lubricating oil flows through the circular hole into the measuring cup; finally, recording the time it takes for the measuring cup to be full, so the average flow rate can be obtained" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003535_j.mechmachtheory.2021.104436-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003535_j.mechmachtheory.2021.104436-Figure6-1.png", "caption": "Fig. 6. Configuration principle of PB-group.", "texts": [ " Therefore, only 2 PB-limbs are needed to completely control the position of O2. According to the principle of permutation and combination, any 2 of 6 PB-limbs can be randomly selected for combination, and then 21 different PB-groups can be obtained. In order to further study the constraint performances of all PB-groups, with 3 groups [RR] [RRR]& [RR] [RR], [RR] [RRR]& [RR]R and [RR] [RRR]& [PRR]R being an example, the constraint characteristics of each limb in the group are analyzed based on the screw theory, which is shown in Fig. 6. The PB-group [RR] [RRR]& [RR] [RR] in Fig. 6(a) is considered to be an example: its motion screw axes $11, $12, $21, $22 and O1O2 always intersect at O1, and the angle between 2 adjacent axes remains unchanged. This indicates that a spherical five-bar closed loop with rotating axes of $11, $12, $21, $22 and O1O2 is generated inside the group, O1O2 acts as an invisible axis. Similarly, PB-groups [RR] [RRR]& [RR] [R] and [RR] [RRR]& [PRR] [R] shown in Figs. 6(b) and (c) have these characteristics. It is known that the spherical fivebar closed loop has 2 rotational DOFs" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003479_0954407021999483-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003479_0954407021999483-Figure1-1.png", "caption": "Figure 1. FE model of the 205/55/R16 radial tire: (a) half 2-D axisymmetric cross-section model of tire, (b) symmetric model generation technique is used to create the semi-3-D tire, and (c) full 3-D tire model obtained by reflecting the semi-3-D tire model.", "texts": [ " The tire model includes carcass rubber, sidewall rubber, wear-resistant rubber, apex rubber, bead, inner liner, body plies, steel belts, and nylon caps. The tread pattern only retains the longitudinal tread pattern which has great influence on the tire. In this paper, the tire finite model of 205/55/R16 radial tire is followed by three main stages: half 2-D axisymmetric tire cross-section model, 2-D model generation, and semi-3-D model reflection. Firstly, a half 2-D axisymmetric tire cross-section model is established as shown in Figure 1(a), in which the rubber element types are CGAX3H and CGAX4H, and the carcass embedded elements such as cord layer are SFMGA1. The rim assembly simulation and tire inflation simulation are also completed in this step simultaneously. Then, through the keyword of *SYMMETRIC MODEL GENERATION in ABAQUS software, the semi-3-D tire model as shown in Figure 1(b) is generated by rotating 360 about its axis of revolution using the symmetric model generation method in ABAQUS, and the interval between circumferential element is settled as 6 . The tire load condition simulation is completed in this step. Finally, the full 3-D tire model as shown in Figure 1(c) is generated by reflecting the semi-3-D model through its symmetry plane. At this time, the element types are changed to C3D6H, C4D8H, and SFM3D4R, respectively. The full 3-D tire finite element model shown in this paper contains 97,803 elements and 157,442 nodes. During the simulation, parametric modeling is adopted, and the analysis steps are related by restart analysis, and the results of each analysis step are transferred by the keyword *SYMMETRIC RESULTS TRANSFER, which effectively reduces the modeling and simulation calculation time" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001843_acs.analchem.7b01012-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001843_acs.analchem.7b01012-Figure3-1.png", "caption": "Figure 3. The printed battery. (a) Schematic of a two cell battery; (b) Photo of the three cell 4.5 Vnom battery. (c) Discharge curve at 1 mA.", "texts": [ " These batteries can be manufactured by screen printing technology and can accommodate a range of operational voltages, currents and energy capacities by tailoring the geometries, numbers and configurations of cells employed. This battery concept and some applications have already been described. 13- 19 The battery was developed on a PEN foil substrate. A stacked, as opposed to a lateral battery configuration was selected as having greatest energy capacity, while also reducing cell footprint. This required electrodes to be printed on top of one another, with separators and electrolyte, with each half cell printed on a separate substrate, forming a sandwich and further sealed within a final PEN layer (Fig. 3a). The energy content of this chemical system is dependent on the amount of material within the battery cell. Screen printing was used to deposit layers of the required thickness in the range of 10 to 80 \u00b5m to maximize energy capacity, while also maintaining a planar configuration. One of the significant advantages of the screen printing process is that a series connection of batteries can be designed and easily manufactured. In the current setup, a series connection of three single cells was designed to deliver a voltage of 4.5 Vnom to drive conventional silicon circuitry (see Device operation) (Fig. 3b). The battery requirement for the system was defined as >3V with a current flow of 1 mA for up to 600 s. The resulting battery was able to supply >3.5 V for 1,000 s at a 1 mA discharge rate (Fig. 3c). The blue trace illustrates the typical performance of cells manufactured in this way, while the red trace illustrates batteries which occasionally fail early. However, they were still capable of driving the appropriate voltage for the duration of the assay. Page 3 of 10 ACS Paragon Plus Environment Analytical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Circuit design" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000879_1.4026264-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000879_1.4026264-Figure2-1.png", "caption": "Fig. 2 Concept of spiral bevel gear hobbing", "texts": [], "surrounding_texts": [ "The optimization method presented by Artoni et al. [14] is applied to systematically define the optimal head-cutter geometry and machine-tool settings to simultaneously maximize the EHD load-carrying capacity of the oil film and minimize the power losses in the oil film. The procedure is treated here as a mathematical programming (optimization) problem. Hence, its formulation requires that proper manufacturing variables, targets (objective function), and constraints be defined. 2.1 Manufacturing Variables. The intact oil film between the meshing tooth surfaces and the power losses in the oil film are extremely sensitive to any small-level variations in the headcutter geometry and machine-tool settings. Appropriate modifications of existing basic manufacturing parameters can significantly enhance the EHD performance characteristics of the gear drive. For this reason, the following manufacturing parameters are taken as the basis of the proposed optimization formulation: the radii of the head-cutter blade profile (rprof1 and rprof2, Fig. 1(b)), the difference in head-cutter radii for the manufacture of the contacting tooth flanks of the pinion and the gear (Drt0), the tilt (j) and swivel (l) angles of the cutter spindle with respect to the cradle rotation axis (Figs. 2 and 3), the tilt distance (hd , Fig. 3), the variation in the radial machine tool setting (De, Figs. 2 and 3), and the variation in the ratio of roll in the generation of the pinion tooth 071007-2 / Vol. 136, JULY 2014 Transactions of the ASME Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/27/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use surface (Dig1). Therefore, the EHD load-carrying capacity of the oil film and the friction factor due to shear stresses in the oil film depend on the eight manufacturing parameters: W mp\u00f0 \u00de \u00bc W rprof1; rprof2;Drt0;j;l; hd;De;Dig1 fT mp\u00f0 \u00de \u00bc fT rprof1; rprof2;Drt0; j; l; hd;De;Dig1 (1) 2.2 Objective Function and Constraints. As pointed out earlier, the goal is to simultaneously maximize the EHD loadcarrying capacity of the oil film and to minimize power losses in the oil film while satisfying the boundary conditions. The objective function and constraints for the optimization problem at issue are obtained by converting the above concepts into mathematical requirements. The applicable objective function can be expressed by the linear combination f mp\u00f0 \u00de \u00bc cW W mp\u00f0 \u00de W0 \u00fe cf fT mp\u00f0 \u00de fT0 (2) where W0 and fT0 are the EHD load-carrying capacity of the oil film and the friction factor obtained for the initial values of the manufacturing parameters, and cW and cf are non-negative weight coefficients, expressing their relative importance. Journal of Mechanical Design JULY 2014, Vol. 136 / 071007-3 Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/27/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use Taking into consideration, the possible misalignments inherent in the gear pair, the objective function is transformed to f mp\u00f0 \u00de \u00bc cW 1\u00f0 \u00de W\u00f01\u00de W0 1\u00f0 \u00de \u00fe cW 2\u00f0 \u00de W\u00f02\u00de W0 2\u00f0 \u00de \u00fe ::::cW 8\u00f0 \u00de W\u00f08\u00de W0 8\u00f0 \u00de \u00fe \u00fe cf 1\u00f0 \u00de fT 1\u00f0 \u00de fT0 1\u00f0 \u00de \u00fe cf 2\u00f0 \u00de fT 2\u00f0 \u00de fT0 2\u00f0 \u00de \u00fe ::::cf 8\u00f0 \u00de fT 8\u00f0 \u00de fT0 8\u00f0 \u00de (3) where cW\u00f0i\u00de and cf \u00f0i\u00de are the weighting coefficients corresponding to the assumed negative and positive values of misalignments Da, Db, eh, and ev (Fig. 4), respectively. The symbols and coordinate systems shown in Figs. 1\u20134 are fully described in Ref. [69]. Proper constraints need to be devised to cause the satisfaction of the boundary conditions and the pressure distribution to remain inside the pre-assigned tooth boundaries. This leads to the requirement that the oil pressure exerted outside the instantly possible contact area be zero. This equality constraint is easily computable through the EHD lubrication analysis. For this, a single variable C needs to be initialized to zero and its value is simply and cumulatively incremented by the nonexisting pressure read at each point of the potential contact area of the instantaneously engaged tooth pairs throughout the mesh cycle. As such a variable will ultimately have to be zero, the constraint can simply be denoted by C mp\u00f0 \u00de \u00bc 0 (4) where C is the total of the nonexisting tooth-surface points under pressure, that depends on the tooth-surface topography through the manufacturing parameters mp. In conclusion, the optimization problem to be solved can be stated as follows: min mp f mp\u00f0 \u00de \u00bc min mp cW 1\u00f0 \u00de W\u00f01\u00de W0 1\u00f0 \u00de \u00fe cW 2\u00f0 \u00de W\u00f02\u00de W0 2\u00f0 \u00de \u00fe ::::cW 8\u00f0 \u00de W\u00f08\u00de W0 8\u00f0 \u00de \u00fe \u00fe cf 1\u00f0 \u00de fT 1\u00f0 \u00de fT0 1\u00f0 \u00de \u00fe cf 2\u00f0 \u00de fT 2\u00f0 \u00de fT0 2\u00f0 \u00de \u00fe ::::cf 8\u00f0 \u00de fT 8\u00f0 \u00de fT0 8\u00f0 \u00de (5) subject to C mp\u00f0 \u00de \u00bc 0 It is important to emphasize that all the functions in Eq. (5) are numerically available through the EHD lubrication analysis, as follows. 2.3. EHD Lubrication Analysis. The pertinent equations governing the pressure and temperature distributions and the oil film shape are the Reynolds, elasticity, energy, and Laplace equations. Point contact EHD lubrication analysis is applied because of the theoretical point contact of mismatched gear pairs. The following general Reynolds equation is used @ @x F2 @p @x \u00fe @ @y F2 @p @y \u00bc @ @x F3 F0 U1 U2\u00f0 \u00de @ @y F3 F0 V1 V2\u00f0 \u00de \u00fe q W1 W2\u00f0 \u00de (6) The full energy equation is applied q cp u @T @x \u00fe v @T @y \u00fe w @T @z k0 @2T @x2 \u00fe @ 2T @y2 \u00fe @ 2T @z2 \u00bc aT T u @p @x \u00fe v @p @y \u00fe g @u @z 2 \u00fe @v @z 2 \" # (7) The equation governing the heat transfer in the pinion and the gear teeth is the Laplace\u2019s equation @2Tm @x2 \u00fe @ 2Tm @y2 \u00fe @ 2Tm @z2 \u00bc 0 (8) where m\u00bc 1 for the pinion tooth, m\u00bc 2 for the gear tooth. The boundary conditions for Eqs. (6\u20138) are presented in Refs. [31,35, and 38]. 071007-4 / Vol. 136, JULY 2014 Transactions of the ASME Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/27/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use The composite normal elastic displacement of the contacting surfaces in point P(x,y), caused by the pressure distribution p(X,Y), is given by d x; y\u00f0 \u00de \u00bc Kd \u00f0xmax xmin \u00f0ymax ymin p X;Y\u00f0 \u00deffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x X\u00f0 \u00de2\u00fe y Y\u00f0 \u00de2 q dX dY (9) where Kd \u00bc 1 p 1 l2 1 E1 \u00fe 1 l2 2 E2 The oil film thickness is defined by the expression h x; y\u00f0 \u00de \u00bc h0 \u00fe d x; y\u00f0 \u00de \u00fe s x; y\u00f0 \u00de (10) The geometrical separation of the contacting surfaces, s(x,y), is determined by the real shape of the pinion and gear teeth, generated by the method described in Ref. [69]. In the instantaneous contact point of the tooth surfaces s\u00f0x; y\u00de \u00bc 0. The minimum oil film thickness, h0, is the minimal clearance of the two tooth flanks caused by the geometry and the elastic deformations of the flanks. The viscosity variation with respect to pressure and temperature and the density variation with respect to pressure are included: g \u00bc g0 eag p bg T Tg0\u00f0 \u00de; q \u00bc q0 1\u00fe a1 p 1\u00fe b1 p (11) In the viscosity\u2013pressure relationship, the exponent ag is a constant in the case of the Barus equation and it is pressure dependent in Roelands\u2019 expression [70]: ag \u00bc ln c1 g0\u00f0 \u00de p 1\u00fe p c z 1 h i (12) The EHD load-carrying capacity of the oil film is calculated from the pressure by simple integration W \u00bc \u00f0xmax xmin \u00f0ymax ymin p dx dy (13) The friction factor is defined by the ratio of the frictional force to the load and it can be written as fT \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi F2 Tx \u00fe F2 Ty q W (14) where FTx \u00bc \u00f0xmax xmin \u00f0ymax ymin g @u @z z\u00bc0 dx dy FTy \u00bc \u00f0xmax xmin \u00f0ymax ymin g @v @z z\u00bc0 dx dy The Reynolds, elasticity, energy, and Laplace\u2019s equations represent a highly nonlinear integro-differential system. This system of equations is solved by using the finite difference method and numerical integration. The finite difference method is based on a three-dimensional grid mesh in the oil film and in the teeth. The intervals used to divide the coordinates along the oil film are irregular; they decrease gradually as they approach the pressure peak. The use of such a nonuniform mesh reduces the computational time considerably. Automatic mesh generation in the oil film and in the gear teeth is included. The systems of linear equations, obtained by using finite difference approximation of the Reynolds, elasticity, energy, and Laplace\u2019s equations, are solved by the successive-over-relaxation method. Details of the presented theoretical background are described in Refs. [31,35, and 38]." ] }, { "image_filename": "designv10_9_0003079_s40430-020-02491-3-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003079_s40430-020-02491-3-Figure1-1.png", "caption": "Fig. 1 a Three-dimensional finite element model (side view); b laser scan strategy of SLM process", "texts": [ " The element is applicable to a 3-D, steady-state or transient thermal analysis. The element also can compensate for mass transport heat flow from a constant velocity field. The size of the top SS316L powder layer and the substrate layer was 2.6 \u00d7 0.6 \u00d7 0.12\u00a0mm3 and 2.4 \u00d7 0.4 \u00d7 0.03\u00a0mm3, respectively. Considering the computational efficiency, the powder bed was fine meshed with hexahedral elements (0.05 \u00d7 0.05 \u00d7 0.03\u00a0mm3), while the much coarser tetrahedron elements were adopted for the substrate (Fig.\u00a01a). The time step used by the model calculation is 4.55 \u00d7 10\u22125 s. From Fig.\u00a01b, the laser beam scans the metal powder in a zig\u2013zag scanning path with four continuous scanning tracks along the x-axis. Six typical points were chosen to study the SLM process. P1, P2, and P3 were the starting point, the middle point, and the ending point of track I, respectively, which can reflect the temperature field distribution of the same track. P4, P5 and P6 were the middle points of tracks II, III and IV, respectively, which can reflect the combination between two adjacent tracks. In this study, a fiber laser was used during the SLM process (Nd:YAG, \u03bb = 1064\u00a0nm), so the heat source model had a Gaussian distribution" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003373_j.mechmachtheory.2021.104348-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003373_j.mechmachtheory.2021.104348-Figure6-1.png", "caption": "Fig. 6. The four configurations (phases) of the leg-wheel module with ground contact. (a) wheeled phase, (b) upper-rim phase, (c) lower-rim phase, and (d) foot phase.", "texts": [ " The virtual work of the leg-wheel is as follows: 2 \u03c4m \u03b4\u03b8 = mg\u03b4G y (22) or \u03c4m = mg\u03b4G y 2 \u03b4\u03b8 (23) where \u03c4m is the torque applied by the actuator. The results satisfying the constraints listed in Table 4 were then inspected visually. The one with the smoothest torque profile was selected, as shown in Fig. 4 . The final design of the leg-wheel module, which utilized the selected dimensions and parameters, is shown in Fig. 5 (a), and the associated 2-DOF driving module is shown in Fig. 5 (b). The first step in motion planning involves understanding the possible configurations (phases) of the leg-wheel module. As shown in Fig. 6 , they are categorized as follows: \u2022 In the wheeled phase, where \u03b8 = \u03b80 and the wheel rim contacts the ground, it does not matter which portion (the upper/lower or left/right rim) is used. \u2022 The upper-rim phase, where \u03b8 = \u03b80 , and the upper rim contacts the ground. \u2022 The lower-rim phase, where \u03b8 = \u03b80 , and the lower rim contacts the ground. \u2022 The foot phase, where \u03b8 = \u03b80 , and only point G contacts the ground. This is the nominal phase when the module is operated in legged mode. In some special circumstances, the upper and lower rim phases can also be utilized for legged locomotion", " The reinforcement material (continuous carbon fiber) is printed in a concentric pattern with two rings in each layer. A bicycle tire tread is mounted on the wheel rim to increase the traction force. The specifications of three generations of leg-wheel modules are listed in Table 5 for reference. The maximum leg length of the linkage leg-wheel module is much longer than its two previous versions, and the weight of the single module is also lighter than that of the TurboQuad. The leg-wheel module is actuated using a 2-DOF driving module, as shown in Fig. 6 (b), which provides two coaxial and rotational outputs. The module was modified from the driving module utilized in TurboQuad [21] , which has one translational output and one rotational output. With a timing pulley, which has a transmission ratio of 1:1, motorL transmits its motion \u03d5 L to the shaft coaxial to that of motorR. Bearings are added between the two rotational outputs, the output shaft in orange is of motor ( \u03d5 R ), which is connected to the right motor bar of the leg-wheel module. The shaft in blue is of motorL through a timing pulley" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003027_530220-Figure11-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003027_530220-Figure11-1.png", "caption": "Fig. 11 - Application of scoring formula to elliptical contact pattern", "texts": [ " The method of approach in the text of this paper would not seem to apply to crown-shaved gears since the hypothesis assumes a, band-shaped contact. Bevel gears with the different radii of curvature providing a certain amount of mismatch between the teeth, also fall in the category of having an elliptical contact pattern. The ratio between the minor and major axes of this contact pattern is, however, extremely small in most cases, rarely exceeding 0.03. The error would be insignificant if an equivalent load We is assumed to form an equivalent band-shaped contact as shown in Fig. 11. This equivalent load should have the same width of the band of contact as the maximum width of the minor axis of the elliptical contact produced by crown-shaved gears and bevel gears. The proportionality found in formula (8) is still true for the elliptical pattern of contact; however, formula (9) is not applicable since, in this case, the maximum compressive stress Sc is proportional to the cube root of the total normal load P, where: C,f (10) Therefore, for the case of crown-shaved gears and bevel gears of normal design, where the length of the contact pattern is no greater than the gear tooth face width, the instantaneous temperature increase at the surface will be proportional to horsepower transmitted by the gears" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000829_s11071-015-2029-x-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000829_s11071-015-2029-x-Figure4-1.png", "caption": "Fig. 4 Uncontrolled wing rock dynamics", "texts": [ " Consider an aircraft with an 80\u25e6 delta wing with L = 479 mm and w = 169 mm. According to the free-toroll experiments described in [4] on the delta wing for AOA = 25\u25e6\u201345\u25e6 and v = 15\u201340 m s\u22121, corresponding to Re = 486000\u20131290000, the coefficients a0\u2013a4 were determined and are shown in Fig 3. Obviously, these parameters vary a lot. It is well known that an uncontrolled wing rock motion results either in limit cycle oscillations or in unstable divergence depending on the initial condition [14]. This is shown in Fig. 4 for two different initial conditions. In the case of initial conditions of x0 = ( 35 \u00b7 10\u22123rad 0rad \u00b7 s\u22121 )T , the wing rock motion results in limit cycle oscillations as shown in Fig. 3a. Step changes of the Reynold number and the AOA affect the oscillation characteristics but do not cause divergence. In the case of initial conditions of x0 = ( 35 \u00b7 10\u22123rad 52 \u00b7 10\u22123rad \u00b7 s\u22121 )T , the wing rock motion results in roll angle divergence as shown in Fig. 4b. Hence, appropriate control strategies should be developed to avoid these effects. Assume an external input disturbance d(t) =\u2211\u221e k=0 [1(t \u2212 100k) \u2212 1(t \u2212 50 \u2212 100k)] added to the control input u(1(t) denotes unit step function) and the steady state error constraint matrix is set to \u03b4 =( 0.01 0.01 0.01 0.01 ) for |\u03c9| \u2208 [ 0, 20rad \u00b7 s\u22121 ] . The ref- erence model is chosen as the second-order system( \u03c6\u0307m \u03c6\u0308m ) = ( 0 1 \u2212\u03c92 m \u22122\u03bem\u03c9m )( \u03c6m \u03c6\u0307m ) . Here, c = ( 0 0 )T because the control objective is to suppress the wing rock dynamics and the desired steady state stable operating point for the system states is x = ( 0 0 )T " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003660_lra.2021.3095035-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003660_lra.2021.3095035-Figure2-1.png", "caption": "Fig. 2. The \u201cgimbal actuator\u201d. (a) Photograph of a gimbal actuator. Joint angles \u03b1i and \u03b2i rotate perpendicular to each other and intersect at the origins of FBi and Fi. (b) Schematic showing the details of the 2-DOF gimbal mechanism. (c) Diagram of orthogonal torques generated by the quadcopter. \u03c4iy points inside the surface.", "texts": [ " Section II introduces the design of the gimbal actuator and the platform. Section III presents the system dynamics. Section IV presents the system control design. Section V analyzes system characteristics and capabilities. Section VI describes the setup of simulation and experiment, while Section VII presents and discusses the results, followed by concluding remarks in Section VIII. A. 2-DOF Gimbal Actuator The regular quadcopter on gimbal is referred to as a \u201cgimbal actuator\u201d in this letter (Fig. 2). i \u2208 {1, . . . , 4} is used to denote the order of each gimbal actuator. The direction of thrust generated by each gimbal actuator is denoted as F\u0302 i, such that F\u0302 i \u2208 S2, where S2 = {F \u2208 R3, \u2016F \u2016 = 1}. We choose a 2-DOF gimbal because achieving rotation in S2 requires a minimum of two rotational joints perpendicular to each other. With the 2-DOF rotation and 1-DOF thrust, each gimbal actuator has 3 DOF in total. The gimbal mechanism consists of several components constructed from PLA plastic by 3D printing (Fig. 2 b). The first rotational joint, \u03b1i, is along the longitudinal direction of the vehicle arm. Two 3D-printed sleeves are fixed at the end of the tube to provide support and allow the gimbal to freely rotate. The second rotational joint, \u03b2i, is perpendicular to the \u03b1i joint, and is realized by a ring fixed on the regular quadcopter body and enclosed by two brackets. The ring is designed to enclose only the central body of the quadcopter so as to minimize its size and weight and prevent interference with the propellers", " The physical properties of the system are listed as follows. The whole platform weights 155 g in total. Each quadcopter weights 27 g, and the 3D-printed gimbal weights 9 g. The maximum thrust of each quadcopter is 0.7 N. The world coordinate frame is denoted as FW , and the platform frame FB is attached to the geometric center of the UAV platform (Fig. 1). To assist the derivation of the controller equations, additional platform frames FBi are defined by rotating FB along +z axis for \u03c0(i\u2212 1)/2 rad and placed at the geometric center of each gimbal (Fig. 2(a)). Actuator frames Fi are attached to the geometric center of the ith quadcopter. X Y R is used to denote rotation matrix in SO(3) from FX to FY . X [\u00b7] is used to denote physical term such as position or velocity expressed in FX other than FW . Also, we have X Y RT = Y XR, and X [\u00b7] = X Y RY [\u00b7]. For simplification purposes, the inertia of the gimbal frame is neglected. The UAV platform consists of five rigid bodies: four gimbal actuators and one central frame. The three-dimensional forces and torques between each gimbal actuator and the central frame are denoted as BN i and BT i respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002022_978-3-319-40036-5-Figure4.1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002022_978-3-319-40036-5-Figure4.1-1.png", "caption": "Fig. 4.1 Illustrated representation of an FDM-based 3D printer. (a) Object is printed from extruded filament deposited on a moving platform. Extruder assembly is mounted on a gantry system that controls deposition in the X and Y directions. (b) Close-up view of the extruder assembly. Adapted from Reference [6] with permission from IOP Publishing", "texts": [ " Generally, layer fabrication in 3D printing is accomplished by deposition of thermoplastics (fused deposition modeling) or viscoelastic materials (syringe deposition or direct ink writing) through a nozzle or syringe, sintering of powdered materials (selective laser sintering), exposure of photocurable resin contained in a reservoir (stereolithography), or inkjet printing of photocurable inks follow by immediate exposure (PolyJet or MultiJet) [4\u20136]. Some important aspects for printing methods relevant to fluidic device fabrication are briefly described in this section. In fused deposition modeling (FDM), a thermoplastic filament (typically 1.75 or 3.00 mm in diameter) is extruded through a heated nozzle (typically ~0.2\u20130.5 mm in diameter) onto a moving platform (Fig. 4.1). The extruder assembly (Fig. 4.1b) is often mounted on a gantry system that controls XY movement, and the platform or stage moves in the Z direction. Fabrication of single objects composed of multiple materials can easily be accomplished with this method simply by including more than one extruder nozzle in the printer design. Typical filament materials include poly(lactic acid), acrylonitrile butadiene styrene, and poly(carbonate). However, there is a great deal of interest in developing composite materials with improved physical and chemical characteristics for various applications" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003208_012183-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003208_012183-Figure2-1.png", "caption": "Figure 2. Stator: 5 is stator disk, 6 is stator winding, 7 is places for fixing", "texts": [ " If the thickness of the dummy air gap is too large (this usually means a large stator thickness), the path of the magnetic flux will pass through the neighboring magnet, rather than the opposite one [7, 8, 9, 10, 11]. Consequently, a very small portion of the magnetic flux will pass in the axial direction (a large leakage flow), and the machine will generate less torque and electromotive force (EMF) [12]. CONMECHYDRO \u2013 2020 IOP Conf. Series: Materials Science and Engineering 883 (2020) 012183 IOP Publishing doi:10.1088/1757-899X/883/1/012183 A low-speed permanent magnet electric generator contains a rotor (Figure 1.) in the form of two flat disks, a stator (Figure 2.) is placed between the rotor disks and is made in the form of a disk connected to a fixed case, the anchor winding is located on the disk along the radii - reel magnets with alternating poles and additional transverse windings mounted on the side parts of the rotor in an amount of 36 to 360 on each disk [13]. The goal is to improve the efficiency of the generator. The technical result is an increase in power, an increase in EMF, a decrease in rpm and rated speed, and a decrease in electromagnetic torque [14]" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002044_j.jmapro.2017.04.017-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002044_j.jmapro.2017.04.017-Figure4-1.png", "caption": "Fig. 4. Surface generation by the laser cladding process.", "texts": [ " However, an excessive sample size will increase the burden of the computer while just a tiny improvement of the accuracy can be achieved. For this reason, a total sample size of 105 is adopted in the present research. The following sections will give some example comparisons between MRR and its relationship with surface integrity factors and tool wear in turning with conventional vs. wiper inserts. 3. Experimental setup 3.1. Surface generation by laser cladding turning of laser cladded parts with conventional vs. wiper insert. 7 Surface was prepared by a self-designed semiconductor/diode laser cladding equipment shown in Fig. 4. Medium carbon steel AISI 1045 with 120 mm in diameter and 200 mm in length was P.R. Zhang et al. / Journal of Manufacturing Processes xxx (2017) xxx\u2013xxx 3 Fig. 3. Schematic diagram of residual ar s u p F t d c s t m s w 5 ( n w 3 i n T elected as the substrate material, while Cr-Ni alloy powder was sed as the cladding material. The powder had the nominal comositions of 0.23 wt.% C, 1.79 wt.% Si, 14.28 wt.% Cr, 3.29 wt.% Ni and e in balance. Prior to each laser cladding process, the substrate had o be descaled by sanding, degreased with gasoline or acetone and ried in air" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003043_j.ymssp.2020.106746-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003043_j.ymssp.2020.106746-Figure1-1.png", "caption": "Fig. 1. The planar illustration of the tractor with N-trailer.", "texts": [ " In addition, R\u00fe denotes positive real numbers. Consider a wheeled mobile robot with n passive trailers subjected to n\u00fe 1 nonholonomic constraints which are connected to each other by passive revolute joints Pi, i \u00bc 0;1; . . . ;n 1 and their motion equations [26] are given by M1\u00f0q\u00de\u20acq\u00f0t\u00de \u00fe C1\u00f0q; _q\u00de _q\u00f0t\u00de \u00fe D1 _q\u00f0t\u00de \u00fe sd1\u00f0t\u00de \u00bc B1\u00f0q\u00desa\u00f0t\u00de \u00fe AT\u00f0q\u00dek; \u00f01\u00de A\u00f0q\u00de _q \u00bc 0; \u00f02\u00de where q :\u00bc \u00bdx; y; hn; hn 1; . . . ; h1; h0 T 2 Rn\u00fe3 denotes a vector of the position and orientations of the trailers and tractor in the earth-fixed frame according to Fig. 1, \u00f0x; y\u00de shows the coordinates of the point Pn on n-th trailer, hi, i \u00bc 1; . . . ;n represents the trailers\u2019 orientations and h0 is the tractor heading, M1\u00f0q\u00de 2 R\u00f0n\u00fe3\u00de \u00f0n\u00fe3\u00de denotes a symmetric positive-definite inertia matrix, C1\u00f0q; _q\u00de 2 R\u00f0n\u00fe3\u00de \u00f0n\u00fe3\u00de shows a matrix of Coriolis and centripetal forces, D1 2 R\u00f0n\u00fe3\u00de \u00f0n\u00fe3\u00de denotes the damping matrix, and sd1\u00f0t\u00de 2 Rn\u00fe3 is a vector of bounded environmental disturbance torque and forces, time-varying unmodeled dynamics, ground friction and unknown dynamics", " From (2), one may find a vector of pseudo-velocities of the system as v\u00f0t\u00de \u00bc \u00bdt\u00f0t\u00de; x\u00f0t\u00de T such that the following kinematic model is obtained for the tractor with N-trailer: _q \u00bc S\u00f0q\u00dev\u00f0t\u00de \u00bc coshn 0 sinhn 0 \u00f01=dn\u00detan\u00f0hn 1 hn\u00de 0 \u00f01=dn 1\u00de tan\u00f0hn 2 hn 1\u00de cos\u00f0hn 1 hn\u00de 0 \u00f01=dn 2\u00de tan\u00f0hn 3 hn 2\u00de cos\u00f0hn 2 hn 1\u00decos\u00f0hn 1 hn\u00de 0 .. . .. . \u00f01=dn k\u00de tan\u00f0hn k 1 hn k\u00deQn 1 i\u00bcn k cos\u00f0hi hi\u00fe1\u00de 0 .. . .. . \u00f01=d1\u00de tan\u00f0h0 h1\u00deQn 1 i\u00bc1 cos\u00f0hi hi\u00fe1\u00de 0 0 1 2 6666666666666666666666664 3 7777777777777777777777775 t\u00f0t\u00de x\u00f0t\u00de |fflfflfflffl{zfflfflfflffl} v\u00f0t\u00de ; \u00f03\u00de where the signal t\u00f0t\u00de represents the linear velocity of the point Pn according to Fig. 1,x\u00f0t\u00de also represents the angular velocity of the tractor subsystem, and S\u00f0q\u00de is called the kinematic matrix. Now, one obtains \u20acq \u00bc _S\u00f0q\u00dev\u00f0t\u00de \u00fe S\u00f0q\u00de _v\u00f0t\u00de by a time derivative of (3) which is substituted into (1) and the result is multiplied by ST\u00f0q\u00de to give the following dynamic equation by recalling A\u00f0q\u00de S\u00f0q\u00de \u00bc 0: M2\u00f0q\u00de _v\u00f0t\u00de \u00fe C2\u00f0q;v\u00dev\u00f0t\u00de \u00fe D2\u00f0q\u00dev\u00f0t\u00de \u00fe sd2\u00f0t;q\u00de \u00bc B2\u00f0q\u00desa\u00f0t\u00de; \u00f04\u00de where M2\u00f0q\u00de \u00bc ST\u00f0q\u00deM1\u00f0q\u00deS\u00f0q\u00de, C2\u00f0q;v\u00de \u00bc ST\u00f0q\u00deM1\u00f0q\u00de _S\u00f0q\u00de \u00fe ST\u00f0q\u00deC1\u00f0q;v\u00deS\u00f0q\u00de, D2\u00f0q\u00de \u00bc ST\u00f0q\u00deD1S\u00f0q\u00de, sd2\u00f0t;q\u00de \u00bc ST\u00f0q\u00desd1\u00f0t\u00de, and B2\u00f0q\u00de \u00bc ST\u00f0q\u00deB1\u00f0q\u00de are new dynamic matrices", " (4) are easily integrated into the following state space representation: _x \u00bc _q _v \u00bc S\u00f0q\u00dev 0 zfflfflfflfflfflffl}|fflfflfflfflfflffl{f \u00f0x\u00de \u00fe 0 M 1 2 \u00f0q\u00deB2\u00f0q\u00de zfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflffl{g\u00f0x\u00de sa\u00f0t\u00de \u00fe 0 M 1 2 \u00f0q\u00deC2\u00f0q;v\u00dev\u00f0t\u00de M 1 2 \u00f0q\u00deD2\u00f0q\u00dev\u00f0t\u00de M 1 2 \u00f0q\u00desd2\u00f0t;q\u00de |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} n\u00f0x\u00de ; \u00f05\u00de where x 2 Rn\u00fe5 is the state vector, f \u00f0x\u00de 2 Rn\u00fe5, g\u00f0x\u00de 2 R\u00f0n\u00fe5\u00de 2 and n\u00f0x\u00de 2 Rn\u00fe5 are smooth vector fields. The above representation lets us to apply the differential geometric control theory for our tracking problem solution. Inspired by [32] and [33], the following output vector is introduced here to solve the control problem: z \u00bc h\u00f0q\u00de \u00bc x\u00fe Xn i\u00bc1 dicoshi \u00fe \u2018cosh0; y\u00fe Xn i\u00bc1 disinhi \u00fe \u2018sinh0 \" #T ; \u00f06\u00de where z represents the coordinates of a virtual reference point PR \u00bc \u00f0xR; yR\u00de in the front of the tractor based on Fig. 1. Then, an input-output model of the vehicle is easily constructed. Toward this end, it is required to differentiate the output Eq. (6) repeatedly such that it is related to torque inputs explicitly. The time derivative of the output equation z in (6) and substituting (5), one obtains the following relation: _z \u00bc Lf h\u00f0q\u00de \u00fe Lnh\u00f0q\u00de \u00fe Lgh\u00f0q\u00de sa \u00bc @h\u00f0q\u00de=@q\u00f0 \u00de S\u00f0q\u00dev\u00f0t\u00de :\u00bc J\u00f0q\u00dev\u00f0t\u00de; \u00f07\u00de where Lf h\u00f0x\u00de \u00bc rh\u00f0x\u00def , Lgh \u00f0x\u00de \u00bc rh\u00f0x\u00de g and Lnh\u00f0x\u00de \u00bc rh\u00f0x\u00den represent the Lie derivatives of h along the vectors f, g, and n, respectively, rh\u00f0x\u00de shows the gradient of h with respect to x and J\u00f0q\u00de is given by J\u00f0q\u00de \u00bc coshn Pn j\u00bc1 sinhn j\u00fe1 tan\u00f0hn j hn j\u00fe1\u00deQn 1 i\u00bcn j\u00fe1 cos\u00f0hi hi\u00fe1\u00de \u2018sinh0 sinhn \u00fe Pn j\u00bc1 coshn j\u00fe1 tan\u00f0hn j hn j\u00fe1\u00deQn 1 i\u00bcn j\u00fe1 cos\u00f0hi hi\u00fe1\u00de \u2018cosh0 2 6664 3 7775: The matrix J\u00f0q\u00de is invertible 8\u2018 > 0 by providing physical limitations between the joints to prevent the controller singularity based on its determinant definition as follows: det J\u00f0q\u00de\u00f0 \u00de \u00bc \u2018cos\u00f0h0 hn\u00de \u00fe \u2018 Xn j\u00bc1 sin\u00f0h0 hn j\u00fe1\u00de tan\u00f0hn j hn j\u00fe1\u00deQn 1 i\u00bcn j\u00fe1cos\u00f0hi hi\u00fe1\u00de : Since _z is still not related to the torque input, we need to differentiate (7) once again: \u20acz\u00f0t\u00de \u00bc L2f h\u00f0x\u00de \u00fe LnLf h\u00f0x\u00de \u00fe LgLf h\u00f0x\u00desa\u00f0t\u00de \u00bc Nd\u00f0q;v\u00de \u00fe D\u00f0q\u00desa\u00f0t\u00de J\u00f0q\u00deM 1 2 \u00f0q\u00desd2\u00f0t;q\u00de; \u00f08\u00de where D\u00f0q\u00de \u00bc J\u00f0q\u00deM 1 2 \u00f0q\u00deB2\u00f0q\u00de shows a decoupling matrix and Nd\u00f0q;v\u00de denotes a vector of unknown nonlinearities which is given by Nd\u00f0q;v\u00de \u00bc @\u00f0J\u00f0q\u00dev\u00de=@q S\u00f0q\u00dev J\u00f0q\u00deM 1 2 \u00f0q\u00deD2\u00f0q\u00dev J\u00f0q\u00deM 1 2 \u00f0q\u00deC2\u00f0q; v\u00dev: \u00f09\u00de RBFNNs have been widely employed for the different NN applications such as functions approximation of uncertain systems according to [34] and references therein" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002989_j.ast.2020.106213-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002989_j.ast.2020.106213-Figure2-1.png", "caption": "Fig. 2. Aerodynamic configuration and forces of the MSL-type entry vehicle.", "texts": [ " The reference trajectory optimization problem for Mars atmospheric entry is treated as a free-terminal-time two point boundary value problem, in which the reference trajectory is optimized without the terminal time constraint. With the predetermined reference trajectory, when designing the trajectory tracking controller, all the trajectory parameters are selected from the reference trajectory, including the terminal time t f . Therefore, in the presented NPC strategy, the terminal time is fixed in Eq. (48) and identical to that of the reference trajectory. To fully determine the three-dimensional Mars entry trajectory tracking algorithm, a proper lateral bank angle reversal logic is required. As shown in Fig. 2, both of the aerodynamic drag and lift forces are generated through the displacement of center-of-mass from the geometric symmetry axis, which is denoted as \u03b4a in Fig. 2. Lateral bank angle reversal logic is to restrain the three-dimensional entry trajectory into a proper corridor by switching the sign of bank angle. When the lateral boundary of the bank angle is reached, the bank angle reversal logic is activated. Consequently, by designing a boundary which is gradually convergent to the target, a \u201czigzag\u201d form of entry trajectory towards the terminal target is generated. The projection of entry vehicle\u2019s velocity vector onto the local horizontal plane is Vh = V cos\u03b3 \u23a1 \u23a3\u2212 cos \u03b8 sin\u03c6 cos\u03c8 \u2212 sin \u03b8 sin\u03c8 \u2212 sin \u03b8 sin\u03c6 cos\u03c8 + cos \u03b8 sin\u03c8 cos\u03c6 cos\u03c8 \u23a4 \u23a6 (50) Similarly, the projection of the vehicle position vector xp = r[cos \u03b8 cos\u03c6, sin \u03b8 cos\u03c6 sin \u03c6]T to the target position vector xp,d = rd[cos \u03b8d cos\u03c6d, sin \u03b8d cos\u03c6d sin \u03c6d]T can be obtained as = xp,d \u2212 xp = rd \u23a1 \u23a3cos \u03b8d cos\u03c6d sin \u03b8d cos\u03c6d sin\u03c6d \u23a4 \u23a6 \u2212 r \u23a1 \u23a3cos \u03b8 cos\u03c6 sin \u03b8 cos\u03c6 sin\u03c6 \u23a4 \u23a6 (51) And the projection of onto local horizontal plane is p = ( xp,d \u2016xp,d\u2016 \u00d7 ) \u00d7 xp,d \u2016xp,d\u2016 (52) Combining Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003090_j.mechmachtheory.2020.104045-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003090_j.mechmachtheory.2020.104045-Figure2-1.png", "caption": "Fig. 2. (a) Planet gear, bearing and pin assembly and (b) Spherical roller bearing [28] .", "texts": [ " Problem formulation This analysis aims to minimize the total weight and power loss of industrial planetary gearbox, considering the entire range of design constraints with mixed integer type design variables. Fig. 1 shows the planetary gearbox considered for the MOO problem. It consists of the input shaft, sun gear, three planet gears, three spherical roller bearings (each planet gear has one spherical roller bearing), and ring gear. The input to the planetary gearbox is at the sun gear shaft and output is obtained from the carrier, keeping the ring gear fixed. The assembly of the planet gear, spherical roller bearing, and planet pin is as illustrated in Fig. 2 (a). Many industrial planetary gearboxes available in the market have more than three planet gears. The new trend in planetary gearbox design is to include more planet gears. However such multi-planetary standard gearbox is not available in AGMA [27] to compare the results of our MOO approach, hence the planet gears are restricted to three. Various parameters used in the design for the planetary gearbox systems such as shaft material, gear material, factor of safety, input power etc are given in Table 1 . The gear material used is surface hardened Chrome-Nickel-Moly Carburising Steel and shaft material is hot rolled SAE 1010 carbon steel. From SKF bearing catalogue [28] , the spherical roller bearing of series 223 is chosen as shown in Fig. 2 (b); the bearing dimension values and dynamic load rating of the bearing are given in Table 2 . In the first case, the MOO results are compared with the industrial gearbox provided by the AGMA 6123-C16 [27] ; in the second case, the results of MOO, with and without scuffing constraint for six different grades oils are compared to find the best oil. Minimization of the weight of the planetary gearbox is considered as the first objective function g 1 ( X ), which includes the weight of the gears W gears , shafts W shafts and planet bearing W Pb as given by Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000415_978-3-642-37552-1-Figure4.4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000415_978-3-642-37552-1-Figure4.4-1.png", "caption": "Fig. 4.4 Self-alignment by capillary force. Photos of alignment patterns are shown on the left side. The tables and schematic drawing of the floating plate and base plate pairs are shown on the right side. Reprinted with permission from [19]. Copyright 2010 American Chemical Society", "texts": [ " A bar made of nickel was patterned on the surface of the floating plates. The nickel layer was deposited by sputtering, and the nickel bar was formed by etching with H3PO4. The bar was 2 \u00b5m thick, and approximately 5 \u00b5m wide (the width was not precise because of the wet etch process). Figure 4.3 shows photos of the fabricated floating plates and lists their shapes and the lengths of the nickel bars. When a droplet is sandwiched between the base plate and floating plate, the floating plate is stabilized at a particular position, as shown in the photos of Fig. 4.4. If the floating plate and the base plate have the same frequency of perturbations (in rad\u22121), the directions of the patterns match those in Fig. 4.4. If the floating plate is displaced from the stabilization point, a restorative torque is generated. The torque is measured by applying a magnetic field varying with the rotational displacement. The measurement principle is depicted in Fig. 4.5. The torque Tm caused by the magnetic field Hext (in Oe) is Tm = \u03bc0 MHext cos\u03c6 (4.1) where \u03bc0 is the magnetic permeability (4\u03c0 \u00d7 10\u22127 N/A2), M (in electromagnetic unit, emu) is the magnetic moment and \u03c6 the rotational displacement.1 When the 1 Please note that 1 Oe is 103/4\u03c0A/m and 1 emu is 10\u22123 A m2" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001546_j.jmbbm.2015.11.024-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001546_j.jmbbm.2015.11.024-Figure7-1.png", "caption": "Fig. 7 \u2013 Static (S) and dynamic (D) friction coefficient as a function of velocity for each roughness.", "texts": [ " Friction coefficient The typical force\u2013time curve observed during the friction tests showed a peak, followed by a region of decay (Fig. 6). The peak force occurred just before the body started moving, which corresponds to the static friction coefficient. The dynamic friction coefficient was calculated for the last 20% of the interval defined by the initial peak and the specimen stop, in which the force was approximately constant. Considering the average for all the plates and velocities, the static friction coefficient (0.29570.056) was significantly higher than the dynamic (0.25570.086) (Fig. 7). The static friction coefficient was significantly smaller for the 0.2 mm/s velocity compared to those for the other two velocities, and there was no significant difference between the static friction coefficients for 1.8 and 10 mm/s. There was no significant difference in the static friction coefficient with respect to the roughness of the plates. The statistical significance for the dynamic friction coefficient presented the same trend as that described for the static coefficient. As there was no significant difference of the static and dynamic friction coefficients with respect to the roughness of the plates, the coefficients were averaged for each insertion velocity as shown in Fig. 7. In the characteristic force\u2013time curves (Fig. 8) it was possible to identify the different parts of the experiment. The negative peak at the beginning corresponds to the puncture, followed by the insertion phase, characterized by several minor peaks. Next, the region of constant force is when the needle rests after insertion. Finally, a positive peak is observed that decreases constantly during extraction. The Pearson linear correlation coefficient of the force\u2013position curve during extraction was in the range 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001785_0954406215627831-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001785_0954406215627831-Figure1-1.png", "caption": "Figure 1. The meshing point on the gear teeth surface.", "texts": [ " Backlash generated by tooth surface wear for one pair of mating teeth Under the condition of dry running, nonlubrication, and neglecting the impact of contact ratio on the wear in one meshing cycle, in this section a model to calculate the backlash excitation generated by tooth accumulated wear in time domain for one pair of mating teeth is built to lay the foundation to quantify the backlash excitation for compound planetary gear set. For one pair of mating teeth, that is to say, under the condition that the contact ratio equals to one, in one meshing cycle, the meshing position moves from the dedendum (L1) to addendum (L2) on tooth of driving gear, as shown in Figure 1. However, if the contact ratio is greater than one, the moving distance of meshing position along the line of action is shorter than the meshing limit L1L2 in one meshing cycle. A proportional relation for the moving distance of meshing position exists between the conditions that contact ratio equals to one and does not equal to one in one meshing cycle. Therefore, this section focuses on the modeling approach to quantify the backlash excitation due to tooth accumulated wear for one pair of mating teeth (the contact ratio equals to one)", " Static tooth surface wear prediction methodology The static tooth surface wear prediction used in this study is based on the model proposed by Flodin and Andersson,8 where Archard\u2019s wear equation is employed to determine the wear depth based on single-point observation method.7 For a meshing pair of mating gears, although the meshing position always changes along tooth profile from entrance into meshing to separating, the line of action contains all the observation points that stand for meshing position, as shown in Figure 1, where the distance between dedendum and addendum along line of action equals to L1L2. Yk is the distance between the kth observation point in mesh and the pitch point P and is described in Appendix 1 in detail. Dividing L1L2 by one pitch of base circle is the contact ratio of that meshing pair. The computational methodology to predict the tooth accumulated wear of one meshing pair is shown in Figure 2. A MAPLE16 program is developed to calculate the wear distribution along the individual observation point on the line of action", " In the subsequent analysis, even if under the condition that contact ratio is greater than one, the impact of \u2018\u2018single\u2013double\u2019\u2019 tooth changing in mesh on tooth accumulated wear is neglected, for the reason that the section of single tooth in mesh locates in the position nearby pitch point, where sliding speed of the observation point in mesh is low according to the definition of sliding speed in Appendix 1, as well as making conveniences of incorporating with dynamic equation set of compound planetary gear set. The values of parameters used in calculating the wear distribution in Figure 3 are listed in Appendix 1, Table 2 and Table 3. In order to associate the results with compound planetary gear set, the tooth number at UNIV CALIFORNIA SAN DIEGO on January 27, 2016pic.sagepub.comDownloaded from of driving gear is larger than that of driven gear in Figure 1, which results in a smaller wear depth at the entrance into mesh than that at exit out of mesh (Figure 3). The increasing backlash generated by tooth surface wear With the wear distribution on tooth in time domain available, the next step is to build the quantified interaction between backlash excitation and tooth surface accumulated wear in time domain. There are three essential additions that must be taken into account to achieve this purpose: (1) the static tooth surface wear prediction describes tooth surface accumulated wear in time domain under the condition that contact ratio equals to one" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001131_j.mechmachtheory.2013.01.004-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001131_j.mechmachtheory.2013.01.004-Figure4-1.png", "caption": "Fig. 4. Geometric description of Hoberman's angulated element.", "texts": [ " The Hoberman's angulated element can be considered as a parallel mechanism. It consists of the linkage ABE and linkage CDE, which are connected by a common joint E. Its mobility can be analyzed by the method, which is based on the screw theory, as proposed in Ref. [21]. It is assumed that the subtended angle between line AD and line BC is denoted by 2\u03b1. It should be noted that amovable closed loop linkage according to Fig. 2 can be built up by n identical scissor elements if the condition 2\u03c0=2\u03b1*n is fulfilled. The orthogonal coordinate oxy is shown in Fig. 4. The axis oxpasses through the point of intersection of theAD and line BC and the point E, and the axis oy is perpendicular to the ox axis in the mechanism plane. Now, the kinematics of the link ABE is studied firstly. There are a revolute joint and a slide joint at point A. Then the twists, which represent the velocity of a rigid body as an angular velocity around an axis and a linear velocity along this axis, of the RP chain are given as \u03a6A \u00bc \u03a6AR \u03a6AS \u00f01\u00de (a) (c) (b) Fig. 1. Scissor like elements", " where Then the twist of joint E can be given as \u03a6E \u00bc \u03a6ER \u03a6ABE : \u00f09\u00de The terminal constraints exerted to joint E by the link ABE can be obtained by solving the reciprocal screw equation \u03a6E TE\u0393E \u00bc 0: \u00f010\u00de The terminal constraints are given as \u0393E \u00bc \u03b21 0 0 0 \u03b22 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 \u03b23 0 0 0 8>>>< >>>: 9>>>= >>>; f 9 f 10 f 11 f 12 2 664 3 775 \u00f011\u00de \u03b21 \u00bc xE \u00fe 1 2 yA\u2212yB\u00f0 \u00de tan\u03b1\u2212 xA \u00fe xB\u00f0 \u00de\u00bd \u03b22 \u00bc \u22121 2 yA \u00fe yB\u2212 xA\u2212xB\u00f0 \u00de cot\u03b1\u00bd \u03b23 \u00bc \u22121 2 xE yA \u00fe yB\u2212 xA\u2212xB\u00f0 \u00de cot\u03b1\u00bd : 8>>>< >>>: \u00f012\u00de Similarly, the terminal constraints exerted to joint E by the link CDE can be obtained as \u0393E0 \u00bc \u03b21 0 0 0 0 \u03b22 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 \u03b23 0 0 0 0 8>>>< >>>: 9>>>= >>>; f 13 f 14 f 15 f 16 2 664 3 775 \u00f013\u00de \u03b21 0 \u00bc xE \u00fe 1 2 yD\u2212yC\u00f0 \u00de tan\u03b1\u2212 xD \u00fe xC\u00f0 \u00de\u00bd \u03b22 0 \u00bc \u22121 2 yD \u00fe yC\u2212 xD\u2212xC\u00f0 \u00de cot\u03b1\u00bd \u03b23 0 \u00bc \u22121 2 xE yD \u00fe yC\u2212 xD\u2212xC\u00f0 \u00de cot\u03b1\u00bd 8>>>< >>>: \u00f014\u00de It can be found that the Hoberman's angulated element will be movable if the terminal constraints exerted to joint E by the link ABE and the link CDE are equal, which is \u0393E \u00bc \u0393E0 : \u00f015\u00de It can be seen from Fig. 4(a) that \u0394ADE and \u0394BCE is symmetric about the axis ox. This leads to the geometric relations of the coordinates of the joints as xA \u00bc xC; yA \u00bc \u2212yC xB \u00bc xD; yB \u00bc \u2212yD : \u00f016\u00de The relations between the coordinates of the joints and the subtended angle \u03b1 are tan\u03b1 \u00bc yB xB \u00bc yC xC tan\u03b1 \u00bc \u2212 yA xA \u00bc \u2212 yD xD : 8>< >: \u00f017\u00de If the length of the element CE and DE is assumed to be p, the coordinates of joint D are xD \u00bc xE \u00fe p sin\u03b3 yD \u00bc \u2212p cos\u03b3 \u00f018\u00de \u03b3 is the angle between line DE and the oy direction. where Then the coordinates of joint C are xC \u00bc xE\u2212p cos \u03c0 2 \u2212 2\u03b1 \u00fe \u03b3\u00f0 \u00de h i yC \u00bc p sin \u03c0 2 \u2212 2\u03b1 \u00fe \u03b3\u00f0 \u00de h i : 8>< >: \u00f019\u00de Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003480_lra.2021.3061388-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003480_lra.2021.3061388-Figure7-1.png", "caption": "Fig. 7. The results of quarter-circle experiment; (a) The skull clamp and the test path in experiment; (b) The executed human-guided path; (c) The human-guided force in x,y and z direction; (d) The velocity in Cartesian space.", "texts": [ " The results were provided in Fig. 6(e). After the demonstration and learning for each iteration (different and only one gesture for each iteration), this learned switching condition was used in our work to execute the proposed VF. For the testing process, a human-guided testing force (for one drilling operation and one retreating operation) along the z-axis was conducted for each gesture iteration after converging the GMMs. Moreover, 5 experiments along a quarter circle of the skull clamp were also conducted in Fig 7. The admittance value of velocity and force in the Cartesian space represented the tested VFs\u2019 performance. For the drilling process, the lower velocity in the x and y-direction yield better performance. Moreover, for the quarter-circle movement, the higher admittance value in the x and y direction results in the better performance. The mean quotient of velocity and the equivalent forces was 0.0347 which is similar to the value of Cali. This similarity demonstrated the successful execution of the admittance controller" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000931_9781118703274.ch2-Figure2.28-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000931_9781118703274.ch2-Figure2.28-1.png", "caption": "Figure 2.28 Relative motion of rotating blades for a wind turbine under azimuth angle yawing", "texts": [ " For high-speed wind turbines, turning the plane of rotation out of the wind by a predetermined amount provides a slow-acting means of protecting the machine. This procedure can be carried out by an active yaw-control system. Here, skewing the rotational plane with respect to the wind exerts moments on the rotating blades, the behavior of which must be formalized if their influence on the control system is to be determined. Further, the following considers the accelerations and moments occurring in a two-bladed model such as that shown in Figure 2.28. The frame of reference x\u2032, y\u2032, z\u2032 is fixed with respect to the rotor. Then, for the centre of mass of a stiff blade, for the speed in this coordinate system dr\u2032 dt = \ud835\udc63\u2032 = 0 holds, with the equivalent acceleration d\ud835\udc63\u2032 dt = b\u2032 = 0. For a yaw velocity of \ud835\udf14A at the head pivot, a turbine rotating with a velocity of \ud835\udf14R gives a resultant angular velocity of \ud835\udeda = \ud835\udedaA + \ud835\udedaR (2.47) and a rotor head yaw velocity of v0 = \ud835\udeda \u00d7 r0 = \ud835\udedaA \u00d7 r0. (2.48) The total velocity of the centre of mass [2.15] is then v = v0 + v\u2032 + \ud835\udeda \u00d7 r\u2032 = \ud835\udedaA \u00d7 r0 + \ud835\udeda \u00d7 r\u2032 (2" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003340_j.addma.2021.101881-Figure20-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003340_j.addma.2021.101881-Figure20-1.png", "caption": "Fig. 20. The (a) longitudinal and (b) vertical residual deformation before (BSR) and after support removal (ASR) using 4-layer ELLM with three tuned MPMs.", "texts": [ " As a benefit, only 8 load steps are needed for the 32-layer model. The computational time can be further reduced compared to the 2-layer and 3-layer ELLM case in Sections 4.1.1 and 4.1.2. Adjusted parameters of the involved fourth MPM (#4) in this example are already given in Table 2. It takes a lot shorter time to finish the 8-step simulation than the above two ELLM cases and the 32-step benchmark case. The obtained residual deformation before and after removal of the teeth-like structures is shown in Fig. 20. Compared to those results in the benchmark case (see Fig. 14), the overall trend of the residual deformation before and after removal of support structures matches well. However, the prediction error increases more significantly due to the lumping effect. The gray color area, which suggests residual deformation magnitude beyond the maximum value of the legend color band, becomes obviously larger in Fig. 20 compared with Fig. 19. One possible reason for the slightly increased prediction error is attributed to the geometry of the cantilever beam. The sudden transitional change of cross sections in the build direction, like the solid-support interface of the cantilever beam, is not considered in the meso-scale modeling. However, due to layer lumping operation, four adjacent layers are deformed in the same load step including the 21st to 24th equivalent X. Liang et al. Additive Manufacturing 39 (2021) 101881 layers containing the solid-support interface. Given the weak constraint of the teeth-like lower layers, the upper layers above the solid-support interface can shrink more in the longitudinal direction as shown in Fig. 20(a). Moreover, the vertical deformation near the solid-support interface already increases a little before cutting. Thus, after cutting the support, vertical residual deformation becomes even larger compared with the benchmark 32-step simulation. In fact, this reason can also explain the slight increase of the simulation error in the 3-layer ELLM case in Section 4.1.2. Therefore, in order to address this issue, a reasonable correction is to divide the entire cantilever beam into two sections in the build direction" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003027_530220-FigureI-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003027_530220-FigureI-1.png", "caption": "Fig. I - Elliptical load distribution and band contact pattern for theoretical development of Blok's temperature formula", "texts": [], "surrounding_texts": [ "A New Look at the Scoring Phenomena of Gears\nB. W . K e l l e y , caterpillar Tractor CO.\nThis paper was presented at the SAE National Tractor Meeting, Milwaukee, Sept. 11, 1952.\nU P to recent years occasional gear-scoring problems were subdued without much technical difficulty, although always with costly production changes, by modifying gear geometry in a trial and error manner or by changing oil characteristics. However, scoring is becoming a real problem now that the engineer prefers a lighter nonadditive oil. He prefers this type of oil because :\n(1) It facilitates cold starting and gives protection before normal operating temperatures are reached.\n(2) It is always convenient, and sometimes necessary, to use a common light lubricant in connected mechanisms such as a transmission-torque converter combination.\n(3) High operating temperatures require oils that have maximum stability, a property which is often not a characteristic of gear oils having maximum ability to prevent scoring.\n(4) Requirements for decreasing gear and bearing wear normally include a filter which, at the present time, restricts the use of gear oils containing certain additives. More accurate formulas are needed to cope with the lesser ability of light oils to provide scoring protection.\nA scored gear will not put a machine immediately out of operation but the damage caused by the apparently superficial failure is threefold. First, it produces a noisy pair of gears and no one dislikes noise as much as a driver. Second, scoring\nTHIS paper points out that the advantages of using light, nonadditive oils are often sacrificed because of lack of fundamental knowledge about gear-scoring problems. Most formulas that have been developed to determine the scoring resistance have been totally empirical and have proved inadequate for stringent design requirements.\nThe author discusses the excellent correlation that exists between scoring test results and a hypothesis on the failure of straight mineral oils. This correlation also encompasses the test results of ball and roller scoring test machines, showing the probable universal application of the hypothesis.\nThe method of approach to the scoring problem of gears as discussed in this paper is a fundamental one, which combines the factors affecting the conversion of frictional energy into surface temperature with gear tooth geometry, stiffness, and surface finish, and points a way to design gears of higher scoring resistance.\nB. W. KELLEY has been with the Caterpillar Tractor Co. since 1946 He was first with the Field Test Division of the Research Department and then with the Research Laboratory,' where he has specialized in gear research for the past four years. Mr. Kelley is a civil engineering graduate of the University of Illinois. During World War II he spent two years overseas as a heavy equipment officer with the Seabees.\nVolume 61, I953 175", "releases small particles of metal that attack oil systems and aggravate the wear of bearings and other gears in the same oil supply. Third, scoring destroys the gear-tooth profile, increasing its sensitivity to pitting and tooth breakage.\nCharacteristics of Scoring\nThe phenomena have been called a variety of terms such as roping, burning, scratching, abrasion, galling, and abnormal wear. These terms are often misused but they commonly indicate the appearance of the scored area. The different appearances are the result of the characteristics of the material, the loads at which scoring occurred, and the properties of the oil. Many times they result from a single cause, however - failure of the lubricant.\nIt is necessary, before continuing, to define the scoring that we are concerned with here. Two of the terms mentioned, scratching and burning, are very mild cases of the failure. Scratching may be described as a few light lines, indicating mild\nseizure at random locations on the tooth face. Naturally, the direction of these lines is in the direction of sliding. This is not a form of scoring which has been recognized as being detrimental. The high points on the surfacc that cause this scratching are eventually leveled off and the score marks will tend to heal over with no apparent ill effects. Burning is indicated by a darkly discolored area, normally in the addendum of the tooth where no gross amount of material has been removed. This discoloration generally precedes the actual welding and true scoring of the material. It is a danger sign, but although there is some evidence of its causing somewhat more than normal wear, it will not be considered serious for our purposes.\nScoring, as it is considered in this paper, is a welding and tearing action resulting from metal to metal contact, which removes material rapidly and continuously as long as the loads, speeds, and other operating conditions remain the same. This is the type of scoring that causes noise, aggravates pitting, and eventually leads to the complete destruction of the gear. Naturally, this is the form of scoring we should design to avoid.\nThe most important reason why scoring phenomena have not been adequately expressed in a formula is due to our lack of specific knowledge of lubrication. If the physicochemistry of lubrication were fully understood the approach to the problem would be more obvious. Instead, the designer has been forced to rely largely upon purely empirical formulas. None of these has been universally accepted by gear designers because of the lack of precise test data. Supporting data for previous formulas has been meager, or has not covered a wide enough set of variables. This makes purely empirical criteria acceptable only within narrow limits of gear design.\nMost of these formulas include some relation between pressure and sliding velocity. The use of two variables simplifies calculation but causes inaccuracy. The seven factors listed below are considered as having significant effect on scoring resistance.\n1. Pressure. 2. Absolute surface velocities and the resultant relative sliding velocity. 3. Viscosity and composition of the oil. 4. Temperature of the oil bath. 5. Properties of the material. 6. Surface finish. 7. Surface treatment. Since these factors are all common variables of modern gearing practice, our formula must take proper cognizance of them to be an effective design tool.\nScoring may be looked upon as a combination of two separate and distinct phenomena. The first one is the failure of the oil film in the contact area. The second, which is visible evidence of the first, is the metallic welding and tearing that occurs.\n176 SAE Transactions", "There is no contention here that full, thick film lubrication exists between gear teeth, for in most cases it does not. Nevertheless, a supporting layer of oil in some form, such as an adsorbed film, must exist, and its destruction in the area of contact is almost instantaneous when final scoring occurs.\nIn an analysis of scoring, a pair of gear teeth may be likened to two rollers pressing against each other at some area of contact on their periphery, rotating in such a manner as to simulate the combined rolling and sliding of gear teeth. Assuming that the rollers are of a known material, having a known surface condition and finish, and that the oil which is lubricating them is of known viscosity and quality, three variables remain which will score the rollers - namely, contact pressure, surface velocity, and oil supply temperature.\nAlthough surface temperature, as a result of sliding and pressure, has been implied in most formulas, it is not adequately treated, and the effect of bulk oil temperature has been largely ignored. It will be shown in this paper that temperature alone may be the ultimate basis for the failure of straight mineral oils.\nSurface Temperature\nIn 1937, H. Blok (at that time research engineer with the Shell laboratories in Holland, and now professor of mechanical engineering at Technical University at Delft) developed a theoretical formula for instantaneous surface temperature that he called a \"temperature flash.\" It is based upon the conversion of friction energy to heat. In the Delft publication1 which presented this interesting work, Blok postulated that straight mineral oils have a critical temperature at which they fail, dependent only upon their viscosity grade. His postulate included the premise that such critical temperatures would limit the use of mineral oils on gears.\nA brief summary of Blok's work follows: A band-shaped contact pattern is assumed, having a parabolic load distribution such as in Fig. 1. The parabolic distribution is chosen in place of the actual elliptic one because of ease of calculation. The error is not significant for our purpose. A surface temperature pattern is formed in the contact area due to sliding, as in Fig. 2. Notice that this instantaneous surface temperature change T2 is added to the bulk temperature of the material T1 to form a final surface temperature Tt. It is interesting to note that the peak of the temperature pattern lags the center line of the contact band width b, the amount being dependent upon the surface velocities. This heat penetrates only a small distance into the material, and the temperature quickly returns to the blank temperature as contact passes. Blok's original formula appears\nbelow. For consistency throughout the paper the liberty has been taken of changing some of the nomenclature to fit commonly used terminology in the United ,States.\nK f Wn (F, - F,)\n(d VFO V - I 2\n(1)\nwhere: K = Constant1\nf = Coefficient of friction Wn = Normal load per unit length V1 and V2 = Surface velocities\nC1 and C2 = Constants of the materials which include their thermal conductivities, specific heats, and densities.\nb = Width of the band of contact as calculated by the Hertzian elasticity formula for cylindrical objects.\nIt is important to note that the formula includes three of the seven variables mentioned as having an effect on scoring: load, velocity, and character-\n1 See \"Les Temperatures de Surface dans les Conditions de Graissage sous Pression Extreme,\" by H. Blok. Second World P'etroleum Congress, Paris, June, 1937.\nVolume 61, 1953 177" ] }, { "image_filename": "designv10_9_0002147_j.ymssp.2019.02.033-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002147_j.ymssp.2019.02.033-Figure4-1.png", "caption": "Fig. 4. Beam model.", "texts": [ " (5) yields: F\u00f0x\u00de \u00bc kx k2x2 4f y 0 6 x 6 2f y=k f y x P 2f y=k ( \u00f06\u00de For the adjusted Iwan model, the ratio of the stiffness of the parallel linear spring element to the total stiffness of the Iwan model can be assumed as a \u00bc ka=k, and the corresponding restoring force function can be expressed as: F\u00f0x\u00de \u00bc kx \u00f01 a\u00de2k2x2 4f y 0 6 x 6 2f y=\u00f01 a\u00dek f y \u00fe akx x P 2f y=\u00f01 a\u00dek 8< : \u00f07\u00de The Iwan model satisfies the Masing criterion [37], thus, the restoring force function of the Iwan model under vibration load is: Fl\u00f0x\u00de \u00bc F0 \u00fe 2F x0\u00fex 2 _x P 0 loading Fu\u00f0x\u00de \u00bc F0 2F x0 x 2 _x 6 0 unloading ( \u00f08\u00de in which Fl\u00f0x\u00de and Fu\u00f0x\u00de are the restoring force during loading and unloading, respectively. x0 and F0 are the maximum displacement and restoring force in a cycle, respectively. As shown in Fig. 4(a), the mechanical model of linear elastic beam element can be simplified to a configuration with two linear spring elements. Each node of the beam element contains two degrees of freedom, that is, a vertical deflection v and a rotation angle h, and the corresponding shear force and bending moment are Q and M, respectively. Then, the deformations of the two linear spring elements can be represented as: D1 \u00bc L 2 \u00f0h1 \u00fe h2\u00de \u00fe \u00f0v1 v2\u00de D2 \u00bc h 2 \u00f0h1 h2\u00de \u00f09\u00de where L and h are length and height of the beam element, respectively", " Q1 \u00bc f 1 M1 \u00bc L 2 f 1 \u00fe h 2 f 2 Q2 \u00bc f 1 M2 \u00bc L 2 f 1 h 2 f 2 \u00f011\u00de By assuming the stiffnesses as k1 \u00bc 12EI=L3, k2 \u00bc 4EI=Lh2, and substituting Eqs. (9) and (10) into Eq. (11), we can get: Q1 M1 Q2 M2 8>>< >>: 9>>= >>; \u00bc EI L 12 L2 6 L 12 L2 6 L 6 L 4 6 L 2 12 L2 6 L 12 L2 6 L 6 L 2 6 L 4 2 66664 3 77775 v1 h2 v2 h2 8>>< >>: 9>>= >>; \u00f012\u00de Obviously, the force-displacement relationship presented by Eq. (12) is equivalent to that of the two-dimensional finite element for beam element. In order to simulate the energy dissipation mechanism and nonlinear phenomena of bolted joints, the Iwan beam element shown in Fig. 4(b) can be obtained by replacing the linear spring elements in Fig. 4(a) with the adjusted Iwan models. Q1 \u00bc f 1\u00f0D1; h1\u00de M1 \u00bc L 2 f 1\u00f0D1; h1\u00de \u00fe h 2 f 2\u00f0D2; h2\u00de Q2 \u00bc f 1\u00f0D1; h1\u00de M2 \u00bc L 2 f 1\u00f0D1; h1\u00de h 2 f 2\u00f0D2; h2\u00de \u00f013\u00de where h1 and h2 are the loading history of displacement D1 and D2, respectively. The restoring force f 1\u00f0D1; h1\u00de and f 2\u00f0D2; h2\u00de can be calculated by restoring force Eqs. (7) and (8) of the adjusted Iwan model. In order to analyze the nonlinear characteristics of the bolted joints, a cantilever beam structure with a bolted joint, as shown in Fig. 5, was designed for dynamic tests", " The time history curves of acceleration responses are shown in Fig. 12. Nonlinear dynamic response analysis is one of the difficulties for the bolted structure. Combined with the Iwan beam element presented in Section 2.3, corresponding finite element model can be established to simulate the bolted cantilever beam structure. With reasonable numerical calculation methods, nonlinear dynamic responses of the structure can be obtained. As shown in Fig. 13, the cantilever beam structure is discretized, and the Iwan beam element shown in Fig. 4(b) is used to simulate the bolted joint. The other parts are simulated by using the conventional linear elastic beam element shown in Fig. 4(a). For the ith linear elastic beam element, the dynamic equation in its local coordinate system is: feelastic; i \u00fe feinternal; i \u00bc Me i \u20acde i \u00fe Ke id e i de i \u00bc v1 h1 v2 h2f gT feelastic; i \u00bc Q1 M1 Q2 M2f gT \u00f014\u00de where Me i and Ke i are mass matrix and stiffness matrix of beam element, respectively. feelastic; i and feinternal; i are external force and internal force, respectively. Similarly, for the ith Iwan beam element, the dynamic equation in its element coordinate system can be expressed as: feAIBE; i \u00fe feinternal; i \u00bc Me i \u20acde i \u00fe fes; i \u00bc Me i \u20acde i \u00fe f 1\u00f0D1; h1\u00de L 2 f 1\u00f0D1; h1\u00de \u00fe h 2 f 2\u00f0D2; h2\u00de f 1\u00f0D1; h1\u00de L 2 f 1\u00f0D1; h1\u00de h 2 f 2\u00f0D2; h2\u00de 8>>< >>: 9>>= >>; \u00f015\u00de in which fes; i is external force, and feAIBE; i is internal force of Iwan beam", " Therefore, considering the introduction of Rayleigh damping, the dynamic equation becomes: \u00f0Melastic \u00feMAIBE\u00de\u20acd\u00fe C _d\u00fe Kelasticd\u00fe Fs\u00f0d\u00de \u00bc Fexternal C \u00bc a\u00f0Melastic \u00feMAIBE\u00de \u00fe b\u00f0Kelastic \u00fe KAIBE e \u00de \u00f017\u00de in which a and b are Rayleigh damping coefficients. KAIBE e is linear elastic stiffness matrix of Iwan beam element. For nonlinear structural systems, the linear superposition principle will no longer be applicable. Therefore, a time-domain direct integration method should be used to solve the nonlinear structural dynamic equation. In this paper, the Forward Incremental Displacement Central Difference Method [38] is used to solve the dynamic Eq. (17) so as to obtain dynamic responses of the structure. As shown in Fig. 4(b), the Iwan beam element is made up of two one-dimensional adjusted Iwan models. Therefore, each Iwan beam element contains six parameters to be updated: total stiffness ki, macroscopic yield force f yi and post-yield stiffness ratio ai \u00f0i \u00bc 1;2\u00de. Among them, the equivalent stiffness ki can be given under the condition of stick without slip, while f yi and ai need to be obtained through the analysis of nonlinear characteristics of the bolted structure. Therefore, a novel twosteps strategy is introduced to update the nonlinear bolted structure: in the first step, linear natural frequency of the structure under low amplitude excitation is taken as the target, and the total stiffness of the structure is updated, that is, linear updating; in the second step, the macroscopic yield force and the post-yield stiffness ratio of the structure are updated based on the instantaneous characteristics of the principal dynamic response components (nonlinear characteristic index), that is, nonlinear updating" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000160_acc.2009.5160136-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000160_acc.2009.5160136-Figure4-1.png", "caption": "Fig. 4. Simplified sketch of the OMF with compressed springs.", "texts": [ " A large inertia is needed to get sufficient dampening at low engine speeds. As a high inertia on the crankshaft delays the engine response to input changes, solid ftywheels are not suited for mid-range, luxury class and sporty cars. 2) The Dual Mass FI~vheel: In a DMF design, the ftywheel inertia is split up into two parts: the primary Inass is still attached to the crankshaft while the secondary mass belongs to the clutch (see Fig. 3). Both masses have two small stoppers, each one able to pick up the two arc springs (see Fig. 4). As the arc springs are deflected within the arc channel, they transfer torque froln one flywheel to the other. When the arc springs slide through their channel, friction adds dalnpening characteristics to the Dual Mass Flywheel. In this section two torsion experiments are presented. The lnain effects observed in these experiments will be modeled Jpri ~pri == Tens - qr TSt1 +q~ T St6 +Tfric.pri (1) Jsec ()Opri + < >: \u00f01\u00de where D and \u03b1 are the helix diameter and helix angle of CHS respectively", " (2) and (3) with trigonometric function 1 cos2\u03b1 \u00bc 1 \u00fe tan2\u03b1, \u03b1 can be eliminated, and the relationship between D, L, N and h can be deduced as D \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi L2 h2 N2\u03c02 s \u00f04\u00de By combining Eq. (3) with trigonometric functions sin\u03b1 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffi tan2\u03b1 1 \u00fe tan2\u03b1 q and cos\u03b1 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 \u00fe tan2\u03b1 q , sin\u03b1 and cos\u03b1 can be respectively described as sin\u03b1 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h2 h2 \u00fe N2\u03c02D2 s \u00f05\u00de cos\u03b1 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi N2\u03c02D2 h2 \u00fe N2\u03c02D2 s \u00f06\u00de According to assumption (2) and Fig. 4, cross\u2010section area, inertia moment, polar moment of inertia and section modulus of helix cross\u2010section can be respectively written as A \u00bc \u03c0 d21 d20 4 \u00f07\u00de Ip \u00bc \u03c0 d41 d40 32 \u00f08\u00de I \u00bc \u03c0 d41 d40 64 \u00f09\u00de W \u00bc \u03c0 d31 d30 32 \u00f010\u00de where d1 and d0 are the outer diameter and inner diameter of helix cross\u2010section respectively. Actually, in the compressive process of CHS, geometric parameters change with the increase of compressive load (shown in Fig. 3). According to assumption (2), geometric parameters of CHS (i", " The same iterative calculation is performed m times until CHS fail or the same iterative calculation is performed n times until the maximum compressive displacement of CHS is reached without failure (shown in Fig. 3). When CHS can be compressed to closely contact with two adjacent circles and no failure occurs, the maximum compressive displacement can be obtained from the initial geometric configuration of CHS. \u03b4max \u00bc h1 N1d1 \u00f016\u00de The composite used to prepare CHS can be unidirectional reinforced composite or two\u2010dimensional fabric composite (shown in Fig. 4a). Frenet unit vectors (i.e. x, y, z = tangential, normal and binormal unit vectors) are used to describe the stress resultants of CHS under the axial compressive load increment \u0394P. The stress resultants of CHS on the any cross\u2010section A are shown in Fig. 4(b), including the twisting moment increment around the direction of x axis in the ith step, the bending moment increment around the direction of z axis in the ith step, the axial force increment along the direction of x axis in the ith step and the shear force increment along the direction of z axis in the ith step. According to Fig. 4(b), twisting moment increment, bending moment increment, axial force increment and shear force increment of CHS in the ith step can be respectively shown as \u0394Ti \u00bc \u0394PDi 2 cos\u03b1i \u00f017\u00de \u0394Mi \u00bc \u0394PDi 2 sin\u03b1i \u00f018\u00de \u0394Fi \u00bc \u0394Psin\u03b1i \u00f019\u00de \u0394Qi \u00bc \u0394Pcos\u03b1i \u00f020\u00de The strain energy expression of CHS in the ith step can be expressed as \u0394P\u0394hi 2 \u00bc Z L 0 \u0394T2 i 2GxyIp 1 cos\u03b1 ds\u00fe Z L 0 \u0394M2 i 2ExI 1 cos\u03b1 ds\u00fe Z L 0 \u0394F2 i 2ExA 1 cos\u03b1 ds \u00fe Z L 0 kS\u0394Q2 i 2GxyA 1 cos\u03b1 ds \u00f021\u00de Where Ex and Gxy are the elastic modulus of composite laminate of CHS in the tangential direction of helix centre\u2010line (i", " The constitutive model of the composite laminate of CHS is N M \u00bc A B B D \u025b0 \u03ba \u00f0A1\u00de where A \u00bc A11 A12 0 A12 A22 0 0 0 A66 2 64 3 75 \u00f0A2\u00de and Aij \u00bc \u2211 n k\u00bc1 Q ij k ts \u00f0A3\u00de where ts is the ply thickness and the components Q ij are Q 11 \u00bc Q11cos 4\u03b8 \u00fe 2 Q12 \u00fe 2Q66\u00f0 \u00desin2\u03b8cos2\u03b8 \u00fe Q22sin 4\u03b8 \u00f0A4\u00de Q 12 \u00bc Q11 \u00fe Q22 4Q66\u00f0 \u00desin2\u03b8cos2\u03b8 \u00fe Q12 cos4\u03b8 \u00fe sin4\u03b8 \u00f0A5\u00de Q 22 \u00bc Q11sin 4\u03b8 \u00fe 2 Q12 \u00fe 2Q66\u00f0 \u00desin2\u03b8cos2\u03b8 \u00fe Q22cos 4\u03b8 \u00f0A6\u00de Q 16 \u00bc Q11 Q12 2Q66\u00f0 \u00desin\u03b8cos3\u03b8 \u00fe Q12 Q22 \u00fe 2Q66\u00f0 \u00desin3\u03b8cos\u03b8 \u00f0A7\u00de Q 26 \u00bc Q11 Q12 2Q66\u00f0 \u00desin3\u03b8cos\u03b8 \u00fe Q12 Q22 \u00fe 2Q66\u00f0 \u00desin\u03b8cos3\u03b8 \u00f0A8\u00de Q 66 \u00bc Q11 \u00fe Q22 2Q12 2Q66\u00f0 \u00desin2\u03b8cos2\u03b8 \u00fe Q66 sin4\u03b8 \u00fe cos4\u03b8 \u00f0A9\u00de where Q11 \u00bc E1 1 \u03bd12\u03bd21 \u00f0A10\u00de Q22 \u00bc E2 1 \u03bd12\u03bd21 \u00f0A11\u00de Q12 \u00bc \u03bd21E2 1 \u03bd12\u03bd21 \u00f0A12\u00de Q66 \u00bc G12 \u00f0A13\u00de R \u00bc J 1 Then, elastic modulus of composite laminate of CHS in the tangential direction of helix centre\u2010line is Ex \u00bc 1 R11 \u00f0A14\u00de Shear modulus of composite laminate of CHS in the x\u2013y direction is Gxy \u00bc 1 R33 \u00f0A15\u00de Poisson\u2019s ratio of composite laminate of CHS is \u03bdyx \u00bc Ex\u03bd21 E1 sin4\u03b8 \u00fe cos4\u03b8 1 E1 \u00fe 1 E2 1 G12 Exsin2\u03b8 \u00fe cos2\u03b8 \u00f0A16\u00de The coordinate axis is shown in Fig. 4(b). The area moment of cross\u2010section is S z\u00f0 \u00de \u00bc R d0 2 z 2z ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d1 2 2 z2 q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d0 2 2 z2 q dz \u00fe R d1 2 d0 2 2z ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d1 2 2 z2 q dz 0 < z < d0 2 R d1 2 z 2z ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d1 2 2 z2 q dz d0 2 < z < d1 2 8>< >: \u00f0B1\u00de The width of cross\u2010section is b z\u00f0 \u00de \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d1 2 2 z2 q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d0 2 2 z2 q 0 < z < d0 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d1 2 2 z2 q d0 2 < z < d1 2 8>< >: \u00f0B2\u00de Then, shape shear factor of circular cross\u2010section is kS \u00bc A I2 ZZ Ayz S z\u00f0 \u00de2 b z\u00f0 \u00de2 dA \u00f0B3\u00de According to the rule of mixtures of elastic modulus, the longitudinal and transverse elastic modulus of M40 / epoxy648 composite laminate can be calculated respectively E1 \u00bc EfV f \u00fe Em 1 V f\u00f0 \u00de \u00f0C1\u00de E2 \u00bc EfEm Ef 1 V f\u00f0 \u00de \u00fe EmV f \u00f0C2\u00de According to the rule of mixtures and constitutive relationship, poisson's ratio of epoxy 648 composite laminate can be obtained respectively \u03bd21 \u00bc \u03bdfV f \u00fe \u03bdm 1 V f\u00f0 \u00de \u00f0C3\u00de \u03bd12 \u00bc \u03bd21 E2 E1 \u00f0C4\u00de According to the constitutive relationship between elastic modulus and shear modulus of isotropic materials, the shear modulus of epoxy 648 composite laminate can be obtained Gm \u00bc Em 2 1\u00fe \u03bdm\u00f0 \u00de \u00f0C5\u00de According to the rule of mixtures of shear modulus, the shear modulus of the M40/epoxy648 composite laminate can be obtained G12 \u00bc GfGm Gf 1 V f\u00f0 \u00de \u00fe GmV f \u00f0C6\u00de Supplementary data to this article can be found online at https://doi" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000527_j.electacta.2014.04.019-Figure8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000527_j.electacta.2014.04.019-Figure8-1.png", "caption": "Fig. 8. Comparison of the sensitivity of various modified electrodes in the simultaneous determination of G, A, T, and C.", "texts": [ " Large numbers of coordination sites in G and allow the preferential adsorption of G and A when compared to and T at ZSM-5 based modified electrodes investigated in this tudy. High surface area and intercrystalline mesoporoes facilitate ll four DNA bases to reach the active sites in the case of Nano-ZSM- based electrodes, therefore the oxidation peaks corresponding o the electrochemical oxidation of G, A, T, and C are observed at ano-ZSM-5 based modified electrodes investigated in this study. A comparison of the sensitivity for various modified elecrodes toward the simultaneous electro-catalytic oxidation of G, , T, and C is shown in Fig. 8. Based on the experimental evience, one can conclude that Nano-ZSM-5/MIM exhibited superior ensing ability and current sensitivity compared to other modied electrodes investigated in this study. This improved analytical erformance is attributable to the high conductivity of Nano-ZSM/MIM and significantly strong hydrogen boding of MIM with NA bases. Less hydrophobic nature of MIM compared to BMIM nhances the affinity of analytes on the surface of Nano-ZSM/MIM and facilitates the oxidation of analytes at electrode surface" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003481_j.optlastec.2020.106782-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003481_j.optlastec.2020.106782-Figure1-1.png", "caption": "Fig. 1. (a) Finite element model and (b) laser scanning strategy in SLM process where node 1 is at the centre of the first layer, node 2 is at the centre of the second layer, and node 3 is at the centre of the third layer.", "texts": [ " In this study, a 3D transient numerical model of SLM manufacturing 316L stainless steel was established using the finite element analysis software ANSYS19.0 (APDL). First, the temperature distribution of the finite element model was obtained through non-linear transient thermal analysis. After that, the thermal element was automatically converted into a structural element for stress field analysis, and the temperature obtained from the previous transient thermal analysis was used as the load for the stress field solution. The finite element model and the laser scanning strategy are shown in Fig. 1. In the temperature field analysis, the eight-node hexahedral element Solid 70 was used to mesh the substrate and powder bed. The size of the powder bed and that of the substrate were 1.16 mm \u00d7 0.5 mm \u00d7 0.105 mm and 1.6 mm \u00d7 0.9 mm \u00d7 0.25 mm, respectively, and the material used was 316L stainless steel. The red box indicates the scanning area of the heat source (1.04 mm \u00d7 0.4 mm). The powder bed was divided into three layers, each with five scanning tracks and a thickness of 0.035 mm. In order to improve the efficiency and accuracy of calculation, the finite element mesh division method was optimized" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002993_icra40945.2020.9197229-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002993_icra40945.2020.9197229-Figure1-1.png", "caption": "Fig. 1. (a) The framework diagram of the LFMAS modelling (The notations 0, 1, and 2 denote Leader, Follower 1, and Follower 2, respectively); (b) Communication topology network of the LFMAS structure.", "texts": [ " Before giving the controller designs, it is important that how to model the interaction relation among them appropriately such that the both low limbs and the LLE can achieve their mutual communication. Inspired by the area of cooperative distributed control, leader-follower mechanism has been successfully applied on multi-agent systems [26], which allows information interaction among agents in a distributed way. In this paper, the unaffected leg of the hemiplegic patients and the both lower extremities of exoskeleton are modeled as a LFMAS. Fig. 1 (a) gives the structure of the LFMAS for exoskeleton system with hemiplegic individuals, where the exoskeleton with hemiplegia is divided into three components: one Leader and two Follower agents. That is, the unaffected leg of patient is treated as the Leader of LFMAS, along with an Inertial Measurement Unit (IMU) sensors which is used to measure its joints\u2019 states. Furthermore, both two lower extremities of the LLE system are defined as two Follower agents, which can be described as follows: 1) Follower 1 is the exoskeleton leg of unaffected side, which synchronizes the leader agent\u2019s (unaffected side of patient\u2019s leg) motion immediately", " To achieve better assistance control performance, the information interaction scheme should be designed for both lower extremities and patient\u2019s legs, which allows them transmit their information (LLE\u2019s state and control signal) with their neighbors. Thus, we introduce an information exchange rule to describing the evolution of the agents\u2019 communication. 1) Information Evolution Rule: The information update for Follower agent i (i = 1,2) includes combining its own information with those received from its neighbors, and Leader can transmit its information to Follower. Assume that each agent has a weight vector ai = [ai j], in which each element ai j represents that agent i assigns to the information obtained from a neighboring agent j. Fig. 1 (b) denotes the communication topology network between agents where arrows indicate the direction of information flow. 2) Weight Rule: Let N (i) be the neighbors set of the ith Follower agent. For arbitrary i\u2208 {1,2}, if j \u2208N (i), ai j > 0; if j /\u2208N (i), ai j = 0. Let \u2211 j\u2208N (i) ai j = di be the sum of the neighbors\u2019 weights for agent i. In this paper, the dynamics of the LLE system is described as a general nonlinear mechanical system (i.e., Eulerlagrange system). Therefore, the dynamics of the both lower extremities, i" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001880_j.mechmachtheory.2018.04.001-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001880_j.mechmachtheory.2018.04.001-Figure3-1.png", "caption": "Fig. 3. Coordinate systems of the pinion generator.", "texts": [ " The equation for this curve is: \u03b4( \u03d5 1 ) = c 0 + c 1 \u03d5 1 + c 2 \u03d5 1 2 + c 3 \u03d5 1 3 + ... + c 10 \u03d5 1 10 + c 11 \u03d5 1 11 (1) where c i (i = 0 , 1 , 2 , ..., 10 , 11) are polynomial coefficients and \u03d51 is the pinion meshing angle. The locus of the tool surface is given by the following equations: r p ( s p , \u03b8p ) = \u23a1 \u23a2 \u23a3 ( R p + s p sin \u03b11 ) cos \u03b8p ( R p + s p sin \u03b11 ) sin \u03b8p \u2212s p cos \u03b11 1 \u23a4 \u23a5 \u23a6 (2) n p ( \u03b8p ) = [ cos \u03b11 cos \u03b8p cos \u03b11 sin \u03b8p \u2212 sin \u03b11 ] (3) where s p , \u03b8p are tool surface parameters, R p is the cutter radius, and \u03b11 is the profile angle. Fig. 3 presents the coordinate systems of gear generator, where S p and S 1 are connected with the cutter-head and pinion, respectively. Three sets of parameters describe the gear generator: the tool parameters, the polynomial coefficients of the auxiliary tooth surface correction motion, and the original machine settings. During cutting, the original machine settings and the tool parameters remain unchanged, whereas the auxiliary tooth surface correction motion is adjusted to generate the design pinion meeting functions" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003584_tte.2021.3054510-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003584_tte.2021.3054510-Figure1-1.png", "caption": "Fig. 1. Structure of the EMA", "texts": [ " is derived; In section III, the NDO-based chattering suppression FTSM control strategy is implemented and the stable conditions of the control system are analyzed; The simulation and experimental results of the braking system with the proposed control strategy are shown in section IV; Finally, the conclusion of this research is drawn in section V. II. MATHEMATICAL MODEL OF EMA FOR ELECTRIC BRAKING SYSTEM In this section, the composition structure and operating principle of the EMA system as well as its mathematical model will be discussed and analyzed in detail. The composition structure of EMA is shown in Fig. 1. Usually, an EMA consists of a BLDCM, a reduction gear, a ball screw, and other related sensors [32]. When the BLDCM rotates under the control of the electromechanical actuator controller, the reduction gear will rotate along with the motor at a slower speed, which will drive the screw nut to rotate as well. And the rotational motion of the screw nut will transform into the linear motion of the screw rod. Then, the screw rod will produce axial brake force and compact the brake disc, thus realizing the aircraft brake" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000284_0022-2569(67)90005-5-Figure9-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000284_0022-2569(67)90005-5-Figure9-1.png", "caption": "Figure 9 A polar plane and lines of a linear complex in a mechanism containing a higher pair.", "texts": [ " (This is a mechanism that seems to have been rather ignored as a source of coupler curves. A point Q on member 3 could, effectively, move in a plane or some other surface and trace certain loci that could be used for transmitting motion. If $13 can be determined without too much difficulty, a study of such motions could be simplified.) 3.3. Phillips [8] uses the spatial velocity image to assist him in locating ISAs in certain spatial mechanisms. One that he examines is essentially similar to that illustrated in Fig. 9. $13 may, however, be determined quite easily by geometry alone. The axes 12 and 23 are given, and $12 (with zero pitch) coincides with the former. $23 (lying along 23) has an unknown instantaneous pitch, since 23 is a cylindrical pair. The pair 13 is made up of a ball, centre A, constrained to remain in a trough that fits the ball neatly and is fixed to 1; the trough is shown curved, but this doesn't affect the present method, since it is the tangential velocity of A relative to 1 (shown with an arrow) that is important in identifying the polar plane = perpendicular to this velocity", " This method can now be further simplified, for, since wl and w2 are a pair of conjugate lines, only one line belonging to the required complex need be selected to allow the procedure of 2.17 to be applied. Such a line is the unique line through A in plane ct that is at right-angles to w 2 (but not in general intersecting w2). For then, when the diametral plane Z is found, as in Fig. 5, the line g will be bound to intersect w 2 at right-angles. 3.5. The instantaneous value of the pitch of $23 (Fig. 9) is unknown, and may be found independently by locating any line in that linear complex pertinent to the instantaneous movement of 2 relative to 3, the central axis of this linear complex being $23. Such a line is the one through A lying in plane ~ and intersecting axis 12. r and 0 (see 2.2) can then be determined and the pitch calculated from equation (2). All the polar planes with poles on 23 must have 23 normal to them; 23 is one of a pair of conjugate lines, the other line of the pair then being at infinity and perpendicular to 23, confirming the statement in parenthesis in 2.12.4. 3.6. If the pairs 12 and 23 were interchanged, i.e. 12 made a cylindrical pair and 23 a revolute, the method of 3.4 can be applied in the same way except that now the line through A in plane ~ must be at right-angles to the axis of 12 instead of 23. 3.7. A lower-pair linkage with instantaneous first-order kinematic equivalence to the mechanism of Fig. 9 can be constructed with two different members numbered (1) and (4) (intentionally in parentheses and shown dotted in Fig. 9), replacing the whole of the original member 1. Member (4) joins a spherical pair at A to a revolute pair (41) placed at the centre of curvature of the trough at A with its axis (41) perpendicular to the osculating plane of the trough at A, i.e. perpendicular to the arrowed relative velocity of A and lying in plane ~. (This equivalent linkage may be written as 1-RIz-2-C23-3-G34-4-R~l- 1; R, C and G respectively signify revolute, cylindrical and global (spherical) pairs, the numbers indicating the members joined by them" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002062_j.surfcoat.2017.08.059-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002062_j.surfcoat.2017.08.059-Figure3-1.png", "caption": "Fig. 3. Diagrams of (a) scanning procedure for the multi-layer deposition, (b) wear test specimen, and (c) Charpy impact test specimen (unit: mm).", "texts": [ " 2 shows the morphology of the M4 powders (supplied by Carpenter Co.). Table 1 shows the chemical composition of each material. The material efficiency was determined indirectly from the amount of powder discarded. Approximately 60% (2.7 g/min) of the fed powder (4.5 g/min) was delivered into the melting pool and deposited. Table 2 presents the processing conditions established through preliminary experiments. The beam had a top-hat intensity distribution and a diameter of 1.0 mm. Hence, each track overlapped the adjacent tracks with a pitch of 0.5 mm. Fig. 3(a) shows a single layer deposited along an \u201calternating stripes\u201d path. In this manner, subsequent layers were consecutively deposited on the previously deposited layers. The deposited plate was subsequently wire-cut into wear test and Charpy test specimens, with dimensions shown in Fig. 3(b) and (c), respectively. The wear specimens were prepared with a 1.0-mm-thick layer deposited onto a cylindrical substrate, as shown in Fig. 3(b). The specimen for the impact test was prepared from a 10mm\u00d7 10mm\u00d7 55mm block with a 5.0-mm-thick deposited layer, as shown in Fig. 3(c). The Charpy specimen also has a 2-mm-deep V-notch following the ASTM E23 standard. To investigate the effects of post-deposition heat treatment on the deposited M4 steel, both tempering and quenching\u2013tempering were adopted. The mechanical properties of the post-deposition heat treated materials were compared by using different samples with the quenched\u2013tempered D2, untreated M4, post-deposition quenched\u2013 tempered M4, and post-deposition tempered M4. For the quenching, the specimen was austenitized at 1293 K for 180 min in a vacuum and quenched to room temperature" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002864_s40430-020-02510-3-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002864_s40430-020-02510-3-Figure2-1.png", "caption": "Fig. 2 Parameters and variables of the i-th limb", "texts": [ " The 3[P2(US)] parallel manipulator under study consists of a moving platform termed the end-effector and a fixed platform named the base, joined together via three identical limbs as depicted in Fig.\u00a01. Each limb is comprised of an active prismatic joint, installed at an inclination relative to the base and a parallelogram linkage. As the name implies, each parallelogram consists of two parallel rods with universal and spherical joints at their both extremities. Geometric parameters and variables of one of the limbs are illustrated in Fig.\u00a02. Three limbs are connected to the base through points Ai , which are located on an imaginary circle with radius R and centered at the origin of reference frame. Similarly, the points Bi are placed on a circle with the radius r and show the connection between the limbs and the end-effector. Active prismatic joints are installed at the angle to the base and are connected to the parallelogram Journal of the Brazilian Society of Mechanical Sciences and Engineering (2020) 42:443 1 3 Page 3 of 15 443 via universal joints at the points Ci . The length of each parallelogram is specified with l. By kinematic analysis, the relative displacement, velocity and acceleration of the links of the manipulator are derived. Jacobian matrix, which provides a mapping between the velocity of active joints and the velocity of the end-effector, is extracted in this section. Looking at Fig.\u00a02, it is obvious that the magnitude of rBiCi , representing the length of ith parallelogram, is constant, so From the loop closure equation, we can write where As can be seen in Fig.\u00a02, i is zero, since Ai coincides the X axis. Replacing Eqs.\u00a0(4\u20137) into Eq.\u00a0(3) and simplifying the resulting equation yields the following constraint equation from which the forward and inverse kinematics of the manipulator can be extracted [42]. (1) |||rBiCi ||| = l (2)rBiCi = rOAi + rAiCi \u2212 rPBi \u2212 rOP (3)leBiCi = ReAi + qieAiCi \u2212 rePBi \u2212 p (4)eAi = [ cos i sin i 0 ]T (5)eAiCi = [ cos i cos sin icos sin ]T (6)ePBi = [ cos i sin i 0 ]T (7)p = [ xp yp zp ]T Journal of the Brazilian Society of Mechanical Sciences and Engineering (2020) 42:443 1 3 443 Page 4 of 15 Direct differentiation of the kinematic Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001963_iet-cta.2014.0342-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001963_iet-cta.2014.0342-Figure1-1.png", "caption": "Fig. 1 Car model", "texts": [ " The proof is actually the same as for the previous theorem, because of the effective decoupling of the system. Consider a simple MIMO (\u2018bicycle\u2019) model of car control [31] x\u0307 = V cos \u03d5, y\u0307 = V sin \u03d5, \u03d5\u0307 = V tan \u03b8 V\u0307 = \u03bc1Tnet(V , \u03c1) \u2212 \u03bc2V 2 \u2212 \u03bc3Rx, \u03bc3Rx = \u03b5(1 \u2212 cos(5\u03b8)) \u03bc1Tnet(V , \u03c1) = (2.5 sin \u03c1 \u2212 0.7)(1 \u2212 0.001(V \u2212 9)2) \u03b8\u0307 = u1, \u03c1\u0307 = u2 where x and y are Cartesian coordinates of the rear-axle middle point, \u03d5 is the orientation angle, V is the longitudinal velocity, is the length between the two axles and \u03b8 is the steering angle (i.e., the first real input) (Fig. 1), Tnet(V , \u03c1) is the net combustion torque of the engine, \u03c1 is the throttle angle (i.e., the second real input), \u03c1 \u2208 [0, \u03c0/2], Rx is the rolling resistance of the tires. Parameters \u03bc2 = 0.005, = 5 m were taken. For simplicity brakes are not applied. Usually Tnet is available as a table function of the engine angle velocity and \u03c1. It is presented here by some regression roughly approximating the data from [31], Fig. 9-6. The rolling resistance is voluntarily represented here by a function, corresponding to some mechanical car damage, \u03b5 = 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002277_978-3-319-27131-6-Figure2.1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002277_978-3-319-27131-6-Figure2.1-1.png", "caption": "Fig. 2.1 Rigid rotors with two-bearing support", "texts": [ " The rotor of the electric machine is supported by two bearings A (fixed bearing) and B (loose bearing), in which both bearings are fixed to the rotor shaft. However, the bearing A is additionally fixed to the bearing housing, and the bearing B is loose to the bearing housing. As a result, the thrust load of the pulley only acts upon the fixed bearing; the loose bearing is free of any thrust load. Using the balance of forces and moments on the rotor, the bearing forces acting on the bearings are computed (s. Fig. 2.1). The balance of forces on the rotor gives 2.2 Computing Loads Acting upon Bearings 21 X Fx \u00bc Fa \u00fe Pa \u00bc 0;X Fy \u00bc F1 \u00fe F2 P1 P2 \u00bc 0 \u00f02:1\u00de The balance of moments on the rotor givesX MA \u00bc F2l\u00fe P1a1 P2a2 \u00bc 0 \u00f02:2\u00de Having solved Eqs. 2.1 and 2.2, one obtains the bearing forces: F1 \u00bc P1 1\u00fe a1 l \u00fe P2 1 a2 l ; Fa \u00bc Pa; F2 \u00bc P1 a1 l \u00fe P2 a2 l \u00f02:3\u00de where P1 is the force acting on the pulley and P2 is the sum forces of the rotor weight, unbalance force, and UMP force acting upon the rotor in the radial direction y" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002022_978-3-319-40036-5-Figure6.3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002022_978-3-319-40036-5-Figure6.3-1.png", "caption": "Fig. 6.3 Microcantilevers (a\u2013e) and a microring resonator (f) made from silicon. (a) Schematic diagram of waveguides and microcantilever array layout on die. (b) Optical image of two microcantilevers in a fabricated array. (c) Close up scanning electron micrograph (SEM) image of the unclamped end of a microcantilever (left of 165 nm gap) and the differential splitter capture waveguide (right of gap). (d) Photograph of complete integrated device showing the fluid microchannels (red) and control valves (green). (e) Cross-section of fluid microchannel at a microcantilever array. (f) Top-view SEM image of a microring resonator and linear waveguide, visible through an annular opening in the fluoropolymer cladding layer [14]. Reproduced with permission from American Chemical Society", "texts": [ " In the end, selecting the material will affect either the device cost or the device function. The key to selecting an adequate material for a microfluidic device comes down to the device\u2019s application. In many cases, many materials need to work together to yield the desired functionality. An example of this can be seen with glass, whose elastic modulus is highly dependent on the glass\u2019s composition; as a result constructing active components with more dynamic valves and pumps require multiple materials to form hybrid devices such as the one seen in Fig. 6.3 [18]. Glass has many other favorable traits that become paramount to a microfluidic device\u2019s function. One of the most important and well-known traits is its compatibility with biological samples. Since glass has the property of relatively low nonspecific adsorption and is not gas permeable, it is an ideal material for working with biologics where cell kinetics and gas incubation need to be controlled. 150 P. Manickam et al. One pitfall of utilizing silicon and glass substrates is the costly conditions under which the micromachining of channels and structures need to take place" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000411_aim.2011.6027137-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000411_aim.2011.6027137-Figure2-1.png", "caption": "Fig. 2. Free-body diagram of a rod. In (a), a rod experiencing gravity and a force and a moment at its tip is shown. Illustration (b) shows force and moment balance on a portion of a rod", "texts": [ " The position vector [ ] 3( ) ( ) ( ) R T s X s Y s= \u2208r and rotational angle ( ) Rs\u03b8 \u2208 are defined as functions of s, to specify the characteristics of a rod at each point (Fig. 1). Therefore, \u03b8(s) is the rotational angle from the reference coordinate XY to the local coordinate x-y that is attached to the rod at r(s). Based on Fig. 1, for non-extensible rods we have ( ) ( )( ) ( ) sin ( ) cos ( ) Td s s s s ds \u03b8 \u03b8\u2032= = \u2212 r r . (1) B. Statics In order to solve the mechanics of a rod, like what is shown in Fig. 2(a), the force and moment balance equations must be considered first. Fig. 2(b) shows a portion of a rod and the forces and moments experienced by that. In Fig. 2(b), body forces or distributed external forces applied to the rod are specified by f(s), which is typically equal to gravity loading. The other two-element variable n(s) specifies the contact forces and is equal to the sum of all the forces acting from the tip of the rod to a point s. Similarly, m(s) shows the contact moments. According to Fig. 2(b), the force and moment balance equations for a portion of rod from s=a to s=b, are ( ) ( ) ( ) 0 s c s c d\u03b6 \u03b6\u2212 + =n n f , (2) \u02c6 \u02c6( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) b a m b m a b b a a s s ds \u2212 + \u00d7 \u2212 \u00d7 + \u00d7 = k k r n r n r f 0 , (3) where k\u0302 shows the unit vector perpendicular to X-Y plane. By differentiating these equations with respect to s, we obtain ( ) ( ) 0s s\u2032 + =n f , (4) \u02c6( ) ( ) ( ) ( ) ( ) ( ) ( ) 0 m s s s s s s s \u2032 \u2032 \u2032+ \u00d7 + \u00d7 + \u00d7 = k r n r n r f . (5) Finally, substituting (4) in (5), we simplify the moment balance equation as \u02c6( ) ( ) ( ) 0m s s s\u2032 \u2032+ \u00d7 =k r n ", " For (1), the boundary condition is simply the position of the base of the robot, which is commonly given. Therefore, r(0) is given. Similarly, the orientation of the base is given, which is \u03b8(0). However, (0)\u03b8 \u2032 is not known prior to the solution of the robot. Solving (8) for \u03b8 \u2032 , we have 1(0) ( ) (0)EI m\u03b8 \u2212\u2032 = , but the moment at the origin is dependant to the whole configuration of the rod. That is because the torques of all forces acting on the robot depends on the configuration, as shown in Fig. 2(a). On the other hand, we consider the moment at the tip of the robot known, which is f( )m s \u03c4= , where sf is the length of the rod. Therefore, 1 f( ) ( )s EI\u03b8 \u03c4\u2212\u2032 = is known. For (11), boundary conditions might be so simple or so complicated. In simple cases, forces exerted on the rod are not dependent on the rod configuration. For instance in Fig. 2(a), neither gravity forces nor the tip force F are dependent on configuration. In such cases, one can consider n(sf)=F and integral (11) to calculate n(s) all along the rod. On the other hand, when the robot interacts with an impedance environment, or is in contact with objects or obstacles, the interaction forces are dependent on the robot configuration. Thus the boundary conditions will be much more complicated. However, here we only consider the simple cases, where all forces are independent of configuration, and (11) can be solved independently of all other equations" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003492_j.jmapro.2021.04.020-Figure10-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003492_j.jmapro.2021.04.020-Figure10-1.png", "caption": "Fig. 10. Effect of position of as-built components on the baseplate on the residual stress development.", "texts": [ " Journal of Manufacturing Processes 66 (2021) 189\u2013197 varying from 10 % to 25 % with a standard deviation of 5 %, indicating that marginal difference among the two post-processing techniques compared. Therefore, it is a more economical approach to adopt the proposed CPP technique on a case by case basis. The residual stress is influenced not only by SLM process parameters such as laser power, laser speed, layer thickness and hatch spacing but also due to the components\u2019 locations on the baseplate. In the present study, the sequence of HPNGV component SLM fabrication was in the order of 1, 3 and 2, respectively (see Fig. 2). Fig. 10 shows the residual stress values compared to as-built HPNGV components placed at different positions on the baseplate. It can be seen that in the case of the as-built condition, HPNGV component \u201c2\u201d shows significantly lower residual stress values compared to component \u201c1\u201d at all measurement points. This trend may be due to the synergetic effect of the HPNGV component placement on the baseplate, dwell time during SLM among the fabrication of the components, and geometry of the deposition system or the action of the re-coater blade" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003373_j.mechmachtheory.2021.104348-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003373_j.mechmachtheory.2021.104348-Figure1-1.png", "caption": "Fig. 1. Leg-wheels of the Quattroped (a) and TurboQuad (b) robots. The leg-wheels of both robots have one translational and one rotational motion DOF, which the symbols ( r, \u03b8) represent. The green arrow in (a) indicates the extra DOF for leg-wheel transformation. The TurboQuad (b) utilizes its linear DOF for leg-wheel transformation, so no additional DOF are needed.", "texts": [ " Section IV discusses the experimental setup and evaluation. Section V concludes this paper. We are interested in developing a leg-wheel hybrid robot because its legged and wheeled modes can complementarily compensate each other in locomotion. Although many different methods can be used to hybridize the legs and wheels on the same robot platform, the series of leg-wheel transformable robots in our lab were designed to satisfy certain criteria. The first version of the robot, Quattroped [20] , has the leg-wheel module design shown in Fig. 1 (a). It utilizes the reconfiguration of two half-circular pieces to act as a wheel or leg. The half-circular leg is widely utilized in RHex [27] robots [28 \u201332] . The robot has a novel leg-wheel transformation mechanism that utilizes the same set mechatronics and actuation system for both wheeled and legged motion (i.e., the hardware is hybrid), but the leg-wheel transformation requires the robot to stop its original locomotion (i.e., it is not hybrid in operation). Therefore, the redesigned robot, TurboQuad [21] , has the leg-wheel module design shown in Fig. 1 (b). It utilizes its own translational DOF to shift two half-circular legs to form an S-shaped leg. The robot can smoothly switch between legged and wheeled modes, as well as among different gaits in legged mode, without stopping locomotion. Furthermore, the robot uses one unified bio-inspired control strategy to handle all gait and mode generation, coordination, and transitions. Hence, the robot is hybrid not only in hardware but also in operation. With the added sensing system, the robot can automatically select the most suitable gait and mode according to the environmental conditions" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001723_s00170-015-7481-8-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001723_s00170-015-7481-8-Figure1-1.png", "caption": "Fig. 1 Schematic of the single powder stream", "texts": [ " Based on the experimental research about powder feed behavior [18], it can be found that the movement state of the powder particles in each stream are mainly decided by their own inertia when the powder particles leave the nozzle exit, and the particles account for a very small volume fraction in the powder flow so that the interaction of the powder streams has little effect on the particles movement in this area. Therefore, the powder flow of the coaxial nozzle can be considered as the superposition of a series of powder flow units. In this study, the powder flow of a discontinuous coaxial nozzle with four tips was investigated. The total powder flow can be considered as a superposition of four powder streams. Figure 1 shows the schematic of the single powder stream. In Fig. 1, \u03c6 stands for the angle between the center line of the single powder stream and the horizontal axis, the plane x-O1-y is normal to the center line of the single powder stream, and the intersection point O1 of them was defined as the origin which is at a distance S from the nozzle exit plane, and the extended lines of the single powder stream contour focus on the virtual sourceO\u2032. Based on the balance of the flux, the flux in the plane x-O1-y is equal to the one in the nozzle exit, so Z \u221e \u2212\u221e Z \u221e \u2212\u221e cpvpdxdy \u00bc c0vp\u03c0r0 2 \u00f01\u00de where vp is the powder particle velocity, cp shows the powder particle mass concentration in the plane x-O1-y, c0 shows the powder particle mass concentration near the nozzle exit, and r0 expresses the radius of the nozzle exit", " In this study, the single powder stream was considered as a turbulent jet stream, and according to turbulent jet theory, the mass concentration in any cross-section of turbulent jet stream meets the Gaussian distribution [19], so Eq. (3) can be transformed as c cm \u00bc exp \u2212 ffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2 \u00fe y2 p b !2 2 4 3 5 \u00f04\u00de Substitution of Eq. (4) into Eq. (1) yields Z \u221e \u2212\u221e Z \u221e \u2212\u221e cmvpexp \u2212 ffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2 \u00fe y2 p b !2 2 4 3 5dxdy \u00bc \u03c0cmvpb 2 \u00bc mp 4 \u00f05\u00de From the geometric relationship in Fig. 1, the characteristic radius can be written as b \u00bc a l \u00fe L\u00f0 \u00de \u00f06\u00de where L is the distance between the plane x-O1-y and the nozzle exit, a is a proportional constant, and l is the distance between the virtual sourceO\u2032 and the nozzle exit. Substitution of Eq. (6) into Eq. (5) yields cm \u00bc mp 4\u03c0vp l \u00fe L\u00f0 \u00de2a2 \u00f07\u00de Substituting Eqs. (6) and (7) into Eq. (4), the powder mass concentration at any point (x, y) in the plane x-O1-y can be expressed as c \u00bc mp 4\u03c0vp l \u00fe L\u00f0 \u00de2a2exp \u2212 ffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2 \u00fe y2 p l \u00fe L\u00f0 \u00dea !2 2 4 3 5 \u00f08\u00de From the geometric relationship in Fig. 1, the distance L between the plane x-O1-y and the nozzle exit can be obtained by L \u00bc Scsc\u03c6 \u00f09\u00de With substitution of Eq. (9) into Eq. (8), the mass concentration of powder stream in the plane x-O1-y can be calculated by c \u00bc mp 4\u03c0vp l \u00fe Scsc\u03c6\u00f0 \u00de2a2exp \u2212 ffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2 \u00fe y2 p l \u00fe Scsc\u03c6\u00f0 \u00dea !2 2 4 3 5 \u00f010\u00de In Fig. 1, the point (x1, y) in the horizontal plane x1-O1-y also belongs to the section which is at a distance L* from the nozzle exit, and the coordinate is (x*, y) in the section. From the geometric relationship, the following transform relationships can be given: L* \u00bc Scsc\u03c6\u2212x1cos\u03c6 \u00f011\u00de x* \u00bc x1sin\u03c6 \u00f012\u00de With substitution of Eqs. (11) and (12) into Eq. (8), the mass concentration of the single powder stream in the plane x1-O1-y at the distance S below the nozzle exit plane can be calculated by c x1; y; S\u00f0 \u00de \u00bc mp 4\u03c0vp l \u00fe Scsc\u03c6\u2212x1cos\u03c6\u00f0 \u00de2a2 exp \u2212 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x1sin\u03c6\u00f0 \u00de2 \u00fe y2 q l \u00fe Scsc\u03c6\u2212x1cos\u03c6\u00f0 \u00dea 0 @ 1 A 22 64 3 75 \u00f013\u00de Further, the mass concentration of the symmetric double powder streams can be investigated based on the analysis of the single powder stream, and the interaction of two powder streams can be considered as a simple superposition in the same coordinate system" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000931_9781118703274.ch2-Figure2.39-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000931_9781118703274.ch2-Figure2.39-1.png", "caption": "Figure 2.39 Moments arising from blade bending", "texts": [ "61) The total restoring torque on the blade can be determined using Equation (5.13). Blade bending causes displacement of the lift and centre of mass. This generally results in an increase to the angular moment working against blade restoration, i.e. the moment Mlift, developed as a result of lifting forces, usually becomes larger due to aerofoil deflection. Due to mass shifts, extra propeller moments are generally developed. Furthermore, the moment of inertia of the deformed blade becomes significantly greater than it is in its undeformed state (see Figure 2.39). Moments resulting from rotor teetering and the associated changes in pitch, which arise mainly in teetered hub models, are mainly dependent on blade angle and the amplitude of teeter during blade rotation (see Figure 2.40). In symmetrical blade arrangements, moments engendered (e.g. due to the acceleration of inert masses) cancel each other out with respect to the external drive. Propeller moments, on the other hand, can change considerably. Because of the significant influences and the continually changing conditions during the rotation of a blade, these effects cannot be handled as they stand without unacceptable computing effort" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001070_s1003-6326(17)60289-9-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001070_s1003-6326(17)60289-9-Figure1-1.png", "caption": "Fig. 1 Sketch of LARed specimen with prefabricated defect", "texts": [ " In order to obtain a deep understanding of the LARed Ti17 titanium alloy with small LDZ ratio, the microstructure, micro-hardness and room temperature tensile behaviors of LARed specimen were investigated systematically in this work. The microstructure evolution in the laser deposited zone during LARed process was further discussed. Considering the common surface defects on the loading structural components, typical hole-defect with 2 mm in diameter and 0.5 mm in depth (0.5% LDZ ratio) was prefabricated on the plate tensile specimen of forged Ti17 titanium alloy. The sketch is shown in Fig. 1. The LAR process was carried out on a LAM system typed LSF-IV, established by State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, which consisted of a 300W pulsed YAG laser, a five-axis numerical control working table, a powder feeder with a coaxial nozzle and a chamber filled with pure argon gas with the oxygen content less than 50\u00d710 \u22126 . The Ti17 powders with the diameter of 80\u2212120 \u03bcm prepared by plasma rotating electrode were employed as the cladding materials" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003110_j.mechmachtheory.2020.104122-Figure13-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003110_j.mechmachtheory.2020.104122-Figure13-1.png", "caption": "Fig. 13. Structure of two wave generators: ( a ) Automatic alignment and integral structures, ( b ) Automatic alignment mechanism.", "texts": [ " The output lag characteristic is a disadvantage of HD particularly when it needs to reverse frequently. In this case, the lag component plays an important role in the transmission accuracy. It occurs due to the clearance of contact pairs and the torsional flexibility property of the drive. Under the ideal no-load condition, the torsional flexibility is not considered. Clearance exists in various places such as gear teeth, bearings, and shaft assembly. The backlash between gear teeth and the clearance of WG are considered in this study. As shown in Fig. 13 , the common configuration of the WG includes two types: automatic alignment and integral structures [33] . For the first structure, the automatic alignment mechanism is presented in Fig. 13 ( b ), which is designed according to the principle of the cross-slide mechanism. The clearance mainly comes from the automatic alignment mechanism [33] . For the integral structure, the WG clearance is not considered. As shown in Fig. 14 , the geometric center O F of the FS coincides with the geometric center O C of the CS for HD with automatic alignment WG. Let e b be the clearance of WG (see Fig. 14 ). The dynamic coordinate system x 1 O C y 1 is fixed on WG. The y 1 -axis of the dynamic coordinate system is along the direction of the straight groove 1" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003492_j.jmapro.2021.04.020-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003492_j.jmapro.2021.04.020-Figure1-1.png", "caption": "Fig. 1. Inconel718 HPNGV components built using SLM process.", "texts": [ " The block type support structure was employed for the anchoring of the HPNGV component to the baseplate. It was used due to its ease while removal of the support during post-processing. In the present work, the most frequently employed stripe with contour scanning strategy was used for the fabrication of the HPNGV component with a 67-degree layer to layer N. B. K et al. Journal of Manufacturing Processes 66 (2021) 189\u2013197 rotation angle. Three Inconel718 HPNGV components were printed on a baseplate as shown in Fig. 1. The sequence of printing of HPNGV components was in the order of 1, 3 and 2, as shown in Fig. 1. Among them, component-1 was considered in as-built condition and the other two (2 and 3) in heattreated conditions for measurements of residual stresses during various post-processing techniques. The two post-processing techniques used in the present study are illustrated in Fig. 2. Figs. 3 and 4 show the residual stress measurement scheme adopted for the HPNGV component during CPP and SPP flow, respectively. The heat treatment was carried out in an induction furnace as per AMS 5662, i.e., solution annealing at 980 \u25e6C (1800 \u25e6F) for 1 h with argon cooling", " The diffraction peak of FCC Nickel with Young\u2019s modulus of 200 MPa was employed for all stress value determination. The various X-ray diffraction measurement variables used for the residual stress determination are shown in Table 3. The plot of 2\u0398 vs sin2\u03a8 was used with a maximum of 10 \u201c\u03a8\u201d values, and through fitting a least square regression line method, the slope \u201cM\u201d was calculated. By standard practice, a positive slope in the plot shows tensile stresses and negative slope demonstrates the presence of compressive stresses. The surface residual stresses were measured on components 1, 2 and 3 shown in Fig. 1 at different locations of the Inconel718 HPNGV component. Fig. 5 shows the variation of residual stresses values in as-built condition measured at various HPNGV component locations during customized post-processing techniques (Figs. 2a and 3). It could be seen that the entire surface stresses are tensile in nature in the as-built condition along with the baseplate at all locations. Location 4 near the support structure (shown in Fig. 5) has a maximum tensile residual stress of ~ 600 MPa (with minor elastic deformation), whereas a minimum tensile residual stress of ~ 175 MPa was seen at the top surface shown as location 1" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003090_j.mechmachtheory.2020.104045-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003090_j.mechmachtheory.2020.104045-Figure1-1.png", "caption": "Fig. 1. Simple planetary gearbox.", "texts": [ " The above-mentioned shortcomings were addressed in the present paper, and a MOO problem with minimization of the total weight and power loss in a planetary gearbox was formulated; scuffing constraint along with constraints on the bearing selection were considered for the first time in the planetary gearbox analysis. Most design constraints were formulated in accordance with American Gear Manufacturing (AGMA) standards [25\u201327] and the Pareto front was obtained using NSGA-II for different gear profiles, with different grades of ISO oils. 2. Problem formulation This analysis aims to minimize the total weight and power loss of industrial planetary gearbox, considering the entire range of design constraints with mixed integer type design variables. Fig. 1 shows the planetary gearbox considered for the MOO problem. It consists of the input shaft, sun gear, three planet gears, three spherical roller bearings (each planet gear has one spherical roller bearing), and ring gear. The input to the planetary gearbox is at the sun gear shaft and output is obtained from the carrier, keeping the ring gear fixed. The assembly of the planet gear, spherical roller bearing, and planet pin is as illustrated in Fig. 2 (a). Many industrial planetary gearboxes available in the market have more than three planet gears" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001876_j.mechmachtheory.2018.04.002-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001876_j.mechmachtheory.2018.04.002-Figure2-1.png", "caption": "Fig. 2. The tangent vector t a 1 and vector n a 1 at the edge contact point M a .", "texts": [ " One of the required edge contact conditions is that the position vectors of the pinion tooth edge and gear tooth surface coincide at the edge contact point, which can be represented as r 1 h ( u 1 , v 1 , \u03d5 1 ) = r 2 h ( u 2 , v 2 , \u03d5 2 ) (4) A second requirement is for the tangent vector of the pinion tip curve to be perpendicular to the normal vector of the gear tooth surface at the edge contact point, which can be represented as \u2202r 1 h ( u 1 , v 1 , \u03d5 1 ) \u2202 u 1 n 2 h ( u 2 , v 2 , \u03d5 2 ) = 0 (5) It is difficult to describe the tangent vector of a pinion tooth edge in the differential form of the position vector. However, as shown in Fig. 2 , it can be described in system S 1 in another form as t a 1 = n 1 ( u 1 , v 1 , \u03d5 1 ) \u00d7 n a 1 (6) where n a 1 = [ \u2212 sin \u03b4a 1 cos \u03b4a 1 0 ] T and \u03b4a 1 is the face cone angle of the pinion. The tangent vector t a 1 can be represented in system S h by the matrix equation t a h = L h 1 t a 1 (7) where L h 1 is a coordinate transformation matrix from system S 1 to S h . So, Eq. (5) can be substituted with t a h \u00b7 n 2 h ( u 2 , v 2 , \u03d5 2 ) = 0 (8) In addition, the tip curve generated by the pinion face cone, intersecting the pinion tooth surface, should satisfy the following condition: ( x 1 \u2212 D a 1 ) tan \u03b4a 1 \u2212 \u221a y 2 1 + z 2 1 = 0 (9) Eqs. (4) , (8) and (9) are equivalent to the five independent scalar equations, such that the solution to the system of nonlinear equations can be used to define the edge contact point. For the case where the pinion tooth surface contacts the gear tooth tip, the gear tip curve replaces the pinion tip curve in Eqs. (8) and (9) for determining the edge contact point. The instantaneous edge contact curve can be established using a two-dimensional iteration search algorithm, as shown in Fig. 2 . Given the radius r , the closest points between the two meshing tooth surfaces can be found. The method for finding these is based on the tangent plane of the gear tooth surface at the edge contact point, and iterations are carried out in tiny increments of angle \u025b . If the minimum gap between the two surfaces is less than the preset surface separation, \u03b4 = 0 . 00635 , the two corresponding points are considered to be on the instantaneous edge contact curve. Furthermore, another iteration process can be conducted to determine the contact length in very small increments of radius r " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000415_978-3-642-37552-1-Figure13.3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000415_978-3-642-37552-1-Figure13.3-1.png", "caption": "Fig. 13.3 Transpiration based microactuator: a A micrograph of a device in its initial rest state. b An illustration of how the strain energy of the spine is calculated, using a constant arc length with an", "texts": [ " In the ideal case, there are no fabrication defects, the ribs are distributed evenly along the spine, each of the cells comprised of two ribs is completely filled with water, and the evaporation rate for each cell is the same at any given time. The model seeks to find the equilibrium state of the system. Transient response is not being modeled. The model is further based on the following statements: \u2022 Devices are designed to have an initial stress free shape that is curved like a circle. A micrograph of an actual device is shown in Fig. 13.3a. The energy of the stress free curve is zero; \u2022 The model assumes no shear forces and no out-of-plane distortion; \u2022 The spine was designed to have uniform radius of curvature in its stress-free shape. The assumption of no shear implies that any deformed shape of the spine will also have uniform radius of curvature. An illustration of how the strain energy of the spine is calculated is shown in Fig. 13.3b. A constant arc length with an increasing radius of curvature, \u03c1, is used to calculated tip deflections, \u03b4, using (13.1): \u03b4 = \u221a (xi \u2212 x0)2 \u2212 (yi \u2212 y0)2 (13.1) \u2022 Ribs are assumed to be rigid so that they do not store any deformation energy. As the device deforms due to surface tension the strain energy in the spine increases. Equilibrium is reached when the total potential energy is at a minimum. The total system energy for a device experiencing various spine deformations, or curves, like those in Fig. 13.3b, is calculated and given in Fig. 13.4a. Each curve number corresponds to a different uniformly curved arc, \u03c1, for which both the strain energy of the spine and the surface energy of the water within the ribs was calculated and summed to find the total potential energy of the actuator. The curve with the lowest potential energy indicates the curve for the equilibrium state. Simulated deformation curves are shown in Fig. 13.4b for the point of equilibrium between the strain energy of the spine and the surface energy of the water for devices with varying spine thickness or 10, 20, and 30 \u00b5m and a rib length of 400 \u00b5m" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001545_j.engstruct.2015.09.008-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001545_j.engstruct.2015.09.008-Figure7-1.png", "caption": "Fig. 7. The figure shows the coordinates used for the formulation. Each gear is represented by a rigid body with its own set of coordinates. In the formulation, the displacements of each gear due to the vibrations are projected into the line of action in order to obtain the gear mesh displacements of Eq. (4).", "texts": [ " The EOM are obtained using Lagrange\u2019s equation and are arranged in a linear time-invariant (LTI) state space formulation (3), with state matrix A, input matrix B, output matrix C and state transition matrix E; where the states (x) correspond to the displacements and velocities of each DOF in the system. The numerical solution is found by using the ode23tb solver from Matlab/Simulink. _x \u00bc Ax \u00fe Bu y \u00bc Cx \u00fe Eu \u00f03\u00de The displacement coordinates for a parallel and planetary gearbox, respectively, are: qpa \u00bc xg ; yg ; hg ; xp; yp; hp and qpl \u00bc xc; yc; hc;f xi; yi; hi; . . . ; xN; yN; hN; xs; ys; hsg. The subscripts g; p; c; i; s denote the gear, pinion, carrier, planets and sun respectively (N is equal to the total of planets). Both stages are depicted in Fig. 7. From here, the formulation for the gear mesh displacements are defined as: dsi \u00bc ys sinwsi yi sinwsi \u00fe zs coswsi zi coswsi \u00fe rshs \u00fe rihi rchc cosar ; dri \u00bc yi sinwri zi coswri \u00fe rrhr rihi rchc cosas; dpg \u00bc yg sinag yp sinag \u00fe zg sinag zp sinag \u00fe rghg \u00fe rphp \u00f04\u00de where wsi \u00bc wi as; wri \u00bc wi ar; wi is the location angle of the planet with respect to the y coordinate in the fixed reference system, as; ar and ag are the pressure angles of the sun, ring and gear, respectively. The expressions from Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003252_tia.2020.3040142-Figure15-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003252_tia.2020.3040142-Figure15-1.png", "caption": "Fig. 15. Flux density distribution of optimal case 2. (a) Nonlinear HMM. (b) FEA.", "texts": [], "surrounding_texts": [ "For a specific application scenario, the gear ratio, stack length, air-gap length, and outer diameter of a CMG is fixed, and the other geometrical parameters can be optimized. Besides, the material of PMs and silicon steel are settled before optimization, and they are selected as N35H and 50JN270, respectively. The eddy current loss of PMs and iron loss of silicon steel within CMGs is small compared to the power it transmits when it works at rated condition. Additionally, the efficiency of CMGs can be maintained at a high level if the silicon steel within CMGs are not highly saturated, and the output torque of CMGs will decrease if its silicon steel part is highly saturated. Therefore, individuals with low efficiency can be tossed out automatically by optimization algorithm as long as the output torque is set as an optimization objective. Besides, the torque ripples of CMGs are very low if the pole-pair combinations of CMGs are well selected [17]. This can also be observed in Fig. 9, the torque ripple of CMG1 is about 8%, while the torque ripple of CMG2 is below 1%, which is almost ignorable. Thus, the efficiency and torque ripple are not set as the optimization objectives. The weaknesses of CMGs are its low torsional stiffness and high manufacture cost compared to mechanical gearboxes [29]. The torsional stiffness is directly determined by the peak transmitted torque of CMGs, which is represented by Tp. The high cost of CMGs is caused by the usage of PMs since the price of NdFeB is almost one hundred times of that of steel. Thus, the torque versus PM volume ratio should be maximized, which is represented by Tp/VPM. Additionally, the rotational inertia of CMGs is an important index, since a smaller rotational inertia means a better dynamic response characteristic. Since the lowspeed rotor is connected to the output shaft, its rotational inertia J is set as an optimization objective, which can be expressed as J = 1 4 \u03c1La [ \u03b21 ( R4 mid,1 \u2212R4 4 ) + \u03b22 ( R4 mid,2 \u2212R4 mid,1 ) +\u03b23 ( R4 5 \u2212R4 mid,2 )] (38) where \u03c1 is the density of the silicon steel. Furthermore, we should avoid the irreversible demagnetization of PMs on the CMGs during rated operation. Since the rated operating temperature of gearboxes varies from scenarios to scenarios, we choose the gearbox in wind turbine for instance, where the rated operating temperature is about 60 to 70 \u00b0C [30]. In this article, Trated is set as 60 \u00b0C. As can be observed in Fig. 11, the irreversible demagnetization occurs when the magnetic flux density within the PMs drops below the knee point [31], and the knee point decreases with the increase of temperature. Hence, the absolute magnetic flux density on the outer surface of the PMs on the low-speed rotor and high-speed rotor should be above the magnetic flux density on the knee point at rated operating The individual number in one generation is set as 20; the maximum number of generations is set as 100. Besides, a CMG with 4 pole-pair PMs on the high-speed rotor and 11 pole-pair PMs on the stator is selected for the optimization study, and the value range of design variables are given in Table III. The airgap, the inner radius, the outer radius, and the axial length of the studied CMG are set as constants during optimization, whose values are 0.5 mm, 30 mm, 100 mm, and 60 mm, respectively. Additionally, the remanence and knee point magnetic flux density of N35H at rated operating temperature are 1.15 T and 0.22 T, respectively." ] }, { "image_filename": "designv10_9_0003162_s12652-020-01809-2-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003162_s12652-020-01809-2-Figure1-1.png", "caption": "Fig. 1 Wheeled mobile robot and its tracking target pose", "texts": [ " In the global coordinate system, the whole process of the wheeled mobile robot from the initial starting point to the tracking of the desired trajectory on the tracking can be observed. The desired trajectory is essentially composed of an infinite number of desired pose points, each of which can be represented in a global coordinate system. The actual position and attitude of the wheeled mobile robot can be expressed in the global coordinate system, that is, the coordinates of the x-axis and the y-axis and the angle between the longitudinal axis of the wheeled mobile robot body and the positive direction of the x-axis of the global coordinate system. Figure\u00a01 is a schematic diagram of the wheeled mobile robot of the research object and the tracking position of the wheeled mobile robot in the global coordinate system. Among them, the M point is the coordinate of the geometric center of the wheeled mobile robot. Combined with the kinematics and dynamics model of mobile robots, the TSK-CMAC neural network is used to approximate the uncertainty caused by nonlinear system parameters and non-parameters, and the robust controller is used to compensate the approximation error of TSK-CMAC neural network" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001655_j.mechmachtheory.2018.01.012-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001655_j.mechmachtheory.2018.01.012-Figure6-1.png", "caption": "Fig. 6. Projection of tooth surface boundary of conical worm gear in axial section.", "texts": [ " The results are listed as: equation of addendum : x R1 tan \u03b41 \u2212 y R1 + r a = 0 , (62) equation of pitch cone : x R1 tan \u03b41 \u2212 y R1 + r = 0 , (63) equation of toe : x R1 = \u2212L w 2 , equation of heel : x R1 = L w 2 (64) where r a and r are the radii of the top and pitch circles of the enveloping spiroid at the middle point of its thread length, respectively. Their computing formulae are tabulated in Table 1 . In the axial section of the conical worm gear, a coordinate system O 2 \u2212 x R2 y R2 can be built as shown in Fig. 6 , and the following coordinate relations are in existence by right of Eq. (40) as x R 2 = \u2212y \u2217o1 , y R 2 = \u221a ( x \u2217 o1 + a )2 + ( z ow + z 0 ) 2 , (65) where z 0 = z A + L w 2 . According to the location of the reference point M on the helicoidal surface of the enveloping spiroid, it is possible to infer that the conjugate point of the reference point is located on the dedendum cone of the conical worm gear on its convex flank at its little end as illustrated in Fig. 6 . The blank dimensions of the conical worm gear are determined on the basis of this. In Fig. 6 , the point M 1 is the intersection point between the addendum and the toe of the conical worm gear. In the light of the geometric relation depicted in the figure, the coordinates of the point M 1 in the coordinate system O 2 \u2212 x R2 y R2 can be computed as x M1 = M x \u2212 h \u2217 w m \u03b4 sin \u03b4a 2 , y M1 = M y + h \u2217 w m \u03b4 cos \u03b4a 2 (67) where \u03b4a 2 is the half addendum taper angle of the conical worm gear and h \u2217w is the coefficient of the working tooth height. The point M 2 is the intersection point between the addendum and the heel of the conical worm gear. According to the geometric relation depicted in Fig. 6 , the coordinates of the point M 2 in the coordinate system O 2 \u2212 x R2 y R2 can be computed as x M2 = x M1 + k g a tan \u03b4a 2 , y M2 = y M1 + k g a (68) where k g is the tooth width coefficient of the conical worm gear. Based on the points M, M 1 and M 2 , the boundary equations of the tooth surface of the conical worm gear can be estab- lished in the coordinate system O 2 \u2212 x R2 y R2 . The related results are listed as below: equation of gear addendum : x R2 tan \u03b4a 2 \u2212 y R 2 + y M1 \u2212 x M1 tan \u03b4a 2 = 0 , (69) equation of gear pitch cone : x R2 tan \u03b4a 2 \u2212 y R 2 + y M0 \u2212 x M0 tan \u03b4a 2 = 0 , (70) equation of gear toe : x R2 cot \u03b4a 2 + y R 2 \u2212 y M1 \u2212 x M1 cot \u03b4a 2 = 0 , (71) equation of gear heel : x R2 cot \u03b4a 2 + y R 2 \u2212 y M2 \u2212 x M2 cot \u03b4a 2 = 0 (72) where x M0 = 1 ( x M1 + M x ) and y M0 = 1 ( y M1 + M y ) ", " As for the both tooth surface couples [ (1) 1 , (1) 2 ] and [ (2) 1 , (2) 2 ] , the regions A 1 B 1 C 1 D 1 E 1 and A 2 B 2 C 2 D 2 E 2 are the conjugate zone of the enveloping spiroid drive. The conjugate zone computation can be boiled down to the typical point computation of its boundaries. 6.2.1. Computing boundary typical points of conjugate zone for [ (1) 1 , (1) 2 ] As to the conjugate zone A 1 B 1 C 1 D 1 E 1 , the point A 1 is the intersecting point of the addendum and toe of the conical worm gear, i.e. the point M 1 in Fig. 6 . As a result, in the light of Eq. (65) , the parameters u, \u03b8 , \u03d5 and \u03d51 at such a point should satisfy the following equations x R 2 = x M1 and y R 2 = y M1 . In these equations, the values of u and \u03d51 can be worked out from Eqs. (54) and (58) , respectively. Based upon this and by means of Eqs. (31) and (55) , the system of nonlinear equations to determine the point A 1 can thus be established as { f A 1 ( \u03b8, \u03d5 ) = ( A x B d \u03d5 + b x ) sin ( \u03d5 1 \u2212 \u03d5 ) + ( a y \u03d5 + b y ) cos ( \u03d5 1 \u2212 \u03d5 ) \u2212 x M1 A d = 0 g A 1 ( \u03b8, \u03d5 ) = ( \u02c6 x\u2217 o1 \u2212 a A d )2 + ( a z \u03d5 + a 0 ) 2 \u2212 ( y M1 A d ) 2 = 0 , (73) where \u02c6 x\u2217 o1 = ( A x B d \u03d5 + b x ) cos ( \u03d5 1 \u2212 \u03d5 ) \u2212 ( a y \u03d5 + b y ) sin ( \u03d5 1 \u2212 \u03d5 ) and a 0 = b z \u2212 z 0 A d ", " Hence the nonlinear equation to compute the point D 2 is Eq. (79) . The images of the curves f (i ) D 2 (\u03b8 ) ( i = 1 , 2 ) are painted in Fig. 17 and the image of the curve f (1) D 2 (\u03b8 ) has an intersecting point with the abscissa axis in the neighborhood of the point \u03b8 = 4 . 716 . This point can thus be employed as the initial value to solve the nonlinear equation f (1) D 2 (\u03b8 ) = 0 iteratively. Then the point D 2 can be determined. The point E 2 is the intersecting point of the heel and addendum of the conical worm gear, i.e. the point M 2 in Fig. 6 . As a result, in the light of Eq. (65) , the parameters u, \u03b8 , \u03d5 and \u03d51 at such a point should satisfy the following equations x R 2 = x M2 and y R 2 = y M2 . In these equations, the values of u and \u03d51 can be worked out from Eqs. (54) and (58) , respectively. Based upon this, replacing x M1 and y M1 in Eq. (73) with x M2 and y M2 gives rise to the system of nonlinear equations to determine the point E 2 as { f E2 ( \u03b8, \u03d5 ) = ( A x B d \u03d5 + b x ) sin ( \u03d5 1 \u2212 \u03d5 ) + ( a y \u03d5 + b y ) cos ( \u03d5 1 \u2212 \u03d5 ) \u2212 x M2 A d = 0 g E2 ( \u03b8, \u03d5 ) = ( \u02c6 x\u2217 o1 \u2212 a A d )2 + ( a z \u03d5 + a 0 ) 2 \u2212 ( y M2 A d ) 2 = 0 " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001655_j.mechmachtheory.2018.01.012-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001655_j.mechmachtheory.2018.01.012-Figure1-1.png", "caption": "Fig. 1. Classical spiroid drive.", "texts": [ " An approach based upon the elimination method and the geometric construction is put forth to detect the solution existence and to provide the reasonable initial value for iteratively solving the systems of nonlinear equations met during computing the conjugate zone and the contact line. The outcome of the numerical example investigation makes clear that, the working length of an enveloping conical worm can almost cover its whole thread length and the conjugate zone can nearly run through the whole tooth surface of the mating conical worm gear. The local meshing performance of an enveloping conical worm gearing is also excellent. \u00a9 2018 Elsevier Ltd. All rights reserved. 1. Introduction As reported by Litvin [1] , the classical spiroid drive, as shown in Fig. 1 , was originally invented by Oliver E. Saari at the Illinois Tool Works (ITW) in the 1950s. Bohle [2] and Nelson [3] made the contributions for the early developments of the spiroid gearing. Roughly by 1959, the Illinois Tool Works had realized the serialization of the spiroid reducer production under the trademark of the spiroid drive [4] . An overview on the spiroid gear set was performed in Ref. [5] . In the 1980s, Dong [6] made a systematical and in-depth investigation on the spiroid drive. His work included the mesh- ing analysis, the computing approach of the geometric parameters, the design methodology, etc" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002022_978-3-319-40036-5-Figure5.7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002022_978-3-319-40036-5-Figure5.7-1.png", "caption": "Fig. 5.7 By inserting a piece of dissolvable film between two channels it is possible to create a pressurised channel between the front of the advancing liquid and the dissolvable film, as the frequency of rotation is increased the advancing liquid reduces the volume of air within the channel thereby creating a counteracting pressure gradient that restricts the flow of liquid (Image (a)). Only when the frequency of rotations increased to the burst frequency can the liquid advance enough to come in contact with the dissolvable film (Image (b)). At this point the film dissolves the pressure is released, thereby releasing the total volume of liquid to pass towards the reaction chamber (Image (c) and (d))", "texts": [ " Generally, spin stands use a stroboscopic system to visualise a disc during rotation. Here, a camera and strobe are synchronised such that, as the motor spindle passes through a particular angular location, a pulse is generated which triggers the 126 B. Henderson et al. camera and strobe. Thus, each image of the disc is acquired at the same orientation; a video generated from these still frames shows liquid moving about these apparently still discs. A typical configuration of a spin stand can be seen in Fig. 5.7. Images acquired using a spin stand can be seen in Fig. 5.24. The most critical aspect for good operation of a spin stand is the correct synchronisation of the motor and strobe. This usually incorporates two steps; generating a signal from the motor as the spindle passes through a particular angular location and filtering this signal before it reaches the camera/strobe. A stepper or servo-motor should be chosen which has sufficiently high a maximum speed to overcome capillary effects and pump liquids about the disc", " Through channels were cut in a layer of PMMA to allow the movement of fluid between layers in both directions, this layer also forms a support structure and seal for the layers above and below. Similar to the microchannel layer the final layer of PSA allows fluid movement connecting the above valves to further microchannels. Once fabrication and assembly are complete the Lab-on-a-disk design requires testing to ensure that all unit operations (Valving, Metering, routing, etc.) work correctly, this is done using the custom spin stand described above in Fig. 5.7. To test the Lab-on-a-disk design, the reagents intended for use are replaced with water coloured with food dye so that the movement of fluid around the disk can be more easily visualised against the white background of the disk. The spin rate of the disk can be controlled manually to assess the specific burst frequency\u2019s required, if the 140 B. Henderson et al. spin rates are known it is possible to create an automated programme to control the change in spin rate at specific times throughout the process" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002069_s11837-017-2610-5-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002069_s11837-017-2610-5-Figure1-1.png", "caption": "Fig. 1. (a) Illustration of the EBM system. (b) and (c) SEM images showing Ti-6Al-4V powder under different magnifications. (d) Pictures of asbuilt samples prepared by an Arcam EBM machine and (e) impeller after machining from the wrought Ti-6Al-4V plate. (f) Illustration and dimensions of specimens for microhardness measurement and tensile test. (g) Temperature (measured by a thermocouple placed beneath the start plate) dependence of build time during the electron beam melting process.", "texts": [ "16,17 Fabricating a component with different mechanical properties may give the possibility of combining the advantages of EBMbuilt Ti-6Al-4V and wrought Ti-6Al-4V, if the component is loaded differently at various locations. Thus, the present study focuses on directly building a Ti-6Al-4V impeller part onto a wrought Ti-6Al-4V plate. The defects, hardness, microstructure, and tensile properties of the as-built parts have been investigated. Part fabrication was achieved using an EBM A2X system (as schematically illustrated in Fig. 1a) from Arcam AB. A wrought Ti-6Al-4V plate with dimensions of 150 9 150 9 30 mm and pre-alloyed Ti-6Al4V powder were used for the part fabrication. The Ti-6Al-4V plate was first ground to give a flat surface and then cleaned with acetone to avoid any contamination. The microstructure of the as-received wrought Ti-6Al-4V is shown in Fig. 2a and b. Deformed a plates with high aspect ratio were observed. The powder size ranged from 45 lm to 105 lm. The powder particles were observed with perfectly spherical morphology and clean surface (see Fig. 1b and c). The built parts consisted of four rectangular blocks and two tubes with a build height of 30 mm near the four edges of the top surface of the plate, and a centrifugal impeller with the bottom half \u2018\u2018buried\u2019\u2019 (by 4.9 mm, which was the basement thickness of the impeller) in the plate and the top part was built onto the plate, as shown in Fig. 1d. After machining, a combined centrifugal impeller with a wrought base plate and an EBMbuilt part was obtained, as revealed in Fig. 1e. The detailed EBM process was described in our previous report,9 and the whole build time was around 16 h. Figure 1g shows the temperature (measured by a thermocouple placed beneath the start plate) dependence of build time during the electron beam melting process. The impeller was machined from the wrought Ti6Al-4V start plate, and an x-ray computed tomography (CT) was applied to evaluate the fusion between the EBM-built zone and wrought Ti-6Al4V start plate. The experimental details of x-ray CT can be found elsewhere.9 For metallographic analysis, the as-fabricated specimen was sectioned into 15 9 20 9 5 mm rectangular blocks, as shown in Fig. 1f. To examine the porosity and microhardness, the specimen was mounted and polished to mirror finish using the preparation method for titanium alloys. The microhardness measurement was carried out by using a Matsuzawa MMT-X3 Vickers hardness tester at 100 g for 15 s. From the interface, at least seven measurements were taken at each distance from 150 lm to 1500 lm at an interval of 150 lm, and from 1500 lm to 4500 lm, an interval of 600 lm, from each of the extreme ends. For microstructural analysis, the polished specimens were etched in a Kroll\u2019s Reagent (2\u20133% HF, 4\u20135% HNO3, 92\u201394% H2O). The tensile specimens with a diameter of 6 mm and gauge length of 24 mm, according to ASTM E8 (Fig. 1f), were machined from as-fabricated rectangular blocks. The tensile test was conducted at room temperature in air, at an initial strain rate of 3.3 9 10 4 s 1, using the Instron 5982 universal tensile testing machine with a load cell capability of 100 kN. In addition, a non-contacting extensometer, Advanced Video Extensometer, was applied to measure the tensile strain. At least three specimens for each condition were examined to obtain the yield strength, ultimate tensile strength, and elongation to failure", " However, no clear equiaxed prior b grain zone was observed near the interface with the start plate. This observation is different from the parts fabricated on the stainless steel start plate.10,11 Although the cooling rate at the first few layers is high, no equiaxed prior beta grain was formed as there is lack of contaminants that may lead to more nucleation.11 This suggests that the formation of equiaxed prior b grain is affected by the contaminants. Martensite was not considered as the annealing time (at least 10 h at around 923 K, as shown in Wang, Nai, Lu, Bai, Zhang, and Wei Fig. 1g) was long enough to achieve complete decomposition,10,21 which was also confirmed by the XRD analysis. The heat affected zone (Fig. 2e) was between the fusion zone and annealed wrought zone, which includes two subzones: (I) temperature higher than the b transus and (II) temperature lower than the b transus but high enough to cause globularisation. Therefore, there was a thin layer (subzone I) just below the fusion zone that undergoes similar decomposition as the EBM part and exhibited the lamellar a + b phase (Fig", "9 Previous studies have revealed that both the higher temperature and longer annealing time results in higher percentage of globularisation (or equiaxialisation) in the wrought Ti-6Al-4V.22,23 The annealing takes place through the build time, but the part nearer to the surface is higher in temperature. Thus, there is a greater percentage of globularisation near the interface; down the temperature gradient, the equiaxed grains start to diminish and eventually elongated lamellar grains dominate. For the annealed wrought zone (Fig. 2e and g), a coarsened microstructure was observed, in comparison with the as-received wrought microstructure (Fig. 2a and b). As indicated in Fig. 1g, the whole EBM process takes around 16 h, and the start plate was exposed to temperatures ranging from 923 K to 1003 K for more than 10 h. This temperature range is a grain growth region of the Ti-6Al-4V;24 therefore, grain coarsening was observed after the build cycle. Figure 3a shows the microhardness profile across the interface of the EBM-built Ti-6Al-4V on the wrought Ti-6Al-4V plate under as-fabricated condition. The hardness values taken from the EBM part were near 380 HV, with a relatively low standard deviation at different distances from the center of interface" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001341_tmag.2013.2281477-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001341_tmag.2013.2281477-Figure1-1.png", "caption": "Fig. 1. (a) Machine schematic and (b) prototype.", "texts": [ " Since the two axes of motion are highly dependent position-wise, a simple yet effective decoupling mechanism based on the net torque methodology is introduced for the elimination of coupling between the two motions. The PID position controllers for independent control of each axis are then implemented. The experimental results verify that the steady errors of rotary and position tracking can be controlled within 0.3\u00b0 and 10 \u03bcm for the rotary and linear axis, respectively. By adding an extra identical stator ring with windings and extending the length of the rotor, the machine with two degrees of freedom can be achieved, as shown in Fig. 1(a). It is composed of a rotor and two identical stator rings with windings at zero phase shift, stator base, and rotary\u2013linear ball bearings on the fixture. The stator rings conform to the typical 6/4 SR motor topology. Instead of the integrated fiber optic switches for angular position detection [8], a rotary optical encoder is concentrically mounted on the shaft. A linear magnetic encoder is installed for linear stroke measurement. Fig. 1(b) shows the prototype of the machine. Major specifications are listed in Table I. The advantages of the machine topology can be summarized as follows: 1) least winding arrangement and simple winding scheme with coils mounted on the stator; 2) robust mechanical structure for the doubly salient motor topology; 0018-9464 \u00a9 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003017_j.addma.2020.101822-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003017_j.addma.2020.101822-Figure1-1.png", "caption": "Fig. 1. Terminology illustration of (a) surface texture (b) surface roughness (Ra).", "texts": [ " The manufacturing process affects the surface quality, with microscale variations being introduced with grinding or millimeter-scale variations from sand casting. Surface roughness influences many properties of the product such as friction, wear resistance, fatigue test, and heat conduction. Therefore measuring it accurately is important for industry [1,2]. Small, local deviations of the surface from its nominal shape is called its surface texture. The surface texture consists of two main irregularities: surface roughness and waviness. These irregularities usually have a pattern and have a dominant direction (Fig. 1(a)). Waviness surface irregularities are larger in magnitude than the surface roughness, and may be due to machine tool vibrations, or localized deflections due to cutting forces. The roughness is caused by \u2018high frequency\u2019 variations that are superimposed on the waviness of the surface. To measure the surface roughness, other larger-scale noise such as waviness and the nominal geometry profile should be eliminated. A skidded tactile roughness tester filters most of the macro surface textures mechanically but the remaining noise that affects the roughness values can be filtered mathematically [3]", " Contents lists available at ScienceDirect Additive Manufacturing journal homepage: www.elsevier.com/locate/addma https://doi.org/10.1016/j.addma.2020.101822 Received 14 August 2020; Received in revised form 4 December 2020; Accepted 24 December 2020 Additive Manufacturing 38 (2021) 101822 Ra = 1 L \u222b L 0 |R \u2212 m|dx (2) \u2018R\u2032 is the variable in Eq. (1) because it is the height of points from the reference line. In this case, the reference line is the X-axis. In Eq. (2), the \u2018m\u2032 value determines the height of the mean line from the reference line and \u2018L\u2032 is the measurement length (Fig. 1(b)). The lay is another surface texture measurement term, and is defined by the direction of the predominant surface pattern. The lay is typically caused by a production process. The interest to use additive manufactured (AM) products is increasing significantly in the industry, as this process can produce customized and complex products with minimal process planning. However, the surface quality of AM built products may limit their application compared to other processes like machining [8]. The staircase effect is a consequence of layer-based property in AM processes" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003137_j.mechmachtheory.2020.104180-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003137_j.mechmachtheory.2020.104180-Figure1-1.png", "caption": "Fig. 1. DH frames of the first kind robot.", "texts": [ " One important reason is that the simplified wrist obtained only by offsetting axis has the same orientation as that of the original wrist under the same joint angles. Therefore, there only exists position error between the ends of simplified and original wrists, which is the foundation of the new numerical algorithm of inverse kinematics proposed in Section 4 . When the axes of joints 4, 5 and 6 do not intersect at one point, the most common case is that the three axes pairwise intersect as shown in Fig. 1 where the angle between the axes of joint 4 and joint 5 is \u03b21 and the angle between the axes of joint 5 and joint 6 is \u03b22 . According to the DH frames shown in Fig. 1 , DH parameters of the first kind robot can be obtained and listed in Table 1 . According to the proposed simplification principle, it only needs to offset the axis of joint 6 to pass through the intersection point P \u2032 of the axes of joint 4 and joint 5. The changes in wrist structure before and after simplification are shown in Fig. 2 , where solid lines denote the axes of the actual joints and the axis of joint 6 after simplification is depicted by the dotted line. The position of the end of robot transfers from point P to point P \u2032 through simplification" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003369_j.mechmachtheory.2021.104386-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003369_j.mechmachtheory.2021.104386-Figure7-1.png", "caption": "Fig. 7. Correction roll angle for tooth pair (left) and base helix angle (right).", "texts": [ " 6 ( n = p, g for the pinion and gear, respectively) and can be calculated as follows: { \u03be1 ,p = \u03be0 + \u03beT \u2212 \u03beH \u2212 \u03be2 ,p \u03be1 ,g = a \u00b7sin \u03b1wt \u2212\u03be0 \u00b7r b,p r b,g \u2212 \u03be2 ,g , (16) { \u03be2 ,p = \u03c0 2 z p + inv \u03b1wt \u03be2 ,g = \u03c0 2 z g + inv \u03b1wt , (17) where \u03beT and \u03beH represent the correction roll angle according to the number of meshes and the helix angle, respectively; a denotes the center distance of the helical gear pair; \u03b1wt is the operating pressure angle in the transverse plane; r b,p and r b,g denote the base circle radii of the pinion and gear, respectively; and z p and z g represent the number of teeth in the pinion and gear, respectively. The involute function, inv, is defined as inv \u03b1wt = tan \u03b1wt \u2212 \u03b1wt . (18) Fig. 7 shows the difference in the instantaneous roll angle according to the number of meshes and the helix angle. Since the central angle for the circumferential pitch on the working pitch circle is the same, \u03beT , which is the angle between the first pinion tooth to any other pinion tooth in the mesh is calculated, as shown in Eq. (19) . \u03beH is the central angle for the deviation length on the base circle of the j th slice from the slice at the end and is calculated using Eq. (20) . \u03beT = ( t \u2212 1 ) \u00d7 2 \u03c0 z p , (19) \u03beH = b j \u00d7 tan \u03b2b r , (20) b where t denotes t th tooth pair in the mesh and has a value from 1 to a rounded integer of the contact ratio; b i represents the distance from the end of the gear to the j th slice; and \u03b2b is the base helix angle, which is defined as \u03b2b = \u23a7 \u23a8 \u23a9 + \u03b2b 0 \u2212 \u03b2b if a gear pair has left \u2212 hand helix angle if a gear pair is a spur gear pair if a gear pair has right \u2212 hand helix angle " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003462_s12555-020-0311-2-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003462_s12555-020-0311-2-Figure1-1.png", "caption": "Fig. 1. n-link manipulator with flexible-joint driven by DC motors.", "texts": [ " Let R and R+ respectively denote the spaces of real number and positive real one, Rn and Rn\u00d7n respectively denote the set of all the n-dimensional real vector space and the n\u00d7 n matrix space. For a matrix A \u2208 Rn\u00d7n, A\u22121 denotes its inverse matrix. Let \u2016 \u00b7 \u2016 denote the Euclidean norm for a vector or the induced norm for a matrix. For a function \u03d5(t) defined on [0,+\u221e), supt\u22650 \u03d5(t) denotes its supremum, liminft\u2192+\u221e \u03d5(t) and limsupt\u2192+\u221e \u03d5(t) denote the inferior and superior limits of \u03d5(t), respectively. 2. PROBLEM FORMULATION 2.1. System description This paper considers a flexible-joint n-link robotic manipulator driven by DC motor (as shown in Fig. 1 whose dynamics are formulated by the following equations with variables and parameters being introduced in Table 1 ([10]): D(q)q\u0308+C(q, q\u0307)q\u0307+G(q) = K(\u03b8 \u2212q)+d1, J\u03b8\u0308 +B\u03b8\u0307 \u2212K(q\u2212\u03b8) = KT I +d2, LI\u0307 +RI +KB\u03b8\u0307 = u+d3, (1) where q, \u03b8 , I \u2208 Rn are respectively the states of the links, joints and motors, u \u2208 Rn is control input, di \u2208 Rn is disturbance arising in separated path (i = 1, 2, 3); D(q), C(q, q\u0307) \u2208 Rn\u00d7n, G(q) \u2208 Rn are unknown matrices which are called inertia matrix, centripetal and Coriolis matrix, gravity vector, respectively; K = diag(Ki), J = diag(Ji), B = diag(Bi), KT = diag(KTi), L = diag(Li), R = diag(Ri), KB = diag(KBi) \u2208 Rn\u00d7n are all unknown diagonal and positive-definite matrices" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000027_icorr.2011.5975445-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000027_icorr.2011.5975445-Figure4-1.png", "caption": "Fig. 4 Bump detection.", "texts": [ " For this reason, the user might lose his/her balance and fall down by the effect of the additional modification force of the perception-assist. To prevent such case, the robot takes into account ZMP in the perception-assist algorithm. The laser range finder is used to recognize the environment in front of the user. A bump in front of the user is detected by the laser range finder and the distances from the user\u2019s toe to the bump and the height of the bump are calculated. The robot is careful with the user\u2019s motion so that the user does not stumble on the bump. The measured points from the laser range finder are shown in Fig. 4. As shown in Fig. 4, each vector is calculated based on these adjacent measured points. Then, k which is the angle between these vectors and the horizontal vector can be calculated. The robot estimates whether there is a bump or not based on k. When the absolute value of k is small enough, the robot judges that the ground is flat. On the other hand, when the absolute value of k is large enough, the robot judges that there is a bump in front of the robot. When the absolute value of k is middle, the robot judges that the ground is slope" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002277_978-3-319-27131-6-Figure5.26-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002277_978-3-319-27131-6-Figure5.26-1.png", "caption": "Fig. 5.26 Calculation of principle stresses using Mohr\u2019s circle diagram", "texts": [ " In a three-dimensional case, all six components of normal and shear stresses in the directions of x, y, and z exist in the asperities. Using the coordinate transformation between the inertial coordinate system (x,y,z) and principle coordinate system (1, 2, 3), we obtain only the normal stresses \u03c31, \u03c32, and \u03c33 in the directions 1, 2, and 3 in which the shear stresses \u03c41, \u03c42, and \u03c43 equal zero. Applying the Mohr\u2019s circle diagram, the related stresses in the principle coordinate system (1, 2, 3) are calculated graphically from the principle normal stresses \u03c31, \u03c32, and \u03c33, as shown in Fig. 5.26. The maximum principle shear stresses in the planes inclined 45 to the principle normal stress axes in the directions 1, 2, and 3 are calculated as \u03c41 \u00bc \u03c32 \u03c33j j 2 ; \u03c42 \u00bc \u03c31 \u03c33j j 2 ; \u03c43 \u00bc \u03c31 \u03c32j j 2 \u00f05:47\u00de The normal stresses perpendicular to the principle shear stresses result as \u03c3\u03c41 \u00bc \u03c32 \u00fe \u03c33 2 ; \u03c3\u03c42 \u00bc \u03c31 \u00fe \u03c33 2 ; \u03c3\u03c43 \u00bc \u03c31 \u00fe \u03c32 2 \u00f05:48\u00de The maximal shear stress for any plane in the asperity is the largest shear stress of the principle shear stresses from Eq. 5.47: \u03c4max \u00bc max \u03c41; \u03c42; \u03c43\u00f0 \u00de \u00f05:49\u00de 114 5 Tribology of Rolling Bearings All states of stress (\u03c3, \u03c4) in the asperities occur in the shaded area, which lies in the upper half plane outside the two small circles and inside the large one displayed in the Mohr\u2019s circle diagram in Fig. 5.26. 1. Hamrock, B., Schmid, S.R., Jacobson, B.O.: Fundamentals of Fluid Film Lubrication, 2nd edn. Marcel Dekker, New York (2004) 2. Khonsari, M., Booser, E.: Applied Tribology and Bearing Design and Lubrication, 2nd edn. Wiley, New York (2008) 3. Kennedy et al.: Tribology, Lubrication, and Bearing Design \u2013 The CRC Handbook of Mechan- ical Engineers. CRC Press (1988) 4. Bhushan, B.: Modern Tribology Handbook \u2013 Two-Volume Set. CRC Press, Boca Raton, Florida (2000) 5. Bhushan, B.: Introduction to Tribology" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001524_s12206-014-0931-7-Figure17-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001524_s12206-014-0931-7-Figure17-1.png", "caption": "Fig. 17. The 5(rT)2PS parallel mechanisms (1R or 1T).", "texts": [ " By changing one limb phase, both the two can change to 1T2R while 2R can go to 3R and 1T1R can become 2T1R respectively. By further changing one more limb phase, 3R will be 1T3R and 2T1R will become 2T2R. 1T2R can be both 1T3R and 2T2R. After then, all mechanism will have 5DOFs with 2T3R and 6DOFs by altering the left two limb phases one by one. In fact, from one topology the mechanism can be changed to any other by changing one or more limbs at the same time, e.g. from mobility 2 to 6 by changing all the four limbs at once. When constructing metamorphic parallel mechanisms with five (rT)2PS limbs as in Fig. 17, five constraint planes will be considered and their relationship can be classified into four types: (1) five or four parallel planes; (2) three parallel with the other two parallel or intersecting; (3) two parallel with another two parallel and one intersecting, or with the other three intersecting; (4) five intersecting planes. Based on the analysis in Sec. 5.1, when the four constraint planes are parallel the fourth limb is redundant. Thus, the first type with five or four parallel planes is redundant case and the mechanisms have the mobility of two translations and one rotation" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003264_j.apor.2020.102460-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003264_j.apor.2020.102460-Figure2-1.png", "caption": "Fig. 2. Coordinate frames of the vehicle.", "texts": [ " The aerial and underwater vehicle is driven by four waterproof motors, which are mounted at the end of each arm. Fig. 1 shows the mechanical sketch of the vehicle. The central hull is the enclosure for battery and electronic components. To improve the stability of the vehicle, the center of buoyancy needs to be exactly above the center of gravity. Two pairs of motors (1,3) and (2,4) spin in opposite directions. The attitude of the vehicle is controlled by changing the speed of the motors. The coordinate frames are shown in Fig. 2. Let G: {XG, YG, ZG} denote the global coordinate frame and B: {XB, YB, ZB} denote the body coordinate frame. The origin of the body coordinate frame is fixed to the center of gravity. \u03b7 = (\u03d5, \u03b8, \u03c8) is the Euler angle vector (roll, pitch, and yaw angle) of the vehicle related to the global coordinate frame, and \u03c9 = (\u03c9x, \u03c9y, \u03c9z) is the angular velocity vector in the body coordinate frame. The relationship between \u03b7 and \u03c9 can be expressed as \u03b7\u0307 = R\u03c9 (1) R = \u239b \u239d 1 sin\u03d5tan\u03b8 cos\u03d5tan\u03b8 0 cos\u03d5 \u2212 sin\u03d5 0 sin\u03d5/cos\u03b8 cos\u03d5/cos\u03b8 \u239e \u23a0 (2) where R is the rotation matrix of the vehicle from the body coordinate frame to the global coordinate frame" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001880_j.mechmachtheory.2018.04.001-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001880_j.mechmachtheory.2018.04.001-Figure4-1.png", "caption": "Fig. 4. Spatial relationship between gear and pinion.", "texts": [ ", D k ] T (12) where i designates the number of topography grid points, and r \u2217 denotes the position vector of the pinion target surface obtained from the function-oriented design. Finally, the polynomial coefficients of the auxiliary tooth surface correction motion are used in the optimal model presented in Eq. (13) . The polynomial coefficients are design variables, and the least sum of the squared errors of the tooth surface deviations is the object. { min f ( a i , b i ) = D T D a i , b i \u2208 [ x 1 , x 2 ] (13) where x 1 and x 2 are minimum and maximum values of the design variables, respectively. The meshing quality of gears can be analysed using the TCA method. Fig. 4 shows that there are four misalignment factors: the distance change between axles ( E ), gear axial misalignment ( G ), pinion axial misalignment ( P ), and shaft angle change ( ). The position and unit normal vectors for pinion and gear represented in the meshing coordinate system are as follows:{ r (1) h = M h 1 ( \u03d5 1 , P ) r (1) 1 ( \u03b8p , \u03c6p ) n (1) h = L h 1 ( \u03d5 1 , P ) n (1) 1 ( \u03b8p , \u03c6p ) (14) { r (2) h = M h 2 ( \u03d5 2 , E, , G ) r (2) 2 ( \u03b8g , \u03c6g ) n (2) h = L h 2 ( \u03d5 2 , E, , G ) n (2) 2 ( \u03b8g , \u03c6g ) (15) where s j , \u03b8 j ( j = p, g) are tooth surface parameters, M h 1 , and M h 2 are the homogeneous coordinate transformation matrices from S 1 to S h , and from S 2 to S h , respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000806_j.mechmachtheory.2012.08.011-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000806_j.mechmachtheory.2012.08.011-Figure4-1.png", "caption": "Fig. 4. FEMmodels of the thin-rimmed straightweb gears used for centrifugal deformation and stress analyses. (d) Left straight web gear. (e) Center straight web gear. (f) Right straight web gear.", "texts": [ " Structural dimensions of these gears are also shown in Fig. 2. Torque load is 294 Nm and this condition is used for all the calculations in this paper. Fig. 3 is the FEM models used for deformation and stress analyses of the thin-rimmed inclined web gears under the centrifugal load conditions. Fig. 3(a), (b) and (c) are used for the left, the center and the right inclined web gears respectively. Joint circles of the webs with the bosses are fixed as FEM boundary conditions as shown in Fig. 3. Fig. 4 is the FEMmodels used for the deformation and stress analyses of the thin-rimmed straight web gears under the centrifugal load conditions. Fig. 4(a), (b) and (c) are used for the left, the center and the right straight web gears respectively. Also, the joint circles of the webs with the bosses are fixed as the FEM boundary conditions. Fig. 5 is the FEMmodel used for LTCA of the thin-rimmed gears deformed by the centrifugal loads when these deformed gears are engagedwith the solid mating gear shown in Fig. 2(d). The joint circles of thewebs with the bosses of the thin-rimmed gears are also fixed as the FEM boundary conditions in LTCA (used to calculate the deformation influence coefficients with the FEM)" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003338_taes.2021.3053134-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003338_taes.2021.3053134-Figure2-1.png", "caption": "Fig. 2. Illustration of kinematic constraints.", "texts": [ " Authorized licensed use limited to: University of Exeter. Downloaded on June 02,2021 at 05:26:58 UTC from IEEE Xplore. Restrictions apply. 0018-9251 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. The final goal for relative position tracking is to steer the pursuer to the desired anchoring point lying on the \u2212x-axis of T , i.e., \u03c1d = [\u03c1d, 0, 0]> (\u03c1d < 0), as shown in Fig. 2. To this aim, the position and velocity tracking errors can be defined as \u03c1e = \u03c1 \u2212 \u03c1d and ve = v (due to \u03c1\u0307d = 0). In addition, considering that the actuators are fixed in the pursuer\u2019s body frame P , the control force f in T should be rewritten as f = R>PT fc, where fc denotes the control force in P , and RPT = RPIR > T I with RPI and RT I being calculated by (7) in terms of qp and qt, respectively. In view of this, the translational tracking error dynamics can be derived that \u03c1\u0307e = ve, (9) Mv\u0307e +Cve +G = R>PT fc, (10) where G = D\u03c1+ g. For safety concern, the position controller to be developed, except from achieving the final goal, it should also ensure that the pursuer is within a certain approach corridor, as shown in Fig. 2. This is called here the path constraint. In the following, an APF free of local minima will be designed to handle this constraint. Although the following contents pertain to the path constraint are almost the same as that in [7], they are still given to make the paper self-contained. The path constraint boundary can be given as: ht(\u03c1) = (\u03c1\u2212 xo)>Wt(\u03c1\u2212 xo), (11) with Wt = diag{1,\u2212 cot2(\u03b1),\u2212 cot2(\u03b1)}, where xo = [a, 0, 0]> and \u03b1 > 0 represent, respectively, the vertex and half-aperture of the approach corridor", " Lemma 2: Under the condition that \u2016\u03c1\u2016 6= 0 and x\u03c1 6= \u2212xF , the unit quaternion q\u0304 satisfying RFT x\u03c1 = xF certainly exists, and a feasible solution is given by q\u0304v = S(xF )x\u03c1\u221a 2(1 + x>\u03c1 xF ) , q\u03044 = \u221a 1 + x>\u03c1 xF 2 . (16) Proof: Since the above extraction problem and its counterpart stated in Lemma 1 of [33] represent, in essence, a common problem, readers are referred to [33] for the proof. Remark 1: A singularity problem will occur when \u2016\u03c1\u2016 = 0 or x\u03c1 = \u2212xF . With closer inspection, it can be claimed that these two conditions do not hold when the path constraint is satisfied. Specifically, from Fig. 2, one can intuitively observe that \u2016\u03c1\u2016 6= 0 if the pursuer keeps maneuvering within the approach corridor. On the other hand, if x\u03c1 = \u2212\u03c1/\u2016\u03c1\u2016 = \u2212xF holds, it then follows that \u03c1 = [\u03c11, 0, 0]> with \u03c11 > 0. Obviously, \u03c1 locates on the +x-axis of the frame T , and hence lies outside the approach corridor, indicating that x\u03c1 6= \u2212xF in the approach corridor. Thus, we conclude that the singularity problem will not occur, as long as Problem 1 is solved. Actually, q\u0304 satisfies q\u0304 = q\u2217t qf , whereby it follows that qf = qt q\u0304", " Then, the relative angular velocity of P w.r.t. F resolved in P can be defined as \u03c9e = \u03c9PIP \u2212RPF\u03c9FIF . Now, the rotational tracking error dynamics can be expressed as [16] q\u0307e = 1 2 Q(qe)\u03c9e = 1 2 (qe ~\u03c9e), (17) Jp\u03c9\u0307e = \u2212S(\u03c9PIP)Jp\u03c9 P IP + Jp(S(\u03c9e)\u2126\u2212 \u2126\u0304) + \u03c4c, (18) where ~\u03c9e = [\u03c9>e , 0]> \u2208 R4 is an extended version of \u03c9e, \u2126 = RPF\u03c9 F IF , and \u2126\u0304 = RPF \u03c9\u0307 F IF . Since the FOV of the vision sensor is limited, the pursuer needs to perform constrained attitude maneuvers to ensure that the target is always in sight, as shown in Fig. 2. This is the FOV constraint, whose constraint equation is of the form: xFR > PFxP > cos\u03b2. (19) UsingRPF in (19) and after some algebra, the FOV constraint can be expressed as the following quadratic inequality: hr(qe) = q>e Wrqe > 0, (20) where Wr is a symmetric matrix given below: Wr = [ 2xFx > P \u2212 (x>FxP + cos\u03b2)I3 xP \u00d7 xF (xP \u00d7 xF )> x>FxP \u2212 cos\u03b2 ] . With additional consideration of the unwinding phenomenon, the permissible set for the attitude tracking error qe is represented as Kqe = {qe \u2208 S3 : hr(qe) > 0, qe4 6= 0}" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003197_j.mechmachtheory.2020.103948-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003197_j.mechmachtheory.2020.103948-Figure2-1.png", "caption": "Fig. 2. Effects of flexibility on the meshing mechanism: a) position of the HPC in the case of rigid gears b) Variation of the highest point of the single tooth contact (HPC); c) loss of tangent condition on the HPC", "texts": [ " The paper is organized as follows: in the second section, profile modification shapes are introduced with a mention about the effect of the torque increase in order to better explain the need for the adoption of profile modification; the third section reports the implementation and calibration of the MUBOCOF model; in the fourth part, a numerical example is presented and results in quasi-static conditions are reported; fifth part, a validation with experimental data taken from literature is reported and then, an example of application in off-design torque condition is performed to demonstrate the possibility to use the MUBOCOF model as support tool in gear design. The resistant torque plays a fundamental role in the transmission error shape. Due to its importance in the profile modifications, the objective of this section is to analyze the effects induced by the increase of the resistant torque on the STE. The increase of resistant torque generates an increase of the total deflection of the system. The direct consequences are depicted in Fig. 2 where the effects of flexibility on the meshing mechanism are shown. M1 represents, the highest point of contact in the case of ideal system operation (for example in the case of gears are infinitely rigid or the resistant torque is neglected). With the introduction of flexibility, we observe that the point M1 Please cite this article as: M. Cirelli, O. Giannini and P.P. Valentini et al., Influence of tip relief in spur gears dynamic using multibody models with movable teeth, Mechanism and Machine Theory, https://doi", " From a practical point of view, this displacement leads to an increase in the contact ratio since the first pair of teeth comes into contact before, while the second pair of teeth come out of the contact afterward. Consequently, the angular deviation that occurs between the pinion and the driven gear generates a change in the position of the initial (and final) contact point. This change causes the conjugate profile condition to be missing in the new contact start point. For this reason, the profiles at the start contact point will no longer be tangents as can be observed in Fig. 2 c. The loss of tangent condition can be noticed by extending the involute profile of the driven gear over the HPSTC. It can be seen how the extended profile (dotted line) overlaps the involute profile of the pinion. This phenomenon represents the cause of the abrupt jump that occurs in the transmission error when switching from a single pair to two pairs of teeth in meshing. This occurrence also represents the major cause of the noise produced by the gears during dynamic operations. Under dynamic conditions, in fact, this interference generates impacts that induce the oscillation of the teeth", " The direct consequence of this is the increase of the contact ratio (CR) as the transmitted torque increases. E.g. the cinematic contact ratio of CR = 1.78 increases to 2.04 for T = 300Nm. Another crucial aspect influenced by torque variation is the mesh stiffness. Fig. 6 depicts the mesh stiffness as a function of the mesh cycle. As can be seen, an increase of the mesh stiffness with the increase of the resistant torque is recorded. It is due to the change of the HPSTC position. Referring on Fig. 2 b, with the increase of the resistant torque M1 moves to M1\u2019. In this last configuration, the contribution of the load along the tooth axis transverse direction decreases. Please cite this article as: M. Cirelli, O. Giannini and P.P. Valentini et al., Influence of tip relief in spur gears dynamic using multibody models with movable teeth, Mechanism and Machine Theory, https://doi.org/10.1016/j.mechmachtheory.2020. M. Cirelli, O. Giannini and P.P. Valentini et al. / Mechanism and Machine Theory xxx (xxxx) xxx 9 The first parameter analyzed is the relief amount" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003121_ffe.13372-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003121_ffe.13372-Figure3-1.png", "caption": "FIGURE 3 X-ray CT scan results throughout the gage section of the laser beam powder bed fused (LB-PBF) 316L stainless steel (SS) specimens from (A) non-preheated (NP) and (B) preheated to 150 C (P150) conditions", "texts": [ " The low cooling/solidification rates provide more time for the gas-entrapped pores to escape from the melt pool during solidification, and the sufficient overlap depth in the P150 condition reduces the chance of LoF formation, or at least smaller LoF defects are expected to be formed. There may be a height dependency for the effect of preheating the build platform on the part's structure. To evaluate such effects, gage sections of an NP and a P150 specimen were scanned from bottom to top, and the change in the size distribution of volumetric defects in each condition is compared visually in Figure 3. It can be seen that preheating the build platform (Figure 3B) decreases the size and population of the defects throughout the gage section as compared with the condition where the build platform is not preheated (Figure 3A). As was expected, the effect of preheating on the structure is alleviated slightly towards the top of the specimen's gage section ( 40\u201345 mm far from the build platform); fewer and smaller defects are observed in the bottom and middle of the gage section as compared with the top part. Note that the bottom part of the gage section is almost more than 25 mm far from the build platform, and still preheating the build platform impacts the defects' size and number up to an approximate height of 45 mm from the build platform", " Therefore, one should be careful with taking advantage of preheating the build platform for taller parts; however, the affected height may be increased by increasing the preheating temperature. The effect of an increased preheating temperature beyond 150 C is to be studied systematically in the future. The X-ray CT results presented in Figure 4 show both the visual and statistical evaluation of volumetric defects in the middle of the gage section for NP and P150 specimens. Similar to the results presented in Figure 3, there are more and larger volumetric defects in NP condition (Figure 4A) as compared with the P150 one (Figure 4B); some examples of LoF defects and gas-entrapped pores are highlighted in Figure 4A,B by red and green colours, respectively. The diameter of the defects, obtained by taking the square root of the projected area of each defect on the loading plane for NP and P150 specimens, was also compared statistically in Figure 4C. The statistical results show that the NP specimens possess more and larger volumetric defects (i" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003208_012183-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003208_012183-Figure3-1.png", "caption": "Figure 3. General view of the generator: 8-shaft, 9-body", "texts": [], "surrounding_texts": [ "In recently in the power engineering sector of the industry in Uzbekistan has growing interest in developing synchronous generators with permanent magnets. Some parameters of the synchronous generators such as mass and size of the generator with permanent magnets are determined by its main dimensions. In this study, the nature of the influence of the main geometric dimensions of the massdimensional parameters and the air gap on the energy indicators of the generator is estimated. The installation of additional cross windings ensures the efficiency of the proposed low-speed electric generator with permanent magnets. Because in the research the magnetic field of a low-speed generator with permanent magnets and additional windings in the rotor for low-power wind turbines and micro hydroelectric power plants using the method of finite element analysis are studied." ] }, { "image_filename": "designv10_9_0003603_jestpe.2021.3065997-Figure12-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003603_jestpe.2021.3065997-Figure12-1.png", "caption": "Fig. 12. (a) Cross section view of the machine flux lines. (b) Flux lines on the plates surface.", "texts": [ " To overcome this problem, the claw root should be larger and the claw head should be smaller. For easier manufacturing, the step cut claw is adopted as shown in Fig. 10. (a) V. WORKING FEATURES In this section, the performances of the machine designed above are investigated. The performance parameters include no-load flux distribution, back-EMF, cogging torques and torque density. Main design parameters and machine performances are concluded in table III and table IV. The flux distribution of the machine is shown in Fig. 12. It is indicated in Fig. 12(a) that part of the magnetic field created by the rotor with 10 pole-pairs couples with with the stator winding directly. This part of the field mainly goes through the claws. And, the rest interacts with the stator slots and is modulated into the 2 pole-pairs magnetic field. This part goes mainly through the claw plates as indicated in Fig. 12(b). Both fields contribute to the machine output. Authorized licensed use limited to: University of Technology Sydney. Downloaded on May 20,2021 at 04:22:13 UTC from IEEE Xplore. Restrictions apply. 2168-6777 (c) 2021 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 line-to-line back-EMF of the machine running at 300rpm is shown in Fig. 13. From the Figure, the back-EMF of the machine is relatively sinusoidal" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002629_s00170-019-04558-5-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002629_s00170-019-04558-5-Figure1-1.png", "caption": "Fig. 1 a\u2013c Propeller plane drawing", "texts": [ " Samples are also analyzed by both optical and scanning electron microscope (SEM) to determine the microstructure of the simulator. A propeller is made up of several blades and a hub. The blades were typical complex spatial curved surfaces whose section was constantly changing. The blueprint of a propeller contains a side view, a projected and expanded outlines, a maximum thickness distribution section shape, a profile offsets and geometry parameters of designed propeller, and so on. In the planar layout of a propeller, blade reference line is defined as the main lead in the center of the blade, as is shown in Fig. 1a, line OU. The angle \u03b8 between the blade reference line and the blade axis is called trim angle; YR the trim amount. Figure 1 c shows the stretched contour map which contains information like 0.2 R-0.9 R blade section, screw pitch, and distance from maximum thickness to the trailing edge. In order to produce high-precision propeller components for WAAM, an accurate 3D model of the propeller must be created. The propeller blades are complex spatial surfaces. A high-precision propeller blade surface model thus must be obtained by fitting the feature points as shown in Fig. 1c. In accordance with the process shown in Fig. 2, an accurate model of the propeller is built in the 3D modeling software Unigraphics NX software developed by Siemens. To begin with, create a DAT format point cloud file with 3D coordinates provided by the feature points table; import the file to Unigraphics NX software and fit points of the same height with B-spline curve as well as smooth curves chain. Then, geometry transformation is performed. These transformations include rotation shift where the helix angles \u03b1 are calculated by screw pitch, translation shift based on the trim amount YR and distance from maximum thickness to the trailing edge, andwinding shift that winds the section curve to the respective heights of the cylinder" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002977_s40194-020-00970-8-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002977_s40194-020-00970-8-Figure4-1.png", "caption": "Fig. 4 Sample extraction locations for microstructural observation, microhardness test, and uniaxial tensile test with corresponding orientations in additive layer deposition", "texts": [ " 0\u00b0 (tensile axis of the sample is perpendicular to the build-up direction), 45\u00b0 (tensile axis of the sample is 45\u00b0 to the buildup direction), and 90\u00b0 (tensile axis of the specimen is parallel to the build-up direction), to know the anisotropic properties of the WAAM cylinder along the built-up direction. A total of nine specimens were tested, and the average ultimate tensile strength (UTS) is presented. The location of the samples extracted from the WAAM cylinder for tensile test and microhardness evaluation is shown in Fig. 4. The measurement of Vickers microhardness of additive deposited material was recorded as per the ASTM E384-11e1 [27] standards using Matsuzawa MMT-X series machine at 0.1 kg load, 0.5 mm in between indentations along the additive deposited material from bottom to top layers. In each zone of the WAAM cylinder, a total of seven indentations were made and repeated five times in horizontal direction for each indentation point to measure the average microhardness. The microstructure of the WAAM cylinder was observed using a Leica optical microscope (OM) and JSM-6010 make scanning electron microscope" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001215_b978-0-08-100433-3.00006-3-Figure6.5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001215_b978-0-08-100433-3.00006-3-Figure6.5-1.png", "caption": "Figure 6.5 Schematic illustration of the stereolithography process. AM, additive manufacturing.", "texts": [ " STL is based on exposure of an ultraviolet-curing photopolymer (resin) that is deposited layer-wise by a sweeper before the cross section is scanned by a focused laser beam according to three-dimensional (3D) computer-assisted design3D (CAD) data. Typical layer thicknesses of 5e20 mm are generated by a downward movement of the build platform. Because overhangs are not supported by the slurry, additional supporting structures are necessary to produce complex parts. The basic setup for STL is illustrated schematically in Fig. 6.5. Patented in 1986 [5], STL represents one of the first AM methods used for manufacturing 3D objects. The technology was commercialized by 3D Systems [6] in the late 1980s and has since been subject to constant advancements concerning the scope of processable materials [7,8] and the hardware [9]. Early investigations of STL for ceramics show that the final density is crucially affected by the content of ceramic particles loaded into the polymer resin. Ceramic loading is supposed to be in the range of 45e70 vol% [8,10]" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003016_j.oceaneng.2020.108257-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003016_j.oceaneng.2020.108257-Figure4-1.png", "caption": "Fig. 4. Structure of the counterweight system on AUV2000.", "texts": [ " ( lc \u2212 xp ) (4) where Sc is the cross section of cylinder, lc is the length of cylinder, and xp is the piston position. From Fig. 3 the formula for determining the buoyancy center of AUV can be expressed as rcb \u0305\u2192=[xB, 0, 0]T = \u23a1 \u23a2 \u23a3 Vvar lc+xp 2 + Vfixlfix Vvar + Vfix , 0, 0 \u23a4 \u23a5 \u23a6 T (5) and the buoyancy of AUV is: B= \u03c1g ( Vfix +Vvar ) (6) where \u03c1 is the density of fluid, g is the gravitational acceleration. 2.1.3.2. Analysis of the counterweight system. Denote the total weight of AUV without counterweight (Fig. 4) as mh, and let rh \u2192 = [lhx, lhy, lhz] T be the mass center of mh in the body-fixed frame. Because the counterweight\u2019s mass mm is evenly distributed around the x-axis, the mass center of the counterweight in the body-fixed frame is r\u2192m = [xm, 0,0]T where xm is the counterweight position. As a result, the center of gravity of AUV can be determined by the following formula: rcg \u0305\u2192= mh rh \u2192+ mmrm \u2192 mh + mm = [xG, yG, zG] T = [ mhlhx + mmxm mh + mm , mhlhy mh + mm , mhlhz mh + mm ]T (7) and the weight of AUV is: W =mg=(mh +mm)g (8) Remark 1" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003580_j.mechmachtheory.2020.104238-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003580_j.mechmachtheory.2020.104238-Figure5-1.png", "caption": "Fig. 5. Mesh force diagram of internal gear with tooth tip chipping.", "texts": [ " 2 R b ( \u03b12 \u2212 \u03b1) cos \u03b1( cos \u03b11 ) 2 GA \u2032 x d\u03b1 (32) 1 k a = x + \u222b \u03b1s \u03b12 ( \u03b12 \u2212 \u03b1) cos \u03b1( sin \u03b11 ) 2 2 EL [ sin \u03b1 + ( \u03b12 \u2212 \u03b1) cos \u03b1] d\u03b1 + \u222b \u03b12 \u2212\u03b1a ( \u03b12 \u2212 \u03b1) cos \u03b1( sin \u03b11 ) 2 2 EL [ sin \u03b1 + ( \u03b12 \u2212 \u03b1) cos \u03b1] d\u03b1 + \u222b \u2212\u03b1a \u2212\u03b11 R b ( \u03b12 \u2212 \u03b1) cos \u03b1( sin \u03b11 ) 2 EA \u2032 x d\u03b1 (33) The Hertzian contact stiffness k h can be expressed as: k h = \u03c0E ( L \u2212 d 2 ) 4 ( 1 \u2212 \u03bd2 ) (34) Therefore, the total mesh stiffness can be obtained by substituting Eqs. (7) , (31) - (34) , into Eqs. (9) - (10) . For internal gears, the diameter of the addendum circle is less than the diameter of the tooth root circle, and to ensure that the tooth profile curve at the tooth tip is involute, the diameter of the base circle is less than the diameter of the addendum circle. For a standard gear, the tooth space width is equal to the tooth thickness on the reference circle. The mesh force diagram of the internal gear with tooth tip chipping is shown in Fig. 5 . In the UOV coordinate system, O is located at the center of the base circle, the U -axis passes the starting point of the involute, and the V -axis is perpendicular to the U -axis. In the XOY coordinate system, O is located at the center of the base circle, the Y -axis passes through the symmetry line of the gear tooth, and the X -axis is perpendicular to the Y -axis. The involute Eq. L 1 in the XOY coordinate system can be expressed by Eq. (35) as follows: { x = R b { [ sin ( tan ( \u03b1x ) ) \u2212 tan ( \u03b1x ) cos ( tan ( \u03b1x ) ) ] cos ( \u03b32 ) + [ cos ( tan ( \u03b1x ) ) + tan ( \u03b1x ) sin ( tan ( \u03b1x ) ) ] sin ( \u03b32 ) } y = R b { [ cos ( tan ( \u03b1x ) ) + tan ( \u03b1x ) sin ( tan ( \u03b1x ) ) ] cos ( \u03b32 ) \u2212 [ sin ( tan ( \u03b1x ) ) \u2212 tan ( \u03b1x ) cos ( tan ( \u03b1x ) ) ] sin ( \u03b32 ) } (35) herein \u03b1x is the pressure angle at arbitrary point of the involute" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003166_tmech.2020.2974296-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003166_tmech.2020.2974296-Figure1-1.png", "caption": "Fig. 1. A diagram of the soft manipulator", "texts": [ " Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Assuming that each part is regarded as a constant-curvature segment(refered to as CCS hereafter), let \u03a6u,ru(i = 1,2,3\u2026n) be the bending plane angles and curvature radii of the CCS on the upper part, \u03a6l,rl(i = 1,2,3\u2026n) be the bending plane angles and curvature radii of the CCS on the lower part. All the quantities are depicted in Fig.1. Some specifics of \u03a6u, ru, \u03a6l, rl can be found in [15]. Space.(findependent) \ud835\udc7b\ud835\udc7b\ud835\udc43\ud835\udc431 0 , \ud835\udc7b\ud835\udc7b\ud835\udc43\ud835\udc432 1 , which denotes the homogeneous transformation matrix from the base frame (O-x0y0z0) to frame O-xp1yp1zp1 and from O-x1y1z1 to O-xp2yp2zp2, can be obtained via (7) in [15]. Thus \ud835\udc7b\ud835\udc7b\ud835\udc43\ud835\udc432 0 can be obtained by \ud835\udc7b\ud835\udc7b\ud835\udc43\ud835\udc432 0 = \ud835\udc7b\ud835\udc7b\ud835\udc43\ud835\udc431 0 \ud835\udc7b\ud835\udc7b\ud835\udc43\ud835\udc432 \ud835\udc43\ud835\udc431 . In this paper, we simplify \ud835\udc7b\ud835\udc7b\ud835\udc43\ud835\udc431 0 as \ud835\udc7b\ud835\udc7b\ud835\udc43\ud835\udc431 0 = \ud835\udc54\ud835\udc54(\ud835\udf19\ud835\udf19\ud835\udc62\ud835\udc62, \ud835\udc5f\ud835\udc5f\ud835\udc62\ud835\udc62,\ud835\udf03\ud835\udf03\ud835\udc43\ud835\udc431) and so forth for brevity. In [15], the Jacobian matrix \ud835\udc71\ud835\udc71\ud835\udc61\ud835\udc61\ud835\udc61\ud835\udc61\ud835\udc61\ud835\udc61 relating the velocity of frame (O-x2y2z2) to " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003535_j.mechmachtheory.2021.104436-Figure15-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003535_j.mechmachtheory.2021.104436-Figure15-1.png", "caption": "Fig. 15. The construction principle of chain PRU^R and its equivalent chain.", "texts": [ " Since the input chains of OB-limbs [RRR] [RR] and [PRRR] [RR] are chains [RR] and [PRR] respectively, the equivalent chain [TRR] (or chain UR) and chain [TPR] (or chain UP) given in Section 3.3 are used to replace them, which can directly construct the compact OElimb. The typical examples [TRRR] [RR] and [TPRR] [RR] are shown in Fig. 13. For the OB-limbs RU^ [RR], PRU^ [RR], RU^R and PRU^R, 2 types of the equivalent chains are proposed below: The first equivalent chain of OB-limbs also concerns the RCM. As shown in Fig. 14(a) / (b) and Fig. 15(a) / (b), the equivalent chains TRU^R and TPU^R are obtained by using the RCM to replace the driving links of chains RU^R and PRU^R. According to the RCM properties, the axis O1B of the R-joint is always located in the v-plane and rotates around the plane normal O1A. The axis O1B is parallel J. Zhang et al. to vectors a, b and c (links a, b and c). The parallel link a is set as the driving link of this chain. The vector a is always parallel to axis O2D. Compared with this first equivalent chain, the second equivalent chain of OB-limbs has simpler structure", " The axis O1B is a moving axis that rotates around plane normal O1A in the v-plane. Obviously, the motion effect of this combination is similar to S-joint, so this cooperation is defined as \u2019SR and Sp-joint\u2019. The parallel link a is set as the driving link of this chain. The vector a is always parallel to the axis O2D. Obviously, the motion axes in Fig. 14(a), (b) and (c) have exactly the same relative positional relationship, and their v-planes are perpendicular to the base platforms. The motion axes in Fig.15(a), (b) and (c) have exactly the same relative positional relationship, their v-planes are parallel to the base platform. In detail, all axes O1A in the 2 figures always pass through O1 and are perpendicular to the v-plane. For each subfigure, the axis O1B always passes through O1 and rotates around axis O1A in the v-plane. The axis O2D is always parallel to O1B. Both O2D and O1B intersect with the O1O2, all O1O2 length have a fixed value l. Based on the screw theory, it can be analyzed that the chains RU^R, TRU^R and SRR have the same motion and constraint characteristics, and the chains PRU^R, TPU^R and SPR have the same motion and constraint characteristics as well" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002107_j.measurement.2018.07.031-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002107_j.measurement.2018.07.031-Figure4-1.png", "caption": "Fig. 4. Illustration of waviness (a) Waviness model of inner raceway (b) Representation of race waviness as sinusoidal wave.", "texts": [ " The waviness causes additional vibrations at distinct frequencies. The interaction of inner race surface waviness defect with rolling element occur in both loaded and unloaded region because ball moves with cage speed and inner race surface waviness defect moving continuously with shaft rotational speed. It is assumed that there is pure rolling motion of ball. It means rolling element always in contact with inner race and it is also considered inner race has a circumferential sinusoidal wavy surface. Fig. 4 represents the detail of inner race waviness. The initial amplitude of waviness (A0) is considered as radial clearance present between balls-raceway contacts. Hence the amplitude of the inner race surface waviness is described as: = + \u03c0 \u03bb A A A sin(2 L )in 0 m (16) The arc length (L) of inner race wave at the contact angle is given by, = r\u03c6L i in (17) The wavelength (\u03bb) of inner race is the ratio of length of the inner race circumference to the number of waves on circumference, which is termed as: =\u03bb \u03c0r2 Nw (18) Amplitude of wave on inner race surface waviness for ith ball is given by following relation" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002339_s10846-018-0884-7-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002339_s10846-018-0884-7-Figure1-1.png", "caption": "Fig. 1 Coaxial tricopter and robotic arm system with relevant frames", "texts": [ " In Section 4, fuzzy-neuro control approach with the parameter update rules is presented. In Section 5, the simulations are conducted in order to evaluate and verify the performance of the proposed control solution. In Section 6, the experimental flight tests are performed to validate the proposed controller. Lastly, conclusions and future work are drawn in Section 7. In this section, we describe the kinematics and dynamics of the coaxial tricopter equipped with the four-DOF robotic arm. With reference to the system shown in Fig. 1, we have the world-fixed reference frame CW , the body-fixed frame CB with origin at the center of mass of the coaxial tricopter, and the frame CE attached to the end-effector of the robotic arm. The position of the coaxial tricopter with respect to CW is described by the vector pB = [x y z]T \u2208 R 3\u00d71, its attitude is denoted by the Euler angles B = [\u03c6 \u03b8 \u03c8]T \u2208 R 3\u00d71, while the joints angles of the robotic arm are defined by the vector = [\u03b81 \u03b82 \u03b83 \u03b84]T \u2208 R 4\u00d71 (see Fig. 2). Hence, the generalized coordinate variables can be expressed by the vector q = [pT B T B T ]T \u2208 R 10\u00d71" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000064_10402000903452848-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000064_10402000903452848-Figure2-1.png", "caption": "Fig. 2\u2014A three-dimensional view of a control volume H (m) 1j showing backlash and end flow areas.", "texts": [ " The windage pocketing phenomenon is defined through the squeezing action of any control volume formed between a gear tooth and the mating tooth cavity over successive rotational positions, as illustrated in Fig. 1. In this figure, the pockets (control volumes) formed between the teeth are filled by air (or a mixture of air and oil, in case of fluid and air entrainment), instead of the incompressible lubricant. As this compressible medium gets squeezed out from the openings at the ends and at the backlash (as seen in Fig. 2) due to successive compression of the control volume until the volume reaches its minimum at a certain rotational gear position, a pressure differential is created between the ambient environment and inside the control volume. In the process, the medium inside the control volume is squeezed out at typically high velocities through the respective discharge areas. The high velocity of compressible fluid ejected through the flow areas results in power losses. D ow nl oa de d by [ \"U ni ve rs ity a t B uf fa lo L ib ra ri es \"] a t 0 8: 05 0 7 O ct ob er 2 01 4 Considering the phenomenon of pocketing more closely from a physics-based point of view, the prime mover for the mass efflux between ambience and the flow areas is due to the pressure difference between them", " Some of the fluid will in fact be transported into the opposing control volume having less pressure, and will then be forcefully ejected through the end discharge area corresponding to that control volume, reinforcing the velocity of the compressible fluid already being ejected through that particular end flow areas by augmenting the mass flow rate of the fluid ejected through that area. In order to alleviate computational concerns about the physics of broaching the problem through either means of thought, in this article, the control volumes or pockets will be considered as independent entities. Referring to Fig. 2, areas of the openings of a given cavity H(m) ij (j th cavity of gear i) at a rotational position m along its backlash and end (side) openings, A(m) b,ij and A(m) e,ij , are defined at a rotational incremental angle of \u03b8im = \u03b8i0 + m\u03b8\u0304i/M (m \u2208 [0, M \u2212 1]), where \u03b8i0 = [(r2 si/r2 bi) \u2212 1]1/2 and \u03b8\u0304i = [(r2 oi/r2 bi) \u2212 1]1/2 \u2212 [(r2 si/r2 bi) \u2212 1]1/2, respectively (Seetharaman and Kahraman (3)). Here, roi , rbi , and rsi are the radii of gear i at the outside circle, base circle, and at the start of active profile, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002277_978-3-319-27131-6-Figure5.16-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002277_978-3-319-27131-6-Figure5.16-1.png", "caption": "Fig. 5.16 Amplitude density function (ADF) of the surface roughness profile", "texts": [ " Obviously, the material ratio equals 0% at the maximum peak because no peak is cut; the material ratio arrives at 100% at the minimum valley since all cutting lengths equal the total length. However, in practice, one moves the ordinate surface height c from the initial position of Rmr\u00bc 0\u20135% (experience value) in the direction of the abscissa material ratio Rmr. Therefore, it makes sure that the reference line cref lies at the highest peak of the surface height because of initial wears after a short operating period. In other way, the Abbott curve can be derived using the amplitude density function p(c) of the surface roughness profile, as shown in Fig. 5.16 [5]. z x crn ll \u03bb55 == iz R ,c \u03bb mz maxR mean line Fig. 5.14 Mean roughness depth Rz and maximum roughness depth Rmax 5.7 Surface Texture Parameters 101 The amplitude density function p(c) is the number of surface heights between the two cutting heights z and z+ dz. The cumulative distribution function P(c) of the amplitude density function p(c) of the surface roughness height is in fact the material ratio at the dimensionless surface height c (s. Appendix A): 102 5 Tribology of Rolling Bearings P c\u00f0 \u00de \u00bc \u00f01 c p c\u00f0 \u00dedc Rmr c\u00f0 \u00de \u00f05:26\u00de Thus, Rmr (cmax)\u00bcP(cmax) 0% at the highest peak of the surface height" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003340_j.addma.2021.101881-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003340_j.addma.2021.101881-Figure4-1.png", "caption": "Fig. 4. Residual deformation of the 2 mm tall cantilever beam obtained by the (a) 5L5S case and (b) experiment.", "texts": [ " As a result, the stress relaxation effect on the lower layers is weakened, resulting in a little overestimation of the residual stress. When the residual stress is released, vertical bending deformation becomes significantly larger. As shown in Fig. 3, results of case 10L10S and 5L5S have a better match with the experimental results. Especially, the 5L5S case using the LAT of 0.4 mm shows slight overestimation of the residual deformation. Comparison of the overall residual deformation obtained in the 5L5S case and the experiment is shown in Fig. 4. Good agreement in the residual deformation distribution can be seen in the figure. Moreover, it is better to adopt such a LAT in the layer-wise simulation because an overestimation in the residual stress and deformation can provide a conservative evaluation for a large metal component. In fact, this finding is consistent with our previous finding. A similar LAT ranging from 0.4 to 0.6 mm was mentioned in our previous work as a direct numerical study on feasible equivalent layer thickness [28]. However, that conclusion was made based on some preliminary and simple numerical trials" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001328_j.renene.2014.03.036-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001328_j.renene.2014.03.036-Figure6-1.png", "caption": "Fig. 6. Hydraulic suspension system.", "texts": [], "surrounding_texts": [ "The third configuration, the hydraulic suspension (HS), is a variant of the TBC. In this system themain shaft is also supported by two main bearings. The gearbox, however, is not connected to the nacelle by means of a torque arm and bushings. Instead, the upper rubber mount, filled with hydraulic fluid, on one side is connected to the lower rubber mount on the other side by a hydraulic pipe. The fluid from one mount can flow to the other mount freely. The two other mounts are connected in a similar way. Therefore the gearbox is allowed to move freely in upward and downward direction while being constrained in the torque DOF. Figs. 6 and 7 illustrate the principle of the HS [18]." ] }, { "image_filename": "designv10_9_0000039_978-1-84996-220-9-Figure8.4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000039_978-1-84996-220-9-Figure8.4-1.png", "caption": "Figure 8.4 NAMO CR-space partitioned into components: (a) C1 = C acc R (W 0); (b) C f ree R Components; (c) Keyhole solution", "texts": [ " Even if the change seems to decrease immediate accessibility it is possible that manipulation opens space for a future displacement of another object. Some manipulation actions, however, are more clearly useful than others. To identify them, let us return to the sets of configurations defined in Section 8.2.3. We already observed that C acc R \u2208 C f ree R is a subspace of configurations that can be reached from one another by a single Navigate action. Suppose that the robot was in a free configuration outside of C acc R . There would also be a set of configurations accessible to the robot. In fact, as shown in Figure 8.4(b), we can partition the robot free space, C f ree R , into disjoint sets of robot configurations that are closed under Navigate operators: {C1,C2, . . . ,Cd}. The goal configuration lies in one of these subsets, CG. Partitioning the free space results in an abstraction for identifying useful manipulation subgoals. Consider the effect of Manipulate in Figure 8.4(c). After the action, 8 Autonomous Manipulation of Movable Obstacles 215 configurations in C2 become valid goals for Navigate. The illustration shows part of the solution to a keyhole in this NAMO problem. Definition 8.1. A keyhole, K(W 1,Ci), is a subgoal problem in NAMO that specifies a start state, W 1, and a component of free space, Ci. The goal is to find a sequence of operators that results in W 2 s.t. every free configuration in Ci is accessible to the robot: Ci \u2229C f ree R (W 2) \u2282 C acc R (W 2) and Ci \u2229C f ree R (W 2) = /0", " For at least one sequence of free space components this inductive definition ensures that once the robot has reached a configuration in Ci it can always access Ci+1. Condition (3) guarantees the existence of a final keyhole solution such that the goal is in CG \u2229C f ree R (W n). Although this definition allows for arbitrary k, in this section we will focus on problems that are linear of degree 1 or L1. Even when only one Manipulation operator is permitted, it is often possible to find a keyhole solution that blocks a subsequent keyhole. For instance, in Figure 8.4(c), consider turning the table to block a future displacement of the couch. We propose to broaden the scope of problems that can be represented as L1 by constraining the action space of the robot. We have considered two restrictions on the placement of objects: Occupancy Bounds: Any displacement of an object must not occupy additional free space that is not accessible to the robot:X Oi R (Wt+1)\u2282(X Oi R (Wt)\u222aC acc R (Wt)). This implies that any solution to (Wt\u22121,Ct) results in Wt s.t. Ct \u2229C f ree R (Wt) =Ct " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003463_s11665-020-05403-7-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003463_s11665-020-05403-7-Figure1-1.png", "caption": "Fig. 1 Locations of sample extraction on the cast pump housing for: (a) surface roughness (S), density (D), and hardness (H) measurements; (b) machined surface type; (c) as-cast, horizontal surface type; and (d) as-cast, vertical surface type", "texts": [ " The pump would be connected to the transmission stator shaft and act as the main pressure source in the transmission, enabling circulation of oil through the transmission cooler and pressure in the valve body that controls the clutches. The service conditions include operating temperatures from 30 to + 120 C and operating pressures of up to 1.5 MPa. The service fluid may vary between different types of automatic transmission fluid. Test samples were extracted from the pump body using a vertical band saw for large cuts and a precision cutoff saw for small cuts. Figure 1(a) shows the locations where samples were cut for density, surface roughness, and hardness tests. Three surface types on the cast pump housing were also characterized for wear and corrosion behavior: the machined surface, and two perpendicular as-cast surfaces (referred to as \u2018\u2018horizontal\u2019\u2019 and \u2018\u2018vertical\u2019\u2019 surface types). These experiments required nine samples per surface type to be cut from the pump housing, with one flat surface of approximately 1 cm2. Figure 1(b), (c), and (d) highlights the areas where the samples for each surface type were extracted. The surface types were selected due to differences in surface texture visible to the human eye (ascast/machined) and surface orientation relative to the base of the part (horizontal/vertical), and are shown with more detail in Fig. 4(a). Note that all machined surfaces had a horizontal orientation. A handheld x-ray fluorescence (XRF) analyzer (Thermo Scientific Niton XL3t XRF Analyzer) was used to provide nondestructive bulk chemical analysis of the surface of the cast pump housing", "%, the pump housing had more than double the Si content of the AlSi10Mg powder and exceeded the OEM specification. There was also a discrepancy between the XRF and EDX measurements of Cu, which was slightly above specification for the XRF surface measurements and slightly below for the EDX measurements. This may indicate that some level of solute macrosegregation occurred during the casting process. Figure 5(a) shows optical micrographs of the cast pump housing at various magnifications, taken at location H2 on the pump housing (shown in Fig. 1(a)). It features a dendritic matrix of Al (light) with three visible secondary phases (dark), likely composed of Si, Cu, and Fe-rich precipitates. The morphology of the secondary phases included coarse flakes (Fig. 5i), a broken network of discrete, coarse particles between dendrites (Fig. 5ii), and a fine, semi-continuous network of precipitates (Fig. 5iii). SEM was also used to examine the microstructure, as shown in Fig. 5(b). In the SEM micrographs (secondary electron mode), the Al matrix appears as dark gray, while the secondary phases appear as light gray and white; features shown in the SEM micrographs are consistent with the observations captured in optical micrographs" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003224_tmag.2020.3018457-Figure8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003224_tmag.2020.3018457-Figure8-1.png", "caption": "Fig. 8. Magnetic network model of the motor excited by only one PM. (a) Model I; (b) Model II.", "texts": [ " Therefore, the equivalent magnetic network model of one permanent magnet can be established for calculation firstly. As shown in Fig. 7(b) and (c), after passing through the air gap, the flux generated by one permanent magnet may enter one or two secondary iron cores. Moreover, the air gap flux path and the secondary iron core flux path will change with the primary component movement. The period of the motor flux linkage is the secondary pole pitch. In one period, two magnetic network models need to be used for magnetic circuit equivalence, as shown in Fig. 8. In Fig. 8, pG , aG , sG , fG , and mG are the permeance of the primary core patch, the air gap patch, the secondary core patch, the flux barrier patch, and the PM patch, respectively. aF and mF are armature and PM magnetic motive forces, respectively. With the change of relative position between the primary and secondary components, aG , sG and fG will change. After calculating the permeance of each patch, the magnetic network equation can be established, and then the magnetic field distribution of the motor can be obtained by iterative solution" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002805_tte.2019.2956867-Figure14-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002805_tte.2019.2956867-Figure14-1.png", "caption": "Fig. 14. Part of the stator and rotor. (a) PMs. (b) Stator lamination. (c) Rotor. (d) Stator.", "texts": [ " Also, it can be found that the temperature rise of both winding and PM in the 12/24/28 machine are reduced by ~32\u2103 as compared with that of the 12/24/29 one. As can be seen, the selection of slot-pole combination has great effects on machine performances especially the losses and temperature rise. Hence, the selection of the appropriate slot-pole combination is very essential to design the DPMEV machine. (a) To experimentally validate the design effectiveness of the DPMEV machine, a 12/24/28 DPMEV machine is built as shown in Fig. 14. Fig. 14(a) shows the NdFeB and ferrite PMs, 0 0.05 0.1 0.15 0.2 0.25 1 4 7 10 13 16 19 22 25 28 31 34 37 F lu x d en si ty ( T ) Harmonic order v 4 (0.217T) 8 (0.07T) 16 (0.06T) 24 (0.056T) 28 (0.118T) 32 (0.152T) 0.05 2332-7782 (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. in which the black part is ferrite. As shown in Fig. 14(c) and (d), the slots of rotor and stator are embedded with ferrite and NdFeB PMs. During the machine design and analysis process, the optimal simulation results are selected. However, considering the actual manufacture and installation level, the shapes of NdFeB PMs on the stator and ferrite PMs on the rotor of the prototype machine are modified slightly to simplify the manufacture and installation process. As shown in Fig. 15, the experiment platform of the three phase DPMEV prototype machine is built" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000879_1.4026264-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000879_1.4026264-Figure6-1.png", "caption": "Fig. 6 Pressure distribution in the oil film for the optimal values of the machine-tool setting parameters", "texts": [], "surrounding_texts": [ "The optimization problem formulated according to Eq. (5) is a nonlinear constrained optimization problem, belonging to the general framework of nonlinear programming. In addition functions f mp\u00f0 \u00de and C mp\u00f0 \u00de are not available analytically and are only computable, that is, they exist numerically through the EHD lubrication calculation. Therefore, the problem defined by Eq. (5) also falls within the category of simulation-based optimization. In the simulation-based optimization setting [71], the computer simulation of EHD lubrication must be run, repeatedly, in order to compute the various quantities needed by the optimization algorithm. As a consequence, a good deal of numerical noise is introduced into the model, that causes the calculation of partial derivatives for the gradient-based optimization algorithms to be quite impractical. For this reason, a nonderivative method is selected to solve this particular optimization problem. One of the direct search methods described in Ref. [71] can be adopted. Here, the Hooke and Jeeves pattern search method [72] will be used. This method is designed to solve nonlinear optimization problems, even for nonsmooth cases, when function derivatives are unavailable or their calculation would be impractical or unreliable. A computer program was developed to implement the formulation provided above. The program searches for a local minimum, beginning from the starting guess. The program works by taking steps from one estimate of a minimum, to another (hopefully better) estimate. Taking big steps achieves the minimum more quickly, at the risk of stepping right over an excellent point. The step size is controlled by the parameter Dmp. At each iteration, the step size is multiplied by Dmp (0 < Dmp < 1), so the step size is successfully reduced. Small values of Dmp correspond to big step size changes, which make the program run more quickly. However, there is a chance (especially with highly nonlinear functions) that these big changes will accidentally overlook a promising search vector, leading to nonconvergence. Large values of Dmp correspond to small step size changes, which force the program to carefully examine nearby points instead of optimistically forging ahead, This improves the probability of convergence. In this program, parameter Dmp is set to 0.5. The calculations have shown that in this case it is a reliable value." ] }, { "image_filename": "designv10_9_0001710_j.cja.2015.03.003-Figure11-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001710_j.cja.2015.03.003-Figure11-1.png", "caption": "Fig. 11 Region for the error compensation experiment.", "texts": [ " A Faro SI laser tracker is used to measure the optimum grid step in the experiment (see Fig. 10). During the experiment, the Please cite this article in press as: Tian W et al. Determination of optimal samples dx.doi.org/10.1016/j.cja.2015.03.003 robot is under zero load and is operated in a working temperature environment of 15\u201318 C. The target orientation and the operating speed of the robot are kept constant. The common working region of the robot is selected. The size of the region is 1000 mm \u00b7 1200 mm \u00b7 1000 mm (see Fig. 11). The accuracy requirement of TCP is preset as \u00b10.3 mm in each degree of freedom. The analysis of the absolute position error of the robot in Section 2 shows that the error plane is spatially variable. The accuracy compensation effects in different areas in any selected region may be different. Therefore, based on the characteristics of the workspace, 5 grid central points are selected (see Table 3). A growth step of 60 mm is selected. The grid\u2019s central point is selected as the start point and the step is gradually increased from 20 mm to 500 mm to establish 9 cubic grids" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003603_jestpe.2021.3065997-Figure16-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003603_jestpe.2021.3065997-Figure16-1.png", "caption": "Fig. 16. Stress distribution. (a) S45C rotor. (b) SMC rotor. During the operation of the machine, there will be eddy current induced on the rotor. The no-load torque waveform calculated by FEA for two conditions are shown in Fig. 17. From the figure, for the machine with eddy current rotor, there will be a reverse torque of 2.6Nm. But for the SMC rotor, there is no brake torque.", "texts": [ " However, due to the difficulties of SMC manufacturing, the rotor material was finally selected to be S45C. The main material properties of them are listed in Table V. Firstly, the claws are manufactured by wire cutting. Then, the two claws are assembled with magnets position remained there. Next, the magnets and rotor claws are filled up with glue on the surface. At last, the magnets are inserted into the remained position. The rated speed of the machine is not high. Thus, the mechanical stress on the rotor is not high as shown in Fig. 16. It is also worth mentioning that the structure parameters of two materials are identical, which leads to similar stress distribution. In no-load condition experiments, a servo motor drags the prototype to 300rpm/min, which is its rated speed. The line-toline back-EMFs in experiment and FEA under rated speed are Authorized licensed use limited to: University of Technology Sydney. Downloaded on May 20,2021 at 04:22:13 UTC from IEEE Xplore. Restrictions apply. 2168-6777 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000829_s11071-015-2029-x-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000829_s11071-015-2029-x-Figure1-1.png", "caption": "Fig. 1 Aileron deflection influence on the roll motion, modified from http://en.wikipedia.org/wiki/Aileron", "texts": [ " Moreover, the presence of wing rock during the approach or landing phase can have severe influence on the operational safety of the aircraft. From the stability point of view, wing rock phenomenon arises from a nonlinear aerodynamic mechanism and is associated with the nonlinear trend of roll damping derivatives, leading to hysteresis and sign changes of the stability parameters when increasing the AOA during aircraft maneuvers [10,13]. The wing rock is usually controlled by appropriate ailerons deflection, as shown in Fig. 1. Controlling wing rock is a challenge to both aircraft designers and control engineers. Many researchers have tackled the problem of controlling wing rock motion. Adaptive feedback linearization approaches were proposed in [8,18], while suboptimal and optimal feedback algorithms were discussed in [1,24]. Kalman filter-based control [19] was shown to be a good candidate to solve the wing rock motion problem. Fuzzy [20,21], fuzzy adaptive [15] and fuzzy neural [14] approaches gained popularity during the last decade" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002942_j.jmapro.2020.04.022-Figure10-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002942_j.jmapro.2020.04.022-Figure10-1.png", "caption": "Fig. 10. Simulation results for the cutting area in passes 1-3.", "texts": [ " For all the elements of cutting edge Ej,i(t), S\u2019j,i is expressed as follows; =S S S E E Et t t t ' ( ) ( ) \u00b7 ( ) | ( )|j,i j,i j,i j,i j,i 2 j,i (4) The angle between S\u2019j,i(t) and \u2013Hj,i(t) is the effective rake angle \u03b1j,i (t). = H S H S t t t t t ( ) cos ( ) ' ( ) | ( ) ' ( )|j,i 1 j,i j,i j,i j,i (5) In accordance with the foregoing method, the cutting area when the skiving tool rotates was simulated for pass 1 to pass 3. In the simulation, the rotation angle of the skiving tool with respect to the x-axis shown in Fig. 5 was divided into 100 steps in the range of \u221240\u00b0 to 40\u00b0 (\u22122\u03c0/ 9< \u03c6t(t)< 2\u03c0/9). Fig.10 shows the cutting area for pass 1 to pass 3. The areas of green and gray stripes in the figure correspond to the machined surface generated by the process; the color alternates between green and gray every five calculation steps. From this figure, it can be seen that in the first process pass 1, the cutting is started from the left side of the tooth surface, and the tool is detached from the material. However, in the third process (pass 3), the cutting is started from the right side and the tool is detached from the left side" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002084_j.ymssp.2018.03.033-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002084_j.ymssp.2018.03.033-Figure6-1.png", "caption": "Fig. 6. Schematic of the gear with the crack propagating through tooth: (a) yP > 0, (b) yP < 0.", "texts": [ " Considering the orientation of the parabolic curve needs to be consistent, hx can be calculated by: hx \u00bc yQ yP \u00f0xQ xP \u00de2 \u00f0x xP\u00de2 \u00fe yP yP > yQ yP yQ \u00f0xP xQ \u00de2 \u00f0x xQ \u00de2 \u00fe yQ 0 < yP < yQ 8< : \u00f017\u00de When the y coordinate of the crack tip is greater than the tooth profile tip (yP > yQ ), the bending stiffness and shear stiffness can be written as follows: 1 kb \u00bc Z xP lrim 3\u00bdcosa1\u00f0d x\u00de sina1h 2 2EL\u00f0r2f x2\u00de32 dx\u00fe Z l xP 12\u00bdcosa1\u00f0d x\u00de sina1h 2 EL\u00bd\u00f0r2f x2\u00de12 \u00fe yP 3 dx\u00fe Z a3 a1 12r3bf1\u00fe cosa1\u00bd\u00f0a2 a\u00de sina cosa g2\u00f0a2 a\u00de cosa EL yQ yP \u00f0xQ xP \u00de2 frb\u00bdcosa\u00fe \u00f0a a2\u00de sina xPg2 \u00fe yP \u00fe rb\u00bdsina\u00fe \u00f0a2 a\u00de cosa n o3 da \u00f018\u00de 1 ks \u00bc Z xP lrim 3 cos2 a1 5GL\u00f0r2f x2\u00de12 dx\u00fe Z l xP 6 cos2 a1 5EL\u00bd\u00f0r2f x2\u00de12 \u00fe yP dx\u00fe Z a3 a1 1:2rb cos2 a1\u00f0a2 a\u00de cosa GL yQ yP \u00f0xQ xP \u00de2 frb\u00bdcosa\u00fe \u00f0a a2\u00de sina xPg2 \u00fe yP \u00fe rb\u00bdsina\u00fe \u00f0a2 a\u00de cosa n o da \u00f019\u00de When the y coordinate of the crack tip is less than the tooth profile tip and the crack tip does not exceed the central line of the tooth (0 < yP < yQ ), the bending stiffness and shear stiffness, similarly, can be written as follows: 1 kb \u00bc Z xP lrim 3\u00bdcosa1\u00f0d x\u00de sina1h 2 2EL\u00f0r2f x2\u00de32 dx\u00fe Z l xP 12\u00bdcosa1\u00f0d x\u00de sina1h 2 EL\u00bd\u00f0r2f x2\u00de12 \u00fe yP 3 dx\u00fe Z a3 a1 12r3bf1\u00fe cosa1\u00bd\u00f0a2 a\u00de sina cosa g2\u00f0a2 a\u00de cosa EL yP yQ \u00f0xP xQ \u00de2 frb\u00bdcosa\u00fe \u00f0a a2\u00de sina xQg2 \u00fe yQ \u00fe rb\u00bdsina\u00fe \u00f0a2 a\u00de cosa n o3 da \u00f020\u00de 1 ks \u00bc Z xP lrim 3 cos2 a1 5GL\u00f0r2f x2\u00de12 dx\u00fe Z l xP 6 cos2 a1 5EL\u00bd\u00f0r2f x2\u00de12 \u00fe yP dx\u00fe Z a3 a1 1:2rb cos2 a1\u00f0a2 a\u00de cosa GL yP yQ \u00f0xP xQ \u00de2 frb\u00bdcosa\u00fe \u00f0a a2\u00de sina xQg2 \u00fe yQ \u00fe rb\u00bdsina\u00fe \u00f0a2 a\u00de cosa n o da \u00f021\u00de (2) TVMS of the gear with CPT The crack propagation through the tooth is significantly different from the crack propagation through the rim, which mainly affects the gear tooth stiffness. It is not monotonous because there is an inflection point on the crack propagation path (see Fig. 6). The mesh stiffness is mainly related to the position of the crack tip when the crack does not propagate to the inflection point. Therefore, the bending stiffness and shear stiffness of the cracked gear under this condition can be the same as that of the gear with CPR (see Eqs. (18)\u2013(21)). When the crack propagates to the inflection point (see Fig. 6b), the effective area moment of inertia and the cross-section area at the position of x should consider the influence of the inflection point, which can be calculated as follows: Ix \u00bc 1 12 \u00f02hf \u00de3L lrim < x < xmin 1 12 \u00f0hf \u00fe yP\u00de3L xmin < x < l 1 12 \u00bdhx \u00fe y 3L x > l 8>< >: \u00f022\u00de Ax \u00bc 2hf L lrim < x < xmin \u00f0hf \u00fe yP\u00deL xmin < x < l \u00f0hx \u00fe y\u00deL x > l 8>< >: \u00f023\u00de where xmin is the x coordinate of the inflection point. The distance from the parabolic curve to the central hx can be obtained from Eq. (17). According to the simulation result, the inflection point only exits below the central line (yG < 0)" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003310_j.mechmachtheory.2021.104428-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003310_j.mechmachtheory.2021.104428-Figure1-1.png", "caption": "Fig. 1. An overview of the configuration and description of sensors in WT CMS.", "texts": [ " Although failures are inevitable, by monitoring the health status of the gearbox and discovering potential failures in time, the losses caused by sudden faults and damages can be minimized. In recent years, with the development of offshore wind power, its accessibility for operation and maintenance tasks are getting worse, and higher requirements have been put forward for condition monitoring and fault diagnosis of the WT gearbox. Hence, vibration-based condition monitoring systems (CMS) are widely used in WT, especially for the WT gearbox [3\u20135], see Fig. 1, which displays an overview of the configuration and description of sensors in the CMS. Therefore, analyzing the vibration data obtained from CMS to understand the real behavior of the WT gearbox and discover early failures opportunely is of great concerns to researchers [6\u201310]. Vibration analysis of the sensor-perceived signal is a popularly adopted technique for condition monitoring due to the fact that the gearbox has particular frequency features for its health status, which will change with the development of damage", " Without any loss of generality, \u03b32 and \u03b33 are set to be 0 for simplicity in this paper. The vibration v2(t)/v3(t) generated by the meshing of the g1-g2/g3-g4 gear pair can be expressed as v2(t) = \u2211K k=1 v2kcos(kwm2t), (7) v3(t) = \u2211K k=1 v3kcos(kwm3t), (8) where v2k and v3k are the amplitude of the kth harmonic of the vibration v2(t) and v3(t). There are multiple gear pairs (s-p gear pairs, r-p gear pairs, g1-g2 gear pair, and g3-g4 gear pair) in the WT gearbox. Each gear pair can be regarded as a vibration source. Besides, as shown in Fig 1, there are generally three accelerometers (A3, A4, and A5) installed on the outer surface of the gearbox, among them, A3 is mounted on the gearbox casing at the ring gear directly, A4 is mounted on the lowspeed shaft bearing, and A5 is mounted on the high-speed shaft bearing. Each accelerometer can receive the vibrations generated by the meshing of the gear pairs through multiple transmission paths. In previous studies [16,19,21\u201324], researchers pointed out that in a single-stage planetary gearbox, the s/r-p meshing points moves with respect to the fixed sensor as the planet carrier rotates, resulting in a periodic time-varying transmission path" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001144_j.mechmachtheory.2013.09.001-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001144_j.mechmachtheory.2013.09.001-Figure4-1.png", "caption": "Fig. 4. Coordinate systems for the hobbing of a work gear with longitudinal crowning teeth.", "texts": [ " (1), (2), (3), (5), and (6), the right side surface locus vector and its unit normal vector of the modified VTT hob can be obtained by rp \u00bc xp u1; v1;\u03c61\u00f0 \u00de; yp u1; v1;\u03c61\u00f0 \u00de; zp u1; v1;\u03c61\u00f0 \u00de;1 h iT ; \u00f08\u00de and np \u00bc nxp u1; v1;\u03c61\u00f0 \u00de;nyp u1; v1;\u03c61\u00f0 \u00de;nzp u1; v1;\u03c61\u00f0 \u00de h iT : \u00f09\u00de Tooth profile of the proposed VTT hob is defined by considering Eqs. (7) and (8), simultaneously. 3. Mathematical model for the work gear generated by the proposed modified hob with VTT The proposed longitudinal crowning of the work gear is carried out by applying the diagonal feed hobbing with a modified VTT hob, as shown in Fig. 4. Herein, coordinate systems S1(x1,y1,z1) and S2(x2,y2,z2) are rigidly attached to the hob and work gear, respectively, while coordinate system Sa(xa,ya,za) is rigidly attached to the frame of hobbing machine. On a modern gear hobbing machine, there are three hob movements: traverse movements za(t) along the axis of the work gear, diagonal feed zs(t) along the axis of the hob, and radial feed-in Eo along the center distance between the hob and work gear. The crossed angle \u03b3 between the hob and work gear axes is usually a machine-tool setting. For conventional longitudinal crowning of a hobbed work gear, it is accomplished by applying the radial feed-in Eo to a second order polynomial, such as Eo \u2212 aza 2(t), as shown in Fig. 4. However, such a center distance variation will cause a tooth flank twist on the work gear. Our approach, in contrast, the work gear is hobbed by a modified hob with VTT and kept the radial feed-in as a constant but modifying the hob's tooth thickness as a second order polynomial and setting the diagonal feed in a function of the hobs traverse feed (i.e., the diagonal feed in the hobbing process). The parameters \u03d51 and \u03d52(\u03d51) are the rotating angles of the hob and work gear, respectively, in the work gear generation process. The relationship between the hob's diagonal feed zs(t) and traverse movement za(t) is proposed as follows: zs t\u00f0 \u00de \u00bc cza t\u00f0 \u00de: \u00f010\u00de According to Fig. 4 and Eq. (10), the hob is shifted diagonally in the process of gear hobbing if c \u2260 0. The position vector r1 and unit normal n1 of the modified VTT hob equal the position vector rp and unit normal np, respectively, as defined in Eqs. (8) and (9). Hence, the locus of the modified VTT hob r2 represented in coordinate system S2 can be obtained by where r2 u1; v1;\u03d51;\u03c61; za t\u00f0 \u00de\u00f0 \u00de \u00bc M21 \u03d51; za t\u00f0 \u00de\u00f0 \u00de r1 u1; v1;\u03c61\u00f0 \u00de; \u00f011\u00de M21 \u00bc M2c Mc1; \u00f012\u00de M2c \u00bc cos\u03d52 sin\u03d52 0 cos\u03d52 E0\u2212az2a t\u00f0 \u00de \u2212 sin\u03d52 cos\u03d52 0 \u2212 sin\u03d52 E0\u2212az2a t\u00f0 \u00de 0 0 1 \u2212za t\u00f0 \u00de 0 0 0 1 2 66664 3 77775; \u00f013\u00de and where and Mc1 \u00bc \u2212 cos\u03d51 \u2212 sin\u03d51 0 0 cos\u03b3 sin\u03d51 \u2212 cos\u03b3 cos\u03d51 sin\u03b3 cza t\u00f0 \u00de sin\u03b3 \u2212 sin\u03b3 sin\u03d51 cos\u03d51 sin\u03b3 cos\u03b3 cza t\u00f0 \u00de cos\u03b3 0 0 0 1 2 664 3 775: \u00f014\u00de After some mathematical operations, the locus of the modified VTT hob can be obtained by r2 u1; v1;\u03c61;\u03d51; za t\u00f0 \u00de\u00f0 \u00de \u00bc x2 u1; v1;\u03c61;\u03d51; za t\u00f0 \u00de\u00f0 \u00de; y2 u1; v1;\u03c61;\u03d51; za t\u00f0 \u00de\u00f0 \u00de; z2 u1; v1;\u03c61;\u03d51; za t\u00f0 \u00de\u00f0 \u00de;1\u00bd T ; \u00f015\u00de x2 \u00bc cos\u03d52 Eo\u2212az2a t\u00f0 \u00de\u2212x1 cos\u03d51\u2212y1 sin\u03d51 \u00fe sin\u03d52 cos\u03b3 x1 sin\u03d51\u2212y1 cos\u03d51\u00f0 \u00de \u00fe z1 \u00fe cza t\u00f0 \u00de\u00f0 \u00de sin\u03b3\u00bd ; \u00f016\u00de y2 \u00bc sin\u03d52 az2a t\u00f0 \u00de\u2212Eo \u00fe x1 cos\u03d51 \u00fe y1 sin\u03d51 \u00fe cos\u03d52 cos\u03b3 x1 sin\u03d51\u2212y1 cos\u03d51\u00f0 \u00de \u00fe z1 \u00fe cza t\u00f0 \u00de\u00f0 \u00de sin\u03b3\u00bd ; \u00f017\u00de z2 \u00bc z1 \u00fe cza t\u00f0 \u00de\u00f0 \u00de cos\u03b3\u2212za t\u00f0 \u00de \u00fe y1 cos\u03d51 sin\u03b3\u2212x1 sin\u03d51 sin\u03b3: \u00f018\u00de The rotation angle between the hob and work gear can be expressed as \u03d52 \u00bc N1 N2 \u03d51 \u00fe \u03d520; \u00f019\u00de N1 and N2 are the number of teeth of the hob and gear, respectively", " Therefore, a properly chosen coefficient d is very important to the designer, and it can be simulated by the proposed gear mathematical model and TCA method. sjki circular tooth thickness, j = b, o, p; k = t, n; i = 1, 2, 3. \u03b3 crossed angle \u03b2jki helix angle, j = b, o, p; k = t, n; i = 1, 2, 3. mjki module, j = b, o, p; k = t, n; i = 1, 2, 3. Ni number of teeth, i = 1, 2, 3. Eo operating center distance \u03b1jki pressure angle, j = b, o, p; k = t, n; i = 1, 2, 3. rjki radius of the cylinder, j = b, o, p; k = t, n; i = 1, 2,3. a center distance variation coefficient (refer to Eq. (15) and Fig. 4) b hob normal tooth thickness variation coefficient (refer to Eq. (4) and Fig. 1) c hob diagonal shifting coefficient (refer to Eq. (10) and Fig. 4) d tooth profile modification coefficient (refer to Eq. (1) and Fig. 2) subscripts n measured in the normal section t measured in the transverse section o operating pitch circle p pitch circle 1 hob 2 proposed work gear 3 standard involute gear The authors are grateful to the National Science Council of the R.O.C. for financial support. Part of this work was performed under Contract No. 101-2218-E-035-010. [1] F.L. Litvin, Gear Geometry and Applied Theory, PTR Prentice Hall, Englewood Cliffs, NJ, 1994" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002700_tmech.2020.3015133-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002700_tmech.2020.3015133-Figure1-1.png", "caption": "Fig. 1. Design of the notch continuum manipulator: (a) Prototype of notch continuum manipulator, (b) the structure of guidewire disc and (c) elastic skeleton.", "texts": [ " Downloaded on August 24,2020 at 08:11:28 UTC from IEEE Xplore. Restrictions apply. 1083-4435 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. mm. There is a 2.4 mm channel inside the manipulator which can be used for the vision units and energy equipment. The continuum manipulator is composed of an elastic skeleton and a plurality of guidewire discs, as shown in Fig.1. The continuum manipulator which contains two DOFs is driven by the wires. Each DOF is controlled by a pair of antagonistic wires. One end of the wire is fixed at the distal end of the continuum manipulator, and the other end is transmitted to the proximal end through the thread eyes of the guidewire discs, as shown in Fig.1(a). The wire contacts with the guidewire discs during the movement, and the force generated during the contact force the continuum manipulator to bend. The continuum manipulator can traverse the space points as two pairs of antagonistic wires are driven. The structure of the guidewire disc is shown in Fig.1(b). The outer diameter of the guidewire disc is 6 mm. The inner diameter(2 \u2217 R1) of the rigid unit alignment hole is 3 mm, and the inner diameter(2 \u2217 R0) of the other parts is 4.6 mm. Four thread eyes are drilled evenly on the circumference of the guidewire disc to pass the wires. The top and bottom arcs of the guidewire discs are perpendicular to each other. The height of the guidewire disc is the sum of the top and bottom radii and the height of the rigid unit alignment hole. The length of the bending unit is the sum of the radii of the top and bottom arcs of adjacent guidewire discs", " The role of the elastic skeleton is to ensure that the system realizes continuous posture changes after the driving force of the wire changes. Since the Nitinol alloy has better allowable strain and structural strength, a Nitinol alloy tube with an outer diameter of 3 mm and an inner diameter of 2.4 mm is used as the elastic skeleton. The elliptical notches are cut orthogonally on the elastic skeleton through the Wire Electrical Discharge Machining(WEDM). The elastic skeleton can be divided into rigid units and flexible units as shown in Fig.1(c). After assembly, the rigid unit alignment hole of the guidewire disc is maintained in alignment with the rigid unit of the elastic skeleton. The proposed notch continuum manipulator is composed of multiple flexible units and rigid units. The posture of the continuum manipulator is determined by the deformation of the flexible unit, which is affected by the driving force. Therefore, the kinematic model has multiple mapping relationships, e.g. the mapping from driving space to joint space and the mapping from joint space to Cartesian space, as shown in Fig 2" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002956_tte.2020.2997607-Figure14-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002956_tte.2020.2997607-Figure14-1.png", "caption": "Fig. 14. Prototype components: (a) stator; (b) inner rotor; (c) outer rotor; (d) test bench; (e) drive circuit.", "texts": [ " The control strategies are similar if there is an open-circuit fault or phase-to-phase fault. If the fault is severe, the DRMWM can cut off whole three-phase windings and adopt either pure electric mode or pure turbine mode that is still in healthy state. That is an excellent characteristic for multi-phase structure in coping with faults. V. EXPERIMENTAL VALIDATION A prototype has been manufactured and the corresponding test bench has been constructed to validate the design and analytical model of DRMWMs. The geometrical parameters of DRMWM is based on that in TABLE II. Figure 14 shows the components of the DRMWM, the test bench, the DC power source and the drive circuit. A DC motor is used to simulate the ICE and a servomotor is utilized to simulate the propeller in propulsion system of HEAs. Since there are nine phase windings in the proposed DRMWM, a drive circuit that contains nine IGBT modules are adopted. Besides, encoders are installed on both rotors of the DRMWM to obtain the position information, and the rotating speed of two rotors and required current frequency can be calculated" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003025_bf02919918-Figure14-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003025_bf02919918-Figure14-1.png", "caption": "Fig. 14. Mechanical oscillators.", "texts": [ " 12d. The symbol for the motor was derived from fig. 13a. As a consequence of the view adopted, a system of parallel mechanical impedances corresponds to an electric system with the analogous electric impedances likewise parallel, and a mechanical series system corresponds to an electric series system. This is represented in fig. 6b and c, and fig. 7b and c. M e c h a n i c a l o s c i l l a t o r s . Fig. 14arepresentsan-oscillator formed by a mass m suspended by a spring with compliance c, and fig. 14b-e represent schemes of it. In the pendulum of fig. 14/, the horizontal component of the tension is F = Tx/1, so that the suspension by the chord works as a gravitational compliance c = l IT = l/mg, and hence we arrive likewise at the schemes of fig. 14b-d (the scheme represents the way in which elements are interconnected, not the direction in which they move). M e c h a n i c a l w a v e s y s t e m s . The elastic rod of fig. 15a, vibrating longitudinally, works as a combination of springs and masses (cf. fig. 15b). The scheme of the system is given in fig. 15c, and the analogous electric scheme in fig. 15d. We arrive likewise at these schemes when we consider a transversally vibrating string. w 7. Mechanic-hydraulic systems. P i s t o n-m e c h a n i s m s" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000193_j.cma.2011.04.006-Figure12-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000193_j.cma.2011.04.006-Figure12-1.png", "caption": "Fig. 12. Contact patterns for: (a) case A1b, (b) case A1c, (c) case A1d and (d) functions of transmission errors for previous cases of design.", "texts": [ " Each investigated gear drive, case of design and misalignment condition will be denoted by three letters. As an example, case B2a will correspond to a skew gear drive, with whole crowned surfaces, and aligned conditions (see Tables 2\u20134). Fig. 11 shows the contact pattern and the obtained function of transmission errors for case A1a corresponding to a straight nonmodified and aligned bevel gear drive. The bevel gear drive, under aligned conditions, has no transmission errors, and the contact pattern covers the whole surface of the teeth. Fig. 12 shows the contact patterns for cases A1b (12(a)), A1c (12(b)), and A1d (12(c)). Fig. (12(d)) shows the obtained functions of transmission errors for previous cases of design. The shortest distance between axes DE (misaligned condition b) and the change of shaft angle DR (misaligned condition c) do not cause high transmission errors for the non-modified bevel gears. However, function of transmission errors is very sensitive to the axial displacement of the pinion (misaligned condition d) and the axial displacement of the gear (not shown in this paper), having in these cases lineal functions of transmission errors that are the source of high levels of noise and vibration of the gear drive" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002661_tia.2020.2987897-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002661_tia.2020.2987897-Figure6-1.png", "caption": "Fig. 6. Open-circuit flux distributions of the 12-slot/10-pole HESFPM machine when \u03c8f1 is minimum and maximum.", "texts": [], "surrounding_texts": [ "When the machine is only supplied by three-phase armature currents, i.e., without PMs and field coils excitations, a voltage pulsation exists in the DC winding as the rotor rotates as shown in Fig. 7(a). As shown in Fig. 7(b), the harmonic orders of the induced voltage are 6k, in which k is a positive integer. This part is the armature current induced DC winding voltage, which is due to the interaction between the armature currents and the mutual inductances between AC and DC windings. When the machine operates under on-load condition as shown in Fig. 2(a), the induced voltage is the on-load DC winding induced voltage, which consists of the open-circuit induced voltage and the armature current induced voltage, respectively. Consequently, the on-load DC winding induced voltage harmonic orders are 6k (k=1, 2, 3. . .) as shown in Fig. 2(b) due to the effect of the open-circuit and armature current induced voltages. (a) Waveforms As shown in Fig. 8, the peak to peak values of the on-load DC winding induced voltages vary against the current advance angle and hence the varied induced voltage ratio. It should be emphasized that the DC winding resistive voltage drop is constant as the current advance angle varies. Consequently, the waveforms of the induced voltage and the induced voltage ratio are the same. When the current angle changes, the permeability of the lamination steel varies as well. Consequently, both the open-circuit and armature current induced voltages are affected by the current angle and hence the on-load induced voltage. As shown in Fig. 9, the maximum torque of the machine occurs at around 0o current angle, which indicates negligible reluctance torque for the machine topology." ] }, { "image_filename": "designv10_9_0001584_j.jsv.2016.08.014-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001584_j.jsv.2016.08.014-Figure4-1.png", "caption": "Fig. 4. Leg notation.", "texts": [ " Geometric, structural and inertial parameters are reported in Tables 1 and 2. To obtain the GDSM of the Agile Eye the generalized dynamic stiffness matrices of each leg must be assembled. First, we consider a case in which rigid body rotations are forbidden locking the actuated revolute joints at given angles. This condition implies that the proximal links become cantilevers clamped to the fixed BP. Then, we study the flexible body-flexible body coupling between the proximal and the distal link. Referring to Fig. 4 Eq. (24) is used to write K pi \u00bcK 1v hR2i ;GO2i ;K pi , where R2i refers to the middle revolute joint of the i-th limb, GO2i is derived through Eq. (16) considering a vector dp going from the second node of the proximal to the first adjacent node of the distal link, and finally K pi is the dynamic stiffness matrix of the i-th proximal link. Then the i-th distal link is connected to the MP through the revolute joint R3i, thus K di \u00bcK 1v hR3i ;GO3i ;K di , in which GO3i is built considering the vector dd going from the end-effector node to the second node of the distal link, and K di is the dynamic stiffness matrix of the i-th distal link" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001855_j.matpr.2017.06.291-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001855_j.matpr.2017.06.291-Figure1-1.png", "caption": "Fig. 1 Schematic arrangement of laser cladding test setup [1].", "texts": [ " However, the improvement in the surface hardness of the target material does not promise for any enhancement in erosion wear resistance [1-2]. Laser cladding may be defined as the formation of a surface layer by melting of the coating material and a thin surface layer of the substrate with a scanning laser beam. The main objective of laser cladding is to form a thin interfacial layer of metal or alloy on a given substrate with minimum dilution of the clad layer for improving the surface wear and corrosion [3]. Fig 1 shows schematic view of arrangement of laser cladding test setup. Laser cladding process is categorized as a single-step or a two-step process and known by the method through which the coating material is supplied [4]. Fig. 2 shows the principal of laser cladding process, in single-step process, the material is feeding continuously at the laser generated melt pool, usually in the form of a fine powder. Where as in a two-step process, a thin layer of material is first deposited on the substrate surface, for example, as slurry and subsequently melted by using the laser beam" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001655_j.mechmachtheory.2018.01.012-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001655_j.mechmachtheory.2018.01.012-Figure3-1.png", "caption": "Fig. 3. Drawings to account for formation of enveloping spiroid.", "texts": [ " [22] , the two principal directions of g can be determined as follows: ( g1 ) a = \u2202 ( ra ) a \u2202u \u2223\u2223\u2223 \u2202 ( ra ) a \u2202u \u2223\u2223\u2223 = m a ( \u03b8, \u03b4g ) = sin \u03b4g cos \u03b8 i a + sin \u03b4g sin \u03b8 j a + cos \u03b4g k a , (3) ( g2 ) a = ( n) a \u00d7 ( g1 ) a = na ( \u03b8, \u03b4g ) \u00d7 m a ( \u03b8, \u03b4g ) = \u2212 ga ( \u03b8 ) = sin \u03b8 i a \u2212 cos \u03b8 j a . (4) Accordingly, a right-handed principal frame, \u03c3P { P ; g1 , g2 , n} , can be established at an arbitrary point P on the generating conical surface g . Along the two principal directions of g , its two principal curvatures can be figured out as k 1 = 0 , k 2 = \u2212 1 u tan \u03b4g . (5) 3. Cutting engagement of enveloping spiroid 3.1. Setting of coordinate systems As shown in Fig. 3 , in the process of grinding an enveloping spiroid, a static coordinate system \u03c3o1 { O 1 ; i o1 , j o1 , k o1 } is attached with the roughcast, and the unit vector k o1 is along its axial line. The point O 1 is the middle point of the thread length of the enveloping spiroid and the plane O 1 \u2212 j o1 k o1 is horizontal. A rotating coordinate system \u03c31 { O 1 ; i 1 , j 1 , k 1 } is used to denote the current position of the worm roughcast, whose rotating angle is indicated by the symbol \u03d5. The distance between the points O 1 and O od along the axis j o1 is the operating center distance, a d , during machining the spiroid blank. The straight line \u2212\u2212\u2212\u2212\u2192 O od O d is parallel to the straight generatrix of the pitch cone of the enveloping spiroid so that its tilt angle with respect to the axial line k o1 is the pitch cone angle, \u03b41 , of the enveloping spiroid. During the generating process, the enveloping spiroid blank should have performed screw motion. Therefore, according to the rotation direction depicted in Fig. 3 (b), the blank needs to rotate around the axis k o1 and move to the positive direction of this axis at the same time because it is right-handed. However, in the course of the practical machining, the blank only performs rotary motion so that the grinding wheel has to implement the translational motion toward the negative direction of the axis k o1 so as to guarantee to realize the preceding relative motion effect. At the present position shown by Fig. 3 (b), the length of the straight line section | \u2212\u2212\u2212\u2212\u2192 O od O d | = p\u03d5, in which p is the helix parameter of the enveloping spiroid along the generatrix of its pitch cone. Two translational coordinate systems, \u03c3od { O d ; i od , j od , k od } and \u03c3d { O d ; i d , j d , k d } , are utilized to express the location of the grinding wheel carrier. The angle between the axis k od and the horizontal plane O 1 \u2212 j o1 k o1 is \u03b3 m , which is the lead angle of the enveloping spiroid at the reference point designated" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000806_j.mechmachtheory.2012.08.011-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000806_j.mechmachtheory.2012.08.011-Figure5-1.png", "caption": "Fig. 5. FEM model of the thin-rimmed center inclined web gear with the solid gear used for LTCA.", "texts": [ " 3(a), (b) and (c) are used for the left, the center and the right inclined web gears respectively. Joint circles of the webs with the bosses are fixed as FEM boundary conditions as shown in Fig. 3. Fig. 4 is the FEMmodels used for the deformation and stress analyses of the thin-rimmed straight web gears under the centrifugal load conditions. Fig. 4(a), (b) and (c) are used for the left, the center and the right straight web gears respectively. Also, the joint circles of the webs with the bosses are fixed as the FEM boundary conditions. Fig. 5 is the FEMmodel used for LTCA of the thin-rimmed gears deformed by the centrifugal loads when these deformed gears are engagedwith the solid mating gear shown in Fig. 2(d). The joint circles of thewebs with the bosses of the thin-rimmed gears are also fixed as the FEM boundary conditions in LTCA (used to calculate the deformation influence coefficients with the FEM). For the solid mating gear, boundary nodes on the three surfaces as indicated with \u201cFixed\u201d in Fig. 5 are fixed as the FEM boundary conditions. Though only the FEMmodel of the thin-rimmed center inclinedweb gear is given in Fig. 5, the FEMmodels for the other thin-rimmed gears can bemade automaticallywith the developed softwarewhen gearing parameters, engagement position parameters, structural dimension parameters and web angle are given. (a) Left straight web & 0min-1 (b) Left inclined web & 0min-1 Deformation and stress analyses are conducted for all the three types of the thin-rimmed inclined web gears shown in Fig. 2(a), (b) and (c) when the centrifugal loads are applied. In order to understand the centrifugal deformation of these gears, the calculated centrifugal deformation of all the gears is increased by 2000 times and images of the gears deformed by the centrifugal loads are illustrated in Fig", " 6(a), (b) and (c), the teeth of the inclinedweb gears have only a small inclination angle while the teeth of the straight web gear have a large inclination angle as shown in Fig. 6(d). It is very clear that a small inclination of the contact teeth shall have a little effect on tooth contact pattern and contact stress distributionwhile a large inclination of the contact teeth shall havemuch effect on the tooth contact pattern and contact stress distribution. This is confirmed in Section 6 by LTCA. Tooth radial deformation (in the direction of Y axis as shown in Fig. 5) of the inclined web gears under the centrifugal loads is calculatedwhen gear speed is 5000, 10,000, 20,000 and 40,000 min\u22121 respectively. Calculation results are given in Fig. 7. In Fig. 7, the horizontal axes are tooth longitudinal dimension and the vertical axes are the radial deformation of the tooth tip at themedian plane of the tooth. Fig. 7(a), (b) and (c) are the results of the left, the center and the right web gears respectively. Fig. 7(d) is a comparison among the three types of the gears at 40,000 min\u22121" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001520_j.jsv.2014.09.004-Figure14-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001520_j.jsv.2014.09.004-Figure14-1.png", "caption": "Fig. 14. Schematic diagram of the experimental set-up.", "texts": [ " Thus the peak at 4fe is small in the response. In summary, we can see that not only the spectra of Gi\u00f0\u03c9\u00de's but also the Ui\u00f0\u03c9\u00de's changes the spectrum of U\u00f0\u03c9\u00de. This illustrates the importance of the accuracy of Ui\u00f0\u03c9\u00de's, which is governed by the modal properties of the structure. This issue is revisited in the next subsection. To further examine the validity of the proposed method, the computed results are compared with measured data. The schematic diagram of the experimental set-up used to measure the acceleration is shown in Fig. 14. The test condition is briefly stated as follows. The rotor shaft of the motor is attached to a dynamometer to apply a mechanical load of 50 Nm. The stator is attached to a base plate and fixed to the ground. A triaxial accelerometer is attached to the rim of the stator core, which corresponds to the evaluation point shown in Fig. 5. During the test, the dynamometer was controlled such that the rotational speed of the rotor becomes 1500 rev/min, and the current flowing in the motor windings was measured by the current probes", " In summary, many of the significant peaks in the frequency spectra of the measured acceleration are captured well, in terms of the frequencies. However, especially for the high frequency ranges, the magnitude of the computed results does not agree well with the measured data. These discrepancies will be further discussed later in Section 4. In this section, a case study for the reanalyses required for the IPM motor at various operating conditions is provided. The same IPM motor was used as an example electric machine. Using the experimental set-up shown in Fig. 14, the acceleration of the evaluation point on the stator core was measured during a run-up test of the motor. The measurements of the acceleration started when the rotational speed reached approximately N\u00bc500 rev/min and ended when it reached approximately N\u00bc2800 rev/min. The load torque for the motor was T\u00bc50 Nm. The frequency\u2013speed diagram of the measured acceleration is shown in Fig. 16. As in the previous results, the frequency\u2013speed diagram is split into significant frequency bands. In Fig. 16(a), there are several significant peak lines originating from the origin, and designated as (A), (B), (C), (D), (E), and (F) in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002994_j.mechmachtheory.2020.104126-Figure27-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002994_j.mechmachtheory.2020.104126-Figure27-1.png", "caption": "Fig. 27. Optimal mechanism ( E = 0.0142; E p = 0.0067 and E s = 0.0075).", "texts": [], "surrounding_texts": [ "This study has proposed an optimal dimensional synthesis procedure for the general case of the four-bar linkage, which perfects the classical formulation of the gradient method. On the one hand, the error function is reformulated to include as additional characteristic the slope of the tangent to the curve at each prescribed point. On the other hand, a series of indicators has been established which enable the adequate identification of branches and circuits in each case. Moreover, use of these indicators makes it possible to define the actuation mode in each case, without recourse to penalty functions. The great majority of published studies limit the mechanism design to four-bar linkages with crank input, but in this study, thanks to the complete characterization of circuits and branches, designs with rocker input that produce no defect can be obtained. On occasion, as demonstrated in Example 3 , the optimal mechanism with rocker input can attain a smaller error than if only crank inputs were allowed. The reformulation of the error function, by adding the slope of the tangent to the curve at each prescribed point, not only enables a closer adjustment to the desired curve, but also achieves this with a smaller number of prescribed characteristics, lightening the minimization effort and reducing computational cost. It should be noted that according to the usual classical approach, each additional point implies the addition of two more characteristics (the two position coordinates), but if the tangent is included as a characteristic for an existing point, this amounts to adding only one characteristic. The proposed procedure makes it possible to obtain all the partial derivatives analytically, including those associated with the passive variables of the mechanism, by using the functional dependency tree between the set of parameters and variables that appear in the synthesis problem. This methodology is valid both for path generation and for the case of rigid body motion. Its effectiveness and the good results that it obtains have been demonstrated with various illustrative examples. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper." ] }, { "image_filename": "designv10_9_0003015_ffe.13406-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003015_ffe.13406-Figure2-1.png", "caption": "FIGURE 2 Finite element (FE) harmonic analysis of AlSi7Mg specimens: (A) displacement results and (B) stress results [Colour figure can be viewed at wileyonlinelibrary.com]", "texts": [ " The eddyNCT 3010 used to measure displacement is positioned under the specimen to determine the strain amplitudes on the basis of \u0394\u03b5 = \u0394l/l formulation.31 Finite element (FE) modal and harmonic analysis are performed in mapping out natural frequencies, displacement and stress responses of test specimens in resonance conditions. The FE harmonic analysis is carried out to determine the stress and displacement distribution of across the entire length of the stack including test specimens as shown in Figure 2. The FE displacement responses are correlated with displacement measurements using the eddy current displacement sensor. The measured displacements and calculated strain/stress amplitudes on the basis of Hook's law showed good agreement with the FE analysis results. The present authors30,32 provided design and development details of the ultrasonic fatigue testing system, for example, a power supply/signal generator, piezoelectric converter, horn, booster, test specimen, data acquisition and control systems", "36 Table 4 indicates the average and peak roughness values for test materials of AlSi7Mg and AlSi10Mg measured by a Mitutoyo SJ-301 surface roughness measuring instrument. Dimensional specifications of AlSi7Mg and AlSi10Mg specimens are shown in Figures 3 and 4, respectively. AlSi7Mg and AlSi10Mg test specimens were machined according to tolerance specifications shown in Figures 3 and 4 respectively. A dog bone style dumbbell specimen was used with a continuous reduced cross-sectional area. Both ends of the test specimen undergo maximum displacement whereas the centre location of the specimen experiences zero displacement as shown in Figure 2A. This ensures that the gauge length of the specimen will experience maximum stress guaranteeing that failure only occurs along this length. Because the material is constantly being stressed well below its yield strength in the elastic domain, it is considered that the material deformation has a linear elastic response on the basis of Hooke's law.31 The steel stud is used to attach the aluminium specimen to the horn. If the threaded hole is tapped in one end of the test specimen and the specimen is attached to the horn using the attachment stud made of the same material of the test specimen, symmetrical specimens are ideally used", " However, a mass adjustment in the form of asymmetrical specimen was made to the dumbbells of the specimen in order to maintain the resonating characteristics of the acoustic stack and ensure that the maximum strain/stress occurs at the centre of the gauge length. The top dumbbell is shortened to account for the different mass density of the steel stud when compared with the aluminium specimen. The FE harmonic analysis is performed to verify displacement and stress behaviours of the stack and asymmetrical specimen under harmonic loading conditions. Displacement and stress distribution along the asymmetrical dumbbell specimen are shown in Figure 2A,B, respectively. FE results show that test specimens experience maximum stress in the gauge length with the implementation of the asymmetrical specimens as illustrated in Figure 2B. Ultrasonic fatigue tests were conducted using dog bone specimens to characterize fatigue performance of additively manufactured AlSi10Mg and AlSi7Mg alloys in HCF and VHCF regimes. The AlSi7Mg and AlSi10Mg specimens were tested as-machined conditions by being subjected to fully reversed constant amplitude load cycles. All tests were run until failure, and no run out condition was established for the tested specimens. Figure 5 shows test specimens failed close to the midgauge section with the exception of one specimen. Failure locations of the asymmetrical specimens also verify that specimens experience the maximum stress distribution in the gauge length as shown in Figure 2. Fatigue data in Figures 6\u20138 indicates a clear trend for the increase of fatigue life as stress decreases with no data points which would suggest the presence of a fatigue limit beyond 109 cycles. Test results show that the AlSi10Mg showing better fatigue response to be subjected to higher stresses than AlSi7Mg under similar range of life cycles. The fatigue life data collected for AlSi10Mg was plotted and compared with published fatigue data* in Figures 6 and 7 to assess the correlations between the data acquired and the previously published data" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002107_j.measurement.2018.07.031-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002107_j.measurement.2018.07.031-Figure5-1.png", "caption": "Fig. 5. Waviness model of outer raceway.", "texts": [ " Hence the amplitude of the inner race surface waviness is described as: = + \u03c0 \u03bb A A A sin(2 L )in 0 m (16) The arc length (L) of inner race wave at the contact angle is given by, = r\u03c6L i in (17) The wavelength (\u03bb) of inner race is the ratio of length of the inner race circumference to the number of waves on circumference, which is termed as: =\u03bb \u03c0r2 Nw (18) Amplitude of wave on inner race surface waviness for ith ball is given by following relation. = + \u2217\u03c6A A A sin(N )i in i in 0 m w (19) Contact angle \u03c6i in for inner raceway waviness for ith rolling element is given as follows. = \u2217 \u2212 + \u2212 \u2217\u03c6 \u03c0 i \u03c9 \u03c9 t2 ( 1) N ( )i in b c s (20) The outer race surface waviness remains stationary, while rolling elements move at the cage rotational speed. Fig. 5 represents the waviness on outer race surface. The ith ball makes contact angle, \u2018\u03d5i out\u2019 with outer race wavy surface with respect to x axis is calculated through Eq. (25), which is also mentioned in Fig. 5. The outer race has circumference sinusoidal wavy surface, and the amplitude of outer race waviness is given by; = + sin \u03c0 \u03bb A A A (2 L )out 0 m (21) The arc length (L) of the outer race wave at the contact angle is given as follow =L R\u03c6i out (22) The wavelength of outer race is ratio of length of the outer race circumference to the number of waves on circumference which are given by: =\u03bb \u03c0R2 Nw (23) Amplitude of wave on outer race surface waviness is given by following relation. = + \u2217A A \u03c6A sin(N )i out i out 0 m w (24) Contact angle \u03c6i out for outer raceway waviness for ith rolling element is given as follows" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003535_j.mechmachtheory.2021.104436-Figure8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003535_j.mechmachtheory.2021.104436-Figure8-1.png", "caption": "Fig. 8. The construction principle of chain [PRR]R and its equivalent chain.", "texts": [ " In the cooperation of the SRS-link and the RCM, the motion of the SRS-link is described as the rotation about the axis O1B (line B1B2), and the axis O1B is the moving axis that rotates about the plane normal O1A in the v-plane. Obviously, the movement effect of this cooperation is similar to the U-joint, so it is defined as the \u2019UR and Up-joint\u2019. The link a is set as the driving link of this chain. The vector a is always perpendicular to O1O2. Obviously, the motion axes in Fig. 7(a), (b) and (c) have exactly the same relative positional relationship, and their v-planes are perpendicular to the base platforms. The motion axes in Fig. 8(a), (b) and (c) have exactly the same relative positional relationship, and their v-planes are parallel to the base platform. In detail, all axes O1A in the 2 figures always pass through O1 and are perpendicular to vplane, all axis O1B always passes through O1 and rotates around axis O1A in v-plane. The axis O2C is parallel to axis O1B, and both of them are perpendicular to O1O2. All O1O2 have a fixed length l. Based on the screw theory, it can be analyzed that chains [RR]R, [TRR]R and URR have the same motion and constraint characteristics, and chains [PRR]R, [TPR]R and UPR have the same motion and constraint characteristics" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000979_s00034-012-9402-5-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000979_s00034-012-9402-5-Figure1-1.png", "caption": "Fig. 1 The configuration of the X-33 hypersonic unmanned aerial vehicle", "texts": [ " (3) The rotational matrix R(\u03b3 ) \u2208 {R1(\u03b3 ), R2(\u03b3 )} is given by R1(\u03b3 ) = \u23a1 \u23a3 1 tan \u03b8 sin\u03d5b tan \u03b8 cos\u03d5b 0 cos\u03d5b \u2212 sin\u03d5b 0 sin\u03d5b/ cos \u03b8 cos\u03d5b/ cos \u03b8 \u23a4 \u23a6 , \u03b3 = \u23a1 \u23a3 \u03d5b \u03b8 \u03c8 \u23a4 \u23a6 ; R2(\u03b3 ) = \u23a1 \u23a3 cos\u03b1 0 sin\u03b1 0 1 0 sin\u03b1 0 \u2212 cos\u03b1 \u23a4 \u23a6 , \u03b3 = \u23a1 \u23a3 \u03d5 \u03b1 \u03b2 \u23a4 \u23a6 , where R1(\u03b3 ) is used in the ascent phase and R2(\u03b3 ) is used in the reentry phase. \u03b3 represents the attitude angle of UAV. \u03d5b , \u03b8 , \u03c8 are roll angle, pitch angle and yaw angle, respectively; \u03d5, \u03b1 and \u03b2 are bank angle, angle of attack and sideslip angle, respectively. It is well known that the command torque u is related to the deflection command vector \u03b4, namely, u = B\u03b4, where B \u2208 R 3\u00d7m, m is the number of the control-surface deflection variables. In this paper, we choose the X-33 hypersonic unmanned aerial vehicle as the studied plant. Figure 1 shows the configuration of the X-33 hypersonic unmanned aerial vehicle. It has four sets of control surfaces: rudders, body flaps, inboard and outboard elevons, with left and right side for each set. Each of the control surfaces can independently be actuated with one actuator for each surface. The control-surface deflection variables, collectively known as the effector vector, are given by \u03b4 = [\u03b4rei, \u03b4lei, \u03b4rft, \u03b4lft, \u03b4rvr, \u03b4lvr, \u03b4reo, \u03b4leo]T , where \u03b4rei and \u03b4lei are the right and left inboard elevons, \u03b4rft and \u03b4lft are the right and left body flaps, \u03b4rvr and \u03b4lvr are the right and left rudders, \u03b4reo and \u03b4leo are the right and left outboard elevons" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002277_978-3-319-27131-6-Figure5.17-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002277_978-3-319-27131-6-Figure5.17-1.png", "caption": "Fig. 5.17 Roughness Rpk, Rk, and Rvk and material ratios Mr1 and Mr2", "texts": [ " The cumulative distribution function P(c) of the amplitude density function p(c) of the surface roughness height is in fact the material ratio at the dimensionless surface height c (s. Appendix A): 102 5 Tribology of Rolling Bearings P c\u00f0 \u00de \u00bc \u00f01 c p c\u00f0 \u00dedc Rmr c\u00f0 \u00de \u00f05:26\u00de Thus, Rmr (cmax)\u00bcP(cmax) 0% at the highest peak of the surface height. Rmr (0)\u00bcP(0) 50% at the mean line (c\u00bc 0). Rmr (cmin)\u00bcP(cmin) 100% at the lowest valley of the surface height. \u2013 Roughness Rpk, Rk, and Rvk (DIN EN ISO 13565-1 and -2) Rpk is the reduced peak height in the Abbott curve in Fig. 5.17 that indicates the peak roughness of the surface; Rk is the core roughness depth indicating the plateau shape of the roughness surface; Rvk is the reduced valley height of the surface indicating the oil reservoir in the roughness surface. The material ratios Mr1 andMr2 are the smallest and largest material ratios at Rpk and Rvk, respectively. Both material ratios determine the shape of the Abbott curve that indicates the important tribological parameter besides the mean roughness Ra and mean roughness depth Rz. In the following section, the roughness Rpk, Rk, and Rvk and the material ratios Mr1 andMr2 are determined in the Abbott curve in Figs. 5.15 and 5.17. At first, we create the secant ABwith Rmr (A) of 40% in Fig. 5.15. Then, we rotate the secant AB about point A until it is tangential to the left half branch of the Abbott curve at the point A. The prolonged secant, called the straight line P1AP2, cuts the ordinates with Rmr\u00bc 0% and 100% at P1 and P2, respectively, as plotted in Fig. 5.17. The corresponding surface heights z1 and z2 at P1 and P2 intersect the Abbott curve at Q1 and Q2, respectively. Therefore, the smallest and largest material ratiosMr1 and Mr2 are found at Q1 and Q2 (s. Fig. 5.17). The area Ap is the sum of all peak surfaces Ai above the cutting surface height z1. In the Abbott curve, the triangle P1Q1R1 is constructed so that its area equals Ap. The altitude P1R1 is defined by the reduced peak height Rpk. Similarly, the reduced valley height Rvk is equal to P2R2 that is derived from the triangle P2Q2R2 whose area equals Av of the total groove area below the cutting surface height z2. Finally, the core roughness depth Rk is the surface roughness height of P1P2, as shown in Fig. 5.17. The reduced peak and valley heights are calculated as Rpk \u00bc 2Ap lnMr1 100% \u00f05:27\u00de Rvk \u00bc 2Av ln 100 Mr2\u00f0 \u00de 100% \u00f05:28\u00de Generally, the core roughness depth Rk (<~1\u20132 \u03bcm) should be small in the bearings to increase the bearing load capability because the bearing surface has less plateau shape. Note that the smaller the reduced peak height Rpk (<~0.5\u20131 \u03bcm) is, the better 5.7 Surface Texture Parameters 103 the surface quality becomes. On the contrary, the reduced valley height Rvk (<~1\u20132 \u03bcm) should be larger than Rpk to maintain the reserved lubricating oil in the valley grooves" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003252_tia.2020.3040142-Figure14-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003252_tia.2020.3040142-Figure14-1.png", "caption": "Fig. 14. Flux lines distribution of optimal case 1. (a) Nonlinear HMM. (b) FEA.", "texts": [], "surrounding_texts": [ "For a specific application scenario, the gear ratio, stack length, air-gap length, and outer diameter of a CMG is fixed, and the other geometrical parameters can be optimized. Besides, the material of PMs and silicon steel are settled before optimization, and they are selected as N35H and 50JN270, respectively. The eddy current loss of PMs and iron loss of silicon steel within CMGs is small compared to the power it transmits when it works at rated condition. Additionally, the efficiency of CMGs can be maintained at a high level if the silicon steel within CMGs are not highly saturated, and the output torque of CMGs will decrease if its silicon steel part is highly saturated. Therefore, individuals with low efficiency can be tossed out automatically by optimization algorithm as long as the output torque is set as an optimization objective. Besides, the torque ripples of CMGs are very low if the pole-pair combinations of CMGs are well selected [17]. This can also be observed in Fig. 9, the torque ripple of CMG1 is about 8%, while the torque ripple of CMG2 is below 1%, which is almost ignorable. Thus, the efficiency and torque ripple are not set as the optimization objectives. The weaknesses of CMGs are its low torsional stiffness and high manufacture cost compared to mechanical gearboxes [29]. The torsional stiffness is directly determined by the peak transmitted torque of CMGs, which is represented by Tp. The high cost of CMGs is caused by the usage of PMs since the price of NdFeB is almost one hundred times of that of steel. Thus, the torque versus PM volume ratio should be maximized, which is represented by Tp/VPM. Additionally, the rotational inertia of CMGs is an important index, since a smaller rotational inertia means a better dynamic response characteristic. Since the lowspeed rotor is connected to the output shaft, its rotational inertia J is set as an optimization objective, which can be expressed as J = 1 4 \u03c1La [ \u03b21 ( R4 mid,1 \u2212R4 4 ) + \u03b22 ( R4 mid,2 \u2212R4 mid,1 ) +\u03b23 ( R4 5 \u2212R4 mid,2 )] (38) where \u03c1 is the density of the silicon steel. Furthermore, we should avoid the irreversible demagnetization of PMs on the CMGs during rated operation. Since the rated operating temperature of gearboxes varies from scenarios to scenarios, we choose the gearbox in wind turbine for instance, where the rated operating temperature is about 60 to 70 \u00b0C [30]. In this article, Trated is set as 60 \u00b0C. As can be observed in Fig. 11, the irreversible demagnetization occurs when the magnetic flux density within the PMs drops below the knee point [31], and the knee point decreases with the increase of temperature. Hence, the absolute magnetic flux density on the outer surface of the PMs on the low-speed rotor and high-speed rotor should be above the magnetic flux density on the knee point at rated operating The individual number in one generation is set as 20; the maximum number of generations is set as 100. Besides, a CMG with 4 pole-pair PMs on the high-speed rotor and 11 pole-pair PMs on the stator is selected for the optimization study, and the value range of design variables are given in Table III. The airgap, the inner radius, the outer radius, and the axial length of the studied CMG are set as constants during optimization, whose values are 0.5 mm, 30 mm, 100 mm, and 60 mm, respectively. Additionally, the remanence and knee point magnetic flux density of N35H at rated operating temperature are 1.15 T and 0.22 T, respectively." ] }, { "image_filename": "designv10_9_0000424_s10010-012-0151-1-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000424_s10010-012-0151-1-Figure2-1.png", "caption": "Fig. 2 Measurement arrangement on a single-stage planetary gearbox", "texts": [ " On the other hand, it has been observed that different epicyclic gearboxes can produce vibrations with different spectral structures. However, it will be shown in Sect. 4 that it is still possible to speak of a spectral pattern, although not unique as in the case of fixed-shaft gearboxes. The analysis provided in Sect. 4 makes use of a vibration model which describes the vibrations generated on a single-stage planetary gearbox, when measured with a sensor mounted on the outer part of the ring\u2014or annulus\u2014gear, as shown in Fig. 2. Now, the development of the model is presented. It is important to notice that the final expression of the model presented in this work does not essentially differ from the model originally proposed by McFadden et al. [3]. Nevertheless, the complete development of the model is presented here for two reasons: (i) we believe the interpretation is more illustrative than the one provided by McFadden et al., and (ii) by following the development, a comprehensive overview of the vibration situation in planetary gearboxes is achieved", " The phase difference \u03b3ri between the vibration generated in i-th planet/ring meshing process vr i (t) and the vibration generated on the meshing of the first planet gear with the ring gear vr 1(t), depends on the relative angular position of both planets around the sun gear. The planets can be assembled only at angular positions \u03c8i that are integer multiples of \u03c8 = 2\u03c0/(ZS +ZR) [4]. Therefore, \u03b3ri is specific for each planetary gearbox. Considering that the angular pitch of the ring gear is given by \u2220R = 2\u03c0/ZR , the phase difference \u03b3ri between vr i (t) and vr 1(t) can be calculated as follows \u03b3ri = \u03c8i \u2220R = \u03c8iZR 2\u03c0 . (1) The term \u03c8i in Eq. (1) is the relative angle between the position of the i-th planet gear and the first planet gear (\u03c81 = 0\u25e6), as illustrated in Fig. 2. Equation (1) can also be understood as the number of angular tooth periods between the relative angular position of the i-th planet and planet 1. Thus, the vibrations generated on the meshing process of the i-th planet and the ring gear vr i (t) can be expressed as the time-shifted version of the vibration generated on the meshing process between the first planet and the ring gear vr 1(t) by taking their relative phase difference (Eq. (1)) into account vr i (t) = vr 1 ( t \u2212 \u03b3riT p g ) , (2) where T p g = 1/f p g (i", " Consequently, the sensor measures the sum of all amplitude-modulated vibrations, which can be expressed as follows xr(t) = N\u2211 i=1 xr i (t) = N\u2211 i=1 ar i (t)v r i (t) = N\u2211 i=1 ar 1 ( t \u2212 \u03c8iTC 2\u03c0 ) vr 1 ( t \u2212 \u03b3riT p g ) . (5) Equation (5) is illustrated in Fig. 6. Please note that this expression considers that the reference planet gear (i.e. planet 1) is located at the sensor position at the measurement start (t = 0), which is also clear from the plot of ar 1(t) in Fig. 4. In practice, the position of the planets is not known at the measurement start. This moment is represented in Fig. 2, where \u03b81 is not known. Note that since the relative angle \u03c8i is a constant value, the position of the i-th planet is determined by the position of planet 1. To account for the unknown position of planet 1, a time shift t1 is introduced to the amplitude modulation functions of Eq. (5). Note that t1 = \u03b81 2\u03c0fC ; however, since \u03b81 is\u2014in general\u2014not known, the notation t1 is kept and Eq. (5) yields xr(t) = N\u2211 i=1 ar 1 ( t \u2212 t1 \u2212 \u03c8iTC 2\u03c0 ) vr 1 ( t \u2212 \u03b3riT p g ) . (6) The expression of Eq. (6) describes the vibrations generated in a planetary gearbox as measured by a sensor mounted on the outer part of the ring gear" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000931_9781118703274.ch2-Figure2.42-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000931_9781118703274.ch2-Figure2.42-1.png", "caption": "Figure 2.42 Moments arising from the acceleration of air masses and from air damping during blade positioning", "texts": [ " Frictional moments are also dependent on the speed of rotation. As an approximation, when starting a movement the load-dependent component can usually be doubled. The sum of frictional moments over all bearings active during pitch variation yields the total frictional moment MFrict = n\u2211 k=1 MRLk, (2.65) where n is the number of bearings involved. When the pitch of a rotating blade is altered, further moments act on the system, originating from the acceleration of air masses around the profile and from air damping (see Figure 2.42). A description of these quantities, which hamper movement, is only possible under predefined conditions. For the limited case of \u2022 blades that are stiff under bending and twisting, \u2022 with an axis of rotation at a quarter of the chord (tB\u22154), \u2022 when the blade is turned about the pitch variation axis only (i.e. no blade deflection), these moments can be approximated per span-width element by the relation [2.16] dML dr = \ud835\udf0b\ud835\udf0cd4 { \u2212 ( 1 8 + a2 ) \u23df\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23df\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23df inertia of accelerating air masses \ud835\udefd + [ a \u2212 1 2 + 2 ( 1 4 \u2212 a2 ) C (k) ] \ud835\udc63r d " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003580_j.mechmachtheory.2020.104238-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003580_j.mechmachtheory.2020.104238-Figure2-1.png", "caption": "Fig. 2. Diagram of the tooth tip chipping part for the tooth.", "texts": [ " k b2 , k s 2 and k a 2 correspond to driven gear. For the double teeth mesh region, the total mesh stiffness can be described as Eq. (10) [19] : k t = 2 \u2211 i =1 1 1 k h,i + 1 k b1 ,i + 1 k s 1 ,i + 1 k a 1 ,i + 1 k f 1 ,i + 1 k b2 ,i + 1 k s 2 ,i + 1 k a 2 ,i + 1 k f 2 ,i (10) where i = 1 for the first pair of gear mesh and i = 2 for the second pair of gear mesh. Due to the stress concentration, when the tooth tip chipping fault occurs, part of the material near the tooth tip breaks away, as shown in Fig. 2 (a). The intersection line between the fracture surface and the tooth profile is the curve AC in the figure. After the gear is machined, the tooth top surface is a cylindrical surface, and the intersection line between the fracture surface and the tooth top surface is also a curve, as shown the curve BC in Fig. 2 (a). However, when the potential energy method is applied to calculate mesh stiffness, the part above the cross section of the tooth tip has no influence on the calculation of the mesh stiffness, so the cylindrical surface of the tooth tip is approximated to the tooth tip plane, as shown in plane D 1 D 2 D 3 D 4 in the Fig. 2 (a). The intersection line between the fracture surface and the tooth end face is a straight line, as shown AB in Fig. 2 (a). Fig. 2 (b) shows a cross section diagram of a fault location. When the fault occurs, it will affect the position of the neutral surface of the gear tooth, thus affecting the moment of inertia on the cross section. In the Cartesian coordinate system UOV in Fig. 1 , the involute Eq. can be described by Eq. (11) as follows: { u = R b [ sin ( \u03b8x + \u03b1x ) \u2212 ( \u03b8x + \u03b1x ) cos ( \u03b8x + \u03b1x ) ] v = R b [ cos ( \u03b8x + \u03b1x ) + ( \u03b8x + \u03b1x ) sin ( \u03b8x + \u03b1x ) ] (11) Converting it into the XOY coordinate system, the Eq. of the involute L 1 in Fig. 2 (a) becomes: { x = R b { [ sin ( tan ( \u03b1x ) ) \u2212 tan ( \u03b1x ) cos ( tan ( \u03b1x ) ) ] cos ( \u03b12 ) \u2212 [ cos ( tan ( \u03b1x ) ) + tan ( \u03b1x ) sin ( tan ( \u03b1x ) ) ] sin ( \u03b12 ) } y = R b { [ sin ( tan ( \u03b1x ) ) \u2212 tan ( \u03b1x ) cos ( tan ( \u03b1x ) ) ] sin ( \u03b12 ) + [ cos ( tan ( \u03b1x ) ) + tan ( \u03b1x ) sin ( tan ( \u03b1x ) ) ] cos ( \u03b12 ) } (12) herein \u03b8x is the evolving angle of the involute. \u03b1x is the pressure angle at arbitrary point on the involute. The three-dimensional Cartesian coordinate system OXYZ can be established by configuring the Z -axis to perpendicular to the plane XOY in Fig. 1 and point to the outside. Supposing that the point A in Fig. 2 is located on the tooth profile curve whose coordinates are ( x a , y a , 0 ), point B is located on the top line of gear tooth end face (equivalent to to a line) whose coordinates are ( x b , y b , 0 ) and point C is on the top edge of the tooth profile whose coordinates are ( x c , y c , z c ), the Eq. 2 of fracture plane can be determined by Eq. (13) : z = [ ( x \u2212 x a ) ( y a \u2212 y b ) \u2212 ( x a \u2212 x b ) ( y \u2212 y a ) ] ( x a \u2212 x ) ( y a \u2212 y c ) + ( y a \u2212 y ) ( x c \u2212 x a ) z c (13) b b Combining Eq. (12) and (13) , the intersection curve L 2 of fracture surface and cylindrical surface of tooth profile can be obtained, as shown in Fig. 2 (a). The Eq. of line L 3 in Fig. 2 (a) can be expressed as Eq. (14) : x = x a \u2212 x b y a \u2212 y b ( y \u2212 y a ) + x a (14) The coordinates of point A can be defined by pressure angle, as expressed in Eqs. (15) - (17) as follows: x a = R b cos ( \u03b1a ) sin ( \u03b2a ) (15) y a = R b cos ( \u03b1a ) cos ( \u03b2a ) (16) \u03b2a = \u03c0 2 Z \u2212 [ ( tan ( \u03b1a ) \u2212 \u03b1a ) \u2212 ( tan ( \u03b10 ) \u2212 \u03b10 ) ] (17) wherein \u03b1a is the pressure angle at point A which is determined by the position of the fracture plane on the tooth profile curve. For point B , x b is determined by the position of the fracture plane on the tooth tip line of the tooth end face", " (18) and (19) : y b = m 2 ( Z + 2 h \u2217 a ) cos ( \u03b2t ) (18) \u03b2t = \u03c0 2 Z \u2212 [ ( tan ( \u03b1t ) \u2212 \u03b1t ) \u2212 ( tan ( \u03b10 ) \u2212 \u03b10 ) ] (19) where h \u2217a is the addendum coefficient, and \u03b1t is the addendum circle pressure angle. For point C , z c is determined by the position of the fracture surface on the top edge of the tooth profile, and x c , y c can be expressed by Eqs. (20) and (21) : x c = R b cos ( \u03b1t ) sin ( \u03b2t ) (20) y c = R b cos ( \u03b1t ) cos ( \u03b2t ) (21) When the tooth tip chipping fault occurs, the position of the neutral axis and the centroid of the cross section at the fault location will change, as shown in Fig. 2 (b). The inertia moment of the cross section can be deduced using Eqs. (22) - (26) as follows: d 1 = | y x L 1 | \u2212 | y x L 3 | (22) d 2 = | z x L 2 | (23) A \u2032 x = 2 h x L \u2212 1 2 d 1 d 2 (24) d y = 1 2 d 1 d 2 ( h x \u2212 1 3 d 1 ) 2 h x L \u2212 1 2 d 1 d 2 (25) I \u2032 x = I x \u2212 [ d 2 d 3 1 36 + 1 2 d 1 d 2 ( h x \u2212 1 3 d 1 )2 ] \u2212 [ 1 2 d 1 d 2 ( h x \u2212 1 3 d 1 )]2 2 h x L \u2212 1 2 d 1 d 2 (26) herein the x in the subscript represents arbitrary point on the involute. y x L 1 is the y-coordinate of the intersection of cross section and curve L 1 , y x L 3 is the y-coordinate where the cross section intersects the straight line L 3 ", " Assume that there are k teeth participating in mesh at the same time, the total mesh stiffness can be expressed as: k t = k \u2211 i =1 1 1 k h,i + 1 k b1 ,i + 1 k s 1 ,i + 1 k a 1 ,i + 1 k b2 ,i + 1 k s 2 ,i + 1 k a 2 ,i + 1 k f 2 ,i (54) In Section 2 , the mesh stiffness of gears is estimated by means of the potential energy method. In this section, it is verified by finite element modelling and compared with the method in literatures. The parameters of gears used in this study are shown in Table 1 . The failure point positions of the tip chipping fault for external gear are illustrated by referring to Fig. 2: A is described by its pressure angle \u03b1A on the involute profile, B is determined by the distance l B from B to the central plane of the tooth, and C is defined by the distance l C from C to the end face of the tooth. For the internal gear, the definition of point A, B and C is the same as the external gear. In the finite element model of the fault gears, \u03b1A is assigned the value of 20 \u25e6, l B is selected as 0mm for external gear and -1mm for internal gear and l C is equal to 15mm. The finite element model of gears is shown in Fig", " The angular displacement corresponding to a mesh cycle is 18.95 \u00b0, where the double-tooth mesh area account for 10.30 \u00b0 and the single-tooth mesh area 8.65 \u00b0. And the angular displacement corresponding to the entire tooth surface is 29.25 \u00b0. Due to stress concentration or grinding crack propagation and other reasons, tooth tip chipping fault often occurs in gear meshing [45] . Since there are three variables to determine the fault severity, namely the positions of point A, point B and point C in Fig. 2 , we will study the influence of them on the mesh stiffness respectively. The schematic diagram of the tooth tip chipping fault is shown in the Fig. 9 , and the fault location is listed in Table 2 . Herein, A is represented by its pressure angle \u03b1A , B is determined by the distance l B from B to the central plane of the tooth, and C is defined by the distance l C from C to the end face of the tooth. In order to analyze the effect of \u03b1A on mesh stiffness, the value of l B and l C should be constant", " 10 , as the fault severity aggravation, the attenuation of the mesh stiffness will also increase. And for a certain tooth tip chipping fault, when the meshing position gradually approaches the tooth tip with the rotation of the gears, the mesh stiffness reduction is also increasing. Compared with a larger value, if \u03b1A is smaller, it means the fault area enters mesh sooner, and the mesh stiffness attenuation is greater at the same angular displacement. This is because A \u2032 x and I \u2032 x of the cross section shown in Fig. 2 (b) will gradually decrease as the mesh position continues to approach the tooth tip which results in an increase in mesh stiffness reduction. The attenuation ratio of mesh stiffness is calculated by Eq. (57) and its variation with the angular displacement is shown in Fig. 11 . p = k th \u2212 k t f k \u00d7 100% (57) th where k th and k t f represent the mesh stiffness of healthy tooth mesh and fault tooth mesh, respectively. As Fig. 11 displayed, when the angular displacement is between 18.95 \u00b0 and 22.52 \u00b0, 18" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002994_j.mechmachtheory.2020.104126-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002994_j.mechmachtheory.2020.104126-Figure1-1.png", "caption": "Fig. 1. Parameters of the four-bar linkage.", "texts": [ " In Section 3 , the analytical formulation of the branches and circuits of the coupler curve is established, as well as the way the proposed synthesis method approaches all possible situations. Section 4 presents the optimization methodology, including the formulation, the definition of the new error function including the slope of the curve and the algorithm flowchart. In Section 5 , several examples demonstrate the validity of the methodology, and in Section 6 , the computational data is included. Finally, in Section 7 , the conclusions derived from this work are established. Fig. 1 represents the dimensional parameters ( a 1 , a 2 , . . . , a 9 ) and the input variable, \u03d5, of the four-bar linkage that will be used in optimization. It should be noted that ( a 1 , . . . , a 4 ) must be always positive because they stand for bar lengths, while ( a 5 , . . . , a 9 ) can be also negative since they have vector meaning. The figure also shows the local (O A , X 0 , Y 0 ) and global ( O, X, Y ) reference systems as well as the secondary variables ( \u03b8 , \u03c8). Next, starting from the Freudenstein equation, Eq", " The process is repeated iteratively until the stop criterion is met (explained in Section 4.2 ). Example 1. path composed of 2 straight sections and 2 circumferential arcs. The prescribed curve is made up of 4 sections: straight line\u2014circumferential arc\u2014straight line\u2014circumferential arc. Fig. 11 defines the path geometrically, and the 35 prescribed points extracted from it are indicated in Table 3 . The optimal solution obtained, represented in Fig. 13 , is a four-bar linkage with a rocker input. The quantities to be optimized are 9 dimensional parameters (the 9 shown in Fig. 1 ) and the input parameters (35, the same number as the precision points), which is considered the unprescribed timing option. This means that a total of 44 parameters will be optimized. Figs. 12 and 13 represent the initial and optimal mechanisms, respectively. In this example and in all others presented here, the input bar is highlighted with a greater thickness. Table 4 gives the parameters associated with these mechanisms. in the curves, so that the error decreases from 10.8534 in the initial mechanism to 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001038_1350650116689457-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001038_1350650116689457-Figure5-1.png", "caption": "Figure 5. Bearing test rig and load devices: (a) photo of test rig; (b) sketch of load devices; (c) photo of load devices.", "texts": [ " Then, the cage is exposed to larger surface area, which ensures the eddy probes to transduce perfect motion signals of the cage as shown in Figure 3(b). The motions of the cage in radial directions are measured by two probes (yc, zc) installed in the bearing house 90 apart and in the corresponding grooves in the outer ring. The axial motions are also measured by the two probes (xc1, xc2), which are fixed on a panel (shown in Figure 4) and mounted parallel to the bearing axis, focused on the cage side face, 180 apart. The bearing test rig is established as shown in Figure 5, which consists of motor, coupling, rotating shaft, supporting and tested bearings, and load devices. The tested bearing is mounted on one side of the cantilever shaft. As shown in Figure 5, the bearing is applied in the radial and axial forces directly through the bearing house. On applying the moment to the bearing and the screw bolt, apart from the bearing axis, a certain distance (e.g. s) in axial direction is adopted. When all the three screw bolts are used on the tested bearing, the corresponding force values of F1, F2, and F3 are monitored by the force transducers as shown in Figure 5. The external loads Fa, Fr, and M of the bearing can be calculated in Table 2. Radial and axial motions of the cage The measured radial and axial motions of the cage mass center including yc, zc in the horizontal and vertical directions and xc1, xc2 in the axial direction are analyzed by FFT and compared under various operating conditions. The experimental cases are listed in Table 3. The motion of cage in radial direction. The radial motions of the cage (yc \u2013 horizontal, zc \u2013 vertical) under the various operating conditions shown in Table 3 are illustrated in Figure 6, when both axial and radial forces of 1000N are applied and rotating speed is 4800 r/min" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000193_j.cma.2011.04.006-Figure22-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000193_j.cma.2011.04.006-Figure22-1.png", "caption": "Fig. 22. Contact patterns for: (a) case B3b, (b) case B3c, (c) case B3d and (d) functions of transmission errors for previous cases of design.", "texts": [ " (21(d)) shows the obtained functions of transmission errors for previous cases of design. Although for cases of design B2b and B2c the contact pattern is localized inside the contacting surfaces, avoiding undesirable edge contacts, when an axial displacement of the pinion occurs, the contact pattern is shifted towards the edge of the gear as shown in Fig. 21(c). All functions of transmission errors are obtained with parabolic shape, absorbing efficiently the lineal functions of transmission errors caused by errors of alignment for non-modified bevel gear tooth surfaces. Fig. 22 shows the contact patterns for cases B3b (22(a)), B3c (22(b)), and B3d (22(c)). Fig. (22(d)) shows the obtained functions of transmission errors for previous cases of design. For this design, the contact patterns are also localized inside the contacting surfaces, avoiding edge contacts, and the predesigned function of transmission errors is able to absorb the lineal functions of transmission errors caused by errors of alignment. 6. Conclusions The performed research work allows the following conclusions to be drawn: 1" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002879_j.procir.2020.09.164-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002879_j.procir.2020.09.164-Figure1-1.png", "caption": "Fig. 1. MiCLAD machine with LMD station (green) and milling spindle.", "texts": [ " Although the processing of such amount of data can typically not occur fast enough to do it in real-time, nonetheless, the processing can run in parallel to the part building process and corrections or changes in the part geometry can still be performed over multiple layers, rather than only instantaneously. A second advantage is that such offline methods can consider the full history, not only of the part, but of also of the machine and all the input parameters (i.e.: geometry, deposition strategy and trajectory, material & powder characteristics, process parameters, etc.) In order to take full advantage of this benefit the Micron precision Milling Closed-Loop Additive (MiCLAD) research platform was built at the Vrije Universiteit Brussels, Belgium. Figure 1 shows a CAD render of the inside of the MiCLAD machine designed by the author at the VUB. The machine combines a powder blown laser metal deposition head with a high-speed mechanical milling tool. Hence, both addition and removal of material is capable and corrections to the part can be either additive or subtractive. It was illustrated by [7] that the correction of a local excess deposition in a particular layer typically takes up to tens of layers to compensate for the error. Hence, having the opportunity to also decide for removal of excess material can significantly decrease the additional number of layers required to compensate for the excess. A more in-depth look to the MiCLAD machine is given in the next section. 2. MiCLAD hybrid LMD machine 2.1. Machine concept MiCLAD (Figure 1) is the in-house developed hybrid laser metal deposition and high-speed milling machine of the Vrije Universiteit Brussel. By opting for a hybrid machine with both additive and subtractive capabilities, the machine allows to correct the part geometry over multiple layers. With only an additive possibility, once too much material is deposited, no correction in the machine is possible anymore. A separate milling spindle and laser deposition head were chosen to allow for a fast transition from additive to removal capability" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002277_978-3-319-27131-6-FigureD.1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002277_978-3-319-27131-6-FigureD.1-1.png", "caption": "Fig. D.1 Angular speeds of rolling bearings", "texts": [ "mat return end % ------------------------------------------------------------------------- function [Jr,Ja] = LoadInt_JrJa(x,e,n) % ------------------------------------------------------------------------- % Load function Jr Jr = 1/(2*pi)*(1. -(1.-cos(x))/(2.*e))^n *cos(x); % Load function Ja Ja = 1/(2*pi)*(1. -(1.-cos(x))/(2.*e))^n; return end The computational results are shown in Figs. 2.10, 2.11, and 2.12. 222 Appendix C: Simpson\u2019s Rule To calculate the angular speeds of the cage \u03c9c and rolling element \u03c9b (ball or roller), a simple bearing model is used in Fig. D.1. The inner race is fixed to the shaft, and it rotates with the rotor speed \u03c9i; the outer race rotates with an angular speed \u03c9o. The rolling element contacts the inner and outer races at the radius ri and ro, respectively. The rolling element diameter is Dw; the pitch diameter Dpw is defined as the diameter of the rolling element centers. The angular speed of the bearing cage \u03c9c about the bearing axis Oba is written in \u03c9c \u00bc vi \u00fe vo\u00f0 \u00de 2rp \u00bc vi \u00fe vo Dpw \u00f0D:1\u00de The circumferential speed vi at the contact area between the inner race and the rolling element results as vi \u00bc \u03c9iri \u00bc \u03c9i 2 Dpw Dw cos \u03b1 \u00bc \u03c9i 2 Dpw 1 Dw cos \u03b1 Dpw \u00f0D:2\u00de Similarly, the circumferential speed vo at the contact area between the outer race and the rolling element is written as vo \u00bc \u03c9oro \u00bc \u03c9o 2 Dpw \u00fe Dw cos \u03b1 \u00bc \u03c9o 2 Dpw 1\u00fe Dw cos \u03b1 Dpw \u00f0D:3\u00de Substituting Eqs" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002844_j.mechmachtheory.2020.103930-Figure9-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002844_j.mechmachtheory.2020.103930-Figure9-1.png", "caption": "Fig. 9. Load distributions of the spur gears at 20 0 0r/min of driving gear.", "texts": [ " When the input speed is 500 r/min or 1700 r/min, the mating gear teeth is always in full contact condition due to relatively smaller dynamic displacement, and the dynamic mesh force fluctuation is obviously smaller than that when the input speeds are near the main resonance and harmonic resonance speeds of the system. The instantaneous three-dimensional dynamic contact states of the tooth surface during the speed-up and speed-down process at the input speed of 20 0 0 r/min are investigated respectively. The corresponding dynamic load distributions on the plane of action are given in Fig. 9 . It can be observed that the meshing tooth surface is always in a full contact condition in a mesh cycle during the speed-up process. However, during the speed-down process, the total contact loss condition appears in the mating gear teeth at the same input speed. It reflects that the gear system is a typical strong nonlinear system when the input speeds are near the resonance speed of the system, and the dynamic response of the system shows a great sensitivity to the change of initial condition of the system" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003017_j.addma.2020.101822-Figure33-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003017_j.addma.2020.101822-Figure33-1.png", "caption": "Fig. 33. Point cloud of Case 2 sample (a) partitions 1\u20134 (b) partitions 5\u20138.", "texts": [ " In the MATLAB program, the distance between two boundary planes is set to f = 0.4 mm, and the distance coefficient set to n = 5 for all measurements. Fig. 32 compares the Ra results achieved by 3D point cloud program with the mount solution results. The diagrams show that there are similar trends for the two methods. The Ra values are usually smaller for 3D point cloud method when compared to the mount solution, and the curves have less oscillations. Also it shows that Ra for the inner surface is comparably less than the values for the outer surface. In Fig. 33, the point cloud results for partitions 1\u20134 and partitions 5\u20138 for the Case 2 sample are shown. The average point density is approximately 110 and 70 points/mm2 for partitions 1\u20134 and partitions 5\u20138, respectively. The surface roughness results for partitions 1\u20134 are presented in Fig. 34 for the inner and outer edges. The curve patterns match the result curves for the mount sample. As with the previous example, the curves from the 3D point cloud solution tend to have smaller values. The dimensional inaccuracy of the input data explains some of the shift between the mount and the 3D point cloud data illustrated in the diagrams" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002808_j.rcim.2019.101907-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002808_j.rcim.2019.101907-Figure2-1.png", "caption": "Fig. 2. A SCARA robot and linear robot path.", "texts": [ " Piecewise linear robot path in Cartesian space is usually specified by a sequence of positions and orientations of the end-effector TCS (Tool Coordinate System) relative to the robot-base RCS (Robot Coordinate System). A SCARA robot has three rotation joints and a translation joint along the Z direction. As the z-axis of TCS is always coincident with the z-axis of RCS, the only DOF of the orientation is a rotation angle around the Z-axis. The lone orientation angle plus three position axes form the 4 DOF of SCARA robot paths. As shown in Fig. 2, piecewise-linear SCARA robot path can be represented by a series of 4D points =P x y z{ ( , , , )}i i i i i i N 0, in which, (xi, yi, zi) is the position and \u03b8i is the rotation angle of TCS relative to RCS. Using 4D points to represent SCARA robot path ensures unified parameterization of positions and orientations. Vector operations of 4D points such as addition, subtraction, scale multiplication and derivation are similar to those in R3. The linear interpolation of 4D points is consistent with the linear algebra in R3" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002893_tia.2020.3036328-Figure32-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002893_tia.2020.3036328-Figure32-1.png", "caption": "Fig. 32. Structure of rotor with different tooth widths.", "texts": [ " 31 demonstrates that the dummy slot dimensions will not help decrease the torque ripple to a low level. What is worse is that improper dummy slot dimensions may increase the torque ripple greatly. Authorized licensed use limited to: California State University Fresno. Downloaded on June 26,2021 at 14:21:53 UTC from IEEE Xplore. Restrictions apply. 5) Different Tooth Widths: Different tooth widths also help to diminish harmonics, and thus decrease the torque ripple [47]. Tw1 and Tw2 represent the tooth widths of two adjacent teeth, as shown in Fig. 32. The contour plot Fig. 33(a) shows that there are three minimum torque ripple areas. The contour plot, Fig. 33(b), shows when the tooth width is 3 or 4 mm, the average torque reaches its maximum value. When both the average torque and the torque ripple are taken into consideration, we should choose the two adjacent tooth width as 2 and 6 mm. The torque ripple is reduced to 30% and the torque decreased by 19%. In summary, several means can be used to reduce the torque ripple. Step skewed rotor, shifted rotor teeth, and different tooth widths share a similar way for the reduction of cogging torque" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002969_tmag.2020.3007439-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002969_tmag.2020.3007439-Figure6-1.png", "caption": "Fig. 6. Dummy rotor for measuring the mechanical loss.", "texts": [ " As the no-load electromagnetic loss is generated by the field magnets, the mechanical loss can be measured directly by measuring the no-load loss of the specimen with dummy rotor [2], [4], [10]. Although there is a segregation method of the mechanical loss suggested by the IEC standard, the method using the dummy rotor is more effective because the method suggested by the IEC standard includes uncertainty by measurements [10]. The dummy rotor was manufactured with non-magnetized materials such as S45C shown in Fig. 6 but its weight was the same as that of the magnetized rotor. The experiments were conducted by installing the specimen with the dummy rotor in the experimental setup of Fig. 5(a). The speed range of the experiments was the same as that of the experiments for measuring the no-load loss. Fig. 7 shows the measured no-load loss from the exper- iment with magnetized rotor and mechanical loss from the experiment with dummy rotor. Each loss increases as the rotating speed increases. As the no-load loss includes the electromagnetic loss, the mechanical loss is lower than the measured no-load loss" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003079_s40430-020-02491-3-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003079_s40430-020-02491-3-Figure3-1.png", "caption": "Fig. 3 a The schematic of the main directions of SLMprocessed parts; b geometry of SLM-processed sample for tensile testing", "texts": [ " The main (7)kp = ks(1 \u2212 p) 1 + \u03a8ks / kg Table 1 Thermal property parameters of 316L stainless steel [22] Temperature (K) Conductivity ( W (m \u25e6C)\u22121 ) Specific Heat ( J (kg \u25e6C)\u22121 ) Density ( kg m\u22123 ) Table 2 The compositions of SS316L powder (wt%) Composition Fe Mo Cr Mn Ni Si S C Percent (wt%) Bal. 2.37 17.85 0.057 12.63 0.94 0.0016 0.017 Fig. 2 SEM morphology: a size distribution; B particle size of the powder Journal of the Brazilian Society of Mechanical Sciences and Engineering (2020) 42:402 1 3 402 Page 4 of 14 direction of the SLM-processed cubic parts is shown in Fig.\u00a03a. Detailed dimensions of the tensile samples are shown in Fig.\u00a03b. The effect of laser power, scanning speed, hatch spacing and layer thickness on the SLM process was analyzed by optimization experiments (Table\u00a0 4). Considering the combined effects of these four factors on the SLM process, the laser energy density (LED) was used as a comprehensive parameter to evaluate its impact on the SLM process. The laser energy density (LED), laser energy volume, is defined as (8): where P is the laser power, v is the laser scanning speed, s is the hatch spacing, and h is the layer thickness of the powder bed" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001584_j.jsv.2016.08.014-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001584_j.jsv.2016.08.014-Figure6-1.png", "caption": "Fig. 6. FEA modes for the first two natural frequencies: wireframe lines for the undeformed system, coloured total deformations superimposed to the mode shapes. (For interpretation of the references to colour in this figure caption, the reader is referred to the web version of this paper.)", "texts": [ " The first eighteen natural frequencies of the Agile Eye for the two cases have been analysed. The results coming from the two cases have been compared to Ansys\u00a9 for validation as reported in Tables 3 and 4. Table 3 reveals that the model based on the GSDM and the FE model differ for the modal crossing occurring every triplets of natural frequencies. The first mode obtained through Ansys\u00a9 is a global rotation about the symmetry axis, the mode shape of the robot is similar to a screw, as shown in Fig. 6(a). The second and third modes are symmetric w.r.t. two orthogonal horizontal axes, as shown in Fig. 6(b). It is noteworthy that the relative error should be judged with attention as it refers to results with different mode orders. For the pose 1 the results reported in Table 4 reveal that there is no modal crossing between the two models. The first natural frequency is strongly influenced by the change of pose and its value decreases w.r.t. the home pose case. The first two modes are plotted in Fig. 6(c) and (d). As can be observed in Table 4, for low-range frequencies the relative error reveals that the inertial contribute of the MP, comparable to that of all legs, disturbs the dynamic stiffness model. The same error lessens for highrange frequencies including local modes of the legs. The reason of this behaviour is due to the addition of the lumped mass/ inertia of the MP, here considered rigid. Besides, it should be stressed that the FE model is based on tetrahedral elements; holes, fillets and other geometric features not represented into the dynamic stiffness formulation" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000643_tie.2011.2126539-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000643_tie.2011.2126539-Figure1-1.png", "caption": "Fig. 1. Phasor diagram of induction machine.", "texts": [ " (10) This gives \u03c8e dr = Lr Lm ( V e qs \u03c9e \u2212 \u03c3Lsi e ds ) . (11) Similarly, eliminating rotor current term ieqr from (4) with the help of (8) and rearranging \u03c8e qr = \u2212(Lr/Rr)\u03c9sl\u03c8 e dr. (12) In addition, elimination of iedr from (3) by (7) gives Rr(\u03c8e dr \u2212 Lmieds)/Lr \u2212 \u03c9sl\u03c8 e qr = 0. (13) Therefore, from (12) and (13) (\u03c8e dr \u2212 Lmieds) + \u03c8e2 qr \u03c8e dr = 0. (14) Equation (14) can be rewritten as \u03c8e qr = \u2212 \u221a (Lmieds \u2212 \u03c8e dr) \u03c8e dr. (15) The negative sign for \u03c8e qr is taken for the given orientation of the d\u2013q reference frame, as shown in Fig. 1. The rotor flux magnitude can be calculated from (15) as \u03c8e r = \u221a Lmieds\u03c8 e dr. (16) Alternately, the steady-state rotor flux magnitude in rotor-fluxoriented d\u2013q reference frame can be expressed as \u03c8r = Lmisd (17) where isd is the rotor magnetizing component of the stator current in rotor flux orientation. Therefore, combining (16) and (17) isd = \u221a ieds\u03c8 e dr/Lm. (18) In almost all the drive controllers, a linear magnetizing curve is considered, which signifies a constant magnetizing inductance Lm throughout the operating region" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003040_j.mechmachtheory.2020.103837-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003040_j.mechmachtheory.2020.103837-Figure2-1.png", "caption": "Fig. 2. Simulation mechanism of the Exechon hybrid manipulator.", "texts": [ " 82604 \u00d7 10 Y 11 02 + 2 . 36575 \u00d7 10 2 Y 10 02 \u2212 3 . 65341 \u00d7 10 2 Y 9 02 + 1 . 07005 \u00d7 10 3 Y 8 02 \u22121 . 25782 \u00d7 10 3 Y 7 02 + 2 . 12624 \u00d7 10 3 Y 6 02 \u2212 1 . 83311 \u00d7 10 3 Y 5 02 + 1 . 66847 \u00d7 10 3 Y 4 02 \u2212 9 . 42688 \u00d7 10 2 Y 3 02 +2 . 15344 \u00d7 10 2 Y 2 02 \u2212 13 . 9073 Y 02 + 0 . 26938 = 0 , From the above equation, Y o 2 can be solved as shown in Table 1 . Table 1 shows that Y o 2 has 12 solutions. Using the CAD software, a simulation mechanism of the Exechon hybrid manipulator can be created as seen in Fig. 2 . The details for establishing the simulation mechanism can be seen in reference [37] . Based on the simulation mechanism, the value of Y o 2 can be obtained. The result shows that the simulation solution is in accordance with the third solution in Table 1 . Thus, (0.3 m 0.3809 m 1.8 m \u221250 \u00b0 \u221230 \u00b0 \u22126 \u00b0) can be seen as one feasible 6-dimensional position and orientation vector of n 2 for the Exechon hybrid manipulator. After Y o 2 is solved, other kinematic parameters are solved based on the kinematics process as: \u03b11 = \u221216 . 88 o , \u03b21 = 10 . 42 o , Z 01 = 1 . 0942 Then the inverse displacement of the Exechon hybrid manipulator can be solved as: r 1 = 1 . 1504m , r 2 = 1 . 0257m , r 3 = 1 . 3355m , \u03d1 1 = \u221246 . 3155 o , \u03d1 2 = \u221211 . 0461 o The result is also verified by its simulation mechanism (see Fig. 2 ). Under this pose, the terminal constraint is solved as: S r = [ \u22120 . 765458 0 . 641715 \u2212 0 . 0477065 1 . 32973 1 . 16465 \u2212 0 . 608961 ] T The result shows that the terminal constraint of the Exechon hybrid manipulator is a screw with its pinch h = \u22120.2414. The 6 \u00d7 5 form forward Jacobian is solved as: J F = \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 \u22121 . 564 0 . 03956 1 . 6640 0 0 0 . 9484 \u22121 . 7770 0 . 9715 0 0 0 . 4281 0 . 7178 \u22120 . 1052 0 0 \u22120 . 4050 0 . 9874 \u22120 . 4966 0 . 1808 0 . 6793 \u22120 . 9239 \u22120 . 0799 0 . 9674 0 . 2856 \u22120 " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000089_kem.447-448.785-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000089_kem.447-448.785-Figure1-1.png", "caption": "Fig. 1 Schematic illustration for consolidating metal powder", "texts": [ "General Universitaria, Sevilla, Spain-08/06/15,19:17:51) position is calculated from the amount of strain change measured by the strain gauge when the consolidated structure is cut layer by layer with an end mill. The influences of the thickness of the base plate and the height of consolidated structure on the residual stresses are experimentally investigated. In addition, the effect of the pre-heating by a laser beam irradiation on the base plate and the laser condition for the layered manufacturing on the reduction of the residual stress are evaluated. Consolidation procedure The schematic illustration for consolidating a metal powder is given in Fig. 1. This system is composed of a Yb:fiber laser (IPG Photonics Corp.: YLR-SM) and the consolidation facility of a metal powder. The intensity of laser beam relative density measured by beam profile system (OPHIR Corp.: Beam star FX-50) is shown in Fig. 2. The laser beam formed a Gaussian shape and the focal diameter was \u03c6 =100 \u00b5m. The metal powder is deposited on the base plate at a thickness of 50 \u00b5m with a recoating blade. The laser beam then was irradiated to the powdered surface through a galvanometer mirror, and scanned on it with programmed NC data" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003476_j.triboint.2021.106951-Figure10-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003476_j.triboint.2021.106951-Figure10-1.png", "caption": "Fig. 10. Lubricant distribution and streamline diagrams at three speeds.", "texts": [ " In addition, during a short period when the gear has just started to run, the operation is not stable, and the churning losses are relatively large. Therefore, the churning losses appear a decreasing trend from a certain value in 0\u20130.05s, and this result is also consistent with the conclusions in literature [10,27]. The model and simulation conditions which are the same as those of Section 3.2.2 are selected except the rotating speed of driving gears, and the oil flow rate and oil distribution diagrams of oil guide holes at different rotational speeds when turning right are obtained, as shown in Fig. 9 and Fig. 10. Figs. 9 and 10 show that the oil flow rate of the four oil guide holes has the same changing trend at different rotational speeds. The oil flow rate at higher speed is slightly lower than that at lower speed. The reason is that the driving gear stirs the oil faster when the rotational speed is higher, resulting in the more turbulent distribution of oil. The oil flow rate of hole 1 and hole 2 is much more than that of hole 3 and hole 4 and the oil tilts to one side, which is the same as described in section 3" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003169_j.mechmachtheory.2020.103844-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003169_j.mechmachtheory.2020.103844-Figure7-1.png", "caption": "Fig. 7. The Pa (2-UU)-&- R UU PM: (a) architecture; (b) 6-dimension distal wrenches.", "texts": [ " In this case, 1 S DW = (B 1,1 C 1,1 ; c 1,1 \u00d7 B 1,1 C 1,1 ); 2 S DW = (B 1,2 C 1,2 ; c 1,2 \u00d7 B 1,2 C 1,2 ); 3 S DW = (B 2,1 C 2,1 ; c 2,1 \u00d7 B 2,1 C 2,1 ); 4 S DW = (B 2,2 C 2,2 ; c 2,2 B 2,2 C 2,2 ; 5 S DW = (B 3,1 C 3,1 ; c 3,1 \u00d7 B 3,1 C 1,1 ); and 6 S DW = (B 3,2 C 3,2 ; c 3,2 \u00d7 B 3,2 C 3,2 ), where c i, j represents the position vector of point C i, j . The distal application point d A 1 = C 1,1 ; d A 2 = C 1,2 ; d A 3 = C 2,1 ; d A 4 = C 2,2 ; d A 5 = C 3,1 ; and d A 6 = C 3,2 . The distal wrench identification of the Delta PM is similar to that in [36] , however, the method in this paper is not limited to the characteristic of PMs with six supporting SS links but is instead more practical. In fact, this approach can be applied to general PMs whose distal parts are supported with six-dimension wrenches from limbs. One case can be seen in Fig. 7 . As shown in Fig. 7 (a), the Pa (2-UU)-&-RUU PM ( Pa , actuated parallelogram joint) is composed of a normal R UU limb and a Pa (2-UU) limb in which there is a closed loop B1,1-B1,2-C1,2-C1,1-B1,1. The presented Pa (2-UU)-&- R UU PM is a 2-DOF manipulator which is inspired by the IRSBot-2 robot [41] . When the two actuated joints are blocked, as shown in Fig. 7 (b), the mobile platform gets six-dimension wrenches from two limbs. In this case, 1 S DW = (B 1,1 C 1,1 ; c 1,1 \u00d7 B 1,1 C 1,1 ); 2 S DW = ( 0; n 1,1 ); 3 S DW = (B 1,2 C 1,2 ; c 1,2 \u00d7 B 1,2 C 1,2 ); 4 S DW = ( 0; n 1,2 ); 5 S DW = (B 2 C 2 ; c 2 \u00d7 B 2 C 2 ); and 6 S DW = ( 0; n 2 ), where n i, j ( n i ) represents the normal vector of the universal joint located at point C i, j (C i ). The distal application point d A 1 = d A 2 = C 1,1 ; d A 3 = d A 4 = C 1,2 ; and d A 5 = d A 6 = C 2 . Moreover, this approach can be further applied to articulated-platform PMs, such as the Par4 and Heli4 high-speed PMs whose distal parts are supported with 8-dimension wrenches from their closed-loop passive limbs", " The goal of the optimization problem is to find i S PW = l \u2211 k =1 \u03b8k k S i W (4) so that the instantaneous power i W IP between the unit proximal wrench i S u PW and the unit actual proximal twist i S u APT from the actuated joint is i W IP = ( i S u PW \u25e6i S u APT ) \u2192 max (5) subject to i S PW \u2208 i WS = span { 1 S i W , . . . , k S i W , . . . , l S i W } , (6) where k S i W is the k th element while l is the total number of elements in the wrench space i WS inside the i th limb of the investigated PM. The identification schematic of the proximal wrench in Fig. 7 is just an indication of the proximal wrench identification, which needs to be determined according to the PM\u2019s topological structure. To measure the effect of the proximal wrench on the actuated joint, the power coefficient of the unit actual proximal twist i S u APT and its corresponding unit proximal wrench i S u PW is defined as \u03b3i = | i S u PW \u25e6i S u APT | | i S u PW \u25e6i S u APT | max , (7) where | i S u PW \u25e6i S u APT | max = \u221a (h PW + h APT ) 2 + d 2 max . h PW and h APT are the pitches of i S u PW and i S u APT , respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003151_lra.2020.2965863-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003151_lra.2020.2965863-Figure3-1.png", "caption": "Fig. 3. The process of the angle calculation on the images", "texts": [], "surrounding_texts": [ "In order to make the surgical instruments at the center of the left image, let a \u2208 R2 denote a task function defined as the sample mean: 1 1 1 1 m l i i a m l i i u m v m where m is the number of the surgical instruments detected on the left image and the ,l l i iu v is the coordinate of the i-th surgical instrument\u2019s tip on the left image. The time derivative a is given by: 1 1 1 2 2 02 I c c I I I c c I I a a a a c I ck ck k I I p J J p J J J J X J J Q p J J where 2 4 2 4 1 [ ]a a a m J g g and 2 4 a g is the 2 4 matrix repeated for m times. 2 4 1 0 0 0 0 1 0 0 a g . ci IJ is the ith target\u2019s Jacobian for image represented in the camera frame. p I i is the time derivative of the ith p I ." ] }, { "image_filename": "designv10_9_0003025_bf02919918-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003025_bf02919918-Figure3-1.png", "caption": "Fig. 3 a. Fluid joint; b. Electric joint; c. Rigid joint.", "texts": [ " Meanwhile it may transmit a discharge Q from the low- to the high-potential side. It therefore delivers hydraulic power IV = (P2 - - Pi) Q. Practically a pump has always internal energy losses; hence the potential difference still depends on the discharge delivered. An oscillating membrane or piston may produce sinusoidally varying discharges and heads, in a similar way as an ordinary pump produces constant discharges and heads. F 1 u i d j o i n t. We consider a joint of two or more hydraulic systems (fig. 3a). We idealize the joint by neglecting the effects of inertia and friction in the liquid and by supposing the solid walls to be rigid and not leaking. Then all the systems have the same potential at the joint, and the algebraic sum of the discharges towards the joint is zero: (Hence at least one of the discharges is negative, i.e. opposed to the sense indicated in fig. 3a). S e r i e s a n d p a r a l l e l c o u p l i n g . When two systems AB and CD are coupled in such a way that the terminals A and C form one entrance, and likewise the te rminals BC, the sys tems AB and CD are said to be parallel. Then the poten t ia l difference on AB is the same as on CD and the same as on the whole sys tem, and the discharge t r a n s m i t t e d th rough the whole sys t em is the sum of the discharge th rough AB and tha t th rough CD. When the two sys tems are coupled in such a w a y t h a t B is connected to C, the sys tems are said to be in series", " An electric element or other generator produces a tension, while it may transmit a current from the low- to the high-potential side. I d e a 1 t r a n s f o r m e r. When the coupling of a transformer is perfect and the inductance so great that it may be idealized as infinite, the primary voltage and current are in a definite proportion transformed into a secondary voltage and current in such a way that primary and secondary power are equal. E l e c t r i c j o i n t . When we idealize the joint of a set of electric systems (see fig. 3b) by neglecting inductance, resistance, capacity and leakage at the joint, the formulae for the joint are U1 = U 2 = U3 . . . . . ; 11 + 1 2 + 1 3 + . . . . . O. (The latter formula shows that at least one of the currents is negative, i.e. opposed to the sense indicated in fig. 3b). S e r i e s a n d p a r a l l e l s c h e m e s . The rules for elementary electric impedances in series or parallel schemes are: Electric In series Parallel resistances Re = Rel + Re2 G = G 1 + G 2 inductances L = L 1 + L 2 1/L = 1/L1 + 1/L 2 capacitances 1/C = 1 / C 1 @ 1/C 2 C = C 1 + C x w Hydraulic-electric analogy. C o m p l e t e a n d i n c o m - p l e t e a n a l o g y . When we compare the formulae of w 3 for electric systems to those for hydraulic systems as deduced in w 2, it will be clear that the following analogy exists: Complete analogy H y d r a u l i c E l e c t r i c volume charge discharge current potential difference potential difference resistance resistance deliverance conductance inertance inductance capacitance capacitance kinetic energy magnetic energy gravitational energy electric energy sea earth generator (pump) generator (element) If we consider only the formulae for the impedances, we might also arrive at the following analogy: H y d r a u l i c discharge potential difference resistance deliverance inertance capacitance kinetic energy gravitational energy Incomplete analogy E l e c t r i c potential difference current conductance resistance capacitance inductance electric energy magnetic energy The rules for joints, however, have then been disregarded", " The nose entrance of the pitot tube is acted upon by the total head and the side entrance by the static head (height plus pressure head). Thus it is the velocity head (v2/2g) that activates the system, and the manometer in the form of the fl-tube will indicate this head as long as the velocity remains constant. When the velocity is varying, the inertance and resistance in the tubes cause deviations of the indication of the manometer from the actual value of the velocity head. Since the manometer works as a bi-terminal storage member (fig. 3b), the system can be represented by the scheme of fig. 9b, where the generator denotes the action of the varying velocity head. The resistances and inertances in the scheme of fig. 9b may be composed according to the rules of series coupling, and then we obtain the simplified scheme of fig. 9c. The pitot meter is analogous to an electric system as represented schematically in fig. 9d. The electromotive force of the generator represents the velocity head to be measured, and the tension on the condensor represents the reading of the manometer", " P a i r o f l e v e r s . A pair of levers as indicated in fig. 13b operates according to the formulae F 1/ F 2 = (v12 - - %2) / (v l l - - v21) = =12/ l 1. This means tha t a small force and a great velocity difference m a y be t ransformed into a great force and a small velocity difference or conversely, the power remaining the same. R i g i d j o i n t . At a rigid and massless joint of two or more solid bodies all the bodies have the same movement and the sum of the forces working on the joint is zero (see fig. 3c): v l = v 2 = v 3 . . . . . ; F1 + F 2 + F a + . . . . = 0 . These rules may be interpreted both vectorially for the total velocities and forces and algebraically for the components of all velocities and forces in any particular direction. (At least one of the forces is negative, i.e. opposed to the sense indicated in fig. 3c). S e r i e s a n d p a r a l l e l c o u p l i n g . Two mechanical systems AB and CD are coupled parallel to each other if A is joined to C and B to D. Then the movement of B relative to A is the same as that of D relative to C, and the force transmitted by the whole system is the sum of the forces transmitted by AB and CD separately. Two mechanical systems AB and CD are coupled in series if B is joined to C. Then the force transmitted by AB is the same as that transmitted by CD, and the movement of D relative to A is the sum of the movement of D relative to C and that of B relative to A" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002705_j.mechmachtheory.2020.104006-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002705_j.mechmachtheory.2020.104006-Figure1-1.png", "caption": "Fig. 1. Simplified model of redundant sliding manipulators: (a) circular-sliding manipulator, (b) curved-sliding manipulator, (c) linear-sliding manipulator.", "texts": [ " Section 3 introduces the analytical inverse kinematic parameterized method for redundant circular-sliding manipulators and extends it to all types of redundant sliding manipulators. Section 4 verifies the effectiveness and universality of the proposed method through simulation and physical experiments. Section 5 presents conclusions and outlines future work. The redundant sliding manipulator studied in this paper is composed of different types of sliding rails as the mobile base and a 6-DOF redundant manipulator, as shown in Fig. 1 . For a 6-DOF manipulator, the inverse kinematics is very complex. On the basis of establishing the kinematics equation by D-H method, after certain analytical calculations, it is found that there are often many inverse kinematics solutions to the position of the manipulator, which cannot be closed effectively. Therefore, the Pieper method is based on this research and found that if the manipulator satisfies one of two sufficient conditions, the analytical inverse kinematic parameterized method in this paper will be used to obtain the closed solution of inverse kinematics", " Therefore, the redundant sliding manipulator studied in this paper has the advantages of large working space, light weight, high fault tolerance, strong robustness, high operating accuracy, easy replacement of different types of rails to complete various operating tasks and so on. This section introduces the kinematics modelling of the redundant circular-sliding manipulator, and extends to all types of rail-type redundant sliding manipulators. The 7-DOF circular-sliding rail-type redundant sliding manipulator consists of a rail-type mobile base and a 6-DOF manipulator. Therefore, the circular-sliding redundant sliding manipulator can be regarded as a 7-DOF redundant manipulator with the link l 0 with a fixed length. The configuration is simplified as shown in Fig. 1 (a). At this time, the circular-type rail is regarded as a rotational DOF in kinematic model, and the length of the link l 0 is equal to the radius R 0 of the circulartype rail. The inverse kinematics of the circular-sliding redundant sliding manipulator will be converted into the inverse kinematics of a 7-DOF arm with link l 0 , which has a fixed length. The link configuration of the circular-sliding redundant sliding manipulator is as follows, l 0 = R 0 (1) where R 0 represents the rule that the radius of the circular-type rail. The length of link l 0 is substituted into the analytical formula for the inverse kinematics of the circular-sliding manipulator in Section 3 to solve the inverse kinematics problem. The curved-sliding redundant sliding manipulator can be regarded as a 7-DOF redundant manipulator with a link l 0 with a variable length. The configuration is simplified as shown in Fig. 1 (b). At this time, the inverse kinematics of the manipulator is converted into the inverse kinematics of the 7-DOF manipulator with link l 0 , which has variable length. The link configuration of the curved-sliding redundant sliding manipulator is as follows, l 0 = R (\u03b8 ) (2) where R ( \u03b8 ) represents the rule that the radian radius R of the curve changes with the value of the joint angle \u03b81 . The length of link l 0 is substituted into the analytical formula for the inverse kinematics of the curved-sliding manipulator in Section 3 to solve the inverse kinematics problem", " According to the configuration of the curved-sliding redundant sliding manipulator, the parametric inverse kinematics calculation process and calculation method are the same as the inverse kinematics calculation based on the redundant circular-sliding manipulator. Due to the configuration of the linear-sliding redundant sliding manipulator, it can be regarded as a fixed value of joint angle \u03b81 , where the constant value is 0 and the length of link l 0 changes; that is, joint \u03b81 of the linear-sliding manipulator is a telescopic joint. According to Fig. 1 (c), the linear-sliding manipulator is simplified to a 7-DOF redundant mechanical arm. At this time, the calculation of its inverse kinematics is converted into the calculation of the inverse kinematics solution of the 7-DOF redundant mechanical arm with a telescopic joint. The link configuration of the linear-sliding manipulator is as follows, l 0 = L + L (3) where L + L represents the change rule of the value of the length of link l 0 . The length of link l 0 is substituted into the analytical formula of inverse kinematics of the curved-sliding manipulator in Section 3 to solve the inverse kinematics", " This method can be extended to all types of redundant sliding manipulators according to the kinematic modelling proposed in Section 2 . Moreover, the parameterized method is compared with other numerical iterative methods, so as to get the superiority of this method. Table 1 D-H parameters of the redundant circular-sliding manipulator. Axis \u03b8 i d i a i \u03b1i 1 \u03b8 1 0 0 0 2 \u03b8 2 0 \u2212l 0 0 3 \u03b8 3 l 1 0 \u2212\u03c0/ 2 4 \u03b8 4 0 l 2 0 5 \u03b8 5 0 0 \u03c0 /2 6 \u03b8 6 l 3 0 \u2212\u03c0/ 2 7 \u03b8 7 0 l 4 \u03c0 /2 According to the simplified kinematics model shown in Fig. 1 (a), the corresponding D-H parameters of the redundant circular-sliding manipulator are shown in Table 1 . The pose (position and attitude) between adjacent member coordinate systems can be expressed by a homogeneous transformation matrix i-1 T i , i \u22121 T i = \u23a1 \u23a2 \u23a3 c \u03b8i \u2212s \u03b8i c \u03b1i s \u03b8i s \u03b1i a i c \u03b8i s \u03b8i c \u03b8i c \u03b1i \u2212c \u03b8i s \u03b1i a i s \u03b8i 0 s \u03b1i c \u03b1i d i 0 0 0 1 \u23a4 \u23a5 \u23a6 (4) where c = cos, s = sin, and the pose of the end coordinate of the manipulator in the base coordinate system is 0 T 7 = ( 0 T 1 )( 1 T 2 ) \u00b7 \u00b7 \u00b7 ( 6 T 7 ) (5) Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001677_s11661-018-4771-4-Figure15-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001677_s11661-018-4771-4-Figure15-1.png", "caption": "Fig. 15\u2014(a) Schematic of the welded joint between DMLS CoCrMo and cast FSX414; (b, d) representative optical micrographs from DMLS CoCrMo, Nozzalloy filler wire, and cast FSX414 after postweld heat treatment, with legends displaying the grain size, porosity, and hardness. (e) Collage of images taken from the tensile-tested specimen revealing the failure to take place in the cast FSX414.", "texts": [ " Fractographs of solution-treated samples tested at the room temperature are shown Figures 14(c) and (d). Some cracks can be observed at low magnification along with dimples at higher magnification (Figure 14(c)). The fractographs of the solution-treated samples tested at high temperature (925 C) show dimples, indicative of ductile failure (Figures 14(e) and (f)). Figures 14(g) through (j) are fractographs representative of the solution-treated and aged samples at the room temperature and at 925 C, respectively, revealing predominantly intergranular fracture. Figure 15(a) is a schematic showing the welded joint between DMLS CoCrMo and cast FSX414. Figures 15(b) through (d) compares the microstructure of DMLS CoCrMo, the weld joint and cast FSX414 after the post weld heat treatment. The weldment showed a Table III. Chemical Analysis of Various Phases in the As-Printed DMLS CoCrMo Specimen Using TEM-EDS Elements Co Cr Mo Mn Si Bright Precipitate wt pct 44.2 27.4 22.3 2.7 3.3 at. pct 44.7 31.4 13.0 3.0 7.0 Dark Precipitate wt pct 55.1 28.4 7.6 3.0 5.8 at. pct 51.2 30.0 4.4 3.1 11.3 Matrix wt pct 60.4 26.4 7.4 3.0 1.8 at. pct 58.4 29.1 4.5 3.9 3.7 METALLURGICAL AND MATERIALS TRANSACTIONS A uniformmicrostructure, indicating a sound weld between the DMLS and cast alloy. The legends denotes pct porosity, microhardness, and grain size. The room-temperature tensile strength of the weldment was found to be 415 MPa (0.2 pct YS) and 630 MPa (UTS). The collage of images in Figure 15(e) have been taken from a tensile test specimen after the room-temperature tensile test, indicating the location of failure to be on the side of the cast FSX414, thereby indicating that the weld joint to DMLS CoCrMo is sound. METALLURGICAL AND MATERIALS TRANSACTIONS A The process parameters in this study were developed to ensure a nearly dense microstructure with little porosity, details of which can be found in Reference 30. Some sporadic fine pores do appear in the microstructure. The pores have a spherical and an irregular morphology" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002680_tec.2020.3000753-Figure19-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002680_tec.2020.3000753-Figure19-1.png", "caption": "Fig. 19. The geometry of the U-type IPM motor.", "texts": [ " TABLE V GEOMETRY PARAMETERS OF THE U-TYPE IPM MOTOR Symbol Value Symbol Value l11 4.50 mm lad1 0.25 mm l12 1.96 mm lad2 3.40 mm l2 1.00 mm lau1 2.00 mm l3 1.00 mm lau2 4.54 mm w1 5.16 mm lam1 0.50 mm wm 6.55 mm lam2 3.50 mm wri 7.25 mm \u03b1p 0.70 lm 13.00 mm \u03b2 0.91 lri 1.00 mm \u03b3 1.50 TABLE VI NO-LOAD COMPARISON RESULTS OF U-TYPE IPM MOTOR It can be seen from the above comparisons that the proposed method can accurately calculate the magnetic field and related electromagnetic parameters of the V-type IPM motor. The geometry of the U-type IPM motor is shown in Fig. 19, and the rotor parameters are listed in Table V. The stator structure of the U-type IPM motor is the same as that of the V-type IPM motor. The no-load air-gap flux density and back EMF obtained by FEA and the proposed method are shown in Fig. 20, and the corresponding values are listed in Table VI. It can be seen that the no-load results of the U-type IPM motor obtained by the two methods have a good consistency. 2) Load results verification Similarly, in order to verify that the proposed method can accurately consider the stator saturation, the same excitation conditions as the rated point of V-type IPM motor are selected (current effective value I= 93" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002354_j.vacuum.2018.09.007-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002354_j.vacuum.2018.09.007-Figure1-1.png", "caption": "Fig. 1. Schematic representation of EBM system.", "texts": [ " The vacuum level inside the electron gun is necessary to prevent scattering of the electron beam due to collisions with gas atoms. The vacuum system provides a base pressure of 1\u00d710\u22125 mbar or better throughout the entire build cycle. During the actual melting process a partial pressure of He is introduced to 2\u00d710\u22123 mbar. This clean and controlled build environment is important to maintain the chemical specification of the built material [19]. A schematic representation of EBM system is shown in Fig. 1. In the next paragraphs, an overview of the material used in this study, as well as the process parameters, the test specimens and the method used for assessing dimensional accuracy will be given. Specimens used in this study were manufactured by using Ti6Al4V gas atomized powder with spherical morphology. The spherical shape may contribute to improved flowability, and thus, may ensure high build rates and part accuracy [20]. The powder flow rate measured according to ASTM B213 was found 25 s/50 g" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002833_j.ymssp.2020.106778-Figure16-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002833_j.ymssp.2020.106778-Figure16-1.png", "caption": "Fig. 16. Schematic diagram of power supply for different phases of three-phase 12/8 SRM. (a) A-phase power supply. (b) B-phase power supply. (c) C-phase power supply.", "texts": [ " The radial force and vibration characteristics under two common control strategies are analysed below. The first one is only the APC, and the second one is to add the CCC on the basis of the APC. First of all, the motor is still powered by a DC voltage of 72 V, and the chopping current is 100 A. The motor starts the CCC at about 1000 r/m, so this paper makes a comparative analysis of the electromagnetic force and vibration under two control strategies at 1000 r/m. The schematic diagram of the power supply for different phases of the three-phase 12/8 SRM is given in Fig. 16. Only the A-phase winding is powered when the rotor is in the position shown in Fig. 16(a). Then, when the rotor is in the position shown in Fig. 16(b) (the rotor rotates 15 degrees counterclockwise), the A-phase winding is de-energized and the Bphase winding is powered. Finally, when the rotor is in the position shown in Fig. 16(c) (the rotor rotates 15 degrees again counterclockwise), the B-phase winding is de-energized and the C-phase winding is powered. The above-mentioned control is called the APC. However, in order to prevent the damage to the circuit resulting from too large phase current under heavyload conditions, the current chopping control (CCC), which is based on the APC, is used to limit the value of the phase current. Therefore, the phase current starting the CCC is much smaller than that controlled by the APC, which is shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001710_j.cja.2015.03.003-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001710_j.cja.2015.03.003-Figure4-1.png", "caption": "Fig. 4 Method to get the robot\u2019s A1 axis using a laser tracker.", "texts": [ " Because equalinterval cubic grid points are used, the optimum grid step is the primary parameter for the planning of sampling points. The robot coordinate system is located at the bottom of the robot. It is the reference coordinate system of the robot\u2019s mechanical structure. Because of the robot installation method and the restriction on the measuring range of the laser tracker (FARO SI), the robot coordinate system often cannot be directly measured in practice. The measurement software included in the laser tracker system can be used to establish the robot coordinate system by fitting as follows (see Fig. 4): Step 1: The robot is maneuvered to the mechanical zero position. Step 2: The base plane is determined. The base plane is located at the bottom of the robot. The SMR (spherically-mounted reflector) is placed on the installation plane of the robot through spatial scanning. As many points as possible are measured along the base of the robot for plane fitting. The base plane is obtained by offset of the fitted plane by the radius of the SMR. Step 3: The origin and the Z-direction of the robot coordinate system are determined" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003281_j.jmatprotec.2021.117139-Figure10-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003281_j.jmatprotec.2021.117139-Figure10-1.png", "caption": "Fig. 10. LMD laser power input plot for (a) long unidirectional raster scan, (b) bidirectional raster scan, (c) short unidirectional raster scan.", "texts": [], "surrounding_texts": [ "Journal of Materials Processing Tech. 294 (2021) 117139\nmeasurement. After the tensile tests, the specimens\u2019 fracture surface topologies were scanned using the Zeiss Smart Zoom 5, via a 3D depthof-focus reconstruction method using 34 times magnification with a 30 \u03bcm resolution. The specimens were sectioned at the grip length area, 30 mm away from the edge, and the sectioned surface was etched in a solution of 5% vol. nitric acid, 5% vol. hydrochloric acid, and 90 % vol. ethanol. The section location and measurement surface are illustrated in Fig. 6.\nMicrographs of the microstructure were captured using a Zeiss Light Microscope and characterised using Fiji software. To measure the grain size, the ASTM E112\u2212 13\u2019s Abrams Three-Circle procedure was used due to its suitability for measuring non-equiaxed grain structures, typically observed for LMD-built materials (ASTM, 2014). The results were then plotted against the yield strength from the tensile tests and correlated via the Hall-Petch relationship. The Hall-Petch relationship describes the correlation between microstructural grain size and yield stresses via the following equation (Kashyap and Tangri, 1995; Hansen, 2004):\n\u03c3y = \u03c30 + k \u0305\u0305\u0305 d \u221a (1)\nwhere \u03c3y is yield strength, \u03c30 is a material constant that governs the\nstresses for grain dislocation movement, k is the Hall-Petch slope coefficient, and d is the grain size. The Hall-Petch relationship generally describes how the yield strength of the material increases with decreasing microstructural grain size.\nSEM images were captured using Zeiss EVO SEM equipment and analysed with Inca software. Aztec software was further used to conduct Energy-dispersive X-ray spectroscopy (EDX) analysis. SEM was set at Backscatter Electron (BSE) mode, 300 times magnification, 9 mm working distance and an Extra High Tension (EHT) voltage level of 15 kV.\nSubsequently, micrographs of the deposition track body and fusion zones were captured using the Zeiss Light Microscope. Vickers micro hardness tests were conducted with accordance to ASTM E384\u2212 17 using an Innova Test Falcon 500 micro hardness tester (ASTM, 2016a,b). A micro-indentation load of 500 g and a 15 s dwell time were used at fusion zones and deposition track body locations.\nMelt pool characteristics were measured and recorded during the LMD process. Three individual melt pool image captures taken in 0.5 s intervals were modelled in a 3D heat map shown in Fig. 7. The heat map shows a distinctively steep thermal gradient toward the leading edge of the melt pool, and a more gradual thermal gradient toward the rear edge of the melt pool. This observation in the heat mapping is a result of the laser source\u2019s gaussian energy distribution that can be expressed using the double ellipsoid volumetric source heat input model (Goldak, Chakravarti et al. 1984). The model describes the heat source\u2019s power distribution as an expression of two ellipsoidal quadrants, where the front quadrant is steeper than the rear quadrant.\nFrom each sample\u2019s heat mapping, the melt pool size, melt pool temperature characteristics were measured and recorded. The process monitoring data was subsequently modelled respective to their XYZ coordinates and the laser power input as shown in Figs. 8\u201310. The mean melt pool temperature, melt pool size, and laser power input per deposition layer during the LMD process were graphed in Fig. 11. A high\nE. Tan Zhi\u2019En et al.", "Journal of Materials Processing Tech. 294 (2021) 117139\ndegree of melt pool homogeneity was achieved during LMD process as a result of the in-situ adjustment of the laser power input as seen in Figs. 8 and 9. The mean laser power input across the LMD build for each condition was 1440 \u00b1 45 W for the long unidirectional raster scan condition, 1304 \u00b1 55 W for the bidirectional raster scan condition, and 1330 \u00b1 77 W for the short unidirectional raster scan condition. To maintain a high degree of melt pool homogeneity, the laser power regulation for each condition varies widely, with the long unidirectional raster scan condition requiring approximately 8\u201310 % more energy input than the other two conditions.\nThe first deposition layer exhibited a lower melt pool temperature and smaller melt pool size due to the initial thermal conditions of the LMD process. The substrate\u2019s temperature at the point of the LMD initiation is cooler and hence requires a higher laser power input to achieve the necessary energy required to melt the deposited powder particles in the first deposition layer as seen in Fig. 11 (c). Beyond the first deposition layer, the heat energy and dissipation reaches a quasiequilibrium state that results in a consistent mean melt pool temperature and melt pool size as seen in Fig. 11 (a) and (b). Each new deposition layer\u2019s initiation point is located diagonally across the previous\nE. Tan Zhi\u2019En et al.", "Journal of Materials Processing Tech. 294 (2021) 117139\nlayer\u2019s initiation point. During the deposition head\u2019s translation to the new initiation point for the next layer, the previously deposited layer undergoes a significant cooling effect that necessitates a higher laser power input to achieve the target energy density. Furthermore, as more layers are deposited, lower laser power input is required for the LMD process due to the thermal energy build-up within the component body, that acts as a pre-heating element for each new layer that is deposited as seen in the decreasing laser power input reading from layer to layer in\nFig. 11 (c). The long unidirectional raster scan\u2019s pattern that runs longitudinally across the long edge of the LMD block that produces a longer interval from one raster deposition path to the next, compared to the short unidirectional raster scan. The longer interval allows the area adjacent to the deposition area to cool down significantly before the subsequent deposition path in the raster pattern is produced. Hence, a higher energy density in the laser input is required to compensate for this cooling effect that results in a higher laser input for the long\nE. Tan Zhi\u2019En et al." ] }, { "image_filename": "designv10_9_0003198_j.mechmachtheory.2020.103960-Figure9-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003198_j.mechmachtheory.2020.103960-Figure9-1.png", "caption": "Fig. 9. Deformations of 3(3RRlS 2 ) configuration under different actuation distributions.", "texts": [ " When the motions of all 3RRlS RPMs are given as follows: t oz = 50 mm , \u03d5 = 5 \u25e6, \u03b7 = 10 \u25e6, \u02d9 toz = 10 mm /s , \u02d9 \u03d5 = 1 \u25e6/s , \u02d9 \u03b7 = 3 \u25e6/s , \u0308oz = 1 mm / s 2 , \u03d5\u0308 = 1 \u25e6/ s 2 , and \u03b7\u0308 = \u22121 \u25e6/ s 2 , the deformations of the end platform are solved, as shown in Fig. 8 , where red lines represent Case 1; blue lines represent Case 2. The figures show that in the directions of six DOFs, the deformations of 3(3RRlS 2 ) configuration with three external loads are greater than that of 3(3RRlS 2 ) configuration with an external load. When the motions of all 3RRlS RPMs are given as follows: t oz = 30 mm , \u03d5 = \u03b7 = 0 , \u02d9 toz = 15 mm /s , \u02d9 \u03b7 = 6 \u25e6/s , \u03b7\u0308 = \u22121 \u25e6/ s 2 , the deformations are solved, as shown in Fig. 9 , where red lines represent 3(3RRlS 2 ) configuration with three actuators for each RPM; blue lines represent 3(2RRlS 2 -RRlS 1 ) configuration with three actuators for each RPM; green lines represent 3(2RRlS 2 - RRlS 1 ) configuration with two actuators for each RPM. In the directions of constrained DOFs, i.e., the displacement along Z-axis and the rotation around X-axis, the deformations of 3(3RRlS 2 ) configuration and 3(2RRlS 2 -RRlS 1 ) configuration which both have three actuators for each RPM are equal, but less than the deformation of 3(2RRlS 2 -RRlS 1 ) configuration with two actuators for each RPM" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001038_1350650116689457-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001038_1350650116689457-Figure4-1.png", "caption": "Figure 4. The subpanel and transducers arrangement: (a) sketch; (b) practicality picture.", "texts": [ "5mm depth, as shown in Figure 3(a). The grooves do not reach the outer raceway. Then, the cage is exposed to larger surface area, which ensures the eddy probes to transduce perfect motion signals of the cage as shown in Figure 3(b). The motions of the cage in radial directions are measured by two probes (yc, zc) installed in the bearing house 90 apart and in the corresponding grooves in the outer ring. The axial motions are also measured by the two probes (xc1, xc2), which are fixed on a panel (shown in Figure 4) and mounted parallel to the bearing axis, focused on the cage side face, 180 apart. The bearing test rig is established as shown in Figure 5, which consists of motor, coupling, rotating shaft, supporting and tested bearings, and load devices. The tested bearing is mounted on one side of the cantilever shaft. As shown in Figure 5, the bearing is applied in the radial and axial forces directly through the bearing house. On applying the moment to the bearing and the screw bolt, apart from the bearing axis, a certain distance (e" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002859_tmag.2020.3012193-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002859_tmag.2020.3012193-Figure6-1.png", "caption": "Fig. 6. Magnetic field distributions for different DC currents of the field winding when the armature winding is open-circuit.", "texts": [ " Hence, compared with traditional wound field flux modulated machine, the torque of the proposed DS-HPMVM can be improved by 43.0%. In addition, for machine II, the average torque is 4.08 Nm. Furthermore, Fig. 5 also shows the flux regulation capability of the DS-HPMVM. By controlling the DC current of the field winding with -3 A, 0 A and +10 A, respectively, the corresponding average torque of the DS-HPMVM can be regulated to 2.21 Nm, 4.08 Nm and 11.54 Nm, respectively. It demonstrates the DS-HPMVM has good flux regulation capability. The magnetic field distributions for different field currents are shown in Fig. 6. The armature winding is open-circuit. It shows the magnetic field distribution clearly varies when applying different DC currents of the field winding. For the case of flux weakening (-3A), the magnetic flux linkage in the stator is less. On the other hand, the magnetic flux linkage in the stator is much larger for the case of flux enhancing (+5 A), Hence, the results show that the flux regulation can be realized by controlling different DC currents of the filed winding. Fig. 7 shows the input voltage and current waveforms of phase A of the DS-HPMVM, Machine I and Machine II" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002894_tte.2020.3035180-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002894_tte.2020.3035180-Figure2-1.png", "caption": "Fig. 2. Circumferential integration of force harmonics.", "texts": [ " Therefore, the modulated radial force density can be expressed as cos( ) 2 cos(( ) ) ( > 2 , ) ( , ) v v v r v m m rv v Q p v t v Q p v kQ t v t t (16) where pm is the modulated radial force (N/m2), \u03c3v, \u03c9v and \u03c6v are the magnitude (N/m2), angular velocity (rad/s) and initial phase (rad) of the modulated radial force. The radial force on stator teeth can be equivalent to the concentration force, which can be obtained by circumferential integration of the force harmonics as shown in Fig. 2. Therefore, the modulated radial force on the stator teeth can be expressed as 2 , - 2 2 2 2 2 cos + , 2 = cos ( ( ) ( , ) + , 2 ) q q q q q q r q is r v v is r v v mF d Q LR v t d v Q LR v kQ t d v t p t (17) where Fr,q is the concentration force (N), \u03b8q is the angle of the qth stator tooth (rad), \u0394\u03b8 is the tooth pitch (rad), L is the stack length (m), and Ris is the inner radius of stator (m). Due to the limitation of the motor stator teeth number, the high-order radial forces acting on the stator teeth surface will be modulated to the low-order ones" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001159_0959651814525371-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001159_0959651814525371-Figure1-1.png", "caption": "Figure 1. Geometry of air-breathing hypersonic vehicle.", "texts": [ " Last but not the least, the upper bound of uncertainties is not required to be known in advance. Adaptive law is designed to estimate the upper bound, and the robustness is ensured at the same time. The nonlinear equations of motion of FAHV used in this study are taken from Williams et al.39 The descriptions of the coefficients that are derived using curvefitted approximations are according to Bolender.40 This model is called CFM for FAHV and only utilized for simulation. A longitudinal sketch of the vehicle geometry showing the location of the control surfaces is given in Figure 1 and referred from Sigthorsson and Serrani.41 The longitudinal dynamic equations of a FAHV that describe velocity, altitude, FPA, angle of attack (AOA), pitch rate and flexible modes are given as _V= T cosa D m g sing \u00f01\u00de _h=V sin g \u00f02\u00de _g = L+T sina mV g cosg V \u00f03\u00de _a=Q _g \u00f04\u00de _Q= Myy Iyy \u00f05\u00de \u20achi = 2jivi _hi v2 i _hi +Ni, i=1, 2, 3 \u00f06\u00de In equations (1)\u2013(6), thrust T, drag D, lift L, pitching moment Myy and three generalized forces N1, N2 and N3 are complex algebraic functions of both the system states and inputs, and they must be simplified to render the model analytically tractable" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002022_978-3-319-40036-5-Figure2.22-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002022_978-3-319-40036-5-Figure2.22-1.png", "caption": "Fig. 2.22 Device for the stacking lateral flow immunoassay; (a) The exploded view of the device. The test assembly consists of a sample pad, a reagent pad, a flow regulator, a test strip and an absorbent pad. The test assembly is housed in the cassette; (b) The assembled stacking flow device; (c) Photograph of the stacking flow device prototyped with a 3D printer (Reproduced from Yi et al. [74] with permission from the Royal Society of Chemistry)", "texts": [ " But major limitation of salivary fluid as a sample is that it cannot be applied directly to commercially available lateral flow test strips because it causes the non-specifically binding of conjugated particles to the nitrocellulose membrane. To overcome this problem, Yi et al. [65] recently developed a rapid test for the detection of anti-DENV IgG in saliva. They introduced samples and reagent in separate flow paths. The sample flowed through a matrix of fiber glass which reduces the non-specific adhesion caused by the salivary substances. Figure 2.22 shows the design of device for dengue detection. The device gave good results in saliva samples spiked with IgG but requires further improvement to detect IgG extracted directly from the blood of dengueinfected patients. To improve the sensitivity (It is the ability of a paper based assay test to correctly recognize patients who have a given disease or disorder.) and 2 Microfluidics Overview 59 specificity (It is the ability of a paper based assay test to correctly exclude the healthy individuals) of the dengue detection, a methodology has been developed which combines reverse transcription loop-mediated isothermal amplification (RT-LAMP), paper based device and fluorescence based colorimetric detection [74]" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003479_0954407021999483-Figure9-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003479_0954407021999483-Figure9-1.png", "caption": "Figure 9. Details of tread wear for: (a) no wear and (b) wear 2 mm.", "texts": [ " The reason is that as the load gradually increases, the amplitude of the increase in vibration frequency gradually decreases, and when the load increases to a certain value, the stiffness of the tire increases and decreases, or even no longer increases. Influence of tread wear on tire modal In this section, the tire inflation pressure is 0.24MPa and the load is 0N. The tread thickness of the tire used in the simulation in this paper is 8mm. Assuming that the tire is uniformly worn, the wear simulations are no wear, 2mm, 4mm, and 6mm, respectively. The details of the model tread with no wear and 2mm wear are shown in Figure 9, and the other two wear amount tread details are not given. As in the previous section, this time only the influence of tread wear on the tire radial increase frequency is analyzed. The results are shown in Figure 10. It can be seen from Figure 10 that the radial increase frequency of the tire increases with the increase of the tire wear amount, and the natural frequency discrimination between different wear amounts is obvious. This is because the wear of the tire tread causes the total mass of the tire to decrease, and therefore the natural frequency of the tire increases" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003397_j.mechmachtheory.2021.104476-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003397_j.mechmachtheory.2021.104476-Figure1-1.png", "caption": "Figure 1. Parameters relating to basic rack tooth profile in normal section", "texts": [ " ZH zone factor ZE elasticity factor ZNT life factor Z\u03b5 contact ratio factor Z\u03b2 helix angle factor \u03b1n pressure angle (degree) \u03b5\u03b1 transverse contact ratio \u03b5\u03b3 overlap ratio \u03b51,2 addendum contact ratio, pinion/wheel \u03b2 helix angle (degree) \u03b2b helix angle at base circle (degree) \u0394l strip width (mm) \u03b4ij Tooth deflection at contact point \u03c1 density of gears (kg/mm3) \u03c1fP root radius coefficient \u03b7oil dynamic viscosity of oil operating temperature (\u25e6C) \u03c3H contact stress (MPa) \u03c3Hlim nominal stress number of contact (MPa) \u03c3HP permissible contact stress (MPa) \u03c3F bending stress (MPa) \u03c3Flim nominal stress number of bending (MPa) \u03c3FP permissible bending stress (MPa) \u03bcmZ mean coefficient of friction of the gear mesh \u03b7M lubricant viscosity (mPa\u2219s) \u03c61 roll angle from the tooth center to the tangent of the base circle C. Choi et al. Mechanism and Machine Theory 166 (2021) 104476 Figure 1 shows a basic rack tooth profile defined by ISO 53 and a standard cross-sectional tooth profile of an external gear where the number of teeth and the radius have infinite values. In line P - P of the basic rack tooth profile, the tooth thickness and the space-width are the same. The distance from line P - P to the tooth top line is defined as the addendum (haP), whereas the distance from line P-P to the tooth root line is defined as the dedendum (hfP). Moreover, the clearance between the basic and the mating basic rack tooth is defined as the bottom clearance (Cp)" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000559_1.4731663-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000559_1.4731663-Figure1-1.png", "caption": "FIG. 1. (a) Statistical model of an azobenzene elastomer. Each network strand consists of N freely jointed rod-like Kuhn segments bearing Nch azobenzene chromophores in side chains. (b) Orientation structure of azobenzene chromophores inside a Kuhn segment.", "texts": [ " III, the light-induced deformation of azobenzene elastomers is calculated and the results obtained in the framework of the three introduced network models are compared. In Sec. IV, the effects of the molecular weight distribution of network strands on the light-induced deformation are discussed. In Sec. V, the light-induced bending is calculated and compared with experimental data. An azobenzene elastomer is modeled as an ensemble of monodisperse polymer chains between network junctions (network strands). Each network strand consists of N freely jointed rod-like Kuhn segments (see Figure 1(a)). Thus, in the framework of this chain model the effects of finite extensibility of network strands are explicitly taken into account. Each Kuhn segment contains Nch azobenzene chromophores which are covalently attached to it (Figure 1(b)). An orientation structure of the chromophores inside the Kuhn segments is characterized by the orientation distribution function, W (\u03b1, \u03b2). Here, \u03b1 is the angle between the long axis of a chromophore and a Kuhn segment; the angle \u03b2 characterizes an azimuthal rotation of chromophores around the long axis of a Kuhn segment (Figure 1(b)). Short fragments of polymer molecules bearing azobenzene chromophores possess, as Downloaded 10 Aug 2012 to 128.148.252.35. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissions a rule, a planar symmetry.39\u201341 Thus, the Kuhn segments of network strands can be considered as symmetric objects and the azimuthal angle \u03b2 is introduced as the angle between the plane of symmetry of the Kuhn segment and the plane formed by the long axis of the chromophore and by the long axis of the Kuhn segment (Figure 1(b)). Varying the form of the function W (\u03b1, \u03b2), we can describe both the main-chain azobenzene elastomers (when \u03b1 = 0 for all chromophores) and the side-chain azobenzene elastomers. In the latter case, the function W (\u03b1, \u03b2) is defined by the potentials of internal rotations and by the length of spacers connecting the chromophores with the main chains. As a rule, one uses the spacers with symmetrical potentials of internal rotation, e.g., polyethylene\u2019s spacers.3, 4, 35\u201338 Due to the symmetry of the spacers, the orientation distribution of chromophores inside the Kuhn segments is symmetrical and obeys the following relations: W (\u03b1, \u03b2) = W (\u03b1,\u2212\u03b2) and W (\u03b1, \u03b2) = W (180\u25e6 \u2212 \u03b1, \u03b2)", "17\u201321, 42 Since the interaction of chromophores with the light is determined only by the angle and is independent of the rotation of chromophores around their long axes, the chromophores are considered below as axially symmetric rod-like objects. Under the influence of the orientation potential (1), each Kuhn segment reorients and an azobenzene elastomer changes its shape. Due to an axial symmetry of the problem, the elastomer demonstrates a uniaxial deformation along the electric vector of the light E. We assume that the vector E is directed along the x-axis (see Figure 1); \u03bb is the elongation ratio of a sample along the x-axis. To calculate the dependence \u03bb(V0), we use a spherical approximation in which the average positions of the end-to-end vectors of network strands in an isotropic azobenzene elastomer at the absence of any external stimuli are assumed to be distributed on a surface of a sphere with the radius |b| = l \u221a N , see Figure 2(a). The value |b| = l \u221a N is the mean-square end-to-end distance of a freely jointed chain consisting of N rod-like Kuhn segments" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000990_j.mechmachtheory.2013.05.006-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000990_j.mechmachtheory.2013.05.006-Figure3-1.png", "caption": "Fig. 3. Relative positions of roller slices to inner and outer raceways. a) Roller slice and outer ring. b) Roller slice and inner ring.", "texts": [ " 2, and the transformation matrix from the coordinate system of roller j to the fixed coordinate system is: Tia \u00bc 1 0 0 0 cos \u03b8j sin \u03b8j 0 \u2212 sin \u03b8j cos \u03b8j 2 4 3 5 cos\u03d5j 0 sin\u03d5j 0 1 0 \u2212 sin\u03d5j 0 cos\u03d5j 2 4 3 5 cos \u03c8j sin \u03c8j 0 \u2212 sin \u03c8j cos \u03c8j 0 0 0 1 2 4 3 5 \u00bc cos\u03d5j cos \u03c8j cos\u03d5j sin \u03c8j sin\u03d5j \u2212 sin \u03c8j cos \u03b8j\u2212 sin\u03d5j cos \u03c8j sin \u03b8j cos \u03c8j cos \u03b8j\u2212 sin\u03d5j sin \u03c8j sin \u03b8j cos\u03d5j sin \u03b8j sin \u03c8j sin \u03b8j\u2212 sin\u03d5j cos \u03c8j cos \u03b8j \u2212 cos \u03c8j sin \u03b8j\u2212 sin\u03d5j sin \u03c8j cos \u03b8j cos\u03d5j cos \u03b8j 2 4 3 5 \u00f02\u00de Where, \u03b8j is the azimuthal angle of roller j. \u03d5j and \u03c8j are tilt angle of roller j round its y-axis and skew angle of roller j round its z-axis respectively. Relative positions between rollers and raceways in tilted rings are shown in Fig. 3. obxbybzb is the azimuthal coordinate system of the roller. Where, the origin o is at the center of the roller, x-axis is along the axial direction of the roller, z-axis is along the direction from the center of outer ring to the center of rollers, y-axis is determined by the right hand rule. Slicing rollers perpendicular to the axis, positions of these slices are determined by the azimuthal angle of rollers in fixed coordinate system and the location of slices in roller coordinate system. The position of slice k in roller j is represented as: \u03941jk b \u00bc Tia T \u22c5 x1k y1k R1\u00bd T\u2212 Tia T \u22c5 0 rj sin\u03b8j rj cos\u03b8j \u00fe xk 0 Dw=2\u00bd T \u03942jk b \u00bc Tia T \u22c5 0 rj sin\u03b8j rj cos\u03b8j \u00fe xk 0 \u2212Dw=2\u00bd T \u2212Tia T \u22c5Tir T \u22c5 x2k y2k R2\u00bd T \u00f03\u00de Where, R1, R2 and rj are the distance from outer raceway, inner raceway and roller j to the center of bearings respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002606_s00170-019-04141-y-Figure15-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002606_s00170-019-04141-y-Figure15-1.png", "caption": "Fig. 15 3D models of the component. a Entity visualization. b Contour line visualization. c Uneven parallel slicing method", "texts": [ "808 kg/h, and MU increased from 88.51 to 92.71%. This is particularly beneficial to reduce post-processing and improve effective deposition rate. Although raising the WFS helps to improve these process output attributes, more slicing layers are needed due to a smaller block height. Additionally, higher WFS would lead to severe distortion of the final parts, thus the process parameters should be reasonably planned according to different optimization criteria. Regarding the geometrical features of the component (seen in Fig. 15), the geometry shape of cross section transforms from circle to irregular pentagon along with the constantly changing building direction. Generally, this kind of component is considered difficult to fabricate using traditional process planning method due to the inconsistent layer thickness along building direction. One layer was extracted from the 3D model as a case layer to plan the blocks, as shown in Fig. 15c. In order to show the capability of unit block on controlling the output attributes, the parameter solution No. 1 and No. 20 were selected from Fig. 13, and the corresponding dimensional and output attributes were listed in Table 7. Two planning strategy were shown in Fig. 16, and the corresponding description was drawn as follows: Case I: The minimumHblock (1.12mm) was used at vertical side (marked with red line and \u03b1 = 90\u00b0), the inclined walls number 1 3.3 0.353 9.35 6 1.95 407.9 0.488 88.51 20 5" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003139_tbme.2020.3046513-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003139_tbme.2020.3046513-Figure2-1.png", "caption": "Fig. 2. Design and fabrication of GHM. (a) Structural design of the GHM. (b) 3D-printed GHM. (c) Scanning electron microscopy image of the main body. Scale bar: 1 mm.", "texts": [ " The GHM can achieve mechanical revascularization via drilling as well as steering and propelling against the strong blood flow in vessels. We demonstrate the performance of the GHM in rats with artificial blockages mimicking the CTO in humans. The paper is organized as follows. Section II presents design and fabrication of the GHM. Section III presents the control strategy and the performance validation in both in-vitro and invivo environments are shown in Section IV. Section V provides conclusions and future works for further clinical applications. II. DESIGN AND FABRICATION OF GHM Fig. 2(a) presents the structure of the GHM, and Fig. 2(b) depicts the fabricated prototype and a scanned electron microscopic image of the main body. Considering the physiological coronary artery size (normally varying between 1.6 mm and 4.5 mm [44]), the body diameter of the GHM was designed to be 1.6 mm. The GHM could be inserted into small vessels through a commercially available catheter. The spiralshaped main body of the helical microrobot includes an inner space to fix a cylindrical permanent magnet (NdFeB, N52, JL magnet, Korea), which can interact with the external electromagnetic actuator", " The spherical joint resulted in two free rotations along with both axial and colatitude directions simultaneously. The axial directional rotation along with the robot body length enabled helical rotations with respect to the fixed guidewire, which was eventually performed for drilling into the thrombus. The colatitude directional rotation perpendicular to the axial direction of the robot provided free bending between the tip and guidewire, which enabled the GHM to steer toward the desired direction. The maximum free bending angle, \u03c6, was set to 10\u00b0, as shown in Fig. 2(a). The guidewire resulted in a stronger resisting force against blood flow while approaching the target thrombus. This ultimately led to stable robot motion as well as easy and safe retrieval of the device after completion of the procedure. Table 1 summarizes the geometric parameters of the designed GHM. The components of the GHM, including the helical shaped body, a ball housing, and a spherical joint, were designed with computer-aided design software (Solidworks, Dassault Syst\u00e8mes, USA) and constructed using a photopolymer jetting 3D printer (Object Eden260VS, Stratasys, USA) with a transparent material (VeroClear-RGD810, Stratasys, USA)" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000182_j.mechmachtheory.2011.04.011-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000182_j.mechmachtheory.2011.04.011-Figure1-1.png", "caption": "Fig. 1. A set Z with local dimensions: dimA Z=1, dimB Z=dimC Z=2.", "texts": [ "] Similarly, away from the origin, we have a biholomorphism between Z2 and C2 given by the maps \u03d52 : x; y; z\u00f0 \u00de\u21a6 x; y\u00f0 \u00de; \u03c82 : x; y\u00f0 \u00de\u21a6 x; y;0\u00f0 \u00de: Neither of these pairs of maps covers all the points in the neighborhood of the origin, (0, 0, 0), where the two components Z1 and Z2 meet. The origin is singular while all other points of Z are smooth. The local dimension at two of the smooth points is: dim(0,0,1)Z=1 and dim(1,1,0) Z=2. The origin has neighbors in Z1 and in Z2, so the local dimension at the origin is the greater of these two: dim(0,0,0) Z=2. Fig. 1 illustrates a related example, where Z consists of a surface and a curve, each nonlinear. In Example 3.1, it is easy to write down maps that establish the local dimension at smooth points, but in general, this is not so simple. However, there is one frequently occurring situation where local dimension is easy to establish, as stated in the following well-known proposition. For a system of m analytic functions in N variables, f x1;\u2026; xN\u00f0 \u00de = f1;\u2026; fmf g : CN\u2192Cm, we denote the m\u00d7N Jacobian matrix of f as df, having elements dfij=\u2202fi/\u2202xj" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002339_s10846-018-0884-7-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002339_s10846-018-0884-7-Figure2-1.png", "caption": "Fig. 2 Joint angles and link frames of the robotic arm", "texts": [ " With reference to the system shown in Fig. 1, we have the world-fixed reference frame CW , the body-fixed frame CB with origin at the center of mass of the coaxial tricopter, and the frame CE attached to the end-effector of the robotic arm. The position of the coaxial tricopter with respect to CW is described by the vector pB = [x y z]T \u2208 R 3\u00d71, its attitude is denoted by the Euler angles B = [\u03c6 \u03b8 \u03c8]T \u2208 R 3\u00d71, while the joints angles of the robotic arm are defined by the vector = [\u03b81 \u03b82 \u03b83 \u03b84]T \u2208 R 4\u00d71 (see Fig. 2). Hence, the generalized coordinate variables can be expressed by the vector q = [pT B T B T ]T \u2208 R 10\u00d71. The position and orientation of end-effector with respect to CW can be written as [2]{ pE = pB + RBpB E, RE = RBRB E, (1) where RB is the rotation matrix describing the orientation of CB relative to CW , while RB E and pB E are the orientation and position of CE with respect to CB , respectively. Let p\u0307B and p\u0307B B denote the linear velocity of the coaxial tricopter described in CW and CB , respectively, while its angular velocity with respect to CW and CB are expressed as \u03c9B = [\u03c9x \u03c9y \u03c9z]T \u2208 R 3\u00d71 and \u03c9B B = [\u03c9B x \u03c9B y \u03c9B z ]T \u2208 R 3\u00d71, respectively", " As for the linear and angular velocities of the end-effector described in CW , they are obtained by the differentiation of (1){ p\u0307E = p\u0307B \u2212 S(RBpB E)\u03c9B + RBp\u0307B E, \u03c9E = \u03c9B + RB\u03c9B E, (3) where S(*) is the skew-symmetric matrix operator in SO(3) [48], while p\u0307B E and \u03c9B E are the linear and angular velocities of the end-effector expressed in CB , respectively. In the following section the dynamics of the entire system will be determined. Hence, it is worth introducing the coordinate frame for each link of the robotic arm. The origin of the frames is placed at the center of mass of the corresponding links as shown in Fig. 2. Then, we can denote the position of the center of mass of the link i described in CW and CB as pLi and pB Li , respectively, and show that they are related in the following manner (i = 1, 2, 3, 4) pLi = pB + RBpB Li . (4) Furthermore, in [47] the following relationship are considered{ p\u0307B Li = J Li P1 \u03b8\u03071 + J Li P2 \u03b8\u03072 + J Li P3 \u03b8\u03073 + J Li P4 \u03b8\u03074 = J Li P \u0307, \u03c9B Li = J Li O1 \u03b8\u03071 + J Li O2 \u03b8\u03072 + J Li O3 \u03b8\u03073 + J Li O4 \u03b8\u03074 = J Li O \u0307, (5) where p\u0307B Li and \u03c9B Li are the linear and angular velocities of the i-frame of the robotic arm expressed in CB , while J Li O and J Li P are the contribution of the Jacobian columns to the velocity of joints up to the link i" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000329_1.4003180-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000329_1.4003180-Figure2-1.png", "caption": "Fig. 2 T2R1-type parallel manipulator with uncoupled and bifurcated spatial motion of the moving platform: \u201ea\u2026 constraint singularity and \u201e\u201eb\u2026 and \u201ec\u2026\u2026 branches with spatial motion; limb topology P P \u00b8R R-P \u00b8R P \u00b8R R-P \u00b8R \u00b8RS", "texts": [], "surrounding_texts": [ "w b\nw\n\u2190 E r d n c W r a\np\n3\nc p i t m W c f t s o v v\nb p\nJ\nDownloaded Fr\nEquations 1 \u2013 6 are suitable for any parallel mechanism, in hich no joint belongs to more than one limb. This condition can e expressed by\np = j=1\nk\npGj 7\nhere pGj is the number of joints of jth limb. In a singular configuration of the parallel mechanism F G1-\u00af -Gj-\u00af -Gk, at least one of the structural parameters in\nq. 5 is instantaneously altered. We denote by an anterior supeior index i the instantaneous values of the structural parameters efined above and associated with the constraint singularity. We ote that, in general, any structural parameter used in Eqs. 1 \u2013 6 an be affected by singular configurations excepting f j and q. hen the anterior superior index i is missing, the structural paameters in Eqs. 1 \u2013 6 define the full-cycle values characterizing n entire branch.\nThe following steps can be used for the calculation of structural arameters of a parallel mechanism based on formulas 1 \u2013 7 .\nStep 1: Identify the total number of links m including the fixed base and the moving platform and the total number of joints p in the parallel mechanism. Step 2: Calculate the number of independent closed loops q in the parallel mechanism, q= p\u2212m+1. Step 3: Determine the number of limbs k connecting the moving platform to the fixed base such that no joint belongs to more than one limb and check Eq. 7 . Step 4: Identify the basis of RGj j=1,2 , . . . ,k by observing the independent motions between distal link nGj and 1Gj in the kinematic chain associated with the Gj-limb disconnected from the parallel mechanism. Step 5: Calculate the connectivity between distal links nGj and 1Gj in the kinematic chain Gj disconnected from the parallel mechanism, SGj =dim RGj . If necessary, calculate the rank of the forward velocity Jacobian JGj of the Gj-limb disconnected from the parallel mechanism, SGj =rank JGj . Step 6: Calculate the connectivity between the distal links n nGj and 1 1Gj in the parallel mechanism given by Eq. 4 . Step 7: Determine the number of joint parameters that lose their independence in the closed loops that may exist in each limb. Step 8: Calculate the total number of joint parameters that lose their independence in the closed loops that may exist in the limbs of the parallel mechanism given by Eq. 6 . Step 9: Calculate the total number of joint parameters that lose their independence in the parallel mechanism given by Eq. 5 . Step 10: Calculate mobility MF, number of overconstraints NF, and redundancy TF of the parallel mechanism given by Eqs. 1 \u2013 3 .\nBifurcation in Constraint Singularities The term of constraint singularity CS have been recently oined 30 to characterize the configuration of lower mobility arallel manipulators in which both the connectivity of the movng platform and the mobility of the parallel mechanism increase heir instantaneous values. From a constraint singularity, the\nechanism can escape by branching or without branching 31 . hen branching occurs in a constraint singularity, the mechanism\nan reach different configurations, called branches, and have diferent independent motions of the moving platform. In this case, he constraint singularity is also called branching or bifurcation ingularity. A branch refers to a free-of-singularity configuration f the mechanism in which each structural parameter keeps its alue in the entire workspace of the branch. For this reason, this alue is called global or full-cycle value for a branch.\nTwo types of branching in constraint singularity BCS have een defined in Ref. 31 . Branching of type BCS1 occurs when a arallel mechanism F\u2190G1-\u00af -Gj-\u00af -Gk escapes from a con-\nournal of Mechanisms and Robotics\nom: http://mechanismsrobotics.asmedigitalcollection.asme.org/ on 06/13/2\nstraint singularity in different branches characterized by the same mobility and the same connectivity of the moving platform but with different bases of the vector space of relative velocities between the moving and fixed platforms. Branching of type BCS2 occurs when a parallel mechanism F\u2190G1-\u00af -Gj-\u00af -Gk escapes from a constraint singularity in different branches characterized by distinct values of mobility and connectivity of the moving platform. The parallel manipulators presented in this paper have constraint singularities with branching of type BCS1. Branching of type BCS2 occurs in kinematotropic mechanisms 32\u201335 .\nThe finite displacements and the velocities in the actuated joints are denoted by qi and q\u0307i, the linear velocities of the characteristic point H situated on the moving platform by v1= x\u0307 and v2= y\u0307, and the angular velocity of the moving platform by = = \u0307 or\n= = \u0307. In both branches, the moving platform undergoes a spatial motion consisting of two planar translations and one rotation around an axis lying in the plane of translation. In one branch, the axis of the angular velocity = = \u0307 is parallel to the x0-axis and\nin the other branch = = \u0307 is parallel to the y0-axis. With these notations, the linear mapping between the actuated joint velocity space and the end-effector velocity space for a branch of the T2R1-type PMs is defined by\nv1\nv2\n= J q\u03071\nq\u03072 q\u03073 8\nwhere J is the forward velocity Jacobian matrix. In Secs. 4 and 5, we will show that in the bifurcation singularity, the T2R1-type parallel manipulators proposed in this paper have instantaneously iMF= iSF=4 and iRF = v1 ,v2 , , . The bifurcation in this constraint singularity can be used to change the motion type of the moving platform. In the two distinct branches, the parallel mechanism is characterized by MF=SF=3 and RF = v1 ,v2 , or RF = v1 ,v2 , . In the constraint singularity, both connectivity of moving platform and mobility of parallel manipulator increase their instantaneous values. More details about the behavior of parallel manipulators in a constraint singularity and the associated structural parameters can be found in Ref. 31 .\n4 Solutions With Uncoupled and Bifurcated Motion To simplify the notations of the links eGj j=1, 2, 3, and e =1, . . . ,n by avoiding the double index in Fig. 1, we have denoted by eA the elements belonging to limb G1 eA eG1 by eB, and eC the elements of limbs G2 eB eG2 and G3 eC eG3 .\nThe moving platform 6 of the parallel manipulators F \u2190G1-G2-G3 with uncoupled motions in Figs. 1 and 2 is connected to fixed base 1 by three simple limbs actuated by three linear motors mounted on the fixed base. No closed loops exist inside a simple limb, that is irl=rl=0. Just revolute R, prismatic P, and spherical S joints are used in these solutions, in which two consecutive revolute and prismatic joints have parallel or perpendicular axes/directions. The notation in P P R R indicates that the axis of the first revolute joint is perpendicular to the direction of the second prismatic joint and parallel to the direction of the first prismatic joint. The first prismatic joint of each limb is actuated underlined joint . The directions of the actuated joints in the three limbs are reciprocally orthogonal.\nThe limbs isolated from the parallel mechanisms in Figs. 1 and 2 have the following degrees of connectivity: SG1=4, SG2=5, and SG3=6. In the configuration associated with bifurcation singularity in diagram a Figs. 1 and 2 , vector spaces iRGj have the following bases: iRG1 = v1 ,v2 , , , iRG2 = v1 ,v2 ,v3 , , , and iRG3 = v1 ,v2 ,v3 , , , . In this configuration, Eq. 4 gives iSF=4 with iRF = v1 ,v2 , , . The moving platform has instantaneously four independent motions two translations\nFEBRUARY 2011, Vol. 3 / 011010-3\n014 Terms of Use: http://asme.org/terms", "a s t l l\nF f s t\n0\nDownloaded Fr\nnd two rotations and the PM has instantaneously the following tructural parameters: iMF=4, iNF=1, and iTF=0, given by Eqs. 1 \u2013 3 . This bifurcation occurs when q3=0. In this configuration, he rotation axes of the two last revolute joints of limbs G1 and G2 ie in the same plane. The axes of the last revolute joint of the G2\nig. 1 T2R1-type parallel manipulator with uncoupled and biurcated spatial motion of the moving platform: \u201ea\u2026 constraint ingularity and \u201e\u201eb\u2026 and \u201ec\u2026\u2026 branches with spatial motion; limb opology P P \u00b8R R-P \u00b8R \u00b8R \u00b8R R-P \u00b8R \u00b8RS\nimb and the last but one revolute joint of the G1 limb coincide.\n11010-4 / Vol. 3, FEBRUARY 2011\nom: http://mechanismsrobotics.asmedigitalcollection.asme.org/ on 06/13/2\nThe PMs can escape from this constraint singularity by bifurcating in one of the two branches presented in diagrams b and c see Figs. 1 and 2 . The bifurcation in constraint singularity can be used to change the motion type of moving platform 6. To achieve this change, one of the last revolute joints of the G1- or G2-limb has to be instantaneously locked up when the moving platform\npasses through constraint singularity. By locking up the last revo-\nTransactions of the ASME\n014 Terms of Use: http://asme.org/terms", "l b G s a\nf v g m =\nf v g m =\nc t z d\nw f\n5 t\nu p g o a p w a m e r\n4 S l f t i t f b t o s o i\nJ\nDownloaded Fr\nute joint of the G1-limb, the parallel mechanism goes in the ranch with spatial motion of the moving platform in diagram b Figs. 1 and 2 . By locking up the last revolute joint of the\n2-limb, the parallel mechanism works in the branch with the patial motion of the moving platform in diagram c see Figs. 1 nd 2 .\nThe branch in diagram b Figs. 1 and 2 is characterized by the ollowing parameters: RG1 = v1 ,v2 , , , RG2 = v1 ,v2 , 3 , , , and RG3 = v1 ,v2 ,v3 , , , . Equation 4 ives SF=3 and RF = v1 ,v2 , . In this branch, the parallel echanism has the following structural parameters: MF=3, NF 0, and TF=0, given by Eqs. 1 \u2013 3 . The solutions in diagram b Figs. 1 and 2 are not overconstrained NF=0 . The branch in diagram c Figs. 1 and 2 is characterized by the ollowing parameters: RG1 = v1 ,v2 , , , RG2 = v1 ,v2 , 3 , , , and RG3 = v1 ,v2 ,v3 , , , . Equation 4 ives SF=3 and RF = v1 ,v2 , . In this branch, the parallel echanism has the following structural parameters: MF=3, NF 0, and TF=0, given by Eqs. 1 \u2013 3 . The solutions in diagram c Figs. 1 and 2 are not overconstrained NF=0 . We note that independent linear velocities v1, v2, and v3 of haracteristic point H and angular velocities , , and of he moving platform have directions parallel to the x0-, y0-, and 0-axes of the reference frame. For the parallel manipulator in iagrams b and c Figs. 1 and 2 , Eq. 8 becomes\nv1\nv2\n= 1 0 0 0 1 0\n0 0 1 r1 cos q\u03071 q\u03072 q\u03073 9\nhere r1=HG=HK defines the dimensions of the moving platorm and = for the solution in diagram b Figs. 1 and 2 and = for the solution in diagram c Figs. 1 and 2 .\nMaximally Regular Solutions With Bifurcated Spaial Motion\nMaximally regular solutions can be derived from the PM with ncoupled motions in Figs. 1 and 2 by replacing the actuated rismatic joint with translational motion q3 by a planar paralleloram loop Pa of type R R R R Figs. 3 and 4 . A revolute joint f the parallelogram loop is actuated and q3 represents its rotation ngle. If r1=HG=HK=MN, the Jacobian matrix of linear maping Eq. 8 of the parallel manipulators in diagrams b and c Figs. 3 and 4 is the 3 3 identity matrix throughout the entire orkspace. A one-to-one correspondence exists between the actuted joint velocity space and the operational velocity space of the oving platform v1= q\u03071, v2= q\u03072, and = q\u03073 . Three joint paramters lose their independence in the planar parallelogram loop l G3=3 and Eq. 6 gives rl=3.\nThe limbs isolated from the parallel mechanisms in Figs. 3 and have the following degrees of connectivity: SG1=4, SG2=5, and\nG3=6. In the configuration associated with the constraint singuarity in diagram a Figs. 3 and 4 , the vector spaces iRGj have the ollowing bases: iRG1 = v1 ,v2 , , , iRG2 = v1 ,v2 ,v3 ,\n, , and iRG3 = v1 ,v2 ,v3 , , , . In this configuraion, Eq. 4 gives iSF=4 with iRF = v1 ,v2 , , . The movng platform has instantaneously four independent motions two ranslations and two rotations and the PM has instantaneously the ollowing structural parameters: iMF=4, iNF=4, and iTF=0, given y Eqs. 1 \u2013 3 . This constraint singularity occurs when q3=0. In his configuration, the rotation axes of the two last revolute joints f limbs G1 and G2 lie in the same plane as in the counterpart olutions in Figs. 1 and 2. One of the last revolute joints of the G1r G2-limb has to be instantaneously locked up, as in the solutions n Figs. 1 and 2, when the moving platform passes through the\nournal of Mechanisms and Robotics\nom: http://mechanismsrobotics.asmedigitalcollection.asme.org/ on 06/13/2\nconstraint singularity diagram a Figs. 3 and 4 for bifurcating into one of the two branches in diagrams b and c Figs. 3 and 4 .\nThe branch in diagram b Figs. 3 and 4 is characterized by the following parameters: RG1 = v1 ,v2 , , , RG2 = v1 ,v2 ,\nv3 , , , and RG3 = v1 ,v2 ,v3 , , , . Equation 4\nFEBRUARY 2011, Vol. 3 / 011010-5\n014 Terms of Use: http://asme.org/terms" ] }, { "image_filename": "designv10_9_0002769_s00170-019-03847-3-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002769_s00170-019-03847-3-Figure4-1.png", "caption": "Fig. 4 Schematic illustration of the sample geometry printed", "texts": [ " Since Ti-5553 is classified as a metastable \u03b2 titanium alloy, no martensitic transformation is expected to occur [19]. In addition, Fig. 3(b) illustrates the X-ray diffraction (XRD) pattern of the feedstock Ti-5553 powder. It is found that the Ti-5553 powder is mainly composed of \u03b2 phase which was expected due to the high cooling rate of the plasma atomization process. In order to investigate the printability of the Ti-5553 powder, 27 cylindrical samples, with a diameter of 10 mm and a Element wt.% Cumulative mass Diameter (\u03bcm) height of 15 mm, were printed using a Renishaw AM400 machine. As shown in Fig. 4, a cone-shaped design was used at the bottom of the samples as the support. After detachment of the samples from the build plate, an IsoMet 1000 precision cutter (Buehler) was used to cut the support from the samples. The cut plane is highlighted in Fig. 4. It is essential to optimize the heat input to develop a print recipe for a new material. One can express the heat input by VED which is defined as the average energy transferred to a volume of material. The VED range chosen in this study covers a comprehensive range varying from 21 J/mm3 to 584 J/mm3. In this research, VED is calculated as follows: VED \u00bc P vdl \u00f01\u00de where P is the laser power, v is the laser scan speed, d is the laser spot diameter (70 \u03bcm), and l is the layer thickness. Scanning speed can also be defined as: v \u00bc pd et \u00f02\u00de where pd is the point distance (which is the distance between the centers of the successive melt pools) and et is the exposure time (which is the length of time that the laser is on for each point)" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001824_0954406217693659-Figure13-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001824_0954406217693659-Figure13-1.png", "caption": "Figure 13. Photograph of the experimental system.", "texts": [ " Testing spindle can assemble multiple configurations of bearings. A high-precision axial loading measurement device consisting of the axial displacement measurement system, load device module, force measurement system, flexible rod, and data acquisition system; the measurement of axial displacement including target record disk and three eddy current displacement sensors. The axial loading is applied by the rotating screw, then the force can be calculated accurately. The photograph of the experimental system is shown as in Figure 13. The pre-load force and stiffness of the spindle are measured by pre-load force measurement device. Then the stiffness of the spindle can be calculated by the displacement when acquired from the sensor. Figure 14 shows the principle of load\u2013displacement measurement. The stiffness of the bearing at the front of the spindle is KA, at the end of the spindle is KB, when the spindle is under push load, Fpush, the axial load is superposed by bearings, before the bearing unload, the relationship between the displacement and Fpush is, Fpush \u00bc KA \u00fe KB\u00f0 \u00de 1; when Fpush exceeds the unloading force of the bearing at the end of the spindle, Fpush \u00bc KA 1; same is observed when the spindle under pull load, Fpull" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001600_iros.2016.7759824-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001600_iros.2016.7759824-Figure1-1.png", "caption": "Figure 1. Schematic of FMWMR", "texts": [], "surrounding_texts": [ "Mecanum wheels are used in various homes, military, nuclear power plant, industrial, hospital and space applications. A lot of research has been done using three universal wheels but trajectory control for four Mecanum wheeled mobile robot (FMWMR) in presence of uncertainties still needs attention. Thus, to obtain smooth motion of mobile robots, with chattering free control input, in presence of uncertainties and external force disturbances, a robust and adaptive control is necessary. In view of these aspects, this paper extends the use of adaptive sliding mode controller for trajectory tracking of FMWMR. The effectiveness of proposed controller is verified using two case problems. Simulation results are presented for the verification of proposed controller for FMWMR. Further, experiments are conducted using position and orientation sensor to show the performance of the controller in real world environment. Simulation and experimental results revealed that FMWMR is capable of tracking any type of trajectories.\nI. INTRODUCTION\nIn recent years, the study of mobile robots subjected to non linear disturbances has gained popularity. Mobile robots are classified as conventional wheeled mobile robots and omnidirectional wheel mobile robots. Owing to advantages such as better maneuverability, ability to turn in any direction without reorientation, and capability to move in confined spaces, omnidirectional wheeled mobile robot has become a major interest for research. Among various types of omnidirectional robots, four wheeled omnidirectional mobile robot (FMWMR) is one of them, which is a holonomic system that has three degrees of freedom in a horizontal plane [1].\nThe kinematic and dynamic modeling of an omnidirectional wheeled mobile robot has been investigated by many researchers. [2] proposed a practical opproach to model an omnidirectional robot. The dynamics of a FMWMR is well presented in [3]. As these mobile robots can be extensively used for transporting and carrying materials in hospitals, nuclear power plants, and industries, it is inevitable to derive the dynamic equation where linear and angular velocities are the output states. In order to do the same, we have used Newton Euler method to derive a generalised equation of motion in world coordinate frame.\n*Research supported by Visvesvarya National Institute of Technology, Nagpur-440010, India Veer Alakshendra is with Department of Mechanical Engineering, Visvesvarya National Institute of Technology, Nagpur-440014, India (phone: +91 8446985971; e-mail:alakshendra.veer@gmail.com) Shital S. Chiddarwar is with Department of Mechanical Engineering, Visvesvarya National Institute of Technology, Nagpur-440014, India (email:shitalsc@mec.vnit.ac.in)\nAs the mobile robots are exposed to dynamic environment, non linearities associated with it are bound to alter the desired trajectory. Hence, a non linear controller is necessary to minimize the tracking error. Out of various non linear control methods such as sliding mode control, H control, artificial intelligence techniques etc., sliding mode control has gained popularity owing to advantages such as insensitivity to disturbances [4] and [5]. Inspired by the past researchers, sliding mode control (SMC) method is selected in this work to control the FMWMR subjected to uncertainties and friction. Although, sliding mode control is robust against uncertainties but its implementation becomes difficult when the bounds of uncertainties keeps changing. Moreover, it has a major disadvantage of increased chattering due to use of switching function during the sliding phase. Hence, to counter these disadvantages adaptive control law has been implemented [6] and [7].\nThe main goal of our work is to make the FMWMR to track the reference trajectory in presence of uncertainties and external force disturbances. The major contributions, comparison with previous works and organization of this paper are summarized below:\n1) In the previous work a generalized dynamic equation in world coordinate frame taking kinematic equations into consideration was not derived which has been done in our paper (Section II). Moreover, we have not simplified the obtained second order nonlinear equation by using linearization methods.\n2) The previous researchers have derived adaptive sliding mode control law for either a single input single output (SISO) system such as inverted pendulum or on a conventional mobile robots, whereas in our work we have derived it for a FMWMR (Section III)\n3) Further as our mobile robot has three degrees of freedom, we have shown two trajectories in which the angular displacement is kept constant in first trajectory whereas in the second it is changing with time (Section IV).\n4) At last, most of the earlier work based on SMC has been reported based on simulation results whereas we have attempted the proposed algorithm on a real robot using position and orientation sensors (Section VI).\nConclusions drawn from this study are presented in Section VI.\nII. KINEMATIC AND DYNAMIC MODELING OF FMWMR\nA four wheeled omnidirectional mobile robot has four Mecanum wheels in which peripheral rollers are inclined at a\n978-1-5090-3762-9/16/$31.00 \u00a92016 IEEE 5606", "constant slope angle ( ). In this case 0 45 , hence the\nwheel moves freely at an angle 0 45 with the driven motion.\nA. FMWMR kinematics\nwhere ,, irix and iz are wheel angular velocity around the hub, angular velocity of roller and wheel angular velocity about the contact point, i R is the wheel radius and i r is the roller radius. Using transformation robot velocity vector in\nframe r O is written as\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n100\n10\n01\niy\nix\nr\nr\nr\nr d\nd\ny\nx\nP\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nwi\nwi\nwi\ny\nx\n\n\n\n(2)\nwhere ix d and iy d are translational distance between r O and\nwi O in x and y direction respectively. Substituting (1) in (2)\niir qJP (3)\nwhere 33\n RJ i\nis the Jacobian matrix of i th wheel and is\nobtained as\n\n\n\n\n\n\n\n\n\n\n\n100\n)cos(\n)sin(0\niyiii\nixii\ni drR\ndr\nJ \n\nand izirixi q .\nRemark 1: 00)sin( iiiii RrJ . Hence, there is no\nsingularity present in Mecanum wheels.\nRemark 2: Rank( i J )=3, therefore each wheel has three degrees of freedom (DOF).\nConsidering all wheels to be identical, kinematic parameters for each wheel can be written as\n,,,, 11 bdadrrRR yxii \nbdadbdadbdad yxyxyx 443322 ,,,,, . Thus,\n\n\n\n\n\n\n\n\n\n\n\n100\n2/\n2/0\n1 brR\nar\nJ ,\n\n\n\n\n\n\n\n\n\n\n\n\n\n100\n2/\n2/0\n2 brR\nar\nJ ,\n\n\n\n\n\n\n\n\n\n\n\n\n\n100\n2/\n2/0\n3 brR\nar\nJ ,\n\n\n\n\n\n\n\n\n\n\n\n\n\n100\n2/\n2/0\n4 brR\nar\nJ . Using\n(3) and Jacobian matrices for each wheel, inverse kinematics model of the mobile robot is obtained as [8]\n \n\n\n\n\n\n \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n4\n3\n2\n1\n/1/1/1/1\n1111\n1111\n4\n\n\n\n\n \n\n\n\n\n\n\nbabababa\nR y\nx\nr\nr\nr\n(4)\nwhere )4,3,2,1( i i\n is the angular velocity of each wheel.\nFurther, velocity vector in world coordinate frame q O is\ngiven as rqqq PRyxP )( , where\n\n\n\n\n\n\n\n\n\n \n\n100\n0)cos()sin(\n0)sin()cos(\n)( \n\nR is the rotation matrix of\nmoving frame r O with respect to frame q O .\nB. FMWMR dynamics For the dynamic modeling of the FMWMR it is assumed that coordinate frame r O lies on the center of gravity of the robot(Fig. 2) .\n\nz \nb2\na2\nr y\nr x\nq x\nq y\n1x F\n2x F\n3x F\n4x F\n1y F\n2y F\n3y F\n4y Fr\nO\nq O\nex F\n\nh", "such that rr\nq q SRS )( and\nrr\nq\nq FRF )( . Thus (5) , can be\nmodified as\n rr q rr q rr q FRSRSRM )()()( (7)\n \n\n \n )sin( )cos( 0 0 ex ex ry rx yr xr rr rr F F y x F F xy yx M M \n\n\n (8)\nwhere r S and r F are the position and force vector\nrespectively in r O . xr F and yr F are total forces in x and\ny direction respectively. x and y are linear friction\ncoefficients in x and y direction respectively. ex F is the external force disturbance acting at an angle with\nr y direction at a distance h from upper edge of the mobile\nrobot . Further Euler equation is written as\n))(sin()cos( hbFaFI exexzq\n (9)\nwhere q I is the moment of inertia of the robot about its c.g ,\n is the moment about the c.g and z is the linear coefficient\nof friction in z direction. The driving d i F is generated by the DC motor attached to each wheel which is given as [9]\niiid i ruiF )4,3,2,1( (10)\nwhere i u is the input voltage at each motor, and are DC motor coefficients obtained from manufacturer's catalogue.\nUtilizing (10) xr F , yr F and can be written as\n)( 2\n1 4321 ddddxr FFFFF (11)\n)( 2\n1 4321 ddddyr FFFFF (12)\n)( 2 )( 2 43214321 dddddddd FFFF\nb FFFF a \n(1 3)\nUsing (8) to (13) the dynamic equations for the FMWMR can be represented in the form ))(,()()()()( tuttuxgxftx (14)\nwhere T qq yxtx )( ,\n ,)( 321\nT\nuuutu \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n))(2/1(\n)42)(2/1(\n)42)(2/1(\n)(\n4321\n54321\n54321\nccccI\nybbybyxbxbM\nxaaxaxyayaM\nxf\nq\nqqqxqq\nqqqyqq\n\n\n\n\n\n\n,\n\n\n\n\n\n\n\n\n\n\n\n1 41 31 21 1\n1 41 31 21 1\n1 41 31 21 1\n)(\ncccc\nbbbb\naaaa\nxg and ))(,( tut consists of\nmatched and unmatched uncertainties satisfying the\ncondition max ))(,())(,( tuttut . The variables mentioned\nin )( xf and )( xg are described below:-\n),2sin(),2sin( 21 yx\naa ))((cos2 2\n3 yx a ,\n)sin()sin(2 4 ex Fa , )cos()cos(2 5 ex Fa ,\n)2sin(),2sin( 21 yx\nbb , ))((cos2 2\n3 yx b ,\n)cos()sin(2 4 ex Fb , )sin()cos(2 5 ex Fb ,\n)),cos()(sin( 2 1 31 1 \n \nM aa\n))cos()(sin( 2 1 41 2 \n \nM aa ,\n)),cos()(sin( 2 1 31 1 \n \nM bb\n)),cos()(sin( 2 1 41 2 \n \nM bb and\n).( 2 1 41 31 21 1 ba I cccc\nq\n \nIII. CONTROLLER DESIGN\nThe objective here, is to develop a control law in presence of external force and matched and unmatched uncertainties, such that the robot can track the desired trajectory. Moreover, it should be noted that the trajectory to be followed by the robot is available beforehand due to known arena. In such scenario, utilization of robust adaptive controller, is more appropriate due to its reliability and efficiency to handle uncertainties and disturbances. The localization approach may not be feasible in such cases due to high computational overhead, dependency on the sensors and confined workspace.\nA. Sliding mode control law\nLet T\ndqdqdd yxRtx ][)( is the desired trajectory,\n)()()( txtxte d is the trajectory error, and T\ntttt ])()()([)( 321 is the sliding surface. The important condition for first order sliding mode control is that 0)( t and 0)()( tt . To reduce the computation load\nduring real-time implementation, conventional sliding surface is selected [10]\n)()(\n1\nte dt\nd t\nn\nc\n\n (15)\nwhere c is a positive constant and 2n being order of system. Differentiating (15) yields\n)()()( tetet c\n (16)\nUsing (14) , (16) is written as\n )))(,()().()(\n)(())()(()(\ntuttuxgxf\ntxtxtxt ddc\n\n\n\n (17)\nAccording to ideal sliding surface condition trajectory error )(te converge to zero as 0)( t .Hence, reaching phase control law is obtained as\n)))(,(()()(()()( 1\ntutxfxxxxgtu ddcr\n (18)\nThe control law mentioned in (18) is unable to converge the error in real environment when the uncertainties are present. Hence, to make the system robust against these uncertainties, switching function is incorporated for the sliding phase and the sliding phase control is defined as\n)))((.()()( 1\ntsignGxgtu sw\n (19)" ] }, { "image_filename": "designv10_9_0002748_tec.2019.2892744-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002748_tec.2019.2892744-Figure1-1.png", "caption": "Fig. 1. (a) the eccentric PM-inset machine, (b) ESC and the eccentric rotor in the Z-plane, (c) ESC and the concentric rotor in the W-plane, (d) The cross-section of the slotted PM-inset machine in the FEA.", "texts": [ " Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 2 for the slotless machines, it cannot predict the cogging torque in the slotted machine. Finally, in IV, the proposed model is verified by means of Finite Element Analysis (FEA). II. PRESENTATION OF THE WORK The eccentric PM-inset machine is shown in Fig.1 (a). Only the coils of the phase a are shown in Fig.1 (a). Following assumptions are made in the analytical modeling process. The magnetic permeability of the iron parts is infinite. The stator is slotless and the armature current is considered as a current sheet at the stator bore. 2D symmetry is adopted and the end effects are neglected. A. Uniqueness theorem Based on the uniqueness theorem in Electromagnetics, there are the same field distributions in two equivalent problems. For this equality, there must be the same geometries, the same materials, and the same boundary conditions in the problems. In Fig.1 (b), the stator of the eccentric PM-inset machine in Fig.1 (a) is removed and replaced with an ESC with the current density of JESC. The distribution of the ESC is selected such that the same boundary condition at the stator bore, S, in Fig.1 (a) and (b) is provided. Therefore, the problems in Fig. 1 (a) and (b) are equivalent and have the same field distribution in their air gap regions (between the rotor and the stator bore). From the physical point of view, the ESC is the magnetization surface current appearing on the surface of the ferromagnetic materials which are imposed in a magnetic field [22]. B. The work procedure The field of the PMs in Fig.1 (b) is simply predicted by using the SA method. Since the rotor and the ESC are eccentric in Fig.1 (b), it is difficult to apply the SA method to find the magnetic field of the ESC. Fortunately, the governing equation on the magnetic field of the ESC is in the form of the Laplace equation and applying CTs is allowed. Therefore, by neglecting the PMs in Fig.1 (b) and using the CT in (1), the eccentric geometry in the Z-plane (Fig.1 (b)) is mapped on the concentric one in the W-plane (Fig.1 (c)), where, Rs and Rr are the radii of the stator and rotor, and \u03b5 is the distance between the centers of the rotor and stator as shown in Fig.1 (a). 2 2 2 2 , 4 , , 2 s s r s s z cR w cz R R R B B B c R (1) The field distribution of the mapped concentric ESC in the W-plane (Fig.1 (c)) could be obtained easily by using the SA method. Since ESC is unknown in the first step of the field computation, the field components of ESC are expressed as functions of unknown Fourier coefficients of JESC in the Wplane. The exact distribution of the ESC could be found by applying the boundary condition at the stator bore, S, in Fig.1 (b). In fact, the boundary condition at the stator bore in Fig.1 (a) and the contour S in Fig.1 (b) must be the same to satisfy the condition of using the uniqueness theorem. The crosssection of the slotted PM-inset machine which is used for FEA and comparing the results of the developed analytical model is shown in Fig.1 (d). Although the developed model is presented for the static eccentricity, it could be developed easily for the dynamic and mixed eccentricity conditions. In these cases, it is enough to consider the instantaneous value of \u03b5 in (1) and taking into account the instantaneous value of the rotor angular position \u03b8r. III. FIELD COMPUTATION A. The PM flux density To obtain the flux density due to the PMs in Fig.1 (b), P+1 regions are considered as expressed in (2), where Rm is the PM radius and \u03c6ki and \u03c6ke are the angles of the rotor slot walls in the kth rotor slot as shown in Fig.2 (b). Region I, Air : Region k, PM :k {2, 3, .. 1} and m ki k e r m R r P R r R (2) The PMs could have any magnetization pattern, but for the sake of simplicity, only radial magnetization is considered. Since there is an odd symmetry in the magnetic variables of the PM regions, only one region is considered in the analytical solution", " sin ( ) sin( ) ( ) sin( ) n n n n p I II n r n n r n r n n r A b r p r A d R r R r K R r R (8) Unknown coefficients in (8) have to be found by considering the continuity conditions at R=Rm as given in (9). , , m m I I II II R R R R A A A A r r (9) Applying the correlation technique [2] on the equalities in (9), the unknown coefficients in (8) are obtained as (10). max max 1 1 3 1 3 ... ... T N T V d d d b b b 11 12 21 22 L Ld G = L Lb H d b (10) where, the superscript T denotes for the matrix transposition operator and the new variables are defined in the appendix A.1. Therefore, the PM flux density components in the air gap region of Fig.1 (a) are calculated as (11) 1,3,... 1 1,3,... cos sin p rPM m p PM b B pr p R B b pr p (11) B. The flux density of ESC The map of the rotor geometry in the W-plane is shown in Fig.1 (c). It is worth mentioning that the rotor slot walls in the W-plane are not exactly in the radial direction. In addition, the map of the contour r=Rr (in the Z-plane) is not a true arc in the W-plane. However, it is almost true to suppose radial slot walls and assuming the map of r=Rr as an arc with r*=R* r. These assumptions do not affect the field distribution while they make simplifications in the solution process. Therefore, to obtain the flux density due to the ESC in the W-plane (Fig.1 (c)), P+2 regions are considered as expressed in (12), where, R* s, R* r, and R* m are the radii of the mapped stator, rotor and magnet in the W-plane, respectively, and * ki and * ke are the angular limits of the kth region in the W-plane (see Fig.1 (c)). * * * * * * * * * * Region I, Air : Region k, Rotor slots :k {2, 3, .. 1} : and Region P+2, Air : * m s k i k e r m s R r R P R r R R r (12) Hereafter, the superscript * is used to show that the variable is in the W-plane. Against the previously solved problem (the field of the PMs in Fig.1 (b)), there is no geometrical symmetry in the arc span of the rotor slots in the W-plane. The reason is that the rotor slots are individually deformed by applying the CT on the geometry of Fig.1 (b). Therefore, the governing equations and boundary conditions of all regions have to be considered simultaneously. The governing equations and the general solution of the field in the defined regions are expressed in (13) and (14), respectively. 2 * 0, 1, 2, ..., 1, 2iA i P P (13) * * * * 1 2 * * * 3 4 * * * 1 ( 2 ) * * * * * 2 ( ) cos + ( ) sin ( ) cos ( ) + ( ) sin ( ) ( cos sin ) kn kn kn kn I k kn kn kn kk P n kn kn kn k n m P m m m A a r a r n a r a r n A b r c r d r e r A r f m g m (14) where, * * * * * , , 2 ek ik k k n ek ik n (15) The tangential field at the iron borders of the rotor slots is zero", " b b J J \u0393 \u039b \u03a8 U L Q \u039e 0 \u03a9 H 0 0 \u039e \u0394 0 H (23) Therefore, the air gap flux density components of ESC in the W-plan are calculated as (24) and (25), respectively. 1 1 * 1 1 * * * * *0 2* * * * *0 4* ( ) sin 2 ( ) cos 2 ES Cc r ES C s ES Cs s J r B a r R J r a r R (24) 1 1 * 1 1 * * * * *0 2* * * * *0 4* ( ) cos 2 ( ) sin 2 ES Cc ES C s ES Cs s J r B a r R J r a r R (25) At this step ESC is unknown. Hereafter, distribution of ESC is obtained by applying the required boundary conditions at the stator bore of the eccentric machine in Fig.1 (a). C. Computation of ESC The exact distribution of the ESC must be found by considering the boundary condition at the stator bore of the eccentric machine, S, in Fig.1 (b) as given in (26). 0tPM tES C arB B J (26) where, BtPM and BtESC are the tangential fields due to the PMs and ESC at the contour S, respectively, and Jar is the armature current density. The tangential field at S is the projection of the flux density vector on the tangential unitary vector of the contour S [19]. In addition, the boundary condition in (26) must be mapped from the Z-plane to the W-plane by applying the CT in (1) as expressed in (27). Mapping process of the boundary conditions is described in [19]", " The back-emf, and the self- and mutual- inductances of the eccentric machine could be obtained by knowing the air gap flux density due to the PMs and armature current [11]. The machine self- and mutual- inductances for the phases a and b for the eccentric machine are analytically computed versus the rotor position and compared with the FEA results for the slotted machine in Fig.5 (a). Since the mutual inductance of Lac is the same as Lab, it is not shown in Fig.5 (a). In addition, the back-emf of the coils 1 and 2 (see Fig.1 (a)) at \u03c9r=188 rad./s, for the healthy and eccentric machines are compared with the FEA results for the slotted machine in Fig.5 (b). The UMF is obtained by the Maxwell stress tensor as (31), where, the resultant field components are presented in (32). 2 2 2 0 0 ( 2 ) 2 jstk r r rL B B jB B e d UMF (31) , , r rPM rESC PM ESCB B B B B B (32) It is worth mentioning that \u03b5 is a complex function. The amplitude of \u03b5 reveals the distance between the rotor and stator and its angle reflects the angle between the rotor and stator reference axes", " Using the Maxwell stress tensor, the electromagnetic torque is obtained as given in (33). 2 2 0 0 stk r r L T B B d (33) In Fig.8 (a) and (b), the electromagnetic torque and reluctance torque of the considered PM-inset machine with the stator current (ia=6A, ib=ic=0) are illustrated and compared with FEA, respectively. As seen in Fig.8, the electromagnetic and reluctance torque components are symmetric spite of the rotor eccentricity. The reason is that the coils of one phase are located diametrical symmetric as shown in Fig.1 (d). It should be noted that the machine cogging torque is not predicted by the developed model. The presence of the cogging torque in the result of FEA for the slotted machine is obvious in Fig.8 (a). In addition, the reluctance torque is obtained by removing the PMs and considering the armature currents. In such a condition there is no cogging torque component. From Figs. 2-8, it is obvious that the developed model is capable of presenting a very exact and accurate prediction of the performance of the eccentric PM-inset machines" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002911_j.triboint.2020.106839-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002911_j.triboint.2020.106839-Figure2-1.png", "caption": "Fig. 2. Measurement positions of the gear-tooth profile.", "texts": [ "1 cSt at 100 \u25e6C. The lubricant temperature was fixed at around 80 \u25e6C; however, due to the limitations of the cooling system, this temperature reached 85 \u25e6C for the tests under the highest load. Therefore, the oil had to be cooled from the 90 \u25e6C, as described in Ref. [14]. Before each test, teeth 1, 9, and 17 of the wheel were measured as comparative baselines. After each test, these teeth were measured again in situ, as shown in Fig. 1. Six profiles along the width of each tooth were measured, as shown in Fig. 2. Therefore, both the same tooth profile and the tooth surface evolution could be monitored. Detailed descriptions of the in situ gear-tooth-profile-measurement setup can be found in Refs. [10,12]. Due to the space limitations of the gearbox, the pinion was disassembled and measured with a profilometer before and after the test. Human visual inspection of the pinion and wheel were also performed after each test. To quantitatively evaluate the wear on the surfaces of gear teeth during the tests, the tooth profiles beforehand were used as the baselines" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000239_iros.2011.6094415-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000239_iros.2011.6094415-Figure5-1.png", "caption": "Fig. 5. Illustration of new hand mechanism", "texts": [ " Although there are several measured items concerning human hands in the database, the principal dimensions were selected from the database for designing the new hand. Fig. 3 shows the selected dimensions and the average for young Japanese females. Based on the design concepts D), E) and F), the new hand was developed. During the mechanical design stage, the link length and thickness of the new hand were deformed to be from 90% to 110% of the average dimension of a young Japanese female. Fig. 4 shows the new developed hand and its principal dimensions. As shown in Figs. 3 and 4, the dimensions of the new hand are almost that of a young Japanese female. Fig. 5 shows an illustration of the new hand mechanism. Fig. 5(a) shows the exterior of the new hand which has a (Note: Left picture doesn't show the strict size of Japanese female standard.) thumb and 4 fingers. The new hand, without its palm plate, is shown in Figs. 5(b) and 5(c). These figures tell us that the 1st servomotor with the 1st planetary gear (see servomotor #1 and planetary gear #1 in Figs. 5(b) and 5(c)) enables abduction and adduction of the thumb. The new hand, without its palm plate and thumb mechanism, is shown in Figs. 5(d) and 5(e). As shown in these figures, the 2nd servomotor and the 2nd planetary gear (see servomotor #2 and planetary gear #2 in Figs. 5(d) and 5(e)) are also located inside the new hand. Pulleys and timing belt are also located between them. The output torque of the 2nd planetary gear is transmitted to proximal links of 4 fingers (index, middle, ring, and little fingers), which are locked together, via a parallel crank mechanism as shown in Fig. 5(d). Since each distal link and each middle link are linked with proximal links, 4 fingers work together during extension and flexion when driven by the 2nd servomotor. The previous hand and the new hand are shown side by side in Fig. 6. The left side of Fig. 7 shows a real Japanese female hand. Her hand length from crease is 170.0[mm], while the average for young Japanese females is 167.8 [mm]. The right side of Fig. 7 shows the new hand on which is overlaid the mechanism. Fig. 6 shows how small the new hand is compared to the previous one" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003642_s42835-021-00807-4-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003642_s42835-021-00807-4-Figure1-1.png", "caption": "Fig. 1 Schematic diagram of spoke with parameters", "texts": [ " in [7] have concluded that the natural frequencies of the motor play a vital role in determining the structural resonances and the level of noise vibrations. From the analysis, it is evident that the choice of slot and pole combination is vital to the performance enhancement of permanent magnet motors. In this perspective, this paper presents a comprehensive study of the effect of slot and pole combination on the performance of spoke type BLDC motor through electromagnetic and structural analysis. The structure of Spoke type BLDC motor configuration is shown in Fig.\u00a01 and its dimensions are given in Appendix\u00a01. The difference between the IPM and Spoke type motor is based on the arrangements of magnet with respect to the rotor. To evaluate the performance of the motor, a Finite Element Analysis (FEA) based CAD package \u2018MagNet 7.5\u2019 is employed. The flux lines of the Spoke type BLDC configuration are illustrated in Fig.\u00a02. The characteristics of the 1 3 Spoke type BLDC motors are comparable to that of the IPM type BLDC motors. FEA analysis is performed on both the motors of equal rating and their corresponding average and cogging torques are compared" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003535_j.mechmachtheory.2021.104436-Figure11-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003535_j.mechmachtheory.2021.104436-Figure11-1.png", "caption": "Fig. 11. OB-limb configurations.", "texts": [ " The U^-joint is a composite joint, which means connecting a R-joint at the front end of parallel four-bar chain. The origins of the fixed coordinate system (system {1}) and moving coordinate system (system {2}) coincide with O1 and O2, respectively. The line O1O2 is referred to the limb double center line. According to the basic properties of GSPM, the O1O2 length should always be equal to l. The links directly connected with the base platform are driving links of OB-limb. A series of OB-limbs meeting the requirements are shown in Fig. 11, and their constraint performances are analyzed based on the screw theory. J. Zhang et al. Mechanism and Machine Theory 166 (2021) 104436 The constructed OB-limbs [RRR] [RR], RU^ [RR], RU^R, [PRRR] [RR], PRU^ [RR] and PRU^R are coded as limb-i (i=7, 8, 9, A, B, C) in sequence. The origin of the limb coordinate system is set to coincide with O2, and the z-axis is along the O1O2 direction, which is shown in Fig. 11. $ij and$r ijrepresent the jth motion and constraint screws of limb-i respectively. As shown in Fig. 11(a) and (d), the limb-i contains 5 rotating axes O1Ai, O1Bi, O2Ci, O2Di and O2Ei (i=7 or A). The axes O1Ai, O1Bi and O1Ci intersect at O1, the axis O1Ai is perpendicular to axis O1Bi, and the axis O1Bi is perpendicular to axis O1Ci. The axes O2Di and O2Ei are perpendicular to each other and intersect at O2, the axis O2Di is parallel to axis O1Ci, and the axes O2Di and O1Ci are perpendicular to O1O2. The $i1, $i2, $i3, $i4 and $i5 represent the motion screws of rotating axes O1Ai, O1Bi, O2Ci, O2Di and O2Ei, respectively", " They form the motion screw system of the limb-i, which can be expressed as \u23a7 \u23aa \u23aa \u23a8 \u23aa \u23aa \u23a9 $i1 = (ai11 ai12 ai13 ; lai12 \u2212 lai11 0 ) $i2 = ( ai21 ai22 ai23 ; lai22 \u2212 lai21 0 ) $i3 = ( ai31 ai32 0 ; lai32 \u2212 lai31 0 ) $i4 = ( ai31 ai32 0 ; 0 0 0 ) $i5 = ( ai51 ai52 ai53 ; 0 0 0 ) (26) where i=7 or A. By the calculation of reciprocal screws of Eq. (26), the constraint screw system can be obtained as $r i1 = ( 0 0 1 ; 0 0 0 ) (27) Eq. (27) indicates that the constraint screw systems of the limb-7 and limb-A contain one constraint force along the O1O2 direction exclusively. As shown in Fig. 11(b) and (e), the motion screw system of limb-i (i=8 or B) contains 5 motion screws. The axes O1Ai and O1Bi are perpendicular to each other and intersect at O1, and the axes O2Di and O2Ei are perpendicular to each other and intersect at O2. The axis O2Di is parallel to axis O1Bi, and O1O2 is always parallel to line Bi Di. The translation direction of the parallel four-bar chain is along line Ci Di, which is perpendicular to line BiDi. The $i1, $i2, $i4 and $i5 represent the motion screws of rotating axes O1Ai, O1Bi, O2Di and O2Ei in the limb-i respectively, and the $i3 represents the motion screw corresponding to the translation line O2Ci", " These 5 motion screws form the motion screw system of the limb-i, which can be written as \u23a7 \u23aa \u23aa \u23a8 \u23aa \u23aa \u23a9 $i1 = (ai11 ai12 ai13 ; lai12 \u2212 lai11 0 ) $i2 = ( ai21 ai22 ai23 ; lai22 \u2212 lai21 0 ) $i3 = ( 0 0 0 ; ai21 ai22 0 ) $i4 = ( ai21 ai22 ai23 ; 0 0 0 ) $i5 = ( ai51 ai52 ai53 ; 0 0 0 ) (28) where i=8 or B. by the calculation of reciprocal screws of Eq. (28), the constraint screw systems can be obtained as $r i1 = ( 0 0 1 ; 0 0 0 ) (29) Eq. (29) indicates that the constraint screw systems of both limb-8 and limb-B contain only one constraint force along the O1O2 direction. As shown in Fig. 11(c) and (e), compared with the motion screw systems of the limb-8 and limb-B, the ones of the limb-9 and limb-C do not have the $i5 (axis O2Ei), which is expressed as \u23a7 \u23aa \u23a8 \u23aa \u23a9 $i1 = (ai11 ai12 ai13 ; lai12 \u2212 lai11 0 ) $i2 = ( ai21 ai22 ai23 ; lai22 \u2212 lai21 0 ) $i3 = ( 0 0 0 ; ai21 ai22 0 ) $i4 = ( ai21 ai22 ai23 ; 0 0 0 ) (30) where i=9 or C. By the calculation of reciprocal screws of Eq. (30), the constraint screw system can be obtained as { $r i1 = ( 0 0 1 ; 0 0 0 ) $r i2 = ( 0 0 0 ; ci21 ci22 ci23 ) (31) where the parameters ci21, ci22 and ci23 must meet the following requirements: J" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002508_j.triboint.2019.03.048-Figure13-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002508_j.triboint.2019.03.048-Figure13-1.png", "caption": "Fig. 13. 3D structural drawings of oil guide devices for comparison of flow rate in oil guide tubes.", "texts": [ " From the above observations, it can be inferred that the structure of the oil guide device is the key factor affecting the oil flow rate of the oil guide tubes which indirectly determines the oil supply for the bearings. Therefore, without changing the shape and overall size of the oil guide device, three parameters including the oil tank capacity, the hole diameter and fillet radius of oil tubes are determined as the structural influence parameters. To study the influence of the above mentioned parameters on the oil flow rate of the oil guide tubes, several simulations are performed with different operating conditions shown in Table 4, and the corresponding 3D structural drawings are shown in Fig. 13. In Table 4, the so-called reference case includes parameters of the current oil guide device. Fig. 14 shows the oil flow rate of the oil guide tube with different oil tank capacities. For oil guide tube 1, the average oil flow rates of V=6.67ml, 13.34ml and 20.01ml after rotation number R=4r are 3.04, 2.6 and 3.07 L/min, respectively; for oil guide tube 2, they are 2.1, 2.44 and 2.67 L/min, respectively. It can be inferred that the capacity of the oil tank only exerts little influence on the oil flow rate of oil guide tubes" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001524_s12206-014-0931-7-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001524_s12206-014-0931-7-Figure5-1.png", "caption": "Fig. 5. The 3(rT)2PS with parallel constraint planes.", "texts": [ " When constructing a metamorphic parallel mechanism with three rTPS limbs, there will be three constraint planes of which the normal relationships describe the topologies of the mechanisms. Generally, there are three categories: all three planes are parallel, two of them are parallel and intersecting with the third one, and all three planes intersect. Comparing with the two-limb mechanisms in Sec. 3, a main difference is that the local DOF on the platform vanishes if the three spherical joint centers are not in-line. When three constraint planes are parallel to each other, there is n1 = n2 = n3 as in Fig. 5. Any line segment of the three, A1A2, A2A3 and A1A3, follows the rule in Sec. 3.2 with two parallel constraint planes. Based on Fig. 5 and Eq. (3), constraint equations of the 3(rT)2PS with parallel constraint planes can be obtained as: 1( ). ( 1,2,3)i id i\u00a2 + = =Ra q n (10) which can be rewritten in the matrix form as: T 11 1 1T 2 2 1T 33 1 .( ) 1 . ( ) 1 . ( ) 1 . d d d \u00e6 \u00f6\u00e6 \u00f6\u00a2 \u00e6 \u00f6\u00e7 \u00f7\u00e7 \u00f7 \u00e7 \u00f7\u00e7 \u00f7\u00e7 \u00f7\u00a2 = \u00e7 \u00f7\u00e7 \u00f7\u00e7 \u00f7 \u00e7 \u00f7\u00e7 \u00f7\u00e7 \u00f7\u00a2 \u00e8 \u00f8\u00e7 \u00f7\u00e8 \u00f8\u00e8 \u00f8 u na v n a w n a q n (11) where w.n1 = u\u00d7v.n1 is dependent on u.n1 and v.n1. Thus, u.n1, v.n1 and q.n1 can be taken as independent parameters and solved directly from Eq. (11), which shows they are constant values in the mechanism kinematics", " (10) can be written as: 1 1 1 1 2 1 12 12 1 1 2 1 3 1 13 12 1 1 3 ( ). ( ( ). . ( ( ). . d l d d l d d \u00a2 + =\u00ec \u00ef \u00a2 \u00a2 \u00a2- = = -\u00ed \u00ef \u00a2 \u00a2 \u00a2- = = -\u00ee R R R R R a q n a a n m n a a n m n (12) where l1i is the distance between points A1 and Ai (i = 2,3) which are on the same line. Then (d1-di)/l1i is the same when i = 2,3. Thus the last two equations in Eq. (12) constrain the same rotation between line A1A2 and normal n1. One of limb 2 and limb 3 becomes redundant. In order to assemble the 3(rT)2PS parallel mechanism in Fig. 5, the three parallel constraint planes cannot be located arbitrarily. The intrinsic constraint for this can be investigated by fixing constraint planes for limb 1 and limb 2 first and then identifying the conditions for limb 3. When giving spherical joint centers A1 and A2, the geometric constraints for the third spherical joint center A3 can be obtained by intersecting constraint plane \u22113 with a circle centered at point A30 with radius A3A30 as in Fig. 6. The circle is the intersecting of two spheres centered at point A1 and A2 with radii A1A3 and A2A3 respectively", " The first and third equations indicate that translations of the moving platform along normal n1 and n3 depend on the platform rotations. Thus, there are two independent parameters in rotation matrix R and one in translation q based on Eq. (16). Hence, this mechanism has two rotational DOFs and one translational DOF with direction perpendicular to both n1 and n3. When the three spherical joint centers are in line, the mobility is the same but includes a local rotation. This is different with the case with all three planes parallel in Fig. 5 in which the third limb is used to constrain one more rotation and it is redundant when the three spherical joint centers are in line. In the mechanism in Fig. 8, the third limb gives one more constraint on the translation which is not redundant when the points are in line. In fact, except the case in Fig. 5, the third limb is not redundant in the following sections under the in-line condition. When the constraint planes of the three limbs have different normals with n1\u2260n2\u2260n3 as in Fig. 9(a), a general configuration of the 3(rT)2PS parallel mechanism is illustrated. This gives three intersecting lines and considering relations among these lines will show different topologies of the mechanism. There are basically two different relations including three intersecting at one point and three parallel to each other" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002977_s40194-020-00970-8-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002977_s40194-020-00970-8-Figure6-1.png", "caption": "Fig. 6 Representation of mesh for modelled WAAM cylinder", "texts": [ " The chemical composition of both materials (ER4043 and AA6061-T6) is almost similar, and the thermal and mechanical properties of the material will be alike. Hence, the additive layer material properties are assumed to follow substrate material properties [35]. Mesh element 16056 numbers have been generated on substrate and additive layers after performing mesh convergence tests. The element family constituted of hexagonal shape, seed size 0.002, DC3D8 (an 8-node linear heat transfer brick for heat transfer analysis), and C3D8R (an 8-node linear brick, reduced integration, hourglass control for structural analysis) as represented in Fig. 6. The macrograph depicting the cross-section view of the additive layers is shown in Fig. 7(a). The formation of layers is evident from the macrograph due to the superimposed additive deposited layers. It appears that, as the thick wall of the cylinder is developed through successive multi-bead and multi-layer deposits, the lateral surface seemed corrugated [36]. The produced WAAM cylinder exhibited a stable integrated structure and strong bond between inter-layered deposits. A distinctive microstructure transition is seen at the top, middle, and bottom layers of the additive deposited material" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001370_0954406215621097-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001370_0954406215621097-Figure6-1.png", "caption": "Figure 6. Equivalent trapezoidal tooth model used to calculate the deformation of one tooth.", "texts": [ " The number of \u2018engaging into\u2019 teeth can be approximated as ZR \u00bc Zc 2 arccos 2 xcj j dc 4 2 666 3 777 \u00f05\u00de where Zc is the number of teeth of the circular spline. To calculate the stiffness of one practical tooth pair Kms, the deformation of each tooth at the meshing point along the direction of the unit meshing force must first be obtained. As every tooth in harmonic drive is still rigid body in small scale, the method proposed by Cornell18 is used to evaluate the tooth deformation. The practical tooth is simplified as a trapezoidal tooth whose lower bottom length and height are Lb and Ht respectively, for ease of calculation, as shown in Figure 6. The tooth is divided into n short cantilever beams, and the thickness, section area and section modulus of the i th beam are Ti, Ai, and Ii, respectively, as shown by the shading in Figure 6. The distance along the x-axis from the beam to the meshing point j is Lij, half of the tooth thickness at the meshing point is yj, Poisson\u2019s ratio is , the elastic modulus is E, and the angle between the unit meshing force Fj and the y-axis is j. The deformation Bij at point j caused by the i thbeam considering the at TEMPLE UNIV on June 5, 2016pic.sagepub.comDownloaded from bending, shearing and compression of one tooth can then be determined as follows18 Bij \u00bc Fj 1 2 E cos2 j T3 i \u00fe 3T2 i Lij \u00fe 3TiL 2 ij 3Ii \" #( cos j sin j T2 i yj \u00fe 2TiyjLij 2Ii \u00fe cos2 j 12\u00f01\u00fe \u00deTi 5Ai \u00fe sin2 j Ti Ai \u00f06\u00de The deformation Bj at point j caused by all of the short cantilever beams of one tooth is thus Bj \u00bc Xn i\u00bc1 Bij \u00f07\u00de Because of the stretching effect of wave generator and meshing effect, an approximate cone deformation of flexspline will be produced and make the harmonic drive different from rigid planar gear in teeth contact condition" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003617_tec.2021.3070039-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003617_tec.2021.3070039-Figure1-1.png", "caption": "Fig. 1. FRPM machine topologies. (a) Conventional Halbach. (b) Proposed DA-Halbach.", "texts": [ " Both machines have been optimized aiming at maximum torque and their electromagnetic performance has been comprehensively analyzed and compared using finite element (FE) method. The topologies of conventional and proposed FRPM machine S Authorized licensed use limited to: Carleton University. Downloaded on May 29,2021 at 04:36:46 UTC from IEEE Xplore. Restrictions apply. 0885-8969 (c) 2021 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. with 12 stator slots and 14 rotor slots are presented in Fig.1 (a) and (b), which are designated as Halbach and DA-Halbach. For both machines, halbach array magnets including one radially magnetized middle PM and two circumferentially magnetized PMs on two sides, are placed in the stator slot opening. Based on the conventional Halbach machine, another set of armature winding is added in the rotor slots in proposed DA-Halbach machine and both armature windings make contribution to the output torque production. Two sets of armature windings in DA-Halbach machine are supplied independently" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001524_s12206-014-0931-7-Figure15-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001524_s12206-014-0931-7-Figure15-1.png", "caption": "Fig. 15. The 4(rT)2PS with intersecting planes.", "texts": [ " (22) Thus, the two constraints are dependent and the mechanism at this configuration has one translational and two rotational DOFs about normal n1 and n3. However, when the mechanism rotates about any direction of the two, Eq. (22) does not exist. There will be two rotational constraints and the mechanism has one rotational DOF only. This indicates that the mechanism has bifurcated rotation at the configuration described by Eq. (22) with two branch rotations about two orthogonal directions. When none of any two of the four constraint planes are parallel to each other, it comes to a new topology of the mechanism in Fig. 15(a) which follows: 1 1 1 2 2 2 3 3 3 4 1 1 2 2 3 3 1 4 1 1 2 4 2 2 3 4 3 3 1 1 2 2 3 3 4 ( ). ( ). ( ). ( ). ( ). ( ). d d d k k k k k k k d k d k d d \u00a2 + =\u00ec \u00ef \u00a2 + =\u00ef \u00ef \u00a2 + =\u00ef \u00ed = + +\u00ef \u00ef \u00a2 \u00a2 \u00a2 \u00a2- + - \u00ef \u00a2 \u00a2+ - = + + -\u00ef\u00ee R R R R R R a q n a q n a q n n n n n a a n a a n a a n . (23) As there are no parallel planes, generally three of them are independent and the forth normal n4 can be represented by the first three ni with coefficient ki (i = 1,2,3) as in Eq. (23). Thus, Eq. (23) gives three translational and one rotational constraints, leading to that the mechanism has two rotational DOFs" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000879_1.4026264-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000879_1.4026264-Figure1-1.png", "caption": "Fig. 1 Head-cutter blade profiles", "texts": [ " The intact oil film between the meshing tooth surfaces and the power losses in the oil film are extremely sensitive to any small-level variations in the headcutter geometry and machine-tool settings. Appropriate modifications of existing basic manufacturing parameters can significantly enhance the EHD performance characteristics of the gear drive. For this reason, the following manufacturing parameters are taken as the basis of the proposed optimization formulation: the radii of the head-cutter blade profile (rprof1 and rprof2, Fig. 1(b)), the difference in head-cutter radii for the manufacture of the contacting tooth flanks of the pinion and the gear (Drt0), the tilt (j) and swivel (l) angles of the cutter spindle with respect to the cradle rotation axis (Figs. 2 and 3), the tilt distance (hd , Fig. 3), the variation in the radial machine tool setting (De, Figs. 2 and 3), and the variation in the ratio of roll in the generation of the pinion tooth 071007-2 / Vol. 136, JULY 2014 Transactions of the ASME Downloaded From: http://mechanicaldesign" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002952_tbme.2020.2994152-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002952_tbme.2020.2994152-Figure2-1.png", "caption": "Fig. 2. Method used to estimate foot flat by thresholding the difference between shank segment velocity and ankle angle velocity.", "texts": [ " The weighting factor was used to smooth the orientation update by biasing it toward the previous estimate, and was tuned to minimize the mean absolute orientation error over the course of one trial as compared to data extracted from a 12-camera Vicon motion capture system. The term SaY /g was used to estimate sin(\u03b1) assuming g \u2248 |S~a|, per satisfaction of Eq. (1). Finally, \u221a 1\u2212R2 2,1 was used to estimate cos(\u03b1) per the Pythagorean trigonometric identity. For position resets we employed a threshold on the norm difference between sagittal shank rotational velocity S\u03c9X and ankle rotational velocity \u03b8\u0307. As illustrated in Figure 2, the assumption underlying this calculation was that these values would be closest when the foot is flat on the ground. The calculation and threshold we employed can be expressed as: \u03b4 = |S\u03c9X \u2212 \u03b8\u0307| \u2264 \u03c9\u0302 (6) where \u03b8\u0307 was filtered using a 50Hz, 2nd order low pass Butterworth filter and \u03c9\u0302 = 1.2rad/s. This threshold was chosen empirically to allow for at least one velocity/position reset per stance period, and was likely high due to deflection of the prosthetic foot during roll-over. At the velocity reset time t(i)R , integrated signals were reset by modeling the shank as a vertical lever rotating in the sagittal plane about a fixed hinge at the ankle joint: ~pA(t (i) R ) := [0; 0; 0] (7) ~vA(t (i) R ) := [0; 0; 0] (8) ~pK(t (i) R ) := L[0;R2,1(t (i) R );R1,1(t (i) R )] (9) ~vK(t (i) R ) := L\u03c9X [0;R1,1(t (i) R );\u2212R2,1(t (i) R )] (10) where the components represent, in order, the frontal, anteriorposterior, and longitudinal axes" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003535_j.mechmachtheory.2021.104436-Figure13-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003535_j.mechmachtheory.2021.104436-Figure13-1.png", "caption": "Fig. 13. Schematic of OE-limbs [TRRR] [RR] and [TPRR] [RR].", "texts": [ " Mechanism and Machine Theory 166 (2021) 104436 In order to solve the interference problem of basic GSPM, the equivalent replacement method suitable for OB-limbs is proposed. Since the input chains of OB-limbs [RRR] [RR] and [PRRR] [RR] are chains [RR] and [PRR] respectively, the equivalent chain [TRR] (or chain UR) and chain [TPR] (or chain UP) given in Section 3.3 are used to replace them, which can directly construct the compact OElimb. The typical examples [TRRR] [RR] and [TPRR] [RR] are shown in Fig. 13. For the OB-limbs RU^ [RR], PRU^ [RR], RU^R and PRU^R, 2 types of the equivalent chains are proposed below: The first equivalent chain of OB-limbs also concerns the RCM. As shown in Fig. 14(a) / (b) and Fig. 15(a) / (b), the equivalent chains TRU^R and TPU^R are obtained by using the RCM to replace the driving links of chains RU^R and PRU^R. According to the RCM properties, the axis O1B of the R-joint is always located in the v-plane and rotates around the plane normal O1A. The axis O1B is parallel J" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000039_978-1-84996-220-9-Figure4.12-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000039_978-1-84996-220-9-Figure4.12-1.png", "caption": "Figure 4.12 Supporting edge and pivoting problem modeling. (a) The pivoting sequence is planned using rotation of the endpoints of this edge. (b) The 3D pivoting problem is reduced to how to displace a line segment on vertices A or B", "texts": [ " keeping dynamic balance. Note that the task of keeping the gaze direction towards the end-effector target position is taken into account in this experiment. The final CoM apparently goes out of the initial support polygon: this means the reaching task could not have been performed without stepping. Manipulation requiring whole-body motion is one task that is appropriate for humanoid robots. In order to manipulate cumbersome object, humans often manipulate without lifting but by using contact with the ground (Figure 4.12). In this research, we apply such a manipulation method to humanoid robots. 4 Planning Whole-body Humanoid Locomotion, Reaching, and Manipulation 113 There are several task-specific whole-body motions that have been intensively investigated: pushing [12, 9, 31], and lifting [10], and pivoting [33, 37]. Currently, many researchers are working to integrate these recent developments with a global motion planner. Among them, the pivoting manipulation has several advantages such as precise positioning, stability and adaptability over other methods like pushing or lifting" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000560_j.mechmachtheory.2013.06.001-Figure8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000560_j.mechmachtheory.2013.06.001-Figure8-1.png", "caption": "Fig. 8. Four bar mechanism with error in link-2.", "texts": [ " If one can imagine an elastic bladder inside the mechanism and blown with air, then the condition corresponds to an expanded position assumed by the mechanism. Total bandwidth quantifies the effect of manufacturing errors and depending on the functional requirements, designer can specify individual tolerances in the chosen mechanism. Another common error is in the center distance between two holes/pins in a link which is termed as \u2018link-error\u2019 in this work. This is designated as a bilateral error and the link can have a dimension, r \u00b1 \u0394 as shown in Fig. 7. This link-error can be treated as virtual prismatic joint and represented by a screw $v. Fig. 8 shows four-bar mechanism with virtual prismatic joint representing error on link-2 and its associated screw $12. Eq. (5) for first open chain is modified to include the effect of virtual prismatic joint, 3p \u00bc A1A12A2 3p0 : \u00f012\u00de From Table 4, the Rodrigues parameters are taken and the transformation matrices are obtained as A1 c\u03b82 \u2212s\u03b82 0 0 s\u03b82 c\u03b82 0 0 0 0 1 0 0 0 0 1 0 BB@ 1 CCA; A12 \u00bc 1 0 0 \u03942 0 1 0 0 0 0 1 0 0 0 0 1 0 BB@ 1 CCA and A2 \u00bc c\u03b83 \u2212s\u03b83 0 r2 1\u2212c\u03b83\u00f0 \u00de s\u03b83 c\u03b83 0 \u2212r2s\u03b83 0 0 1 0 0 0 0 1 0 BB@ 1 CCA: \u00f013\u00de Taking 3p0 \u00bc r2 \u00fe r3 0 0 1 0 BB@ 1 CCA \u00f014\u00de Ta R llowing the procedure outlined in Section 3" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002277_978-3-319-27131-6-Figure1.6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002277_978-3-319-27131-6-Figure1.6-1.png", "caption": "Fig. 1.6 Nominal contact angle of a ball bearing", "texts": [ " The misalignment angle \u03b2 between the inner and outer raceways of the ball bearing is defined using Eq. 1.1 as \u03b2 \u00bc tan 1 Ga Dpw \u00bc tan 1 2Ga Di \u00fe Do \u00f01:10\u00de Generally, the misalignment angle is between 120 and 160 for deep-groove ball bearings and between 30 and 40 for cylindrical roller bearings. They are suitable values to avoid the bearing damage caused by the angular misalignment. The nominal (free) contact angle \u03b10 of the bearing is the angle between the contact line of the balls at the inner and outer raceways to the transversal axis, as shown in Fig. 1.6. Using trigonometric relations of the bearing geometry, the nominal contact angle is calculated as [2, 3] Table 1.1 Influences of the bearing osculation Bearing characteristics Large osculation Small osculation Axial clearance Large Small Misalignment angle Large Small Basic load ratings Co, C Small Large Bearing lifetime Lh10 Reducing Increasing Bearing friction Small Large Bearing wear Less More Hertzian pressure at the contact area Increasing Reducing NVH Reducing Increasing Electric arcing at high currents More sensible Less sensible Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002893_tia.2020.3036328-Figure26-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002893_tia.2020.3036328-Figure26-1.png", "caption": "Fig. 26. Structure of shifted rotor tooth.", "texts": [ " When the 2nd harmonic is minimum, the 4th harmonic is maximum. Therefore, if the torque ripple needs to be further decreased, a step skewed rotor should be combined with other techniques such as rotor shaping, uneven tooth, shifted rotor tooth, etc., or the step number be increased. 2) Shifted Rotor Tooth: Shifted rotor tooth can be used to reduce the cogging torque, since the phase difference of cogging torque waveforms of two adjacent rotor teeth would make the peak to peak value much smaller [34], [37], as shown in Fig. 26. The torque ripple can be reduced in the same way. In Fig. 27, although there are two valleys with the change of rotor shift angle, the torque ripple cannot be reduced as low as the 12S16P FRPM machine or its consequent pole type. Naturally, this way would reduce output torque to 2.35 Nm with 34.3% torque ripple and 1.96 Nm with 28.5% torque ripple at two valley points. 3) Shaped Rotor Tooth: Stator tooth or rotor tooth can be shaped to reduce the rate of change of the airgap permeance [38]\u2013[40], as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003046_j.simpat.2020.102080-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003046_j.simpat.2020.102080-Figure7-1.png", "caption": "Fig. 7. Pressure coefficient of the single bevel gear: (a) 4486 r/min; (b) 6708 r/min; (c) 8203 r/min; (d) 10,031 r/min; (e) 12,286 r/min; (f) 15,000 r/min.", "texts": [ " In order to analyze the change laws of windage power losses intuitively and clearly, the bevel gear surface is selected as the reference plane. In this analysis, the gear rotational speed is set to 4486 r/min, 6708 r/min, 8203 r/min, 10,031 r/min, 12,286 r/min and 15,000 r/min, respectively, the gear rotates counterclockwise (A) viewed from the toe. The calculated results of static pressure are shown in Fig. 6. Furthermore, the pressure distribution under different rotating speeds as it is generally preferred in fluid dynamics is also plotted in Fig. 7. It shows that the distribution of the pressure coefficient is similar to the static pressure. Referring to the existing public literature [1], the static pressure is chosen as an index to measure the windage power losses. As can be seen in Figs. 6 and 7, the pressure on the convex surface is higher than the concave side due to the counterclockwise rotation of the bevel gear. Meanwhile, it is also noted that the maximum static pressure can be obtained around the heel of the bevel gear, and the distribution of static pressure at high speeds have periodic changes (see Figs" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001370_0954406215621097-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001370_0954406215621097-Figure2-1.png", "caption": "Figure 2. Operation of the harmonic drive. ni, input rotational velocity; no, output rotational velocity.", "texts": [ " In the Test experiment and attribute evaluation section, a testing apparatus is set up, the attributes of this specific system are calculated, and the experimental data are analysed to verify or identify the model\u2019s key attributes for a high precision prediction. In the Verification and discussion of model performance section, the mathematical equations of the model are solved, the theoretical response are predicted and compared with the experimental response, and the model performance is discussed. In the last section, some conclusions are given. Harmonic drive model formulation Transmission mechanism of the harmonic drive Figure 2 shows a picture of the actual operation of the harmonic drive, and the partial enlargements clarify the deformation of the flexspline and the change in the teeth engagement condition. Note that when the harmonic drive is in operation, the elliptical cam rotates and forces the round flexspline to deform elliptically through the thin-walled ball bearing to push the outer teeth near the major axis of the flexspline into the inner teeth on the round rigid circular spline. As a result of the meshing effect, the teeth on the flexspline cause it to rotate in the opposite direction of the input motion" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003017_j.addma.2020.101822-Figure21-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003017_j.addma.2020.101822-Figure21-1.png", "caption": "Fig. 21. Case 2 sample that contains partitions 1\u20134.", "texts": [ " 20 shows there is no dominant frequency within partition 3. At a macro scale, this is expected because FFT analysis is performed for one partition. The slice height is not constant (it is increasing), and there are no transition points. H. Kalami and J. Urbanic Additive Manufacturing 38 (2021) 101822 The first four partitions of the Case 2 are in mount 1, and the second four are in mount 2. In the first mount, the measurement starts from the bottom layer and measures the surface roughness up to the end of partition 4 (Fig. 21). It can be detected that within the partitions, roughness variation are limited and that the surface is smooth; whereas, there is a small bulge at transition points between partitions. Fig. 22 depicts the Ra results for the partition 1\u20134 set. Although the Ra is almost constant within the partitions, the Ra rises suddenly at transition points between partitions. The reason for the sudden increase in roughness at the connection points is because of the sudden change in nozzle orientation. Fig. 23 indicates nozzle orientation in the first 3 partitions" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001326_1.3640593-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001326_1.3640593-Figure2-1.png", "caption": "Fig. 2 Translating point mass", "texts": [ " Application of equation (11) is straightforward although laborious in a complex problem. In the next section two relatively simple illustrations are presented. We note finally that the translational acceleration of the main vehicle's mass center is given b y equation (10) and that the position and velocity would follow b y appropriate integration. Applications A Translating Point Mass on a Vehicle M o v i n g in Two Dimensions. W e make the following identification of terms between equation (11) and Fig. 2, which shows the schematic: Unit Vectors e,<\u00b0> = kco &)'<\" = 0, q, = - i n + j?7(i) External Forces and Moments F = M = 0 Performing the manipulations required by equation (11), we find first q, = i[aco2 \u2014 r) co \u2014 2tojj] -F j[ \u2014 TJCO2 \u2014 aco + ", " I t is easily verified that the coefficient of co is the instantaneous moment of inertia of the system about the instantaneous combined mass center, while the terms involving r; and 77 represent the moments of the Coriolis and relative acceleration forces with respect to the same point. An interesting observation is found in the coefficient of the damping term. The implication is that there is positive damping whenever rjri > 0, but an instability tendency whenever 7777 < 0. Equation (12) is valid irrespective of the physical mechanism whereby TO executes the motion qi. The action-reaction forces between M and m can be of any type; e.g., elastic, electrostatic, or magnetic. For this reason no specific mechanism has been indicated in Fig. 2. A S w i v e l e d Rocket Engine on a Veh ic le M o v i n g in T w o D imens ions . Fig. 3 shows the schematic. Again we make an identification of terms between equation (11) and Fig. 3. As noted earlier, the assumption is made that the variations in mass and inertia associated with thrust production are negligible. NH = TO, / . . ( i ) = 1 a 4 8 8 / S E P T E M B E R 1 9 6 2 0 Jy 0 As in the previous example, since the motion is assumed to be two dimensional, the inertias I x , I v and J x , J u are immaterial" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001686_j.promfg.2018.07.121-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001686_j.promfg.2018.07.121-Figure1-1.png", "caption": "Fig. 1. FEM model construction.", "texts": [ " / Procedia Manufacturing 26 (2018) 941\u2013951 Wang and Shi / Procedia Manufacturing 00 (2018) 000\u2013000 3 scale simulation strategy. In this strategy, the mesoscale 3D finite element analysis is used for the calculation of temperature field. The calculated temperature history is exported to the micro-scale 2D phase field simulation for the calculation of dendrite structure. For FEM simulation, a 5\u00d71\u00d71 mm3 workpiece is constructed and non-uniform grid size with tetrahedron shape is used to mesh the part (with finest grid at the melt pool center, with size of 12.5 \u03bcm approximately), as shown in Fig. 1. Due to the symmetric temperature distribution against YZ plane, we define laser beam to scan along the long edge (OY axis) of the part in the simulation so that only half of realistic heat transfer is calculated to save computational resource. A commercial FEM package, Abaqus, is used to carry out the meso-scale simulation. It should be noted that the material to be built experiences cyclic solidification/re-melting during the additive process. To be specific, the upper portion of solidified melt pool will be re-melted in the subsequent laser scans to ensure tight bonding of each layer", " Although there is no information exchange between the FE model and phase field model regarding heat/mass transport during the simulation, an additional term is incorporated in the governing heat transfer equation of the FE model to account for latent heat of solid-liquid phase transition. Such strategy simplifies the mathematical calculation while guarantees reliable and realistic simulation results. Similar sequentially coupled FE and phase field analysis has been adopted in literature [14][15]. Fig. 1. FEM model construction. Fourier heat conduction theory is mostly adopted in the formulation of heat conduction for laser additive processes, as shown by the following equation, where T is the temperature, t is simulation time, k is the thermal conductivity, \u03c1 is the material density, is the specific heat, and q is a combination of heat loss at boundary, latent heat of fusion, as well as laser beam induced internal heat. Fig. 2. FEM model construction. (1) To obtain the solution from the differential equation of heat transfer, the boundary condition needs to be defined", " / Procedia Manufacturing 26 (2018) 941\u2013951 943 Wang and Shi / Procedia Manufacturing 00 (2018) 000\u2013000 3 scale simulation strategy. In this strategy, the mesoscale 3D finite element analysis is used for the calculation of temperature field. The calculated temperature history is exported to the micro-scale 2D phase field simulation for the calculation of dendrite structure. For FEM simulation, a 5\u00d71\u00d71 mm3 workpiece is constructed and non-uniform grid size with tetrahedron shape is used to mesh the part (with finest grid at the melt pool center, with size of 12.5 \u03bcm approximately), as shown in Fig. 1. Due to the symmetric temperature distribution against YZ plane, we define laser beam to scan along the long edge (OY axis) of the part in the simulation so that only half of realistic heat transfer is calculated to save computational resource. A commercial FEM package, Abaqus, is used to carry out the meso-scale simulation. It should be noted that the material to be built experiences cyclic solidification/re-melting during the additive process. To be specific, the upper portion of solidified melt pool will be re-melted in the subsequent laser scans to ensure tight bonding of each layer" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003476_j.triboint.2021.106951-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003476_j.triboint.2021.106951-Figure5-1.png", "caption": "Fig. 5. Force diagram of helicopter fuselage when turning.", "texts": [ " The lift force can be decomposed in the horizontal direction which is opposite to the inertial force (centrifugal force) and vertical direction which is the reverse direction of gravity. Besides, the inclination of the rotor disc causes the fuselage to form a gradient angle equal to the roll angle between the fuselage and the horizontal plane. The horizontal component of the lift increases with the gradient angle increasing, which increases the turning rate of the helicopter. The force diagram is shown in Fig. 5. The helicopter may turn left or right when turning, and the position of the lubricating oil level in the intermediate gearbox which is relative to gears and oil guide holes is different in different turning directions. To perform simulations with turning left and right, the intermediate gearbox is set to complete the motion of increasing the roll angle from 0\u25e6 to 60\u25e6 and then decreasing to 0\u25e6 within 2s. The oil distribution and oil flow rate of four oil guide holes are monitored during simulations, as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003642_s42835-021-00807-4-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003642_s42835-021-00807-4-Figure2-1.png", "caption": "Fig. 2 Flux lines of spoke type BLDC motor", "texts": [ " In this perspective, this paper presents a comprehensive study of the effect of slot and pole combination on the performance of spoke type BLDC motor through electromagnetic and structural analysis. The structure of Spoke type BLDC motor configuration is shown in Fig.\u00a01 and its dimensions are given in Appendix\u00a01. The difference between the IPM and Spoke type motor is based on the arrangements of magnet with respect to the rotor. To evaluate the performance of the motor, a Finite Element Analysis (FEA) based CAD package \u2018MagNet 7.5\u2019 is employed. The flux lines of the Spoke type BLDC configuration are illustrated in Fig.\u00a02. The characteristics of the 1 3 Spoke type BLDC motors are comparable to that of the IPM type BLDC motors. FEA analysis is performed on both the motors of equal rating and their corresponding average and cogging torques are compared. Figures\u00a03 and 4 illustrates the comparison of average and cogging torque characteristics of both the configurations and the corresponding numerical values are given in Table\u00a01. From Table\u00a01, it is evident that the average torque produced by the Spoke type BLDC motor consisting of Ferrite Magnets is comparable to that produced by the IPM type BLDC motor employing NdFeB magnets" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002661_tia.2020.2987897-Figure23-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002661_tia.2020.2987897-Figure23-1.png", "caption": "Fig. 23. Illustration of unequal rotor teeth.", "texts": [ " As aforementioned, the 6th harmonic and its multiples may exist in the on-load DC winding induced voltage, in which the 6th and 12th are dominant harmonics as shown in Fig. 2(b). Both the amplitude and initial phase of the 6th and 12th harmonics are affected by the rotor outer pole arc as shown in Figs. 21 and 22. As a consequence, it is expected that the onload DC winding induced voltage may be suppressed by designing a rotor with unequal teeth. Consequently, unequal rotor teeth as illustrated in Fig. 23 is subsequently employed to reduce the on-load DC winding induced voltage. The mechanism behind this method is to cancel the corresponding on-load DC winding induced voltage harmonics by a pair of rotor outer pole arcs. In order to minimize EPP_OL, all available combinations of rotor outer pole arcs 1 and 2 are calculated by the FE method. EPP_OL and Tave are plotted against rotor outer pole arcs 1 and 2 as shown in Figs. 24 and 25. It is shown in Fig. 24 that a smaller Authorized licensed use limited to: University of Exeter" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002680_tec.2020.3000753-Figure8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002680_tec.2020.3000753-Figure8-1.png", "caption": "Fig. 8. The distribution of the q-axis magnetic field.", "texts": [ " Urd1, Urdx, and Urd2 in the d-axis RMP model determine the values of the above-mentioned nonlinear reluctances and are also affected by these reluctance values; hence iterative calculation is needed to solve these unknown parameters. The specific iterative calculation processes are shown in Fig. 7. In this paper, the magnetic field generated by the q-axis current component is called the q-axis magnetic field, and the corresponding RMP model is called the q-axis RMP model. 1) Analysis of the q-axis RMP model The distribution of the q-axis magnetic field is shown in Fig. 8. It can be seen from Fig. 8: Authorized licensed use limited to: University of Exeter. Downloaded on June 21,2020 at 05:19:05 UTC from IEEE Xplore. Restrictions apply. 0885-8969 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. a) Similarly, the permeability of the rotor yoke and the pole cap region is regarded as infinite. And the flux lines do not pass through the PMs and the reluctance Rri; hence the RMP in the pole cap region is equal to zero. b) Affected by the flux path reluctance, the flux lines are separated in the middle position of the bridge (i.e., m=0.5 in Fig. 8). Considering the saturation effects in the bridge region of the d-axis magnetic field, the q-axis RMP reaches the maximum value at point B, and decreases along the flux lines to both sides, reaching points A and C respectively. c) The q-axis magnetic field is less affected by the non-uniform saturation of the bridge; hence it is considered that the magnetic potential of points A and C are the same. Moreover, since only radial flux exists between point C and point D, there is no magnetic potential drop between them", " Due to the existence of the PMs, the d-axis magnetic field is larger than the q-axis magnetic field. It is less affected by the cross-coupling. Therefore, the influence of the q-axis magnetic field is neglected in the processes of solving the d-axis RMP model. On the contrary, the q-axis magnetic field is greatly affected by the cross-coupling. In order to obtain accurate results, the influence of the d-axis magnetic field should be taken into account in the processes of solving the q-axis RMP model. When there is only the q-axis current component, it can be seen from Fig.8 that the bridge is not saturated, whereas the overflow region is saturated. Therefore, the actual saturation situation of the bridge is only affected by the d-axis magnetic field; that is, the reluctance of this region is only determined by the d-axis magnetic field. Whereas the actual saturation situation of the overflow region is affected by both the d-axis magnetic field and q-axis magnetic field; hence the reluctance of this region is determined by both the d-axis magnetic field and q-axis magnetic field", " 10, Fsq1 and Fsq2 are the MMF at the corresponding stator teeth generated by the q-axis current component. When the stator saturation is neglected, their values can be directly obtained by using winding function [16]. When considering the stator saturation, their values are solved by the iterative calculation method proposed in this paper. Rgq is the air-gap reluctance under half of the stator tooth. Rb is the reluctance of the half-bridge. Nonlinear reluctances Rs1 and Rs2 correspond to the reluctances of the overflow regions on the left and right sides of the bridge, respectively (as shown in Fig. 8). From the above analysis, Rb is only determined by the d-axis magnetic field, and its expression is given by b 11 b b b 2 rd2 2 , ( ) (B ) B wwR B l l U \u03bc \u03bc = = (16) where Bb is the average flux density of the bridge under the condition that only the d-axis magnetic field exists, and \u03bc(Bb) is the permeability corresponding to Bb. For the nonlinear reluctances Rs1 and Rs2, when there are both the d-axis magnetic field and q-axis magnetic field in the motor, the flux density vector (B vector) directions of the d-axis and q-axis magnetic field are the same in Rs1 region, whereas those are opposite in Rs2 region" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002820_j.compstruct.2020.111883-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002820_j.compstruct.2020.111883-Figure5-1.png", "caption": "Figure 5: Final configuration of a square laminate (12 in x 12 in) and [0/90] as predicted from finite element", "texts": [ " Figure 6: Final configuration of a [0/90] square laminate- Only 1 bending curvature exists [8]. The reason for this is due to the competition for and gaining dominance for deformation (in bending) in the two different directions. Perfectly, the bending stiffness along the two directions ExIx and EyIy have same magnitude but opposite in direction. This is due to the [0/90] lay up sequence and the equal lengths of both sides. If the two quantities keep being the same throughout the cooling process, then the configuration as shown in figure 5 should result. However in real structure, there are variations in material properties from location to location. If one quantity (say ExIx) is slightly larger than the other, then bending will be preferred in the y direction. Once bending is more along the y direction, the additional deformation would increase the difference between the two stiffness values and one direction for bending would become more definitely favored. This favorable selection is demonstrated below. Consider the case of a rectangular laminate of dimensions 12 in x 6 in with the lay up sequence [0/90]", " This gives confidence in the method and it may be used for the prediction of deformation of other laminates with different lay up sequence. However caution needs to be taken for the prediction of the deformed configuration for the situation of square laminates with lay up sequence having the same number of layers in conjugate directions, for example, [0/90], [02/902] or [0m/90m]. This is because for this type of geometry and lay up sequence, theoretically, the two sides should have equivalent deformation, giving rise to a saddle configuration, as shown in figure 5. However in reality, only one curvature exists as shown in figure 6. The reason for this is that in reality, there may be un-uniform spatial distribution of the properties of the material in the laminate. This can make one direction weaker (or stronger) than the other direction. Once an initiation begins, the following action would favor one direction over the other giving rise to the final configuration as shown in figure 6. This issue can not be addressed using analytical technique, which does not take into account the variability in the material properties" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000931_9781118703274.ch2-Figure2.46-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000931_9781118703274.ch2-Figure2.46-1.png", "caption": "Figure 2.46 Pitch-regulation mechanism using rotating masses, with the possibility of varying the return spring moment (Br\u00fcmmer). Reproduced by kind permission of Hermann Br\u00fcmmer", "texts": [ " Such mechanisms are usually simple and their solid construction usually makes for reliable operation. The energy they deploy for control processes is derived from themovement of rotatingmasses. To use such an arrangement for pitch regulation, however, the system must be accurately dimensioned, which in turn requires that the precise moments engendered in the blades during operation must be known. This is necessary, since modifying and adapting the parameters of mechanical devices usually involves considerable expense. Figure 2.46 shows a pitch-regulation mechanism in which rotation of the turbine sets up a centrifugal force in a set of flyweights. Should the centre of mass lie outside the plane of rotation, the moments acting tend to bring it back into the plane. Load and restoring torques are applied by means of springs. By varying their length of travel the springs can be adjusted to suit machine and wind characteristics. In the model shown in Figure 2.46, the pitch of each blade is regulated separately. In this way, every blade can be acted upon to protect the turbine from over-revving. Such in-built redundancy promotes reliability. The three separate regulation mechanisms can, however, lead to different regulation procedures. These cause aerodynamic \u2018imbalance\u2019, which can place the rotor, hub and yaw gear under considerable loads. Figure 2.47 shows a centrifugal-force-based arrangement, used in the 1950s on Allgaier machines (see Figure 1.10). This mechanical regulation and positioning system was supposed to limit the speed of the turbine to its nominal speed" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003481_j.optlastec.2020.106782-Figure11-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003481_j.optlastec.2020.106782-Figure11-1.png", "caption": "Fig. 11. Stress distribution at t = 1.58 ms (magnification of deformation effect by 10 times): (a) von Mises stress, (b) \u03c3x and (c) \u03c3y.", "texts": [ " The size of the molten pool was very small, the effective overlap between the track and the track could not be formed, and the layers could not be effectively fused together, which led to unmelted defects. This not only deteriorated the mechanical properties but also affected the surface quality of the parts. However, the size of the molten pool was very large, which resulted in poor stability. At the same time, it absorbed the powder around the molten tracks, resulting in the lack of powder in the adjacent molten tracks and the appearance of pores [28,29]. Therefore, an appropriate molten pool size played a positive role in determining the SLM parts\u2019 quality and performance. Fig. 11 is the stress distribution at t = 1.58 ms (the deformation effect was magnified by 10 times), where \u03c3x represents the stress parallel to the laser scanning direction, \u03c3y represents the stress perpendicular to the scanning direction, the positive sign represents tensile stress, and the negative sign represents compressive stress. In the SLM manufacturing process, the rapid movement of the heat source produced extremely high heating and cooling speeds. It can be seen from Fig. 11, due to the fact that the thermal expansion and contraction of the material, the hightemperature area irradiated by the heat source showed the effect of expansion, while the low-temperature area during the cooling process showed the effect of shrinking. It was subjected to compressive stress in the high temperature zone, and the maximum compressive stress appeared on the substrate, while the low temperature zone in the Z. Li et al. Optics and Laser Technology 140 (2021) 106782 cooling process showed tensile stress [30]" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003476_j.triboint.2021.106951-Figure19-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003476_j.triboint.2021.106951-Figure19-1.png", "caption": "Fig. 19. Multi-condition test rig for splash lubrication of gearboxes.", "texts": [ " 18 shows the churning losses significantly increase during acceleration compared with the situation when the gearbox at rest and amplitude also increases as the acceleration increases. Besides, the churning losses greatly fluctuate with time, and show a decreasing trend Fig. 14. Mass flow rates of four oil guide holes. Fig. 15. Curve of churning loss. X. Hu et al. from a certain value in 0\u20130.05s, which is the same as previous attitudes. To verify the feasibility of the above-mentioned numerical simulation method, a test rig is specially made to perform experiments on the splash lubrication performance of a gearbox under various attitudes, as shown in Fig. 19. A gearbox with a pair of standard spur gears is used for experiments to reduce the machining error and assembling difficulty and also to facilitate the observation of the oil distribution inside the gearbox. The main components of the test rig are a gearbox, a torque sensor, three motors, a crank slider mechanism and a platform which can be divided into two parts. The gearbox, torque sensor and motor are installed on the upper platform which is driven by a servo motor and can realize the declination of the gearbox" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000931_9781118703274.ch2-Figure2.67-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000931_9781118703274.ch2-Figure2.67-1.png", "caption": "Figure 2.67 Simplified representation of a mechanical drive train", "texts": [ " Because of the shock load that can be expected and the possible reversal of the energy flow, play in gearing and clutch is to be avoided, or at least kept as low as possible. It will therefore be ignored in the following. Calculations based on existing machines show that to make an approximate determination of the behavior of the transmission, the mechanical drive train, gears, clutches, etc., can usually be regarded as having zero mass according to the low moment of inertia within the system as a whole. This leaves only the two main components \u2018rotor\u2019 and \u2018generator\u2019, with an elastic, damped coupling existing between them (see Figure 2.67). Frictional components in the drive train can be ignored. The torque at the generator coupling MKu can be represented by the simplified relation MKu = kTS ( \ud835\udf00W \u2212 \ud835\udf00G ) + kDK d ( \ud835\udf00W \u2212 \ud835\udf00G ) dt (2.88) or MKu = MTT +MTD (2.89) as the sum of moments of torsion\u2013elastic (MTT) and damping (MTD) properties, where MAW drive moment at the turbine rotor MAG drive moment at the generator MKu coupling torque at the generator MTD damping component of the drive train moment MTT torsionally elastic component of the drive train moment MWG electrical load torque in the generator \ud835\udf00W angle of rotation of the rotor \ud835\udf00G angle of rotation of the generator \u0394\ud835\udf00 = \ud835\udf00W \u2212 \ud835\udf00G angle of torsion kTS torsion resistance kDK damping constant TG run-up time constant of the generator TW run-up time constant of the rotor In stationary-state operation d(\ud835\udf00W \u2212 \ud835\udf00G)\u2215dt = 0, so that the coupling torque reduces to its torsionally elastic component MKu = MN = MTT = kTS ( \ud835\udf00W \u2212 \ud835\udf00G ) " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000618_ilt-11-2011-0098-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000618_ilt-11-2011-0098-Figure1-1.png", "caption": "Figure 1 Typical straight fluted bearing Figure 2 Experiment apparatus for water-lubricated rubber bearings", "texts": [ " The bearings have excellent performance against wear and can resist the abrasion of solid particles floating in the water, so they are popular in applications where the lubricant is \u201cdirty\u201d, such as using in sewage pump. The bearings are able to tolerate misalignment of the shaft far better than equivalent rigid bearings. Water-lubricated rubber bearing was accidentally discovered in the1920s (Busse andDenton, 1932).Thefirst design of these bearings had a plain bore, but this was modified several times in order to improve the operation of thebearing.Themost popular design used today and the type focused on in this work is the straight fluted bearing as illustrated in Figure 1. This design of bearing consists of a number of load carrying lands or staves, separated by flutes orientated axially in the bearing. The flutes supply the bearingwith lubricant, which enters at one end of the bearing and leaves at the other.The flexible rubber bearing liner is bonded onto the outer rigid shell. The special fluted configuration leads to boundary lubrication and low load capacity of the rubber bearing (Fogg and Hunswick, 1937). Recently with the development of the heavy load and high speed The current issue and full text archive of this journal is available at www" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001833_j.engfailanal.2017.04.017-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001833_j.engfailanal.2017.04.017-Figure6-1.png", "caption": "Fig. 6. Schematic graph of local breakage.", "texts": [ " Bending fatigue breakage starts with a crack in the root section and progresses until the tooth or part of it breaks off. Overload breakage appears as a stringy, fibrous break that has been rapidly pulled or torn apart. Random fracture can occur in areas such as the top or the end of a tooth, rather than the usual root fillet section [16]. This damage results in the decrease of contact area between teeth. In this work, a local breakage at the end of engagement of one tooth (located at tip of the tooth) on pinion is assumed, as shown in Fig. 6. The parameter wb in Fig. 6(b) is the projection of involute arc B1B2 (shown in Fig. 6(a)) into plane of action and specified in simulation. In addition, for simplification, the projection of edge B2B3 of the breakage into plane of action is assumed to be a straight line. hb denotes the length of breakage along tooth width and tb the thickness. The variable \u03b8b represents the angle between the hypotenuse and the transverse section of tooth, indicating relative position between the hypotenuse and contact line. And there're two situations here (see Fig. 7). a) \u03b8b < (\u03c0/2\u2212 \u03b2b) In this case, the actual length la(t) of contact line with local breakage can be calculated by \u23a7 \u23a8\u23aa \u23a9\u23aa l t l t t t l v t \u03b5p w sin \u03b8 sin \u03c0 \u03b8 \u03b2 t t t t t t ( ) = ( ) \u2264 (t) \u2212 ( \u22c5 \u2212 ( \u2212 )) ( 2 \u2212 \u2212 ) < \u2264 0 < \u2264 a bs t b bs be be total t t bt b b b (29) where t \u03b5p w v= ( \u2212 ) tbs bt b (30a) t \u03b5p h \u03b2 v= ( \u2212 tan )b tbe bt b (30b) t \u03b5p v=total tbt (30c) \u03b8 arc h w= tan( )" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003603_jestpe.2021.3065997-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003603_jestpe.2021.3065997-Figure6-1.png", "caption": "Fig. 6. Magnetic field distribution in the rotor (a) flux density distribution figure (b) flux lines in the claw plates", "texts": [ " Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. More intuitively, from the equivalent magnetic circuit as shown in Fig. 4, the plates provide a path for other field harmonics with different pole-pair number when rotor rotates. Thus, the low pole-pair number working harmonic, which is modulated by stator slots, is enhanced. To verify the statement, the flux distribution in the claw plate is shown in Fig. 6. It is indicated in the figure that the claw plate is with low flux density and the main flux lines flow in the plate is with 2 pole-pairs. Fig. 7(a)(b) show the flux distribution along the line in fig. 6 (a) at the junction of claws and plate. From the results, the 2 polepairs magnetic field in the claw plates is with the largest magnitude. Thus, the modulation process that produces low pole-pair number magnetic field is enhanced and the flux closes through the path of the claw plate. D.Performances comparison Four 12 stator slots/ 10 rotor pole-pairs machines are designed with same outer diameter, effective length. Their main design specifications are concluded in table II. From the results, the SPMV machine is with the smallest excitation ability and its working harmonics are the lowest among the four topologies" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002314_j.matchar.2018.03.032-Figure14-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002314_j.matchar.2018.03.032-Figure14-1.png", "caption": "Fig. 14. (a) The slip plane of different glides for Ti64. (b) The different deformation behaviors of initial defects for LSF-Ti64 under compressive and tensile loading.", "texts": [ " However, the higher strain rates (1000 and 3000/s) result in the sharp increase of \u0394\u03c30.2, the value of which increases from 80MPa at 0.001/s to 270MPa at 3000/s. Compared to other Ti64 alloys, such as the forged-Ti64 mentioned above, the electron beam single melt (EBSM) Ti64 alloy [38] and the traditional commercial Ti64 alloy [39], the LSFTi64 alloy possesses a much greater value of \u0394\u03c30.2 as seen in Fig. 13 (c). The tension-compression asymmetry of LSF-Ti64 alloy arises from the activation of different slip systems under the compressive and tensile loading, as summarized in Fig. 14(a). The possible deformation systems are demonstrated with the tension and compression axes. Under the compressive loading condition, the pyramidal< c+ a> slip should be first slip system activated in the compressive specimens. In contrast, the prismatic< a> slip system will be activated firstly in the tensile specimens. The pyramidal< c+ a>glide appeared at the quite beginning of plastic deformation, accounting for the high value of compressive yield stress. In fact, the pyramidal< c+a> slip system is not centro-symmetric while all the other slip systems are centro-symmetrical", " The high critical resolved shear stress (CRSS) of asymmetric< c+ a>glide is not as same as the reversal of resolved shear stress, leading to that the compressive yield stresses are higher than tensile yield stresses [40,41,42]. In addition, it is found in Fig. 13 (c) that the level of tension-compression asymmetry of LSF-Ti64 (regarded as \u0394\u03c30.2) is much higher than that of the other two types of Ti64 alloys. Except for the activation of different slip systems, the more prominent tension-compression asymmetry of the LSF-Ti64 alloy is attributed to the different plastic-deformation behaviors of the initial defects, such as voids and lack-offusion pores, upon tensile and compressive loading, as summarized in Fig. 14(b). These initial defects exhibit flat or angular morphologies and are associated with unmelted layer surface, incompletely melted powder particles and unescaped gas, as described earlier. The defects are extremely harmful for the mechanical properties especially when there is applied tensile stress. Upon tensile loading, the voids or lack-offusion pores will be elongated and torn apart into larger region of stress concentration. After that, they expand and evolve into the crack initiation and propagation sites" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003660_lra.2021.3095035-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003660_lra.2021.3095035-Figure4-1.png", "caption": "Fig. 4. Shown are the effects of the singularity at vertical hovering. (a) Configuration of the UAV platform hovering at a vertical pose. Gimbal 1 and 3 are in singularity (the \u03b11 and \u03b13 joints are ill-conditioned). (b) Force envelope and (c) torque envelope of the platform. The red/blue regions are the envelope with/without singularity handling (setting \u03b11 and \u03b13 to zero). Selected data points indicated the edges of the regions.", "texts": [ " Taking derivatives of the normalized thrust F\u0302 i in (26), the rate of change of joint angles \u03b1\u0307i and \u03b2\u0307i can be written as \u02d9\u0302F i = J(\u03b1i, \u03b2i) [ \u03b1\u0307i \u03b2\u0307i ] = \u23a1 \u23a3 0 c\u03b2i \u2212c\u03b1ic\u03b2i s\u03b1is\u03b2i \u2212s\u03b1ic\u03b2i \u2212c\u03b1is\u03b2i \u23a4 \u23a6[ \u03b1\u0307i \u03b2\u0307i ] (33) where J(\u03b1i, \u03b2i) is the Jacobian matrix [17]. When \u03b2i = \u00b1\u03c0/2, J(\u03b1i, \u03b2i) will lose rank and \u03b1\u0307i will be close to infinity; in result, the control will attempt to track infinitely large joint speeds, which is not a viable input command for the system. The singularity occurs when a thrust direction is aligned with its \u03b1i axis, so there are at most two gimbals in singularity given that the desired trajectory of the platform is slow. Fig. 4 a illustrates an example: the top and bottom gimbals are in singularity when the system is hovering sideways. The singularity can be handled by manually overwriting the values of \u03b1i to prevent large angular velocity command. By setting \u03b1i = 0 in (26), Fiy = 0. Because F i is determined by allocation from Bu in (24) and W is a constant matrix, at most two columns in W (that correspond to Fiy) are removed, and W maintains full rank. This singularity-handling method does not affect the overactuated configuration of the platform. The maximum wrench of the platform is evaluated when hovering at 90\u00b0 pitch angle. At hovering, the gimbal actuators provide thrusts to balance the gravity. The extra thrust capabilities are used for trajectory tracking and disturbance rejection. The maximum force and torque envelopes (Fig. 4 b, 4 c) represent the range of the extra body wrench. The maximum force is obtained by setting the torque to zero, and vice versa. Although the singularity-handling Authorized licensed use limited to: University of Gothenburg. Downloaded on September 01,2021 at 11:05:04 UTC from IEEE Xplore. Restrictions apply. method reduces the maximum wrench and robustness, the whole platform is still controllable in all six DOF. The torque used to control the gimbal angles is jointly generated by four propellers, and the maximum torques that actuate \u03b1i and \u03b2i are related to each other" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002354_j.vacuum.2018.09.007-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002354_j.vacuum.2018.09.007-Figure2-1.png", "caption": "Fig. 2. Design of the build aimed at investigating: a)orientation; b)location in the layer; c)height.", "texts": [ " Since the algorithm is covered by copyright, beam current and beam speed time dependent diagrams are hided to the users. A line offset of 0.1 mm was set. The EBM process was carried out in vacuum. In order to evaluate the robustness of the EBM process in terms of dimensional accuracy a simple test case, consisting in rectangular parallelepiped (50\u00d7 10\u00d710mm) samples manufactured in Ti6Al4V, was chosen. A suitable Design of Experiment (DOE) was developed in order to investigate on the following intra-build process parameters: \u2022 Samples orientation (Fig. 2a): samples were built according to n.4 different orientations: x, y, 45\u00b0 and Z (90\u00b0). The x and y oriented samples were built horizontally and they were, respectively, parallel and perpendicular to the rake movement direction. The 90\u00b0 oriented samples were built vertically. \u2022 Location of the sample in layer (Fig. 2b): the group of samples shown in Fig. 2a was built in n.5 different zones in the x-y plane which are named hereafter: Z1, Z2, Z3, Z4 and Z5. The Z5 zone was the central one while all the other zones were representative of the four corners of the x-y plane. Such configuration was chosen in order to guarantee a high build envelope symmetry. \u2022 Height in the build chamber (Fig. 2c): the group of samples shown in Fig. 2b was built at n. 3 different levels in the build chamber which are named hereafter: h1, h2 and h3. More in detail, the h1 level starts at z= 40mm, the h2 level starts at z= 170mm and the h3 level starts at z= 300mm. Hence, n.60 samples were manufactured in a single job. In order to test EBM process repeatability, two identical jobs (hereafter named run1 and run 2 respectively) were carried out in the same conditions for a total of n.120 samples. The orientation and the location of the samples in the build chamber were set by using the Materialize Magics software", " Indeed, according to the used measurement method, the thickness of the x oriented samples is affected by the y scale factor, the thickness of the y oriented samples are affected by the x scale factor, the thickness of the 45\u00b0oriented samples are affected by the x, y and z scale factors and the thickness of the 90\u00b0 oriented samples are affected by the x and y scale factors. That is, the thickness of 45\u00b0 oriented samples is the only one affected by the z scale factor. As a consequence, an improvement in the choice of the z scale factor may be needed in order to get more homogenous results, while the x and y scale factors, recommended by ARCAM AB, were found suitable for each growth direction. The 5 different zones in the x-y plane where a group of samples were built are shown in Fig. 2b. In each zone and for each height level a mean average thickness was computed by considering the aggregated measurement database as shown in Fig. 12. In such figure, the dotted red line represent the nominal thickness value of the specimens. Also in this case, eligible dimensional accuracy was found. Nevertheless, results are not homogenous since the mean average thickness of the specimens built in zone 5 was found significantly lower with respect to the mean average thickness of the specimens built in the other zones (see Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000284_0022-2569(67)90005-5-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000284_0022-2569(67)90005-5-Figure7-1.png", "caption": "Figure 7. One common normal q, and two revolute axes as a pair of conjugate lines can determine a linear complex.", "texts": [ " Finally, given two polar planes ~t and fl and their respective poles A and B together with one other line q, the lines wl and w 2 are (from 2.12.1), respectively, the line of intersection of at and fl, and the line AB. 2.20. The following section consists entirely of examples on the location of screw axes by purely geometrical means. Sometimes a basic kinematic understanding is taken for granted (e.g. a self-evident direction of a velocity vector), but no kinematic quantities are introduced at all. 3.1. By reason of the theorem quoted in 2. ! 5 a pa~ of conjugate lines is often readymade. Figure 7 shows a mechanism for which w I and w 2 are both axes of given revolute pairs, and q is the common normal at the single point where the two profiles touch at Q. $12 and $13 are both completely known; they are in fact w I and w2, and they have zero pitch. $23 may be located by direct application of the method described in 2.17. Thence, using the line q of the complex, r and 0 may be found (see 2.2 above) and from Eq. (2) the pitch h o\u00a3 $23 determined. 3.2. If, in the configuration shown in Fig. 7, members 2 and 3 were joined not by a profile pair but by a baH-ended coupler AB of any len~h aligned along q, the construction for $.,3 would be precisely the same for the instant in question. But a fourth member, the coupler, is now introduced, free to spin about its axis AB, and thus possesses two degrees of freedom relative to 1 unless provided with one additional constraint. Such a constraint is shown in Fig. 8. Here the members have been re-numbered, and it is required to find $1 a. The velocity vector va is perpendicular to a plane shown as = containing A and the shaft axis 12, and v B is likewise perpendicular to plane ft" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002441_9781119509875-Figure11.1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002441_9781119509875-Figure11.1-1.png", "caption": "Figure 11.1 Proposed mechanical structure of Ro CIF VIP with 5 DOF", "texts": [ " al [13] have developed a virtual application for testing a 3D vehicle inside the Unity3D software. Also, research on virtual environment provided by Unity3D was not limited to terrestrial vehicles, but was also conducted on aerial UAVs [14]. Certain researchers have even used Unity3D to simulate through animation, testing of real robots by connecting them with the virtual environment through specific interfaces [15, 16], allowing the robot to experience different simulated scenarios. The proposed mechanical structure Ro CIF VIP [17] with 5 degrees of freedom is presented in Figure 11.1. The structure is made to apply induction hardening treatment on metallic profiles of length no more than 60cm. The structure can be divided into 4 main sections according to their designation. The first section contains two prismatic joints. One joint is for grabbing the metallic profile (top green part in Figure 11.1) when the user inserts it inside the machine, and the other is for sliding it down through the inducer (top yellow part in Figure 11.1). The second section is made out of the inducer and cooling system (the inducer has magenta color in Figure 11.1). At this point this section has no degree of freedom. The third section is similar to the first as it consists of two prismatic joints. The first one will grab the metallic profile (bottom green component in Figure 11.1) as it comes out of the inducer, and the second will slide the profile down through and out of the inducer section (bottom yellow component in Figure 11.1). The fourth and final section is the extraction system (blue part in Figure 11.1). This is made out of one prismatic joint and Advanced Intelligent Robot Control Interfaces 139 it will take out of the mechanical system the metallic profile when the induction process was completed. For each prismatic joint described and presented in Figure 11.1, we have had to simulate it in the virtual environment. This was achieved by adding prismatic joints to all 5 degrees of freedom. Unity3D provides many tools for building a virtual simulation but it does not provide a specific prismatic joint component. This is why we have had to add one, ourselves. The main advantage in working with Unity3D is that it provides the possibility to create new components, starting from existing ones or just starting from scratch. The other advantage is working with C# which is an advanced programming language", " The second component called Interface is the GUI component of this virtual simulation, and it is initialized using the root object within the simulation. This means that this component does not depend on the robot behavior within the simulation scene, and will even be present if the robot is switched with another. Figure 11.7 presents the class diagram of SimStarter object. Comparing with Figure 11.6, we identify the parameter responsible with linking the application with the robotic structure of Ro CIF VIP, named cifPrefab. This component stores the link to the prefab file that contains the entire robot structure from Figure 11.1. Using this reference we can even add multiple robots in the same virtual environment. Advanced Intelligent Robot Control Interfaces 143 Figure 11.8 presents the Interface class diagram. This class has few variables, but has several methods called when the user presses a button to do an action. With the tools that Unity provides, we can build a good GUI in a short time that will fulfill our every need. The first 4 parameters of Interface class are values required to use with the intelligent interfaces" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001753_tia.2014.2301862-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001753_tia.2014.2301862-Figure1-1.png", "caption": "Fig. 1. BLDC motor description and specification.", "texts": [ " In Section V, the performance criterion is presented and used to compare the two types of windings but particularly the two technologies. Section VI presents the first prototype of a winding printed on a flex-PCB and its experimental characterization. Section VII finally summarizes the main contributions of this paper. 0093-9994 \u00a9 2014 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 slotless BLDC motor under study is presented in Fig. 1. It is a three-phase two-pole motor with a parallel magnetized permanent magnet (PM). The three-phase winding inserted in the air gap can be characterized both by the shape of the loops it is made and by the technology used to manufacture it. There are different types of air-gap windings [5]. In this paper, we investigate generalized versions of the skewed winding (see Fig. 2) and of the rhombic winding (see Fig. 3), the two most widely used air-gap windings. This generalization is achieved through two reduction factors fr and frL, which, when they are set to zero, degenerate both windings into their basic shape" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001380_s12555-015-0064-5-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001380_s12555-015-0064-5-Figure2-1.png", "caption": "Fig. 2. Tilt angles of the rotor w.r.t fixed body frames.", "texts": [ " Let FE : { OE ; XE , YE , ZE } be a world inertial fram and FB : { OB; XB, YB, ZB } be the quadrotor body frame attached to its center of gravity Fig.1. In addition, the rotors-fixed frames are taken to be parallel to each other and parallel to the quadrotor body frame and are given by FPi : { OPi ; XPi , YPi , ZPi } , i = 1, ...,4. The orientation of each of the rotors is controlled by two rotations with respect to the rotor-fixed frame; \u03b1i, a rotation about YPi , and \u03b2i , about ZPi . As shown in Fig.2, this rotation creates a second rotating frame for the rotors, FPi : { OPi ; XPi , YPi , ZPi } , i = 1, ...,4. When the rotors are aligned along ZPi , rotor 1 and rotor 2 are assumed to rotate counter-clock-wise CCW, while rotor 3 and rotor 4 rotate clock-wise CW. The forward direction is taken arbitrary to be along XB Let RPi Pi be the rotational matrix from the rotors-rotating frame OPi to the rotors-fixed frame OPi . Since the rotorsfixed frames OPi are parallel to the body-fixed frame OB at the center of gravity, then RPi Pi = RB Pi = 0 0 C\u03b2iS\u03b1i 0 0 S\u03b2iS\u03b1i 0 0 C\u03b1i , (1) where C(" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000415_978-3-642-37552-1-Figure11.7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000415_978-3-642-37552-1-Figure11.7-1.png", "caption": "Fig. 11.7 a Schematics of the test setup. b Photographs of Ga-seals through a glass cylinder under normal operation conditions, and c after seal failure. Adapted from [6]", "texts": [ " In what follows, experiments performed to verify the above theory will be discussed. First, we used an inclined drop method to measure the advancing and receding contact angle of Ga on a steel plate with a roughness of 5\u00b5m Ra. The in this particular experiment, advancing contact angles up to 163\u25e6 and receding angles of 117\u25e6 were measured. Next, the operation of surface tension seals is tested on a glass cylinder, providing direct visual information on the deformation of the seal under the applied pressure. As depicted in Fig. 11.7a, the piston of this setup comprises internal channels to convey Ga from a reservoir to an annular seal cavity. The piston is made by turning on a precision lathe, and the seal cavities are fabricated by wire-\u00b5EDM. The diameter of the piston is 1.6 mm and the clearance between the piston and the cylinder is about 20\u00b5m. As the seal pressure is steadily increased, it reaches a point where seal failure occurs as illustrated in Fig. 11.7c. In a test setup with a total clearance of approximately 22\u00b5m, the maximum seal pressure was 90 KPa, and in the case of a total clearance of approximately 44\u00b5m, the seal pressure was 50 KPa. This corresponds to the theoretical expectations provided by (11.23), taking into account the uncertainties on the seal gap and the surface tension. During these experiments it was also ascertained that the seals are leak-tight in normal operation conditions. Next a more complex seal design was tested on the actuators described in previous section" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000039_978-1-84996-220-9-Figure2.7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000039_978-1-84996-220-9-Figure2.7-1.png", "caption": "Figure 2.7 Virtual linkage model for humanoid robots. We define a virtual linkage model anchored through contact CoPs. It enables the characterization of internal tensions and moments against contact surfaces. The virtual linkage model abstracts the behavior of internal and CoM forces with respect to reaction forces. These characteristics make the virtual linkage model a powerful tool for the analysis and efficient control of CoM maneuvers and contact interactions", "texts": [ " Note that placing contact CoPs at the centers of the links is not a necessary constraint. They can be placed at any position below the links in contact, but away from contact vertices and edges to prevent rotations. Therefore, in this paper we only consider flat surface contact interactions. Extensions to corner and edge contacts could also be explored using a similar methodology We associate a virtual linkage model connecting all contact centers of pressure. In the scenario shown in 2 Compliant Control of Whole-body Multi-contact Behaviors in Humanoid Robots 41 Figure 2.7 each body in contact introduces a tension with respect to its neighboring nodes as well as normal and tangential moments. For contacts with ns > 2 we can independently specify 3(ns \u2212 2) tensions, ns normal moments, and 2ns tangential moments describing the centers of pressure. Any additional link in contact introduces three new tensions with respect to its neighbors and three more moments. No more than three tensions between neighboring nodes can be independently specified for a given contact. Internal tensions and normal moments characterize the behavior of contact bodies with respect to the friction cones and rotational friction properties of the surfaces in contact" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000162_detc2009-86548-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000162_detc2009-86548-Figure6-1.png", "caption": "Figure 6: Coordinate System ),,( \u03b4YXS", "texts": [], "surrounding_texts": [ "In order to visualize the tooth flank form errors, a local coordinate system ),,( \u03b4YXS shown in Figure 5 and 6 is defined for each side of tooth flanks. The origin of ),,( \u03b4YXS is coincide with the reference point. We assume that the positive direction of axis \u03b4 is the same as that of the tooth surface normal vectors whose positive directions are defined as pointing out of the tooth from inside to outside. Under this assumption, a positive error indicates a thicker tooth than the theoretical one, and a negative error indicates a thinner tooth. Using a Coordinate Measuring Machine (CMM), tooth surfaces are measured according to a given mn \u00d7 grid. The measured tooth flank form coordinates are obtained and numerically represented as, [ ]Ti m i m i m i m zyx )()()()( =r )2,...2,1( mni \u00d7= (7) The deviation between the nominal data of target tooth surfaces and the measured tooth surfaces for each grid point can be determined by, )()()()( )( iii m i nrr \u22c5\u2212=\u03b4 )2,...2,1( mni \u00d7= (8) Equation (8) can be visually represented by error surfaces referenced at the reference point where the error is zero. Using a regression method, the error surfaces may be represented by polynomials of two variables up to the 6th order as, \u23a9 \u23a8 \u23a7 ++++++= ++++++= 6 27 2 54 2 3212 6 27 2 54 2 3211 ... ... YbYbXYbXbYbXb YaYaXYaXaYaXa \u03b4 \u03b4 (9) Here, 1\u03b4 and 2\u03b4 represent error surfaces of concave side and convex side respectively. The goal of correction is to compensate for error surfaces 1\u03b4 and 2\u03b4 by an appropriate adjustment of the universal motion coefficients. Since coordinates X and Y correspond to the tooth profile and lengthwise directions respectively, the coefficients in Equation (9) indicate specific geometric meanings. For instance, 1a and 2a are first order errors or pressure angle and spiral angle errors respectively; 3a , 4a and 5a are second order errors in profile, warping, and lengthwise curvatures and so on. Using the universal motions represented by Equation (3), we may minimize the higher order components of the error surfaces. In face-hobbing process, the two sides of tooth surfaces are generated by a single set of machine settings and the correction calculation has to be applied simultaneously on both sides, including the correction of the tooth thickness error. Therefore, compared with face-milling single-side method, face-hobbing has fewer freedoms of motion to correct the surface errors. A large error in tooth thickness needs to be corrected by adjusting the tool parameters such as the reference radii. Difference angle is conventionally defined as the angle made between the radii at the reference points of the convex and concave tooth surfaces in the plane of radial cross-section. The difference angle is used to control tooth thickness or tooth size whose deviation from the nominal data represents the surface zero order error. In correction calculation, the difference angle has to be held or corrected simultaneously together with the surface errors." ] }, { "image_filename": "designv10_9_0001941_s11432-015-5349-z-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001941_s11432-015-5349-z-Figure1-1.png", "caption": "Figure 1 An illustration of a typical HMA\u2019s modes based on X-24B configuration. (a) The three views of vehicle in retracting mode; (b) the three views of vehicle in stretching mode. Modified from [24].", "texts": [ " In Section 4, we conduct two simulation studies to test and verify the effectiveness of the switching control. Finally, conclusions are presented in Section 5. A hypersonic flight vehicle with retracted winglets is researched in this paper. The data comes from an experimental aircraft model. The only difference between retracting mode and stretching mode is the mode of the winglets which are used to adjust the lift-drag ratio, mean aerodynamic chord and reference area. Illustrations of typical HMA retracting and stretching winglet modes based on X-24B configuration [24] are shown in Figure 1. According to the longitudinal force and moment equilibrium, the longitudinal dynamics model of HMA [25] can be obtained as follows. V\u0307 = T cos\u03b1\u2212D m \u2212 \u03bc sin \u03b3 r2 , (1) \u03b3\u0307 = L+ T sin\u03b1 mV \u2212 ( \u03bc\u2212 V 2r ) cos \u03b3 V r2 , (2) q\u0307 = My Iy , (3) \u03b1\u0307 = q \u2212 \u03b3\u0307 (4) h\u0307 = V sin \u03b3, (5) \u03b2\u0308 = \u22122\u03be\u03c9\u03b2\u0307 \u2212 \u03c92\u03b2 + \u03c92\u03b2c. (6) In this model, V , \u03b3, q, \u03b1, h are the velocity, flight path angle, pitch rate, angle of attack, and altitude, respectively; \u03b2, \u03c9, \u03be are the throttle setting, natural frequency, and damping coefficient, respectively; m, \u03bc, r, My, Iy are the mass, gravitational constant, radial distance from the earth\u2019s center, pitching moment, and moment of inertia, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002277_978-3-319-27131-6-Figure9.7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002277_978-3-319-27131-6-Figure9.7-1.png", "caption": "Fig. 9.7 Angular velocities and wavelengths in a rolling bearing", "texts": [ " Bearing noises are induced by wavy surfaces of the bearing components, such as the inner and outer raceways, cage, and rolling elements. Due to imperfect manufacturing processes of grinding and honing, they cause the surface waviness that consists of global sinusoidal shapes of the bearing surfaces (cf. Chap. 5) [1, 2]. The amplitude of the surface waviness in small rolling bearings is on the order of few nanometers [6]. To characterize the surface waviness, the angular wavenumber K (simply wavenumber) in rad/m is defined as the number of radians per unit length of the wavelength \u03bb: K \u00bc 2\u03c0 \u03bb \u00f09:15\u00de Figure 9.7 shows that the shorter the wavelength, the larger the wavenumber involves. In the case of a large wavenumber, the surface consists of a larger number of wave peaks per radian. It causes the excitation frequencies when the rolling elements with a spinning velocity \u03c9b contact the inner and outer raceway surfaces. Vibrations with the excitation frequencies cause the airborne noise of the rolling bearings that emits to the environment via the bearing housing. The airborne-noise intensity increases with the amplitude of the surface waviness" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001710_j.cja.2015.03.003-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001710_j.cja.2015.03.003-Figure1-1.png", "caption": "Fig. 1 Schematic of spatial grid generation.", "texts": [ " The concept of error similarity has been proposed by for robot calibration based on error similarity, Chin J Aeronaut (2015), http:// Zhou et al.18 The error similarity for error vectors of any two poses is defined as: x \u00bc 1 e1 \u00bc e2 1=je1 e2j e1 \u2013 e2 \u00f011\u00de where e1 and e2 are the position vectors, and x is the position error similarity. In this study, inverse weighted interpolation is used to calculate the position error. The method generates an evenly spaced grid according to a particular step in the workspace of a robot (see Fig. 1). The grid vertex position errors are used to establish an error model for the grid through the inverse distance weight method (see Fig. 2). The error similarity between an arbitrary point P and the vertex Pi\u00f0i \u00bc 1; 2; . . . ; 8\u00de is negatively correlated to the distance. The correlated weight expression is as follows: Table 1 Identified kinematic errors of a Kuka KR210 robot. Link No. Da (mm) Dd (mm) 1 0.32 1.64 2 1.40 2.5 \u00b7 10 5 3 0.78 3.59 \u00b7 10 4 0.18 0.29 5 2.89 \u00b7 10 2 2.5 \u00b7 10 6 3 \u00b7 10 5 9 \u00b7 10 2 Please cite this article in press as: Tian W et al" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000931_9781118703274.ch2-Figure2.60-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000931_9781118703274.ch2-Figure2.60-1.png", "caption": "Figure 2.60 Airflow behavior and forces at the rotor blade as wind speed increases from (a) to (b)", "texts": [ " We will first discuss passive stall operation, which has predominated up until now. The vast majority of all installed wind power plants in the class up to approximately 1000 kW that supply power to the public grid are without blade positioning mechanisms, instead using so-called stall control to limit power extraction. Such plants are constructed up to an order of magnitude of 1.5MW and are generally fitted with asynchronous generators (see Figure 1.22(d)). In normal operation, laminar flow predominates at the rotor blades (Figure 2.60(a)). In these conditions, the lift values corresponding to the angle of attack are reached at low drag components (see Figure 2.60(c)). Thus in partial loading ranges a high degree of aerodynamic efficiency is attained. If, on the other hand, the wind speed approaches the value at which the generator reaches its maximum permanent load (usually the nominal power), further torque development at the rotor must be inhibited. The largely rigid grid connection means that the generator (within the relatively narrow slip range of asynchronous machines) keeps the turbine at a near-constant speed; i.e. the peripheral speed \ud835\udc63p is approximately constant. Wind speeds exceeding nominal levels cause higher angles of attack and thus (in the appropriate design) stalling (Figure 2.60(b)), when the airflow \u2018unsticks\u2019 from all or part of the blade profile. Depending upon the angle of attack, therefore, as shown in Figure 2.5, the lift coefficient ca = f (\ud835\udefc) and the lift forces dFA (see Figure 2.4) are reduced in certain ranges and the drag coefficients cw = f (ca, \ud835\udefc) or the drag forces increase. As a result, the torque-creating tangential force Ft (the sum of all partial forces dFt) does not significantly exceed its nominal values (Figure 2.60(d)). When the turbine is under full load and the wind speed climbs beyond the nominal range, this results \u2013 in spite of the greater levels of energy available \u2013 in lower rotor torque and lower performance coefficients. The performance characteristics (Figure 2.61, top) of machines such as this are therefore largely dictated by their construction. In comparison with pitch-regulated turbines, stall-regulated machines are often designed with asynchronous generators of higher nominal output. Rigid grid coupling \u2013 a basic requirement for safe operation \u2013 is thereby obtained" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002022_978-3-319-40036-5-Figure5.8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002022_978-3-319-40036-5-Figure5.8-1.png", "caption": "Fig. 5.8 Spin stand Operation (a) shows an image of a typical spins stand. The motor is mounted vertically and the camera is mounted above it. A fibre-guided strobe light is mounted on a movable arm. In this case the camera is mounted on an electrical positioning stage (for lateral movement) and a manual positioning stage (to move closer to or further from the disc) (b) is a schematic of how a low-cost photodiode and LED can be used to generate one digital pulse per disc rotation. This option is suitable if the motor is not fitted with an encoder that can generate a pulse per revolution (c) the typical signal that is generated at one pulse per revolution. Note that in this approach the entire disc must be imaged and images are only acquired at a single angular position (d) the typical signal generated by a two channel encoder. The \u2018home\u2019 channel (red) shows one pulse per revolution while the second channel (green) shows four pulses per revolution. A filter box, with a dial to input value \u2018m\u2019, permits the angular position where the disc is imaged to be changed. Where m\u00bc 0 the offset is 0 while m\u00bc 1 results in 90 offset. In a typical encoder the channel resolution will be 1000 pulses/revolution and thus the angular resolution will be 0.36", "texts": [ " The resulting centrifugal force is also influenced by the radial location of the liquid (volume) of the disc. Similarly, a motor should be chosen which can permit high acceleration / deceleration of the disc as this is critical for some applications such as centrifugo-pneumatic siphon valves [27]. The motor should also be chosen which can generate a digital signal once per rotation. If a motor is otherwise suitable, an encoder can be purchased separately and fitted to the motor. Alternatively, an optical sensor can be manufactured using a low-cost LED and photodiode detector [28] (Fig. 5.8). 5 The Centrifugal Microfluidic: Lab-on-a-Disc Platform 127 128 B. Henderson et al. If the motor generates just one digital pulse, at the home position, per rotation then the disc can only be images in at one particular angular rotation. This is also the case if a LED/photodiode based triggering system is used. In this configuration, the entire disc should be imaged. The images acquired can be post-processed (rotated and cropped) using commonly available software. However, in some cases, particularly if imaging particles or cells, imaging the entire disc is not feasible" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001520_j.jsv.2014.09.004-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001520_j.jsv.2014.09.004-Figure5-1.png", "caption": "Fig. 5. FE models of the IPM motor: (a) 2D mesh for magnetostatic FEA (1/8 model); (b) 3D mesh for structural dynamics FEA.", "texts": [ " 4(c), large peaks can be found at 2f c7 f e. Peaks can also be found at 3f c7 f e, 3f c72f e, and 3f c74f e, in Fig. 4(d). These spectra mean that the input current can be regarded as a wave with fundamental frequency of fe, with many higher order frequency components including the side band spectra associated with the integer multiples of fc. The input currents were applied to the 2D magnetostatic FEA and used to compute the magnetic force. The FE mesh used for the magnetostatic FEA is shown in Fig. 5(a). The FE models were created based on measured geometric dimensions and magnetic properties of the real motor. The FE model consists of rotating and stationary domains. The rotating domain consists of the rotor core, which is assumed to be made of electrical steel, permanent magnets, and air-gap region. The stationary domain consists of the stator core, which is also made of the electrical steel, coils, and air-gap region. The input currents are applied in the regions for the coils as current densities", " It should also be noted that the frequency spectra seen in these participation factors are different from the pattern seen in the input current (Fig. 4). This is due to the fact that the functional relationships between the current and the magnetic force vector is nonlinear, because there is a nonlinearity between the constitutive relationship between B and H, as well as the relationship between \u03c3M and B (Eq. (8)). In parallel with the magnetostatic FE calculations, modal analysis was performed by an FEA, and eigensolution pairs were computed. The FE mesh of the stator core used for the modal analysis is shown in Fig. 5(b). The FE model was fixed at the three designated regions to simulate the bolted condition of the real stator. The stator core is assumed to be made of standard structural steel with density \u03c1\u00bc 7850 kg=m3, Young's modulus E\u00bc200 GPa, and Poisson's ratio \u03bd\u00bc 0:33. Any material anisotropy and inhomogeneity caused by the stacking of electrical sheets, as well as the effects of coil and varnish impregnation that exist in the real motor assembly are neglected in the FE model. The FE model was discretized by 3D solid elements and the resulting mesh has the total number of 33,306 DOF", " They have strong correlations with cos \u00f016\u03b8\u00dee\u03b8 and cos \u00f024\u03b8\u00dee\u03b8 . Using the results of G\u00f0\u03c9\u00de, as well as b, the displacement field was constructed by the evaluation of Eq. (28). The Rayleigh damping coefficients were set as \u03b1\u00bc 5:12 rad/s, \u03b2\u00bc 1:05 10 5 s/rad that were estimated from modal testing of the real motor assembly. The number of vibration modes used in the analysis was n\u00bc500, whose natural frequencies range from 1975 Hz to 52,193 Hz. The radial component of the acceleration was evaluated at the evaluation point shown in Fig. 5(b), and the results are shown in Fig. 11. To see the convergence nature of the proposed method with respect to the number and the type of the magnetic force modes, the results with different sets of magnetic force modes are shown in Fig. 5. Along with the result of the proposed method, the result of frequency response calculations using the conventional FEA is also shown in Fig. 11. As can be seen in the figure, the proposed method well captures the reference result in the wide frequency ranges. Furthermore, it can be seen that the method well captures the results only with the mode indices i\u00bc 1;16;17, which are the first three dominant magnetic force modes, as shown in Fig. 6. To better understand the convergence characteristics of the solution in terms of the number of magnetic force modes, the sum of the absolute error with respect to the reference FE results was computed for the entire frequency range for each set of magnetic force modes, as shown in Fig", " To further examine the validity of the proposed method, the computed results are compared with measured data. The schematic diagram of the experimental set-up used to measure the acceleration is shown in Fig. 14. The test condition is briefly stated as follows. The rotor shaft of the motor is attached to a dynamometer to apply a mechanical load of 50 Nm. The stator is attached to a base plate and fixed to the ground. A triaxial accelerometer is attached to the rim of the stator core, which corresponds to the evaluation point shown in Fig. 5. During the test, the dynamometer was controlled such that the rotational speed of the rotor becomes 1500 rev/min, and the current flowing in the motor windings was measured by the current probes. Then, the acceleration in radial direction was measured during the operation at 1500 rev/min. The measured acceleration as well as the computed result is plotted in Fig. 15. In Fig. 15(a), the measured and the computed magnitudes of the peaks at 2fe, and 6fe are in good agreement. In contrast, the peak at 4fe found in the measured data is larger than the computed one" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000415_978-3-642-37552-1-Figure13.5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000415_978-3-642-37552-1-Figure13.5-1.png", "caption": "Fig. 13.5 Definition of geometric variables used in the calculation of strain energy and surface energy of the actuator: a The two components in the total surface energy of water: Area A indicates the side area of the meniscus which depends on rib length, l, (\u00d72) to account for the front and back areas and Area B indicates the area of the meniscus above the ribs which depends on the device depth, w. The spine thickness is represented by h. b Variables used in the calculation of the length of the meniscus Lm: r is the radius of curvature of the meniscus between two ribs, H is the distance between the tip of the ribs, \u03b8c is the contact angle between water and rib, 2\u03b1 is the angle sweeping the arc length of the meniscus, and \u03c6 is the angle between two ribs. Reprinted with permission from [12]. Copyright 2006 Institute of Physics", "texts": [ " A sum of squares is at its minimum when all of the elements are equal. Thus, the energy of the spine would be at its minimum when all of the angles are equal, or equivalently, when the shape is in the form of a circular arc. The strain energy, Wstrain, of a spine at deformed curve radius, \u03c1, radius of rest shape curve, \u03c10, Young\u2019s modulus of the spine material, E , length of spine, L , and rectangular cross-section of the spine defined by w and h, is given in (13.3) [26]. Wstrain = Eh3wL 24 ( 1 \u03c1 \u2212 1 \u03c10 )2 (13.3) As shown in Fig. 13.5a, w is defined as the depth of the device into the page and l is the in-plane thickness of the spine. The stress-free curvature, \u03c10, is given by (13.4), where \u03b8initial is the angle of the arc swept by the curved spine. The bending stiffness, E I , or the product of Young\u2019s modulus, E , and the moment of inertia of the spine, I , is given by (13.5), where h and w are as defined above. 1 \u03c10 = \u03b8initial L (13.4) E I = Eh3w 12 (13.5) As previously mentioned, the equilibrium state of the device deformation is when the total energy in the system, comprised of strain energy and surface energy, is at a minimum. The surface of the volume of water filling in the region between adjacent ribs is actually a complex three-dimensional shape. In the presented analysis, this surface has been approximated as set of trapezoids for the pair of side areas which touch both the adjacent ribs and the spine, as shown in Fig. 13.5a, Area A, and as a partial cylinder of appropriate radius for the top areas which touch just the adjacent ribs, as shown in Fig. 13.5a, Area B. The sum of these two regions provides an approximation of the surface area of the volume of water present between the ribs. The work done by the surface tension of water, Wsurface, for a given spine deformation is expressed by (13.6) where \u03b3 is the surface tension of water, A is the area of the side meniscus on both sides of the device, B is the area of the top meniscus between the tips of a set of ribs, and n is the number of ribs. Wsurface = 2 ( n\u2211 0 A ) + n\u2211 0 B (13.6) The area of the side meniscus, A, can be approximated by a trapezoid that depends on the length of the rib, l, as given by (13" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000066_0278364909101786-Figure8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000066_0278364909101786-Figure8-1.png", "caption": "Fig. 8. Representation of the position of the needle during step 3 using a fixation point. Here n is the angle of the part of the needle under the tissue and H is the set of possible positions of the handling point H when N is fixed in I . The particular position is determined by angles , and .", "texts": [ " With the four available DOFs for the needle holder, any point of the needle can be driven to any point of the abdominal cavity. Let us consider a point M of the abdominal cavity with coordinates Q M X M YM ZM T in Q and a point N of the needle with coordinates J N X N YN Z N T in J . The superimposition of N on M is a third-order task, and hence there is one DOF left for the system, namely the rotation of the system around axis QM . Hence, when N is fixed on M any point of the needle holder or the needle can move onto a circle, and the possible motions of the needle holder span a cone with vertex Q (see Figure 8). Let us use H to denote the circle spanned by H . The superimposition of N on M also imposes the equality QN QM . Since the position of N in Q can be written QN Q RK K TJ J J N (2) Q RK X N YN dz ZN (3) this leads to dz QM 2 X2 N Y 2 N ZN (4) Let now define a frame M centered in Q with axis zM along QM . (In contrast to the general notation M is not centered in M . It is denoted in this way to recall that it is linked with the point M of the abdominal cavity.) The rotation between Q and M can be written Q RM Rx x Ry y (5) with x arctan YM ZM and y arcsin X M dz In M , the position of the needle holder is completely defined by the rotation matrix M RJ and the depth dz ", " Equation (7) can then be written for 0 without loss of generality which leads to 0 0 dQM dzs 0 dzc Ry Rz X N YN Z N (11) at OAKLAND UNIV on June 2, 2015ijr.sagepub.comDownloaded from and one solution for , and dz is arctan YN X N if X N 0 2 if X N 0 (12) arcsin c X N s YN dQM (13) dz dQM c Z N (14) Consequently, the position of the needle can be defined by a fixation point Q M , an angle n between the tip of the needle and the point N fixed in M and the angle of rotation of the needle around QM (see Figure 8). We represent this configuration with Q M n c. This analysis of the possible positions of the needle is very useful to describe the position of the needle with respect to the tissues to be sutured. Let us suppose that we know that the needle intersects the surface of the tissues in I . The state of the needle can be described using five parameters: the position of the intersection point Q I , the angle of the part of the needle under the tissue n and angle (see Figure 8). (There is actually a redundant parameter, since I could be described with two parameters on the surface of the tissues. However, for the sake of simplicity, we prefer to use the redundant representation.) The classical representation of the position of the needle holder can be obtained from this state representation, by using Equations (4), (5) and (6). Let consider that the surface of the tissues separates the abdominal cavity into two half-spaces. A point is said to be \u201coutside\u201d of the tissues if it lies in the same half-space as the incision point Q" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003017_j.addma.2020.101822-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003017_j.addma.2020.101822-Figure7-1.png", "caption": "Fig. 7. Polar projection lines and mean points.", "texts": [ "txt file that contains point coordinates on the surface edge. Another txt file is needed that contains 3 points, two at both ends and one in the middle of the mount edge. The number of projection lines is entered as an input. Then, all points project onto the projection lines. The logic is projecting each point to the respective nearest line. Several points are projected on each projection line that needs to be substituted with just one point. The location of the mean point is calculated from Eq. (4) (Fig. 7). R = 1 np \u2211np 1 Rp (4) The distances from the origin to the mean point and projected points are R and Rp, respectively. The np represents the number of points on a projection line. After the mean points for the measurement region are isolated, a new arc is best-fit through them. The reason for this operation is to eliminate macro noise such as waviness. As Fig. 8 shows, the general fitted arc is not appropriate for the measurement region which has a lifted texture. If the same center of the general fitted arc is used for regional roughness measurement, the result would be incorrect" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002430_tmag.2019.2941699-Figure17-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002430_tmag.2019.2941699-Figure17-1.png", "caption": "Fig. 17. Contour plot of vector magnetic potential within subdomains. (a) and (b) FEA and analytical for the no-load case. (c) and (d) FEA and analytical for the flux lines from the armature reaction current. (e) and (f) FEA and analytical for the on-load case.", "texts": [ " The flux density was measured along the arc with the radii rprobe = (R1 + R2/2) and rprobe = (R5 + R6/2) for the internal and external air gaps, respectively. For the on-load condition at the current density of 14.9 A/mm2, the comparison is shown in Figs. 12 and 13 for the internal and external air gaps, respectively. The flux density was also compared with the one inside the slot and inside the internal and external slot openings along the dashed arcs (Fig. 9) for the no-load case. The results are presented in Figs. 14\u201316. The flux lines obtained from the FEA and analytical calculations are presented in Fig. 17(a)\u2013(f) for the no-load case, the flux lines produced by the current when the magnets are off, and the on-load case, respectively. The flux distribution is given for the PM region of the inner and outer rotors, the inner and outer air gaps, the inner and outer slot openings, and the slot subdomains. C. Comparison of Electromagnetic Parameters With FEA The computation of the bEMF has been performed by using the approach described in [2]. The phase bEMF is calculated as follows: Ea,b,c = \u2212\u2202\u03c8a,b,c \u2202 t (75) where \u03c8a,b,c is a flux linkage of an appropriate phase, which can be calculated as follows: \u03c8a,b,c = \u2211 Nturn z " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003027_530220-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003027_530220-Figure2-1.png", "caption": "Fig. 2-Surface temperature pattern in band of contact", "texts": [ " In the Delft publication1 which presented this interesting work, Blok postulated that straight mineral oils have a critical temperature at which they fail, dependent only upon their viscosity grade. His postulate included the premise that such critical temperatures would limit the use of mineral oils on gears. A brief summary of Blok's work follows: A band-shaped contact pattern is assumed, having a parabolic load distribution such as in Fig. 1. The parabolic distribution is chosen in place of the actual elliptic one because of ease of calculation. The error is not significant for our purpose. A surface temperature pattern is formed in the contact area due to sliding, as in Fig. 2. Notice that this instantaneous surface temperature change T2 is added to the bulk temperature of the material T1 to form a final surface temperature Tt. It is interesting to note that the peak of the temperature pattern lags the center line of the contact band width b, the amount being dependent upon the surface velocities. This heat penetrates only a small distance into the material, and the temperature quickly returns to the blank temperature as contact passes. Blok's original formula appears below", " One such question is: to what extent, and in which range of operating conditions does the hydrodynamic formation of pressure in the oil lubricating the meshing tooth faces, play a part in carrying the tooth load?c Finally, in order to render vossible the verification of the author's- views, as against chose propounded previously,d or possibly to be propounded in the future, it is suggested that in his closure the author submit a detailed table of his experimental results and operating conditions. c See Fig. 2 in \"Gear Lubricant- A Constructional Gear Material\" by H. Blok, in De Ingenieur (Holland), Vol. 63, Sept. 28, 1951, pp. 53-64. Artrcle m English.d See ASME Transactions Vol. 73 July 1951 pp 687-696: \"Effect of Oil Viscosity on power-Trasmitting Capacity of 'spir Gears,\" by V. N. Borsoff, J. B. Accinelli, and A. G. Cattaneo. Two Formulas Are Compared in Tests - Darle W. Dudley General Electric Co. M R. KELLEY gives us a sound engineering approach to the scoring problem. The work of Almen and Straube solved the scoring problem for a limited range of work" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001379_978-3-319-22056-7-Figure1.2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001379_978-3-319-22056-7-Figure1.2-1.png", "caption": "Fig. 1.2 Mechanism for tipping a vessel", "texts": [ " They include complex systems such as aircraft, rockets, automobiles, moving robots picking up or lifting objects, as well as simpler systems such as transportation machines, mining machines, excavators, vibrating machines used as conveyors, separators, machines for segregation, rolling mills, metallurgical machines, casting machines, agricultural machines, centrifuges, measuring mechanisms, etc. In these mechanisms, mass of elements and position of their centre of mass and moment of inertia vary during addition or removal of the material. In this chapter various types of machines and mechanisms with mass variable elements are described. Their constructive properties and working procedures are explained. Pouring machine, shown in Fig. 1.2, represents a mechanism with variable mass. Hook of the crane grips the vessel at point B, and rotates it around A, pouring out the molten metal for continuous casting. Basic requirement for the equipment is that pouring of metal from the vessel has to be uniform, and it is regulated by the velocity of the hook. To estimate the process of lifting of the vessel and to give good control it is necessary to take into consideration the mass variation of the vessel, because it is the basic cause of uniform flow of metal" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002508_j.triboint.2019.03.048-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002508_j.triboint.2019.03.048-Figure6-1.png", "caption": "Fig. 6. Simplified model of intermediate gearbox.", "texts": [ " [12] and Concli and Gorla [11,36] to obtain other methods to solve this problem. Besides, according to investigations by [8,36\u201339], squeezing losses, which the separation method can't capture, are parts of churning losses; however, because squeezing losses are excluded from churning losses by all simulations in this paper, the change tendency of churning losses with different structures of oil guide device would not be affected. The simplified model of the intermediate gearbox and parameters of the spiral bevel gears are illustrated in Fig. 6 and Table 2, respectively. Fig. 7 shows the reference geometric model of the oil guide device, where the oil guiding tank capacity is 13.34ml and the diameter of the oil guiding pipe is 5mm. Table 3 gives main physical parameters used in simulations. The mesh inside the gearbox is discretized with unstructured tetrahedron elements which can undergo a certain degree of mesh deformation so that the mesh can adapt better to the complex geometric shape of the spiral bevel gear pair. Besides, mesh surrounding gears and the oil guide device is locally refined while that of other positions is sparser and coarser than the former, aiming to guarantee simulation precision and improve calculation efficiency at the same time" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001389_s00170-016-9447-x-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001389_s00170-016-9447-x-Figure4-1.png", "caption": "Fig. 4 The machine tool used in honing process", "texts": [ " Thus, the equation of the profile modified honing cutter rh(uc, vc, \u03c8h) can be simplified as Rh(uc, vc): Rh uc; vc\u00f0 \u00de \u00bc rh uc; vc;\u03c8h uc; vc\u00f0 \u00de\u00f0 \u00de \u00f07\u00de The unit normal vector of the profile modified honing cutter is represented as follows: nh uc; vc;\u03c8h uc; vc\u00f0 \u00de\u00f0 \u00de \u00bc Lhr \u03c8h\u00f0 \u00de\u22c5nr uc; vc\u00f0 \u00de \u00f08\u00de where the matrix Lhr (\u03c8h) is the upper left 3 \u00d7 3 submatrix of the Mhr (\u03c8h). The five-axis face gear machine tool developed by Beihang University is applied for the profile modified face gear honing. The face gear machine as shown in Fig. 4 has three rectilinear axes (X, Y, Z) and two rotational axes (A, C). The axial rectilinear motion Dx, radial rectilinear motion Dy, and tangential rectilinear motion Dz determine the relative positions of the honing cutter with respect to the face gear. The axial motion Dx and radial motionDy are applied to create the tooth surface along the tooth depth and tooth width, respectively. The rotational motions \u03c6h and \u03c6f are used to produce the generating motion between the honing cutter and the face gear" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000039_978-1-84996-220-9-Figure1.2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000039_978-1-84996-220-9-Figure1.2-1.png", "caption": "Figure 1.2 An example of coarse\u2013fine planning for a mobile robot, where the coarse planning provides a rough path, and the fine planning is performed by a set of trajectories accounting for vehicle dynamics", "texts": [ " For real-world situations, the D* family of algorithms [12] provide inexpensive replanning to moving robots reacting to new sensor data. To further increase performance, or for planning in higher dimensions (such as including velocities), a coarse\u2013fine or hierarchical approach is used in many systems, in which a coarse global plan is first computed, and a finer-grained planner or controller follows the global path, while adjusting for the dynamics of the vehicle and newly-sensed obstacles. An example of this approach for a cart-like robot is shown in Figure 1.2. By layering planners and controllers in this way, the low-level control and planners only need to consider the near future, trusting to the higherlevel planners in the hierarchy that the rest of the path will be executable. By shortening the planners\u2019 horizons, the individual planners can perform much quicker. The planners then replan as the robot begins to execute the plan to fill in details along the remaining path. 1 Navigation and Gait Planning 3 Despite the established research into navigation strategies for mobile robots, there are some significant differences between humanoid robots and wheeled robots" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002454_s11581-018-2517-3-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002454_s11581-018-2517-3-Figure5-1.png", "caption": "Fig. 5 a DPASVs for AuMWCNT/GCE in 2.5 \u03bcmol L\u22121 DOX at various pH values. b Effect of pH on the peak current of DOX. c Effect of the pH on the peak potentials of DOX. d Effect of accommodation time on the peak current of DOX", "texts": [ " The results demonstrated that Au-MWCNTs/GCEwith much higher electrocatalytic activity and high oxidation currents can be used to fabricate an electrochemical sensor for the determination of DOX with good figures of merit. Influence of pH on oxidation peak current To achieve the best peak shape and maximum current, the chemical and instrumental parameters must be optimized. The most important chemical parameter that could influence the peak character is pH. So, the impact of concentration of H+ on the oxidation peak current at Au-MWCNT/GCE was studied over the range of 4.0\u20139.0. Figure 5a illustrates the DPASV of 2.5 \u03bcmol L\u22121 DOX on the proposed sensor at different pHs. It is observed that the peak potential and current of oxidation stripping peaks were remarkably changed when the concentration of H+ was changed. It can be seen that by increasing pH from 4.0 to 7.0, the oxidation current has increased significantly; after that, the response of the electrode for oxidation of DOX has decreased by increasing pH value to 9.0. Therefore, the pH = 7.0 was chosen as an optimum value (Fig. 5b). According to the studies, potentials of the oxidation peak were linearly shifted in the negative values, when the pH of the solution increased over the studied range (Fig. 5c). The linear relation between the pH and oxidation peak potential for DOX was obtained as E = \u2212 0.0623 pH + 1.6715 (R2 = 0.9935). According to the Nernst equation (Ep = K \u2212 (0.059) m/n pH) and the slope of the equation for stripping oxidation of DOX at different pHs (0.0562 V/pH), it can be concluded that the number of electrons transferred during electrooxidation of the analyte on the surface of Au-MWCNTs/GCE is equal to the number of protons and in this case, two electrons and protons. Based on these obtained results and previous report about the paclitaxel as a molecule with same structure [46], an electrooxidation mechanism for DOX at AuMWCNT/GCE is suggested as Scheme 2. The two instrumental parameters of accumulation step that include accumulation potential and time were examined. According to the experiments that have been done, accumulation potential has no influence on the current response of DOX at the surface of Au-MWCNTs/GCE and open circuit accumulation was applied in further experiments. The impact of deposition time ranging from 30 to 210 s on the oxidation of DOX at the surface of Au-MWCNT/GCE is as shown in Fig. 5d. The oxidation current has increased gradually as accumulation time increased from 30 to 150 s. However, with further increasing, the accumulation time beyond 150 s the peak current tends to be almost stable. According to this result, the optimal accumulation time of 150 s was employed in further experiments. Scheme 2 Electrooxidation mechanisms of DOX at Au-MWCNT/GCE Effect of scan rate on the electrochemical oxidation of DOX To find out the mechanism responsible for the oxidation of 3.0 \u03bcmol L\u22121 DOX at Au-MWCNT/GCE, CVs of DOX were recorded at different scan rates in the range of 10\u2013250 mV/s (Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003169_j.mechmachtheory.2020.103844-Figure8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003169_j.mechmachtheory.2020.103844-Figure8-1.png", "caption": "Fig. 8. The proximal part of PMs: (a) wrench space; (b) the proximal wrench identification.", "texts": [ " Of note is that the structural parameters inside the closed-loop passive limbs can be adopted as additional design parameters in the DII approach, for example, the parameters B i ,1 B i ,2 or C i ,1 C i ,2 in the Delta, Par4, and heli4 PMs and parameters B i ,1 B i ,2 and C i ,1 C i ,2 in the Pa (2-UU)-&- R UU PM. Actuating means letting all the actuated joints of the investigated PM be actuated. Under this condition, the investigated PM is a movable mechanism. At this point, each input twist of an actuated joint is accompanied by a wrench. The functions of the implicated wrench are to transmit the input twist from the actuated joint to the mobile platform, and resist the external wrenches. Fig. 8 focuses on the proximal part of the PM. The input twist of actuated joints is referred to as the actual proximal twist i S APT . The implicated wrench is referred to as the proximal wrench i S PW . In general, the proximal wrench i S PW depends on two essential factors. One is the wrench space i WS spanned by the physically available wrenches inside the i th closed-loop passive limb (i.e., all the distal wrenches S PW inside the i th closedloop passive limb). The other is the corresponding actual proximal twist i S APT of the actuated joint inside the i th limb. In view of this, two identification principles are given here to identify the proximal wrench i S PW in the i th closed-loop passive limb. \u2666 First, the proximal wrench i S PW belongs to the wrench space inside the limb. That is to say, the proximal wrench i S PW is equal to the linear superposition of the wrench space\u2019s elements k S i W . For example, if the wrench space is a plane , the axis of the proximal wrench should lie on the plane , as shown in Fig. 8 (a). \u2666 Second, the proximal wrench i S PW is the most efficient transmission path in the wrench space i WS to transmit actual proximal twist i S APT . That is to say, the instantaneous power i W IP between the proximal wrench i S PW and the actual proximal twist i S APT from the actuated joint reaches its maximum value among all the transmission paths inside the limb, as shown in Fig. 8 (b). On the basis of these principles, the identification of the proximal wrench i S PW inside the i th closed-loop passive limb can be described as a simple optimization problem. The goal of the optimization problem is to find i S PW = l \u2211 k =1 \u03b8k k S i W (4) so that the instantaneous power i W IP between the unit proximal wrench i S u PW and the unit actual proximal twist i S u APT from the actuated joint is i W IP = ( i S u PW \u25e6i S u APT ) \u2192 max (5) subject to i S PW \u2208 i WS = span { 1 S i W , ", " Like the DII, the larger the value of the PII, the more effectively the power is transmitted from the actual proximal twist to the proximal wrench, and the better the proximal motion-force interaction performance of the PMs. Note that PII \u2208 [0, 1] and is framefree. The proposed DII can be adopted to evaluate the proximal motion-force interactability of the PMs with closed-loop passive limbs. The calculation of d max in the PII is the same as that in the DII. The value of d max is equal to the distance from the proximal application point p A i to the actual proximal twist i S APT when proximal application point p A i lies on the axis of the proximal wrench i S PW . As shown in Fig. 8 (b), d max = p A i p C i . Similar to DISI, the minimum of the reciprocal products of the proximal wrenches and its corresponding actual proximal twists is defined as \u03bd = min i { i S PW \u25e6i S APT } ( i = 1 , 2 , . . . , n ) , (9) where \u03bd is referred to as the proximal interaction singularity index (PISI). Here we give a theorem and a lemma. The proof of the theorem is presented in Appendix. The lemma can be used as a criterion to identify the proximal interaction singularity of PMs. Theorem 2. For a PM, if it is at a proximal interaction singular configuration, at least one of the reciprocal products of proximal wrenches and their corresponding actual proximal twists is equal to zero " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001510_j.mechmachtheory.2014.01.014-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001510_j.mechmachtheory.2014.01.014-Figure4-1.png", "caption": "Fig. 4. Force model for the tooth rim under the action of the contact force from the four-roller WG.", "texts": [ " The bending moment is the largest internal force in the FS tooth rim, and the bending stress caused by the bending moment is the primary determinant of the FS fatigue strength. The circumferential strain is induced by the circumferential force. The stretch in the neutral line of the tooth rim is calculated from the circumferential strain, and this stretch of the neutral line affects the HD engagement. The internal forces in the FS tooth rim under the action of the four-roller WG will be discussed first. A schematic of the tooth rim under the action of the contact forces from the rollers is shown in Fig. 4a. The mechanical analysis shows that there are three internal forces in the horizontal section (\u03c6 = \u03c0/2): X1 (the bending moment), X2 (the circumferential force) and X3 (the shear force) (see Fig. 4b). The symmetry of the vertical and horizontal cross sections requires that the shear force X3 is zero. Therefore, the main task is to calculate the bending moment X1 and the circumferential force X2. Fig. 4c shows the model formulated from the analysis above. By projecting all the forces in the vertical direction, the circumferential force X2 is calculated as follows: Here, X2 \u00bc F cos\u03b2: \u00f01\u00de F is the contact force from the roller. Here, For the force F that is concentrated at the point \u03c6 = \u03b2, the internal forces correspond to two ranges of \u03c6: 0 \u2264 \u03c6 \u2264 \u03b2 and \u03b2 b \u03c6 \u2264 \u03c0 / 2. A force balance in the vertical direction for the model in Fig. 4c can be solved for the circumferential forces in any cross section over the two ranges of \u03c6; a schematic of the force balance is given in Fig. 5. FN1 \u00bc F sin\u03b2 cos\u03c6; 0\u2264\u03c6\u2264\u03b2\u00f0 \u00de FN2 \u00bc F cos\u03b2 sin\u03c6; \u03b2b\u03c6\u2264\u03c0=2\u00f0 \u00de ( \u00f02\u00de FN1 and FN2 are the circumferential forces in any Section. An explicit expression for the bending moment in any section is obtained from a mechanical analysis of the bending moments X1 and circumferential force X2: Here, M1 \u00bc M2\u2212F rm sin \u03b2\u2212\u03c6\u00f0 \u00de; 0\u2264\u03c6\u2264\u03b2\u00f0 \u00de M2 \u00bc X1 \u00fe X2 rm 1\u2212 sin\u03c6\u00f0 \u00de; \u03b2b\u03c6\u2264\u03c0=2\u00f0 \u00de: ( \u00f03\u00de M1 and M2 denote the bending moment in any section" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000039_978-1-84996-220-9-Figure3.6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000039_978-1-84996-220-9-Figure3.6-1.png", "caption": "Figure 3.6 Step response of attractor system", "texts": [ " They are closely related to the biological findings, and yield further advantages like robustness against perturbations and dynamic environments. We apply a simple attractor system [18, 62] to the task elements to be controlled. The same attractor dynamics are applied to other controllers that are not related to the inverse kinematics, such as \u201cclosing the fingers to a power grasp\u201d, etc. Given two points x\u2217k and x\u2217k+1 we shift the attractor point continuously from one to the other. This is captured by the linear interpolated trajectory rt \u2208R m. In Figure 3.6 this is illustrated by the dashed line. Point rt is taken as attractor point to a second order dynamics which generates the task trajectory xt \u2208 R m: xt+1 = xt +\u03c0(xt ,xt\u22121,rt+1) (3.17) \u03c0(xt ,xt\u22121,rt+1) = a(rt+1 \u2212 xt)+ b(xt \u2212 xt\u22121) . (3.18) The step response of the scheme is depicted as the solid line in Figure 3.6. We choose the coefficients a and b according to 76 M. Gienger, M. Toussaint and C. Goerick a = \u0394 t2 T 2 mc + 2Tmc\u0394 t\u03be +\u0394 t2 b = T 2 mc T 2 mc + 2Tmc\u0394 t\u03be +\u0394 t2 , (3.19) with a relaxation time scale Tmc, the oscillation parameter \u03be , and the sampling time \u0394 t. We select \u03be = 1, which leads to a smooth non-overshooting trajectory and an approximately bell-shaped velocity profile. In common classical motion control algorithms the tracking of the desired trajectories is very accurate. In many cases the tracking accuracy of a reference trajectory is not very critical, or there are at least some phases where the accuracy may be lower than in others" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003015_ffe.13406-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003015_ffe.13406-Figure4-1.png", "caption": "FIGURE 4 Dog bone specimen dimensions of AlSi10Mg specimens", "texts": [], "surrounding_texts": [ "Ultrasonic fatigue tests were conducted using dog bone specimens to characterize fatigue performance of additively manufactured AlSi10Mg and AlSi7Mg alloys in HCF and VHCF regimes. The AlSi7Mg and AlSi10Mg specimens were tested as-machined conditions by being subjected to fully reversed constant amplitude load cycles. All tests were run until failure, and no run out condition was established for the tested specimens. Figure 5 shows test specimens failed close to the midgauge section with the exception of one specimen. Failure locations of the asymmetrical specimens also verify that specimens experience the maximum stress distribution in the gauge length as shown in Figure 2. Fatigue data in Figures 6\u20138 indicates a clear trend for the increase of fatigue life as stress decreases with no data points which would suggest the presence of a fatigue limit beyond 109 cycles. Test results show that the AlSi10Mg showing better fatigue response to be subjected to higher stresses than AlSi7Mg under similar range of life cycles. The fatigue life data collected for AlSi10Mg was plotted and compared with published fatigue data* in Figures 6 and 7 to assess the correlations between the data acquired and the previously published data. In light of the fact that there are no standardized process parameters established for the production of AM specimens/parts, it is difficult to draw definitive conclusions regarding quantified correlations between the data acquired by the present authors and the data from previous works. Figure 6 shows the fatigue life results of preceding research works for as-built AlSi10Mg AM specimens which were not subjected to heat treatment. On the other hand, Figure 7 shows the comparison of AlSi10Mg specimens subject to heat treatment with the new fatigue data *References 23, 24, 28, 33, 34, 37\u201339. generated. It can be seen that even though the AlSi10Mg specimens tested in this paper were subjected to heat treatment post-process, the fatigue data are in better agreement with the data of as-built specimens of previous works without any heat treatment. This is somewhat in agreement with Tridello et al. works39 that the heat treatment does not improve fatigue life of AM specimens because of the improper heat treatment effect. The authors suggested that heat treatment could even have detrimental effects on the VHCF performance in the light of the microstructural changes. This is contrary to the fatigue data published by other researchers that heat-treated parts can have higher fatigue performance than non-heattreated parts for given same life cycles.24,34 These contradicting results indicate that heat treatment process for improving the fatigue life of aluminium AM specimens should be further investigated for underlying reasons for shortened fatigue life (e.g., effects of heat treatment on material microstructure). Due to lack of published fatigue data of additively manufactured AlSi7Mg, experimental life data collected for AlSi7Mg is compared with fatigue data of A356 (AlSi7Mg) cast alloy40 in Figure 8, and it shows a reasonable agreement. It is also known that fatigue life is closely related to microstructure, for example, heterogeneous distribution of grains and internal and surface defects.41\u201343 As sizes of the small defects come closer to microstructural dimensions in the short crack regime, the boundary between different crack growth mechanics became unclear and crack initiation sites and interaction with the defects can yield a very complex crack growth behaviour.44\u201346 There are many interplay factors affecting fatigue behaviour of AM parts. These factors are considered as microstructural aspects such as anisotropy, grain characteristics, defects, surface roughness and residual stresses. Some of the process parameters, for example, energy source input, build path, hatch spacing, layer thickness and scanning speed, are considered to be the most important factors in influencing fatigue performance of AM fabricated parts. In addition to process parameters and resulting microstructural factors, many other factors such as heat treatment, test/load and environmental conditions could significantly affect fatigue performance of AM fabricated parts. The compared data between present work and literature could have differences in many perspectives in terms of those factors; therefore, effects of heat treatment on VHCF performance need further investigations through extensive experimental studies before concrete conclusions on effects of heat treatment on fatigue behaviour of AM alloys can be reached. Quantification of effects of many controlling factors on fatigue performance in HCF and VHCF regimes should be addressed before applications of AM materials in critical load bearing conditions can be widely considered." ] }, { "image_filename": "designv10_9_0003195_s10846-019-01129-4-Figure11-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003195_s10846-019-01129-4-Figure11-1.png", "caption": "Fig. 11 Test T4. Printed versions of the common architecture C. a-b Electromechanical connector; c Standard module; d Internal view of the module", "texts": [ " We installed the electrical parts in the printed parts, and these sectors were evaluated to considering passage and connection of wires in devices. When energized, boards were able to dissipate heating without damaging the plastic parts (Fig. 10); \u2013 T4. Full standard module and connector mechanical test. A generic standard module and a connector, in natural scale, were built. We established a high power circuit with 14,8V for powering devices, and the low power circuit as 5V for feeding most of the electronic devices and boards. All wires were placed in the internal wall of the modules (Fig. 11). The module was tested to evaluate aspects like mechanical design, mechanical robustness, weight, gaps, and so on. The mechanical structure shows itself sufficiently robust even when dealing with a printed device for the next tests. Wires were able to be accessed from all derivation points, observing that one power circuit was able to feed up to two circuits. Fig. 12 presents the connection step by step. The mechanical design was, then, approved; \u2013 T5. Propulsion module test. A propulsion module was built with the actuators and ESC as described in previous sections" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001389_s00170-016-9447-x-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001389_s00170-016-9447-x-Figure3-1.png", "caption": "Fig. 3 Coordinate systems for generating the honing cutter", "texts": [ " The equation of the profile modified rack cutter is expressed as follows: rr uc; vc\u00f0 \u00de \u00bc uc \u2212sin\u03b1c \u00fe mvc\u00f0 \u00de uccos\u03b1c vc\u2212v0 1 2 664 3 775 \u00f02\u00de The unit normal vector nr(uc, vc) of the profile modified rack cutter is represented as follows: nr uc; vc\u00f0 \u00de \u00bc \u2202rr \u2202uc \u2202rr \u2202vc \u2202rr \u2202uc \u2202rr \u2202vc \u00bc cos\u03b1c sin\u03b1c\u2212mvc \u2212muccos\u03b1c 2 4 3 5 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1\u22122mvcsin\u03b1c \u00fe m2v2c \u00fe m2u2ccos2\u03b1c p \u00f03\u00de To generate the honing cutter surface, the coordinate systems as shown in Fig. 3 are established. The coordinate systems \u03c3r (xr, yr., zr), \u03c3h (xs, ys, zs), and \u03c3n (xn, yn, zn) are attached to the rack cutter, honing cutter, and machine frame, respectively. In Fig. 3, rh is the pitch radius of the honing cutter, \u03c8h is the rotation angle of the honing cutter, and rh\u03c8h represents the displacement of the rack cutter. The parameters \u03c8h and rh\u03c8h define the rotational and translational displacements of the honing cutter with respect to the rack cutter. In the coordinate system \u03c3h (xh, yh, zh), the equation of the profile modified honing cutter is expressed as follows: rh uc; vc;\u03c8h\u00f0 \u00de \u00bc Mhr \u03c8h\u00f0 \u00de\u22c5rr uc; vc\u00f0 \u00de f h uc; vc;\u03c8h\u00f0 \u00de \u00bc nr uc; vc\u00f0 \u00de\u22c5v rh\u00f0 \u00de r uc; vc;\u03c8h\u00f0 \u00de \u00bc 0 \u00f04\u00de where Mhr (\u03c8h) is the coordinate transformation matrix from \u03c3r (xr, yr" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000165_j.epsr.2011.03.017-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000165_j.epsr.2011.03.017-Figure1-1.png", "caption": "Fig. 1. Three-phase winding with inter-turn fault in the phase as.", "texts": [ " Finally, the comparison of the results of the ault model simulation and experimental results allowed verifying he precision of the proposed dynamic model for different levels of ault severity. The fault model is used to study the behaviour of PM achine under various fault conditions. . PM machine inter-turn fault dynamic model An inter-turn fault denotes an insulation failure between two indings in the same phase of the stator. The insulation failure s modelled by a resistance, where its value depends on the fault everity. The stator winding of a PMSM machine with inter-turn ault is represented in Fig. 1. In this figure, the fault is occurred in he phase as and rf represents the fault insulation resistance. The ub-windings (as1) and (as2) represent the healthy and faulty part f the phase winding a respectively. When fault resistance (rf) decreases toward zero, the insulation ault evaluates toward an inter-turn full short-circuit. The evolution f fault insulation resistance between rf =\u221e and rf = 0 is very fast n most insulation materials. It is important to predict the interurn fault when it is not high developed and the fault resistance is till not very near to zero. Therefore, in our fault model, the fault nsulation resistance is included and the machine behaviour with arious fault resistances is studied. .1. Fault model in abc-coordinates Setting up the mesh equations for the circuit in Fig. 1 will express he voltage equations as: Vs] = Rs[Is] + [Lss] d[Is] dt + [Es] \u2212 [R0]if \u2212 [L0] dif dt (1) s Research 81 (2011) 1715\u20131722 where [Vs], [Is] and [Es] are the stator voltage, current and back-EMF vectors: [Vs] = [ vas vbs vcs ]T [Is] = [ ias ibs ics ]T [Es] = [ eas ebs ecs ]T Rs is the phase resistance and [Lss] is the inductance matrix of the healthy PMSM respectively: [Lss] = [ Ls M M M Ls M M M Ls ] (2) where the inductance Ls is the phase self inductance and M is the mutual inductance between phase windings of the healthy PMSM. The matrixes [R0] and [L0] are the fault resistance and inductance matrix in the faulty part of the winding (as2): [L0] = [ La2 + Ma1a2 Ma2b Ma2c ] T [R0] = [ Ra2 0 0 ]T (3) Ra2 and La2 are the resistance and the self inductance of the faulty winding as2 (Fig. 1). Ma1a2 , Ma2b and Ma2c are respectively the mutual inductances between the as2 and respectively as1, bs and cs. The fault current through the insulation fault resistance ri is also called if. The voltage equation of the faulty loop (as2) is: Ra2 ia + (La2 + Ma1a2 ) dia dt + Ma2b dib dt + Ma2c dic dt + ea2 = (Ra2 + rf )if + La2 dif dt (4) For the machine having one slot per pole and per phase, Ma2b can be considered equal to Ma2c . Then we have: Ra2 ia + (La2 + Ma1a2 \u2212 Ma2b) dias dt + ea2 = (Ra2 + rf )if + La2 dif dt (5) The expression of the electromagnetic torque (Te) and the mechanical equation are given as follows: Te = [Es] T [Is] \u2212 ea2 if \u02dd Te \u2212 Tl = J d\u02dd dt (6) where J is the moment of inertia and Tl is the load torque" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003151_lra.2020.2965863-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003151_lra.2020.2965863-Figure2-1.png", "caption": "Fig. 2. The model of the stereo vision system. l and l represent the left and right image coordinate systems, respectively. c represents the camera coordinate system.", "texts": [ " In order to make the surgical instruments at the center of the left image, let a \u2208 R2 denote a task function defined as the sample mean: 1 1 1 1 m l i i a m l i i u m v m where m is the number of the surgical instruments detected on the left image and the ,l l i iu v is the coordinate of the i-th surgical instrument\u2019s tip on the left image. The time derivative a is given by: 1 1 1 2 2 02 I c c I I I c c I I a a a a c I ck ck k I I p J J p J J J J X J J Q p J J where 2 4 2 4 1 [ ]a a a m J g g and 2 4 a g is the 2 4 matrix repeated for m times. 2 4 1 0 0 0 0 1 0 0 a g . ci IJ is the ith target\u2019s Jacobian for image represented in the camera frame. p I i is the time derivative of the ith p I . As shown in Fig. 2, the depth information of each tip of the surgical instruments can be obtained by the following equation: c i l r i i bf z u u where c iz is the depth information of the ith surgical instrument\u2019s tip. ,l l i iu v and ,r r i iu v are the coordinates of the ith surgical instrument\u2019s tip on the left image and right image, respectively. Let b \u2208 R1 denote a task function defined as the mean depth of the target, which can be shown as follows: 1 1 1 1m m b i l r i i i i bf z m m u u The time derivative of b is given by: 1 1 1 02 2 2 I I I c c I I I c c b b b b c I I I k ck ck p J J p J J J J X J J Q p J J where 1 4 1 4 1 [ ]b b b m J g g and 1 4 b g is the 1 4 matrix repeated for m times" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002088_j.mechmachtheory.2018.01.015-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002088_j.mechmachtheory.2018.01.015-Figure3-1.png", "caption": "Fig. 3. Link coordinate systems of the laparoscope arm.", "texts": [ " Their basic coordinate systems have to be normalized into a global coordinate system X 0 Y 0 Z 0 so that the kinematic models of the three arms are represented in the same coordinate space. The coordinate systems and link parameters are shown in Fig. 2 . We set \u03b80 = 45 \u25e6, which can help ensure the positive values of the arms\u2019 position vectors so that they can be employed with the grey prediction models. Assume that the transformation matrices between the frames X 1 Y 1 Z 1 and X 0 Y 0 Z 0 , X 2 Y 2 Z 2 and X 0 Y 0 Z 0 , X 3 Y 3 Z 3 and X 0 Y 0 Z 0 , are T 1 N0 , T 2 N0 , T 2 N0 , respectively. The link coordinate systems of the 8-DOF laparoscope arm are shown in Fig. 3 . The adjacent transformation matrices between the base frame O la 0 to the tool frame O la 8 are assumed to be la T 1 0 , la T 2 1 , la T 3 2 , la T 4 3 , la T 5 4 , la T 6 5 , la T 7 6 , la T 8 7 , respectively. Therefore, in the global coordinate system X 0 Y 0 Z 0 , the forward kinematics of the laparoscope arm can be expressed based on Eq. (1) . la T 8 N0 = T 3 N0 \u00b7 la T 1 0 \u00b7 la T 2 1 \u00b7 la T 3 2 \u00b7 la T 4 3 \u00b7 la T 5 4 \u00b7 la T 6 5 \u00b7 la T 7 6 \u00b7 la T 8 7 = \u23a1 \u23a2 \u23a3 la n x la o x la a x la p x la n y la o y la a y la p y la n z la o z la a z la p z 0 0 0 1 \u23a4 \u23a5 \u23a6 (1) where [ la n la o la a ] = la R 8 N0 and [ la p x la p y la p z ] T = la p 8 N0 denote the orientation matrix and position vector of the tool frame O la 8 with respect to the global coordinate system X 0 Y 0 Z 0 " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000126_j.wear.2011.12.011-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000126_j.wear.2011.12.011-Figure1-1.png", "caption": "Fig. 1. A 91.5 mm centre distance back-to-back contact fatigu", "texts": [ " The pplied geometry included tip relief of 26 m to avoid undesirable ip contact at higher torque and the pinions were also crowned 15 m) to avoid peak stressing towards end faces. After grinding, he gears were coated by different suppliers, as listed in Table 1. The oatings were applied to a thickness of \u223c2 m at the pitch line of he gear flank. However, the thickness was found to vary along the rofile from \u223c1 m in the dedendum to \u223c3 m at the addendum. 2\u20133 25 300 2\u20133 20\u201325 \u2013 2\u20133 6\u201310 120 The gears were tested on a 91.5 mm centre distance back-toback contact fatigue test rig (Fig. 1) at 3000 rpm (pinion) with Aeroshell oil at 100 \u25e6C. All tests involved an endurance test running for 50 million pinion cycles, at a constant torque. These tests were carried out at two different wheel torque levels, 460 Nm and 570 Nm, that gave peak contact stress levels of 1471 MPa and 1578 MPa, respectively (calculated by finite element tooth contact analysis using Dontyne Systems ISO-6336 rating software). The distribution of contact stresses on the gear flank surface at these wheel torque levels is shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002037_s11071-017-3461-x-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002037_s11071-017-3461-x-Figure2-1.png", "caption": "Fig. 2 The redundantly actuated planar 2DOF PM with parallelogram structure branches [14]: a RAParM-I, b RAParM-II", "texts": [ " Considering the theoretical research significance and practical engineering requirements, we have selected one of some available redundant actuation schemes as the optimum one that encompasses parallelogram structure branches (PSBs) [77] with the help of some selection criteria [14]. The corresponding mechanism is named as RAParM (derived from \u201cRedundantly Actuated Parallel Manipulator\u201d) which possesses two DOFs. Moreover, the optimum redundant actuation scheme determined by us includes two configurations named, respectively, as RAParM-I and RAParM-II based on the layout of thePSBs, as depicted in Fig. 2 [14]. Based upon the two topological configurations, two preliminary virtual prototypes can be constructed by means of commercial software Solidworks , which are shown in Fig. 3 [14], in which some attachments are not shown in detail. Considering the similar structure characteristic between the two configurations of RAParM, in Ref. [14], we have implemented detailed analysis with respect to one of the two configurations, i.e., RAParMI. Owing to the special structure characteristic, this novel PM can achieve 9 potential actuation modes, as illustrated in Table1 [14]" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000353_14763141.2012.660799-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000353_14763141.2012.660799-Figure4-1.png", "caption": "Figure 4. The best-fit trajectory planes of the points: (A) clubhead for the MD\u2013MF phase, (B) clubhead for the ED\u2013MF phase, (C) clubhead for the TB\u2013MF phase, and (D) the shoulder/arm points for the TB\u2013MF phase. Abbreviations: MD, mid downswing; ED, early downswing; TB, top of backswing; and MF, mid follow-through.", "texts": [ ") To improve the time resolution for more accurate event detection, the processed point position data were up-sampled to 2000 Hz using cubic spline-based interpolation. Eight events were identified based on the clubshaft position: take-away (TA), mid backswing (MB), late backswing (LB), top of backswing (TB), early downswing (ED), mid downswing (MD), ball impact (BI), and mid follow-through (MF; Figure 3). Determination of the FSP and MPs. Trajectory-plane fitting was carried out for the clubhead in three different phases: TB\u2013MF (Figure 4A), ED\u2013MF (Figure 4B), and MD\u2013MF (Figure 4C). The RMS and maximum trajectory fitting errors (Equations (7) and (8)) were compared among these phases to identify the phase which provided sufficiently well-defined FSPs. The best-fit planes obtained from this particular phase were used as the FSPs in subsequent analyses. The slope of the FSP (fFSP) was computed as the angle between the ground and the FSP, whereas the angle between the intersection line formed by the FSP with the ground (dFSP) and the Y-axis (direction of the target) was used as the direction angle (uFSP; Figure 5) fFSP \u00bc cos -1\u00f0nFSP\u00b7k\u00de; \u00f09\u00de dFSP \u00bc k \u00a3 nFSP k \u00a3 nFSPj j ; \u00f010\u00de uFSP \u00bc sign\u00f0i\u00b7dFSP\u00de cos-1\u00f0j\u00b7dFSP\u00de; \u00f011\u00de where i, j, and k are unit vectors of the X-, Y- and Z-axes, respectively. An FSP directed to the left side of the target yielded a positive direction angle (Equation (11)). Trajectory-plane fitting was carried out for the shoulders, right elbow, and the left-hand center in the TB\u2013MF phase (Figure 4D). Since the left elbow remains extended during most part of the downswing, its trajectory is highly dependent on those of the left shoulder and hand and, for this reason, left elbow was excluded from plane fitting. Right hand was also excluded from plane fitting as its motion should be similar to that of the left hand. The orientations of the MPs were computed relative to the FSP, not to the ground/target line (Figure 5) fMP \u00bc cos-1\u00f0nFSP\u00b7nMP\u00de; \u00f012\u00de dMP \u00bc nMP \u00a3 nFSP nMP \u00a3 nFSPj j ; \u00f013\u00de uMP \u00bc sign\u00f0-sFSP\u00b7dMP\u00de cos-1\u00f0dFSP\u00b7dMP\u00de; \u00f014\u00de where fMP and uMP are the relative inclination and direction of inclination of an MP, respectively, sFSP is the slope vector of the FSP, and nMP and dMP are the normal and direction vectors of the MP, respectively (Figure 5)", " Therefore, the alignment/misalignment of the arm to the shoulder line at TB may not mean any fundamentally different backswing motions (one plane vs. two planes). Third, a downswing can be divided into the transition and execution phases and alignment/ misalignment of the arm to the shoulder line may affect the transition phase, but not the execution phase. Fourth, the shoulder girdle motion is not as simple as a rotation about the trunk axis, evidenced by the vastly different MPs formed by the two opposing shoulder points (Figure 4; Table IV). One limitation of this study was that foam practice balls, not actual golf balls, were used in an indoor biomechanics laboratory. While participants reported no abnormal feel from hitting the foam balls, it is certainly possible for the clubhead motion immediately after the impact to be altered by the ball used. The purpose of this study was to determine the FSP of the clubhead and the MPs of the key pendulum points (shoulders, left hand, and right elbow) that characterize a golfer\u2019s fundamental downswing motion, and to systematically assess planarity of the golf swing based on the FSP and the MPs" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001646_j.jiec.2018.01.011-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001646_j.jiec.2018.01.011-Figure3-1.png", "caption": "Fig. 3. a) Polarization curves of the EBCs using CNT/PEI/LAC, CNT/PEI/GNP/LAC, CNT/PEI/NPT/LAC and CNT/PEI/[GNP-NPT]/LAC catalysts. For the tests, 40mM glucose solution was circulated with a flow rate of 0.1 mL\u00b7min-1 at air state for anodic reaction. b) Polarization curve of the EBC using CNT/PEI/[GNP-NPT]/LAC catalyst. For the test, 50cc/min H2 gas was supplied for anodic reaction.", "texts": [ " In brief, it is clarified that (i) the grafting effect of PEI on CNT played a key role in immobilizing many laccase molecules, (ii) the increase in onset potential was motivated due to the adoption of NPT and (ii) the GNP-NPT composite played a critical role as the relay for electron transfer. Thus, eventually, of the applied catalysts, CNT/PEI/[GNP-NPT]/LAC was considered the most proper catalyst to maximize positive effects of the included components. To investigate effect of GNP-NPT composite on EBC performance, polarization curves of the EBCs using four different catalysts (CNT/PEI/LAC, CNT/PEI/GNP/LAC, CNT/PEI/NPT/LAC and CNT/PEI/[GNP-NPT]/LAC) as biocathode were measured and the result is represented in Fig. 3. For the measurements of EBC performance, Pt/C was used as anodic catalyst, while 40 mM glucose solution and air were provided as fuel for anode. According to the Fig. 3, maximum power density (MPD) of the EBC using CNT/PEI/[GNP-NPT]/LAC was highest as 13 \u03bcW\u00b7cm-2 and that was clearly better than that of the EBCs using CNT/PEI/LAC (4 \u03bcW\u00b7cm-2), CNT/PEI/GNP/LAC(4 \u03bcW\u00b7cm-2) and ACCEPTED M ANUSCRIP T CNT/PEI/NPT/LAC (7 \u03bcW\u00b7cm-2) catalysts. Moreover, open circuit voltage (OCV) of the EBCs using NPT included catalysts (CNT/PEI/NPT/LAC and CNT/PEI/[GNP- NPT]/LAC) was ~0.7 V and that was quite higher than that of the EBCs using other catalysts (~0.3V), implying that the positive impact of NPT on onset potential obviously affected even the performance of EBC, while the GNPNPT composite also showed positive effect on the EBC performance" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000753_j.engfailanal.2011.11.004-Figure15-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000753_j.engfailanal.2011.11.004-Figure15-1.png", "caption": "Fig. 15. Distribution of the uniaxial stress of the shaft for load case I.", "texts": [ " In compliance with the norms defined in [23], the analysis of the drive shaft of the BWE was carried out for two load cases: the BWE moves forward, the drives of both pairs of caterpillar tracks are involved, shaft loads due to the torque and the corresponding vertical forces on the arm L = 600 mm from the center of mass of the gearbox: T1z,max = 282 kNm and H1max = 31.2 kN \u2013 load case I, the BWE turns right backward, the drive of one pair of caterpillar track is excluded \u2013 the other drive is maximally loaded, the shaft load: T2z,max = 592 kNm and H2max = 65.5 kN \u2013 load case II. The uniaxial stress field, according to the Huber\u2013Hencky\u2013von Mises hypothesis [1,4,8,9], for case I of the load, is presented in Fig. 15 while Fig. 16 presents the maximum values of uniaxial stresses obtained for case II. The characteristic values of the working stress obtained by the finite element method are presented in Table 5. Fatigue analysis at the point of fracture can be carried out by using the Goodman endurance diagram. The minimum recommended value of the amplitude stress is ra = 380 MPa [24], whereas the minimum value of tensile strength is [25]: rm = 1100 MPa. These values are presented by points A and B (Fig. 17) and they define the fatigue boundary line" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001791_j.mechmachtheory.2016.05.001-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001791_j.mechmachtheory.2016.05.001-Figure1-1.png", "caption": "Fig. 1. Sketch of the Exechon PM.", "texts": [ " In section 2, the constraints and Jacobian of the Exechon PM are analyzed based on determining its constrained wrenches. In section 3, the principle for deriving the KIMs is proposed and the KIMs including overconstrained and non-overconstrained PMs for the Exechon PM are derived. In section 4, the unified statics and stiffness model of the Exechon PM and its KIMs is established. Section 5 investigates the differences of stiffness for the Exechon PM and its 6 KIMs. Finally, some concluding remarks are given in section 6. The Exechon PM (see Fig. 1) possesses a moving platform m, a base B, two identical UPR-type active legs ri (i = 1, 3) with linear actuators and one SPR-type active leg r2 with one linear actuator. B is a regular triangle with O as its center and Ai (i = 1, 2, 3) as its three vertices. m is a regular triangle with o as its center and ai (i = 1, 2, 3) as its three vertices. Let Ai, ai (i = 1, 2, 3), O and o be the position vectors of Ai, ai, O and o respectively. Let \u22a5 be a perpendicular constraint and \u2551 be a parallel constraint, respectively. Let Rij (i = 1, 2, 3; j = 1, 2, \u2026) be the j-th R joint in the i-th leg ri from bottom to top. Some geometrical constraints are satisfied for the Exechon PM as follows (see Fig. 1) Ri1\u2551A1A3;Ri1\u22a5Ri2;Ri2\u22a5ri;Ri2\u2551Ri3;Ri3\u2551a2o i \u00bc 1;3\u00f0 \u00de;R21\u2551a1a3;R21\u22a5r2: \u00f01\u00de To facilitate the analysis, {m} is designated as a coordinate system o-xyz fixed on m at its central point o with x, y and z are three coordinate axes. {B} is designated as a coordinate system O-XYZ fixed on B at its central point O and X, Y and Z are three coordinate axes. Some geometrical conditions (x\u2551a1a3, y\u22a5a1a3, z\u22a5m, X\u2551A1A3, Y\u22a5A1A3, Z\u22a5B) are satisfied for the coordinate axes. For the lower mobility PMs, there are constrained wrenches (forces/torques) existed in the limbs", " (b) In each limb of the lower mobility PMs, the constrained torques must be perpendicular to all revolute joints. Rules (a) and (b) show the geometrical properties between constrained wrenches and joints. Based on (a) and (b), one constrained torque Tpi(i = 1, 3) which is perpendicular to Ri1, Ri2 and Ri3 and one constrained force Fpi which is parallel with Ri3 and passes through the center of U joint can be determined in the i-th UPR type leg. In addition, one constrained force Fp2 which is parallel with R21 and passes through S joint can be determined in the SPR type leg (see Fig. 1). The unit vectors \u03c4i of Tpi (i = 1, 3) and the unit vectors f i of Fpi can be determined as follows: \u03c4i \u00bc Ri1 Ri2 i \u00bc 1;3\u00f0 \u00de; f i \u00bc Ri3 i \u00bc 1;3\u00f0 \u00de; f 2 \u00bc R21: \u00f02a\u00de Here, Rij denotes the unit vector giving the direction of revolute joint Rij. From Eqs. (1) and (2a), it leads to Tp1 Tp3; Fp1 Fp3; Tpi\u22a5Fpi i \u00bc 1;3\u00f0 \u00de: \u00f02b\u00de Since the constrained forces/torques do no work to the terminal platform, it leads to [18]: 05 1 \u00bc f T1 d1 f 1\u00f0 \u00deT 0T 3 1 R11 R12\u00f0 \u00deT f T2 d2 f 2\u00f0 \u00deT f T3 d3 f 3\u00f0 \u00deT 0T 3 1 R31 R32\u00f0 \u00deT 2 6666664 3 7777775 v\u03c9 f 1 \u00bc f 3 \u00bc y; f 2 \u00bc x;di \u00bc Ai\u2212o;R11 \u00bc R31 \u00bc X;R12 \u00bc R32 \u00bc y: \u00f03a\u00de Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001190_0954406215621098-Figure18-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001190_0954406215621098-Figure18-1.png", "caption": "Figure 18. Finite shaft element with coordinate system and displacements.", "texts": [ " The centrifugal force Fc and gyroscopic Mg are calculated as Fc \u00bc 1 2 mdm! 2 m \u00f021\u00de Mg \u00bc I!m!r sin 1 2 i \u00fe e\u00f0 \u00de \u00f022\u00de where i and e denote the contact angle between the roller and inner raceway and that between the roller and outer raceway. m, I, and dm are the roller mass, roller mass moment of inertia, and the bearing pitch diameter, respectively. !r and !m are the angular velocity of the roller about its own axis and the orbital angular velocity of the roller, respectively.7 Appendix 2. Finite element shaft\u2013bearing system model Figure 18 shows the finite shaft element with the coordinate systems. The displacement vectors of a shaft element are fysgT \u00bc u1 u2 u3 u4 \u00f023\u00de fzsgT \u00bc u5 u6 u7 u8 : \u00f024\u00de The mass, gyroscopic and stiffness matrices of the shaft element are expressed as ms \u00bc l 420 1\u00fe gm\u00f0 \u00de 2 a1 SYM a2 a5 a3 a4 a1 a4 a6 a2 a5 2 6664 3 7775\u00fe gs \u00f025\u00de gs \u00bc Id 30l 1\u00fe gm\u00f0 \u00de 2 36 SYM a7 a8 36 a7 36 a7 a9 a7 a8 2 6664 3 7775 \u00f026\u00de ks \u00bc EId 1\u00fe gm\u00f0 \u00del3 12 SYM a13 a10 12 a7 12 a13 a11 a13 a10 2 6664 3 7775 \u00f027\u00de where the mass per unit length ( ) is calculated using mass density ( ) and cross section area (A) as \u00bc A: \u00f028\u00de The area moment of inertia of the shaft element, Id, is calculated by the shaft element diameter (d) as Id \u00bc d4 64 : \u00f029\u00de The other parameters in the shaft element matrices are calculated as gm \u00bc 12EId AGl2 \u00f030\u00de a1\u00bc156\u00fe294gm\u00fe140g 2 m a8\u00bc 4\u00fe5gm\u00fe10g 2 m l2 a2\u00bc 22\u00fe38:5gm\u00fe17:5g 2 m l a9\u00bc 1 5gm\u00fe5g 2 m l2 a3\u00bc54\u00fe126gm\u00fe70g 2 m a10\u00bc 4\u00fegm\u00f0 \u00del2 a4\u00bc 13\u00fe31:5gm\u00fe17:5g 2 m l a11\u00bc 2 gm\u00f0 \u00del2 a5\u00bc 4\u00fe7gm\u00fe3:5g 2 m l2 a13\u00bc6l a6\u00bc 3\u00fe7gm\u00fe3:5g 2 m l2 a14\u00bc 4\u00fe2gm\u00feg 2 m l2 a7\u00bc 3 15gm\u00f0 \u00del a15\u00bc 2 2gm g 2 m l2: \u00f031\u00de at Middle East Technical Univ on May 11, 2016pic.sagepub.comDownloaded from where , E and G are the shear coefficient of the shaft cross-section, Young\u2019s modulus and the shear modulus of the shaft material. A bearing is located at a single node, and thus the displacements of bearing are represented by a (2 1) vector. Given a bearing positioned at the left-hand side node of the shaft element (Figure 18), the displacement vectors can be described as fybgT \u00bc u1 u2 \u00f032\u00de fzbgT \u00bc u5 u6 : \u00f033\u00de The bearing stiffness matrices are expressed by kbyy \u00bc kyy ky z k zy k z z ; kbyz \u00bc kyz ky y k zz k z y \" # \u00f034\u00de kbzy \u00bc kzy kz z k yy k y z \" # ; kbzz \u00bc kzz kz y k yz k y y \" # : \u00f035\u00de The bearing damping matrices are assigned as cbyy \u00bc cyy 0 0 0 ; cbyz \u00bc cyz 0 0 0 \u00f036\u00de cbzy \u00bc czy 0 0 0 ; cbzz \u00bc czz 0 0 0 : \u00f037\u00de at Middle East Technical Univ on May 11, 2016pic.sagepub.comDownloaded from" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003299_j.tws.2020.107415-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003299_j.tws.2020.107415-Figure5-1.png", "caption": "Fig. 5. The collapse modes of (a) conventional square tube, long origami-ending tubes based on (b) experiment and (c) simulation; (d) The force-displacement curves of typical tubes [50].", "texts": [ " Thin-Walled Structures 161 (2021) 107415 SEA= \u222b\u03b4 0 F(x)dx / m (2) where F(x) was the crushing force during the crushing process, \u03b4 was the final crushing distance, m was the mass of the tube, which did not change during the crushing. The EEA, which was a dimensionless indicator, was defined as the absorbed energy divided by the product of the tube\u2019s net volume and the yielding stress, as described in Eq [3]. EEA= \u222b\u03b4 0 F(x)dx / V\u03c3y (3) where V was the net volume of the tube, \u03c3y was the yield stress. The conventional square tube was used as a benchmark. It deformed in symmetric mode with a higher Fmax, lower SEA and EEA, as shown in Fig. 5 and Table 2. Compared to the conventional square tube, the long origami-ending tube can deform in diamond mode with an excellent energy absorption performance, as shown in Fig. 5. Therefore, the origami pattern had advantage in terms of energy absorption. Specifically, the Fmax can be reduced by 40%, the SEA and EEA can be increased by about 50% compared to conventional square tube, as shown in Table 2. The perfect FE model was also validated against the experimental results. It presented that the collapse modes of the LOE-E1 and the LOEFEM were both diamond mode, as shown in Fig. 5 (b) and (c). The corresponding force-displacement curve of the LOE-FEM also matched well with the experimental results, as shown in Fig. 5 (d). Additionally, if a tube deformed in diamond mode, the differences of Fmax, SEA and EEA between numerical and experimental results were within 6.0%, as shown in Table 2. Therefore, it can be concluded that the FE model was very reliable to simulate the energy absorption performance of tubes. It was well known that if a tube deformed in diamond mode, two characteristics of deformation had to be present. The first characteristic was that the middle regions of the straight plates of a module moved outward, and the second characteristic was that the corner regions of a module moved inward [35,50]" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000806_j.mechmachtheory.2012.08.011-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000806_j.mechmachtheory.2012.08.011-Figure1-1.png", "caption": "Fig. 1. Face-contact model of a pair of spur gears used for loaded tooth contact analysis. (a) Contact surface of Gear 1. (b) Contact model of Gear 1 and Gear 2.", "texts": [ " Only the centrifugal deformation of the thin-rimmed gears is considered in the LTCA. Tooth load distributions can be obtained through the LTCA. Then tooth contact stresses and root bending stresses of the deformed gears can be calculated using FEM and the tooth loads obtained. FEM programs were successfully developed to do the analyses [8\u201311]. Reliability of the FEM programs was also confirmed in the previous researches [8\u201311]. Simple principle of the LTCA for the gears is stated also in the following. Fig. 1 is a face-contact model used for LTCA of a pair of spur gears. Engagement of a pair of spur gears (Gear 1 and Gear 2) on the geometric contact line is shown in Fig. 1(b). Fig. 1(a) is a three-dimensional view of the engaged tooth surface of the Gear 1. In Fig. 1(a), loaded tooth contact is assumed to be on a reference face with a contact width denoted bywidth. Of course, this reference face is a part of the tooth surface of the Gear 1 and the geometric contact line is located at the center of this reference face. In Fig. 1(a), many lines parallel to the geometric contact line are made artificially. These lines (including the geometric contact line) are called reference lines andmany points on the reference lines aremade artificially. These points are called contact reference points, or simply say reference points. These reference points shall be used as assumed contact points in LTCA. That is to say, tooth contact on the reference face of the Gear 1 shall be replaced by the contacts on the reference points when FEM is used to perform LTCA", " Objective function Z \u00bc Xn\u00fe1 \u00fe Xn\u00fe2 \u00fe\u2026\u00fe Xn\u00fen \u00fe Xn\u00fen\u00fe1: \u00f05\u00de Constraint conditions \u2212 S\u00bd Ff \u00fe \u03b4 ef g \u00fe I\u00bd Yf g \u00fe I\u00bd Z0 \u00bc \u03b5f g \u00f06\u00de ef gT Ff g \u00fe Xn\u00fen\u00fe1 \u00bc P \u00f07\u00de where S\u00bd \u00bc Skj h i \u00bc \u03b1 kj 1\u00f0 \u00de \u00fe \u03b1 kj 2\u00f0 \u00de h i ; k \u00bc 1;2;\u2026;n; j \u00bc 1;2;\u2026;n Z\u2032 n o \u00bc Xn\u00fe1;Xn\u00fe2;\u2026;Xn\u00fen T Ff g \u00bc F1; F2;\u2026; Fk;\u2026; Fnf gT Yf g \u00bc Y1;Y2;\u2026; Yk;\u2026;Ynf gT \u03b5f g \u00bc \u03b51; \u03b52;\u2026; \u03b5k;\u2026; \u03b5nf gT Fk\u22650;Yk\u22650; \u03b5k\u22650; \u03b4\u22650; k \u00bc 1;2;\u2026;n Xn\u00fem\u22650;m \u00bc 1;2;\u2026;n\u00fe 1: In the above equations, akj(1) and akj(2) are deformation influence coefficients of the pairs of the contact points on the engaged tooth surfaces of the Gears 1 and 2 separately. They are calculated with three-dimensional FEM. P is the total load of a pair of spur gears along the line of action. P can be calculated with the Eq. (8). In the Eq. (8), rb is radius of the gear base circle. {\u03b5} is gap array that consists of all the pairs of the contact points on the reference face as shown in Fig. 1(b). {\u03b5} can be calculated geometrically. {F} is an array of the contact loads between the pairs of the contact points. \u03b4 is relative deformation of the pair of gears along the line of action. When akj(1), akj(2), {\u03b5} and P are known, {F} and \u03b4 can be calculated through solving the Eqs. (5), (6) and (7) with the Modified Simplex Method of the mathematical programming principle. P \u00bc Transmittedtorque=rb: \u00f08\u00de When tooth loads distributed on all the reference points of the contact teeth as shown in Fig. 1 are known through the LTCA, a so-called \u201cUnit Force\u201dmethod is used to calculate the contact stresses on tooth surfaces of the contact teeth, it means to calculate the tooth load distributed onunit contact area of the tooth surface [9\u201312]. Tooth root bending stresses of the deformed thin-rimmed gears can be calculated by three dimensional FEMusing themodels shown in Fig. 3when the tooth loads on the reference points are known. Three types of the inclined web gears and a solid mating gear as shown in Fig", " In order to know whether the centrifugal deformation of the thin-rimmed inclined web gears exert effects on tooth contact stresses and root bending stresses or not, LTCA [10\u201312] of the thin-rimmed inclined web gears deformed by the centrifugal loads are conducted at the worst load positions under a torque load when these gears are engaged with the solid mating gear respectively. Calculation results are given in the following. Of course, the root stresses resulted from the centrifugal loads are not included in the following. Contour line graphs of the tooth contact stresses of the left web gear with the centrifugal deformation are shown in Fig. 11. In Fig. 11, the horizontal axes of all the figures are tooth longitudinal dimension and the vertical axes of all the figures are the contact width denoted by thewidth in Fig. 1. Fig. 11(a) is the tooth contact stresses of the straightweb gear at 0 min\u22121. Fig. 11(b), (c), (d), (e) and (f) are the results of the inclined web gear at 0, 5000, 10,000, 20,000 and 40,000 min\u22121 respectively. By comparing Fig. 11(a) with Fig. 11(b), it is found that the tooth contact pattern is affected by theweb inclination. Themaximum contact length of the contact teeth becomes a little shorter and themaximumcontactwidth becomes a little greaterwhen the straight web of the thin-rimmed gear is inclined" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002700_tmech.2020.3015133-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002700_tmech.2020.3015133-Figure7-1.png", "caption": "Fig. 7. D-H coordinate systems of the continuum manipulator.", "texts": [ " The distance of the origin between the adjacent flexible unit coordinates is taken as the equivalent rod length, and the bending angle obtained in section A is taken as the equivalent joint deflection angle. The D-H parameter table of the proposed continuum manipulator is shown in Table I. \u03b1i is the equivalent torsional angle of the rod, li is the equivalent to the length of the rod, di is the equivalent to the offset of the rod, \u03b8i is the equivalent to the joint deflection angle of the rod. The coordinate system of the continuum manipulator is shown in Fig.7. The base coordinate system {x0, y0, z0} is established at the bottom of the manipulator. The x0 axis is the tangent of the bending of the first flexible unit. The z0 axis is perpendicular to the curved plane. And the y0 axis is determined according to the right-hand rule. In order not to lose the generality, the construction of the coordinate system {xi, yi, zi} is described as follows. The origin is selected at the intersection of the tangent of the flexible unit i and the tangent of the flexible unit i+ 1, as shown in Fig. 7. The xi axis is a tangent to the upper end of the flexible unit i and point to the next flexible unit i+1. The zi axis is perpendicular to the curved plane. The yi axis is determined according to the right-hand rule. Based on the assumption 5), a sketch of the relative deflection between flexible units i\u2212 1 and i is shown in Fig. 8. The equivalent rod length can be obtained as li = h0 + 2ax \u03b8i+1 tan \u03b8i+1 2 i = 0 h+ 2ax \u03b8i tan \u03b8i 2 + 2ax \u03b8i+1 tan \u03b8i+1 2 1 < i \u2264 2n\u22121 h1 + 2ax \u03b8i tan \u03b8i 2 i = 2n (18) where h0 , h and h1 are the length of the rigid units; \u03b8i is the deformation of the flexible unit i ; \u03b8i\u22121 is the deformation of the flexible unit i\u22121 ; 2ax is the length of the center layer of the flexible unit" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003495_j.addma.2021.101986-Figure8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003495_j.addma.2021.101986-Figure8-1.png", "caption": "Fig. 8. Diagram of process features.", "texts": [ " Owing to the mismatch between the low acquisition frequency of the thermal imager and the high-speed laser movement, the thermal history extracted directly from the temperature data is incomplete. For example, in this work, the thermal imager\u2019s acquisition frequency was only 7 Hz, while the laser scan speed was 2500 mm/s. When the imager records a temperature image, the laser spot moves by 357.14 mm, and the temperature field changes significantly. The transient temperature field changes much faster than the thermal imager can acquire images. As shown in Fig. 8a, the temperature curve presents dramatic random fluctuations at higher temperatures in the thermal history curve, which is not the actual temperature change. Moreover, owing to laser reheating, the thermal history curve has multiple peaks, which hinders the evaluation of the sintering status. However, as the powder material is softened and sintered at high temperatures, it is essential to determine the temperature change at high temperatures to evaluate the part quality. Therefore, it is necessary to recover the thermal history at high temperatures from the existing temperature data", " The interval of sampling points is subjected to an exponential function to adapt to the thermal curve trend. Subsequently, another input to the feedback model is the process features. More than 50 process parameters affect part quality, but only a small subset of these variables is actively employed in process control [6]. In this work, the process features extracted from the monitored data were scan vector length (LS), heat trace length (LH), heat transfer distance (dH), and cumulative scan time (tC), as shown in Fig. 8. Furthermore, these features were normalized to improve the efficiency of neural network training. This neural network training requires a data set of operational status under the ideal thermal environment, wherein the interlaminar heat accumulation tends to be stable, and each part has the same heat conduction conditions. Therefore, a standard experiment was designed. The layout of parts for the standard experiment is shown in Fig. 9. All parts Q. Zhong et al. Additive Manufacturing 42 (2021) 101986 were kept at the same distance from the center of the build chamber, ensuring they had the same heat conduction conditions" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003660_lra.2021.3095035-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003660_lra.2021.3095035-Figure1-1.png", "caption": "Fig. 1. Prototype of the over-actuated UAV platform with four vectoring thrust actuators. Each actuator consists of a regular quadcopter inside a gimbal with two passive joints and can provide omni-directional thrust to the platform.", "texts": [ " Cables [12], [13] or spherical universal joints [14] have been used as the passive joints, where the angular range is still constrained by mechanical interference. Passive hinges of unlimited continuous rotations have been used [15] in a unique UAV, which connect the main frame to each of four quadcopters that control both the thrusts and hinge angles. However, the real-world hardware attitudes were limited by the maximum thrust magnitude and low thrust efficiencies at non-horizontal poses. In this letter, we present a fully-actuated UAV platform with four novel vectoring thrust actuators (Fig. 1). The actuator is realized by placing a quadcopter on a passive two-axis gimbal, where the copter\u2019s center of mass (COM) is at the gimbal\u2019s center of rotations. Steering of the passive gimbal is achieved by the torque generated by the quadcopter. The actuator has three major advantages over those of other systems: a) capable of generating thrust in any direction, with continuous and unlimited range of angulation; b) simplified dynamics \u2013 the air resistance torques are mostly cancelled among the quadcopter rotors, in contrast to single rotor actuators, and the reaction torques between the actuator and the main frame are nearly zero; c) simple modular units \u2013 system prototyping is mechanically simple because the regular quadcopter integrates thrust generation and steering", " The second rotational joint, \u03b2i, is perpendicular to the \u03b1i joint, and is realized by a ring fixed on the regular quadcopter body and enclosed by two brackets. The ring is designed to enclose only the central body of the quadcopter so as to minimize its size and weight and prevent interference with the propellers. Using the regular quadcopter and 3D printed gimbal frame provides an advantage that different quadcopters can be easily replaced based on the task requirements. The UAV platform is composed of four gimbal actuators mounted on a central frame (Fig. 1). The platform is overactuated as it has a total of 12 DOF. The central frame is a rigid body made by two perpendicular carbon-fiber tubes. Commercial quadcopter Crazyflie 2.1 from Bitcraze [16] is used on the gimbal actuator, and BETAFPV 7x16 mm DC motors are used on the quadcopter. The physical properties of the system are listed as follows. The whole platform weights 155 g in total. Each quadcopter weights 27 g, and the 3D-printed gimbal weights 9 g. The maximum thrust of each quadcopter is 0.7 N. The world coordinate frame is denoted as FW , and the platform frame FB is attached to the geometric center of the UAV platform (Fig. 1). To assist the derivation of the controller equations, additional platform frames FBi are defined by rotating FB along +z axis for \u03c0(i\u2212 1)/2 rad and placed at the geometric center of each gimbal (Fig. 2(a)). Actuator frames Fi are attached to the geometric center of the ith quadcopter. X Y R is used to denote rotation matrix in SO(3) from FX to FY . X [\u00b7] is used to denote physical term such as position or velocity expressed in FX other than FW . Also, we have X Y RT = Y XR, and X [\u00b7] = X Y RY [\u00b7]" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002944_tie.2020.2992020-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002944_tie.2020.2992020-Figure1-1.png", "caption": "Fig. 1. (a) AF-PMA-ECB topology and (b) flux paths.", "texts": [ " Magnetic analysis consists of 2- dimensional (2D) reluctance network modeling, NewtonRaphson nonlinear solver and coupled Faraday\u2019s Law and Ampere\u2019s Law. In thermal analysis, 3D lumped parameter model is used to determine the temperature rise of each component. The proposed approach runs in the time domain and all nonlinear parameters are updated by temperature rise in each time step. II. INVESTIGATED AF-PMA-ECB The investigated AF-PMA-ECB has a single-rotor (brake disc)-single-stator configuration and its structure is illustrated in Fig. 1-(a). PM magnetizations, excitation coils and flux paths are provided in Fig. 1-(b). The magnet driven flux completes its path over yoke without exaction current. PM flux can be altered by DC excitation during braking operation in this topology and it is possible to fully control the braking torque without external mechanisms as to [8]-[13]. The key parameters of the investigated AF-PMA-ECB are provided in Table I. The brake has 180 mm/100 mm of outer-to-inner diameter ratio with an axial air gap, g, of 1 mm. The brake disc has a thickness of 15 mm. The N30UH type NdFeB magnets are used in the slot openings of the brake" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000415_978-3-642-37552-1-Figure13.1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000415_978-3-642-37552-1-Figure13.1-1.png", "caption": "Fig. 13.1 Illustration of the actuation mechanism of fern sporangium: a before and b after evaporation induced opening of annulus to release spores (adapted from [11]). Reprinted with permission from [12]. Copyright 2006 Institute of Physics", "texts": [ " In addition to pumping water through their vasculature using evaporative processes, ferns also make use of water evaporation within specialized microstructures to obtain fast motion and high forces for spore dispersal [11]. As part of their reproductive processes, ferns grow specialized vessels called sporangia which house and disperse spores during certain times of the year. As they dry, these millimeter scale sporangia open violently to release microscale spherical spores into the air. This mechanism is illustrated in Fig. 13.1. Each sporangium is surrounded by a single layer of dead, water-filled cells called an annulus. Each cell is comprised of two rib-like structures filled with water. As the water inside the annulus cells dries, surface tension between the water and the cell wall gives rise to high forces causing a deflection along the outer edge of the annulus. The combined deflection of each wall straightens the entire annulus structure and tears open the spore sac. The discovery of the fern sporangium spore dispersal mechanism is credited to Ursprung and Renner who, in 1915, independently used the sporangium to try and measure the tensile strength of water [11, 13, 45]" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000364_tfuzz.2011.2178854-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000364_tfuzz.2011.2178854-Figure1-1.png", "caption": "Fig. 1. Structure of the inverted pendulum system.", "texts": [ " The effectiveness of the adaptive law (30) will be demonstrated in the next section. Finally, because \u03b8\u0307d = 0 means \u03b8\u0303d = 0, i.e., \u03b5t = \u03b5d , (17) can be rewritten as V\u0307 = \u2212eT Qe + 2eT PB\u03b5d \u2212 2eT PBuc. (31) Since those similar derivations, from (18)\u2013(24), are still hold, the system stability without the adaptation scheme is guaranteed. In the section, the MATLAB command \u201code45\u201d is used to implement the simulation of the control system with a fixed time step size of 0.01 (s). The widely used inverted pendulum system is the plant as shown in Fig. 1 and is described as x\u03071 = x2 x\u03072 = f + gu, f = gr sin x1 \u2212 mt Lx2 2 sin x1 cos x1 mc +mt L ( 4 3 \u2212 m cos2 x1 mc +mt ) , g = cos x1 mc +mt L ( 4 3 \u2212 m cos2 x1 mc +mt ) (32) where x1 (in radians) is the angle of the pole, x2 (in radians per second) is the angular velocity of the pole, gr is the acceleration due to gravity (9.8 m/s2), mc is the mass of the cart (1.0 kg), mt is the mass of the pole (0.1 kg), sgn(g) = 1 is known by testing in advance, and L = 0.5 (in meters) is the length of the pole" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003475_lra.2021.3060708-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003475_lra.2021.3060708-Figure2-1.png", "caption": "Fig. 2. Our magnetic tweezer system and its schematics. (a) Transparent view and (b) front view of a magnetic tweezer with illustrations of the actuation and measurement coordinate systems.", "texts": [ " The haptic interface (Geomagic touch haptic device, 3D Systems, Rock Hill, SC) is operated by a 6-DOF (degree of freedom) pen-type stylus gripper, which is serially connected to the haptic device body. The device can measure the 6-DOF position and orientation of the user\u2019s operation and generate 3-DOF force feedback in x, y, and z directions. The haptic control software is developed using the open-source haptic library CHAI3D to Authorized licensed use limited to: Carleton University. Downloaded on June 15,2021 at 08:59:00 UTC from IEEE Xplore. Restrictions apply. ensure the compatibility over the multiple operating systems and diverse haptic device platforms. As shown in Fig. 2, the magnetic tweezer system consists of six magnetic poles on a double-layer structure with three poles on top and bottom planes, each pole has a magnetic coil of 527 turns, which is made of AWG-25 heavy-built insulation coating copper wire, attached to the end. Additionally, the magnetic yoke is 3D printed with magnetic material that guarantees durability and rigidity, as well as improving magnetic gradient field generation efficiency. Cobalt iron alloy (VACOFLUX 50, VACUUMSCHMELZE GmbH & Co.KG) was selected for magnetic poles due to its high saturation (2" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001824_0954406217693659-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001824_0954406217693659-Figure3-1.png", "caption": "Figure 3. The loads on the ball.", "texts": [ " Both the solution accuracy and its effectiveness are satisfied for engineering applications. Quasi-static model of angular contact ball bearings In this section, a 5-DOF quasi-static model of angular contact ball bearings is constructed based on Hertz\u2019s contact theory. The relative displacement of ball and rings with applied load is as shown in Figure 2. Based on Hertz\u2019s contact theory, the force, Q, acting on ball\u2013raceway contact surface under elastic displacement amount, , is given as Qk \u00bc Kn 3=2 k \u00f01\u00de Figure 3 shows the loads on the ball. Thus, the equilibrium equations of ball are given as Qik sin ik Qok sin ok Mgk D lik cos ik lok cos ok\u00f0 \u00de \u00bc 0 Qik cos ik Qok cos ok \u00fe Mgk D lik sin ik lok sin ok\u00f0 \u00de \u00fe Tck \u00bc 0 8< : 9= ; 9>>>>>= >>>>>; \u00f02\u00de Then, the equilibrium equations of bearings are given as Fx Fy Fz Mx My 2 6666664 3 7777775 \u00bc cos \u2019k 0 0 sin\u2019k 0 0 0 1 0 zp sin \u2019k rp sin\u2019k sin\u2019k zp cos \u2019k rp cos\u2019k cos\u2019k 2 6666664 3 7777775 Qik cos ik \u00fe likMgk D sin ik Qik sin ik likMgk D cos ik likMgk D ri 2 6666664 3 7777775 \u00f03\u00de The equilibrium equations can be solved by the Newton\u2013Raphson method" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002022_978-3-319-40036-5-Figure4.4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002022_978-3-319-40036-5-Figure4.4-1.png", "caption": "Fig. 4.4 3D-printed channels with integrated devices. (a\u2013d) Schematic (a, b) and photographs (c, d) of a device that features a threaded port for incorporating disk-shaped electrodes into a 500 \u03bcm diameter channel. Reproduced from Reference [35] with permission from the Royal Society of Chemistry. (e) Photograph of fluidic channel interfaced with optical fibers for in-channel spectrophotometry. Reproduced from reference [28] with permission from IOP Publishing. (f\u2013h) Fluidic device with integrated needle biosensors for continuous monitoring of glucose and lactate from dialysate. Reproduced by the permission from Reference [37]; copyright American Chemical Society", "texts": [ "5 mM) were delivered into the 3D-printed channel. Membrane inserts provided reservoirs for collecting and measuring adenosine triphosphate 4 3D Printed Microfluidic Devices 109 (ATP) transported from the channel. Erythrocytes stored in the modified AS-1 exhibited greater ATP production than those stored in commonly used AS-1. In addition to membrane inserts, sensing elements like electrodes and optical fibers have also been incorporated into 3D-printed channels to facilitate bioanalytical measurements [17, 25, 28, 30, 35\u201337] (Fig. 4.4). Electrodes can be fastened in channels through access holes, deposited on substrates that are bound to open-sided channels to complete the fluidic device, or housed in threaded fittings that are compatible with threaded ports included in the device design. 0.5 mm carbon and platinum electrodes incorporated in 3D-printed channels have been used to detect viruses that were labeled with cadmium sulfide quantum dots [36]. Dopamine, nitric oxide, ATP, and hydrogen peroxide have also been measured using 3D-printed fluidic devices with integrated electrodes [25, 35]" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000560_j.mechmachtheory.2013.06.001-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000560_j.mechmachtheory.2013.06.001-Figure5-1.png", "caption": "Fig. 5. Four bar mechanism with error in joint-1 (error exaggerated).", "texts": [ " In the present work, it is represented by a virtual link of dimension rv and its angular position is taken to vary from 0 to 360\u00b0, as the contact between the pin and hole can occur anywhere along the circumference. In terms of screw theory, a joint-error can be treated as a virtual link connected to an adjacent link by a virtual screw $v (see Fig. 4(b)). In this section, variation in coupler point position is investigated with error in one joint. Four bar mechanism with one virtual link is shown in Fig. 5. Screw $1\u2032 associated with joint-1\u2032 is also shown. Input is given to link-2 and angle \u03b82 is varied. The virtual link ra is very small in comparison with active links and angle \u03b8a is varied from 0 to 360\u00b0, as the contact can occur along any point on the circumference of the hole/pin for every \u03b82. able 2 odrigues parameters for the four-bar mechanism-without manufacturing errors. Screw si so,i \u03b8i ti First open chain 1 (1, 0, 0) (0, 0, 0) \u03b82 0 2 (1, 0, 0) (r2, 0, 0) \u03b83 0 Second open chain 4 (1, 0, 0) (r1, 0, 0) \u03b84 0 Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001745_j.engfailanal.2014.01.016-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001745_j.engfailanal.2014.01.016-Figure1-1.png", "caption": "Fig. 1. Geometrical values which define the characteristic frequencies of a radial ball bearing.", "texts": [ " The crest factor (peak to rms). f. Statistical moments of higher order such as skewness S and kurtosis K: S \u00bc 1 n Pn i\u00bc0\u00f0xi l\u00de3 r3 \u00f07\u00de K \u00bc 1 n Pn i\u00bc0\u00f0xi l\u00de4 r4 : \u00f08\u00de Certain faults and malfunctions exhibit signal peaks in characteristic frequencies. Faults in rolling element bearings produce signals in frequencies which depend on the geometrical characteristics of the bearing and the rotation frequency. In the case of a single row rolling element bearing with a rotating inner ring and a stationery outer ring (Fig. 1), these frequencies are approximately given from the following equations: fc \u00bc f 2 1 D d cosa \u00f09\u00de fbpfo \u00bc Zfc fbpfo \u00bc Z f 2 1 D d cosa \u00f010\u00de fbpfi \u00bc Z\u00f0f fc\u00de fbpfi \u00bc Z f 2 1\u00fe D d cosa \u00f011\u00de fr \u00bc f 2 d D 1 D d cos a 2 \" # \u00f012\u00de where f is the shaft rotation frequency; fc is the cage rotation frequency; D the rolling element diameter; d is the pitch diameter [ (di + do)/2]; di is the inner raceway diameter; do is the outer raceway diameter; a is the contact angle; fbpfo is the ball pass outer raceway frequency; Z is the number of rolling elements; fbpfi is the ball pass inner raceway frequency and fr is the ball rotation frequency" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003195_s10846-019-01129-4-Figure14-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003195_s10846-019-01129-4-Figure14-1.png", "caption": "Fig. 14 Test T6. Command module final assembly with a Logitech C900 camera and power connections to neighbor modules plugged in an umbilical cord", "texts": [ " Electrical tests were performed, and the module was able to provide/receive electrical power to/from neighbor modules, even while operating. During trials, the temperature in all critical points has always remained within acceptable ranges. In this way, one concern with the architecture (the possible heating due to the circulation of high currents through long circuits) was discarded. \u2013 T6. Command module test. A command module was built according to the specification detailed in previous sections (Fig. 14). A camera was placed in the central position of the module, and an umbilical cord was plugged to distribute the high power to all the circuits of the UAV. The module was tested to assure its capacity to transfer current (up to 120A) and data to neighbor modules and computer. It passed in all tests performed. To evaluate the feasibility of a prototype implemented following DRA, two distinct experiments were conducted with i) a propeller set and ii) a UAV. In the first experiment, we investigated the propulsion set to evaluate the performance of the part in terms of thrust capacity considering the extra load imposed by the architecture" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001341_tmag.2013.2281477-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001341_tmag.2013.2281477-Figure2-1.png", "caption": "Fig. 2. (a) Flux distribution of mutual magnetic paths. (b) Linear force profile. (c) Torque profile. (d) Torque generation from linear current components.", "texts": [ " In the linear region, toque and force can be approximated as [11]{ T = 1 2 \u00b7 \u2202L1 \u2202\u03b8 \u00b7 i2 1 + 1 2 \u00b7 \u2202L2 \u2202\u03b8 \u00b7 i2 2 F = 1 2 \u00b7 \u2202L1 \u2202x \u00b7 i2 1 + 1 2 \u00b7 \u2202L2 \u2202x \u00b7 i2 2 (4) where L1 and L2, i1 and i2 are the total inductance and current from stator rings 1 and 2, respectively. It is clear that torque and force generation are both dependent on phase current of the stators. Current excitation from any phase of either stator ring contributes both torque and force generation. Therefore, the magnetic paths are nonlinear and highly coupled. 3-D finite-element model has been constructed for performance prediction. Flux distribution on the cross section of the x\u2013\u03b8 plane can be found in Fig. 2(a). Calculation of linear force output profile for the fully aligned angle and torque profile versus different angular positions of any one phase can be found in Fig. 2(b) and (c), respectively. It can be observed from Fig. 2(a) that the flux lines of the machine travel not only along the radial direction, but also through the axial direction. Since the radial and the axial fluxes are responsible for the torque and force generation, respectively, force and torque can be generated simultaneously as any phase(s) of either stator is excited. From the FEM results, Fig. 2(d) shows the torque profiles generated from the current components of the linear motion of phase A\u2013C of any one stator at a current level of 2.5 A. It is clear that the net torque profile from the three phases changes with large fluctuations at different mechanical angles. The ultimate goal of decoupling is to make the current component responsible for linear force generation provides minimum contribution to rotary torque generation. The decoupling algorithm is described as the following steps. 1) The current components of linear motion from any stator ring are denoted as Al, Bl, and Cl, respectively. For effective decoupling control from the rotary and linear axis, the following equation must be satisfied: { T (Al) + T (Bl) + T (Cl) = 0 Al + Bl + Cl = d (5) where d is the required total current reference for the linear motion generated from the linear position controller. 2) From Fig. 2(d), it can be seen that the absolute torque values from the negative and positive directions of any phase are approximately equal in certain fixed regions during one period. For example, when the angular position falls into 10\u00b0 to 20\u00b0, the absolute torque value of phase C equals to that of phase A at the same current level. Hence, the net torque value from phases A, B, and C can be regarded as zero, since torque from phase B can be neglected, and it does not effect linear force generation. Therefore, the angular region can be divided into six segments from the mechanical angle period as follows:\u23a7\u23a8 \u23a9 (0\u25e6 \u2212 10\u25e6&80\u25e6 \u2212 90\u25e6), Cl = 0 (10\u25e6 \u2212 20\u25e6), Bl = 0 (20\u25e6 \u2212 40\u25e6), Al = 0 and \u23a7\u23a8 \u23a9 (40\u25e6 \u2212 50\u25e6), Cl = 0 (50\u25e6 \u2212 70\u25e6), Bl = 0 (70\u25e6 \u2212 80\u25e6), Al = 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003085_j.msea.2020.139916-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003085_j.msea.2020.139916-Figure2-1.png", "caption": "Fig. 2. Geometry of the specimen used for all tests.", "texts": [ " 1d, shows a prevalence of basket weave pattern, in some regions recognizable as martensitic acicular. The transition from diffusional \u03b1+\u03b2 to diffusionless \u03b1\u2019 martensitic phase has already been observed [43,45], and this can also be attributed to the high scanning speed. Finally, the estimated microhardness of 340,1 \u00b1 3,7 HV is in compliance with the characteristics of the previously described microstructure, and congruent with results reported in the literature in relation to the same dimensional scale of the specimens [47]. The as-built tensile specimens, all with the same geometry shown in Fig. 2, were subjected to static and dynamic traction as well as static torsion, in order to also evaluate the effects of strain rate and Lode angle deviatoric parameter on the elastoplastic curve and fracture initiation. The dynamic tensile tests were characterized by a nominal strain rate, i. e. the strain rate reached before the necking onset, of 700 and 1000 s\u2212 1 respectively. The torsion tests were carried out in free end mode, i.e. without axial constraints, in order to obtain pure shear conditions" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001753_tia.2014.2301862-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001753_tia.2014.2301862-Figure4-1.png", "caption": "Fig. 4. Classical winding description and specification.", "texts": [ " (1) Traditional skewed or rhombic windings are, like most other kinds of windings, made from round wire, or when appropriate, of Litz wire [9]. Their manufacturing process is complex and requires very specific machines whose cost can be justified only in the case of mass production. Moreover, because the wire section cannot vary with this technology, the consecutive loops cannot be adjacent on all the segments constituting them if they do not have the same slope, which corresponds to the general case depicted in Fig. 4. Consequently, a portion of the winding volume remains untapped when it could be used to increase the wire section and thus to reduce its electrical resistance. Instead, this space filled with air or resin will cause a decrease in the winding thermal conductivity, further increasing the thermal stress on the motor. As announced in the introduction, the flex-PCB technology can be used to produce air-gap windings, including the generalized skewed and rhombic windings presented above. As illustrated in Fig", " 4 and 6, are w\u00a91 =\u0394 R\u0304w frL Lw 2 l\u00a91 (19) w\u00a92 =\u0394 R\u0304w (1\u2212 frL)Lw l\u00a92 . (20) b) Rhombic: Referring to Fig. 3 for the rhombic winding, the segment lengths are l\u00a91 = 1 2 \u221a ((1\u2212 frL)Lw) 2 + ( (1\u2212 fr)\u03c0 R\u0304w )2 (21) l\u00a92 = frL Lw (22) whereas the distances separating them, as illustrated in Figs. 4 and 6, are w\u00a91 =\u0394 R\u0304w (1\u2212 frL)Lw 2 l\u00a91 (23) w\u00a92 =\u0394 R\u0304w. (24) 2) Technology: a) Classic: As explained in Section II, classic windings are made from round wire of constant section. This implies, as illustrated in Fig. 4, that these wires cannot be adjacent to each other on each segment of the winding. Considering the conductor radius rc as a dependent parameter, it can be linked to the minimum distance separating adjacent loops through the following relation: rc = \u03b1 2 min ( w\u00a91 , w\u00a92 ) (25) with \u03b1 as a factor \u2208 [0, 1] that takes into account the thickness of the insulation, assuming that it is proportional to the wire diameter. On this basis, the phase resistance of a classical winding is given by Rph = Nt Nl \u03c1 4 l\u00a91 + 2 l\u00a92 \u03c0 r2c (26) where lengths l\u00a91 and l\u00a92 are taken from (17) and (18) or from (21) and (22) depending on whether the winding is a skewed or a rhombic winding" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000931_9781118703274.ch2-Figure2.32-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000931_9781118703274.ch2-Figure2.32-1.png", "caption": "Figure 2.32 Hydraulic turbine yaw system (Multibrid N5000, 5MW). Reproduced by permission of Aerodyn Energiesystems GmbH", "texts": [ " Because of the moment along the y axis, which engenders a yawing moment on the rotor, swinging the turbine too fast can subject all arrangements of rotor blades to severe and even dangerous stresses. Such steering operations should therefore only be carried out very slowly. Very slow and controlled yawing can be achieved using active positioning mechanisms. Electric azimuth drives are most commonly used. Figure 2.31 shows all the main components of a typical control mechanism, with its motor\u2013gearbox unit, ring gear and yaw control. Hydraulic systems are usually of similar construction. They are, however, used only in large turbines (Figure 2.32). In large turbines, internal ring gears (Figure 2.33(a)) are generally used instead of the external ring gear shown in Figure 2.31. Furthermore, several centrally mounted geared motors (Figure 2.33(b)) are established in the market. Their greater axial length, among other things, makes it easier to climb into the nacelle from the tower. Brake systems (Figure 2.33(c)) stop the yaw movement and thus protect the yaw gears and ring gears in particular. Side-rotor yaw systems were widespread in earlier times, also being found in Dutch windmills (Figure 1" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002088_j.mechmachtheory.2018.01.015-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002088_j.mechmachtheory.2018.01.015-Figure5-1.png", "caption": "Fig. 5. The geometric relationship between the marked points and the visual field of laparoscope.", "texts": [ " The robot-assisted surgical system also consists of a master manipulator system, which is used to control the three arms of the slave system by applying a master-slave control method. Before the surgical operation, surgical assistants place the three slave arms in their correct positions according to a preoperative placement analysis. Electromagnetic clutches fix the positions of the three trocars. The position vectors of the incisions of the three trocars can be calculated by using the information of photoelectric encoders. In robot-assisted laparoscopic surgery, the frequently-used 3D laparoscopic visual angles \u03b8L include 0 \u00b0, 30 \u00b0, 50 \u00b0 (as shown in Fig. 5 ), which are the inclined angles between the sight line of the binocular cameras and the central axis of the laparoscope. After the adjustment of the laparoscopic visual window by the surgeon according to the actual demands, surgeons can carry out the operation through manipulation of the instrument arms using the master-slave manipulation. Similar to conventional motion methods, the master-slave controlling object has to be switched to control the motion of the laparoscope arm by manipulating the master system based on the visual window", " \u03bb in T 8 N0 = T \u03bbN0 \u00b7 in T 1 0 \u00b7 in T 2 1 \u00b7 in T 3 2 \u00b7 in T 4 3 \u00b7 in T 5 4 \u00b7 in T 6 5 \u00b7 in T 7 6 \u00b7 in T 8 7 = \u23a1 \u23a2 \u23a2 \u23a2 \u23a3 \u03bb in n x \u03bb in o x \u03bb in a x \u03bb in p x \u03bb in n y \u03bb in o y \u03bb in a y \u03bb in p y \u03bb in n z \u03bb in o z \u03bb in a z \u03bb in p z 0 0 0 1 \u23a4 \u23a5 \u23a5 \u23a5 \u23a6 (4) \u03bb in P 8 N0 = [ \u03bb in p x \u03bb in p y \u03bb in p z ]T (5) When \u03bb = 1 , the vector 1 in P 8 N0 denotes the position vector of mark point A. When \u03bb = 2 , the vector 2 in P 8 N0 denotes the position vector of mark point B. The kinematic models of the instrument arm, laparoscope arm, and marked points, are the basic spatial geometric relations in the tracking algorithm of the visual window. As shown in Fig. 5 , the replacement process of the autotracking visual window can be divided into four-phase procedures: (1) initial adjustment, (2) current visual window, (3) transitional visual window, and (4) targeted visual window. Points M A , M B , M L , are the fixed points of the parallelogram joints, \u03b3 is the ultrawide angle of the laparoscope\u2019s lens, and points A i , B i , and L i , represent the marked points and the end of the laparoscope, respectively. Points C i and D i indicate the projection points of the marks A i and B i on the plane \u03b1 or \u03b2 , respectively", " Moreover, E i lies on the central axis of the laparoscope, and frame x E i y E i z E i is attached on E i and is parallel to the visual frame x L i y L i z L i . Angle \u2220 C i L i D i = \u03bei is the basic parameter of the laparoscopic visual window, which defines the distribution and proportion of marked points in the visual field. This is the preset parameter selected by the user according to the actual demand and experience. Moreover, c \u03be denotes the circular distribution area of marked points in the visual field. Plane \u03d1 is the same as plane x L i z L i within the visual frame x L i y L i z L i . Fig. 5 (a) shows the initial adjustment of the laparoscopic visual window. The parameters \u03bea , \u03beb , \u03bec , and \u03be0 , explain the initial adjustment processes at the end-points of the laparoscope\u2019s end L a , L b , L c , and L 0 , respectively. As the basic key visual parameter used throughout the autotracking algorithm, \u03be0 is the suitable preset parameter according to the adjustment. Fig. 5 (b) shows the current visual window after the initial adjustment. When the marked points move, Fig. 5 (c) shows the transitional visual window, whereby the actual basic visual parameter \u03be1 is not satisfied with the preset value \u03be0 . Fig. 5 (d) shows the targeted visual window with the stable basic visual parameter \u03be0 , and the solution procedure is presented in the following context. Fig. 5 (b) shows the current visual window. Assume the current position vectors of marks A 0 and B 0 are shown in accor- dance to Eq. (6) with respect to the global coordinate system X 0 Y 0 Z 0 . { P A 0 = [ x A 0 y A 0 z A 0 ]T P B 0 = [ x B 0 y B 0 z B 0 ]T (6) The position vector of mid-point E 0 is given as P E 0 = 1 2 ( P A 0 + P B 0 ) (7) According to the preoperative placement information and forward kinematics of the laparoscope arm, the current posi- tion vectors of points M L and L 0 are defined as { P M L = [ x M L y M L z M L ]T P L 0 = [ x L 0 y L 0 z L 0 ]T (8) We also assumed an auxiliary point V 0 on segment L i E i , and an auxiliary frame x V 0 y V 0 z V 0 associated with point V 0 . The frames x V 0 y V 0 z V 0 and x L 0 y L 0 z L 0 are parallel, as shown in Fig. 5 . We set \u2016 \u2212\u2212\u2192 L 0 V 0 \u2016 = d V 0 . Matrix la T V 0 N0 is noted as the pose matrix of frame x V 0 y V 0 z V 0 with respect to the global coordinate system X 0 Y 0 Z 0 . Additionally, the attitude matrix R V 0 and the position vector P V 0 of la T V 0 N0 can be expressed in accordance to Eq. (9) . la T V 0 N0 = [ R V 0 P V 0 0 1 \u00d73 1 ] = la T L N0 \u23a1 \u23a2 \u23a3 1 0 0 0 0 1 0 0 0 0 1 d V 0 0 0 0 1 \u23a4 \u23a5 \u23a6 (9) which formulate the forward kinematics of frame x V 0 y V 0 z V 0 . The inverse kinematics can be obtained by the inverse transformation method", " { [ P E 0 A 0 1 ]T = T E 0 \u22121 \u00b7 [ P A 0 1 ]T [ P E 0 B 0 1 ]T = T E 0 \u22121 \u00b7 [ P B 0 1 ]T (12) where \u23a7 \u23a8 \u23a9 P E 0 A 0 = [ x E 0 A 0 y E 0 A 0 z E 0 A 0 ]T P E 0 B 0 = [ x E 0 B 0 y E 0 B 0 z E 0 B 0 ]T (13) Thus, with respect to the central visual frame x E 0 y E 0 z E 0 , the position vectors of points C 0 and D 0 can be defined as { P E 0 C 0 = [ x E 0 C 0 y E 0 C 0 0 ]T P E 0 D 0 = [ x E 0 D 0 y E 0 D 0 0 ]T (14) Combining Eqs. (8) and (14) , the vectors \u2212\u2212\u2212\u2192 C 0 D 0 and \u2212\u2212\u2192 L 0 E 0 are defined as { \u2212\u2212\u2212\u2192 C 0 D 0 = P E 0 D 0 \u2212 P E 0 C 0 \u2212\u2212\u2192 L 0 E 0 = P E 0 \u2212 P L 0 (15) Thus, the basic visual parameter \u03be0 can be obtained using Eq. (16) , which is a preset constant parameter in the auto- tracking algorithm of the visual window. \u03be0 = \u2220 C 0 L 0 D 0 = 2 \u00d7 ta n \u22121 \u2225\u2225\u2225\u2212\u2212\u2212\u2192 C 0 D 0 \u2225\u2225\u2225 2 \u2225\u2225\u2225\u2212\u2212\u2192 L 0 E 0 \u2225\u2225\u2225 (16) Fig. 5 (d) depicts the targeted visual window, and shows that the analytical solution for the desired position vector P L 2 is difficult to obtain since it conforms to an elliptical collection. However, a necessary condition for the analytical solution is that points V 2 and E 2 are superposed such that the numerical method can be used in this solution process by considering the constraint conditions, as shown as Eq. (17) . The variable \u03be \u2032 denotes the calculated basic visual parameter during the numerical solving process. Correspondingly, if the percentage error is less than 0.01%, parameter \u03be \u2032 \u2248 \u03be0 can be ensured and used to calculate the desired position vector P L 2 of the visual window. \u23a7 \u23aa \u23aa \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23aa \u23aa \u23a9 0 < \u2225\u2225\u2225\u2212\u2212\u2192 L 2 V 2 \u2225\u2225\u2225 < \u2225\u2225\u2225\u2212\u2212\u2212\u2192 M L E 2 \u2225\u2225\u2225\u2225\u2225\u2225\u2212\u2212\u2192 V 2 E 2 \u2225\u2225\u2225 = 0 \u03be \u2032 \u03be0 \u00d7 100% \u2265 99 . 99% (17) Moreover, the cyclic process ( Fig. 5 (b) to (c) to (d) to (b) to (c) to (d)\u2026) describes the dynamic alternation of the visual window of the laparoscope. This dynamic transformation process is the key conversion mode of the dynamic visual window as shown in Fig. 5 . The limit point F is the end of the trocar, which means that the desired position vector P L 2 cannot enter the internal parts of the trocar. 4. Hybrid grey prediction model-based autotracking algorithm A prediction model is employed to reduce or eliminate the hysteresis effect by using the preset parameter-based tracking algorithm. This is effective in improving the autotracking performance. In the actual master-slave manipulation, the user manipulates the master system. The system then outputs the desired motion trails after tremor filtering and trajectory planning so that the desired motion trails consist of a series of smooth transition functions", ", the inverse kinematics, the visual window angles, and the basic view parameter criteria. Fig. 9 shows the results of the inverse kinematics of laparoscope arm. The corrected and followed results are almost the same, and they meet the joint range of motion, i.e., \u03b8 la 5 \u2208 [ \u221290 , 90] \u25e6, \u03b8 la 6 \u2208 [0 , 60] \u25e6, d la 8 \u2208 [40 , 240] mm . Fig. 10 shows the results based on the visual window angles criterion of the corrected prediction trajectory, whereby angles \u2220 ALB , \u2220 ALE , \u2220 BLE , and \u2220 CLD can be found in Fig. 5 (d) without the subscript, and the basic requirements are such that \u2220 ALB < \u03b3 , \u2220 ALE < 0 . 5 \u03b3 , \u2220 ELB < 0 . 5 \u03b3 , \u2220 ALB < 90 \u25e6, \u2220 ALE < 45 \u25e6, \u2220 BLE < 45 \u25e6, and \u2220 CLD is equal to \u03be0 = 34 . 3775 \u25e6. In these instances, \u03b3 denotes the ultra-wide angle of the laparoscopic lens within 110 \u00b0. The results of Fig. 10 show that a good performance is elicited based on this judging criteria condition. Fig. 11 shows the results of the basic view parameter of the autotracking visual window, and the relative errors indicate that the autotracking algorithm can result in a highly accurate basic view parameter" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002676_j.mechmachtheory.2020.103955-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002676_j.mechmachtheory.2020.103955-Figure4-1.png", "caption": "Fig. 4. Angle mapping process.", "texts": [ "103955 To satisfy the concentric relationship, the axis which the driven gear at first stage and the driving pinion at the second stage rotate around should coincide with the shaft which these two gears are assembled. The relationship is given as L AC \u00d7 sin (\u03b1/ 2) = L BC \u00d7 sin (\u03b2/ 2) (2) where L AC = (d 1 + d 2 ) / 2 and L BC = (d 3 + d 4 ) / 2 . As the lines AC, CB, BD and DA form a quadrilateral, the angles must satisfy the following condition \u03b1 + \u03b2 + \u03b41 + \u03b42 = 2 \u03c0 (3) For smooth and reliable operation, a series of installation conditions should be satisfied. A process of angle mapping is given in Fig. 4 to discuss the situation. Assuming that the gears could mesh simultaneously and perfectly at the position of the pitch points, as illustrated in Fig. 4 (a), where the blue and black dashed lines refer to the dedendum circle of the gears, the blue and black solid lines represent the pitch circle of the gears. The input pinion at the first stage drives clockwise and makes both the driven gears at the same stage and the driving double-helical pinions at the second stage rotate counterclockwise, which results in the output gear generating a clockwise rotation. There exists a phasing angle difference between the driven gear at first stage and the driving pinion at second stage", " According to the assumption of meshing simultaneously, the phasing angle \u03d5 can be measured from the pitch point of the working (driven) flank of the driven gear at first stage to the pitch point of the working (driving) flank of the driving pinion at the second stage. Please cite this article as: Z. Hu, J. Tang and Q. Wang et al., Investigation of nonlinear dynamics and load sharing characteristics of a two-path split torque transmission system, Mechanism and Machine Theory, https://doi.org/10.1016/ j.mechmachtheory.2020.103955 Z. Hu, J. Tang and Q. Wang et al. / Mechanism and Machine Theory xxx (xxxx) xxx 9 Based on the angle mapping procedure, the installation condition can be obtained. First, as given in Fig. 4 (b), we focus on one meshing tooth pair of driving pinion and driven gear at the left branch of first stage, which is marked with red color. All gears are meshing perfectly at the pitch points simultaneously, at this time, there are initial positions for the focused teeth of pinion and gear, which are T 1 \u2212 1 and T 2 \u2212 1 , respectively (here, subscripts 1 and 2 represent pinion tooth and gear tooth, respectively, 1 after dash line refers to first step). As shown in Fig. 4 (c), after the input pinion rotate clockwise angle \u03b1, all gears are still meshing perfectly at the pitch points, the focused pinion tooth has a second position (T 1 \u2212 2) . Meanwhile, the compound gears at the left branch and right branch both rotate counterclockwise angle \u03b1 \u00d7 z 1 / z 2 , and the output gear generates rotation angle \u03b1 \u00d7 z 1 / z 2 \u00d7 z 3 / z 4 . In this step, the focused gear tooth also has a second position (T 2 \u2212 2) . In the third step as illustrated in Fig. 4 (d), the input pinion rotates clockwise angle \u03b2 \u00d7 z 4 / z 3 \u00d7 z 2 / z 1 from the new position achieved by the former procedure. The compound gear connecting the first and second stage and output gear rotate corresponding angle \u03b2 \u00d7 z 4 / z 3 and angle \u03b2 , respectively. After this rotation being finished, the focused pinion tooth and gear tooth would have the finial positions, which are T 1 \u2212 3 and T 2 \u2212 3 , respectively. Considering the driven gear tooth at the first stage, the rotational angle from its initial position to its final position, which is \u03b1 \u00d7 z 1 /z 2 + \u03b2 \u00d7 z 4 /z 3 , should be equal to integer multiples of the pitch value n \u00d7 \u03b82 , here, n is an integer, and \u03b82 = 2 \u00d7 \u03c0/z 2 is the tooth pitch of driven gear" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002354_j.vacuum.2018.09.007-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002354_j.vacuum.2018.09.007-Figure5-1.png", "caption": "Fig. 5. Thickness measurement.", "texts": [ " Such values represent the correction factors between the 3D model and the fabricated object and they were used to scale the CAD model of the samples. The sample thickness was the feature chosen to assess the dimensional accuracy of the EBM process. A coordinate measuring machine (CMM) Prismo Vast of Zeiss was used to measure the thicknesses of the samples. Each sample was fixed vertically on the reference plate of the CMM by means of a bench, as shown in Fig. 4 a probe with a spherical tip of 5mm was used. Fig. 5 shows the thickness measured for each family of samples orientation. In particular: \u2022 for the samples oriented along the x-axis (or y-axis) of the building chamber the two planes that define the thickness of the sample along the y-axis (or x-axis) were measured \u2022 for the sample oriented at 45\u00b0 with respect to the start plate, the two vertical planes that define the thickness of the sample along the building direction were measured. As matter of fact, for these samples, the thickness was allowed to be measured only in this direction since in the other direction the planes could not be inspected due to the presence of wafer support teeth. On the contrary, for the sample built at 90\u00b0, all the four planes oriented vertically were measured in order to calculate both the thicknesses t1 and t2 in Fig. 5; the thickness of the sample at 90\u00b0 was estimated as the average between t1 and t2. For each plane and for three different sections of the sample (one at the middle and the other two close to the sample ends), a set of 30 points were measured and their centroid was computed; three local thicknesses were measured as the distance between the centroids of the opposite planes. The difference among the three measurements for each specimen was found negligible (lower that 0.5%), so the average of the three values was considered as the thickness of the sample" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003476_j.triboint.2021.106951-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003476_j.triboint.2021.106951-Figure6-1.png", "caption": "Fig. 6. Oil flow fields with different rolling directions at different times.", "texts": [ " The helicopter may turn left or right when turning, and the position of the lubricating oil level in the intermediate gearbox which is relative to gears and oil guide holes is different in different turning directions. To perform simulations with turning left and right, the intermediate gearbox is set to complete the motion of increasing the roll angle from 0\u25e6 to 60\u25e6 and then decreasing to 0\u25e6 within 2s. The oil distribution and oil flow rate of four oil guide holes are monitored during simulations, as shown in Fig. 6 and Fig. 7, and churning losses in the first 1s is shown in Fig. 8. The initial oil immersion depth is set to 12.36 mm, which is about 1.46 times the whole depth of the driving gear, and the rotating speed of driving gears is 3000 rpm. According to Fig. 6, it can be shown that the distribution of lubricating oil inside the gearbox at diverse moments is different due to the impact of turning directions. The oil inside the gearbox also tilts with the change of the flight attitude as the intermediate gearbox turns and part of the oil flows tangentially in the direction of rotation of the gear after being stirred up by the gears, and the oil speed is about 10 m/s. The streamline near the tooth surface is also denser. The lubricating oil distributes on the inner wall of the gearbox evenly at 1s and the velocity of oil at this moment is larger than before" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001114_j.enzmictec.2014.09.007-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001114_j.enzmictec.2014.09.007-Figure1-1.png", "caption": "Fig. 1. Illustration of the prepared g", "texts": [ " Electrode fabrication The surface of pencil graphite electrode was covered by poly(GMA-co-VFc) by drop casting and was left to dry. Once polymer dried, electrode was submerged into 0.1 M 3-aminophenylboronic acid for 3 h, for the purpose of forming a linkage between poly(GMA-co-VFc) and FAD. Soon after that, modified electrode was immersed into 0.1 M FAD, and was gently mixed for 3 h. Finally, electrode was placed into Apo-enzyme for a total time of 24 h in order to allow effective reconstitution on the FAD monolayer (Fig. 1). 2.4. Electrochemical measurements Electrochemical measurements were performed using a CHI Model 842B electrochemical analyzer. A pencil carbon working electrode (3 mm diameter), a platinum wire counter electrode (0.2 mm diameter), Ag/AgCl-saturated KCl reference electrode, and conventional three-electrode electrochemical cell were purchased from CH Instruments. All amperometric measurements were carried out at room temperature in 0.01 M pH 7.4 phosphate buffer solution. The analyses were carried out in electrochemical cell containing, carefully immersed, enzyme electrode in stirred buffer solution" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000066_0278364909101786-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000066_0278364909101786-Figure5-1.png", "caption": "Fig. 5. Parameters for the needle handling.", "texts": [ " Without loss of generality it can be centered in I , with axis zT along the normal to the tissue in I . Q is the frame attached to the patient with its origin on the incision point Q. J is attached to the instrument at the center of the jaws with zJ along the axis of the instrument and xJ parallel to the jaws. K is attached to the trocar, centered on the incision point and is such that K RJ 3 and K TJ 0 0 dz T. N is the frame attached to the needle. Its origin is the center of the needle and it is oriented as shown on Figure 5. Position of the Needle Holder As is usually done in laparoscopic surgery (Ortmaier and Hirzinger 2000 Krupa et al. 2003), we consider that the incision in the abdomen is a point, denoted by Q, and that the axis of the instrument goes through Q. The flexibility of the abdominal wall and backlashes of the instrument inside the trocar are neglected and since no physiological movements are considered Q is constant with respect to the world frame W . The position of the needle holder with respect to Q can be described by the rotation matrix Q RK and the depth of the instrument inside the abdomen given by dz ", " (2005b) and Nageotte (2005), where the contact is a pinpoint H , called the handling point. Here H is actually the intersection of the axis of the instrument and the needle. To take into account the handling constraints, the relative position between the needle holder and the needle N RJ N TJ is described by only four parameters, b the distance between H and the tip of the instrument, the angular position of H on the needle, and and the orientation of the needle holder with respect to the needle, so that we have (see Figure 5): N RJ Rz 2 Rx Ry Minimizing tissue deformations and movements is an important criterion for a good stitching. One can distinguish nonrigid motions (with local extent) and global displacement of the tissues (rigid motion). However, since both are unsuitable we do not differentiate between them and we call them \u201cdeformations\u201d. Since physiological motions are not considered, deformations are due to contact between the needle and the tissues which arise during steps 2 and 3. During normal stitching, the contact between the needle and the tissue can be considered as a point contact (the actual entry point I during steps 2 and 3) or two point contacts (the actual entry (I ) and exit (O) points) during steps 4 and 5" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002906_tec.2020.3040009-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002906_tec.2020.3040009-Figure4-1.png", "caption": "Fig. 4. The PM-to-rotor yoke leakage flux loops at the inner and outer radii.", "texts": [ " 3(b) shows the PM-to-rotor yoke leakage flux loop at the effective conductor radius range. In this leakage flux path, the PM reluctance, reluctance of the air-gap part, and reluctance of the rotor yoke core part are modeled by R\u03c3rm, R\u03c3rg, and R\u03c3rr, respectively. These reluctances can be obtained respectively by 0 ( ) o i m rm R rm R h R L r dr (8) ( ) 0 0 1 o i R L r R rg m dzdr R z h (9) 0 3 3 1 ( ) 2 ( ) o i R r rr R rr l dr B R L r (10) where L(r) is the thickness of the leakage flux tube and can be determined by Fig. 4 shows the PM-to-rotor yoke leakage flux loops at the inner and outer radii of the PM. In the inner radius leakage flux loop, the PM reluctance, reluctance of the air-gap part, and reluctance of the rotor yoke core part are modeled by R\u03c3im, R\u03c3ig, and R\u03c3ir, respectively. In the outer radius leakage flux loop, R\u03c3om, R\u03c3og, and R\u03c3or are used to model the leakage reluctance of each part, similarly. All these reluctances can be determined respectively through Based on the flux paths in Fig. 2, the MEC model for a pair of PM poles is established" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001328_j.renene.2014.03.036-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001328_j.renene.2014.03.036-Figure5-1.png", "caption": "Fig. 5. Two bearing configuration.", "texts": [ " Two bearing configuration The main difference between the TPM and the two bearing configuration (TBC) is the use of a second smaller main bearing to support the main shaft of the turbine at the gearbox side. Therefore the system becomes hyperstatic. The main assumption in the market is that if the system is well designed it should be possible to divert all non-torque loading through the two main bearings into the nacelle. In the TBC the gearbox is still connected to the nacelle by means of a torque arm on two bushings. All important components are shown on Fig. 5. The hyperstaticity of the system is the main challenge of this configuration, which requires good insights during the design phase in the overall turbine loading. The third configuration, the hydraulic suspension (HS), is a variant of the TBC. In this system themain shaft is also supported by two main bearings. The gearbox, however, is not connected to the nacelle by means of a torque arm and bushings. Instead, the upper rubber mount, filled with hydraulic fluid, on one side is connected to the lower rubber mount on the other side by a hydraulic pipe" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000552_acc.2014.6858865-Figure12-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000552_acc.2014.6858865-Figure12-1.png", "caption": "Fig. 12: Orientation maneuver corresponding to the initial condition C3(\u22120.99\u03c0), plotted at 2s increments", "texts": [], "surrounding_texts": [ "In this paper, we considered the problem of constrained control of spacecraft attitude dynamics and presented two predictive control schemes, a reference governor and a nonlinear model predictive controller. Both schemes used the Lie group variational integrator to evolve their predictions on SO(3) \u00d7 SO(3). We showed that both schemes guarantee constraint admissibility and convergence to the desired equilibrium and presented numerical results exhibiting these properties. We also showed that in the unconstrained case, both schemes are globally stabilizing and discontinuous, as is required by theory." ] }, { "image_filename": "designv10_9_0002084_j.ymssp.2018.03.033-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002084_j.ymssp.2018.03.033-Figure4-1.png", "caption": "Fig. 4. Geometrical parameters for the fillet-foundation deflection [32].", "texts": [ " [31] derived an analytical method reflecting the effect of the fillet foundation deflection on the gear mesh stiffness. The fillet foundation stiffness can be calculated as follows: 1 kf \u00bc cos2 b EL L uf Sf 2 \u00feM uf Sf \u00fe P \u00f01\u00fe Q tan2 b\u00de ( ) \u00f012\u00de where b is the pressure angle, and the coefficients L\u2044, M\u2044, P\u2044, and Q\u2044 can be approximated using the polynomial function as follows: X i \u00bc Ai=h 2 f \u00fe Bih 2 fi \u00fe Cihfi=hf \u00fe Di=hf \u00fe Eihfi \u00fe Fi \u00f013\u00de where X i refers to the coefficients L\u2044,M\u2044, P\u2044, and Q\u2044; hfi \u00bc rf =rint; uf, Sf and hf are defined in Fig. 4, and the values of Ai, Bi, Ci, Di, Ei and Fi are given in Ref. [32]. According to Ref. [24], the ability of the cracked tooth to bear the axial compressive force is the same as in the perfect condition, thus it can be assumed that the axial compressive stiffness will not change which can be expressed as: 1 ka \u00bc Z l lrim sin2 a1 2EL\u00f0r2f x2\u00de12 dx\u00fe Z a3 a1 sin2 a1\u00f0a2 a\u00de cosa 2EL\u00bdsina\u00fe \u00f0a2 a\u00de cosa da \u00f014\u00de However, the bending stiffness and shear stiffness will change with the crack propagation. In addition, the equations are different between CPT and CPR" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000180_j.mechmachtheory.2010.07.003-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000180_j.mechmachtheory.2010.07.003-Figure7-1.png", "caption": "Fig. 7. Constraint forces \u03bbmi due to the constrained motion on the plane AcAiBiTi.", "texts": [ " Therefore, the velocities of the three joints Ti perpendicular to their corresponding planes AcAiBiTi are constrained to be zero and they are given as: nT i \u22c5GiX\u0307 = 0; i = 1\u223c3 \u21d2 nT 1\u22c5G1 nT 2\u22c5G2 nT 3\u22c5G3 2 64 3 75X\u0307 = 03\u00d71 \u21d2 Am1 Am2 Am3 2 4 3 5X\u0307 = 03\u00d71\u21d2AmX\u0307 = 03\u00d71 \u00f018\u00de ni is the unit normal vector of the plane AcAiBiTi in the Cartesian space. Am = Am1 Am2 Am3 2 4 3 5 is a 3\u00d76 matrix whose rows are the where bases of the constraint forces in the task space. The constraint forces in the task space could thus be expressed as Ami T \u03bbmi where \u03bbmi is the corresponding magnitude. By utilizing the Jacobian analysis, the constraint forces Ami T \u03bbmi in the task space are determined to be \u03bbmini in the Cartesian space as shown in Fig. 7. These constraint forces exist to guarantee that each of the spherical joint Ti would exactly move on its corresponding plane. It should be noted that since the bases \u2202 \u2202Si and \u2202 \u2202\u03b8i of the joint coordinates frame are on the plane AcAiBiTi, the transformation of the constraint forces \u03bbmini from the Cartesian space into the joint space would be zero as shown below. JTi \u22c5\u03bbmini = 02\u00d71; i = 1\u20133 \u00f019\u00de Eq. (19) shows that the constraint forces \u03bbmini will not appear in the dynamic equations of each legs if the reaction forces are decomposed into \u03bbmini and the other components" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003340_j.addma.2021.101881-Figure19-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003340_j.addma.2021.101881-Figure19-1.png", "caption": "Fig. 19. The (a) longitudinal and (b) vertical residual deformation before (BSR) and after support removal (ASR) using 3-layer ELLM with two tuned MPMs.", "texts": [ " In addition to MPM #1 and #2 identical to those parameters in Section 4.1.1, the third MPM (#3) uses the specific material property parameters as seen in Table 2. Given the three MPMs above, the entire cantilever beam model is divided into three sections for layer-wise assignment of material properties accordingly. It takes much shorter time to finish the 11-step simulation than the 2- layer ELLM case and the 32-step benchmark case. The obtained residual deformation before and after removal of the support structures is shown in Fig. 19. Compared to those results in the benchmark case (see Fig. 14), the prediction error is acceptable though it increases slightly due to the lumping effect compared to the 2-layer ELLM case. Note the gray color near the arrow in Fig. 19(a) suggests shrinkage magnitude is beyond the maximum value of the legend color band. Another trial is to develop the 4-layer ELLM in order to accelerate the layer-wise simulation to a further extent. Correspondingly, three additional tuned MPMs (#2~#4) are needed in addition to the real MPM (#1) for IN718. Four adjacent equivalent layers are lumped into a super layer in the 4-layer ELLM case. As a benefit, only 8 load steps are needed for the 32-layer model. The computational time can be further reduced compared to the 2-layer and 3-layer ELLM case in Sections 4", " The obtained residual deformation before and after removal of the teeth-like structures is shown in Fig. 20. Compared to those results in the benchmark case (see Fig. 14), the overall trend of the residual deformation before and after removal of support structures matches well. However, the prediction error increases more significantly due to the lumping effect. The gray color area, which suggests residual deformation magnitude beyond the maximum value of the legend color band, becomes obviously larger in Fig. 20 compared with Fig. 19. One possible reason for the slightly increased prediction error is attributed to the geometry of the cantilever beam. The sudden transitional change of cross sections in the build direction, like the solid-support interface of the cantilever beam, is not considered in the meso-scale modeling. However, due to layer lumping operation, four adjacent layers are deformed in the same load step including the 21st to 24th equivalent X. Liang et al. Additive Manufacturing 39 (2021) 101881 layers containing the solid-support interface" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001516_rm2014v069n03abeh004899-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001516_rm2014v069n03abeh004899-Figure1-1.png", "caption": "Figure 1", "texts": [ " Motion of a rigid body on a plane In what follows we shall consider various cases of a rigid body rolling along a given surface under the action of external forces. We assume that during its motion the body makes contact with the surface only at a single point and rolls without slipping. It is known that such constraints are non-holonomic, and the corresponding equations of motion can be obtained using various approaches (see, for instance, [2], [3], [23], [30], [50], [68], [69], [75], [94]). In this section we give only the definitions and equations needed for the case of a rigid body rolling on a plane. We introduce two coordinate systems (see Fig. 1): \u2022 the fixed reference frame OXY Z, with origin O located at some point in the plane and axis OZ orthogonal to the plane; \u2022 the body frame Cxyz, with origin C at the centre of mass of the body and axes parallel to the principal axes of inertia. Let \u03b1, \u03b2, \u03b3 be the projections of the unit vectors of the coordinate axes of OXY Z on the axes of the body frame Cxyz, and let R = (R1, R2, R3) be the coordinates of the body\u2019s centre of mass in the fixed reference frame OXY Z. Then for the orthogonal matrix Q = \u2225\u2225\u2225\u2225\u2225\u2225 \u03b11 \u03b21 \u03b31 \u03b12 \u03b22 \u03b32 \u03b13 \u03b23 \u03b33 \u2225\u2225\u2225\u2225\u2225\u2225 \u2208 SO(3); (27) the pair (R,Q) \u2208 R3 \u2297 SO(3) uniquely determines the position of the body" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000415_978-3-642-37552-1-Figure4.11-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000415_978-3-642-37552-1-Figure4.11-1.png", "caption": "Fig. 4.11 Schematic drawing of the model and its coordinates and parameters. Reprinted with permission from [19]. Copyright 2010 American Chemical Society", "texts": [ " Since no torque is generated when there is no rotational displacement, the order of the difference in surface area can be roughly estimated by multiplying the torque by the rotational displacement and then dividing the result by the surface energy. Pure water was used in the experiment (surface energy is 72 \u00d7 10\u22123J/m2). Accordingly, the difference in surface areas between both cases is approximately 2 \u00d7 10\u221210 m2. Since the surface area of the 4.5 \u00b5L sphere droplet is 13.2 \u00d7 10\u22126 m2, the difference should be less than 0.002 % of the entire surface. Such a minute difference is hard to distinguish with a finite element method; another method is required. To determine the liquid shape, we set the coordinate system as illustrated in Fig. 4.11. The boundary conditions at the top and bottom plane are given by: ra(\u03c6) = Ra + la cos(n(\u03b8 \u2212 \u03c6)) when z = h (4.3) rb(\u03c6) = Rb + lb cos(n\u03b8) when z = 0 (4.4) where Ra and Rb are the diameters of the plates, la and lb are the amplitudes of the perturbations, n is the frequency of the perturbations, and h is the gap of the plates. The schematic drawing shows the case of n = 4. We considered the liquid\u2019s shape to be a function of the rotational displacement \u03c6 and described it in terms of r(\u03b8, z, \u03c6). As explained in [1] The surface r(\u03b8, z, \u03c6) is obtained by solving the Young-Laplace equation" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001819_j.ijthermalsci.2017.01.011-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001819_j.ijthermalsci.2017.01.011-Figure7-1.png", "caption": "Fig. 7. Solid fraction and temperature distribution at t \u00bc 0.14 s during the stable coating stage: (a) solid fraction distribution; (b) temperature distribution.", "texts": [ " To verify the numerical accuracy, a reference coordinate system according to the layer-substrate interface and the contour edge of the layer was established, and the layer height was measured by equal distance in the direction of fused-coating. Fig. 4 presents the comparison between the experimental results and the layer heights obtained using the model. Fig. 4b is the cross section of calculated solidification morphology and solidification boundary was used for simulation validation. The corresponding 3D solidification morphology are shown in Fig. 7a. Fig. 4 shows a relatively good agreement between the model and experimental measurements. Moreover, the model predicts not only the cross-sectional shape of the coated layer, but also the numerical value. In other words, themodel can be used as a quantitative predictive tool. When the high-temperature melt being extruded from the nozzle once contacts with the weld pool, they will fuse together spontaneously in a very short period of time. Then, physical interactions associated with thermal, solidification and melt flow processes take place in a small volume", " Early-stage development in the second stage of complex free surface evolution encompasses various critically interdependent influence factors involving process stability, bonding quality between layers, and microstructures and solidification morphology of formed parts. In this stage, the temperature field strongly differs temporally and regionally. As the melt flow is very complex and the melt shape fluctuates frequently, they would influence the quality and performance of the formed parts at the initial stage of fusedcoating process. As time goes on, the solidification front and the flow-induced free surface deformation tend to be a stable state. In the relatively stable stage, the mechanism of the material transfer can be illustrated by the flow field in Fig. 7. Fig. 7 demonstrates the free surface shape at the stable stage. The free surface with very small fluctuations can be observed under the combined action of gravity, surface tension, the kinetic energy of melt, and the shear stress near the solidification front. This leads to an equidistribution of thermal (kinetic) energy in the small volume and results in \u2018local thermodynamic equilibrium\u2019. One of the main consequences of the \u2018local thermodynamic equilibrium\u2019 assumption is that the thermal field and the configurations of the melting front and the solidification front in the melt reach a steady state" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000476_1.4007349-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000476_1.4007349-Figure7-1.png", "caption": "Fig. 7 Constraints in the FEA model of three cases", "texts": [ " Nodes in the flange of the hub are fixed. In order to keep the rigid beams from tilting in or out of the plane, the rotational degrees of freedom of race curvature centers along the bearing axis z is constrained (UY\u00bc 0 in the cylindrical coordinate system). Extreme loads of the pitch bearing are applied to the end plane of the blade root. Load values are given in Table 2. The loads on the other two blades are assumed to be small compared with the extreme load and neglected. The constraint conditions are shown in Fig. 7. The constraint areas are with bright color. Because the nodes of the SOLID45 elements only have translation degree of freedom, the constraint translation degrees of freedom (UX, UY, UZ in the x, y, z direction) of the nodes in the bright color area are defined as zero. The constraint of the whole hub case is shown in Fig. 7(a). In order to study the effect of the supporting structure stiffness on the bearing load performance, other cases which the pitch bearing is connected with the partial hub block and the outer ring is fixed as rigid body are also analyzed. Constraints of partial hub case and rigid outer ring case are shown in Figs. 7(b) and 7(c), respectively. The bearing supporting structures in these three cases have different stiffness because of the difference in supporting manner and fixed form. The stiffness matrix of the supporting structure in the whole hub case is given in Eq", " Similarly, the maximal contact angle variation of the rigid outer ring case in the first and second raceway is 12.88 deg and 13.1 deg of a11, respectively, which is the minimum among these three cases. The contact angle variation of the whole hub case is affected by the large elastic deformation of the bearing supporting structure. Furthermore, for the first and second raceways, the maximal contact angles in the whole hub case are about 180 deg opposed to those in the other two cases, which is mainly caused by the constraint difference among these three cases shown in Fig. 7. On the other hand, there is little difference in the contact angle distribution between the first raceway and the second raceway in the same case. The maximum difference of the contact angle at the same circumference angle between the first raceway and second raceway is less than 10 deg. It is interesting that there is no contact angle peak at the location of the load peak affected by hard point in the whole hub case, which is primarily because that the spring deformation is too small to determine the variation of the contact angle" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003643_j.eswa.2021.115380-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003643_j.eswa.2021.115380-Figure1-1.png", "caption": "Fig. 1. UAV and suspended load coordinate system.", "texts": [ " In Sierra and Santos (2019), a neural estimator is used to reject the effect of the wind and changes in the mass. An UAV quadrotor is composed by four perpendicular arms, each one with a motor and a propeller. The four motors drive the lift and direction control. The UAV absolute position is described by the three position coordinates, (x, y, z), and the attitude is given by the three Euler\u2019s angles: roll, pitch and yaw (\u03d5, \u03b8, \u03c8). The system is based on the coupling of four propellers, two by two, which are opposed each other (1, 3) and (2, 4) (Fig. 1). In order to balance the system, one pair of motors turns clockwise while the other one spins counterclockwise. The angular velocity (rad/s) of the rotors is w1 to w4. The increment of the speed of rotor 3 respect to rotor 1 produces a positive pitch (\u03b8 > 0), while increasing the speed of while increasing the speed of rotor 4 regarding rotor 2 produces a positive roll (\u03d5 > 0). The increment of the speeds of rotors 1 + 3 respect to rotors 2 + 4 produces a positive yaw (\u03c8 > 0). In Fig. 1, the suspended-load is a mass, mL (blue circle), hanging from a cable of length L (m). The position of the payload is xL. The position vector p gives the direction of the payload mass regarding the position of the quadrotor, xQ. To determine the differential equations of the mechanical model J.E. Sierra-Garc\u00eda and M. Santos Expert Systems With Applications 183 (2021) 115380 there are typically two approaches: the Lagrangian-Euler and the Newton-Euler methods, based on the representation of the translational and angular dynamics (Fowles & Cassiday, 2005)" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001419_s12540-017-6442-1-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001419_s12540-017-6442-1-Figure1-1.png", "caption": "Fig. 1. (a) Schematic diagram of the scanning procedure for the multi-layer deposition and (b) photographs of DED machine.", "texts": [ " Accordingly, in this study, AISI D2 metal, which is widely used in cold press processes, was hardfaced by depositing H13 tool steel and M2 high-speed tool steel by using DED technology, and the mechanical properties of these surface coatings were investigated. The wear resistance of the deposited metal layer was analyzed, and a Charpy impact test, which can qualitatively evaluate the fracture toughness, was performed. This study also discusses improvement in mechanical properties through hardfacing of H13 and M2 powders by comparing with conventional heat-treated tool steel. The laser-assisted metal lamination equipment used for our research-a direct metal tooling (DMT) MX3 device developed by Insstek (South Korea) Co., Ltd.-is shown in Fig. 1(a). The device consists of a 4-kW CO2 laser that serves as the heat source, a numerical control system (including an industrial operating computer), MX-CAM software, a fiveaxis NC machine tool, and a powder feeding system that consists of three hoppers and a coaxial powder nozzle. Figure 1(b) shows a multi-layer deposited along a \u201czigzag\u201d path, wherein the track follows back-and-forth motions in a fixed direction. The beam spot diameter is 1.0 mm with a top-hat intensity distribution. Thus, overlapping tracks were applied with a pitch of 0.5 mm. The experiments were performed with argon as the shielding gas for the protection of the workpiece against oxidation as well as the carrier gas for the injected powder. The processing head, which was equipped with a coaxial supply of powder, was integrated with the optical system to feed the powder coaxially with the laser beam on the substrate surface, placed 9 mm from the nozzle tip" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001307_1.3663042-Figure16-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001307_1.3663042-Figure16-1.png", "caption": "Fig. 16 Bending. moment distribution for a cantilever plate with Infinite length (Jaramillo)", "texts": [ " \"Helicnl Gearing,\" United States Patent Office No. 1,601 ,750, October 5. 1926. 19 R . W. Fediakian and W. A. Tschechonow, \"Gear Transmission WiLh Novikov System,\" Vestnik Machi1UJslrojenya, no. 4. 1958. 20 R . W. Fediakian and W. A. Tschechonow, \"Calculo.tions for Novikov Gearing,\" Vestnik Machi'Mstrojenya, no. 5, 1958, pp. 11- 19. APPENDIX Jaramillo's solution for the moments at the fixed edge of au infinite cantilever plate due to a concentrated load acting on an arbitrary point on its surface is given in Fig. 16. 220 / AUG U ST 1960 Transactions of the ASME Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/ on 01/27/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000262_j.triboint.2011.03.012-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000262_j.triboint.2011.03.012-Figure3-1.png", "caption": "Fig. 3. Sketch of the conrod containing the test-bearing and showing the three positions to measure the shell-back temperature.", "texts": [ " For the bearing tests SAE10 oil (dynamic viscosity: Z\u00f040 1C\u00de \u00bc 21:410 mPa s, Z\u00f0100 1C\u00de \u00bc 4:084 mPa s; density: r\u00f040 1C\u00de \u00bc 835:50 kg=m3, r\u00f0100 1C\u00de \u00bc 799:20 kg=m3) is used. In daily usage MIBA uses the LP06 for material performance validation and testing the performance margin of different bearings for future engine concepts. For the following investigations in this paper special measurements with additional sensors were conducted to gain the required data for simulation model validation. Important measured quantities are the temperatures of oil inflow and on the backside of the test-bearing shell (see Fig. 3), the frictional torque measured (see Fig. 4) together for all slider bearings in the system and the contact voltage (potential difference) between the drive shaft and the test-bearing. Temperature measurement happens with thermocouple elements of type K with an accuracy of 71 1C; friction torque is logged via a HBM-sensor type T10F with a 0.1 Nm accuracy. The contact voltage is an indicator for the presence and intensity of asperity contact, i.e. for mixed lubrication. A constant voltage of approximately 3 mV between the drive shaft and the test-bearing indicates their total separation, whereas voltages lower than 3 mV result from asperity contact, thus indicating the presence of mixed lubrication" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002449_ac60117a015-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002449_ac60117a015-Figure3-1.png", "caption": "Figure 3. Cross-sectional end view of titration cell compartment and stirring arrangement", "texts": [ " The titration cell compartment is fixed between the monochromator and photometer units. It 5hould be designed to permit simple and rapid insertion and removal of the titration vessel. Also, because continuous and efficient stirring is a prerequisite of the method, the above design objectives should be met while providing the required stirring. Specific Components. Titration Cell Compartment. T h e titration cell compartment consisted of a large 10-cm. cell unit from the Beckman DC spectrophotometer, modified as illustrated in Figure 3 t o facilitate the titration manipulations. A cell with quartz window, described by Malmstadt anti Gohrbandt (9) , could be set in the compartment for titrations requiring ultraviolet radiation. Glass beakers are suitable for titrations in the visible range down to about 350 nip. All of the titrations described herein were erformed in 200-ml. electrolytic beakers which had afout 3/( inch cut off the top so they would fit in the compartment. A polystyrene cell holder, A , was fastened securely in position in the compartment, B, by a plug-in arrangement consisting of tKo banana plugs and jacks, C" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001410_s00170-017-0365-3-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001410_s00170-017-0365-3-Figure2-1.png", "caption": "Fig. 2 Configuration of work specimen. a CAD model of cylindrical specimen and b actual specimen fabricated by EBMwith aluminum support", "texts": [ " The specimen was fabricated through additive manufacturing technique using ARCAM EBM technology. The setup is shown in Fig. 1. Titanium alloy (Ti-6Al-4 V) powder with a nominal particle size distribution ranging between 45 and 100 \u03bcm has been utilized to fabricate the specimen. The powder was supplied by ARCAM (ARCAM AB, Sweden). The specimen has been produced using standard parameters of EBM as listed in Table 1. The specimen comprises of cylindrical shape with a diameter of 20 mm and height of 25 mm as shown in Fig. 2a. It is worth noting that in order to perform secondary machining operations on rotary ultrasonic machine a fixture is necessarily required especially if the size of the workpiece is small. Therefore, the test specimen was mounted on an aluminum support with the help of adhesive. The mounted specimen in real is presented in Fig. 2b. To improve the surface quality of EBM fabricated parts, the experiments were performed on rotary ultrasonic machine (Ultrasonic 20 linear by Deckel Maho Gildemeister, Sauer Ltd. Germany [30]). The machine has five-axis configuration which enables conventional multi-axis milling as well as ultrasonic assisted grinding. The experimental setup of this work mainly consists of an ultrasonic spindle system, a data acquisition system, and a coolant setup. The schematic diagram of the system and ultrasonic 20 linear are shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000262_j.triboint.2011.03.012-Figure13-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000262_j.triboint.2011.03.012-Figure13-1.png", "caption": "Fig. 13. Plot of the asperity contact pressure calculated at a pressure of 75 MPa.", "texts": [ " For 75 MPa the large amount of worn shell material at the corners result in a pressure concentration at the axial center of the bearing. Also in circumferential direction a significant influence of the used wear profile can be seen. Due to higher specific load the area of asperity contact is enlarged, which leads to an increase in friction moment. For 75 MPa the simulation predicts a mean torque of 14.5 Nm which agrees well with the mean torque of 13.572 Nm found in the measurement on the MIBA bearing test rig (Fig. 13). A further possibility to validate the simulation results for the asperity contact is to measure the contact voltage signal at MIBA\u2019s bearing test rig, as described in Section 2. Fig. 14 (top) shows the calculated asperity contact percentage where clearly the beginning and the end of the asperity contact can be distinguished. The asperity contact percentage describes the relation of the area where contact is established against the total bearing area. In the area of zero asperity contact percentage pure hydrodynamic regime prevails" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000180_j.mechmachtheory.2010.07.003-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000180_j.mechmachtheory.2010.07.003-Figure2-1.png", "caption": "Fig. 2. Bases of the local joint coordinates frame.", "texts": [ " (1), the where velocity of each spherical joint Ti is determined as: VTi qi;q\u0307i\u00f0 \u00de = d dt OTi\u00f0 \u00de = S\u0307i \u2202 \u2202Si + \u03b8\u0307i \u2202 \u2202\u03b8i \u00f02\u00de the bases of each local coordinate frame are given as [21]: \u2202 \u2202Si = \u2202fix\u00f0qi\u00de \u2202Si \u21c0 i + \u2202giy\u00f0qi\u00de \u2202Si \u21c0 j + \u2202hiz\u00f0qi\u00de \u2202Si \u21c0 k \u00f03 1\u00de \u2202 \u2202\u03b8i = \u2202fix\u00f0qi\u00de \u2202\u03b8i \u21c0 i + \u2202giy\u00f0qi\u00de \u2202\u03b8i \u21c0 j + \u2202hiz\u00f0qi\u00de \u2202\u03b8i \u21c0 k \u00f03 2\u00de The two bases \u2202 \u2202Si and \u2202 \u2202\u03b8i for each of leg i are attached to the joint Ti where \u2202 \u2202Si is downward parallel to the Z-axis and \u2202 \u2202\u03b8i is perpendicular to the connecting rod BiTi as shown in Fig. 2. Eq. (2) indicates that the motion of the spherical joint Ti can be represented as a serial mechanism which consists of the translation of the slider and the rotation of the connecting rod. Note that that the velocity of the slider Bi is determined as S\u0307i \u2202 \u2202Si in the joint space. Let Q i denotes the generalized force externally applied at the leg i. Since \u03b8i is the un-actuated inclination angle, the generalized force Q i could be expressed as Q i = QSi 0 T where QSi is the externally applied force between the slider Bi and the corresponding ball screw as shown in Fig. 2. The dynamic equations for each of the legs could be expressed as: Mi\u00f0qi\u00deq :: i + Ci\u00f0qi;q\u0307i\u00deq\u0307i + Ni = Q i + JTi Fri; i = 1\u223c3 \u00f04\u00de Mi = \u00f0ms + mL\u00deb \u2202 \u2202Si ; \u2202 \u2202Si N 1 2 mLb \u2202 \u2202Si ; \u2202 \u2202\u03b8i N 1 2 mLb \u2202 \u2202\u03b8i ; \u2202 \u2202Si N 1 3 mLb \u2202 \u2202\u03b8i ; \u2202 \u2202\u03b8i N 2 6664 3 7775 2\u00d72 is the inertial matrix of leg i and b:;:N denotes the inner product of the where corresponding bases. ms andmL denote the mass of the slider and connecting rod, respectively. Ci\u00f0qi;q\u0307 i\u00deq\u0307i denotes the centrifugal and Coriolis forces of the leg iwhile Ni denotes the gravitational force" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001730_s00466-016-1263-5-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001730_s00466-016-1263-5-Figure2-1.png", "caption": "Fig. 2 One step of the trust-region method. The new iterate xk+1 is the minimizer of the quadratic model mk restricted to the ball Bxk (\u03c1k) (shaded region), unless the energy decrease predicted by the model deviates too much from the true energy decrease J (xk) \u2212 J (xk+1)", "texts": [ " To enforce global convergence of this, the trust-region method first replaces the search for a stationary point of mk by a minimization problem for a minimizer sk of mk . As a consequence, iterates of the trust-region method are energy decreasing in all cases. Secondly, it notes that the quadratic model mk is a good approximation of J only in a neighborhood of xk . This observation is made explicit by restricting theminimization problem formk to a ball of radius \u03c1k around xk, the name-giving trust region (Fig. 2). In other words, the Newton step (17) is replaced by sk = arg min s\u2208RN mk(s), \u2225\u2225sk \u2225\u2225 \u2264 \u03c1k . (18) Since we now look for a minimizer on a compact set only, Problem(18) is well-defined even if \u22022 J is not positive definite. Unlike the original Newton method, the trust-region method is monotone in the sense that J (xk+1) \u2264 J (xk) for all k \u2208 N. A more quantitative monitoring of the energy decrease allows to control the trust-region radius, i.e., the trust in the quality of the quadratic approximation" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000193_j.cma.2011.04.006-Figure19-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000193_j.cma.2011.04.006-Figure19-1.png", "caption": "Fig. 19. (a) Contact pattern and (b) function of transmission errors for case B2a (skew(B) whole-crowned(2) aligned(a) bevel gear drive).", "texts": [ " The skew bevel gear drive is very sensitive to the change of shaft angle DR (misaligned condition c) and the axial displacement of pinion (misaligned condition d) and the axial displacement of the gear (not shown in this paper). In order to absorb those lineal functions of transmission errors caused by errors of alignment for the skew bevel gear drive, Designs 2 and 3 (see Table 3) are proposed also for this transmission, with whole-crowned and partial-crowned bevel gear tooth surfaces, respectively. Figs. 19 and 20 shows the contact patterns and the predesigned functions of transmission errors for cases B2a and B3a corresponding to a skew whole-crowned and aligned bevel gear drive (Fig. 19) and to a skew partial-crowned and aligned bevel gear drive (Fig. 20). A parabolic function of transmission errors with maximum level of 7 arcsec has been predesigned for the whole-crowned skew bevel gear drive (Design 2). However, for the case of partial-crowned skew bevel gear drive (Design 3), a function of transmission error of 2 arcsec is obtained taking advantage of an area of non-modified tooth surface due to partial crowning. Again, Design 3 (partial-crowning) allows the contact pattern to cover a larger area of the bevel gear contacting surfaces" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002037_s11071-017-3461-x-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002037_s11071-017-3461-x-Figure1-1.png", "caption": "Fig. 1 The traditional planar 5R PM without redundant actuations [14]", "texts": [ " \u2022 Thirdly, the dynamic performance of the PM with multiple actuation modes is comprehensively investigated via a numerical simulation experiment. Moreover, the validity of the RFDM is exactly verified by a FSM-based VPM which is developed for the first time by virtue of SimMechanics. \u2022 Eventually, owing to the compact form of the RFDMdeveloped in this study, some dynamic controllers can be efficiently designed in future based on the RFDM via some strategies, such as modal synthesis technique. 2 Topology description Figure1 shows the schematic diagram of the traditional planar 5R PM [4]. The output point C where the endeffector can be mounted is connected to the base by two branches, each of which consists of three revolute joints and two links. The two branches are connected to a common point (point C) with the common revolute joint at the end of each branch. In each of the two branches, the revolute joint connected to the base is actuated by one servo motor. Thus, such a manipulator is able to position its output point in a plane" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002037_s11071-017-3461-x-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002037_s11071-017-3461-x-Figure3-1.png", "caption": "Fig. 3 Virtual prototypes (RAParM) [14]: a RAParM-I, b RAParM-II", "texts": [ " The corresponding mechanism is named as RAParM (derived from \u201cRedundantly Actuated Parallel Manipulator\u201d) which possesses two DOFs. Moreover, the optimum redundant actuation scheme determined by us includes two configurations named, respectively, as RAParM-I and RAParM-II based on the layout of thePSBs, as depicted in Fig. 2 [14]. Based upon the two topological configurations, two preliminary virtual prototypes can be constructed by means of commercial software Solidworks , which are shown in Fig. 3 [14], in which some attachments are not shown in detail. Considering the similar structure characteristic between the two configurations of RAParM, in Ref. [14], we have implemented detailed analysis with respect to one of the two configurations, i.e., RAParMI. Owing to the special structure characteristic, this novel PM can achieve 9 potential actuation modes, as illustrated in Table1 [14]. Moreover, we have carried out kinematic analysis about RAParM-I and established the uniformly dynamic model at the level of rigid-body dynamics", " (50), and incorporating the Lagrangian multipliers, one can obtain the complete dynamic model of system as { M\u0304 (s) q\u0308(s) + C\u0304 (s) q\u0307(s)+K\u0304 (s) q(s) + \u03a6T c ( q(s), t ) \u03bb = F\u0304 (s) e \u03a6 ( q(s), t ) = 022\u00d71 (54) where \u03bb \u2208 R 22 is the vector of Lagrangian multipliers which denotes the magnitude of the generalized constraint reactions; F\u0304 (s) e is the column matrix of generalized external forces of system, which can be expressed as F\u0304 (s) e = [ 01\u00d72 \u03c41 01\u00d74n1\ufe38 \ufe37\ufe37 \ufe38 body-1 01\u00d72 \u03c42 01\u00d74n2\ufe38 \ufe37\ufe37 \ufe38 body-2 01\u00d7(4n3+3)\ufe38 \ufe37\ufe37 \ufe38 body-3 01\u00d7(4n4+3)\ufe38 \ufe37\ufe37 \ufe38 body-4 01\u00d72 \u03c45 01\u00d74n5\ufe38 \ufe37\ufe37 \ufe38 body-5 01\u00d72 \u03c46 01\u00d74n6\ufe38 \ufe37\ufe37 \ufe38 body-6 01\u00d7(4n7+3)\ufe38 \ufe37\ufe37 \ufe38 body-7 01\u00d7(4n8+3)\ufe38 \ufe37\ufe37 \ufe38 body-8 ]T (55) where \u03c41, \u03c42, \u03c45 and \u03c46 represent, respectively, the driving torques offered by the servo motors mounted at the base of RAParM-I (see Fig. 3). It is worth noting that different actuation modes can be achieved here via selecting different driving torques as the practical driving ones, for instance, \u2022 when \u03c41 = 0, \u03c42 \u2261 0, \u03c45 = 0, \u03c46 \u2261 0, the actuation mode is \u201c\u2295 \u2295 \u201d; \u2022 when \u03c41 = 0, \u03c42 = 0, \u03c45 = 0, \u03c46 \u2261 0, the actuation mode is \u201c\u2295 \u2295 \u2295 \u201d; \u2022 when \u03c41 = 0, \u03c42 = 0, \u03c45 = 0, \u03c46 = 0, the actuation mode is \u201c\u2295 \u2295 \u2295\u2295.\u201d Likewise, the other actuation modes can also be obtained easily by using analogous method, and the relevant actuation modes are illustrated in Ref" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001038_1350650116689457-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001038_1350650116689457-Figure2-1.png", "caption": "Figure 2. Applied loads on the cage and its degrees of freedom.", "texts": [ " It is assumed that the outer ring is fixed in the bearing house, and the inner ring rotates at a constant angular speed !i around the bearing axis. The external loads are applied on the bearing house, as shown in Figure 1(a), and then the loads of bearing acting on the outer ring are represented as F \u00bc Fa Fr M , as shown in Figure 1(b), where Fa, Fr, and M denote the axial load, radial load, and moment of an angular ball bearing, respectively. The forces on the cage and its degrees of freedom are illustrated in Figure 2. And the cage motion can be represented by its mass center in the dynamic analysis. The cage mass center oc in the inertial frame oxyz can be described by the vector (xc, yc, zc). If the jth ball is in contact with the cage, the normal contact force and friction force on the cage due to this ball are denoted by Fcbj and fcbj, which can be decomposed to Fcbjx, Fcbjy, Fcbjz, fcbjx, fcbjy, fcbjz in x, y, and z directions, respectively. Similarly, if the cage is in contact with the guiding inner ring, the normal contact force and friction force applied by the inner ring will appear, denoted as F 0cix, F 0 ciy, and F 0ciz, where F 0cix is along the x axis of bearing, F 0ciz is along the oc-o direction, and F 0ciy is the tangential direction of F 0ciz. These forces need to be transformed to the components in the inertial frame, and lastly to form the total forces of Fcix, Fciy, and Fciz in x, y, and z directions, respectively. Thus, the cage motions are significantly determined by the ball\u2013cage pocket forces and the cage-inner ring forces. The cage motion equations can be built according to the force components in the inertial frame o-xyz illustrated in Figure 2. Fciy \u00fe XN j\u00bc1 \u00f0Fcbjy \u00fe fcbjy\u00de \u00bc mc \u20acyc Fciz \u00fe XN j\u00bc1 \u00f0Fcbjz \u00fe fcbjz\u00de \u00bc mc \u20aczc Fcix \u00fe XN j\u00bc1 \u00f0Fcbjx \u00fe fcbjx\u00de \u00bc mc \u20acxc \u00f01\u00de Here mc is the mass of cage. The details of the equations are described by Ye and Wang6 or in the similar research by Boesiger et al.15 Description of the cage motions. Due to the cage\u2013ring or cage\u2013balls contact, collision and friction, the cage in an angular ball bearing will whirl except for rotating along the fixed bearing axis. The cage rotating frequency related to that of the inner ring can be written as fc \u00bc fi\u00f01 D cos 0=dm\u00de 2 \u00f02\u00de where fi \u00bc " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003469_jestpe.2021.3058261-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003469_jestpe.2021.3058261-Figure7-1.png", "caption": "Fig. 7. Models of the various PM machines. (a) Model 1: 12/11/1. (b) Model 2: 12/10/2. (c) Model 3: 12/8/4. (d) Model 4: 24/10/10.", "texts": [ " 2) The average torque of PMVMs is associated with both the amplitude and variation gradient of armature working harmonic along the PM radius direction. 3) The power factor of PMVMs is determined by the proportion of armature working harmonic to the total harmonics. III. INFLUENCE OF ARMATURE FIELDS ON TORQUE In this section, the torque capability of various PM machines have been analyzed and compared. Especially, the nature of high torque density in yoke PMVM and low torque density in yokeless PMVM have been deeply investigated from the armature field perspective. As shown in Fig. 7, four PM machines with the same material and size have been built, and the electrical load is also kept the same with selected turns per slot. For a fair comparison, the only differences between them are the stator slot shape and winding pole-pair. Model 1 to 3 are PMVMs with different slot/pole combination Z/pr/pa, which are 12/11/1, 12/10/2 and 12/8/4, respectively. Model 4 is PMSM, constructed with half-closed slot, 10-pole-pair PM and 10-pole-pair armature winding. The main machine size and material parameters are as listed in Table III" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001328_j.renene.2014.03.036-Figure9-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001328_j.renene.2014.03.036-Figure9-1.png", "caption": "Fig. 9. Three point mounting configuration model.", "texts": [], "surrounding_texts": [ "In order to minimize the influence of the specific design of the GRC gearbox on the generality of the overall drive train behavior, it was chosen not to include the gear meshing stiffness in the models. In theory the forces and moments which are introduced in the gearbox should be transferred to the gearbox bushings through a path comprising of the planet carrier, planet carrier bearings and the gearbox housing, as shown in Fig. 12. Unless there is play in the bearings or the planet carrier and/or housing stiffness is insufficient the gear meshing stiffness does not play a role in this mechanism. In addition by excluding the gear meshing stiffnesses it is possible to assure that the housing is an important part of the transfer path. Since the gear meshing stiffness is needed to counteract the torque applied at the rotor, an equivalent total gear meshing stiffness is taken into account in the torsional DOF and superimposed on the stiffness values at both planet carrier bearings. More information on the assumptions that were made can be found on page 5." ] }, { "image_filename": "designv10_9_0000426_tmag.2012.2197734-Figure12-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000426_tmag.2012.2197734-Figure12-1.png", "caption": "Fig. 12. Schematic diagram of flux flows when the auxiliary winding is excited by dc current.", "texts": [ " It is seen from the figure that the close agreement between the calculated and measured values is obtained, and that the torque of the proposed SR motor is improved by exciting the auxiliary windings. Fig. 11 shows the efficiency characteristics of the trial SR motor. The efficiency of the proposed SR motor is also improved. When the auxiliary windings are excited by dc current, the fluxes generated from the magnets and auxiliary windings flow through the stator and rotor poles aligned with each other as shown in Fig. 12. In this state, if the salient rotor is rotated by an external force, the flux path changes periodically since the each phase stator and rotor poles are aligned one after another. As a result, the voltage is induced in each coil. Hence, the proposed SR motor is able to work as a generator with the same circuit as the motor. Fig. 13 shows the auxiliary winding current versus induced voltage characteristic at a rotational speed of 3000 rpm. It is understood that the induced voltage is saturated at an auxiliary winding current of 4 A due to the magnetic saturation effect" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000931_9781118703274.ch2-Figure2.49-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000931_9781118703274.ch2-Figure2.49-1.png", "caption": "Figure 2.49 Hydraulic blade pitch-regulation systemwith direct cylinder transmission (WTS 4, Hamilton Standard): 1, hydraulic cylinder; 2, hydraulic reservoir; 3, generator; 4, control computer; 5, hydraulic pumps; 6, hydraulic fluid cooler", "texts": [ " In the absence of hydraulic power, springs acting in the opposite direction return the blades to their original positions. This means that, if the hydraulic system fails or another emergency situation arises, the turbine is returned to a safe operating mode. Seen from the turbine, the control valves and the hydraulic power unit are located behind the generator. The regulation and adjustment system shown here consists primarily of standard hydraulic drive products. In this way, in addition to the high reliability needed for wind turbines, a high level of solidity and cost-effectiveness can be attained. Figure 2.49 shows the pitch-regulation system layout in the nacelle of a 4MW wind power unit. Four positioning cylinders acting directly upon the blade positioning rods bring the 80 metre-diameter blades of the teetered-hub rotor into the positions dictated by the control system. This positioning system thus makes it possible to control power in both directions. The hydraulic pressure supply with its pumps, fluid cooler and control computer are located at the rear of the nacelle. To provide a redundant backup supply for use during power outages, a hydraulic reservoir is located in front of the rotor hub" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000560_j.mechmachtheory.2013.06.001-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000560_j.mechmachtheory.2013.06.001-Figure7-1.png", "caption": "Fig. 7. Link error and concept of virtual joint. a) Link error, rmax \u2212 rmin. b) Virtual prismatic joint, \u00b1\u0394.", "texts": [ " If one can imagine an elastic bladder inside the mechanism and blown with air, then the condition corresponds to an expanded position assumed by the mechanism. Total bandwidth quantifies the effect of manufacturing errors and depending on the functional requirements, designer can specify individual tolerances in the chosen mechanism. Another common error is in the center distance between two holes/pins in a link which is termed as \u2018link-error\u2019 in this work. This is designated as a bilateral error and the link can have a dimension, r \u00b1 \u0394 as shown in Fig. 7. This link-error can be treated as virtual prismatic joint and represented by a screw $v. Fig. 8 shows four-bar mechanism with virtual prismatic joint representing error on link-2 and its associated screw $12. Eq. (5) for first open chain is modified to include the effect of virtual prismatic joint, 3p \u00bc A1A12A2 3p0 : \u00f012\u00de From Table 4, the Rodrigues parameters are taken and the transformation matrices are obtained as A1 c\u03b82 \u2212s\u03b82 0 0 s\u03b82 c\u03b82 0 0 0 0 1 0 0 0 0 1 0 BB@ 1 CCA; A12 \u00bc 1 0 0 \u03942 0 1 0 0 0 0 1 0 0 0 0 1 0 BB@ 1 CCA and A2 \u00bc c\u03b83 \u2212s\u03b83 0 r2 1\u2212c\u03b83\u00f0 \u00de s\u03b83 c\u03b83 0 \u2212r2s\u03b83 0 0 1 0 0 0 0 1 0 BB@ 1 CCA: \u00f013\u00de Taking 3p0 \u00bc r2 \u00fe r3 0 0 1 0 BB@ 1 CCA \u00f014\u00de Ta R llowing the procedure outlined in Section 3" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001779_j.jmapro.2015.10.002-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001779_j.jmapro.2015.10.002-Figure1-1.png", "caption": "Fig. 1. (a) Surfi-Sculpt production, (b) example of range of S", "texts": [ " One such solution is Surfi-Sculpt\u00ae nvented by TWI Ltd. [1], this surface modification technique uses epeated swipes of an electron or laser beam to produce surface feaures on material surfaces. The laser beam process variant involves ranslating a power beam source across the surface of the substrate n a manner similar to keyhole welding. This melts the material and auses the liquid to flow in the opposite direction to beam translaion. Repeated swipes enable a protruding feature to be produced ith a corresponding intrusion on the material, Fig. 1a. A range of orms can be easily produced by modifying the processing parameers, such as the laser power, the speed of translation or the number f swipes, as shown in Fig. 1b. Traditionally, this surface modification technique has been hought to have been caused only by the surface tension of the olten material [2,3]. More recently, other mechanisms have also een considered, such as the fluid dynamics driven by a laser- nduced thermo-capillary [4]. In this paper, high-speed imaging as been used to show that a protruding liquid filament (jet) is \u2217 Corresponding author. Tel.: +44 0207882 7620. E-mail address: r.castrejonpita@qmul.ac.uk (J.R. Castrej\u00f3n-Pita). ttp://dx.doi", " Firstly, he filament is likely to be bounded to the feature, decreasing the urface area [50], increasing the surface tension force and enhancng the earlier onset of filament breakup. This helps to explain the xponential decrease in additional feature height with increasing umber of swipes [3,4]. Secondly, the texture of the formed feature urface would introduce a shear stress opposing the melt momenum and would also influence capillarity effects \u2013 either positively r negatively. For these reasons the model cannot be applied when roducing features in formations of close proximity, <0.25 mm, here capillary action can act (e.g. star formations, Fig. 1b). With rogressive swipe repeats, thermal energy will build up within the ubstrate. It is hypothesised that an increase in substrate temperture would increase the melt pool width and keyhole dimension. his would in turn affect the expelled jet dimensions and decrease he jet aspect ratio, reducing the prospect of the onset of surface eature production. If this occurs, increasing the processing speed ay counteract the increase in jet diameter by increasing the jet ength. Increasing the processing power is undesirable in this sitution as this would increase the jet diameter and increase heating f the substrate further" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000750_1.3615053-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000750_1.3615053-Figure1-1.png", "caption": "FIG. 1. (Color online) Droplet self-alignment: (a) A droplet of a liquid is dispensed on a pattern. (b) A chip is approaching a pattern with a predefined releasing bias. (c) The droplet wets the chip, and a meniscus is formed between the chip and the pattern. (d) The chip is released and the capillary force aligns the chip to the pattern.", "texts": [], "surrounding_texts": [ "Citation: Applied Physics Letters 99, 034104 (2011); doi: 10.1063/1.3615053 View online: http://dx.doi.org/10.1063/1.3615053" ] }, { "image_filename": "designv10_9_0000321_isie.2011.5984282-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000321_isie.2011.5984282-Figure1-1.png", "caption": "Fig. 1. Tilt\u2013Rotor 3D Cad Model, configuration frame system and real prototype under development", "texts": [ " This paper is structured as follows. In Section II the modeling approach for the Tilt\u2013Rotor at helicopter mode is presented, while in Section III the design and the development of the MPC scheme is analyzed. In Section IV several simulation studies that show the efficacy of the proposed scheme are presented, followed by conclusions in the last section. The motion of the Tilt-Rotor is achieved through the control of the angle position of two servo\u2013motors userv,1,userv,2 and the speed control of the two rotors as shown in Figure 1. The modeling of the system\u2019s dynamics is achieved under the following assumptions: a) the structure is rigid, b) the Center of Gravity (CoG) lies at the center of the distance between the two rotors and under the rotational plane. Under the aforementioned assumptions the torques produced by the two rotating rotors can be formulated as: \u03c4\u03c6 = l(P1 \u2212P2) \u03c4\u03b8 = h(P1 +P2)sin\u03b1 (1) \u03c4\u03c8 = l(P1 \u2212P2)sin\u03b3 where P1, P2 corresponds to the norm of the ascending force produced by the two rotors, l is the horizontal distance between 978-1-4244-9312-8/11/$26" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002277_978-3-319-27131-6-Figure3.5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002277_978-3-319-27131-6-Figure3.5-1.png", "caption": "Fig. 3.5 Rolling and axial directions in bearings", "texts": [ "9, the maximum Hertzian pressure for the ellipse contact in Eq. 3.13 results as pH,max \u00bc 3Q0 2\u03c0ab \u00f03:14a\u00de Generally, the distribution of the Hertzian pressure over the area at the ellipse contact of ball bearings in the rolling direction x and axial direction y is written as [1] pH x; y\u00f0 \u00de \u00bc 3Q0 2\u03c0ab ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 x b 2 y a 2r \u00f03:14b\u00de Obviously, the maximum Hertzian pressure occurs at the center of the contact area, in which x\u00bc y\u00bc 0 (s. Fig. 3.5). 3.2 Procedure of Computing the Hertzian Pressure 53 The distribution of the Hertzian pressure over the area of the rectangular contact with the rectangular footprint in roller bearings with the roller length L in the rolling direction x is written as [1,3] pH x\u00f0 \u00de \u00bc 2Q0 \u03c0Lb ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 x b 2r ; b \u00bc 2 2Q0 \u03c0LE 0 X \u03c1IR;OR !1 2 \u00f03:15a\u00de Obviously, the maximum Hertzian pressure for the rectangular contact occurs at the center of the contact area at x\u00bc 0. pH,max \u00bc 2Q0 \u03c0Lb \u00f03:15b\u00de In the following, an example is demonstrated for computing the Hertzian pressure in the deep-groove radial ball bearing" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000618_ilt-11-2011-0098-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000618_ilt-11-2011-0098-Figure3-1.png", "caption": "Figure 3 Structure of hydrodynamic lubrication rubber bearing with two cavities", "texts": [ " Ro is the outer radius and R is the inside radius of the fluted rubber bearing. So the friction coefficient of the fluted rubber bearing at different temperatures, loads and velocities can be obtained by the experiment. The fluted rubber bearings experiment with three different bearing clearances have been conducted under different temperatures, loads and velocities using the apparatus. A new rubber bearing structure with two cavities which is favorable for constructing continuous hydrodynamic lubrication was designed for experiment as illustrated in Figure 3. Numerical simulation and experimental study were carried out on the rubber bearing structure. In this experiment the fluted rubber bearing in Figure 2 was superseded by the rubber bearing with two cavities used in numerical calculation. The measuring method of the friction coefficient of the hydrodynamic lubrication rubber bearing is the same as that of the fluted rubber bearing. Experimental and numerical study on water-lubricated rubber bearings You-Qiang Wang, Xiu-Jiang Shi and Li-Jing Zhang Volume 66 \u00b7 Number 2 \u00b7 2014 \u00b7 282\u2013288 Themeasurement of the eccentricity ratio of the hydrodynamic lubrication rubber bearing is based on the principle of relative displacement as illustrated in Figure 4" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000560_j.mechmachtheory.2013.06.001-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000560_j.mechmachtheory.2013.06.001-Figure2-1.png", "caption": "Fig. 2. Screw displacement of a rigid body.", "texts": [ " The proposed approach can not only be extended to velocity and higher order analyses, but also be used for synthesis and allocation of dimensions along with the tolerances in an optimal way to achieve the desired output performance. In this section, details of successive screw displacement method used in the present work for position kinematics are briefly presented. According to Chasle's theorem, displacement of a rigid body can be regarded as a rotation about and a translation along some axis. Such a combination of translation and rotation is called screw displacement [22]. Fig. 2 shows displacement of a point P on a rigid body from its first position P0 to next position P1 by a rotation of \u03b8 about a screw axis followed by a translation of t along the same axis. The rotation angle \u03b8 and translational distance t are called screw parameters. The direction of the screw axis is denoted by s = [sx,sy,sz]T and the position vector of a point lying on the screw axis is represented by so = [sox,soy,soz]T with respect to a global Cartesian coordinate system OXYZ. The parameters, s and so, together with the screw parameters (\u03b8, t) are referred to as Rodrigues parameters which completely define the general displacement of a rigid body" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003005_s00170-020-06344-0-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003005_s00170-020-06344-0-Figure6-1.png", "caption": "Fig. 6 (a) Thermal map and (b) schematic representation of melt pool with translation speed vector (Vs) and the normal direction (N)", "texts": [ " Therefore, during the depositions, a superposition of effects that amplify the whole trend occurs. The thermal gradient (or temperature gradient) in general gives the rate of the temperature variation, expressed as the ratio of the temperature variation with respect the distance between a given reference points. The thermal gradients (G) of DLMD depositions were calculated by means of the spatial analysis realized by the IR thermal camera for each characteristic point. The translation speed vector (Vs) and the normal vector direction (N) for the thermal gradient (see Fig. 6 (a)) are determined for each deposition. The thermal gradient is calculated by means of the Eq. (3): Gy \u00bc \u0394T \u0394Y \u00bc Tyi\u2212Tyi\u00fe1 Y i\u2212Y i\u00fe1 \u00f03\u00de Figure 6 (b) shows the slightly tear-dropped shape created by the heat source in movement above the substrate and the vectors considered. The length \u0394Y was estimated considering the camera resolution and the distance of the thermal camera from the treated zone. Comparing the dimensions of the heat zone from pictures (measure in pixels) and the cross section of the clad analysed by the microscope, it was confirmed that every pixel has a dimension of 0.5 mm per side. In Fig. 7, a comparison between the temperature profile and the gradient profile, in the Y-direction, for the different key points of the depositions was represented", " It can be noticed that the influence on the thermal gradient is stronger than on the maximum temperature. This is crucial to take into account for the monitoring of the DLMD process, since a large change in the gradient may cause a modification in the microstructure of the deposition and the related mechanical properties. Combining the parallel (Gx) and normal (Gy) thermal gradients to the translation speed vector (Vs), it gets the planar thermal gradient (Gp) that characterized the heat diffusion of the deposition track on the surface (as shown in Fig. 6 (b)). The vertical component of the thermal gradient (Gz) was difficult to analyse by means of non-destructive thermographic techniques. The thermal gradient is strongly correlated to the volume of the base material. Thus, for reduced thickness of substrate, the vertical component assumes lower values compared to the normal components. This makes the analysis of planar components acceptable to thermally define the depositions. To define the planar gradient G of the deposition, a common temperature range was chosen", " Gx \u00bc \u0394T \u0394t \u0394X \u0394t \u22121 \u00bc \u0394T \u0394X \u00bc Txi\u2212Txi\u00fe1 X i\u2212X i\u00fe1 \u00f04\u00de The thermal gradient Gy along the normal plane at the translation speed vector (Vs) was also estimated in the temperature range between the maximum and the solidus. The temperature at both sides of the molten pool was averaged to overcome the asymmetry of the thermal field. The parallel, normal and planar thermal gradients are summarized in Table 7. The latter is estimated using the Eq. (5): Gp \u00bc \u2016\u2207T\u2016 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi G2 x \u00fe G2 y q \u00f05\u00de Table 7 also indicates the angle of the section of the local heat flow (\u03b1) with respect to the normal plane, which is a function of the thermal gradients Gx and Gy (ref. Fig. 6 (b)). Analysing the effect on the thermal gradients, it is evident that the powder flow rate influences too the angle of the planar thermal flow. In substance, Gy decreases as powder flow rate increases, and consequently the angle \u03b1 tends to grow. As explained by DebRoy et al. [25], this angle is strictly related to the deposition microstructure, where the thermal flux determines the principal dendrite growth directions. Moreover, comparing the dendrite growth angle and the local heat flow angle (\u03b1), the undercooling can be quantified" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003137_j.mechmachtheory.2020.104180-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003137_j.mechmachtheory.2020.104180-Figure3-1.png", "caption": "Fig. 3. DH frames of 7R 6-DOF industrial robot.", "texts": [ " The position error of the end of robot d e caused by simplification can be described by Eq. (1) . d e = \u2225\u2225P \u2212 P \u2032 \u2225\u2225 = \u221a d 2 5 + 2 cos \u03b22 d 5 d 6 + d 2 6 (1) where the components of position error d e in all directions are related to DH parameters \u03b8 to \u03b8 . 1 5 The spraying robots of ABB are the typical 7R 6-DOF industrial robot, such as the ones typed IRB5400 and IRB5500. The specific simplifying approach of wrist structure is introduced by taking IRB5400 for instance. The DH frames of this 7R 6-DOF robot are shown in Fig. 3 . It can be seen that joints 4, 5_1, 5_2 and 6 comprise its wrist structure. When joint 5_1 rotates by \u03b8 angle, joint 5_2 rotates synchronously in opposite directions. Therefore, 7R 6-DOF robot has 7 joints but only 6 degrees of freedom. The angle between the axes of joint 5_1 and joint 4 and the angle between the axes of joint 5_2 and joint 6 are both \u03b2 . When the robot returns to the mechanical zero, it can be found from Fig. 3 that the axes of joint 4 and joint 6 are collinear but the axes of joints 4 to 6 do not intersect at one point. According to the DH frames shown in Fig. 3 , DH parameters of 7R 6-DOF industrial robot can be obtained and listed in Table 2 . Fig. 4 demonstrates the configuration of wrist structure when DH parameter \u03b85 equals to 180 \u00b0. At this time the axes of joints 4 and 6 intersect at point P 1 , and the axes of joints 5_1 and 5_2 intersect at point P 2 . According to the proposed simplification principle, it just needs to offset the axes of joint 5_1 and joint 5_2 together to make their intersection point coincide with the intersection point of the axes of joint 4 and joint 6" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003250_tsmc.2020.3034757-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003250_tsmc.2020.3034757-Figure1-1.png", "caption": "Fig. 1. Diagram of the 2-DOF robotic manipulator.", "texts": [ " Remark 6: The control policies designed in [58]\u2013[60] can achieve uniformly ultimately bounded stability, which implies that tracking errors converge to an unknown neighborhood of the origin as time approaches infinite. In this article, a neural networks-based finite-time control policy is designed by introducing a fractional order term. Under the proposed control, errors converge to a small neighborhood of the origin in finite time, which can better satisfy the requirements for response speed. As shown in Fig. 1, a robotic manipulator with two degrees of freedom is constructed. li, lci, mi, Ii, and g are defined in Table I, i = 1, 2, and define q = [q1, q2]T . The system matrices of the robotic manipulator are M(q) = [ p1 + p2 + 2p3 cos q2 p2 + p3 cos q2 p2 + p3 cos q2 p2 ] C(q, q\u0307) = [\u2212p3q\u03072 sin q2 \u2212p3(q\u03071 + q\u03072) sin q2 p3q\u03071 sin q2 0 ] G(q) = [ p4g cos q1 + p5g cos(q1 + q2) p5g cos(q1 + q2) ] with p1 = m1l2c1 + m2l21 + I1, p2 = m2I2 c2 + I2, p3 = m2l1lc2, p4 = m1lc2 + m2l1, and p5 = m2lc2. The initial position of the robot is set at q = [0, 0]T rad" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000039_978-1-84996-220-9-Figure5.3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000039_978-1-84996-220-9-Figure5.3-1.png", "caption": "Figure 5.3 (a) The humanoid robot ARMAR-III moving in a translational dimension. (b) The effect in workspace when changing the C-space value for the dimension associated with the torso pitch joint", "texts": [ " Therefore, an upper bound for the workspace movements of each limb is used for an efficient and approximated uniform sampling. A change \u03b5trans in a translational component of the C-space moves the robot in workspace by \u03b5trans. All other dimensions of the C-space have to be investigated explicitly to derive the upper bound of the robot\u2019s workspace movement. Table 5.1 gives an overview of the maximum displacement of a point on the robot\u2019s surface 5 Efficient Motion and Grasp Planning for Humanoid Robots 133 when changing one unit in C. The effects of moving one unit in the different dimensions can be seen in Figure 5.3. The different workspace effects are considered by using a weighting vector w whose elements are given by the values of the workspace movements from Table 5.1. In Equation 5.1 the maximum workspace movement dWS(c) of a C-space path c = (c0, ...,cn\u22121) is calculated: dWS(c) = n\u22121 \u2211 i=0 wici. (5.1) To sample a C-space path between two configurations c1 and c2, the vector vstep is calculated (Equation 5.2). For a C-space displacement of vstep it is guaranteed that the maximum workspace displacement is 1 mm" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003252_tia.2020.3040142-Figure16-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003252_tia.2020.3040142-Figure16-1.png", "caption": "Fig. 16. Flux lines distribution of optimal case 2. (a) Nonlinear HMM. (b) FEA.", "texts": [], "surrounding_texts": [ "For a specific application scenario, the gear ratio, stack length, air-gap length, and outer diameter of a CMG is fixed, and the other geometrical parameters can be optimized. Besides, the material of PMs and silicon steel are settled before optimization, and they are selected as N35H and 50JN270, respectively. The eddy current loss of PMs and iron loss of silicon steel within CMGs is small compared to the power it transmits when it works at rated condition. Additionally, the efficiency of CMGs can be maintained at a high level if the silicon steel within CMGs are not highly saturated, and the output torque of CMGs will decrease if its silicon steel part is highly saturated. Therefore, individuals with low efficiency can be tossed out automatically by optimization algorithm as long as the output torque is set as an optimization objective. Besides, the torque ripples of CMGs are very low if the pole-pair combinations of CMGs are well selected [17]. This can also be observed in Fig. 9, the torque ripple of CMG1 is about 8%, while the torque ripple of CMG2 is below 1%, which is almost ignorable. Thus, the efficiency and torque ripple are not set as the optimization objectives. The weaknesses of CMGs are its low torsional stiffness and high manufacture cost compared to mechanical gearboxes [29]. The torsional stiffness is directly determined by the peak transmitted torque of CMGs, which is represented by Tp. The high cost of CMGs is caused by the usage of PMs since the price of NdFeB is almost one hundred times of that of steel. Thus, the torque versus PM volume ratio should be maximized, which is represented by Tp/VPM. Additionally, the rotational inertia of CMGs is an important index, since a smaller rotational inertia means a better dynamic response characteristic. Since the lowspeed rotor is connected to the output shaft, its rotational inertia J is set as an optimization objective, which can be expressed as J = 1 4 \u03c1La [ \u03b21 ( R4 mid,1 \u2212R4 4 ) + \u03b22 ( R4 mid,2 \u2212R4 mid,1 ) +\u03b23 ( R4 5 \u2212R4 mid,2 )] (38) where \u03c1 is the density of the silicon steel. Furthermore, we should avoid the irreversible demagnetization of PMs on the CMGs during rated operation. Since the rated operating temperature of gearboxes varies from scenarios to scenarios, we choose the gearbox in wind turbine for instance, where the rated operating temperature is about 60 to 70 \u00b0C [30]. In this article, Trated is set as 60 \u00b0C. As can be observed in Fig. 11, the irreversible demagnetization occurs when the magnetic flux density within the PMs drops below the knee point [31], and the knee point decreases with the increase of temperature. Hence, the absolute magnetic flux density on the outer surface of the PMs on the low-speed rotor and high-speed rotor should be above the magnetic flux density on the knee point at rated operating The individual number in one generation is set as 20; the maximum number of generations is set as 100. Besides, a CMG with 4 pole-pair PMs on the high-speed rotor and 11 pole-pair PMs on the stator is selected for the optimization study, and the value range of design variables are given in Table III. The airgap, the inner radius, the outer radius, and the axial length of the studied CMG are set as constants during optimization, whose values are 0.5 mm, 30 mm, 100 mm, and 60 mm, respectively. Additionally, the remanence and knee point magnetic flux density of N35H at rated operating temperature are 1.15 T and 0.22 T, respectively." ] }, { "image_filename": "designv10_9_0000415_978-3-642-37552-1-Figure11.1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000415_978-3-642-37552-1-Figure11.1-1.png", "caption": "Fig. 11.1 Outline of the surface tension seal discussed in this chapter", "texts": [ " Whenever two media containing a flowing liquid need to be separated from each other, seals are used. In most cases, rubber contact seals are used such as for instance o-rings, or press-fits. However, when a seal is needed between two components that are sliding with respect to each other, such static seals are inadequate as they hamper the movement of the two bodies and generate high friction. A typical example of applications of such dynamic seals can be found in piston-cylinder actuators which are depicted in Fig. 11.1 [3]. This figure shows a typical hydraulic double acting actuator, which is able to generate both pulling and pushing forces depending whether the pressure is applied to the pressure supply 1 or 2 respectively. These actuators are commonly used in classic mechanical devices including cranes for roadworks. Recently, these actuators have gained the interest of the microsystems community to achieve high forces and power densities at the microscale [3, 4]. However, one of the main challenges in miniaturization of these devices lies in the development of low friction microseals" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003501_tte.2021.3078449-Figure11-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003501_tte.2021.3078449-Figure11-1.png", "caption": "Fig. 11. Illustration of important structure parameters.", "texts": [ " The error is about 1%, and the change trend of two waveforms is highly consistent. Fig. 10 shows the electromagnetic torque (average value) under different phase current under 300Arms. The two wave forms agree very well. Thus, the motor electromagnetic performance under light load condition can be accurately predicted using the proposed analytical model. Since the analytical model calculation results are proved to be reliable, it can be used in analysis and optimization of the motor topology, especially the rotor slots and uneven air-gap length. Fig. 11 is the illustration of rotor slot width Wrs and rotor pole eccentric distance Decc. They are the most important parameters that directly related to the special structures and have great influence on cogging torque and torque ripple, so they are chosen as the investigation object and are optimized using the proposed hybrid model. It should be noted that, the rotor eccentric distance must satisfy minecc ecc sD R R + = \u2212 (39) In which, \u03b4min is 1.3mm. Fig. 12 shows the cogging torque peak-to-peak value under different rotor slot width calculated by the analytical model" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003123_j.matpr.2020.09.756-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003123_j.matpr.2020.09.756-Figure6-1.png", "caption": "Fig. 6. Distribution of temperature at turni", "texts": [ " The temperature at each node element is recorded till the last point in the deposition. The simu- lated TIG arc will remains at one point in the deposition path for the required deposition time as per the considered torch velocity. The TIG arc will move to next point after completing the deposition time that point and will continuously moving for entire single layer deposition. Fig. 5 represent the process flow used for simulation process for obtaining distribution of the temperature in a single layer of deposition. Fig. 6 shows the temperature distribution over the deposited material. The substrate undergoes a continuous thermal cycle of heating and cooling. The molten material temperature increases gradually for each successive point in the deposition but at turning points in the deposition path like point 6 (ref. Fig. 4) and point 11 (ref. Fig. 4) the concentration of the temperature has been observed. The molten pool gets expanded due to this concentration of temperature. The temperature at these points will exceed the melting point temperature (ref. Fig. 6) and causes defects in the deposition. Whereas, no concentration of temperature was observed at all other intermediate points in the deposition. Fig. 6 shows the distribution of temperature fields at point 6. More amount of heat gets accumulated in this region and will cause deterioration in the shape and geometry of the deposited material. The temperature history at some of the selected locations has been recorded as shown in Fig. 4. For better understanding temperature generated at two distinct intermediate points and four successive points at the turning position of the zigzag path has been recorded. The variation in the temperature caused by heating and cooling cycles has been recorded at Point 3, Point 5, point 6, point 8, point 10 and point 11 respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003535_j.mechmachtheory.2021.104436-Figure17-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003535_j.mechmachtheory.2021.104436-Figure17-1.png", "caption": "Fig. 17. Configuration principle and kinematic model of OES-group.", "texts": [ " The groups 2-SR [RR] and SR [RR]&Sp [RR] can be regarded as parts of groups 2-SR [RR]&Sp [RR] and SR [RR]&2-Sp [RR], respectively. Their moving platforms have 3 rotational DOFs around O2, but they only contain 2 driving links, which can not control the orientation of moving platform completely, so they do not belong to the pure OES-group. In order to further study its kinematics performance, the analysis is carried out by taking the 6 OES-group above as examples. However, for the limited length of the paper, the groups 2-SR [RR] and SR [RR]&Sp [RR] are omitted in Fig. 17. As shown in Fig. 17, when 2 or 3 OES-limbs are combined, lines O1O2 of all limbs must coincide, and their v-planes are perpendicular or coplanar to each other. The origin of the fixed coordinate system (system {1}) coincides with O1, the x1 axis is located in the v-plane of the limb SR [RR], the z1 axis is perpendicular upward to the base platform. The y1 axis is determined by the right-hand rule, and lies in the v-plane of another limb. The system {11} is obtained by translating the system {1} along the O1O2 direction with a distance l so that the origin coincides with O2. The origin of the moving coordinate system (system {2}) coincides with O2. The z2 axis is perpendicular upward to the moving platform, which coincides with O2E8. The y2 axis coincides with the axis (O2D9 for Fig. 17(a); O2DC for Fig. 17(b); O2EB for Fig. 17(c); O2EB2 for Fig. 17(d)) of another R-joint on the moving platform, the x2 axis is determined by the right-hand rule. The input parameters of OES-groups are \u03b83, \u03b84, and \u03b85, which are the angles between the driving links of OES-limbs and the x1 axis positive direction, y1 axis positive direction, y1 negative direction respectively. (For Fig. 17, the parameters \u03b832=\u03b831=\u03b83, \u03b842=\u03b841=\u03b84, \u03b852=\u03b851=\u03b85.) In Fig. 17, the ai represents the vector of the driving link ai in the system {1}, (i=8, 81, 82, 9, B, B1, B2, C). The coordinates of vectors a8 and a82 are (cos\u03b84, 0, sin\u03b84), the coordinates of vectors a9 and a81 are (0, cos\u03b83, sin\u03b83), the coordinates of vectors aC and aB1 are (\u2014sin\u03b83, cos\u03b83, 0), the coordinates of vectors aB and aB2 are (\u2014sin\u03b85, \u2014cos\u03b85, 0). The OES-group inputs do not affect the rotation of line O1O2 around O1. In other words, the O2 coordinates (m1, m2, m3) in the system {1} are independent of the OES-group input parameters", " According to axis geometric associations of OES-groups, the y2 and z2 axis coordinates can be respectively calculated as [h1(\u03b83, \u03b84, \u03b85), h2(\u03b83, \u03b84, \u03b85), h3(\u03b83, \u03b84, \u03b85)] and [n1(\u03b83, \u03b84, \u03b85), n2(\u03b83, \u03b84, \u03b85), n3(\u03b83, \u03b84, \u03b85)] in the system {1}. These coordinate parameter are only related to the input parameters (\u03b83/\u03b84/\u03b85) of OES-groups. Specially, the SR [RR]&SRR and SR [RR]&SPR do not involve the parameter \u03b85, so this parameter needs to be omitted in these 2 OES-groups. Since the z2 axis (O2E8) is perpendicular to 2 driving links (a8 and a9 for Fig. 17(a); a8 and aC for Fig. 17(b); a82 and a81 for Fig. 17 (c); a8 and aB1 for Fig. 17(d)) in the OES-group, the z2 axis coordinates (n1, n2, n3) in the system {1} can be easily calculated. The coordinate parameters n1, n2 and n3 are the OSI parameters defined in Section 3.5.2. In Fig. 17, the coordinates of vectors a8 and a82 in the system {1} are (cos\u03b84, 0, sin\u03b84). The coordinates of a9 and a81 are (0, cos\u03b83, sin\u03b83). The coordinates of aC and aB1 are (\u2014sin\u03b83, cos\u03b83, 0). After calculation, the relationship between the input parameters and OSI parameters of OES-groups SR [RR]&SRR, 2-SR [RR] and 2- SR [RR]&Sp [RR] is obtained as \u23a7 \u23a8 \u23a9 n1 = \u2212 cos\u03b83sin\u03b84 n2 = \u2212 sin\u03b83cos\u03b84 n3 = cos\u03b83cos\u03b84 (36) The relationship between the input parameters and OSI parameters of OES-groups SR [RR]&SPR, SR [RR]&Sp [RR] and SR [RR]&2Sp [RR] is obtained as \u23a7 \u23a8 \u23a9 n1 = \u2212 cos\u03b83sin\u03b84 n2 = \u2212 sin\u03b83sin\u03b84 n3 = cos\u03b83cos\u03b84 (37) Eqs", " To facilitate description of calculation, a matrix H is constructed as: H = \u23a1 \u23a2 \u23a2 \u23a3 h1(\u03b83, \u03b84, \u03b85) n1(\u03b83, \u03b84, \u03b85) h2(\u03b83, \u03b84, \u03b85) n2(\u03b83, \u03b84, \u03b85) h3(\u03b83, \u03b84, \u03b85) n3(\u03b83, \u03b84, \u03b85) 0 0 \u23a4 \u23a5 \u23a5 \u23a6 In order to further study the orientation kinematic of the OES-group, the motion descriptions of 4 OES-groups above are given successively based on the D-H method. Thus, their transformation matrices are obtained, and internal relationships between the orientation and input parameters are clarified. The equations describing the relationship between the input parameters (\u03b83/\u03b84/\u03b85) and orientation parameters (\u03b12/\u03b22/\u03b32) of moving platform are defined as \u2019orientation solution equations\u2019 of OES-group, which is represented by \u2019OS equations\u2019. As shown in Fig. 17(a), the posture transformation of the moving platform in OES-group SR [RR]&SRR is described as: 1) The system {1} translates a distance l along the O1O2 direction to transform to the system {11}, so that its coordinate origin coincides with O2. 2). The system {11} rotates \u03b12 around its x11 axis to transform to the system {12}, so that the y12 axis coincides with O2D9. (In this case, the y12 axis is perpendicular to O2E8 and z12 axis). 3). The system {12} rotates \u03b22 around its y12 axis to transform to the system {2}, so that the z2 axis coincides with O2E8", " The matrix H1(\u03b83, \u03b84) of this group is calculated and substituted into the following equation: Tran \u239b \u239c \u239c \u239dm1, m2 , m3 \u239e \u239f \u239f \u23a0 Rot \u239b \u239c \u239c \u239dx, \u03b12 \u239e \u239f \u239f \u23a0 Rot \u239b \u239c \u239c \u239dy, \u03b22 \u239e \u239f \u239f \u23a0 \u23a1 \u23a2 \u23a3 0 \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 h2 1 + h2 2 + h2 3 \u221a 0 0 0 0 \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 n2 1 + n2 2 + n2 3 \u221a 0 \u23a4 \u23a5 \u23a6 T = H1 \u239b \u239c \u239c \u239d\u03b83, \u03b84 \u239e \u239f \u239f \u23a0 After calculation, the OS equations of the OES-group SR [RR]&SRR are calculated as { \u03b12 = \u03b83 \u03b22 = \u2212 arctan(tan\u03b84cos\u03b83) \u21d4 \u23a7 \u23aa\u23a8 \u23aa\u23a9 \u03b83 = \u03b12 \u03b84 = \u2212 arctan ( tan\u03b22 cos\u03b12 ) (39) As shown in Fig. 17(b), the posture transformation of the moving platform in OES-group SR [RR]&SPR is described as: 1) The system J. Zhang et al. Mechanism and Machine Theory 166 (2021) 104436 {1} translates a distance l along the O1O2 direction to transform to the system {11}, so that its coordinate origin coincides with O2. 2). The system {11} rotates \u03b12 around its z11 axis to transform to the system {12}, so that the y12 axis coincides with O2DC. 3). The system {12} rotates \u03b22 around its y12 axis to transform to the system {2}, so that the z2 axis coincides with O2E8", " Based on the geometric conditions that the y2 axis is parallel to the aC, the parameters (h1/h2/h3) and matrix H2(\u03b83, \u03b84) can be calculated and substituted into the following equation: Tran \u239b \u239c \u239c \u239dm1, m2 , m3 \u239e \u239f \u239f \u23a0 Rot \u239b \u239c \u239c \u239dz, \u03b12 \u239e \u239f \u239f \u23a0 Rot \u239b \u239c \u239c \u239dy, \u03b22 \u239e \u239f \u239f \u23a0 \u23a1 \u23a2 \u23a3 0 \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 h2 1 + h2 2 + h2 3 \u221a 0 0 0 0 \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 n2 1 + n2 2 + n2 3 \u221a 0 \u23a4 \u23a5 \u23a6 T = H2 \u239b \u239c \u239c \u239d\u03b83, \u03b84 \u239e \u239f \u239f \u23a0 After calculation, the OS equations of the OES-group SR [RR]&SPR are calculated as \u23a7 \u23aa\u23a8 \u23aa\u23a9 \u03b12 = \u03b83 \u03b22 = \u2212 arctan ( tan\u03b84 cos\u03b83 ) \u21d4 { \u03b83 = \u03b12 \u03b84 = \u2212 arctan(tan\u03b22cos\u03b12) (41) As shown in Fig. 17(c), the posture transformation of the moving platform of OES-group 2-SR [RR]&Sp [RR] is described as: 1) The system {1} translates a distance l along the O1O2 direction to transform to the system {11}, so that its coordinate origin coincides with O2. 2). The system {11} rotates \u03b12 around its x11 axis to transform to the system {12}, so that the y12 axis coincides with O2D81. 3). The system {12} rotates \u03b22 around its y12 axis to transform to the system {13}, so that the z13 axis coincides with O2E8", " The matrix H3(\u03b83, \u03b84, \u03b85) of this group is calculated and substituted into the following equation: Tran \u239b \u239c \u239c \u239dm1, m2 , m3 \u239e \u239f \u239f \u23a0 Rot \u239b \u239c \u239c \u239dx, \u03b12 \u239e \u239f \u239f \u23a0 Rot \u239b \u239c \u239c \u239dy, \u03b22 \u239e \u239f \u239f \u23a0 Rot \u239b \u239c \u239c \u239dz, \u03b32 \u239e \u239f \u239f \u23a0 \u23a1 \u23a2 \u23a3 0 \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 h2 1 + h2 2 + h2 3 \u221a 0 0 0 0 \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 n2 1 + n2 2 + n2 3 \u221a 0 \u23a4 \u23a5 \u23a6 T = H3 \u239b \u239c \u239c \u239d\u03b83, \u03b84, \u03b85 \u239e \u239f \u239f \u23a0 By calculation, the OS equations of the OES-group 2-SR [RR]&Sp [RR] are calculated as \u23a7 \u23aa \u23aa \u23a8 \u23aa \u23aa \u23a9 \u03b12 = \u03b83 \u03b32 = arctan ( \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\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305 1 + tan2\u03b83 + tan2\u03b84 \u221a tan\u03b85 ( 1 + tan2\u03b83 ) \u2212 tan\u03b84tan\u03b83 ) \u03b22 = \u2212 arctan(tan\u03b84cos\u03b83) \u21d4 \u23a7 \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23a9 \u03b84 = \u2212 arctan ( tan\u03b22 cos\u03b12 ) \u03b83 = \u03b12 \u03b85 = arctan ( cos\u03b12 \u2212 sin\u03b22sin\u03b12tan\u03b32 tan\u03b32cos\u03b22 ) (43) As shown in Fig. 17(d), the posture transformation of the moving platform of OES-group SR [RR]&2-Sp [RR] is described as: 1) The fixed coordinate system {1} translates a distance l along the O1O2 direction to transform to the system {11}, so that its coordinate origin coincides with O2. 2). The system {11} rotates \u03b12 around its z11 axis to transform to the system {12}, so that the y12 axis coincides with O2DB1. 3). The system {12} rotates \u03b22 around its y12 axis to transform to the system {13}, so that the z13 axis coincides with O2E8", " Thus, in order to obtain the correct transformation matrix of these 2 mechanisms above, it is necessary to multiply a matrix Rot(z, \u03c0) behind translation transformation matrix Tran(m1, m2, m3) in Eq. (42). The correct transformation matrix above can be expressed as TUS = Tran(m1, m2 , m3) Rot(z, \u03c0) Rot(x, \u03b12) Rot(y, \u03b22)Rot(z, \u03b32) (46) where the O2 coordinates (m1, m2, m3) of UR [RRR]&2-SR [RR]&SP [RR] and UR [RRR]&UP [RRR]&2-SR [RR]&SP [RR] are respectively expressed as Eq. (14) and (15). In order to further solve the limb interference problem, the OES-limb SP [RR] of the OES-group shown in Fig. 17(c) as a whole is rotated clockwise around the z1 axis by 135\u25e6 to the middle of 2 limbs SR [RR], which is shown in Fig. 18. Obviously, the input parameter \u03b85 of the limb SP [RR] at the equilibrium position is \u20141.5\u03c0. Obviously, 2 GSPMs above have the same transformation matrices as the series mechanisms U1S and U2S. They have the same kinematic characteristics as the 5-DOF ankle motion fitting models, and achieve complete decoupling between position and orientation. Table 12 shows the 4-DOF basic GSPM configurations", " The angle between the v-planes of limbs SR [RR] and UR [RRR] is set as 180\u25e6. The input parameters (\u03b81/\u03b82) of PES-groups UR [RRR]&URR and UR [RRR]&UPR are shown in Fig. 10(b) and (d), respectively. The input parameter \u03b83 of the limb SR [RR] is the angle between the driving link a8 and the x1 axis negative direction of the fixed coordinate system, so the coordinates of vector a8 in the fixed coordinate system are (\u2014cos\u03b83, 0, sin\u03b83). Based on the basic properties of the limbs URR, UPR and SR [RR], these 3 limb driving links (a3 for Fig. 10(b); a6 for Fig. 10(d); a8 for Fig. 17) are perpendicular to the z2 axis of the moving coordinate system. Thus, the OSI parameters (n1/n2/n3) can be easily calculated as \u23a7 \u23a8 \u23a9 n1 = cos\u03b81sin\u03b83 n2 = \u2212 sin\u03b81cos\u03b83 n3 = cos\u03b81cos\u03b83 (49) \u23a7 \u23a8 \u23a9 n1 = cos\u03b81sin\u03b83 n2 = sin\u03b81sin\u03b83 n3 = cos\u03b81cos\u03b83 (50) Eqs. (46) and (47) being substituted into the OSI equations (21) and (25) respectively, the complete orientation kinematics of mechanisms UR [RRR]&URR&SR [RR] and UR [RRR]&UPR&SR [RR] can be obtained as \u03b12 = arctan(tan\u03b82cos\u03b81) + arctan(tan\u03b83cos\u03b81) \u21d4 \u03b83 = arctan ( tan(\u03b21 + \u03b12) cos\u03b11 ) (51) \u03b12 = arctan ( tan\u03b82 cos\u03b81 ) + arctan ( tan\u03b83 cos\u03b81 ) \u21d4 \u03b83 = arctan[tan(\u03b21 + \u03b12)cos\u03b11] (52) Obviously, 2 3-DOF GSPMs above have the same transformation matrices as the series mechanisms U1R and U2R" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000193_j.cma.2011.04.006-Figure10-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000193_j.cma.2011.04.006-Figure10-1.png", "caption": "Fig. 10. Errors of alignments: (a) axial displacement of the pinion DA1, (b) axial displacement of the gear DA2, (c) change of the shaft angle DR and (d) shortest distance between axes DE.", "texts": [ " This algorithm for tooth contact analysis does not depend on the precondition that the surfaces are in point contact or the solution of any system of nonlinear equations as the existing approaches, and can be applied for tooth contact analysis of gear drives in point, lineal or edge contact as it will be shown below. Alternative algorithms that can be used for tooth contact analysis are found in [7\u20139]. All TCA analyses are conducted under rigidbody assumptions so that no elastic tooth deformation due to actual loading is considered when TCA results are shown. Fig. 9 represents the applied coordinate systems for tooth contact analysis (TCA) of straight and skew bevel gears. 5.2. Errors of alignment The errors of alignment considered are: (i) DA1 \u2013 the axial displacement of the pinion (Fig. 10(a)), (ii) DA2 \u2013 the axial displacement of the gear (Fig. 10(b)), (iii) DR \u2013 the change of the shaft angle R (Fig. 10(c)), and (iv) DE \u2013 the shortest distance between axes of the pinion and the gear when these axes are not intersected but crossed (Fig. 10(d)). The mentioned errors of alignment can also be observed in Fig. 9. Coordinate systems S1 and S2 are movable coordinate systems rigidly connected to the pinion and gear, respectively. Angles /1 and /2 are the angles of rotation of the pinion and the gear, respectively. Table 1 shows details of coordinate transformation from S2 to S1. Transformation Mml is needed if pinion and gear have been generated following the same coordinate transformations, so that one of the members of the gear drive have to be rotated an angle p to face corresponding surfaces for tooth contact analysis" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000193_j.cma.2011.04.006-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000193_j.cma.2011.04.006-Figure2-1.png", "caption": "Fig. 2. Applied coordinate systems for theoretical generation of a straight bevel gear by an imaginary crown-gear.", "texts": [ " Geometry of the imaginary generating crown-gear The proposed geometry for straight and skew bevel gears is achieved by considering an imaginary generating crown-gear as the theoretical generating tool. The generating surfaces of the imaginary crown-gear will be modified to apply the required surface modifications to the to-be-generated bevel gear. The number of teeth of the theoretical crown gear, Ncg, is given by Ncg \u00bc 2Ro m ; \u00f07\u00de where Ro is the outer pitch cone distance. The number of teeth of the theoretical crown gear can be a decimal number. Fig. 2 shows the applied coordinate systems for the theoretical generation of a straight or skew bevel gear by an imaginary crown-gear. The crown gear is rotated around axis ycg and the being-generated bevel gear is rotated around axis zi. Rotations of the being-generated bevel gear (straight or skew) and the imaginary crown-gear are related by wi \u00bc wcg Ncg Ni ; \u00f0i \u00bc 1;2\u00de; \u00f08\u00de where wi and Ni are the angle of rotation and number of teeth of the pinion (i = 1) or the gear (i = 2), respectively, during their theoretical generation, and wcg is the corresponding angle of rotation of the generating crown-gear", " The proposed new geometry of straight and skew bevel gears is obtained by considering their computerized generation by an imaginary crown-gear, whose geometry has been described in the previous section. A modified crown-gear will be used for the theoretical generation of the pinion whereas a non-modified crown-gear is used for generation of the gear. Fig. 8 shows the coordinate systems applied for the theoretical generation of a bevel gear (straight or skew) by a crown-gear, and complements those coordinate systems illustrated in Fig. 2. Coordinate systems Scg and Si are rigidly connected to the generating imaginary crown-gear and the being generated bevel gear (i = 1 for the pinion and i = 2 for the gear), respectively. Coordinate systems Sj, Sk, and Sl are auxiliary coordinate systems. Angle ci is the pitch angle of the being-generated gear (Eq. (3)). We recall that the imaginary crown-gear generating tooth surfaces are given by Eq. (21). The bevel gear tooth surfaces are determined as the envelope of the family of generating crown-gear Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000039_978-1-84996-220-9-Figure5.14-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000039_978-1-84996-220-9-Figure5.14-1.png", "caption": "Figure 5.14 Target position of the planning task: (a) distance view and (b) narrow view", "texts": [ " The robot model has 43 DoF and for each limb there are two 3D models, one for visualization and one simplified model for collision checking purposes. The robot is operating in a kitchen environment, which is also modeled with full and 5 Efficient Motion and Grasp Planning for Humanoid Robots 155 reduced resolution for visualization and collision checking as described in Section 5.2. The starting position of the robot is located outside the kitchen and a trajectory for grasping an object is searched. In this experiment the target object is placed inside the fridge (Figure 5.14(a)). For this task, the planner uses the subsystems Platform, Torso, Right arm, Right Wrist and Right Hand. In our test setup the subsystem for the right hand consists of six instead of eight joints because the two middle and the two index finger joints are coupled and thus are counted as one DoF. The overall number of joints used for planning, and therefore the dimensionality of the C-space, is 19. We make the assumption that a higher level task planning module has already calculated a goal position for grasping the object, thus cgoal , the target in C-space, is known" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001510_j.mechmachtheory.2014.01.014-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001510_j.mechmachtheory.2014.01.014-Figure5-1.png", "caption": "Fig. 5. Schematic of internal forces in any section under the action of the four-roller WG.", "texts": [ " By projecting all the forces in the vertical direction, the circumferential force X2 is calculated as follows: Here, X2 \u00bc F cos\u03b2: \u00f01\u00de F is the contact force from the roller. Here, For the force F that is concentrated at the point \u03c6 = \u03b2, the internal forces correspond to two ranges of \u03c6: 0 \u2264 \u03c6 \u2264 \u03b2 and \u03b2 b \u03c6 \u2264 \u03c0 / 2. A force balance in the vertical direction for the model in Fig. 4c can be solved for the circumferential forces in any cross section over the two ranges of \u03c6; a schematic of the force balance is given in Fig. 5. FN1 \u00bc F sin\u03b2 cos\u03c6; 0\u2264\u03c6\u2264\u03b2\u00f0 \u00de FN2 \u00bc F cos\u03b2 sin\u03c6; \u03b2b\u03c6\u2264\u03c0=2\u00f0 \u00de ( \u00f02\u00de FN1 and FN2 are the circumferential forces in any Section. An explicit expression for the bending moment in any section is obtained from a mechanical analysis of the bending moments X1 and circumferential force X2: Here, M1 \u00bc M2\u2212F rm sin \u03b2\u2212\u03c6\u00f0 \u00de; 0\u2264\u03c6\u2264\u03b2\u00f0 \u00de M2 \u00bc X1 \u00fe X2 rm 1\u2212 sin\u03c6\u00f0 \u00de; \u03b2b\u03c6\u2264\u03c0=2\u00f0 \u00de: ( \u00f03\u00de M1 and M2 denote the bending moment in any section. Here, Therefore, the energy U of a quarter of the rim can be calculated as follows: U \u00bc rm 2EIz Z \u03b2 0 M1 2d\u03c6\u00fe Z \u03c0=2 \u03b2 M2 2d\u03c6\u00de: \u00f04\u00de EIz is the bending stiffness of the tooth rim" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003216_j.addma.2020.101526-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003216_j.addma.2020.101526-Figure3-1.png", "caption": "Fig. 3. a) Fatigue testing specimen dimensions in mm and b) samples in the asbuilt and post-processed conditions.", "texts": [ "1 kgf on a Wolpert Wilson 402 MVD micro Vickers hardness tester. A combination of ESD, peening, and heat treatments were used to create several post-processed samples for surface profile analysis, microhardness evaluation, and fatigue testing. A breakdown of samples created for each analysis is provided in Table 2. Post-processing of ESD+HP samples for fatigue testing consists of two layers of ESD Inconel 718 applied to the necked region of the fatigue specimens (built in a vertical orientation with dimensions shown in Fig. 3a), with peening performed at the conclusion of each layer. A second set of post-processed HP samples received an equivalent amount of peening as ESD+HP samples, without the application of an Inconel 718 coating using ESD. The last set of post-processed samples (ESD+HP+DA) were processed similarly to the ESD+HP samples, with the addition of a direct aging heat treatment. The resulting postprocessed samples are compared to samples in the as-built condition, shown in Fig. 3b. An Instron 8872 servohydraulic fatigue testing system was used to test the room temperature fatigue performance of LPBF Hastelloy X samples with and without post-processing using a stress ratio (R =S S min max ) of 0.1 in tension-tension mode. Low cycle fatigue testing was performed at a maximum stress of 550MPa while the high cycle fatigue testing was done at a maximum of 350MPa. A frequency of 5 Hz was used for all samples except the post-processed samples tested at high cycle fatigue conditions" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000409_amc.2012.6197032-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000409_amc.2012.6197032-Figure2-1.png", "caption": "Fig. 2. a) Joint configurations, as seen from isometric perspective. b) Joint configurations in the lateral plane. {q1, q2} and {q4, q5} are right and left arm\u2019s active shoulder and elbow joints, respectively. q3 and q6 are passive roll joints in right and left arms. Link information is given in Table I.", "texts": [ "00 \u00a92012 IEEE active exoskeleton system, displayed in Fig. 1. The system includes both lower and upper extremities to deliver an overall power augmentation to the human-wearer. In this paper, we primarily investigate the upper part of the exoskeleton. This part includes a total of 6 DoF, to be able to obtain greater motion flexibility. Each arm includes 2 active joints for shoulder and elbow rotating in pitch axis, and 1 passive joint for shoulder rotating in roll axis. Joint configurations can be observed in Fig. 2. In its actuation module, Harmonic Drive FHA series servo motors are employed. These modules include integrated encoders and harmonic gears and they can accept torque input commands. On the other hand, they are not able to monitor motor current or torque output. The exoskeleton system is also equipped with pressure sensors to measure muscle stiffness. Currently, utilization of these sensors are left for a future study. TABLE I MAXIMUM LINK LENGTHS Waist-Should (Vertical) (pz): 45 [cm] Shoulder to Shoulder (Horizontal) (2py): 40 [cm] Shoulder-Elbow (L1): 28 [cm] Elbow-Wrist (L2): 27", " Expanding (6), we obtain (7) and (8) which indicate gravity compensation torques for shoulder and elbow joints (Tgrs, Tgre), respectively. Tgrs = c3(agrm2(l2s12 + l1s1) + agrm1l1s1) (7) Tgre = c3agrl2m2s12 (8) In (7) and (8), m1, l1, m2, l2, and agr are shoulder-elbow link mass, shoulder-elbow link mass center position, elbowwrist link mass, elbow-wrist link mass center position, and gravitational acceleration, respectively. Moreover, c3, s1 and s12 are cos(q3), sin(q1) and sin(q1 + q2). Joint numbers are indicated in Fig. 2. As understood by the above equations, passive roll joint (q3) should be measured as well. In order to cancel the gravity effect, we calculate necessary torques by using (7) and (8), and then added to the system as depicted in Fig. 3. Estimating the external torque is of special importance in exoskeleton control. For this purpose, we utilize disturbance observers which can output the summation of the following disturbance elements [11]. Td = Tfr + Tgr + Text + Tpar (9) In (9), Tfr, Tgr and Tpar are disturbance torque components based on frictional, gravitational and parameter variation loads" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000259_j.cirp.2010.03.020-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000259_j.cirp.2010.03.020-Figure1-1.png", "caption": "Fig. 1. Kinetostatic model of the 3 3 hexapod.", "texts": [ " (3), depending on six unknowns (nx, ny, nz, cx, cy, and cz) subject to non-linear condition (6). The Lagrange-multipliers method is reduced [12] to the search of eigenvalues of the homogeneous symmetrical matrix: S \u00bc Krot \u00f0Kmix\u00deT\u00f0Ktr\u00de 1Kmix (13) where Ktr, Kmix, and Krot are the 3 3 block-matrices composing matrix K, Eq. (2). Note that minimal TSV (ktr)min presents the minimum eigenvalue of the 3 3 block-matrix Ktr, Eq. (2). A kinetostatic model of the 3 3 Gough\u2013Stewart platform (GSP) mechanism is shown in Fig. 1: the platform is supported on six elastic limbs of identical stiffness values. As a methodological example, a vertical motion (along the Z-axis) of the centrally located and horizontally oriented mobile platform is considered. In this case, the 6 6 stiffness matrix K, Eq. (2), is [13]: K \u00bc 3kl l2 q2 0 0 0 p 0 q2 0 p 0 0 2h2 0 0 0 h2r2 2 0 0 sym h2r2 2 0 0 3r2 1r2 2=2 0 BBBBBBB@ 1 CCCCCCCA (14) where r1 and r2 are the radii of the hinge locations on the base and the mobile platform, respectively; h is height position of the platform; l2 = q2 + h2 is the current limb length; q2 \u00bc r2 1 \u00fe r2 2 r1r2; p = hr2 (r1/2 r2); and kl is the limb stiffness value depending on stiffness values of built-in-limb actuator kact, universal joint kun and spherical joint ksp placed in series" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001785_0954406215627831-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001785_0954406215627831-Figure5-1.png", "caption": "Figure 5. Diagram of Ravigneaux compound planetary transmission. (a) Main view of Ravigneaux compound gear set, (b) left view of Figure 5(a), (c) right view of Figure 5(a).", "texts": [ ",23 is employed to calculate the impact of increasing backlash generated by tooth accumulated wear on vibration, bifurcation behavior, chaotic motion, and load sharing characteristic of compound planetary gear set. In this work, the structure of compound planetary gear set, definition and symbols of internal and external excitation, and equations of motion are as same as the relevant description in Zhang et al.23 The only one difference from Zhang et al.23 is the definition of backlash, which includes the increasing backlash generated by tooth accumulated wear in this work. The structure of a typical Ravigneaux compound planetary gear set used in this work is shown in Figure 5, which is as same as the one in Zhang et al.23 It is seen in Figure 5(a) that there are two types of elements in the structure: the central members (suns s1 and s2, carrier c and ring r), and the planets (an and bn) that are free to rotate with respect to their common carrier c. zi (i\u00bc s1, s2, an, bn, c, r) is the tooth number. The planet mated with sun s1 and also associated with another planet is an (n\u00bc 1, 2, 3 in this work). A planet\u2013planet mesh appears between planets an and bn. In general, n is used for denoting planet number. A central gear meshes with three planet gears which are arranged symmetrical in the space, as shown in Figure 5(b) and (c). In Figure 5(b), Ps2bn (n\u00bc 1, 2, 3) stands for the second sun\u2013planet meshing pairs. In Figure 5(c), Ps1an, Prbn (n\u00bc 1, 2, 3) represent the meshing pair sun\u2013planet and ring\u2013planet, respectively. The planet\u2013planet meshing pairs are denoted as Panbn (n\u00bc 1, 2, 3). In this work, in order to describe the direct impact of tooth accumulated wear on meshing force, a piecewise function of backlash is introduced into the dynamic model as the actual meshing penetration depth, which is defined as follows fj,m \u00bc j backlashini, j Wearj,m\u00f0t\u00de j > backlashini, j \u00feWearj,m\u00f0t\u00de 0 j > backlashini, j \u00feWearj,m\u00f0t\u00de j \u00fe backlashini, j \u00feWearj,m\u00f0t\u00de j 4 backlashini, j Wearj,m\u00f0t\u00de 8>>>>>>>>>>< >>>>>>>>>>: j \u00bc s1an, s2bn, anbn, rbn\u00f0 \u00de \u00f05\u00de where fj is the piecewise linear function and backlashini,j represents the initial backlash of meshing pair Pj", " ns1 is the rotate speed of s1. 60 m 103=ns1 is the running time after s1 runs for m internals. The sources of tooth accumulated wear for central gears and planets are different due to different meshing relations in compound planetary gear set. For a central gear in epicyclic gear train, several planets with symmetrical distribution commonly mesh on it to distribute the power. Therefore, the accumulated wear of a central gear sources from all the meshing pair including that central gear. For a planet gear, such as a1 in Figure 5(b), the tooth accumulated wear sources from all the meshing pairs including a1, e.g. Ps1a1 and Pa1b1. For the planet gear b1, the tooth accumulated wear sources from all the meshing pairs including b1, e.g. Pa1b1, Prb1 and Ps2b1. at UNIV CALIFORNIA SAN DIEGO on January 27, 2016pic.sagepub.comDownloaded from bs1,ps1a1,m (t) is the tooth accumulated wear of one tooth on sun s1 after system running for m internals as defined in equations (2) and (3), due to the meshing action in meshing pair Ps1a1; as the totally accumulated tooth wear of one tooth on sun gear s1, bs1,m(t) contains tooth accumulated wear from all the meshing pair including s1, and have the relation that: bs1,m\u00bc bs1,ps1a1,m\u00fe bs1,ps1a2,m\u00fe \u00fe bs1,ps1an,m; ba1,ps1a1,m is the tooth accumulated wear of one tooth on planet a1, due to the meshing behavior in meshing pair Ps1a1; ba1,pa1b1,m is the tooth accumulated wear of planet gear a1, due to the meshing behavior in meshing pair Pa1b1; as the totally accumulated tooth wear of planet gear a1 at the mth running internal, ba1,m\u00bc ba1,ps1a1,m\u00fe ba1,pa1b1,m" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002844_j.mechmachtheory.2020.103930-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002844_j.mechmachtheory.2020.103930-Figure3-1.png", "caption": "Fig. 3. Dynamic transmission errors testing platform[ 40 ].", "texts": [ " (9) can be rewritten as k md ( DT E \u2212 1 k md N \u2211 i =1 k i \u03b5 i ) = F md (10) As the initial clearances of contact point pairs are different from each other, the dynamic composite mesh error is intro- duced to reflect the comprehensive effect of distributed tooth flank errors, which can be determined as e md = 1 k md N \u2211 i =1 k i \u03b5 i (11) In the proposed model, the error value of each position on the actual three-dimensional tooth surface can be considered (The measured three-dimensional error values on tooth surface can also be introduced). It is well known that the instantaneous three-dimensional contact state of gear tooth surface is closely related to the vibration behaviors of gear system. Hence, the experimental data of dynamic transmission errors from the published works [38\u201340] are employed to validate the proposed model. The testing platform is a set of mechanical power enclosed gear transmission system test device for dynamic transmission error test of spur/helical gears, as shown in Fig. 3 . The basic parameters of the test gears are given in Table 2 , and the stiffness of rolling bearings are given in Table 3 . The comparison of numerical results obtained using the proposed model and experimental results of dynamic transmission errors of the test gear pair with 5 \u03bcm of lead crown are shown in Fig. 4 . It can be observed that the amplitude \u201cjump\u201d phenomenon occurs when the input speed is near the resonance speed of the test gear system due to total tooth separations which are caused by too large relative dynamic displacement along normal line of action" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002277_978-3-319-27131-6-Figure1.9-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002277_978-3-319-27131-6-Figure1.9-1.png", "caption": "Fig. 1.9 Curvatures of the outer raceway of a ball bearing", "texts": [ " The curvatures of the ball (i\u00bc 1) in the orthogonal principle curvature planes ( j\u00bc 1, 2) are the same because the ball has a constant radius in any direction: \u03c111 \u00bc \u03c112 \u00bc 1 r11 \u00bc 1 r12 \u00bc 1 Dw=2\u00f0 \u00de \u00bc 2 Dw > 0 \u00f01:15\u00de Similarly, the curvatures of the cylindrical roller (i\u00bc 1) in the principle curvature planes ( j\u00bc 1, 2) are calculated as \u03c111 \u00bc 2 Dw > 0; \u03c112 \u00bc 0 \u00f01:16\u00de The curvatures of the inner raceway for ball and roller bearings (i\u00bc 2) in the orthogonal principle curvature planes ( j\u00bc 1, 2) are calculated using trigonometric relations of the bearing and Eqs. 1.9 and 1.12 as (s. Fig. 1.8) \u03c121 \u00bc 1 r21 \u00bc 1 Dpw 2 cos \u03b1 Dw 2 \u00bc 2 Dw Dpw Dw cos \u03b1 1 > 0; \u03c122 \u00bc 1 r22 \u00bc 1 Dw\u03bai < 0 f or ball bearings; \u03c122 \u00bc 1 r22 \u00bc 0 f or roller bearings \u00f01:17\u00de The curvatures of the outer raceway for ball and roller bearings (i\u00bc 2) in the orthogonal principle curvature planes ( j\u00bc 1, 2) are calculated using trigonometric relations of the bearing and Eqs. 1.9 and 1.12 as (s. Fig. 1.9) 1.4 Curvatures of Bearings 11 12 1 Fundamentals of Rolling Element Bearings There are two curvature sums for each ball and roller bearing according to Eqs. 1.19a, 1.19b, 1.21a, and 1.21b and Table 1.2. The curvature sum of the ball and inner raceway results from Eqs. 1.14, 1.15, and 1.17 as X \u03c1b=IR \u00bc \u03c111 \u00fe \u03c112\u00f0 \u00de \u00fe \u03c121 \u00fe \u03c122\u00f0 \u00de \u00bc 2 Dw \u00fe 2 Dw \u00fe 2 Dw A 1\u00f0 \u00de 1 Dw\u03bai \u00bc 2 Dw 2\u00fe 1 A 1 1 2\u03bai \u00f01:19a\u00de Analogously, the curvature sum of the ball and outer raceway results from Eqs. 1.14, 1.15, and 1.18 as X \u03c1b=OR \u00bc \u03c111 \u00fe \u03c112\u00f0 \u00de \u00fe \u03c121 \u00fe \u03c122\u00f0 \u00de \u00bc 2 Dw \u00fe 2 Dw 2 Dw A\u00fe 1\u00f0 \u00de \u00fe 1 Dw\u03bao \u00bc 2 Dw 2 1 A\u00fe 1 1 2\u03bao \u00f01:19b\u00de where A is defined using the operating contact angle \u03b1 in Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001215_b978-0-08-100433-3.00006-3-Figure6.6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001215_b978-0-08-100433-3.00006-3-Figure6.6-1.png", "caption": "Figure 6.6 Schematic illustration of the selective laser sintering process. AM, additive manufacturing.", "texts": [ " Among established AM techniques, STL yields high surface qualities, which also qualifies this process for micro-STL [29] and other high-tech applications such as functional heating bodies used for the Mars rover Curiosity, launched by the NASA in 2011 [18]. Commercial fabrication of functional parts for biomedical, luxury, and technical applications are provided by contractors such as 3DCeram [19]. SLS was invented at the University of Texas at Austin and patented by Carl Deckard in 1989 [20]. During processing, thin layers of powder material <100 mm are repetitively deposited by a wiper onto the build platform before the layer information is selectively sintered according to the 3D CAD data, as schematically depicted in Fig. 6.6. Early studies by Bourell et al. [21] discuss the different consolidation mechanisms of viscous flow and low-melting-point phases during laser processing for both metals and ceramics. Depending on the applied raw material, SLS is categorized into direct and indirect SLS: the latter exploits the presence of a fugitive binder with low melting point for consolidation of the green part. Post-processing by thermal treatment or infiltration yields the final dense parts. Indirect SLS exploits the presence of a sacrificial binder with low melting point, which serves as a matrix phase, drastically improving the densities of the green parts compared with direct SLS" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003006_j.triboint.2020.106806-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003006_j.triboint.2020.106806-Figure2-1.png", "caption": "Fig. 2. A schematic view of a heat supply diagram.", "texts": [ " Amanov Tribology International 155 (2021) 106806 Advantages of UNSM over other surface peening technologies for particular AM materials are that it smooths out the surface, which is usually rough after AM and also increases the strength simultaneously. Moreover, it somehow shrinkages pores due to the compressive strike. Ti\u20136Al\u20134V alloy samples were treated by UNSM at 25 \u25e6C and 800 \u25e6C with a static load of 40 N, an amplitude of 30 \u03bcm, a distance between two consecutive scans of 70 \u03bcm and a linear speed of 2000 mm/min. A schematic view of a heat supply diagram is illustrated in Fig. 2. Firstly, the samples were heated up using a furnace and then were brought to the heat supply block that heated up the samples using a cartridge heater and held the temperature, which was controlled using a temperature controller. Real-time temperature of the sample was precisely measured by a thermocouple. The combination of UNSM and LHT was described in our previous study [27]. In UNSM, the main variables are important, while force being the most important because it\u2019s magnitude determines the intensity of strain hardening" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003615_tcyb.2021.3055519-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003615_tcyb.2021.3055519-Figure2-1.png", "caption": "Fig. 2. Kinematic parameters of the snake robot from a (a) top view and (b) side view.", "texts": [ " A novel direction control method and an adaptive LOS path-following law of 3-D motion are proposed in Section III. Extensive simulations and experiments are conducted to verify the proposed direction control and adaptive path-following algorithms in Section IV. Finally, conclusions are given in Section V. To control the 3-D motion of a snake robot as shown in Fig. 1, our prior work [44] has derived a 3-D mathematical model of n-link snake robots, which is applied in this article. The kinematic parameters of the snake robot are shown in Fig. 2. Mathematical symbols used in this model are described in Table I. As derived in [44], positions of the center of mass (CM) of a snake robot and all links in the global frame are calculated as p = \u23a1 \u23a3 px py pz \u23a4 \u23a6 = \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 1 nm n\u2211 i=1 mxi 1 nm n\u2211 i=1 myi 1 nm n\u2211 i=1 mzi \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 = 1 n E \u23a1 \u23a3 x y z \u23a4 \u23a6 (1) x = T\u22121 [\u2212lBC\u03d5 cos \u03b8 px ] = \u2212lKTC\u03d5 cos \u03b8 + epx y = T\u22121 [\u2212lBC\u03d5 sin \u03b8 py ] = \u2212lKTC\u03d5 sin \u03b8 + epy z = T\u22121 [\u2212lB sin \u03d5 pz ] = \u2212lKT sin \u03d5 + epz (2) where E is a transition matrix defined as E = \u23a1 \u23a3 eT 01\u00d7n 01\u00d7n 01\u00d7n eT 01\u00d7n 01\u00d7n 01\u00d7n eT \u23a4 \u23a6 (3) and e = [1, 1, " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000193_j.cma.2011.04.006-Figure14-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000193_j.cma.2011.04.006-Figure14-1.png", "caption": "Fig. 14. (a) Contact pattern and (b) function of transmission errors for case A3a (straight(A) partial-crowned(3) aligned(a) bevel gear drive).", "texts": [ " In order to absorb the lineal functions of transmission errors caused by errors of alignment in general and the axial displacements of pinion or gear in particular, Designs 2 and 3 (see Table 3) are proposed with whole-crowned and partial-crowned bevel gear tooth surfaces, respectively. Figs. 13 and 14 shows the contact patterns and the predesigned functions of transmission errors for cases A2a and A3a corresponding to a straight whole-crowned and aligned bevel gear drive (Fig. 13) and to a straight partialcrowned and aligned bevel gear drive (Fig. 14). Parabolic functions of transmission errors have been predesigned with levels of 8.5 arcsec for whole-crowned surfaces (Design 2) and 5.5 arcsec for partial-crowned surfaces (Design 3). Design 3 (partial-crowning) allows the contact pattern to cover a larger area of the bevel gear contacting surfaces, by creating an area of no modification of the tooth surfaces. The main advantage of this geometry is that the lower the misalignment is, the bigger the contact pattern is obtained, allowing contact stresses to be reduced" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002640_j.optlastec.2019.106041-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002640_j.optlastec.2019.106041-Figure3-1.png", "caption": "Fig. 3. Dimensions (in mm) of the Charpy U-notch impact sample.", "texts": [ " Dry sliding wear tests were carried out by multi-functional tester for material surface (MFT-4000), and the selected wear testing parameters were listed in Table 2. After dry sliding wear tests, the worn surfaces were rinsed with ethanol and dried with electric dryer, and the morphology of the worn surfaces were characterized by FE-SEM. The roughness and 3D surface of worn tracks were characterized by OL3000 confocal laser scanning microscopy (CLSM). The impact properties of Charpy U-notch samples were tested using a screen display impact tester (JBW-500). The dimensions of impact samples (according to ISO 148-1 standard) were shown in Fig. 3. The impact fracture surfaces of the broken samples were observed by FESEM. Cracks, pores, inclusions are the main defects of laser additive manufacturing metal parts, which have a great influence on the formability and performance of the as-deposited samples [16]. Yadollahi et al. [17] studied that X-ray computed tomography (X-ray CT) could more accurately detect the distribution of voids inside as-deposited samples than the Archimede\u2019s drainage method. Fig. 4 visually shows the three-dimensional distribution of defects in DLD-processed 12CrNi2 alloy steel sample fabricated at different laser scanning speed" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003580_j.mechmachtheory.2020.104238-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003580_j.mechmachtheory.2020.104238-Figure3-1.png", "caption": "Fig. 3. Discretization of tooth surface pressure angle.", "texts": [ " (22) - (26) as follows: d 1 = | y x L 1 | \u2212 | y x L 3 | (22) d 2 = | z x L 2 | (23) A \u2032 x = 2 h x L \u2212 1 2 d 1 d 2 (24) d y = 1 2 d 1 d 2 ( h x \u2212 1 3 d 1 ) 2 h x L \u2212 1 2 d 1 d 2 (25) I \u2032 x = I x \u2212 [ d 2 d 3 1 36 + 1 2 d 1 d 2 ( h x \u2212 1 3 d 1 )2 ] \u2212 [ 1 2 d 1 d 2 ( h x \u2212 1 3 d 1 )]2 2 h x L \u2212 1 2 d 1 d 2 (26) herein the x in the subscript represents arbitrary point on the involute. y x L 1 is the y-coordinate of the intersection of cross section and curve L 1 , y x L 3 is the y-coordinate where the cross section intersects the straight line L 3 . z x L 2 is the coordinate of the intersection of the cross section and the curve L 2 along the Z -axis. To establish a relationship between the involute pressure angle and the gear rotation angle, the pressure angle of the involute involved in the engagement is evenly divided, just like l 1 , l 2 and l 3 in Fig. 3 . Due to the geometric characteristics of involute, the angular displacement of gears does not vary linearly with the linear variation of the pressure angle. In Fig. 3 (a), points 1, 2, 3 and 4 are the critical meshing point, respectively correspond to the mesh starting, double-tooth mesh to single-tooth mesh, single-tooth mesh to double-tooth mesh and the disengaging, as shown in Fig. 3 (b). When a pair of teeth comes into mesh, the mesh starting point may not coincide with the involute starting point just like the point K and point P as shown in Fig. 4 . For an arbitrary point on the involute, for example point S in Fig. 4 , when it turns to S \u2032 which is on the mesh line MN , the angular displacement of the driving gear can be calculated by Eqs. (27) - (30) as follows: \u2220 S O 1 S \u2032 = \u2220 S O 1 K + \u2220 K O 1 S \u2032 (27) \u2220 S O 1 K = ( tan \u03b1x \u2212 \u03b1x ) \u2212 ( tan \u03b1s \u2212 \u03b1s ) (28) \u2220 K O 1 S \u2032 = \u03b1x \u2212 \u03b1s (29) \u03b1s = cos \u22121 \u239b \u239d R b1 \u221a R 2 t2 + O 1 O 2 2 \u2212 2 R t2 O 1 O 2 cos ( cos \u22121 R b2 R t2 \u2212 \u03b10 ) \u239e \u23a0 (30) herein \u03b1x is the pressure angle at arbitrary point on the involute", "73 \u00b0, the stiffness attenuation in double-tooth mesh area is greater than that of single-tooth mesh area, and the attenuation rate will growth with the increase of angular displacement which can be observed from the slope of line 1 and line 2. This is because the stiffness attenuation result from the reduction of A \u2032 x and I \u2032 x more than the increase of stiffness value causing by double teeth mesh. when the fault expands along the involute due to the cyclic stress, the mesh stiffness will further attenuate. However, the tooth profile curve is non-linear with the variation of pressure angle, that is, the arc length changes caused by the same value of pressure angle variation are not equal, as shown in Fig. 3 . But the speed of fault attenuation caused by the variation of fault location is different, as shown in Fig. 12 . In Fig. 12 , delta(16 \u00b0-19 \u00b0) represents the stiffness difference when \u03b1A equals to 16 \u00b0 and 19 \u00b0, and other delta in the legend has the same definition. This makes the length of the Hertz contact area unequal at any position in the fault mesh zone when the fault position is different. In other words, when \u03b1A decreases gradually (namely the fault gradually expands along the involute line), the Hertz contact length of the tooth surface decreases nonlinearly, and at the same time, A \u2032 x and I \u2032 x also decrease, resulting in the attenuation speed of mesh stiffness present a non-linear variation" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003373_j.mechmachtheory.2021.104348-Figure14-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003373_j.mechmachtheory.2021.104348-Figure14-1.png", "caption": "Fig. 14. The leg-wheel module: (a) side view of the module and (b) the module with a boom in experiments.", "texts": [ " 9639 t \u2212 50 . 2410 \u03b8 = 5383 . 3 t 3 + 1056 . 7 t 2 \u2212 28 . 7394 t + 17 . 0277 (31) After lift-off and during the flight phase, the leg-wheel module was set to transform into wheeled mode and remain in this mode until touchdown. \u03b2 remained at the same speed as that of take-off, and \u03b8 transformed from \u03b8l max to \u03b80 . This leg-retracting setting allowed the module to negotiate high obstacles. The motion of the module was assumed to follow the projectile motion with lift-off velocity as the initial velocity. Fig. 14 (a) shows the leg-wheel module built for experimental validation. The linkages are made of aluminum, while the joints are comprised of a steel shaft and bearing, and the wheel-rim pieces are constructed from composite materials using 3D printing technology (Mark Two Desktop 3D Printer, Markforged, Inc). The material consists of an Onyx filament (matrix), and continuous carbon fiber is used as reinforcement. The matrix material, Onyx, is printed in a triangular pattern at 37% density. The reinforcement material (continuous carbon fiber) is printed in a concentric pattern with two rings in each layer", " Due to the fast motion, some transition points, such as point 6 \u00a9 (shown in Fig. 15 [d]), show a slight overshoot. The leg length in the experiment ( R = 135 mm , l max = 442 mm ) was less than the desired length ( R = 130 mm , l max = 445 mm ) . We suspect that this was caused by mechanism backlash or inaccurately mounted markers of the VICON motion capture system. The markers were mounted manually based on visual observation. In the wheel-to-leap experiments, the leg-wheel module was mounted on a 1 m boom that could rotate and swing up and down freely, as shown in Fig. 14 (b). It ran on a seven-meter-long runway, and its motion was measured using a motion capture system (four high-speed T20s cameras and five high-speed V5 cameras, VICON Motion Systems). The associated parameters are listed in Table 7 . The wheel-to-leap behavior of the leg-wheel module was then executed in multiple runs. Fig. 16 shows the motion states of the simplified model and the leg-wheel module in experiments from start to take-off. Table 8 lists the critical leap performance of the experimental runs, including leap height and leap distance" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000931_9781118703274.ch2-Figure2.48-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000931_9781118703274.ch2-Figure2.48-1.png", "caption": "Figure 2.48 Hydraulic blade pitch regulators (Aeroman, MAN): (a) pitch adjustment and supply system in the nacelle and (b) setting cylinder and crank system", "texts": [ " The feeding of this energy to the rotating hub and blade positioning device considerably increases construction costs. In spite of this, hydraulic drives are in widespread use, principally in smaller and medium-sized machines, but are also found in large machines. Electrical adjusters, on the other hand, are generally found only in machines of 200 kW nominal output or above. The power for hydraulic pitch-regulation mechanisms is usually supplied from units in the machine house. For turbines in the 10 to 100 kW class, the drive is usually fed directly via the rotor or generator shaft. Figure 2.48(a) shows the pitch-setting and power supply systems for a turbine of the 30 or 40 kW class. The hydraulic pump is driven from the generator shaft. From the generator standpoint, the speed of rotation and power of the turbine are handled as electrical quantities and are compared with given control values. Should any deviation occur, electrohydraulic valves are opened or closed according to control characteristics and the positioning cylinder (see Figure 2.48(b)) is activated. When hydraulic power is applied to the cylinder, it turns the blades towards the plane of rotation. In the absence of hydraulic power, springs acting in the opposite direction return the blades to their original positions. This means that, if the hydraulic system fails or another emergency situation arises, the turbine is returned to a safe operating mode. Seen from the turbine, the control valves and the hydraulic power unit are located behind the generator. The regulation and adjustment system shown here consists primarily of standard hydraulic drive products" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003197_j.mechmachtheory.2020.103948-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003197_j.mechmachtheory.2020.103948-Figure3-1.png", "caption": "Fig. 3. Example of Cn (b) and Ln (a) variation", "texts": [ " After the definition of amount and length it is possible to introduce the following dimensionless quantities to identify the entity of tip relief to be applied, referred to the optimal values of C a the end L a : C n = C C a (4) L n = L L a (5) where C and L are the effective amount and length modifications. In this way, it is possible to perform a sensitivity analysis on the variations of the influence parameters in a dimensionless manner. Since the pattern of the transmission error varies as a function of the realized tip relief and the resistant torque, the first step to understand the effect of modifications is to fix the torque and vary independently the amount and length, as reported in Fig. 3 Considering a generic gear, it is possible to identify three main contributions to the compliance: compliance due to contact stiffness (CS); compliance due to inflection stiffness (IS) and compliance due to gear body foundation stiffness (GBF). These three contributions depend on geometrical and material properties and are not influenced from the engagement mechanism. The main idea of the proposed approach is to adopt a specific multibody model that only needs as input these three terms that can be estimated through analytical formulas" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001328_j.renene.2014.03.036-Figure10-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001328_j.renene.2014.03.036-Figure10-1.png", "caption": "Fig. 10. Four point mounting Configuration model.", "texts": [], "surrounding_texts": [ "In order to minimize the influence of the specific design of the GRC gearbox on the generality of the overall drive train behavior, it was chosen not to include the gear meshing stiffness in the models. In theory the forces and moments which are introduced in the gearbox should be transferred to the gearbox bushings through a path comprising of the planet carrier, planet carrier bearings and the gearbox housing, as shown in Fig. 12. Unless there is play in the bearings or the planet carrier and/or housing stiffness is insufficient the gear meshing stiffness does not play a role in this mechanism. In addition by excluding the gear meshing stiffnesses it is possible to assure that the housing is an important part of the transfer path. Since the gear meshing stiffness is needed to counteract the torque applied at the rotor, an equivalent total gear meshing stiffness is taken into account in the torsional DOF and superimposed on the stiffness values at both planet carrier bearings. More information on the assumptions that were made can be found on page 5." ] }, { "image_filename": "designv10_9_0003216_j.addma.2020.101526-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003216_j.addma.2020.101526-Figure2-1.png", "caption": "Fig. 2. Schematic of hammer peening tool mechanism showing vibration of a rod driven by the rotation of an eccentric weight.", "texts": [ " Ultra-high purity argon shielding gas was delivered coaxially around the electrode during deposition, and ESD parameters of 100 V, 80 \u03bcF and 150 Hz were used based on previous studies that show high density and good mechanical properties [32,33]. Coatings were applied to 10mm by 10mm regions for various spark durations (25 s, 75 s, 125 s) in a raster scan pattern, with the pattern rotated 90\u00b0 between layers. The machine hammer peening tool operates by driving a 2.5 cm long, 4.8mm diameter hardened tool steel rod using a rotating 21 g weight offset by 0.64mm (Fig. 2). Rotation occurs at a frequency of 100 Hz, and the vibration amplitude at the rod tip is 0.5mm. When peening was used, the ESD process was stopped every 12.5 s and peening was applied to the entire coated area. Inconel 718 coated Hastelloy X samples were studied in several heat-treated conditions, described in Table 1. All heat treatments were performed in a horizontal quartz tube furnace under ultra-high purity argon gas, with a flow rate of 4 L/min and 250 Pa of positive pressure. The aging temperature and time is selected based on the industry standard for Inconel 718 [34], and the solution annealing temperature and time is selected based on literature studies of secondary phase dissolution in rapid solidification processed Inconel 718 [35]" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001379_978-3-319-22056-7-Figure3.10-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001379_978-3-319-22056-7-Figure3.10-1.png", "caption": "Fig. 3.10 a Wind turbine rotor after shovel separation, b Model of the shovel separation", "texts": [ " As moment of inertia of the system decreases, due to shovel bending, angular velocity of the system increases and reaches its maximal value for l1 = l/3 and has the value 3.10 Mass Variation of a Wind Turbine 79 1 = 27 19 . (3.283) For higher values of bending, moment of inertia increases and 1 decreases. When shovel bends on its other side with the whole length, angular velocity of the wind turbine become 1 = . It is not so uncommon that a shovel of the wind turbine is \u2018spontaneously\u2019 separated. As it is mentioned, it is the result of material fatigue, stress, etc. In Fig. 3.10, damaged wind turbine and in Fig. 3.11, positions of the shovel after separation are shown. Our aim is to calculate angular velocity of the remainder rotor after shovel separation and to determine motion of the shovel after its separation. Dynamics of motion of the system is divided into three intervals: 1. Motion of the initial rotor 2. Dynamics of rotor separation 3. Motion of the separated shovel. Motion of the Initial Rotor As is previously mentioned, rotor of wind turbine represents a three-shovel system (Fig. 3.5) which rotates with angular velocity . Each shovel of the rotor is modeled as a beam with mass m, length l and moment of inertia 80 3 Discontinual Mass Variation Iz = ml2 3 . (3.284) Moment of inertia of the rotor is IS = ml2. (3.285) Angular momentum of the rotor is Lb = L = ml2 . (3.286) Dynamics of Rotor Separation Let us consider the case when a shovel is separated from the rotor. In Fig. 3.10, final body and model of the shovel separation is shown. If angular velocity of the separated shovel is 2 and velocity of mass centre is vS2, the angular momentum of the separated shovel is L2 = IS2 2 + l 2 mvS2. (3.287) Remainder rotor (unsymmetrical rotor with two shovels) has a new angular velocity 1 and moment of inertia IS1 = 2 3 ml2. (3.288) Angular momentum of the system, after separation, is the sum of the angular momentums of the remainder body and of the separated shovel La = IS1 1 + ( IS2 2 + l 2 mvS2 ) " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002277_978-3-319-27131-6-Figure9.6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002277_978-3-319-27131-6-Figure9.6-1.png", "caption": "Fig. 9.6 Residual unbalance vector Urotor on the rotor", "texts": [ "3 Two-Plane Low-Speed Balancing of a Rigid Rotor 191 FU,max \u00bc melim\u03a92 \u00bc Ulim\u03a92 \u00bc 45 10 3kg mm 1256 rad=s\u00f0 \u00de2 71 N Theoretically, the unbalances would be fully eliminated if the balancing masses were exactly added at the given balancing radii. In practice, the added mass has a tolerance of \u0394m, and the added mass scatters around the given balancing position in the circumferential and radial directions. Therefore, it always remains the small residual unbalances U1,res and U2,res at the balancing planes. The results in Fig. 9.6 show the directions of the residual unbalance vectors at the balancing planes in the rotor ends. Thus, the residual unbalance vector at the mass center of rotor G results as (cf. Fig. 9.6) Urotor \u00bc U1, res \u00fe U2, res \u00f09:14\u00de There are different types of noise in automotive electric machines, such as vibroacoustic (VA), aeroacoustic (AA), and electromagnetic acoustic (EMA) noises. First, VA noises are induced by unbalance whistle of the rotor (1 ), misalignment noise (2 ), loose stator stack, bearing noises, and gear noises [4]. Second, AA noises result from rotating noise and pressure pulsations [4]. Third, EMA noises consist of unbalanced magnetic pull (UMP) due to magnetic asymmetry, rotor eccentricity, and odd number of stator slots; cogging torque (CT) due to different permeances of the air gap between rotor and stator (causing torque pulsations and current ripples), inappropriate shapes of stator slots, unsuitable shapes of electric rotors, and improper combinations of stator slots and rotor poles; and non-sinusoidal current noises using pulse-width modulations (PWM) [5]" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002715_j.neunet.2020.10.005-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002715_j.neunet.2020.10.005-Figure4-1.png", "caption": "Fig. 4. World coordinate system and local coordinate systems in task space.", "texts": [ " The relationship between the actuator space and the configuration space of the ith section of the robot can be formulated as: \u03d5i = arctan (\u221a 3(ui2 + ui3 \u2212 2ui1) 3(ui2 \u2212 ui3) ) (1) i = 2 \u221a u2 i1 + u2 i2 + u2 i3 \u2212 ui1ui2 \u2212 ui1ui3 \u2212 ui2ui3 d(ui1 + ui2 + ui3) (2) i = ui1 + ui2 + ui3 3 (3) where d is the distance from the center of a section to the center of the actuator as illustrated in Fig. 2. The mapping findependent from configuration space to task space s independent of the designs of robots and the methods to ctuate them. It is applicable to all robots that can be approxmated as piecewise constant curvature arcs. In task space, a orld coordinate system Cw and some local coordinate systems are introduced as shown in Fig. 4. The position of the end-effector, which can be represented by a column vector pe \u2208 R3, is fixed and known relative to the coordinate system C3. However, we need to know the position relative to the world coordinate system in order to control the motion of the end-effector. This involves the transformation of the end-effector position relative to different coordinate systems. The relative pose of coordinate systems Ci and Ci+1 can be characterized by a transformation matrix T i+1 i \u2208 R4\u00d74 which consists of a rotation matrix Ri+1 and a translation i v R w T O T w[ w T I a u e n n T m p k i t o m 3 t c 3 f i & w o e f e a ( p F u p i F d F i w ector Oi+1 i " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001328_j.renene.2014.03.036-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001328_j.renene.2014.03.036-Figure4-1.png", "caption": "Fig. 4. Three point mounting configuration.", "texts": [ " In the market several drive train layout configurations are available to constrain the gearbox in the nacelle in order to minimize the effect of the non-torque loading originating from the rotor. This paper focusses on three configurations: the three point mounting, the two bearing configuration or four point mounting and the hydraulic suspension mechanism. In the three point mounting (TPM) configuration, which is the most common in the market, the main shaft is supported at one side by amain bearing and connected at the other side to the planet carrier of the gearbox. A torque arm on two bushings interfaces the gearbox and the nacelle. Fig. 4 shows the different parts of the system. In the TPM all non-torque forces are theoretically transferred to the main bearing on the one side and the interface consisting of the planet carrier, planet carrier bearings, gearbox housing and bushings on the other side. One of the reasons why this design is so popular in the market is that it does not result in a hyperstatic configuration. 3.2. Two bearing configuration The main difference between the TPM and the two bearing configuration (TBC) is the use of a second smaller main bearing to support the main shaft of the turbine at the gearbox side" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001290_j.ces.2015.08.056-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001290_j.ces.2015.08.056-Figure3-1.png", "caption": "Fig. 3. Scheme of the free fall apparatus (Mueller et al., 2015).", "texts": [ " The binderless \u03b3-Al2O3 granules (produced by Sasol Germany GmbH) consist of approximately 98% of \u03b3-Al2O3 and a small content of water as well as traces of carbon, iron-III-oxide, titanium oxide, sodium oxide and silicon oxide (http://www.sasoltechdata. com/alumina_group.asp). The synthetic zeolite 4A granules (produced by Chemiewerk Bad K\u00f6stritz GmbH) consist of approximately 83 ma% zeolite primary particles (Na2O\u2219Al2O3\u22192SiO2\u2219nH2O) and 17 ma% attapulgite binder content (Mg,Al)2Si4O10(OH) 4(H2O) (Mueller et al., 2015). The measured (most relevant) physical and granulometric characteristics of the material samples in the dry state are summarized in Table 1. The free fall tests had been performed using a home-built test rig, see Fig. 3. Fig. 4 presents the schematic representation of the particle movement during the conducted tests. At the beginning of each free fall test, one single particle is fixed using vacuum tweezers before being dropped so that it starts to fall freely without any initial velocity v0\u00bc0 and rotation \u03c90\u00bc0. Different drop heights have been used to ensure different impact velocities in the range 0.3 m/sovAo2.5 m/s. The vacuum-held particle (granule or glass bead) was released from the desired drop height h1, such that it falls freely until impacting on the impact plate (glass plates of different thicknesses H, see Table 2) arranged orthogonal to the trajectory of the falling particle" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000794_s0076-5392(08)62099-8-Figure8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000794_s0076-5392(08)62099-8-Figure8-1.png", "caption": "FIG. 8. Ellipses with axes in identical senses.", "texts": [ "19) now specifies the characteristic velocity for the transfer maneuver. Denoting this by yl'zX and writing it will be found that in case I ( a + a') 112 (a' + b ) and in case I1 a, b, a', b' are the reciprocals of the distances from the center of attraction of the four apses on the terminals. 11. Transfer Between Elliptical Orbits 345 Suppose, first, that the axes of the terminals are directed in the same sense. Then there are two possibilities: (a) the orbits intersect or (b) the orbits do not intersect. These alternative possibilities are illustrated in Fig. 8. The initial orbit will be taken to be that marked \u201cA\u201d and the final orbit to be that marked \u201cB\u201d; reversal of the roles of the two orbits or of the senses of both their axes are trivial modifications which do not lead to any essentially distinct possibilities. The transfer orbits corresponding to the cases I and I1 solutions are also indicated in the figure. In Fig. 8a, it is clear that a > b, a\u2019 < b\u2019, a < d1 b < b\u2019. Employing 346 Derek F. Lawden these inequalities to resolve the ambiguous senses of the differences in Eqs. (11.91) and (11.92), it will be found upon subtraction that 1 v2 - (Xl - X ? ) = (a\u2019 + b)\u201d* - (a\u2019 + a)\u2019/2 - (b\u2019 + b)\u201d2 + (b\u2019 + a)\u201d2 = f(a\u2019, a, b ) - f@\u2019, a, b ) (11.93) where f(x, a, 6) = (z + b)1/2 - (z + a)l/Z (11.94) It is shown in the Appendix a t the end of this chapter that, when a > b, f is an increasing function of z. It accordingly follows from Eq. (11.93) that, since a\u2018 < b\u2019, then XI - Xz < 0. Thus XI < Xz and in Fig. 8a the transfer orbit I is the more economical. In Fig. 8b the following inequalit,ies are valid: a > b, a\u2019 > b\u2019, a < a\u2018, b < b\u2019. From Eqs. (11.91) and (11.92), it now follows that a\u2019 - b a\u2019 - a b\u2019 - b b\u2018 - a + - - 1 - (XI - X , ) = a (a\u2019 + b)1/2 (a\u2019 + . ) l \u2019Z (b\u2019 + b)\u201d2 (b\u2019 + a)1/2 (11.95) (11.96) It is also shown in the Appendix that, when a > 6, the graph of g(z, a, b ) for 2 2 b has the form indicated in Fig. 9, i.e., g first increases monotonically as 2 increases to the value E and then decreases monotonically so that g + 0 as z + m. It is also clear that g(a , a , b ) = g ( b , a , b ) = G" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000560_j.mechmachtheory.2013.06.001-Figure13-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000560_j.mechmachtheory.2013.06.001-Figure13-1.png", "caption": "Fig. 13. Effect of joint-error (joint-1 in Fig. 12). a) Displaced link-axis. b) Tilted link-axis.", "texts": [ " p \u00bc A1A2A3p0 \u00bc c\u03b81 \u2212s\u03b81 0 0 s\u03b81 c\u03b81 0 0 0 0 1 0 0 0 0 1 0 BB@ 1 CCA 1 0 0 0 0 c\u03b82 \u2212s\u03b82 r1s\u03b82 0 s\u03b82 c\u03b82 r1 1\u2212c\u03b82\u00f0 \u00de 0 0 0 1 0 BB@ 1 CCA c\u03b83 0 s\u03b83 \u2212r1s\u03b83 0 1 0 0 \u2212s\u03b83 0 c\u03b83 r1 1\u2212c\u03b83\u00f0 \u00de 0 0 0 1 0 BB@ 1 CCA r3 r2 r1 1 0 BB@ 1 CCA \u00bc r3 c\u03b81c\u03b83\u2212s\u03b81s\u03b82s\u03b83\u00f0 \u00de\u2212r2s\u03b81c\u03b82 r3 s\u03b81c\u03b83 \u00fe c\u03b81s\u03b82s\u03b83\u00f0 \u00de \u00fe r2c\u03b81c\u03b82 r1 \u00fe r2s\u03b82\u2212r3c\u03b82s\u03b83 1 0 BB@ 1 CCA: \u00f023\u00de Transformation matrices A1, A2 and A3 are obtained from the Rodrigues parameters given in Table 8. The manufacturing errors influence the position of CP in the given spatial mechanism. Similar to the planar mechanisms, clearance between a link (pin) and a bush (hole) introduces error in spatial mechanism. When the link contacts the bush along its generator as shown in Fig. 13(a), axis of the link will be displaced by a distance ra which can be represented by a virtual link. Considering all such positions, it can be seen that the other end of the virtual link traces a circular path whose radius is ra. In practice, the link may assume an inclined position as in Fig. 13(b) due to forces acting on it. In this case, contact with the bush occurs at diametrically opposite points and the other end of the link traces a circular path whose size is larger than ra. Therefore, in the present work, axis tilt is taken for analyzing the errors introduced in the spatial mechanism. Accordingly two virtual links are considered as shown in Fig. 13(b) and angular position of bottom virtual link is taken to vary from 0 to 360\u00b0 with top virtual link lagging behind by 180\u00b0. Manufacturing errors may result in axial clearance whose effect can be modeled as a virtual prismatic joint along the link length, similar to the link length error in planar mechanism. However, this effect is not included in this work for sake of simplicity. Nominal surface traced by CP is obtained using Eq. (23) by varying \u03b81 and \u03b83 between \u221220\u00b0 and +20\u00b0 and \u03b82 is taken to be zero for sake of simplicity" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001645_tie.2017.2786205-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001645_tie.2017.2786205-Figure5-1.png", "caption": "Fig. 5. Schematic of operation principle of the proposed PPHEFSLM for aligned structure with only PM excitation. (a) d-axis position. (b) q-axis position. (c) \u2013d-axis position. (d) \u2013q-axis position.", "texts": [ " Without consideration of asymmetry between phases of the linear machine as well as high-order harmonics of phase fluxlinkage, d-q model of the proposed PP-HEFSLMs under constant phase amplitude coordinate transformation can be given as follows [26]: 0 0 0 0 3 / 2 0 fd d d m q q q f f fmf f ML I L I M L I (3) Where \ud835\udf11\ud835\udc51, \ud835\udf11\ud835\udc5e, \ud835\udf11\ud835\udc53 symbolize d- and q-axis flux-linkages, fluxlinkage of excitation windings, respectively; \ud835\udc3f\ud835\udc51 , \ud835\udc3f\ud835\udc5e , \ud835\udc3f\ud835\udc53 symbolize d- and q-axis self-inductances and self-inductance of excitation windings, respectively; \ud835\udc40\ud835\udc53 denotes mutual inductance between excitation windings and d-axis armature windings. \ud835\udc3c\ud835\udc51 , \ud835\udc3c\ud835\udc5e denote d- and q-axis currents; \ud835\udf11\ud835\udc5a , \ud835\udf11\ud835\udc53\ud835\udc5a represent flux-linkages of armature d-axis and excitation windings induced by PMs. HEFSLMs can be expressed as: 3 ( )m q f f q d q d q s F I M I I L L I I (4) Where \ud835\udf0f\ud835\udc60 is secondary pitch and \ud835\udc3c\ud835\udc53 is excitation current. For the proposed PP-HEFSLMs with aligned structure, PM flux paths are exhibited in Fig. 5. Similar to its unaligned counterpart, armature coil flux varies with secondary position as well. Nevertheless, armature coil flux is inherently unipolar. Compared with unaligned structure, the aligned one has small open-circuit phase flux-linkage due to unipolar armature coil flux. In other words, the thrust force constant for aligned structure is smaller than that of unaligned structure, indicating inherently larger thrust force density for unaligned structure. IV. KEY PARAMETERS INVESTIGATION Traditional single-variable optimization method has been used extensively in optimizing PMLM since it is very apparent to show impacts of parameters on thrust force performance" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001968_1.3662549-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001968_1.3662549-Figure1-1.png", "caption": "Fig. 1 Diagram of gear testing machine", "texts": [ " The combination of the two is essential and an accurate solution of the problem is now the outstanding question in the theoiy of gear lubrication. The Russian work, while a useful pointer, contains a number of approximations which limits its accuracy. Apparatus The apparatus is a conventional 5-inch-centers back-to-back gear-testing machine. The loading gears are mounted in a framework which can swing around the axis of one of the shafts. The static torque applied to this frame is transferred by the epicyclic action of the gear in the swinging frame into a circulating torque in the s}rstem, Fig. 1. Two sets of straight spur gears were used. The first set consisted of 19/40 teeth and the second 30/30, the high-speed shaft being directfy coupled to a 2920-rpm 6-hp motor. The gears in both cases were to BSS proportions, with a pressure angle of 22 V2 deg for the 19/40 set and 20 deg for the 30/30 and an addendum of 0.3183 CP and dedendum of 0.4583 CP. The 19/40 gears were of EN34 2 per cent Ni-Mo, case-hardened Journal of Basic Engineering M A R C H 1 9 6 0 / 29 Copyright \u00a9 1960 by ASME Downloaded From: http://fluidsengineering" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000074_10402004.2010.551805-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000074_10402004.2010.551805-Figure5-1.png", "caption": "Fig. 5\u2014Ball angular position and race azimuth.", "texts": [ " [1a] and [1b] may be reduced to two simultaneous nonlinear algebraic equations in terms of the axial and radial displacements, which may be solved by iterative procedures. Similarly, the equilibrium equations for the race are written as: n\u2211 i=1 Qi cos \u03b1i + Fx = 0 [2a] n\u2211 i=1 Qi cos \u03b1i cos\u03c8i + Fr = 0 [2b] where n is the number of rolling elements and Fx and Fr are the applied axial and radial forces, respectively, and \u03c8 is the azimuth angle, which defines the angular position of the rolling element around the bearings, as illustrated in Fig. 5. Once again, Eqs. [2a] and [2b] may be reduced to two algebraic equations in terms of relative axial and radial position of the race, which may be solved by an iterative procedure. Thus, the force equilibrium solution is a two-step process: first, a race position is assumed and the ball equilibrium is solved; race po- sition is then corrected to satisfy the equilibrium equations and ball equilibrium is repeated. The iterative process continues until the race equilibrium equations converge. Such a procedure has a numerical advantage over solving the ball and race equilibrium simultaneously, which, depending on the number of balls in the bearing, may require inversion of a large matrix at each iterative step" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002956_tte.2020.2997607-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002956_tte.2020.2997607-Figure1-1.png", "caption": "Fig. 1. Topology of proposed DRMWMs.", "texts": [ "org/publications_standards/publications/rights/index.html for more information. IEEE TRANSACTIONS ON TRANSPORTATION ELECTRIFICATION 2 states of HEA are elaborated. Then, an analytical model with consideration of saturation effect are constructed to calculate the electromagnetic performances of DRMWMs. Finally, a prototype has been manufactured and tested to validate the effectiveness of the design and proposed analytical model. II. SYSTEM CONFIGURATION The machine topology of DRMWMs is shown in Fig. 1. It can be seen that there are PMs mounted on the outer surface of inner rotor, and modulator pieces and spoke-type PMs are arranged alternatively on the circumferential direction. There are two types of windings on the stator, namely PM windings referring to PM synchronous machine part, and magnetic gear (MG) windings referring to magnetic gear part. The PM windings together with the spoke-type PMs on the outer rotor forms a PM synchronous machine. The MG windings together with the PMs on the inner rotor and the modulator pieces form a MGM" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002460_j.mechmachtheory.2018.03.018-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002460_j.mechmachtheory.2018.03.018-Figure3-1.png", "caption": "Fig. 3. Configuration of the7R 6-DOF robot with spherical wrist.", "texts": [ " A configuration is singular when the rank of the Jacobian matrix decreases. For the 7R 6-DOF robot, singular configurations are defined as rank (J ) < 6 (2) From Eq. (2) , the singular configurations can be identified by obtaining the analytical expression that causes the determinant of the Jacobian matrix to be zero, as expressed in Eq. (3) . However, this analytical expression is too complicated because of the 4R 3-DOF non-spherical wrist. In order to simplify the analysis, firstly a fixed virtual wrist center is introduced [6] as shown in Fig. 3 , resulting in a 7R 6-DOF robot with spherical wrist. The corresponding D-H parameters are expressed as Eq. (4) . det (J ) = 0 (3) d \u2032 4 = d 4 + d 5 cos (\u03b2) , d \u2032 5 = d \u2032 6 = 0 , d \u2032 7 = d 7 + d 6 cos (\u03b2) (4) It is notable that the treatment above would introduce an error on the position of EE, because the fixed wrist center does not exist practically. And the maximum error could be expressed by Eq. (5) . It is obvious that the smaller parameters d 5 and \u03b2 are, the smaller the error will be. As a practical example, the painting robot under study uses \u03b2 = 35 \u25e6 and d 5 which are small enough to validate the rationality [6] " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002720_s11837-020-04433-9-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002720_s11837-020-04433-9-Figure2-1.png", "caption": "Fig. 2. (a) Tensile specimen cut from the sample; (b) dimensions of the tensile specimen (all dimensions in mm, 1.6 mm thickness).", "texts": [ " Microstructure was characterized using an optical microscope (Keyence VHX-7000) and scanning electron microscope (Quanta, FEI) equipped with electron backscatter diffraction (EBSD). Uniaxial tensile tests were performed for the as-printed and heat-treated specimens at room temperature using an Instron universal testing machine. A constant strain rate of 0.001/s was applied during the tensile tests. The tensile specimens were prepared from the printed builds using electrical discharge machining, as seen in Fig. 2a. The tensile loading direction is parallel to the building direction (z-axis). Two tensile specimens were tested from each condition. Zhang, McMurtrey, L. Wang, O\u2019Brien, Shiau, Y. Wang, Scott, Ren, and Sun Synchrotron x-ray diffraction (SXRD) technique was used to measure the residual strain and stress in the as-printed and heat-treated samples. SXRD analysis was performed at beamline 11-ID-C at the Advanced Photon Source (APS) in Argonne National Laboratory. The wavelength of the beam was 0.1173 A\u030a with a beam spot size of 500 lm 9 500 lm" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001791_j.mechmachtheory.2016.05.001-Figure2.4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001791_j.mechmachtheory.2016.05.001-Figure2.4-1.png", "caption": "Fig. 2.4. Sketch of UPU + SPR + UPR PM.", "texts": [ " Since the constrained torques in r1 and r3 are eliminated, r1 and r3 are converted into a SPR-type legs, and then the third KIM (3-SPR PM) (see Fig. 2.3) for the Exechon PM can be obtained from Eq. (7a). Some geometric constraints are satisfied for this PM as follows: Ri1\u22a5ri;Ri1\u2551a2o i \u00bc 1;3\u00f0 \u00de;R21\u2551a1a3;R21\u22a5r2: \u00f07b\u00de Since f1 = R12, it leads to J0;4 \u00fe t1 J0;5 h i v\u03c9 \u00bc f T4 dT 4 f T4 h i v\u03c9 \u00bc 0; f 4 \u00bc f 1;d4 \u00bc d1 \u00fe t1R11 \u00f08a\u00de here t1 is a scalar quantity, d4 = d1 + t1R11 denotes the vector from o to c1, c1 is a point on line R11. (see Fig. 2.4). It is easy to determine that \u00bd f T4 dT 4 f T4 in Eq. (8a) represents one constrained force which is parallel with R12 and passes through c1. Based on the properties of constrained wrenches and Eq. (8a), one UPU-type leg (see Fig. 2.4) which connects A1 to a1 can be determined. Some particular geometric constraints are existed in the UPU leg as follows: R11\u2551A1A3;R11\u22a5R12; r1\u22a5R12;R12\u2551R13;R13\u22a5R14;R14\u22a5m: \u00f08b\u00de From Eq. (8b), it is known that R11, R14 and r1 are coplanar, thus R11 and R14 intersect at c1. This particular configuration can exactly provide the constrained force which is parallel with R12 and passes through the point c1. By adding t1 times the fifth row to the fourth row of Eq. (3c), then by adding \u22121 times the eighth row to the fifth row of Eq. (3c), and combining with Eqs. (4b) and (8a), a novel velocity transmission equation can be derived as following: Vr \u00bc J4 v\u03c9 ;Vr \u00bc vr1 vr2 vr3 0 0 0 0 0 2 66666666664 3 77777777775 ; J4 \u00bc \u03b4T1 e1 \u03b41\u00f0 \u00deT \u03b4T2 e2 \u03b42\u00f0 \u00deT \u03b4T3 e3 \u03b43\u00f0 \u00deT f T4 d4 f 4\u00f0 \u00deT 0T 3 1 0T 3 1 f T2 d2 f 2\u00f0 \u00deT f T3 d3 f 3\u00f0 \u00deT 0T 3 1 R31 R32\u00f0 \u00deT 2 66666666666664 3 77777777777775 : \u00f08c\u00de From J4 and the properties of constrained wrenches, the fourth KIM (UPU + SPR + UPR PM) for the Exechon PM can be derived (see Fig. 2.4). Some geometric constraints are satisfied for this PM as follows: Ri1\u2551A1A3;Ri1\u22a5Ri2;Ri2\u22a5ri;Ri2\u2551Ri3 i \u00bc 1;3\u00f0 \u00de;R13\u22a5R14;R14\u22a5m;R33\u2551a2o;R21\u2551a1a3;R21\u22a5r2: \u00f08d\u00de 3.6. The fifth KIM for the Exechon PM: 2-UPU + SPR PM Using the same method for deriving Eq. (8a), it leads to J0;7 \u00fe t2 J0;8 h i v\u03c9 \u00bc f T5 dT 5 f T5 h i v\u03c9 \u00bc 0; f 5 \u00bc f 3;d5 \u00bc d3 \u00fe t2R31 \u00f09a\u00de here t2 is a scalar quantity, d5 = d3 + t2R31 denotes the vector from o to c2, c2 is a point on line R31(see Fig. 2.5). It is easy to determine that \u00bd f T5 dT 5 f T5 in Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002277_978-3-319-27131-6-Figure1.8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002277_978-3-319-27131-6-Figure1.8-1.png", "caption": "Fig. 1.8 Curvatures of the inner raceway of a ball bearing", "texts": [ " The curvatures of the ball (i\u00bc 1) in the orthogonal principle curvature planes ( j\u00bc 1, 2) are the same because the ball has a constant radius in any direction: \u03c111 \u00bc \u03c112 \u00bc 1 r11 \u00bc 1 r12 \u00bc 1 Dw=2\u00f0 \u00de \u00bc 2 Dw > 0 \u00f01:15\u00de Similarly, the curvatures of the cylindrical roller (i\u00bc 1) in the principle curvature planes ( j\u00bc 1, 2) are calculated as \u03c111 \u00bc 2 Dw > 0; \u03c112 \u00bc 0 \u00f01:16\u00de The curvatures of the inner raceway for ball and roller bearings (i\u00bc 2) in the orthogonal principle curvature planes ( j\u00bc 1, 2) are calculated using trigonometric relations of the bearing and Eqs. 1.9 and 1.12 as (s. Fig. 1.8) \u03c121 \u00bc 1 r21 \u00bc 1 Dpw 2 cos \u03b1 Dw 2 \u00bc 2 Dw Dpw Dw cos \u03b1 1 > 0; \u03c122 \u00bc 1 r22 \u00bc 1 Dw\u03bai < 0 f or ball bearings; \u03c122 \u00bc 1 r22 \u00bc 0 f or roller bearings \u00f01:17\u00de The curvatures of the outer raceway for ball and roller bearings (i\u00bc 2) in the orthogonal principle curvature planes ( j\u00bc 1, 2) are calculated using trigonometric relations of the bearing and Eqs. 1.9 and 1.12 as (s. Fig. 1.9) 1.4 Curvatures of Bearings 11 12 1 Fundamentals of Rolling Element Bearings There are two curvature sums for each ball and roller bearing according to Eqs" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003110_j.mechmachtheory.2020.104122-Figure8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003110_j.mechmachtheory.2020.104122-Figure8-1.png", "caption": "Fig. 8. Displacement increment along the FS reference line with misalignment in planar model.", "texts": [ " 5 cos (arcsin ( J tan \u03b13 (1 \u2212 J 2 ) 0 . 5 ) + \u03b8m ) , J) T (22a) { b 14 = e 2 sin ( \u03b11 + \u03b8m ) b 24 = e 2 cos ( \u03b11 + \u03b8m ) b 34 = 0 (22b) where \u23a7 \u23aa \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23aa \u23a9 H = ( 1 + ( sin \u03b12 tan \u03b13 cos \u03b12 + tan \u03b12 sin \u03b12 ) 2 + ( tan \u03b13 1+ tan 2 \u03b12 ) 2 )\u22120 . 5 I = ( 1 \u2212 ( H tan \u03b13 1+ tan 2 \u03b12 )2 )0 . 5 J = 1 ( tan 2 \u03b1 + tan 2 \u03b1 +1) 0 . 5 (22c) 3 2 Thus, for a clockwise input angle \u03b8m , the corresponding radial displacement can be calculated by \u03b4( \u03b8m ) = max (\u2223\u2223r Q \u2223\u2223\u2212 L W ) , Q \u2208 l WG ( \u03b8m ) (23) As shown in Fig. 8 , if the WG has a misalignment, the meshing point P has a displacement along the CS tooth profile. The angle \u03c8 can be approximated as \u03c8 = \u03b4 tan \u03b1 R (24) CS where \u03b4 is radial displacement, \u03b1 is pressure angle. The equivalent displacement (arc length l AP ) of meshing point along deformed FS reference circle can be expressed as l AP = \u222b \u03c8 0 \u221a \u03c1( \u03b8 ) 2 + [ d\u03c1( \u03b8 ) d\u03b8 ]2 d\u03b8 (25) where \u03c1( \u03b8 ) denotes the polar representation of the deformed FS reference circle. According to the pure kinematic error model in Section 2" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002441_9781119509875-Figure14.1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002441_9781119509875-Figure14.1-1.png", "caption": "Figure 14.1 Two-link inverted pendulum model in the sagittal plane", "texts": [ " In conclusion, if point P is inside the surface defined by BoS, all moments and forces exerted by the body on the ankle are compensated, which necessarily leads to a dynamic balance [1, 2, 10-12]. Combined strategy applies to both ankle and hip strategy to protect the system against external disturbances. We specify that for the dynamic walking robots CoG (or CoM) can be outside of the BoS, but the ZMP, cannot. This chapter uses a two-link inverted pendulum model in the sagittal plane, with actuator at the hip joint - see Figure 14.1. For analyzing the balance control for a biped walking model, can be expressed as one or multi-dimensional inverted pendulum chain. Thus the walking biped can be modeled with The Walking Robot Equilibrium Recovery 181 one-dimensional inverted pendulum [3-5], in this case the system will be described only by-one variable: the angle of the ankle joint. This model is not sufficient to completely explain balance properties, even for standing balance. In many studies is used the double inverted pendulum model [3-5, 13-15]" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003369_j.mechmachtheory.2021.104386-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003369_j.mechmachtheory.2021.104386-Figure5-1.png", "caption": "Fig. 5. Contact line of helical gear and sliced helical gear.", "texts": [ " In this study, the parametric model of a helical gear using the virtual rack is developed to obtain the accurate gear profile. Therefore, if the geometry parameters of a helical gear set are defined and the mesh position is calculated, the exact tooth thickness not only on the involute profile but also on the trochoidal root profile. In this study, an analytical model of helical gears is developed using the slice theory that assumes a helical gear as a combination of several spur gear slices with a small face width. As shown in Fig. 5 , since each slice is a spur gear, the contact line appears parallel to the axis of the face width, and the mesh stiffness can be calculated using the formula for spur gear. It is assumed that the mesh stiffness of each slice is not affected by the mesh stiffness of the neighboring slices. This assumption causes some errors in that the supporting stiffness of other slices affects the mesh stiffness of the slices at both ends of the gear [26] . However, owing to the ease of calculation, the slice theory has been widely used to calculate TVMS using an analytical method [25\u201331] " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001510_j.mechmachtheory.2014.01.014-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001510_j.mechmachtheory.2014.01.014-Figure3-1.png", "caption": "Fig. 3. Curved beam with a rectangular cross section.", "texts": [ " Based on the above analysis, compared with the conventional cam WG, the contact force of the tooth rim from the rollers can be regarded as a concentrated force at the contact position. Therefore, the four-roller WG is considered here to illustrate the principles of analysis and calculation process of the deformation curves and the internal forces of FS without loss of generality. As mentioned above, the FS is a thin-walled cylindrical cup; therefore, the FS structure is usually described by the cylindrical shell model, as shown in Fig. 3a. The length of the neutral line of the FS is assumed to remain constant, which corresponds to neglecting the circumferential strain in the neutral line of the FS. The deformation and the internal forces are obtained using the semi-moment theory of shells. In practice, there is a non-zero circumferential strain in the neutral line of the FS. The stretch of the tooth rim of the FS under the action of the WG can be obtained by accounting for the circumferential strain: the curved beam theory is used to model the circumferential force and the bending moment in this study. Therefore, an elemental rim is cut from the tooth cylindrical shell, perpendicular to the FS axis and with a rectangular cross section, as shown in Fig. 3c. The internal force distribution and the deformation of the FS tooth rim under the action of the four-roller WG are investigated by using the curved beam theory: the resulting deformation is shown in Fig. 2. The rim deflection is modeled by differential equations using the bending theory for a thin beam. The deflection equation is obtained for a rim of uniform thickness h, as shown in Fig. 3b. Within the curved beam theory, three types of internal forces (the bending moment, the circumferential force and the shear force) are generated in the FS tooth rim in reaction to the contact force from the four-roller WG. The bending moment is the largest internal force in the FS tooth rim, and the bending stress caused by the bending moment is the primary determinant of the FS fatigue strength. The circumferential strain is induced by the circumferential force. The stretch in the neutral line of the tooth rim is calculated from the circumferential strain, and this stretch of the neutral line affects the HD engagement" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000155_tie.2011.2157294-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000155_tie.2011.2157294-Figure4-1.png", "caption": "Fig. 4. Two-dimensional half model of the generator cross section.", "texts": [ " The time-stepping FE analysis method requires a complete machine model to be built. The model includes a 2-D generator cross section to be coupled with a set of external circuit components. The latter is used to account for the end effects which cannot be included in the 2-D model (e.g., stator and rotor end windings) and for the electrical sources or loads which are connected to stator and field terminals during machine operation. In this instance, the cross-sectional model of the generator shown in Fig. 4 is imported in the Ansoft/Maxwell environment and characterized with the electrical conductivity and nonlinear B\u2013H curves provided by raw-material suppliers. The external circuit elements shown in Fig. 5 are then linked to the machine 2-D model to account for resistance and endwinding effects. In particular, each of the inductors LU , LV , and LW in Fig. 5 is linked to the set of coils which constitute stator phases U , V , and W , respectively; R is the stator phase resistance, and LE is the stator end-winding leakage inductance (computed as per Section IV-A)" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003054_0954405420911768-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003054_0954405420911768-Figure1-1.png", "caption": "Figure 1. Schematic representation of hatch spacing, vector size and spot size.", "texts": [ " In order to control the part porosity in LPBF and, consequently, its density, the processing parameters, such as energy density, hatch spacing, layer thickness, scan speed, spot size, vector size and powder particle size, must be optimized. LPBF manufacturing has several processing parameters which influence the outcome of the final part. For instance, the laser scanning strategy through the individual cross-sections of the part plays a very important role on the mechanical properties and density, as stated by Hitzler et al.7 These parameters include laser power, hatch spacing, scan speed and spot size, as shown in Figure 1. Nonetheless, there are also other processing parameters which may influence the properties of the part such as powder particle size or layer thickness. The combination of four of the mentioned processing parameters allows us to determine the utilized energy density Ed (J/mm3) according to equation (1), where P is the laser power (W), d the hatch spacing (mm), h layer thickness (mm) and v the scan speed (mm/s) Ed = P dhv \u00f01\u00de Previous work regarding the influence of LPBF processing parameters on 316L stainless steel density of the parts was initially performed without achieving full melting of the metal powder by using a relatively low laser power" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001924_j.conengprac.2018.11.016-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001924_j.conengprac.2018.11.016-Figure1-1.png", "caption": "Fig. 1. Geometry of flexible air-breathing hypersonic vehicle.", "texts": [ " Finally, the tracking control objective of FAHV will be presented. FAHV adopts the design of body coupling structure to enhance its propulsion efficiency. The complex dynamics and aerodynamic characteristics of the hypersonic vehicle make it difficult to build a complete and accurate mathematical model with six degrees of freedom. Concerning the factors above, a simplified longitudinal dynamics of FAHV is introduced in this paper where the flexible modes are reflected through moments and forces. The geometric sketch of the vehicle is depicted in Fig. 1, and the longitudinal dynamics for FAHV is composed of five rigid-body states [\ud835\udc49 , \u210e, \ud835\udefe, \ud835\udefc,\ud835\udc44]\ud835\udc47 and six flexible states \ud835\udf3c = [\ud835\udf021, ?\u0307?1, \ud835\udf022, ?\u0307?2, \ud835\udf023, ?\u0307?3]\ud835\udc47 . The nominal dynamic model of FAHV without uncertainties and disturbances is described as (Fiorentini, Serrani, Bolender, & Doman, 2009) ?\u0307? = (\ud835\udc47 cos \ud835\udefc \u2212\ud835\udc37)\u2215\ud835\udc5a \u2212 \ud835\udc54 sin \ud835\udefe (1) \u210e\u0307 = \ud835\udc49 sin \ud835\udefe (2) ?\u0307? = (\ud835\udc3f + \ud835\udc47 sin \ud835\udefc)\u2215(\ud835\udc5a\ud835\udc49 ) \u2212 \ud835\udc54 cos \ud835\udefe\u2215\ud835\udc49 (3) ?\u0307? = \ud835\udc44 \u2212 ?\u0307? (4) ?\u0307? = \ud835\udc40\ud835\udc66\ud835\udc66\u2215\ud835\udc3c\ud835\udc66\ud835\udc66 (5) ?\u0308?\ud835\udc56 = \u22122\ud835\udf01\ud835\udc56?\u0304?\ud835\udc56?\u0307?\ud835\udc56 \u2212 ?\u0304?2 \ud835\udc56 \ud835\udf02\ud835\udc56 +\ud835\udc41\ud835\udc56, \ud835\udc56 = 1, 2, 3 (6) where \ud835\udc49 , \u210e, \ud835\udefe, \ud835\udefc, and \ud835\udc44 denote velocity, altitude, flight path angle (FPA), angle of attack (AOA), and pith rate respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003603_jestpe.2021.3065997-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003603_jestpe.2021.3065997-Figure1-1.png", "caption": "Fig. 1. Four types of machine for comparison. (a)SPMV. (b)SAPMV. (c)SAPMVB. (d)Proposed topology.", "texts": [ " Later, it is compared with the surface mounted PMV machine, the spoke array PMV machine, and the spoke array PMV machine with alternative bridges. In section IV, the rotor of the proposed machine is designed and machine performances are concluded in section V. At last, experimental results of the machine prototype are shown in section VI before the conclusion is drawn. II. PROBLEMS IN EXISTING PM VERNIER MACHINE In this section, three kinds of existing PMV machine are analyzed. Then, a new kind of claw pole machine is proposed to solve the problem. Basic structure of the four machines are shown in Fig.1. The surface-mounted PMV machine is shown in Fig. 1(a). With stator opening slots, flux created in rotor is modulated into three magnetic field components with pole-pair number of Pr, Z-Pr and Z+Pr. This is the simplest flux modulation machine. However, the air gap flux density of this machine is limited. When we try to increase its no-load flux density by adding magnets thickness, its torque capacity may even decrease since the flux modulation effect is weakened. Lots of researches show that spoke array permanent magnetic machine has high excitation ability" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001215_b978-0-08-100433-3.00006-3-Figure6.7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001215_b978-0-08-100433-3.00006-3-Figure6.7-1.png", "caption": "Figure 6.7 Schematic illustration of the laminated object manufacturing process. AM, additive manufacturing.", "texts": [ " During fabrication, excessive material is sliced and cubed to facilitate manual extraction of the part. Still, post-processing is time intensive and often requires special tools, rendering the production of filigree structures inadequate for this technology. Because LOM is a hybrid between additive and subtractive processing methods, a relatively low material yield is achieved. Green ceramic tapes are typically used for LOM of ceramics; hence, ceramic parts are subject to post-processing steps such as debinding and sintering. Fig. 6.7 gives a schematic illustration of the LOM process. The first investigations of LOM of complex-shaped ceramics were conducted by Griffin et al. [38] using Al2O3 tapes as the raw material; they achieved densities ofw99% after post-processing. The mechanical properties are comparable to those of conventionally pressed Al2O3 ceramics, showing a flexural strength of w310 MPa, a Vickers hardness of 20.1 GPa, and a fracture toughness ofw4 MPa Om, while having an overall shrinkage of 14.1% [38]. Investigations into other materials include the manufacturing of ZrO2 and Al2O3e ZrO2 compounds [39], silicates such as SiC [40] and ceramic composites such as Si/ SiC [41]" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003348_j.addma.2021.101930-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003348_j.addma.2021.101930-Figure4-1.png", "caption": "Fig. 4. One exemplary section of line based notch root radii measurement.", "texts": [ " Additive Manufacturing 40 (2021) 101930 In order to utilize an adapted concept based on Peterson [42], alongside notch-like surface feature depth, the notch root radius needs to be determined. Additively manufactured structures have shown recurring surface texture in terms of valley radii, compare [45]. The repeatability of the layer by layer fusion process may explain this regularity. This uniformity allows to measure radii on a global scale and line based method, as described in Section 1.2. In terms of the most damaging effect, line based evaluation is conducted in axial (loading) direction of the specimen, as shown in Fig. 4. Limitations come with notch radii converging zero, as optical capturing and subsequent evaluation may not be satisfyingly possible in terms of characterization of notch geometry. Furthermore, regarding defects resembling crack shapes, fracture mechanical concepts are well suited for fatigue analysis [12]. The same three-dimensional recordings of the surface texture which are used for evaluating roughness parameters are utilized for notch root radii measurements to negate possible influencing factors by capturing and magnification differences" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003282_j.mtcomm.2021.102241-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003282_j.mtcomm.2021.102241-Figure2-1.png", "caption": "Fig. 2. Experimental setup, highlighting different origins of ejecta and ejecta collection area.", "texts": [ " the measured accumulated results underrate any changes (in principle a factor of two per cycle, in a progressive manner, because of the addition of 50 % virgin powder) compared to isolated recycling. Henceforth, the term \u201crecycling\u201d refers to the recycling procedure described in Fig. 1. The following parameters were kept constant throughout the experiment: 250 W nominal laser power, 3 m/min scanning speed, 100 \u03bcm powder layer thickness. The argon gas tube with a diameter of 20 mm and approximately 18 L/min flow rate was placed locally above the powder bed to prevent material oxidation and remove spatters and other ejecta from the processing area. The experimental setup can be seen in Fig. 2. In general, process parameters and conditions vary depending on the machine supplier. Commercial LPBF systems have a higher scanning speed than the value used in this study and the process is carried out in a chamber filled with inert gas. However, the trends and phenomena identified in this work are still relevant to industrial LPBF. T. Fedina et al. Materials Today Communications 27 (2021) 102241 A stainless steel sheet (150 \u00d7 250 \u00d7 2 mm) was placed behind the powder bed to collect spatters ejected from the melt pool or entrained particles swept away by the gas flow (Fig. 2). Normally, the ejection trajectories vary depending on the parameters and conditions applied; however, it was assumed that most of the ejecta travelled in the direction of the shielding gas flow (opposite to the laser scanning direction). The ejecta that had landed on the ejecta collection area were collected, and the mass of these ejecta (the amount of spatters and entrained particles generated during the production of 60 single tracks) was measured after each recycle. The ejecta mass measurement was performed using a digital scale with a precision of \u00b11 mg", " Materials Today Communications 27 (2021) 102241 In this study, the term \u201cspatter\u201d only refers to metal droplets ejected from the melt pool. Powder particles entrained in the vapor plume will be referred to entrained particles or ejecta. However, the word \u201cejecta\u201d will be used to refer to both spatter and entrained powder particles. This section describes ejecta formation, origin and morphology based on the data obtained during the experiments. SEM and HSI images were used to produce and verify the results. During this study, the ejecta were collected from the ejecta collection area (Fig. 2) for further evaluation and measurement. These data allowed the creation of a classification and mapping system of all the variations of ejecta type. Fig. 5 describes the origin, appearance and landing areas of ejecta in LPBF. Recoil driven spatter is ejected directly from the melt pool due to recoil pressure acting on the surface of the molten material. The ejection is performed when the droplet acquires sufficient energy to overcome the surface tension of the melt pool. This type of ejecta usually has a near spherical shape as it undergoes a similar cooling regime to that experienced during gas atomization" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000456_tmag.2012.2212909-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000456_tmag.2012.2212909-Figure2-1.png", "caption": "Fig. 2. Maxwell\u2019s coils.", "texts": [ " Thus, the mutual inductance and the magnetic force between two treated coils were obtained in a quasi-analytic form for all possible cases. The only terms that must be evaluated numeri- cally are , , and whose kernels are a well-behaved and continuous function over the whole interval of integration. In this paper, we used in the Matlab programming Gaussian integration [33] to solve numerically these integrals. In view of validating the formulas presented above, we used the filament method, which requires subdividing the coils into meshes of filamentary coils (Maxwell\u2019s coils), as shown in Fig. 2. Using the analytic solutions for Maxwell\u2019s coils and superposition, we can easily retrieve the mutual inductance and the force between the coils. The required analytic formulas are [1]\u2013[3] (9) (10) where and are the currents in each coil. Let us consider a subdivision of the coils in elementary coils (see Fig. 3). Each cell in these coils contains one filament, and the line current density in the coil is assumed to be uniform, so that the filament currents are all equal. The mutual inductance and the magnetic force between the coils are given by [12] (11) (12) where To verify the validity of the new formulas, we apply it to the following set of examples" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001791_j.mechmachtheory.2016.05.001-Figure3.3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001791_j.mechmachtheory.2016.05.001-Figure3.3-1.png", "caption": "Fig. 3.3. The constrained force/torque situation of UPU leg.", "texts": [ " (14b), Tp1,2 can be expressed as following: Tpi;2 \u00bc spi;2Tpi; spi;2 \u00bc \u03c4i \u03b4i Ri2\u00f0 \u00de \u00bc Ri1 Ri2\u00f0 \u00de \u03b4i Ri2\u00f0 \u00de: \u00f015b\u00de Thus, Fri for the UPR type leg can be expressed as following: Fri \u00bc Fai Fpi;1 Tpi;1 Tpi;2 2 664 3 775 \u00bc Wi Fei ;Wi \u00bc 1 0 0 0 \u22121 0 0 0 spi ;1 0 0 spi ;2 2 664 3 775: \u00f016\u00de For the UPU-type leg, the constrained force Fpi at ci can be equivalent to a force Fpi,1 at ai and a torque Tpi. Fpi,1 is parallel with Fpi and active in the opposite direction. Tpi is perpendicular with Aici and Fpi (see Fig. 3.3). Tpi can be expressed as following: Tpi \u00bc di Fpi \u00bc hi Ri1 Fpi \u00bc Fpihi Ri1 Ri2\u00f0 \u00de;hi \u00bc dij j \u00bc ci\u2212Aij j: \u00f017\u00de The constrained torque Tpi in the UPU leg can be decomposed into a torque Tpi,1 with its direction along with ri and a torque Tpi, 2 with its direction perpendicular to ri, respectively. Let \u03c4p1,1 and \u03c4p1,2 be the unit vector of Tp1,1 and Tp1,2 (see Fig. 3.3) respectively. From the geometrical constraints in the UPU type leg, it leads to \u03c4pi\u22a5Ri1;\u03c4pi\u22a5Ri2;\u03c4pi;1 \u00bc \u03b4i;\u03c4pi;1\u22a5\u03c4pi;2;\u03c4pi;2\u22a5Ri2;\u03c4pi \u00bc Ri1 Ri2;\u03c4pi;2 \u00bc \u03c4pi;1 Ri2 \u00bc \u03b4i Ri2 : \u00f018\u00de From Eq. (18), Tpi,1 and Tpi,2 can be expressed as following: Tpi ;1 \u00bc Tpi \u03c4pi ;1 \u00bc Fpi hi Ri1 Ri2\u00f0 \u00de \u03b4i \u00bc tpi ;1 Fpi ; tpi ;1 \u00bc hi Ri1 Ri2\u00f0 \u00de \u03b4i: \u00f019a\u00de From Eq. (18), Tp2,2 can be expressed as following: Tpi;2 \u00bc Tpi \u03c4pi;2 \u00bc Fpihi Ri1 Ri2\u00f0 \u00de \u03b4i Ri2\u00f0 \u00de \u00bc tpi;2 Fpi; tpi;2 \u00bc hi Ri1 Ri2\u00f0 \u00de \u03b4i Ri2\u00f0 \u00de: \u00f019b\u00de Thus, Fri for the UPU type leg can be expressed as following: Fri \u00bc Fai Fpi;1 Tpi ;1 Tpi ;2 2 664 3 775 \u00bc Wi Fei ;Wi \u00bc 1 0 0 \u22121 0 tpi ;1 0 tpi ;2 2 664 3 775: \u00f020\u00de From Eqs" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001086_rob.21577-Figure14-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001086_rob.21577-Figure14-1.png", "caption": "Figure 14. Data flows between the leader robot and the base station.", "texts": [ " For this reason, not all the topics are replicated (and thus accessible) from all the nodes (as would be the case in a system with a single ros master), but only those that are strictly necessary. In this project specifically, the ros rt wmp nodes are used to replicate the laser information coming from the robots and their odometry estimation (i.e., their /tf topics) from the robots to the base station, and the joystick, goal, and control commands from the base station to the different nodes. Figure 14 resumes the flows involved in the communication between the leader robot R1 and the base station R0. The evaluation of the system has been carried out by means of both simulations and field experiments. As explained in Section 3.1, two scenarios have been selected. The first is a mazelike underground mine representing a complex scenario for autonomous deployment. The second simpler scenario is a railway tunnel comprising a long corridor and lateral galleries to experiment with a real robot team deployment, where it is possible to evaluate the whole system working in practice and especially the communication issues" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002680_tec.2020.3000753-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002680_tec.2020.3000753-Figure1-1.png", "caption": "Fig. 1. The geometry of the 8-pole/48-slot IPM motor.", "texts": [ " See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. In this paper, an 8-pole/48-slot IPM motor with a V-type PM is taken as an example to model the RMP and calculate the magnetic field, and the proposed method is also applicable to the IPM motors with other PM structures. Assuming the rotor rotates counterclockwise at an electrical angular velocity of \u03c9. When t=0, the rotor d-axis is aligned with the stator A-phase axis. The geometry of the motor is shown in Fig. 1, and the main parameters are listed in Table I and Table II. The stator inner surface MMF considering the effect of stator saturation cannot be obtained directly, and its value needs to be calculated iteratively according to the proposed RMP model. Therefore, the RMP model, which can accurately consider the rotor saturation, is modeled and solved firstly. In this paper, the inner surface of the rotor is selected as the reference surface; that is, the magnetic potential of the rotor inner surface is zero" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000883_elan.201200428-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000883_elan.201200428-Figure1-1.png", "caption": "Fig. 1. Schematic of the molecular imprinting technique for the chlortoluron assay.", "texts": [ " The magnetic nano-NiO particles not only present magnetic prop- 1286 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Electroanalysis 2013, 25, No. 5, 1286 \u2013 1293 erty for magnetic separation, but also possess admirable catalytic property on the electrooxidation of H2O2. Chlortoluron was used as a template. After the removal of the template molecules, H2O2 reached the surface of NiO through the imprinted cavity and was catalytically electrooxidized. The schematic of the molecular imprinting process and determination is shown in Figure 1. The assay is based on the decrease of the H2O2 oxidation current caused by the template molecule blocking cavities on the active NiO electrode surface. H2O2 gets through the imprinted cavities channel and reaches the surface of NiO, the control of imprinted cavities channel is called \u201cgate-controlled\u201d, by controlling the number of gates in order to manipulate the concentration of H2O2 on the NiO s surface. The catalytic degradation of NiO to H2O2 was used as the probe to achieve the purpose of detecting chlortoluron" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002712_tie.2020.3026302-Figure14-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002712_tie.2020.3026302-Figure14-1.png", "caption": "Fig. 14: The drone-pendulum system.", "texts": [ " Downloaded on November 05,2020 at 14:08:45 UTC from IEEE Xplore. Restrictions apply. 0278-0046 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. quadrotor are considered as a type of disturbance. In order to realize a high accuracy estimation of the disturbance, the properties of the disturbance need to be analysed. Considering the equations of payload motion along the y axis as depicted in Fig. 14, the forces acting on the pendulum using Newton\u2019s second law can be expressed as:\u2211 Fy = mLy\u0308, b l \u03b8\u0307 \u2212mLy\u0308cos(\u03b8) +mLl\u03b8\u0308 +mLgsin(\u03b8) = 0, (28) where mL is the mass of payload, \u03b8 is the swing angle, b is the friction constant and g is gravitational constant. Since the swing angle \u03b8 is maintained at the small values around the global equilibrium point by minimizing the acceleration of the payload in the cost function, we can now get its linear approximations: cos(\u03b8) \u2248 1 and sin(\u03b8) \u2248 \u03b8. Substituting these functions into (28), it becomes: b l \u03b8\u0307 \u2212mLy\u0308p +mLl\u03b8\u0308 +mLg\u03b8 = 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003684_tec.2021.3098669-Figure33-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003684_tec.2021.3098669-Figure33-1.png", "caption": "Fig. 33. Endplates without and with static and dynamic rotor eccentricities. (a) Without rotor eccentricity. (b) Static rotor eccentricity. (c) Dynamic rotor eccentricity.", "texts": [ " Therefore, with the small eccentricity ratio and large phase current, the rotor eccentricity has negligible influence on average UMF and the phase current dominates the resultant UMF. However, with the large eccentricity ratio and small phase current, the rotor eccentricity dominates the resultant UMF and the phase current has negligible influence. In this section, the back-EMF and static torque waveforms of the 2-pole/3-slot PM motor with static/dynamic rotor eccentricities are measured to validate the FE predictions, and the prototype is shown in Fig. 32. According to [2], the specifically designed endplates with static/dynamic rotor eccentricities (\u03b5=0.5) are employed, Fig. 33. For static rotor eccentricity, both the bearing and inner sleeve are offset towards the same direction, while for dynamic rotor eccentricity, the bearing is concentric but the inner sleeve is eccentric. In addition, the holes in two endplates are designed for changing the eccentricity angle. Fig. 34 shows the FE predicted and measured three phase back-EMF waveforms of 2-pole/3-slot PM motors without and with static/dynamic rotor eccentricities. It shows that the Authorized licensed use limited to: Tsinghua University" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002994_j.mechmachtheory.2020.104126-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002994_j.mechmachtheory.2020.104126-Figure2-1.png", "caption": "Fig. 2. Example of situation 1.", "texts": [ " This index appears in case (b) of Table 1 and its use is described below. This table completes the classification presented by Ma and \u00c1ngeles in [43] . This reference omitted one of the two possible circuits in situation 3, specifically the option M = \u22121 , which establishes the range I = \u2212[ arccos ( u b ) , arccos ( u a ) ] of case (b). This section explains how to approach the synthesis of the three situations described above. Situation 1 In this case, the branches K = +1 and K = \u22121 remain connected, forming a single circuit (see Fig. 2 ). For each prescribed point, there are two possible solutions, and each one can be encountered on a different branch, although logically they both belong to the same circuit. The solution with the lesser error will be chosen if and only if it does not give rise to an order defect. Situation 2 Eq. (3) gives the value of the passive variable \u03b8 , which combined with Eqs. (7) and (8) yields the values of the synthesis variables ( x, y ) as a function of the input parameter. However, because K can take on two values, there always exist two possible solutions, each one in one circuit (see Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000198_s1672-6529(11)60094-2-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000198_s1672-6529(11)60094-2-Figure7-1.png", "caption": "Fig. 7 The biped hopping robot on simulation platform.", "texts": [ " 6e) is ( )ke ke 2 ke kf kf 2 kf , df k l l F y f f c F y f \u03b3 \u03b8 = \u2212 = \u22c5 = = \u22c5 (6) where Fke and Fkf are output forces of knee extensor and knee flexor, fke and fkf are inner states of motoneurons, l is the spring length at the time when the knee extensor is activated, and ld is the desired length of spring. k and c are constants, and ld is measured by experiments for different hopping height. In this study, ld = 0.13, k = 2500, c = 100. Knee extensor acts when the spring stretches to release energy, and adjusts robot energy supplemented by altering landing duration. Knee flexor acts during flight phase, and is inhibited as the leg is about to stretch for next landing. A biped hopping robot on simulation platform was used to validate the CPG control mechanism, as shown in Fig. 7. The robot can only move in sagital plane. The length of the robot is 0.3 m, the extreme height is 0.3 m, and the weight is 7 kg. The coefficient of kinetic friction is 0.5, and the static friction coefficient is 0.6. The simulation work was done on Adams/Matlab platform. In this experiment, the robot moves forward on a flat surface with a forward velocity of 0.3 m\u00b7s 1 and the gait stability is validated. Phase plane plot of leg A and leg B are respectively shown in Figs. 8a and 8b. In Fig. 8, horizontal axes represent the hip angle of leg A and B, and vertical axes represent the angular velocities" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001372_s11465-016-0389-7-Figure9-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001372_s11465-016-0389-7-Figure9-1.png", "caption": "Fig. 9 Input transmission singularity: (a) RR(Pa)RR kinematic chain and (b) PRR kinematic chain", "texts": [ " That is, the twodimensional couple constraints will always be exerted on the mobile platform and the appropriate constraints can be ensured at all times. Therefore, this PKM has no constraint singularity. 3.2 Input/output transmission singularity 3.2.1 Qualitative analysis Most PKMs in practical applications are actuated by rotational or translational inputs. In this section, RR(Pa)RR and PRR kinematic chains are used as examples to illustrate input transmission singularity. For the RR(Pa)RR chain of the proposed PKM, input transmission singularity will occur when transmission force f and active input \u03c9 are coplanar, as shown in Fig. 9(a) [29]. Under this condition, f $\u03c9 \u00bc 0 and the motion/force transmission from the input is invalid. For the PRR chain, input transmission singularity will occur when transmission force f and active input v are perpendicular to each other, as shown in Fig. 9(b). Under this condition, f $v \u00bc 0 and the motion/force transmission from the input is also invalid. For the PKM illustrated in Fig. 2, the transmission forces along C iPi (i \u00bc 1, 2, 3, 4) in four kinematic chains can be represented by $Ti. If dim f$T1, $T2, $T3, $T4g< 4, then output transmission singularity will occur. The case illustrated in Fig. 10 [29] falls under this condition. If the four axes of $Ti simultaneously intersect with the symmetry axis (i.e., the o0F i in Fig. 10), then an instantaneous rotation around the o0F i -axis will occur" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002991_tcsii.2020.3028175-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002991_tcsii.2020.3028175-Figure1-1.png", "caption": "Fig. 1: Arbitrary time SMC", "texts": [ " The control design for the case when reaching phase time (tr) is known in advance is proposed first followed by the algorithm based design for the case when tr is not known. For normal sliding mode control, the reaching phase con- sumes some finite amount of time and sliding phase dynamics is asymptotic. It is interesting to investigate the possibilities of controlling the total time of stabilization. Our findings reveal that it is possible to reduce the time consumed in the sliding phase. The proposed arbitrary time sliding surface design provides such flexibility. Fig. 1 shows the time engaged in reaching and sliding phases under the action of free-will arbitrary time TSMC. Here, the reaching phase occurs in finite time, and the time of sliding phase can be controlled. The important assumption here is that the chosen arbitrary time of convergence tf should be greater than tr. To mitigate the persistent disturbances after time tf , the sliding surface is switched to a linear surface. It is to be noted here that after time tf , any suitable sliding surface can be selected" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002022_978-3-319-40036-5-Figure5.6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002022_978-3-319-40036-5-Figure5.6-1.png", "caption": "Fig. 5.6 Siphon valves build upon the principle of capillary action as previously described, the walls of the siphon channels draw the liquid from the reagent reservoir back towards the centre of rotation however at a high frequency of rotation (Image (a)) the liquid is held back by the counteracting centrifugal force, this causes the liquid to reach \u201cHydrostatic Equilibrium\u201d at a point beneath the height of the siphon crest. As the frequency of rotation is reduced the adhesive interactions between the liquid and the channel walls begin to dominate over the centrifugal force causing the liquid to advance around the siphon crest and down towards the reaction chamber (Image (b)). It is at this point that the siphon is \u201cPrimed\u201d, the liquid will now flow towards the furthest average radial point from the centre of rotation (Image (c) and (d))", "texts": [ " At rest flow can be restricted from entering the siphon valve by a capillary valve (described above) when the rotation of the disc is increase to the \u201cBurst Frequency\u201d the valve will open and fluid will flow up the siphon until it reaches hydrostatic equilibrium, that is when the force of capillary action is counteracted by the centrifugal force [4, 20]. As this frequency of rotation is lowered the capillary force will become more dominant until the fluid passes around the siphon, it is at this point that the siphon is said to be \u201cprimed\u201d. Next, when the frequency of 122 B. Henderson et al. rotation is increased the fluid will move around the siphon to fill the next chamber. A number of these siphon valves can be placed in series to delay the introduction of different reagents to a reaction chamber [11, 12, 21] (Fig. 5.6). Both the time taken to prime a siphon valve and the burst frequency for each capillary valve can be calculated in order to create simple changes in the speed of rotation to allow the addition of reagents in an automated manner, the time of each speed of rotation can be elongated in order to allow time for specific reactions to take place, as well as mixing of reagents [4, 20]. The time needed to prime each valve t \u00bc 4\u03b7l2 d\u03c3 cos \u03b8 \u00f05:9\u00de Depends on the surface tension, the contact angle \u03b8 and the viscosity\u03b7, the length of the liquid plug l and the channel diameter d" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002321_tec.2018.2811044-Figure12-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002321_tec.2018.2811044-Figure12-1.png", "caption": "Fig. 12. (a) Photograph of sun gear defect - (b) A scheme of a local tooth defect with amount of material removed from entire face of sun gear tooth.", "texts": [ " To demonstrate this fact, a load torque oscillation with a variable frequency (0 to 200 Hz) and the magnitude of 0.1 Nm was applied as a load torque to the WRIG and the amplitude of this frequency component in the stator current spectrum is evaluated as shown in Fig. 11. This could well explain the main reasons why the higher harmonics of fault characteristic frequency are undetectable in the electrical signatures of WRIG. The tooth localized fault is produced by removing a tooth surface of sun gear with depth of 0.3 mm as shown in Fig. 12 [14]. This kind of fault generates the sideband frequency component fi around the mesh frequency fmesh in the classical transverse vibration analysis (fi\u00b1fmesh frequency components in Fig. 13). Implementation of vibration-based condition monitoring method faces several restrictions such as noise due to external perturbation, complex characteristic of vibration spectra because of meshing stiffness frequency of planet-sun and planet-ring and inaccessible place of vibration sensors in some cases [14], [21]" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002417_10426914.2019.1655151-Figure8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002417_10426914.2019.1655151-Figure8-1.png", "caption": "Figure 8. Failure mechanism caused by the impact of the powder recoating blade.", "texts": [ " Because when the blade of the powder recoating system was examined after the manufacturing, it was determined that there were various notches and wear marks on the surface. It is considered that the failure in the parts was caused by the aspect ratio being higher than 1: 8.[34] Fig. 7 shows the deformation of the powder recoating system blade. The causes of the failure have to be analyzed technically. When the samples were examined, the failure was noticed in the same scanning direction of the recoating blade and at the thin section. The failure mechanism is shown in Fig. 8. The failures in the samples were caused by striking the powder recoating system to the manufactured part. The impact of the recoating blade was especially one of the important risks in thin-walled parts. The forces, which were generated by the strike-through of the recoating blade, were not important. Because the outer barrel is designed to strengthen geometry. In order to prevent this type of failure in thin-walled parts, an additional part was positioned around the samples. It was considered to ensure manufacturing samples without failure" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002277_978-3-319-27131-6-Figure1.2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002277_978-3-319-27131-6-Figure1.2-1.png", "caption": "Fig. 1.2 Components of a deep-groove ball bearing", "texts": [ " Therefore, they are mostly applied to various industries: \u2013 Computer and semiconductor industries for hard drives, DVD sputtering, and microprocessor producing equipments \u2013 Electronics industry for liquid crystal panel bonding and LC sealing furnace \u2013 Chemical industry for etching equipments and centrifuges \u2013 Wind turbine generator \u2013 Automotive industry for electric motors, turbochargers, and gearbox \u2013 Aeroplane industry for jet engines \u2013 Steel industry for manufacturing machines, furnace cars, etc. \u2013 Household appliances Note that billion ball and roller bearings have been worldwide produced every year for such applications. Deep-groove ball bearings consist of many components, as shown in Fig. 1.2. The balls are held in a polyamide cage and are supported by the inner and outer raceways. To keep lubricating grease inside the bearing and to protect the bearing from hard particles and contaminants from outside during the operation, two lip seals and shields are installed at both sides of the bearings. The bearing is lubricated using grease that is filled between the balls in the inner and outer raceways. Due to rotation of the balls, in-grease dissolved oil is separated from grease in the oil film between the balls and raceways" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002819_ddf.398.34-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002819_ddf.398.34-Figure1-1.png", "caption": "Fig. 1: A single force F, acting along Fig. 2: A typical four-bar linkage knee. Fig. 3: Configuration of a six-bar the load. mechanism.", "texts": [ " Tahir, 2016, [6]fabricated a trans-femoral prosthetic that was made of four laminated layers (1bamboo,2 carbon fibres and another bamboo layer) instead of the layers of a laminated prosthetic (4 perlon,2 carbon fibres and another 4 layers of perlon),which is presently the most widely used for fabricating prosthetic sockets. Pressures were used as the boundary conditions for simulation with the aid of the ANSYS 14.5 SIMULATION PROGRAM. The data obtained showed an increase in each of the tensile and yield stresses in addition to Young\u2019s modulus and endurance stresses. Knee Mechanism Single Axis Knee Mechanism. The basic engineering mechanics may help to explain how the muscle moments exerted by the amputee influence the load. Consider the diagrams in Fig. 1. This can be explained by considering the combination of joint force and extension moment acting at the hip joint. Consider Figures 3.7(b) and (c). The hip extension moment M in (b) can be replaced by two equal and opposite forces of quantity F separated by a distance D which has a similar extension moment as M:M = (D) x (F). These couples of forces F1 and F2 are now positioned on diagram (c) in a manner such that F2 is in-line with the actual force F and they cancel each other out [7]. Four-Bar Polycentric Knee Mechanism" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001871_s00170-018-1840-1-Figure26-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001871_s00170-018-1840-1-Figure26-1.png", "caption": "Fig. 26 Specimens with two 50% overlapped beads (a). 3D view of specimen with the size of 100 mm\u00d7 30mm\u00d7 6 mm (b). 3D view of specimen with the size of 500 mm\u00d7 30 mm\u00d7 6 mm (c)", "texts": [ " The resulted flatness in these specimens and the specimen with 75 mm\u00d7 35 mm (Pattern 1 in Fig. 21a, b) are shown in Figs. 24 and 25 and Table 9. It is concluded that with larger sizes and cladded area, distortion values increase. Moreover, the effect of the time gap between bead deposition was investigated by comparing the flatness in a specimen with 100 mm and time gaps of 0.5 s and 30 s, as well as a specimen with 500mm length and time gaps of 0.5 s and 60 s. The geometry of specimens are shown in Fig. 26. The results in Table 10 reveal that the time gap does not have a significant effect on the developed distortions. It was shown previously that the ITC technique gives an acceptable result for prediction of residual stress. This technique was further used to determine the residual stresses in the surface cladded specimens. In Table 6, mean residual stress results for three different spiral bead deposition patterns were compared (Fig. 20). This residual stress results in this table reveal that the diagonal filling pattern induced the highest values of mean compressive and tensile residual stresses" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000911_978-1-4939-0292-7-Figure8.10-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000911_978-1-4939-0292-7-Figure8.10-1.png", "caption": "Fig. 8.10 Inverted pendulum", "texts": [ "51) The same parameter values, D 10, D 125, \" D 1, were appropriate for the nonsmooth and discontinuous controller designs. The experimental results, depicted in Figs. 8.8 and 8.9, illustrated capabilities of the proposed nonsmooth and discontinuous designs for adequate periodic tracking. 144 8 Advanced H1 Synthesis of Fully Actuated Robot Manipulators with Frictional. . . A Case Study In order to illustrate the H1 synthesis over sampled-data measurements, we present a simulation study, conducted in [16], for an inverted pendulum, moving in the vertical plane and depicted in Fig. 8.10. The pendulum is driven by an actuator u, using position measurements only. The measurements, which are available at the discrete-time moments j D 0:5j; j D 0; 1; : : :, are made by a nonlinear potentiometer with the standard resistance function sin . The aim is to design a H1 sampled-data measurement feedback H1 controller, locally stabilizing the inverted pendulum around its unstable upright 8.6 Synthesis over Nonlinear Sampled-Data Measurements: A Case Study 145 equilibrium, whose dimensionless model is given in terms of the angular position x1 D and angular velocity x2 D P : Px1 D x2; : x2 D sin" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000007_0005-2744(75)90032-7-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000007_0005-2744(75)90032-7-Figure4-1.png", "caption": "Fig. 4. Flow-through o x y g e n e l e c t r o d e design. (Y) Yellow Springs o x y g e n e l e c t r o d e ; (P) per spex housing; (B) clamping bolts; (i) inlet port; (o) outlet port; (C) flow-through assay chamber; (r) ses~.ng rubber ring.", "texts": [ " Alternatively, glucose was determined polarographically by measuring the consumption of dissolved oxygen during the glucose oxidase reaction by employing a flow-through oxygen electrode incorporated into the standard Technicon flow system shown in Fig. 3. In this system sample stream is first air segmented, and then diluted with 50 mM acetate buffer, pH 5.5, before mixing and perfusion through the nylon tube-glucose oxidase derivative. The emergent stream is debubbled, and the oxygen concentrat ion is moni tored by an oxygen sensor {Yellow Springs Instrument Co., Yellow Springs, Ohio. U.S.A.) fi t ted with a flow-through perspex housing {Fig. 4). The internal volume of the flow-through chamber was about 0.1 ml, thus the residence t ime in the chamber was less than 4 s. Nylon tube extruded from high molecular weight nylon contains relatively few sites for the a t tachment of protein. Thus, if it is required to immobilize a reasonable quant i ty of an enzyme on the inside surface of this type of nylon tube, then either the amount of potential binding sites has to be increased, or new active centres have to be introduced. Inman and Hornby [6] increased the number of free amino groups on the inside of nylon tube by partially hydrolysing the inside surface with HC1", "0 mM using the acid/KI assay method (Figs 5 and 6). Resting blood glucose levels are in the range 3.3--5.5 mM [19] , hence all the nylon tube-glucose oxidase derivatives were sufficiently active to be of use in the clinical estimation of blood glucose. However, the acid/KI assay system may not be suitable for use under all circumstances, since other oxidising substances, which may be present in biological fluids, could also cause oxidation of the acid/KI. The use of the flow-through oxygen electrode (Fig. 4) in the f low circuit shown in Fig. 3, overcomes this problem. In this assay system, only the disappearance of dissolved oxygen is monitored, thus oxidising agents in blood, etc. do not interfere. However, the presence of catalase would interfere, as it would catalyse the conversion of hydrogen peroxide to water, with the simultaneous production of oxygen. This difficulty could be easily eliminated by incorporating a standard Technicon dialyser unit at position X in the flow system shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001389_s00170-016-9447-x-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001389_s00170-016-9447-x-Figure1-1.png", "caption": "Fig. 1 Illustration of the face gear honing process", "texts": [ " Then, the tooth flank equation of the honed face gear including tool setting errors is derived. The effects of tool setting errors on face gear geometry errors are analyzed by numerical examples. Finally, the honing cutter is manufactured, and the honing experiments are performed. The validity of the proposed face gear honing method is verified by experiments. The face gear meshes with the involute spur pinion. Thus, by simulating the pinion motion, the honing cutter can generate the face gear. The face gear honing principle is illustrated in Fig. 1. The honing cutter meshes with the face gear. During the honing process, the tooth surfaces of the face gear and the honing cutter are in line contact at every instant. The face gear tooth profile is enveloped by the honing cutter surface. Thus, the honing process can produce the face gear with tooth profile modification bymodifying the honing cutter profile. In the honing process, the face gear and honing cutter rotate around axis xf and zh, respectively. The relationship between the honing cutter angular velocity \u03c9h and the face gear angular velocity \u03c9f is expressed as follows: \u03c9 f " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001372_s11465-016-0389-7-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001372_s11465-016-0389-7-Figure2-1.png", "caption": "Fig. 2 Kinematic scheme of the parallel robot presented in Fig. 1", "texts": [ " In Section 3, the singularity of the proposed PKM is investigated both qualitatively and quantitatively, and the results are provided. Section 4 concludes the study. In this section, we first introduce a four-DoF spatial PKM with a single-platform structure in detail. Then, we analyze the mobility of this PKM using a line graph method based on Grassmann line geometry. Finally, the inverse kinematic modeling for this PKM is presented. 2.1 Description of the mechanism The CAD model of the PKM presented in this study is shown in Fig. 1, the kinematic scheme is presented in Fig. 2, and a global frame \u211c: o-xyz is established. As shown in Figs. 1 and 2, this PKM consists of four identical kinematic limbs and a single platform. The kinematic chain for each limb can be represented by RR(Pa)RR (R: Active revolute joint; R: Revolute joint; Pa: Parallelogram mechanism composed of four links connected end to end by four revolute joints). The four limbs are in 180\u00b0 symmetry (Fig. 2). The axes of revolute joints B1 and B3 as well as B2 and B4 are coaxial, and B1B3 (which is coaxial with the x-axis) is perpendicular to B2B4 (which is coaxial with the y-axis). The axes of revolute joints B1, B2, B3, and B4 are parallel to the horizontal plane (i.e., plane o-xy). Revolute joints B1, B2, B3, and B4, which are mounted on the base, are active. Similarly, revolute joints P1 and P3 as well as P2 and P4, which have a horizontal axis, are collinear; and P1P3 is perpendicular to P2P4", " Only a line vector that is perpendicular to the two couples or their plane can be identified, and the other elements should be three couples (any two elements are perpendicular to each other). Therefore, the motion line graph of the mobile platform is composed of a line vector and three couples as shown in Fig. 8. The discussed PKM has one rotational DoF around the z-axis and three translational DoFs according to the mobility analysis result presented in Fig. 8. 2.3 Inverse kinematic modeling As shown in Fig. 2, the geometric parameters of the PKM are as follows: Rbase \u00bc r1, Rplatform \u00bc r2, jBiC ij \u00bc l1, and jC iPij \u00bc l2 (i \u00bc 1, 2, 3, 4). The rotational angle of the mobile platform can be represented by \u03c6. The inputs \u03b1i 2 (0\u00b0,180\u00b0) (i \u00bc 1, 2, 3, 4) can be derived accordingly assuming that o0\u00f0x, y, z, \u03c6\u00de is given. As shown in Fig. 2, the coordinates of Pi in the initial position can be expressed as fP\u00ee\u211cg \u00bc P\u00ed1 \u00f0r2, 0, z\u00de P\u00ed2 \u00f00, r2, z\u00de P\u00ed3 \u00f0 \u2013 r2, 0, z\u00de P\u00ed4 \u00f00, \u2013 r2, z\u00de 8>>< >>: 9>>= >>; : (1) The rotation matrix around the z-axis is Rotz\u00f0\u03c6\u00de \u00bc cos\u03c6 \u2013 sin\u03c6 0 sin\u03c6 cos\u03c6 0 0 0 1 2 64 3 75: (2) The vectors in Eq. (1) can be rotated around the z-axis into fP\u00ed\u211cg \u00bc Rotz\u00f0\u03c6\u00defP\u00ee\u211cgT \u00bc P1\u00f0r2cos\u03c6, r2sin\u03c6, z\u00de P2\u00f0 \u2013 r2sin\u03c6, r2cos\u03c6, z\u00de P3\u00f0 \u2013 r2cos\u03c6, \u2013 r2sin\u03c6, z\u00de P4\u00f0r2sin\u03c6, \u2013 r2cos\u03c6, z\u00de 8>>< >>: 9>>= >>; : (3) Accordingly, the coordinates of Pi can be generated as fP\u211cg \u00bc P1\u00f0x\u00fe r2cos\u03c6, y\u00fe r2sin\u03c6, z\u00de P2\u00f0x \u2013 r2sin\u03c6, y\u00fe r2cos\u03c6, z\u00de P3\u00f0x \u2013 r2cos\u03c6, y \u2013 r2sin\u03c6, z\u00de P4\u00f0x\u00fe r2sin\u03c6, y \u2013 r2cos\u03c6, z\u00de 8>>< >>: 9>>= >>; : (4) The coordinates of Bi are fB\u211cg \u00bc B1\u00f0r1, 0, 0\u00de B2\u00f00, r1, 0\u00de B3\u00f0 \u2013 r1, 0, 0\u00de B4\u00f00, \u2013 r1, 0\u00de 8>>< >>: 9>>= >>; : (5) Then, the coordinates of Ci can be derived as fC\u211cg \u00bc C1\u00f0r1, \u2013 l1sin\u03b11, \u2013 l1cos\u03b11\u00de C2\u00f0 \u2013 l1sin\u03b12, r1, \u2013 l1cos\u03b12\u00de C3\u00f0 \u2013 r1, \u2013 l1sin\u03b13, \u2013 l1cos\u03b13\u00de C4\u00f0 \u2013 l1sin\u03b14, \u2013 r1, \u2013 l1cos\u03b14\u00de 8>>< >>: 9>>= >>; : (6) The following results can be derived by constraining jC iPij \u00bc l2: cos\u03b11\u00bc \u2013mz jy\u00fe r2sin\u03c6j ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4l21z 2 \u2013m2\u00fe4l21\u00f0y\u00fe r2sin\u03c6\u00de2 q 2l1\u00bdz2\u00fe\u00f0y\u00fe r2sin\u03c6\u00de2 , (7) where m \u00bc \u00f0y\u00fe r2sin\u03c6\u00de2 \u00fe \u00f0x\u00fe r2cos\u03c6 \u2013 r1\u00de2 \u00fe z2 \u00fe l21 \u2013 l22 and sgn\u00f0 \u00de \u00bc \u00fe, y\u00fe r2sin\u03c6\u00b30 \u2013 , y\u00fe r2sin\u03c6<0 ( ", " For the RR(Pa)RR chain of the proposed PKM, input transmission singularity will occur when transmission force f and active input \u03c9 are coplanar, as shown in Fig. 9(a) [29]. Under this condition, f $\u03c9 \u00bc 0 and the motion/force transmission from the input is invalid. For the PRR chain, input transmission singularity will occur when transmission force f and active input v are perpendicular to each other, as shown in Fig. 9(b). Under this condition, f $v \u00bc 0 and the motion/force transmission from the input is also invalid. For the PKM illustrated in Fig. 2, the transmission forces along C iPi (i \u00bc 1, 2, 3, 4) in four kinematic chains can be represented by $Ti. If dim f$T1, $T2, $T3, $T4g< 4, then output transmission singularity will occur. The case illustrated in Fig. 10 [29] falls under this condition. If the four axes of $Ti simultaneously intersect with the symmetry axis (i.e., the o0F i in Fig. 10), then an instantaneous rotation around the o0F i -axis will occur. Evidently, the number of intersections can vary from one to four. 3.2.2 Quantitative analysis The transmission singularity indices should be defined first to investigate the singularity numerically. The proposed parallel robot has four active inputs, and thus, the rotational input of the i-th chain is denoted by a unit input twist screw $Ii (i = 1, 2, 3, 4). As shown in Fig. 2, the four unit input twist screws can be expressed as $I1 \u00bc \u00f01, 0, 0; 0, 0, 0\u00de $I2 \u00bc \u00f00, 1, 0; 0, 0, 0\u00de $I3 \u00bc \u00f0 \u2013 1, 0, 0; 0, 0, 0\u00de $I4 \u00bc \u00f00, \u2013 1, 0; 0, 0, 0\u00de : 8>>< >>: (12) For each kinematic chain, the active input $Ii is transmitted to the mobile platform through a unit transmission wrench screw $Ti, which is $Ti \u00bc \u00f0CiPi; oCi CiPi\u00de jCiPij : (13) If three inputs, except for the i-th input are locked, then only the transmission wrench screw $Ti will contribute to the motion of the mobile platform", ", \u03c6) of the mobile platform can be identified by considering both input and output transmission singularities. For the pick-and-place manipulation of the presented PKM, rotational capability is an essential performance that requires additional attention. Therefore, the rotational capability defined by \u03c6 2 ( \u2013 45\u00b0,45\u00b0) is adopted as a precondition in the following section to make the singularity analysis meaningful to practical applications. Assuming that the rotational capability of the PKM in Fig. 2 is defined by \u03c6 2 \u00f0\u03c6min, \u03c6max\u00de and \u03c6min\u00a30\u00a3\u03c6max, singularities can be identified according to the definitions in Eqs. (15) and (16) by constraining minfj\u03c6minj, \u03c6maxg \u00bc 45\u00b0. In this study, the horizontal planes defined by z = \u2013 1.8 and z = \u2013 2.4 are two important working planes, and the corresponding singular loci in these planes are plotted in Fig. 12. The singular loci are symmetrical around y = x, which is consistent with the symmetrical structure of the PKM. The meaning of the singular loci presented in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000193_j.cma.2011.04.006-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000193_j.cma.2011.04.006-Figure5-1.png", "caption": "Fig. 5. Towards determination of the geometry", "texts": [ ", each point M of the reference blade profile has its corresponding point M0 on the sphere with radius Ro, the outer pitch cone distance, as shown in Fig. 1. The pitch plane of the generating crown-gear is defined by the pitch line of the reference blade profile and the center of the sphere. The geometry of the imaginary generating crown-gear will be obtained in coordinate system Scg, with origin in the center of the outer sphere and axis zcg containing the origin Oc of the reference blade profile coordinate system Sc, and axes xcg and ycg parallel to axes xc and yc of the reference blade profile, respectively (Fig. 5). of the imaginary generating crown-gear. erating crown-gear and (b) an imaginary skew generating crown-gear. For any given point M of the reference blade profile with coordinates x\u00f0M\u00dec and y\u00f0M\u00dec in coordinate system Sc (see Fig. 5), the corresponding point M0 on the outer sphere is defined considering that: (i) point A0 on the outer sphere is obtained considering that it is in the pitch plane and (ii) the length of arc OcA0 _ is equal to jx\u00f0M\u00dec j. Point M0 on the outer sphere is obtained knowing that the length of arc A0M0 _ measured over the great circle defined by a plane normal to the pitch plane, is equal to jy\u00f0M\u00dec j. An auxiliary coordinate system Sh is defined for description of the geometry of the imaginary crown-gear for each point M0 of the reference blade profile over the outer sphere. Coordinate system Sh has the origin Oh in the center of the outer sphere for a crown-gear generating a straight bevel gear or as mentioned below for generation of skew bevel gears (see Fig. 6). Axis yh is parallel to axis yc of the reference blade profile, and axis zh is contained in the pitch plane of the crown gear with direction of the projection of vector OhM0 on the pitch plane (Fig. 5). Fig. 8. Coordinate systems applied for bevel ge For definition of an imaginary straight crown-gear generating a straight bevel gear, any given point M0 of the reference blade profile over the outer sphere is projected towards the origin Oh of coordinate system Sh, where Oh coincides with the center of the outer sphere (Fig. 6(a)), defining lines of the generating surface of a non-modified straight crown-gear. For definition of a skew imaginary crown-gear generating a skew bevel gear, the projection point Oh, origin of coordinate system Sh, for any given point M0, is not the center of the outer sphere but the tangent point with a circle defined on the pitch plane of the generating crown-gear as shown in Fig", " 6(b)) and negative for a left-hand skew bevel gear. A point P(u,h) on the imaginary generating crown-gear tooth surface (Fig. 7) is defined by profile parameter u of the blade (that defines the reference point M on the reference blade profile and corresponding point M0 on the outer sphere) and its longitudinal direction parameter h, measured from Oh on the projection line OhM0 (Fig. 6). For any given point M0 defined by profile parameter u of the reference blade profile, angles ab and aa can be determined (Fig. 5). Angle ab defines point M0 in coordinate system Sh. Then, by considering angle aa and skew angle b, point M0 might be determined in coordinate system Scg (Fig. 6). Angles ab and aa are given, for a nonmodified imaginary crown-gear, by (see Fig. 5): ab\u00f0u\u00de \u00bc A0M0 _ Ro \u00bc yc\u00f0u\u00de Ro ; \u00f014\u00de aa\u00f0u\u00de \u00bc OcA0 _ Ro \u00bc xc\u00f0u\u00de Ro : \u00f015\u00de ar generation by an imaginary crown-gear. Longitudinal crowning is applied to the generating surfaces of the imaginary crown-gear by modifying angle aa with Daa, determined by Daa\u00f0h\u00de \u00bc ald\u00f0h h0\u00de2 h : \u00f016\u00de Here, ald is the parabola coefficient for longitudinal crowning, h is the longitudinal parameter, defined as mentioned above, and h0 is the value of parameter h where modifications of the generating surface start. By choosing appropriately different values for h0 and ald for the toe and heel areas of the crown-gear generating tooth surface, partial longitudinal crowning can be applied, as shown in Fig", " Parameters \u00f0aldt ; h0t \u00de and \u00f0aldh ; h0h \u00de control the crowning and position of areas D and F, respectively, for longitudinal crowning. By considering h0t \u00bc h0h \u00bc Ro Fw=2 and aldt \u00bc aldh we can take into account a conventional longitudinal parabolic crowned surface for the imaginary crown-gear. Similarly, by considering aldt \u00bc aldh \u00bc 0 we can take into account a non-modified surface in longitudinal direction for the imaginary generating crown-gear. According to the ideas described above, a point P(u,h) is given in coordinate system Sh by (see Fig. 5) rh\u00f0u; h\u00de \u00bc 0 h sinab\u00f0u\u00de h cos ab\u00f0u\u00de 1 2 6664 3 7775: \u00f018\u00de Considering coordinate transformation from Sh to Scg as shown in Fig. 6(b), the generating surfaces of an imaginary skew crown gear are given by rcg\u00f0u; h\u00de \u00bcMcgh\u00f0a a\u00f0u; h\u00de\u00derh\u00f0u; h\u00de; \u00f019\u00de where Mcgh\u00f0a a\u00de \u00bc cos\u00f0b a a\u00de 0 sin\u00f0b a a\u00de Rb cos\u00f0b a a\u00de 0 1 0 0 sin\u00f0b a a\u00de 0 cos\u00f0b a a\u00de Rb sin\u00f0b a a\u00de 0 0 0 1 2 66664 3 77775: \u00f020\u00de Considering Eqs. (18)\u2013(20), Eq. (19) can be represented by rcg\u00f0u; h\u00de \u00bc Rb cos\u00f0b a a\u00de h cos\u00f0ab\u00de sin\u00f0b a a\u00de h sin\u00f0ab\u00de Rb sin\u00f0b a a\u00de \u00fe h cos\u00f0ab\u00de cos\u00f0b a a\u00de 1 2 66664 3 77775: \u00f021\u00de By considering b = 0 in Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002956_tte.2020.2997607-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002956_tte.2020.2997607-Figure3-1.png", "caption": "Fig. 3. Region division of DRMWMs.", "texts": [ " Thus, the three-dimension problem is reduced to a two-dimension one. 2) The permeability of soft-magnetic material (SMM) is regarded as infinite, so the magnetic flux density is on the normal direction of SMM boundary. 3) The geometrical sides of the DRMWM are radial and tangential, so the magnetic flux density direction on the interfaces can be either radial or tangential. Then, the whole machine can be divided into six regions, namely six subdomains, from inner rotor PMs to the stator slot section, as shown in Fig. 3. Besides, region III, V, VI are further divided into several sub-regions by SMM, and they are named as ith spoke PMs, jth slot opening and kth slot, respectively. Generally speaking, there are three different types of twodimension coordinate systems, namely Cartesian, polar and cylindrical coordinate system [28]. Cartesian coordinate is suitable for solving the magnetic field in linear motors, polar coordinate for radial-type motors and cylindrical coordinate for tubular motors. Polar coordinate system is adopted to solve the magnetic field distribution within the DRMWM in this paper" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002084_j.ymssp.2018.03.033-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002084_j.ymssp.2018.03.033-Figure7-1.png", "caption": "Fig. 7. Dynamic model of a gear pair [20].", "texts": [ " When the crack tip propagates to the central line of the tooth, the bending stiffness and shear stiffness can be written as follows: 1 kb \u00bc Z xmin lrim 3\u00bdcosa1\u00f0d x\u00de sina1h 2 2EL\u00f0r2f x2\u00de32 dx\u00fe Z l xmin 12\u00bdcosa1\u00f0d x\u00de sina1h 2 EL\u00bd\u00f0r2f x2\u00de12 \u00fe yP 3 dx \u00fe Z a3 a1 12r3b 1\u00fe cosa1\u00bd\u00f0a2 a\u00de sina cosa f g2\u00f0a2 a\u00de cosa EL yQ yP \u00f0xQ xP \u00de2 frb\u00bdcosa\u00fe \u00f0a a2\u00de sina xPg2 \u00fe yP \u00fe rb\u00bdsina\u00fe \u00f0a2 a\u00de cosa n o3 da \u00f024\u00de 1 ks \u00bc Z xmin lrim 3 cos2 a1 5GL\u00f0r2f x2\u00de12 dx\u00fe Z l xmin 6 cos2 a1 5EL\u00bd\u00f0r2f x2\u00de12 \u00fe yP dx \u00fe Z a3 a1 1:2rb cos2 a1\u00f0a2 a\u00de cosa GL yQ yP \u00f0xQ xP \u00de2 frb\u00bdcosa\u00fe \u00f0a a2\u00de sina xPg2 \u00fe yP \u00fe rb\u00bdsina\u00fe \u00f0a2 a\u00de cosa n o da \u00f025\u00de Based on the TVMS of cracked gear pair, the vibration response and the dynamic load can be extracted using the lumped mass model. In this study, a six degree of freedommathematic model of the cracked gear pair is adopted [20]. The schematic of the gear dynamic model is shown in Fig. 7, where y axis is parallel to the action line of the gear pair. In this paper, the friction force is ignored based on the assumption of good lubrication condition in the gears as did in Refs. [20,24]. Under good lubrication condition, the friction force will be small and cause negligible effect on gearbox dynamic responses. Based on the above assumptions, the vibration in the x direction is free response and will disappear due to inherent damping. Thus, the motion in the y direction is the research emphasis" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002438_j.ijmecsci.2019.105397-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002438_j.ijmecsci.2019.105397-Figure6-1.png", "caption": "Fig. 6. Loaded contact pattern evaluation in high-order topography optimization of grinding tooth flank.", "texts": [ " Optimization model To distinguish with the geometric accuracy demand from the conentional grinding of spiral bevel gears, the tooth flank loaded contact erformance is also required here and the loaded tooth contact pattern s selected as a main physical performance evaluation [24] . Here, under he premise of meeting the processing accuracy, data-driven high-order opology optimization is performed by correlating with the optimal deermination of the loaded tooth contact pattern as an important contraint. Fig. 6 shows the loaded contact pattern evaluation in high-order opography optimization of grinding tooth flank. As described in the preious section, the loaded tooth contact pattern is finally correlated to the achine-tool settings. In the data-driven optimization with respect to nknown design variables namely the given machine-tool settings, the mportant is the determination of the objective function and its accuate solution. Moreover in the actual manufacturing, the loaded contact attern is always an important evaluation item on gear product surface quality by using the V-H rolling test [31] . Generally, the size, direction nd position of the whole loaded contact pattern are required [48,49] . n particular, the edge contact with the whole tooth flank boundary, uch as the tip edge contact, root edge contact, heel edge contact and oe edge contact in Fig. 6 , is needed to be avoided. Moreover, it usully needs to avoid the load offset that the loaded tooth contact pattern hould be in the middle area and not approach to the tooth heel or toe 31] . In full consideration of above requirements, the loaded contact attern LCP is constraint by referring to the new prescribed boundary ondition. Therefore, the target flank topology is p [ \ud835\udc3c\u2217\u2212 \ud835\udc3d\u2217 ] )[ \ud835\udc47\ud835\udc42 ] ( \ud835\udf03, \ud835\udf19\ud835\udc3b ) \u21a6 LCP ( \ud835\udf03, \ud835\udf19\ud835\udc3b ) \ud835\udc60.\ud835\udc61. \u03a9\ud835\udc3f \u2264 \ud835\udc41 \u2211 \ud835\udc56 ( \ud835\udc4f \ud835\udc36\ud835\udc43 ) \ud835\udc56 \u2264 \u03a9\ud835\udc48 \u2127\ud835\udc3f \u2264 ( \ud835\udc4e \ud835\udc36\ud835\udc43 ) \ud835\udc56 \u2212 \ud835\udc43 \ud835\udc40 \ud835\udc3c \ud835\udc37 \u2264 \u2127\ud835\udc48 (33) Where, 1 < I \u2217 < M and 1 < J \u2217 < N, represent the requirement that the dge contact can not exist" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002789_j.jmatprotec.2019.116355-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002789_j.jmatprotec.2019.116355-Figure1-1.png", "caption": "Fig. 1. (a) Schematic of the CC-WAAM; (b) The image of ejected arc and droplets in CC-WAAM.", "texts": [ " Based on that, the authors innovatively proposed a compulsively constricted WAAM (CC-WAAM) technology. Using a metal inert gas (MIG) welding power source, an indirect arc was generated in an argon atmosphere between a non-consumable tungsten electrode and a consumable wire electrode. In this case, the wire takes the indirect arc as the heat source to melt and produces droplets; both the droplets and arc are ejected out of a ceramic nozzle for the AM purpose; reduced heat input and adjustable droplets and arc behaviors were achieved. As shown in Fig. 1-a, the current flows directly through the tungsten and wire instead of through the wire and substrate; under the direction of the electric field, the arc is confined between the wire and the tungsten electrode, and the arc ejected from the ceramic nozzle is the part of the lower temperature of the arc; the distance from torch to the substrate provides sufficient cooling space for molten droplets transfer. Based on the above, the heat input could be significantly reduced. Although the ceramic nozzle has a compulsively restraining effect on the arc and the droplets, when both the arc and the droplets are in an unstable state, a strong thermal shock increases the loss of the ceramic nozzle, and the droplets bound by the nozzle are also ejected irregularly in different directions, resulting in poor forming. At the same time, the arc that is too long under inappropriate parameters will heat the weld bead to a higher temperature, resulting in an increase in heat accumulation. This is obviously contrary to our original intention (shown in Fig. 1-b). Hence, it is extremely necessary to explore the generation processes of arc plasma and molten droplets that are not constrained by ceramic nozzle (Fig. 2). However, the process of parameter development is cumbersome and direct visual assessment of arc and droplet formation is impossible when it takes place within the torch shroud. Therefore, the authors visually investigated the arc and droplets behaviors under different parameters through a high-temperature resistant glass by using high-speed photography which acted as a powerful in situ characterization tool to understand the welding phenomena, described by Tsukamoto (2011). As shown in Fig. 2, this is an illustration of the entire CC-WAAM system shown in Fig. 1, including a heat resistant glass section to allow direct viewing of the process. They possess the same shielding gas flow, the same confined space, the same setup of the tungsten and wire electrodes, and the same setup of power supply. However, the external environment of igniting arc between Figs. 1 and 2 is different. In Fig. 1, the arc is ignited in the narrow space of ceramic nozzle. In Fig. 2, the arc is ignited in the confined space within the torch, not in the ceramic nozzle. In terms of space, the former is much smaller than the latter. Therefore, the arc behaviors and droplet transfer in both cases are definitely different, the Fig. 2 is the simulation of the Fig. 1. It is considered that the parameters under two cases are similar. Subsequent experiments verify the idea. And the appropriate technological parameters can be obtained by the device shown in Fig. 2. It was found that the arc shape and droplets transfer were quite different under different electrical parameters. At low-level electrical parameters (80 A/14.9 V200 A/18.3 V), the droplets transfer modes were a combination of large particle transfer and short-circuit transfer. The long time of the droplet transfer and the large particle size of droplets provided an opportunity for the arc to move irregularly on the surface of the droplets, resulting in a large number of complex welding arc phenomena" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001225_1.4035432-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001225_1.4035432-Figure1-1.png", "caption": "Fig. 1 Coordinate systems rigidly connected to internal gear Sg (Og-xg yg zg), pinion Sp (Op-xp yp zp), and frame SF (OF-xF yF zF)", "texts": [ " This design process requires a new method for determining the helix angle of the cutter. 2.1 Conjugate Pinion. In the previous paper [10], we proposed a tooth geometry design method based on a conjugate pinion to an internal gear to be cut. In order to cut accurate gears, the cutting edge must be on the tooth flank of the conjugate pinion. Using that method, the cutting edge is determined from the intersection curve of the conjugate pinion tooth flanks and the cutter tool face. A conjugate pinion can be obtained by solving the equation of meshing [11]. As shown in Fig. 1, we setup three coordinate systems Sg (Og-xg yg zg), Sp (Op-xp yp zp), and SF (OF-xF yF zF), rigidly connected to an internal gear, conjugate pinion, and frame, respectively. The internal gear and conjugate pinion rotate about the zg- and zp-axes, respectively. When their angles ug and up of rotation are zero, the xF-, xg-, and xp-axes are identical. The origin Op of the pinion coordinate system Sp is on the point (a, 0, 0) in the frame coordinate system SF, where a is the center distance, and the zp-axis is inclined at shaft angle R as shown in Fig. 1. Furthermore, the gear coordinate system Sg rotates about the zg-axis which is identical to the zF-axis with uniform angular velocity xg 033301-2 / Vol. 139, MARCH 2017 Transactions of the ASME Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jmdedb/935992/ on 01/31/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use and the pinion coordinate system Sp rotates about the zp-axis with uniform angular velocity xp. Therefore, the angles ug and up of rotation are given by ug up \u00bc xg xp \u00bc u (1) where u is the gear ratio of the internal gear to the conjugate pinion", " For the reasons as mentioned above, we cannot evaluate negative clearance angles by using this angle. Subtracting an angle between vectors v t and {(v t) v} nt from p/2, therefore, we calculate the instantaneous clearance angle aT aT \u00bc p 2 cos 1 v t\u00f0 \u00de f v t\u00f0 \u00de vg nt jv tj jf v t\u00f0 \u00de vg ntj \" # (11) Figure 8 shows the relative motion of a cutting edge to a working blank in a skiving process; i.e., a groove generated by the cutting edge in the internal surface of a cylindrical working blank. Note that, in Fig. 8, coordinate axes are inverted from those in Fig. 1. Gear data for the internal gear to be cut are listed in Table 1, and gear data for the cutter used is listed in Table 2. This means that the shaft angle, the center distance, and the tool face offset are the same as in the previous example. In Fig. 8, points on the cutting edges are those at which cutting tool parameters are calculated. At the points colored black, no cutting occurred. The color bar in Fig. 8 shows values of the instantaneous depth of cut at each calculated point. The instantaneous depth of cut at each reference point is calculated from the distance along the vector v t between the reference point and the previous groove" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003195_s10846-019-01129-4-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003195_s10846-019-01129-4-Figure7-1.png", "caption": "Fig. 7 Assembly of the parts for the construction of a quadcopter", "texts": [ " PM1 is a central module responsible for the command, computation and instrumentation of the UAV. PM2 is a propulsion module, that accommodate a single actuator. Finally, PM3 is a single layer multipurpose connector. Tables 1, 2 and 3 concentrate the implementation details to build the multirotor drone according to DRAMR1. All specifications are now defined in therms of part models as defined by Eq. 3. A number of these parts organized in some physical arrangement will allow the construction of the drone. Figure 7 presents an overview of the assembly of the parts in order to build a quadcopter. The list of parts include 1xPM1, 4xPM2 and 4xPM3. D = {P1,P2,P3,P4,P5,P6,P7,P8,P9, ,R,H} (6) with: \u23a7 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 P1 = \u3008PM1, \u2205, \u2205, \u2205\u3009 P2 = \u3008PM2,P6, 5, 2\u3009 P3 = \u3008PM2,P7, 6, 2\u3009 P4 = \u3008PM2,P8, 2, 1\u3009 P5 = \u3008PM2,P9, 3, 1\u3009 P6 = \u3008PM3,P1, 1, 2\u3009 P7 = \u3008PM3,P1, 1, 3\u3009 P8 = \u3008PM3,P1, 2, 5\u3009 P9 = \u3008PM3,P1, 2, 6\u3009 (7) The parts and their connections are described in Eq. 7 as 4-tuples according to Eq. 5, and are shown schematically in Fig. 7. A set of modules was built as presented in previous sections. All plastic parts of the prototype were printed in a Movtech Cubica 2 3D printer using fused filament technology (FFT) with spools of colored ABS (Acrylonitrile Butadiene Styrene) with 1.75mm filament diameter. Printed Circuit Boards (PCBs) were prototyped in a LPKF Protomat S63 using a Universal Cutter 0.2-0.5mm. We conducted six preliminary tests (T1-T6) as proof of concept of the proposed architecture: \u2013 T1. Mechanical connections preliminary test" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000498_tec.2012.2185826-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000498_tec.2012.2185826-Figure2-1.png", "caption": "Fig. 2. SHEFS machine with iron flux bridges (SHEFSM3) [15]. (a) Cross section. (b) Field distribution (PM only). (c) Operation principle (PM only). (d) Operation principle (excitation flux only).", "texts": [ " For this group (series hybrid excitation), PMs and excitation windings are in series, the excitation flux pass through PMs, as seen in Fig. 1(d). Due to the magnetic properties of PMs, some drawbacks can be identified [1] as follows. 1) Since the permeability of PMs is close to that of air, the reluctance of the excitation winding\u2019s magnetic circuit is relatively high, which will limit the flux regulation capability. 2) Furthermore, the risk of demagnetization should be considered. In order to overcome the drawbacks of SHEFS machines, [15] has added iron flux bridges as shown in Fig. 2 to the topology of Fig. 1 to enhance the ability of the excitation winding to vary the excitation flux level. As the iron bridge is included and the width is increased the effectiveness of the excitation winding is improved [15]. However, increasing the width of the iron bridges will cause an increase of short-circuit PM flux, as seen in Fig. 2(b). Thus, the utilization ratio of the magnets and machine torque density will be reduced. From the aforementioned analysis, it can be concluded that 1) the series hybrid excitation topologies without iron flux bridge have simple structure, but their excitation current utilization ratio is low, and there is a risk of demagnetization, 2) the series hybrid excitation topologies with iron flux bridge can increase the excitation current utilization ratio to some extent and has no risk of demagnetization; however, high-excitation current utilization ratio and high-PM utilization ratio are contradictory" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000039_978-1-84996-220-9-Figure2.6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000039_978-1-84996-220-9-Figure2.6-1.png", "caption": "Figure 2.6 Forces acting on a supporting body (e.g., the right foot). Establishing the balance of moments on each contact body allows us to determine the position of contact centers of pressure", "texts": [ " For ns links in contact we associate ns contact CoPs. Each contact center of pressure is defined as the 2D point on the contact surface where tangential moments are equal to zero. Therefore, 2ns coordinates describe all contact pressure points. Figure 2.5 illustrates a multi-contact scenario involving three supporting contacts on the robot\u2019s feet and left hand and an operational task designed to interact with the robot\u2019s right hand. We focus on the analysis of the forces and moments taking place on a particular contact body, as shown in Figure 2.6. Based on [60], we abstract the influence of the robot\u2019s body above the kth supporting extremity by the inertial and gravity force fsk and the inertial and gravity moment msk acting on a sensor point Sk. For simplicity, we assume the sensor is located at the mechanical joint of the contact extremity. Here, Pk represents the contact center of pressure of the kth contact extremity, frk is the vector of reaction forces acting on Pk, and mrk is the vector of reaction moments acting on Pk. The frame {O} represents an inertial frame of reference located outside of the robot, and the frame {Sk} represents a frame of reference located at the sensor point" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002664_tec.2020.2990914-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002664_tec.2020.2990914-Figure5-1.png", "caption": "Fig. 5. Topology, flux paths and flux density distribution of (a) the proposed 12/14 SRM and (b) the conventional 12/8 SRM with 5A excited current.", "texts": [ " At this end, two cases are considered: 1) The conventional 12/8 SRM and proposed 12/14 SRM were designed for a common application with frame NEMA24. On the other hand, the both motors have the same stack length, outer diameter and shaft diameter, so the volume of the two motors is identical. In addition, the air gap diameter of the both motors are also identical. 2) 12/8 SRM is optimized similar to the 12/14 SRM based on the flow-chart of Fig. 2. Table III summarizes its optimized parameters and the specifications of the optimized 12/8 SRM are given in Table I. Fig. 5 presents the topology, magnetic flux paths and magnetic flux density distribution within both SRMs when one phase is excited by 5A at the aligned position. As seen in Fig. 5, the magnetic flux densities in the teeth of the stators at the aligned position are almost the same in the both motors Authorized licensed use limited to: University of Canberra. Downloaded on April 29,2020 at 10:11:02 UTC from IEEE Xplore. Restrictions apply. 0885-8969 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. and are near the knee. The stator tooth width of 12/8 SRM is larger than that of the 12/14 SRM, but stator magnetic flux density at the aligned position is equal in the both motors and this depends on the magnetic circuit and reluctance viewed from every stator tooth" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000193_j.cma.2011.04.006-Figure15-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000193_j.cma.2011.04.006-Figure15-1.png", "caption": "Fig. 15. Contact patterns for: (a) case A2b, (b) case A2c, (c) case A2d and (d) functions of transmission errors for previous cases of design.", "texts": [ " Parabolic functions of transmission errors have been predesigned with levels of 8.5 arcsec for whole-crowned surfaces (Design 2) and 5.5 arcsec for partial-crowned surfaces (Design 3). Design 3 (partial-crowning) allows the contact pattern to cover a larger area of the bevel gear contacting surfaces, by creating an area of no modification of the tooth surfaces. The main advantage of this geometry is that the lower the misalignment is, the bigger the contact pattern is obtained, allowing contact stresses to be reduced. Fig. 15 shows the contact patterns for cases A2b (15(a)), A2c (15(b)), and A2d (15(c)). Fig. (15(d)) shows the obtained functions of transmission errors for previous cases of design. For cases of design A2b and A2c, the contact pattern is kept inside de contacting surfaces although for case of design A2d, it is shifted towards the top edge of the wheel, and might cause high contact stresses. All functions of transmission errors are obtained with parabolic shape, absorbing efficiently the lineal functions of transmission errors caused by errors of alignment for non-modified bevel gear tooth surfaces" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000880_0959651812455897-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000880_0959651812455897-Figure1-1.png", "caption": "Figure 1. Force analysis of the rigid longitudinal model of the hypersonic aircraft.", "texts": [ " Second, in each partition zone, we need to select and calculate the set-point in order to obtain the LPV model of the hypersonic aircraft in this partition. Third, using a Jacobian linearization method and tensor-product (TP) model transformation, we obtain the local polytopic LPV model of each partition zone. Combining all the local LPV models via the switching signal, which is determined by the scheduling parameters, we obtain the overall switched LPV model of the hypersonic aircarft. The model of the hypersonic aircraft considered in this paper was developed by Bolender and Doman.29,30 Figure 1 shows the force distributions of the ideal rigid longitudinal model of the hypersonic aircraft. In Figure 1, TH, DH, LH, GH are the thrust, drag, left and graviton force, respectively. The rigid non-linear longitudinal model of a generic hypersonic aircraft can be described as follows14,31 f1 = _VH = TH cosaH DH m mE sinu (RE + h)2 f2= _u= LH +TH sinaH mVH mE cosu VH(RE + h)2 + VH cosu RE + h f3 = _h=VH sinu \u00f01\u00de f4 = _aH = q u f5 = _q= Myy Iyy at MOUNT ALLISON UNIV on June 21, 2015pii.sagepub.comDownloaded from where VH, u, h, aH, q are state variables, representing velocity, flight path angle, altitude, angle of attack and pitch rate, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000221_00207179.2010.541285-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000221_00207179.2010.541285-Figure2-1.png", "caption": "Figure 2. Schematic explanation for triangular structure of .", "texts": [ "1 can be computed from the first vector field 1 of Krener and Isidori frame by setting 1\u00bc l( y) 1 where the function l( y) 6\u00bc 0 is to be determined, by recursion we have i \u00bc \u00bd i 1, f for 2 i n: Consequently, we can derive a relationship between these two frames as follows. Claim 2.1: The following formulae give the relationship between the frame and : 2 \u00bc l 2 \u00f0Lf l \u00de 1, \u00f013\u00de k \u00bc Xk 1 i\u00bc0 1\u00f0 \u00dei i k\u00f0L i f l \u00de k i for 2 k n, \u00f014\u00de where 0 k \u00bc k 1 k \u00bc 1, i k \u00bc i 1 k 1 \u00fe i k 1 for 1 i k 2, i k \u00bc 0 for i k: Proof: The proof of this claim is given in the appendix. \u0153 From (8,9) we have n( 1)\u00bc l( y). As n 1( 1)\u00bc 0, then following diagram of Figure 2 of the appendix, we have n 1( 2)\u00bc l( y). Therefore, one can deduce the following n n matrix: \u00bc \u00bc i j 1 i, j n \u00bc ij 1 i, j n , D ow nl oa de d by [ U ni ve rs ity o f N ew M ex ic o] a t 1 0: 39 1 4 O ct ob er 2 01 4 which has the following triangular-like structure: \u00bc 0 . . . . . . 0 l .. . :: l 2,n .. . :: :: :: .. . 0 l :: .. . l n,2 . . . . . . n,n 0 BBBBBBBB@ 1 CCCCCCCCA and thus is invertible. As a result, we can define the following multi-valued 1-form: ! \u00bc 1 \u00bc !i\u00f0 \u00de1 i n: The 1-forms (!i)1 i n can be computed recursively as follows: ", " Its differential d is a 2-form which can be computed on two vector fields X, Y as follows: d X,Y\u00f0 \u00de \u00bc LX Y\u00f0 \u00de LY X\u00f0 \u00de X,Y\u00bd : \u00f054\u00de If the 1-form is closed thus d \u00bc 0 then the formula gives X,Y\u00bd \u00bc LX Y\u00f0 \u00de LY X\u00f0 \u00de: Moreover, if LY (X)\u00bc 0 then we have X,Y\u00bd \u00bc LX Y\u00f0 \u00de: \u00f055\u00de From the construction of the Krener\u2013Isidori frame (see Equations (8,9) with l\u00bc 1), we can deduce the following facts: n i\u00f0 i\u00fe1\u00de \u00bc 1 for i \u00bc 0, . . . , n 1, n j\u00f0 k\u00de \u00bc 0 for 1 k5 j n 1: To obtain this relationship it is sufficient to use the formula (55) for \u00bc n 1, X\u00bc 1, Y\u00bc 2\u00bc [ 1, f ] and the diagram given in Figure 2 which gives j\u00fe1( k)\u00bc j( k\u00fe1) if j( k)\u00bc 0. Now, since n 1( 1)\u00bc n 2( 1)\u00bc 0, n( 1)\u00bc 1 then n 1( 2)\u00bc 1 and n 2( 2)\u00bc 0. The rest is obtained by induction and by using the same argument. Proof of Claim 2.1: By definition, we have 2 \u00bc \u00bd 1, f \u00bc \u00bdl \u00f0 y\u00de 1, f \u00bc l \u00f0 y\u00de\u00bd 1, f Lfl 1: On the other hand, [ 1, f ]\u00bc 2 hence 2\u00bc l( y) 2 Lfl 1. As a result (13) is true. Now we prove (14) by induction. For this, suppose that the formula (14) is true for a certain index k and show that it is also true for k\u00fe 1. For this, suppose that k \u00bcPk 1 i\u00bc0 1\u00f0 \u00de i i k\u00f0L i f l \u00de k i, then k\u00fe1 \u00bc \u00bd k, f \u00bc Xk 1 i\u00bc0 1\u00f0 \u00dei i k\u00f0L i f l \u00de k i, f \" # : As \u00bd\u00f0Li f l \u00de k i, f \u00bc \u00f0L i f l \u00de k i\u00fe1 \u00f0L i\u00fe1 f l \u00de k i, therefore we have k\u00fe1 \u00bc Xk 1 i\u00bc0 1\u00f0 \u00dei i k\u00f0\u00f0L i f l \u00de k i\u00fe1 \u00f0L i\u00fe1 f l \u00de k i\u00de: Now, the second term of this sum can be written as Xk 1 i\u00bc0 1\u00f0 \u00dei\u00fe1 i k\u00f0L i\u00fe1 f l \u00de k i\u00de \u00bc Xk i\u00bc1 1\u00f0 \u00dei i 1 k \u00f0L i f l \u00de k i\u00fe1\u00de: Hence k\u00fe1 \u00bc 0 kl k\u00fe1 \u00fe Xk i\u00bc1 1\u00f0 \u00dei\u00f0 i k \u00fe i 1 k \u00de\u00f0L i f l \u00de k\u00fe1 i \u00f0 1\u00dek k k\u00f0L k f l \u00de 1 \u00bc l k\u00fe1 \u00fe Xk i\u00bc1 1\u00f0 \u00dei\u00f0 i k \u00fe i 1 k \u00de\u00f0L i f l \u00de k\u00fe1 i: Finally, since i k\u00fe1 \u00bc i k \u00fe i 1 k , we obtain the desired formula k\u00fe1 \u00bc l k\u00fe1 \u00fe Xk i\u00bc1 1\u00f0 \u00dei i k\u00fe1\u00f0L i f l \u00de k\u00fe1 i \u00bc Xk i\u00bc0 1\u00f0 \u00dei i k\u00fe1\u00f0L i f l \u00de k\u00fe1 i, thus we prove Claim 2" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003198_j.mechmachtheory.2020.103960-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003198_j.mechmachtheory.2020.103960-Figure1-1.png", "caption": "Fig. 1. 3RRlS RPM.", "texts": [ " The rest of this paper is organized as follows: In Section 2 , the 3RRlS RPM and the proposed method are described in detail. Section 3 analyzes the constraint wrench system of 3RRlS RPM. Section 4 and Section 5 derive the stiffness matrix of 3RRlS RPM and n(3RRlS) RSPMs, respectively. Finally, Sec. 6 concludes this study. 2. Description of 3RRlS RPM and method 2.1. 3RRlS RPM The 3RRlS RPMs proposed in [5] has three identical limbs symmetrically distributed at three corners of the moving platform and static platform, as shown in Fig. 1 . Each limb is connected to the static platform with a revolute joint whose direction is parallel to the opposite side of the static platform triangle, and connected to the moving platform with a lock- Please cite this article as: C. Zhao, H. Guo and D. Zhang et al., Stiffness modeling of n(3RRlS) reconfigurable series-parallel manipulators by combining virtual joint method and matrix structural analysis, Mechanism and Machine Theory, https: //doi.org/10.1016/j.mechmachtheory.2020.103960 C. Zhao, H", " / Mechanism and Machine Theory xxx (xxxx) xxx 3 able spherical joint. Moreover, each limb consists of two links that are connected by a revolute joint whose direction is parallel to that of the revolute joint connected to the static platform. The directions and the input angles of revolute joint A i are expressed as s i (i = 1 , 2 , 3) and \u03b8i (i = 1 , 2 , 3) , respectively. The fixed coordinate system O j -1 X j -1 Y j -1 Z j -1 and the moving coordinate system O j X j Y j Z j are established, as shown in Fig. 1 (c), with their origins set at the respective center of the two platforms. Moreover, all axes of O j X j Y j Z j always remain parallel to the axes of O j -1 X j -1 Y j -1 Z j -1 . The absolute coordinate of origin O j is expressed as t o = (t ox , t oy , t oz ) T , and the orientation of the moving platform is expressed by the ZXZ Euler angle method, i.e. o ZXZ = (\u03d5, \u03b7, \u03c6) T . The outer radiuses of the static and moving platforms and the lengths of the links are r and d , respectively. Since the lockable spherical joint can be switched between the spherical joint (lS 2 ) and the Hook joint (lS 1 ), the 3RRlS RPM has four configurations, i" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001328_j.renene.2014.03.036-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001328_j.renene.2014.03.036-Figure3-1.png", "caption": "Fig. 3. NON-torque gearbox loading.", "texts": [ " The input for each of these FRFs is the forces at the rotor main shaft coupling. Fig. 2 shows the rotor-main shaft coupling and the corresponding forces. The main response of DOFs is the planet carrier displacements at the rear planet carrier (PLC) bearing location (PLC-B) and the gearbox bushing displacements. Fig. 1 shows the different bearings in the gearbox, whereas Fig. 2 shows the gearbox bushings. The planet carrier motion is investigated, since this parameter is significantly affected by the non-symmetric loading of the gearbox [6]. Fig. 3 illustrates this. Due to the planet carrier displacements the loading conditions in the planet-ring gear meshes can become unfavorable. This can potentially result in non-symmetric planet bearing loading and corresponding overloading of one of the planet bearings [10]. The planet-ring gear meshes displacements are not used in the FRF analysis in this paper since we want to make abstraction of the influence of the gear meshing stiffness on the behavior of the gearbox suspension. An ideal gearbox was assumed in this paper" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001790_j.mechmachtheory.2016.04.010-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001790_j.mechmachtheory.2016.04.010-Figure3-1.png", "caption": "Fig. 3. Schematic diagram of roller slices.", "texts": [ " Where {O;X,Y,Z} is inertial coordinate system of bearing; {om;xm,ym,zm} is coordinate system of roller's mass center; {orc;xrc,yrc,zrc} is coordinate system of roller's axial center; Subscript {i,o} represent inner raceway and outer raceway, respectively; \u03b8j is tilting angle of the jth roller; Nj i, Nj o are normal force between the jth roller and raceways; Tji, Tjo are oil drag force between the jth roller and raceways; MNj i , MNj o are additional moment due to Nj i and Nj o; MTj i , MTj o are additional moment due to Tj i and Tj o; Qcj, Fcj are normal force and tangential friction force between the jth roller and cage's cross beam, respectively; Mcj is additional moment due to Fcj; Fmj is centrifugal force of the jth roller. An improved slice method is applied to the handling of contact issue between roller and raceway [13], see schematic diagram of roller slices shown in Fig. 3. Where NP is the number of slices along the axis of the roller; l is roller length; W (W = l/NP) is width of slice; ls is effective length of roller; lc is distance between roller's mass center Om and roller's axial center Orc; qjmi , qjmo are contact forces between the mth slice and raceways; Tjmi , Tjmo are oil drag forces between the mth slice and raceways; Qcjm, Fcjm are normal force and tangential friction force between the mth slice and cage's cross beam, respectively. The elastic deformations between the mth slice of the jth roller and raceways at azimuth angle \u03c6j are expressed as [2]: \u03b4ijm \u00bc \u03b4r cos\u03c6 j\u2212\u03b4i\u03c6 j \u2212 Pd 2 \u2212Cjm \u03b4ojm \u00bc \u03b4o\u03c6 j \u2212Cjm 8< : \u00f01\u00de In Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001049_j.procir.2016.06.060-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001049_j.procir.2016.06.060-Figure1-1.png", "caption": "Fig. 1. Machine components and sensors position.", "texts": [ " For instance, the \u2018Total Layer Time\u2019 is the parameter that measures the total time spent when manufacturing one single layer. It includes the laser time to melt the layer geometry, the time for layering (number 13 of the table 1), and the time the machine may have been stopped. The latter was called \u2018Idle Time\u2019 (number 14 from table 1) and plays an important role to identify whether an error occurred during the manufacturing process. The position of the considered sensors and monitored machine components are shown in Fig. 1. The numbers are according to table 1. The CMT is a condition monitoring tool that permits an intelligent configuration of pattern recognition algorithms for fault detection and for diagnostics applications [8]. It was developed at Fraunhofer IPK and it has a modular design, which allows the user to interactively configure the algorithms via user interface. CMT composes the needed steps for a successful pattern recognition application, such as: signal preprocessing (e.g. filtering), features extraction and selection (e" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002969_tmag.2020.3007439-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002969_tmag.2020.3007439-Figure1-1.png", "caption": "Fig. 1. Causes of the eddy current losses in PMs and conductors.", "texts": [ " Section III describes the prediction method for mechanical loss by considering the iron loss and eddy current losses. The experimental method using the dummy rotor, the conventional method using no-load loss and iron loss, and the proposed method are compared in this section. Section IV verifies the proposed method by conducting simulations and experiments. The results of predicting the mechanical loss by using each method are compared in this section. Section V concludes this paper. The eddy current losses of PMs and conductors are induced by alternating external magnetic fields. Fig. 1 shows the causes of the eddy current losses and the eddy current path of PMs and conductors. The eddy currents are induced by the space- and time-harmonic components of air-gap magnetic flux density caused by the field flux and the structure of slots even Authorized licensed use limited to: Imperial College London. Downloaded on July 13,2020 at 02:03:54 UTC from IEEE Xplore. Restrictions apply. 0018-9464 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003662_s11665-021-06023-5-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003662_s11665-021-06023-5-Figure1-1.png", "caption": "Fig. 1 A schematic diagram of ultrasonic-assisted CMT arc additive manufacturing system", "texts": [ " Both P and S elements are controlled below 0.001% to ensure the toughness of additively manufactured parts. As a common low carbon steel, Q235 low carbon steel was utilized as base steel in these experiments, including C \u00a3 0.18%, Mn 0.35-0.80%, Si \u00a3 0.30%, S \u00a3 0.040, P \u00a3 0.040 according to GB/T700-2006. Prior to additive manufacturing, the base metal is cut into the size of 200 mm9 100 mm9 10 mm and 100 mm9 100 mm9 5 mm, and then, the rust and oil stains on the surface are removed completely. Figure 1 shows the CMT arc additive manufacturing system used in this study. The welding equipment adopts the TransPlus Synergic 5000 power supply and the matched TransTig 5000 Job G/F wire feeder. The path of the welding torch in the additive manufacturing process is controlled by a 6-axis KUKA robot. The substrate steel is fixed on a worktable that can move in the XY direction controlled by a digital computer. The KMDK1 ultrasonic generator is used as ultrasonic power in this study whose ultrasonic transducer is directly connected with the substrate steel to reduce the loss of ultrasonic propagation at the interface" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001038_1350650116689457-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001038_1350650116689457-Figure1-1.png", "caption": "Figure 1. External loads applied on the bearing: (a) loads on the bearing house; (b) loads on the outer ring.", "texts": [ " The measured cage motions are analyzed by fast Fourier transform (FFT) and motion orbits are described at various operating conditions including rotating speeds, axial and radial forces, or moments. Different patterns of cage motion are obtained based on the results. Dynamics of cage motion and measurement method Dynamic equations of the cage in an angular ball bearing. It is assumed that the outer ring is fixed in the bearing house, and the inner ring rotates at a constant angular speed !i around the bearing axis. The external loads are applied on the bearing house, as shown in Figure 1(a), and then the loads of bearing acting on the outer ring are represented as F \u00bc Fa Fr M , as shown in Figure 1(b), where Fa, Fr, and M denote the axial load, radial load, and moment of an angular ball bearing, respectively. The forces on the cage and its degrees of freedom are illustrated in Figure 2. And the cage motion can be represented by its mass center in the dynamic analysis. The cage mass center oc in the inertial frame oxyz can be described by the vector (xc, yc, zc). If the jth ball is in contact with the cage, the normal contact force and friction force on the cage due to this ball are denoted by Fcbj and fcbj, which can be decomposed to Fcbjx, Fcbjy, Fcbjz, fcbjx, fcbjy, fcbjz in x, y, and z directions, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001321_j.oceaneng.2015.02.006-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001321_j.oceaneng.2015.02.006-Figure2-1.png", "caption": "Fig. 2. Region tracking.", "texts": [ " Ismail and Dunnigan (2010, 2011) have modified the objective function to address the region boundary based control of an AUV where the region boundary is acting as a constraint. The objective function can be varied accordingly as single objective or intersection of several objective functions as per mission requirement. The objective function can also be modified to act as a repulsive region as proposed by Mukherjee et al. (2014) to solve the problem of obstacle avoidance. However, in some applications AUV is required to move within a constrained region as shown in Fig. 2. Li et al. (2010) proposed an adaptive controller where the desired region is time varying and region tracking control problem has been solved instead of region reaching control problem. In order to achieve fault tolerant control scheme for an AUV while region tracking, Ismail et al. (2013) have proposed an adaptive region tracking based controller where thrusters are fired only if the vehicle is outside the desired region. Region tracking control concept results in energy saving but does not provide a solution to the problem of large control input" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003299_j.tws.2020.107415-Figure31-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003299_j.tws.2020.107415-Figure31-1.png", "caption": "Fig. 31. The collapse modes and force-displacement curves of reinforced tubes with different boundary conditions.", "texts": [ " It presented that the consistency of the experimental results was very good for all specimens. This indicated that the experimental results were also stable and reliable. In this section, the influences of boundary conditions, oblique crushing and the number of modules on energy absorption were investigated through numerical simulation. The reinforced tube without imperfection was chosen as an example, and the thickness of the metal sheet was 1 mm. Other FE model details were consistent with Section 2.3. The boundary conditions were analyzed firstly, as shown in Fig. 31. It can be seen that although there were slight differences in the boundary conditions, the collapse modes still belonged to diamond mode overall. The force-displacement curves and the specific data are shown in Fig. 31 and Table 4. It shows that the Fmax of a tube with fixed-fixed condition was larger than that of free-fixed condition, which also larger than that of free-free condition. This was because the boundary conditions had a slight influence on the local stiffness of the tube. The SAE and EEA of the tube with free-fixed condition were the largest, the SAE and EEA of the tube with free-free condition were the lowest. In general, the boundary conditions had less effect on SEA and EEA. Table 5 and Fig. 32 also show the influence of friction coefficient on energy absorption" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001524_s12206-014-0931-7-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001524_s12206-014-0931-7-Figure4-1.png", "caption": "Fig. 4. Two topology changes of the 2(rT)2PS.", "texts": [ " There are two constraints, but the mechanism has three DOFs instead of four, indicating that the mechanism is in structure singularity. Above sections illustrate various topologies of the 2(rT)2PS parallel mechanism using the constraint planes. Based on this, altering the rTPS limb from phase (rT)2PS to phase (rT)1PS one by one in the mechanism will show all the other work phases of the mechanisms. When changing one limb phase, all the topologies in the above sections become the same topology 1(rT)1PS-1(rT)2PS as in Fig. 4(a) which has a translation constraint along normal n1 and is a five-DOF mechanism including the local rotation DOF about line A1A2. When further altering the other limb into (rT)1PS phase, the mechanism changes to another topology 2(rT)1PS as in Fig. 4(b). Since no geometric constraint exists, the 2(rT)1PS parallel mechanism has six DOFs. When constructing a metamorphic parallel mechanism with three rTPS limbs, there will be three constraint planes of which the normal relationships describe the topologies of the mechanisms. Generally, there are three categories: all three planes are parallel, two of them are parallel and intersecting with the third one, and all three planes intersect. Comparing with the two-limb mechanisms in Sec. 3, a main difference is that the local DOF on the platform vanishes if the three spherical joint centers are not in-line", " 7(a), the constraint of limb 1 and limb 2 follows that in Eq. (9) and A1A2 is constantly parallel to n1. In this case, Eq. (12) becomes ( ) ( )3 1 3 1 2 1 13 1. cosd d l j\u00a2 \u00a2 \u00a2 \u00a2- = - - =R a a a a . (15) As \u03c61 is a constant angle of the platform, Eq. (15) is an identical equation, indicating that limb 3 is redundant. In Fig. 7(a), limb 1 and limb 2 can be used to define the place of line A1A2 and limb 3 will determine the rotation of the platform about line A1A2. This shows difference with the 2(rT)2PS mechanism in Fig. 4(b) in which the local rotational DOF exists. Thus, the mechanism in Fig. 7(a) has three DOFs with two translations parallel to the constraint plane and one rotation about normal n1. A further special topology can be obtained by setting the distances between the three constraint planes to zero as in Fig. 7(b) in which all three limbs are constrained in the same plane. The geometric constraint follows that in Eq. (10) with d1 = d2 = d3 and the platform formed by A1A2A3 is constrained on plane \u22111, making the platform have a planar motion with two translations on the plane and one rotation perpendicular to the plane" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001628_s10010-017-0242-0-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001628_s10010-017-0242-0-Figure6-1.png", "caption": "Fig. 6 a Hobbing tool (mn = 0.4mm); b planet low-loss design; c planet standard design", "texts": [ "7 Kg s2K . This value is consistent with the suggested values provided by literature. It appears that by increasing the operating temperature, the heat flux increases linearly while the power losses decrease monotonically. This consideration ensures the possibility to find the equilibrium between the dissipated power PL and the removed heat Q with an iterative procedure. Prototypes were produced in order to validate the results of the calculations. The gears were manufactured with a hobbing tool (Fig. 6a) while the ring gears were produced with an electro-erosion process. All other components such as planet-carrier, bearings and seals are identical for both prototypes (except for the center-distance). The gearboxes have been tested on an energy closed-loop test rig which layout is shown in Fig. 7. The 45Nm electric servomotor (1.) is controlled by an inverter and connected to the tested gearbox (3.) with a metal bellow coupling (2.). A torque-meter (10Nm \u2013 0.1% F.S. (Full-scale value)) (2.) allows the measurement of the input torque" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003240_tpel.2020.3029822-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003240_tpel.2020.3029822-Figure2-1.png", "caption": "Fig. 2. Diagram of the stator current and winding arrangement. (a) Stator current in the proposed drive. (b) Winding arrangement of the 12/8 SRM.", "texts": [ " WORKING PRINCIPLE OF THE DEVELOPED FLUX MODULATED SRM For the proposed flux modulated 12/8 SRM drive, when it is driven by a dc-biased sinusoidal current, the three-phase SRM can be regarded as a new kind of flux modulation machine and the working principle can be analyzed based on the flux modulation principle, including excitation magnetic field generation, flux modulation, and armature magnetic field generation. In the proposed drive, the stator current contains both the ac and dc components, as shown in Fig. 2 (a). The dc-biased current component in the stator current plays the role of an excitation magnetic motive force (MMF) generator, which is similar to permanent magnets in PMSMs. Fig. 2 (b) shows the stator-winding connection of the 12/8 SRM, where the symbols \u201c+\u201d and \u201c-\u201d represent the N and S polarities, respectively. Because the polarities of the stator windings wounded on the adjacent stator teeth are opposite, a six-pole-pair stationary excitation MMF will be generated. By using the Fourier decomposition, the mathematical equation of the excitation MMF can be given by 3,5,7,... 3,5,7,... 1 1 cos( ) cos( ) 2 s f i dc s i dc s i i N F F iP N I i (4) where Fi is the i-th harmonic component of the stationary excitation MMF, Pdc is the pole pair number of the stationary excitation MMF, Ns is the stator slot number, \u03b8s is the air gap mechanical angle, and Ni is the equivalent coil turns number of the stator winding of the i-th harmonic component", " 1 ( ) cos( ) 2 ( ) cos( ) 3 2 ( ) cos( ) 3 a s n a s n b s n a s n c s n a s n N N nP N N nP n N N nP n (10) where Nn represents the winding function of n-th winding harmonic and Pa represents the pole-pair number of the stator winding. By substituting (8) and (10) into (9), the mathematical equation of three-phase back-EMF can be obtained. It is worth noting that only when the coefficient of \u03b8s is equal to 0, the back-EMF can be generated. Hence, the relationship among Ns, Nr, and Pa should satisfy 2 s a r N nP i kN (11) As shown in Fig. 2(b), the stator teeth number, rotor teeth number, and stator winding pole-pair number of the 12/8 SRM are 12, 8, and 4, respectively, which satisfies the relationship in (11). Therefore, the phase back-EMF can be generated by injecting the dc-biased current into the stator winding. The mathematical equation of the phase back-EMF can be given by 2 0 0 2 ( ) [ ( , ) ( ) ] sin( ) s a r a g stk gr s a s s r g stk i dc n s rk r r N nP i kN d e t r l B t N d dt k r l N I N kN t (12) In addition to the fundamental component, there are also harmonic components in the mathematical equation of the phase back-EMF, as shown in (12)" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002040_j.msec.2017.03.311-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002040_j.msec.2017.03.311-Figure2-1.png", "caption": "Fig. 2. Example of 3D topography images a) EB single bead on plate b) EB structure.", "texts": [ " [19] analysed several works about the effect of titanium surface topography on bone integration and concluded that the comparison of roughness values from different investigations was very difficult due to the changing in the surface evaluation. For this reason, in this work, the surface was analysed by using Alicona Infinite Focus microscope. A special focus variation technique allowed to create a 3Dprofile of the studied surface. The EB structured Ti6Al4V samples were recorded with 10\u00d7 and 50\u00d7 objective lenses, with a maximal vertical resolution of 100 nm and 50 nm, respectively. The lateral resolution was 3 \u03bcm for lens of 10\u00d7 and 2 \u03bcm for 50\u00d7. Fig. 2 illustrates examples of acquired surface profiles, the determinedwidth\u0394wanddepth/height \u0394z measurements and the position of measurements (position 1 at 200 \u03bcm and position 2 at 600 \u03bcm from the border) for designed figures. Post structuring heat treatments were performed under vacuum with a heating rate of 300 K/min, up to 650 \u00b0C and 720 \u00b0C, then isothermally held for 8 h, followed by quenching in argon atmosphere to improve the mechanical behaviour of the melted zone. Vickersmicro-hardnessmeasurementwas carried out using aMHT4 (AntonPaar)with an indentation loadof 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000957_2013-01-2117-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000957_2013-01-2117-Figure3-1.png", "caption": "Figure 3. Schematics of two consecutive links under the gravity effect.", "texts": [ " Therefore, only the gravity effects of the links and the weight of the tool on the gearboxes are taken into consideration. Thus, an elasticity model of the gearboxes of joints 2, 3, 4, 5, and 6 is developed. Each gearbox i is modeled as a linear torsional spring, by using one parameter, which represents the constant compliance ki. Torsional, traction and compression effects are neglected. Considering that the deformations are quite small, the superposition theory can be applied and the beam foreshortening neglected. Figure 3 represents a simplified 2D representation of two links. Torques are calculated recursively from joint 6 down to joint 1. Joint i(i = 1, \u2026, 5) is affected by link i and link 6 if affected by link 6 and the end-effector. Knowing that the endeffector is fixed on link 6, they can be considered as one solid having only one gravity center. Thereby, the gravity vector seen by joint i is presented as follows: (11) where g0=[0 0 \u22129.81 1]T, and the homogeneous transformation matrix represents the reference frame of joint b with respect to the reference frame of joint a: (12) The gravity force of link j seen by a previous link i is calculated as follows (13) Also, the center of gravity of link j with respect to reference frame i can be determined as (14) where cj, is the center of gravity of link j with respect to Fj, and should be calculated for all the cases where I \u2264 j" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003532_s00466-021-02079-1-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003532_s00466-021-02079-1-Figure6-1.png", "caption": "Fig. 6 A schematic and the coordinate system of the laser processing", "texts": [ " If flags have any interval between \u20181\u2019s (flaggedup), that is a failed path. This is applied in the same way for inner boundaries for hollow geometries. Also, a similar principle could be applied for detecting the self-colliding paths. The overall flowchart of the dynamic programming process is shown in Algorithm 2. After obtaining all of the possible laser paths, one needs to mathematically model the laser sintering process in order to perform numerical simulations for given laser paths. A schematic of the laser processing is shown inFig. 6.As for the grid configuration, we adopt amaterial grid that is three times finer than the laser grid and includes the laser grid nodes, as shown in Fig. 7. In Fig. 7, yellow circles represent the area covered by laser. While the laser grid points are the positions through which a laser moves as time progresses, the material grid points are the points where numerical simulations are actually performed to evaluate the thermal gradients. The simulation parameters are shown in Table 1. The governing equation is as follows: \u03c1C \u2202\u03b8 \u2202t = \u2207 \u00b7 (K\u2207\u03b8) + Iabs, (3" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000770_cac.2013.6775734-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000770_cac.2013.6775734-Figure2-1.png", "caption": "Fig. 2. Inertia and body coordinate system of the quadrotor", "texts": [ " MATHEMATICAL MODEL The quadrotor helicopter used in this paper is developed by Comb Studio from Beihang University as shown in Fig. 1. The quadrotor UAV consists of four fixed pitch angle rotors powered by four electronic motors which are mounted at the end of an X-shaped frame. The quadrotor vehicle system is composed of four subsystems, the airframe, the power system and the flight control system. To improve the safety of experiments, carbon- fiber tubes are mounted on the airframe [6]. The derivation of the dynamics is based on inertial and body frames. And the definition of the two frames is shown in Fig. 2. Let ( , , )B x y z be the frame attached to the vehicle body and ( , , )E x y z denote the inertial frame. The origin of the inertial frame is set to the take-off point while the origin of body frame is in the vehicle center of gravity (CG). The rotation matrix ( , , )R \u03c6 \u03b8 \u03d5 from body frame to inertial frame depends on the three Euler angles ( , , )\u03c6 \u03b8 \u03d5 representing, respectively, the roll, the pitch and the yaw. To simplify the model process and facilitate the flight control design, the quadrotor is seen as a rigid-body and the center of gravity coincides with the origin of the body coordinate system" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002291_j.optlastec.2016.09.019-Figure8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002291_j.optlastec.2016.09.019-Figure8-1.png", "caption": "Fig. 8. Designed dimension (in mm) of \u201cvase\u201d shaped part.", "texts": [ " Our lab developed a lift distance closed-loop control apparatus based on image sensor measuring [25], after data processing the actual layer height data as feedback values are transferred by ProfiNet to the controller of KUKA robot. Fig. 7 shows the deposition process of a hollow \u201cvase\u201d shaped metal part. The angle of cladding head varied to keep tangential orientation to the \u201cgrowing\u201d part. The largest cladding angle achieved 80\u00b0 in Fig. 7(f). During the deposition process spattered only a little sparks, and no flowing or dripping of molten pool happened. The total manufacture time was 7 h. The cross section drawing of the \u201cvase\u201d shaped part is shown in Fig. 8, and its formed part is shown in Fig. 9. Positions 1\u20137 in Fig. 9 are positions to measure for surface roughness. Only the 7 relative smooth positions are measured. The roughness value of every position is averaged from several data on the ring of equal height. The instrument is TR200 handheld surface roughness tester. And the results are found in Table 3. The best surface roughness measured is in position 6 with Ra=3.864 \u00b5m. The powder efficiency is 62% (mass of formed part/mass of used powder)" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001379_978-3-319-22056-7-Figure1.12-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001379_978-3-319-22056-7-Figure1.12-1.png", "caption": "Fig. 1.12 Sectional model of crane mechanism", "texts": [ " It consists of five rigid bodies: body 1 which is in contact with the ground, body 2 mounted on 1, body 3 connected to 2 bymeans of pivot, body 4 which is an excavator arm connected with 3 by means of a joint, and body 5 which is the excavator scoop and can rotate around the body 4. Excavator scoop has a varying mass. The operating movements can be realized by means of the jib 3, arm 4 or the scoop 5 movements. A crane represents a mechanism for load transportation. A typical sectional model of a crane (Fig. 1.12) consists of four rigid bodies: body 1 which is in elastic contact with the ground, body 2 mounted on 1, body 3 connected with 2 by means of joint and a component 4 connected with 3 by a flexible cord. Component 4 has a time variablemass, because it includes the load. Variation ofmass and its distribution along the elements of a mechanism have a significant influence on belt type automatic dosing devices. The aim of the mechanism shown in Fig. 1.13 is to achieve constant mass flow of material. Mechanism contains: basket 1, belt conveyor 2 and bar mechanism 3" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000476_1.4007349-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000476_1.4007349-Figure6-1.png", "caption": "Fig. 6 Spring elements used for a double row bearing", "texts": [ " All the components except the rolling elements, such as the hub, the plane rib, the root of the blade and the bearing rings are meshed using the SOLID45 elements which are defined by eight nodes having three degrees of freedom at each node: translations in the nodal x, y, and z directions. The balls are simulated by the COMBIN39 elements, which are unidirectional, nonlinear spring elements with the user-defined load and deformation characteristics. There are three degrees of freedom at each node: translations in the nodal x, y, and z directions. No bending or torsion is considered. Figure 6 shows spring elements in the FE model. Two COMBIN39 elements are used at each ball location with one end joined with the curvature center of the raceway. There are 216 balls in the double-row bearing. A total of 432 COMBIN 39 are used. The stiffness of each COMBIN 39 element is determined by the contact stiffness between the ball and the raceway, which is defined by the following equation derived from the Hertzian theory of contact [10], Journal of Tribology OCTOBER 2012, Vol. 134 / 041105-3 Downloaded From: http://tribology" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002624_j.compstruct.2019.111561-Figure16-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002624_j.compstruct.2019.111561-Figure16-1.png", "caption": "Fig. 16. Deployment of Type B-IO-IO with a 3U CubeSat under applied 3V DC. (a)\u2013(d) Deployment of the solar panel, (e) and (f) ultra-light release device completing release function.", "texts": [ " 15(a) and (b) show starting time of 25 s, recovery time of 50 s and recovery ratio more than 98%, approximately. Those with single-circuit heaters in Fig. 15(c) and (d) show prolonged starting time of 40 s, recovery time of 65 s and recovery ratio 95%, approximately. These findings suggest that the release device stimulated by single-circuit heaters still has a good shape memory recovery behavior, therefore the heating reliability is increased. The release of solar arrays is illustrated by \u2018Type B-IO-IO\u2019 with 3V voltage in Fig. 16. The panel begins to expand at 18 s, and is released and fully deploys in 24 s. The release time of 24 s decreases significantly compared with the free recovery of 47 s. The shape recovery ratio is 61.54% when the deployment is completed, which is obviously lower than free recovery ratio of 99.3%. The shape recovery ratio is thus of little value to judge the deployment, but the release time really matters. Therefore, four types of devices are applied to release solar arrays with the release time recorded" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002606_s00170-019-04141-y-Figure11-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002606_s00170-019-04141-y-Figure11-1.png", "caption": "Fig. 11 2D material utilization plot", "texts": [ " Obviously, SW shows an increasing function of the block height. Materials utilization should be considered as the first priority among three attributes when fabricating parts with precious or costly materials. The material utilization can be calculated according to Eq. (13). Analogously to surface waviness, the regression model which describes the dependence of MU on WFS and RWT can be obtained as follows: MU \u00bc \u221218:92\u00fe 29:53WFS \u00fe 7:16RWT\u22121:2WFSRWT\u22121:6WFS 2 \u00f018\u00de which clearly exhibits the dependence of MU on the WFS and RWT. Figure 11 shows the 2D plot of material utilization. The material utilization can be significantly increased by increasing the WFS. Regarding parts with low cost and low manufacturing accuracy, the effective deposition rate should be taken into first consideration. Increasing the deposition efficiency can greatly reduce the processing time and is more suitable for manufacturing large size parts. The calculation method of EDR was presented in Section 3 and the highest deposition rate of the aluminum alloy wire used in this experiment can reach 1" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003110_j.mechmachtheory.2020.104122-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003110_j.mechmachtheory.2020.104122-Figure1-1.png", "caption": "Fig. 1. Harmonic drive components.", "texts": [ " The influences of the wave generator structure (automatic alignment and integral structures) and shape on the pure kinematic error of harmonic drive are discussed and quantitatively evaluated, and the one possible new configuration of the wave generator is presented, which can improve the transmission performance of the drive. The results of this paper are believed to be useful for the design of harmonic drive. \u00a9 2020 Published by Elsevier Ltd. The harmonic drive (HD) is well known for its high reduction ratio, low weight, small volume, and high efficiency [1] , and it is used widely in the field of robotics [2] . These may benefit from its unique transmission principle and simple geometric structure. A HD contains only three main components as shown in Fig. 1 . The wave generator (WG) is an elliptically shaped steel core surrounded by a flexible race bearing. The flexspline (FS) is a thin-walled flexible cup having two fewer teeth on its outer rim than on the inner rim of the circular spline (CS). The CS is a rigid steel ring with teeth machined into the inner circumference. Understanding the mechanism of kinematic error is expected to improve the control performance of harmonic drive-based devices such as robot manipulators [3] , and the transmission performance of HD from a design perspective purposefully" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001382_acc.2016.7526736-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001382_acc.2016.7526736-Figure1-1.png", "caption": "Fig. 1. Hexacopter", "texts": [ " In order to analyze the case where some \u039bii = 0, note that in Vad the term tr ( \u0398\u0303\u0398\u0303 T \u039b ) = \u2211p i=1 \u039bii\u0398\u0303 T i \u0398\u0303i. This means that if \u039bii = 0, the i-th row \u03b8\u0303 T i is not contained in the Lyapunov function. As this also means that the i-th actuator does not influence the dynamics of the system, these parameters are not relevant, but should remain bounded. This is guaranteed by the projection algorithm (10). That a solution \u0398 exists is guaranteed by assuming that BA\u039b has full row rank. For describing the dynamics of the hexacopter we use an inertial frame I and a body-fixed frame B as in Figure 1, such that the origin is at the center of gravity. In this case the dynamics are described by [24] x\u0307 = v, (12) v\u0307 = 1 m t+ g, (13) t\u0307 = RIBTu (T ) \u03c9x \u03c9y T\u0307 = \u2212T\u0307zB +RIBT\u03c9 (T )\u03c9, (14) \u03c9\u0307 = J\u22121 (\u2212\u03c9 \u00d7 J\u03c9 +M) , (15) Here, x \u2208 R3 is the position, v \u2208 R3 is the velocity and \u03c9 \u2208 R3 is the angular rate of the hexarotor. RIB \u2208 SO3 is the rotation matrix which maps a vector from the B-frame to the I-frame and zB \u2208 R3 is the unit vector pointing along the body-fixed z-axis. g \u2208 R3 is the constant gravitational acceleration, m is the mass of the hexacopter and J \u2208 R3\u00d73 is the moment of inertia", " For a detailed derivation of the equations (12)-(15), the reader is refered to [24]. The matrices T\u03c9 \u2208 R3\u00d73 and Tu \u2208 R3\u00d73 are given by T\u03c9 (T ) := 0 \u2212T 0 T 0 0 0 0 0 , Tu (T ) := 0 \u2212T 0 T 0 0 0 0 \u22121 . Furthermore, as all rotors are aligned in the xy-plane, the propulsion force is t = \u2212TzB. (16) Note that T and M can be seen as the virtual controls of the system (12)-(15). The roll and pitch moments depend on the geometrical arrangement of the rotors. The yaw moment depends on the rotation direction of the rotors. Considering the configuration as in Figure 1, it is possible to write their relationship to the angular velocities of the rotors as [25] \u03bd := ( T M ) = BAu, (17) where u = ( \u03c92 1 \u03c92 2 \u03c92 3 \u03c92 4 \u03c92 5 \u03c92 6 )T and BA \u2208 R 4\u00d76 is defined as [25] kT kT kT kT kT kT 1 2 lkT lkT 1 2 lkT \u2212 1 2 lkT \u2212lkT \u2212 1 2 lkT\u221a 3 2 lkT 0 \u2212 \u221a 3 2 lkT \u2212 \u221a 3 2 lkT 0 \u221a 3 2 lkT kM \u2212kM kM \u2212kM kM \u2212kM . The constants kT , kM > 0 \u2208 R are specific rotor parameters and l > 0 \u2208 R is the arm length. For a detailed derivation of the actuator model (17) refer to [25]. As the matrix BA has a full row rank, for a given desired \u03bdd \u2208 R4 it is possible to find a function which maps it into the input space u = u (\u03bdd) so that \u03bd = BAu (\u03bdd) = \u03bdd" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003482_tia.2021.3066955-Figure11-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003482_tia.2021.3066955-Figure11-1.png", "caption": "Fig. 11. Acoustic analysis of the 18/12 SRM. (a) Acoustic body. (b) Imported velocity from mechanical analysis.", "texts": [ " In acoustic analysis, the area around the stator called acoustic body is investigated then the velocity from mechanical analysis is imported as the input of acoustic analysi,s so that all parts of the machine can be suppressed. Acoustic body is the area around investigated electric machine which is useful to observe the generated acoustic noise. In the acoustic analysis, we set the diameter of acoustic body is 1 m while Authorized licensed use limited to: East Carolina University. Downloaded on June 21,2021 at 02:37:14 UTC from IEEE Xplore. Restrictions apply. the depth of acoustic body is similar with the stack length of the SRM. Fig. 11(a) and (b) shows acoustic body in ANSYS acoustic analysis and imported velocity at the stator surface from mechanical analysis, respectively. The hole in the center of acoustic body is suppressed 18/12 SRM. Outer diameter of acoustic body is set to 1 m. Fig. 12 shows acoustic noise spectrum comparison with respect to the square current. Acoustic noise reduction is mostly achieved by all the proposed currents with respect to the square current although the reduction ratio is different in each proposed current" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000620_1.3601565-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000620_1.3601565-Figure5-1.png", "caption": "Fig. 5 Three-dimensional sketch showing major planes used when sectioning fatigue spalls on a cone (inner race of a tapered roller bearing). The type of failure depicted here is the inclusion origin plus hydraulic pressure propagation. The inclusion origin is generally subsurface and forms a semiellipsoidal spall. The hydraulic-pressure propagation may be compared with Figs. 2(a) and 3(fa). The nonmetallic inclusion related to the origin is shown as it is normally seen on the longitudinal plane.", "texts": [ " Failures in Test A had been called \"point surface origin\" because of the arrowhead-shaped spalls, but were found to have nonmetallic inclusions at the origin, when sectioned after testing. Illustrations of typical spalls from test groups A-l and A-2 are given in Fig. 2. Confirmation of the mode of failure in each of the lubricants was made by sectioning typical spalled areas to show the nonmetallic inclusion origin and the extent of the crack propagation. Figs. 3 and 4 show confirmation of the inclusion origin for bearings tested in the low viscosity mineral oil and the SAE 20 oil, respec- tively. A three-dimensional sketch is shown in Fig. 5 to illustrate the location of the nonmetallic inclusion stringer with respect to the spall origin and subsequent cracking as they appear on the transverse and longitudinal planes of sectioning. The predominant mode of failure was the inclusion origin in both test groups but with very little propagation in the SAE 20 and extensive hydraulic pressure propagation occurring in the low viscosity mineral oil. Apparatus and Procedure L i f e T e s t s o f T a p e r e d R o l l e r B e a r i n g s i n M i n e r a l O i l s a n d S y n t h e t i c Fluids" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001546_j.jmbbm.2015.11.024-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001546_j.jmbbm.2015.11.024-Figure3-1.png", "caption": "Fig. 3 \u2013 Needle insertion experimental set up.", "texts": [ " The signal generated by the load cell was recorded using a dynamic strain recorder (DC-104R, TML, Japan) at a rate of 100 Hz. Needle insertion was controlled using a linear stage system (model LP28T, Applied Motion Products, Watsonville, CA). Needle insertion and retraction forces were measured with an axial tension-compression miniature load cell (model 31, Honeywell-Sensotec, Columbus, OH). The needle was attached to the load cell with a custom polyether ether ketone (PEEK) holder which also provided axial alignment. Fig. 3 shows and scheme of the needle insertion experimental set up. Signal from the load cell was recorded using an interface card (DC-104R, TML, Japan) at a rate of 200 Hz. Three needle insertion speeds of 0.2, 1.8, and 10 mm/s were evaluated, which have been used in other insertion studies of electrodes and needles into brain tissue (Casanova et al., 2014a, 2014b; Bjornsson et al., 2006; Rousche and Normann, 1992). Blunt tip 28, 30, and 32 gauge (diameters of 0.36, 0.31, and 0.23 mm, respectively) needles (Hamilton, Reno, NV) were used in the experiments" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002037_s11071-017-3461-x-Figure9-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002037_s11071-017-3461-x-Figure9-1.png", "caption": "Fig. 9 The detailed discretization of RAParM-I using finite element approach. Notice that j-Ei represent element i in flexible body j", "texts": [ " Theoretically, the more the number of elements is, the higher the accuracy is. However, during the practical computation, the complexity of system dynamic model should be taken into consideration. Thus, the number of elements for each flexible body of system should be set reasonably to guarantee the solution efficiency and precision simultaneously. In this paper, RAParM-I encompasses totally 8 flexible bodies. Herein, the total number of elements is set as 20, and the detailed discretization using finite element approach is depicted in Fig. 9. After discretization using finite element approach, the number of flexible generalized coordinates is 80, the number of rigid generalized coordinates is 24 (including 8 rotational angle coordinates of body-fixed coordinate systems and 16 position coordinates of original points of body-fixed coordinate systems), and the total number of generalized coordinates of system is 104. The associated physical parameters of RAParM-I are listed in Table2. 5.2 Design of simulation flow As is mentioned in Remark 3, once the flexibilities of links are not considered, the RFDM derived in this paper will degrade into the rigid dynamic model (RDM), which can be referred to in Ref" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001013_jfm.2011.561-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001013_jfm.2011.561-Figure4-1.png", "caption": "FIGURE 4. A general swimmer lifts two weights.", "texts": [ "3) Now the extra force and moment available to do external work are F\u20321 = (1\u2212 \u03b1)A \u00b7U + (1\u2212 \u03b2)B \u00b7\u2126 , M \u20321 = (1\u2212 \u03b1)C \u00b7U + (1\u2212 \u03b2)D \u00b7 \u2126 . (4.4) We do not know the direction of these forces and moments relative to F1 and M1. However we assume that only the projection of F\u20321 onto \u03b1U and M \u20321 onto \u03b2\u2126 matter. This can be realized by pulling on a string aligned with U attached to a weight, for the force, and letting the extra moment twist up a pully in the plane orthogonal to \u2126 , so as to wind up a string which lifts a second weight, see figure 4. Proceeding as in the previous calculation for the axisymmetric swimmer we arrive at the following expression for thermodynamic efficiency under reduction of data: \u03b7T(\u03b1, \u03b2)= \u03b1(1\u2212 \u03b1)a+ (\u03b1 + \u03b2 \u2212 2\u03b1\u03b2)b+ \u03b2(1\u2212 \u03b2)c \u03c1 + (1\u2212 \u03b1)a+ (2\u2212 \u03b1 \u2212 \u03b2)b+ (1\u2212 \u03b2)c \u2261 N M , (4.5) where a=\u2206\u22121U \u00b7A \u00b7U, b=\u2206\u22121U \u00b7B \u00b7\u2126 , c=\u2206\u22121\u2126 \u00b7D \u00b7\u2126 , (4.6) \u2206= U \u00b7A \u00b7U + 2U \u00b7B \u00b7\u2126 +\u2126 \u00b7D \u00b7\u2126 , (4.7) and again \u03c1 =\u03a622/\u03a611 \u2212 1. We note that a> 0, c> 0, a+ 2b+ c= 1, ac> b2, (4.8) the inequality following from (4.2). We now need a condition ensuring that we are dealing with a physically realizable system, in the sense that non-negative external work is being done under partial tethering" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000931_9781118703274.ch2-Figure2.40-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000931_9781118703274.ch2-Figure2.40-1.png", "caption": "Figure 2.40 Moments arising as a result of teetering", "texts": [ " the moment Mlift, developed as a result of lifting forces, usually becomes larger due to aerofoil deflection. Due to mass shifts, extra propeller moments are generally developed. Furthermore, the moment of inertia of the deformed blade becomes significantly greater than it is in its undeformed state (see Figure 2.39). Moments resulting from rotor teetering and the associated changes in pitch, which arise mainly in teetered hub models, are mainly dependent on blade angle and the amplitude of teeter during blade rotation (see Figure 2.40). In symmetrical blade arrangements, moments engendered (e.g. due to the acceleration of inert masses) cancel each other out with respect to the external drive. Propeller moments, on the other hand, can change considerably. Because of the significant influences and the continually changing conditions during the rotation of a blade, these effects cannot be handled as they stand without unacceptable computing effort. The determination of extreme conditions is often sufficient, however, for dimensioning purposes" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001548_025007-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001548_025007-Figure5-1.png", "caption": "Figure 5.Kinematic systems: (a) the snake-like robot ACM-R5 fromHirose-Fukushima Robotics Lab (left) and (b) the nBot unicycle platform from theGeological Science Center of SouthernMethodist University.", "texts": [ " In closing this example, we note that applying the same considerations to the translations of the floating frame and using the mass center theorem gives = r( ) 0 because no external force is applied to the system. Thus, in this second case, the internal shape motions cannot act on the linear motions of the floating frame, which means that there is no \u2018connection\u2019 between thesemotions. Case 2: kinematic connection Nowwe consider the examples of an undulatory snake and a nonholonomic wheeled (unicycle) platform, as shown in figure 5. The reference frame is attached to the head of the snake and to the platform. Because both systems evolve in the plane, the principal fiber bundle of their configurations is \u00d7 SE(2) , where stands for the space of the snake skeleton in the one case and for the two-dimensional torus of the unicycle wheels in the other. Once again, a connection exists [48, 64, 74] between the internal shape motions and the external net motions of these two systems. This connection is generated by assuming that the contacts between the ground and the snakes\u02bcs scales or the wheels are both modeled by ideal non-sliding (NS) and rolling without slipping (RWS) conditions14" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003608_s11665-021-05603-9-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003608_s11665-021-05603-9-Figure2-1.png", "caption": "Fig. 2 SP testing fixture used at NIST, shown disassembled (a) and assembled (b)", "texts": [ " In most cases, correlations appear to be strongly dependent on the material (or the class of material) under investigation and cannot be expected to be more generally applicable (Ref 5). The fixture developed at NIST for testing SP specimens consists of an upper and a lower die, a rod (100 mm long, 2.5 mm diameter), and a ball (2.5 mm diameter). The combination of the rod and ball constitute the punch, which is driven through the specimen, encapsulated between the upper and lower die. The fixture is shown in Fig. 2 in both disassembled (a) and assembled (b) form. The fixture was mounted on a universal electro-mechanical test machine, equipped with a 5 kN capacity load cell and an extensometer. The extensometer was attached to one of the columns of the machine in order to measure the relative displacement between the machine actuator and the machine frame, in close proximity to the punch. Figure 3 shows the fixture mounted on the test machine and the positioning of the extensometer with respect to the machine actuator" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003580_j.mechmachtheory.2020.104238-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003580_j.mechmachtheory.2020.104238-Figure4-1.png", "caption": "Fig. 4. Schematic diagram of external-external spur gears meshing.", "texts": [ " Due to the geometric characteristics of involute, the angular displacement of gears does not vary linearly with the linear variation of the pressure angle. In Fig. 3 (a), points 1, 2, 3 and 4 are the critical meshing point, respectively correspond to the mesh starting, double-tooth mesh to single-tooth mesh, single-tooth mesh to double-tooth mesh and the disengaging, as shown in Fig. 3 (b). When a pair of teeth comes into mesh, the mesh starting point may not coincide with the involute starting point just like the point K and point P as shown in Fig. 4 . For an arbitrary point on the involute, for example point S in Fig. 4 , when it turns to S \u2032 which is on the mesh line MN , the angular displacement of the driving gear can be calculated by Eqs. (27) - (30) as follows: \u2220 S O 1 S \u2032 = \u2220 S O 1 K + \u2220 K O 1 S \u2032 (27) \u2220 S O 1 K = ( tan \u03b1x \u2212 \u03b1x ) \u2212 ( tan \u03b1s \u2212 \u03b1s ) (28) \u2220 K O 1 S \u2032 = \u03b1x \u2212 \u03b1s (29) \u03b1s = cos \u22121 \u239b \u239d R b1 \u221a R 2 t2 + O 1 O 2 2 \u2212 2 R t2 O 1 O 2 cos ( cos \u22121 R b2 R t2 \u2212 \u03b10 ) \u239e \u23a0 (30) herein \u03b1x is the pressure angle at arbitrary point on the involute. \u03b1s is the pressure angle at the starting point of mesh. O 1 O 2 represents the gear center distance" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000160_acc.2009.5160136-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000160_acc.2009.5160136-Figure1-1.png", "caption": "Fig. 1. Photo of a Dual Mass Flywheel, by cow-tesy of Grau Schnittmodelle, Notzingen. Germany.", "texts": [], "surrounding_texts": [ "Piston engines do not generate a constant torque but a time-varying torque Teng(t). The shape of this torque function depends Inainly on the engine speed >< >>: (12) For each kinematic chain, the active input $Ii is transmitted to the mobile platform through a unit transmission wrench screw $Ti, which is $Ti \u00bc \u00f0CiPi; oCi CiPi\u00de jCiPij : (13) If three inputs, except for the i-th input are locked, then only the transmission wrench screw $Ti will contribute to the motion of the mobile platform" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002277_978-3-319-27131-6-Figure4.2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002277_978-3-319-27131-6-Figure4.2-1.png", "caption": "Fig. 4.2 Hertzian contact areas in rolling bearings", "texts": [ " The lubrication in the rolling bearings occurs in the EHL region at very high loads, in which the rolling element is deformed elastically due to the high Hertzian pressure in the Hertzian contact area between the rolling elements and raceways. For ball bearings, the ellipse contact area with an elliptic footprint has a rolling minor ellipse axis 2b in the rolling direction x that is much smaller than its major ellipse axis 2a in the axial direction y (2b< 2a). In the case of roller bearings, the rectangular contact area between the rollers and raceways has an axis 2b in the rolling direction x and the roller length L in the axial direction (2b< L ) (cf. Fig. 4.2). 66 4 Oil-Film Thickness in Rolling Bearings the contact Hertzian area, in which the bearing operates in the HL regime. However, at high loads on the bearing, the rolling elements strongly deform elastically in the Hertzian contact area, in which the bearing operates in the EHL regime, as shown in Fig. 4.3. The induced oil film in the contact area between the balls and raceways usually operates in the EHL condition under high loads acting upon the balls. The contour of the ball deforms elastically under the Hertzian pressure in the relatively small contact area. The contact area has an elliptic form with the minor ellipse axis in the rolling direction x and the major ellipse axis in the axial direction y of the bearing, as shown in Fig. 4.2. Due to elastic deformation of the ball contour, the oil-film thickness is nearly constant at the height hc in the contact area. The Hertzian pressure pH in the oil film has been calculated in the earlier chapter. The Hertzian pressure is equal to the oil pressure at the inflow of the contact area and strongly increases to the maximum pressure at the contact area center. The maximum Hertzian pressure can vary from 1.5 to 3.2 GPa depending on the maximum load acting upon the ball. Note that the ball contour deforms plastically at a pressure of about 4", " 10 3 \u00f04:16\u00de where N is the rotor speed in rpm, Dpw is the pitch diameter in mm, and Dw is the ball/roller diameter in mm. The dimensionless load parameter W* of the rolling elements is defined as 4.4 Computing the Oil-Film Thickness 73 W* \u00bc W E 0 R2 x ;Rx RIR;OR,x forball bearings; W* \u00bc W E 0 LRx ;Rx RIR;OR,x for rollerbearings \u00f04:17\u00de where W is the maximum equivalent normal load acting upon the Hertzian contact area (s. Fig. 4.3) and L is the length of the roller bearing. The ellipticity parameter k of the contact area is defined as (s. Fig. 4.2) k \u00bc a b 1 \u00f04:18\u00de where a and b are the semimajor and semiminor axes of the elliptic contact zone. However, the ellipticity parameter k can be approximately computed according to [3] as kIR;OR \u00bc 1:0339 Ry Rx 2 \u03c0 1:0339 Ry Rx 0:636 ; Rx RIR;OR,x;Ry RIR;OR,y \u00f04:19\u00de The discrepancy of the approximate ellipticity parameter k of Eq. 4.19 is about 3% compared to the corrected value of Eq. 4.18. Finally, the dimensionless material parameter G* is defined as G* \u00bc \u03b1EHLE 0 \u00f04:20\u00de where \u03b1EHL is the pressure-viscosity coefficient (Barus coefficient) in the regime of elastohydrodynamic lubrication (EHL)", "21 is given in [3, 5] Z 7:81 H40 H100\u00f0 \u00de\u00bd 1:5 F40 \u00f04:22\u00de where H40 \u00bc log10 log10\u03bc40 \u00fe 1:2\u00f0 \u00deat 40 C; H100 \u00bc log10 log10\u03bc100 \u00fe 1:2\u00f0 \u00deat 100 C; F40 \u00bc 0:885 0:864H40 with the dynamic viscosities \u03bc40 and \u03bc100 in mPas of the lubricating oil at 40 C and 100 C, respectively. 74 4 Oil-Film Thickness in Rolling Bearings Usually, the Roelands pressure-viscosity index Z is about 0.60 for mineral oils and between 0.4 and 0.8 for synthetic oils. The Reynolds lubrication equation (RLE) for the oil-film thickness is written in the coordinate system (x, y) as (cf. Fig. 4.2) [3, 8] \u2202 \u2202x \u03c1h3 \u03bc \u2202p \u2202x \u00fe \u2202 \u2202y \u03c1h3 \u03bc \u2202p \u2202y \u00bc 12 um \u2202 \u03c1h\u00f0 \u00de \u2202x \u00fe vm \u2202 \u03c1h\u00f0 \u00de \u2202y \u00f04:23\u00de where um and vm are the mean velocities in the directions x and y, respectively. The following dimensionless parameters are defined using Eqs. 4.8 and 4.11 as x* \u00bc x b ; y* \u00bc y a ; \u03c1* \u00bc \u03c1 \u03c10 ; \u03bc* \u00bc \u03bc \u03bc0 ; U* \u00bc \u03bc0 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u2m \u00fe v2m p E 0 Rx ; He \u00bc h Rx ; pe \u00bc p E 0 ; k \u00bc a b ; \u03b8 \u00bc arctan vm um \u00f04:24\u00de Using Eq. 4.24, the dimensionless RLE is written in a dimensionless form as [3] \u2202 \u2202x* \u03c1*H3 e \u03bc* \u2202pe \u2202x* \u00fe 1 k2 \u2202 \u2202y* \u03c1*H3 e \u03bc* \u2202pe \u2202y* \u00bc 12U* b Rx cos \u03b8 \u2202 \u03c1*He \u2202x* \u00fe sin \u03b8 k \u2202 \u03c1*He \u2202y* \u00f04:25\u00de The oil-film thickness results from the undeformed contour geometry S(x, y) of the rolling elements and races and elastic deformation \u03b4(x, y) at the Hertzian contact area A(x, y): h x; y\u00f0 \u00de \u00bc h0 \u00fe x2 2b \u00fe y2 2a \u00fe 2 \u03c0 ZZ A x;y\u00f0 \u00de pe x 0 ; y 0 dx 0 dy 0ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x x0\u00f0 \u00de2 \u00fe y y0\u00f0 \u00de2 q h0 \u00fe S x; y\u00f0 \u00de \u00fe \u03b4 x; y\u00f0 \u00de ) He h x; y\u00f0 \u00de Rx \u00bc h0 Rx \u00fe S x; y\u00f0 \u00de Rx \u00fe \u03b4 x; y\u00f0 \u00de Rx \u00f04:26\u00de where h0 is the reference oil-film thickness and He is the dimensionless oil-film thickness", " On the contrary, the effective modulus of elasticity E0 and bearing load W have very weak influences on it since their exponents are very small compared to the other exponents. The minimum oil-film thickness hmin for a hard EHL regime at the rectangular contact area with a rectangular footprint results from solving the coupled Reynolds and elasticity equations. Next, using the least squares fit method (s. Appendix E), the dimensionless minimum oil film thickness is calculated according to [3] at the inner and outer raceways as (cf. Fig. 4.2) Hmin hmin Rx \u00bc 1:714U*0:694 G*0:568 W* 0:128 \u00f04:31\u00de Usually, the empirical value 5.007 103 is used for the dimensionless material parameter G* in the roller bearings [3]. writes Eq. 4.31 in hmin \u00bc 1:806 \u03bc0U\u00f0 \u00de0:694 \u03b10:568EHL R0:434 x E 0 0:002\u00f0 \u00de W L 0:128 \u00f04:32\u00de Equation 4.32 shows that the parameters \u03bc0, U, \u03b1EHL, and Rx have strong influences on the minimum oil-film thickness. On the contrary, the bearing loadW has a slight influence on it since its exponent is very small compared to the other exponents" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002430_tmag.2019.2941699-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002430_tmag.2019.2941699-Figure7-1.png", "caption": "Fig. 7. BCs for the PM subdomain of the inner rotor.", "texts": [ "\u221e is the harmonic order, and \u03b41 and \u03b42 are as follows: \u03b41 = \u03bc0q Mrs \u2212 \u03bc0 M\u03b8c (54) \u03b42 = \u2212\u03bc0q Mrc \u2212 \u03bc0 M\u03b8s (55) where Mrs , Mrc , M\u03b8s , and M\u03b8c are the expressions corresponding to the sin and cos parts of the magnetization functions Mi r and Mi \u03b8 of the inner rotor, and are given in (A47)\u2013(A54). Equations (52) and (53) are given for the \u03bdth PM segment of the \u03be th pole pairs. The summation of the solutions from each \u03bdth PM segment of the \u03be th pole pairs gives a complete solution. The unknown coefficients Ai q , Bi q , Ci q , and Di q can be found by considering the following BCs (Fig. 7): \u2202APMi \u2202r \u2223\u2223\u2223\u2223 r=R0 = { 0, forMi r \u2212\u03bc0 Mi \u03b8 , forMi \u03b8 (56) APMi = Agi, atr = R1. (57) The Fourier series expansion for the interval 2\u03c0 for (56) and (57) gives the following equations: \u2212Ai qq R\u2212q\u22121 0 + Bi qq Rq\u22121 0 = \u2212 \u03b41 1 \u2212 q2 , for Mi r (58) \u2212Ai qq R\u2212q\u22121 0 + Bi qq Rq\u22121 0 = \u2212 \u03b41 1 \u2212 q2 \u2212 \u03bc0 M\u03b8c, for Mi \u03b8 (59) \u2212Ci qq R\u2212q\u22121 0 + Di q q Rq\u22121 0 = \u2212 \u03b42 1 \u2212 q2 , for Mi r (60) \u2212Ci qq R\u2212q\u22121 0 + Di q q Rq\u22121 0 = \u2212 \u03b42 1 \u2212 q2 \u2212 \u03bc0 M\u03b8s , for Mi \u03b8 (61) Ai q R\u2212q 1 + Bi q Rq 1 \u2212 Agi q R\u2212q 1 \u2212 Bgi q Rq 1 = \u2212 \u03b41 1 \u2212 q2 R1 (62) Ci q R\u2212q 1 + Di q Rq 1 \u2212 Cgi q R\u2212q 1 \u2212 Dgi q Rq 1 = \u2212 \u03b42 1 \u2212 q2 R1 (63) where Cgi q and Dgi q are the unknown coefficients belonging to the solution for the internal air gap" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000039_978-1-84996-220-9-Figure10.9-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000039_978-1-84996-220-9-Figure10.9-1.png", "caption": "Figure 10.9 Example of a solution coordinating mobility and manipulation skills in order to reach for a low target", "texts": [], "surrounding_texts": [ "Figure 10.8 shows the coordination obtained by the algorithm for solving a given reaching problem. The first image (a) shows that the goal is not in the reachable range of the arm. The next two images (b,c) show the initial and final postures produced by the balance skill from the initial standing posture to a (non-explorative) sampled body posture favoring approximation to the hand target. The reaching skill is then recruited and instantiated at this posture and a bidirectional exploration tree is expanded (image (d)) to connect the current posture to a posture reaching the target. The solution arm motion found by the reaching skill successfully avoids collisions with the table and reaches the goal, as depicted in the bottom sequence (d\u2013f). Further examples are illustrated in Figures 10.9 \u2013 10.12. In all examples, the solutions obtained represent valid collision-free motions. Note that the RRT exploration trees are implemented only using the generic interface for controlling motion skills. Therefore every expansion toward a sampled landmark implies a re-instantiation and application of the skill such that each expansion motion is produced by the skill itself. In its current version the algorithm is limited to sequencing motion skills. A possible extension is to allow a skill to be activated in parallel with the previous skill, for instance to allow reaching to start while stepping or balance is still being executed. These concurrent executions can also be computed as a post-optimization phase in order to reduce the time required to plan the motions. In most of the examples presented, the computation time taken by the planner was in the range 10 to 40 s. Solutions of longer duration, as the one shown in Figure 10.11, require several minutes of computation. In the case of applying planned motions to the HOAP-3 humanoid platform (Figure 10.12) we also rely on a reactive controller running in the robot with the purpose to correct the main torso orientation in order to maximize balance stability in 10 A Motion Planning Framework for Skill Coordination and Learning 291 response to readings from the feet pressure sensors. The results presented demonstrate the capabilities of the multi-skill planning algorithm. 292 M. Kallmann and X. Jiang" ] }, { "image_filename": "designv10_9_0000193_j.cma.2011.04.006-Figure9-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000193_j.cma.2011.04.006-Figure9-1.png", "caption": "Fig. 9. Coordinate systems applied for TCA of bevel gears.", "texts": [ " This algorithm for tooth contact analysis does not depend on the precondition that the surfaces are in point contact or the solution of any system of nonlinear equations as the existing approaches, and can be applied for tooth contact analysis of gear drives in point, lineal or edge contact as it will be shown below. Alternative algorithms that can be used for tooth contact analysis are found in [7\u20139]. All TCA analyses are conducted under rigidbody assumptions so that no elastic tooth deformation due to actual loading is considered when TCA results are shown. Fig. 9 represents the applied coordinate systems for tooth contact analysis (TCA) of straight and skew bevel gears. 5.2. Errors of alignment The errors of alignment considered are: (i) DA1 \u2013 the axial displacement of the pinion (Fig. 10(a)), (ii) DA2 \u2013 the axial displacement of the gear (Fig. 10(b)), (iii) DR \u2013 the change of the shaft angle R (Fig. 10(c)), and (iv) DE \u2013 the shortest distance between axes of the pinion and the gear when these axes are not intersected but crossed (Fig. 10(d)). The mentioned errors of alignment can also be observed in Fig. 9. Coordinate systems S1 and S2 are movable coordinate systems rigidly connected to the pinion and gear, respectively. Angles /1 and /2 are the angles of rotation of the pinion and the gear, respectively. Table 1 shows details of coordinate transformation from S2 to S1. Transformation Mml is needed if pinion and gear have been generated following the same coordinate transformations, so that one of the members of the gear drive have to be rotated an angle p to face corresponding surfaces for tooth contact analysis" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000193_j.cma.2011.04.006-Figure18-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000193_j.cma.2011.04.006-Figure18-1.png", "caption": "Fig. 18. Contact patterns for: (a) case B1b, (b) case B1c, (c) case B1d and (d) functions of transmission errors for previous cases of design.", "texts": [ " The skew bevel gear transmission with main design parameters shown in Table 2 is also designed using parameters shown in Table 3 for three different cases of design. Fig. 17 shows the contact pattern and the obtained function of transmission errors for case B1a corresponding to a skew non-modified and aligned bevel gear drive. The skew bevel gear drive with the proposed geometry, under aligned conditions, has no transmission errors, and the contact pattern covers the whole surface of the teeth as shown in Fig. 17(a). Fig. 18 shows the contact patterns for cases B1b (18(a)), B1c (18(b)), and B1d (18(c)). Fig. (18(d)) shows the obtained functions of transmission errors for previous cases of design. All misaligned conditions (from b to d) cause lineal functions of transmission errors. The skew bevel gear drive is very sensitive to the change of shaft angle DR (misaligned condition c) and the axial displacement of pinion (misaligned condition d) and the axial displacement of the gear (not shown in this paper). In order to absorb those lineal functions of transmission errors caused by errors of alignment for the skew bevel gear drive, Designs 2 and 3 (see Table 3) are proposed also for this transmission, with whole-crowned and partial-crowned bevel gear tooth surfaces, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001799_j.bios.2016.08.005-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001799_j.bios.2016.08.005-Figure1-1.png", "caption": "Fig. 1. The principle of GA measurement. The principle of GA measurement was based on the commercially available GA measurement kit: GA in the blood is digested by protease to release \u03b5-fructosyl lysine (\u03b5-FK), following which \u03b5-FK is oxidized by FAOx and Ru-complex is simultaneously reduced. The amount of reduced Ru-complex formed is measured by chronoamperometry with SPCE.", "texts": [ " GA in the blood is digested by a protease to release \u03b5fructosyl lysine (\u03b5-FK), following which \u03b5-FK is oxidized by FAOx and the Ru-complex is simultaneously reduced. The amount of reduced Ru-complex formed is measured by chronoamperometry with a SPCE, where the enzyme and electron mediator are Please cite this article as: Hatada, M., et al., Biosensors and Bioelectr deposited. The \u03b5-FK concentration contained in protease-digested GA is determined by the concentration of generated reduced mediator (Fig. 1). We evaluated the performance of this new enzymatic electrochemical-based GA sensor, which can be developed in a POCT platform. FAOx was prepared following the method by Kouzuma (Kouzuma et al., 2002). Recombinant human serum albumin was purchased from Merck (Darmstadt, Germany) and its glycated form was prepared as below. Twenty-five grams of recombinant human serum albumin and 80 g of D-glucose (Wako Pure Chemical Industries, Ltd., Osaka, Japan) were dissolved in 500 mL of pure water and incubated for 24 h at 37 \u00b0C" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002003_iccar.2016.7486697-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002003_iccar.2016.7486697-Figure2-1.png", "caption": "Figure 2. The five steps ofthe inverse kinematics solution: I) PI ace the wrist center in the x-z-plane; 2) Determine the elbow zero position for {j = 0; 3) Rotate the elbow about the desired {j angle; 4) Solve the inverse position up to the wrist for 8 1 .. 4 ; 5) Solve the inverse orientation for 8 5,,7", "texts": [ " This is possible because only 81 depends on the real target position, while all other joint angles are independently solvable. Starting with this scenario, the position of the elbow in zero position (0 = 0\u00b0) is easy to determine and is further used to calculate the target elbow position for a desired angle O. Based on this elbow position, all joint angles can be determined geometrically to solve the inverse position problem. Finally, the last three joints can be calculated analytically for the inverse orientation problem. In summary, we will take five steps as shown in Fig. 2. C. Inverse Kinematics Solution Considering the kinematics abstraction in Fig. 3A, let M be the target pose matrix with respect to the BCS. The inverse position is solved to the wrist center position w, calculated by \u00b0M6 = M\u00b7 6M7 -1=: W = [~~] (1) As mentioned before, it is necessary to place the wrist center in the x-z-plane of the BCS in an initial step. To achieve this, we can extract the rotation angle ep out of a projection into the x-y-plane and rotate w around the z-axis (BCS) with (2) and w' = Rz" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002709_j.corsci.2020.109036-Figure18-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002709_j.corsci.2020.109036-Figure18-1.png", "caption": "Fig. 18. Sketches of the molten pool and the fusion line shape during high-deposition-rate laser solid forming (HDR-LSF) and conventional laser solid forming (CLSF) processes on different planes. (a) 3D diagram of the molten pool, 2D sketches of the molten pool for (b) HDR-LSF and (c) C-LSF on ZOY plane, and 2D sketches of the molten pool for (d) HDR-LSF and (e) C-LSF on ZOX plane.", "texts": [ " Corrosion Science 177 (2020) 109036 Further, the local thermal gradient direction is always along the normal of the fusion line in the molten pool, suggesting that the fusion line shape of the molten pool determines the local thermal gradient direction. By contrastive analysis of the fusion line shape in this work and the C-LSF references [17,40,45], as well as the simulation results (Fig. 15), the bottom of the molten pool sketch and the fusion line shape of HDR-LSF and C-LSF on different planes can be given in Fig. 18. Fig. 18a exhibits the sketch of the bottom of the molten pool. Fig. 18b presents that the fusion line of the molten pool exhibits a large curvature on ZOY plane caused by the high-power Gaussian laser during the HDR-LSF process (extracted from Fig. 4a). It means that the local thermal gradient directions changed a lot along the fusion line. Fig. 18c shows that the fusion line is relatively flat for C-LSF process and thus the local thermal gradient direction almost along the build direction. On ZOX plane, the fusion line of the HDR-LSF molten pool exhibits a large curvature shown in Fig. 18d while the C-LSF molten pool presents a small curvature exhibited in Fig. 18e. It can be concluded that the local thermal gradient directions are discrepant and changeable in space for HDR-LSF Alloy 718. As a result, the epitaxial growth property of the columnar grains for HDR-LSF Alloy 718 is much easier to change. On the one hand, when \u03b81 (the angle between local thermal gradient direction and <001> direction of the columnar grain) is larger than 45\u25e6, the growth direction of the dendrite will turn to <010> or <100> direction [46] and thus leads to the direction changed structure (shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003017_j.addma.2020.101822-Figure17-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003017_j.addma.2020.101822-Figure17-1.png", "caption": "Fig. 17. Illustration of layer height increase.", "texts": [ " If the specimen edges are divided into sequential 4 mm-length sections, 5\u20139 measurement regions will be available for the Case 1 and Case 2 samples respectively. Consequently, based on what is shown in Fig. 18, an increment of 0.5 mm is considered between start points of measurement regions. Although this causes a 3.5 mm overlap between measurement fields, it increases the number of resultant Ra data, which makes later interpretations more accurate. The layer height variation is associated with the build geometry, as illustrated in Fig. 17. As the planar slice strategy is used for the dome fabrication, the real layer height increases when the overhang angle increases. The relation between the real layer height and the length of the mount edge arc is calculated by Eq. (12). Reallayerheight = Sliceheight cos ( Lp R ) (12) R is the dome radius (21.5 mm for inner arc and 23.5 mm for outer arc for Cases 1, 2 and 29 mm and 31 mm for Case 3) and Lp is the arc length of the partitions from the bottom layer (Shown in Fig. 17 and the X-axis in Fig. 19). The real layer height equals the slice height (0.5 mm) at the bottom layer of each partition but it increases gradually up 0.7 mm at the top layer of the partition 3 for the Case 1. Fig. 18 depicts the 3rd partition of the 5-axis sample. The measurement direction starts from the bottom layers to the top layers of the partition. The measured Ra variations are shown in Fig. 19. The horizontal axis is the center point location of the measurement region. This figure shows that the Ra of the inner surface of the 3rd partition varies between 25 Table 4 Verification of results made by prepared MATLAB program with results of contact-based measurement" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000931_9781118703274.ch2-Figure2.30-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000931_9781118703274.ch2-Figure2.30-1.png", "caption": "Figure 2.30 Coriolis acceleration of a rotor blade", "texts": [ " Coriolis acceleration From the velocity of the centre of mass \ud835\udedaR \u00d7 r\u2032 = \ud835\udf14Rz \u2032ey \u2212 \ud835\udf14Ry \u2032ez and the corresponding yaw angular velocity \ud835\udedaA \u00d7 ( \ud835\udedaR \u00d7 r\u2032 ) = |||||| ex ey ez 0 0 \ud835\udf14A 0 \ud835\udf14Rz \u2032 \u2212\ud835\udf14Ry \u2032 |||||| = \u2212\ud835\udf14A\ud835\udf14Rz \u2032ex the Coriolis acceleration may be derived: bc = 2\ud835\udedaA \u00d7 ( \ud835\udedaR \u00d7 r\u2032 ) = \u22122\ud835\udf14A\ud835\udf14Rz \u2032ex. (2.55) From this, we obtain, for an observer in a coordinate system x\u2032\u2032, y\u2032\u2032, z\u2032\u2032 having a yaw velocity of \ud835\udf14A but not a rotation of \ud835\udf14R, a Coriolis acceleration bC in the negative x\u2032\u2032 direction when z\u2032\u2032 > 0. For z\u2032\u2032 < 0, bC acts in the opposite direction (see Figure 2.30). Coriolis acceleration engenders moments that act on the rotor blades and on the yaw system in the tower head. When the nacelle is yawed the moment in the x direction acts not with a continuously damping effect, but either to accelerate or decelerate the movement: for a rotor blade of mass mB the moment resulting from Coriolis acceleration with respect to the z\u2032\u2032 or z axis is MCz = \u2212mBbCy \u2032\u2032. (2.56) Where z\u2032\u2032 = r\u2032 cos\ud835\udf14Rt, y\u2032\u2032 = r\u2032 sin\ud835\udf14Rt and sin\ud835\udf14Rt cos\ud835\udf14Rt = 1 2 sin 2\ud835\udf14Rt the moment in the x direction can be written as MCz = \u2212mBr \u20322\ud835\udf14A\ud835\udf14R sin 2\ud835\udf14Rt (2" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000353_14763141.2012.660799-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000353_14763141.2012.660799-Figure5-1.png", "caption": "Figure 5. Orientations of the FSP and the MP. Shaded areas show the projections of the FSP on the ground and the MP on the FSP. nFSP, dFSP, and sFSP are the normal, direction, and slope vectors of the FSP, respectively. nMP and dMP are the normal and direction vectors of the MP, respectively. The slope (fFSP) and direction angle (uFSP) of the FSP were computed relative to the ground and with respect to the Y-axis of the global reference frame, respectively. The relative inclination of the MP (fMP) was computed against the FSP. The direction of inclination of the MP (uMP) was computed with respect to the slope vector (-sFSP) of the FSP.", "texts": [ " The RMS and maximum trajectory fitting errors (Equations (7) and (8)) were compared among these phases to identify the phase which provided sufficiently well-defined FSPs. The best-fit planes obtained from this particular phase were used as the FSPs in subsequent analyses. The slope of the FSP (fFSP) was computed as the angle between the ground and the FSP, whereas the angle between the intersection line formed by the FSP with the ground (dFSP) and the Y-axis (direction of the target) was used as the direction angle (uFSP; Figure 5) fFSP \u00bc cos -1\u00f0nFSP\u00b7k\u00de; \u00f09\u00de dFSP \u00bc k \u00a3 nFSP k \u00a3 nFSPj j ; \u00f010\u00de uFSP \u00bc sign\u00f0i\u00b7dFSP\u00de cos-1\u00f0j\u00b7dFSP\u00de; \u00f011\u00de where i, j, and k are unit vectors of the X-, Y- and Z-axes, respectively. An FSP directed to the left side of the target yielded a positive direction angle (Equation (11)). Trajectory-plane fitting was carried out for the shoulders, right elbow, and the left-hand center in the TB\u2013MF phase (Figure 4D). Since the left elbow remains extended during most part of the downswing, its trajectory is highly dependent on those of the left shoulder and hand and, for this reason, left elbow was excluded from plane fitting. Right hand was also excluded from plane fitting as its motion should be similar to that of the left hand. The orientations of the MPs were computed relative to the FSP, not to the ground/target line (Figure 5) fMP \u00bc cos-1\u00f0nFSP\u00b7nMP\u00de; \u00f012\u00de dMP \u00bc nMP \u00a3 nFSP nMP \u00a3 nFSPj j ; \u00f013\u00de uMP \u00bc sign\u00f0-sFSP\u00b7dMP\u00de cos-1\u00f0dFSP\u00b7dMP\u00de; \u00f014\u00de where fMP and uMP are the relative inclination and direction of inclination of an MP, respectively, sFSP is the slope vector of the FSP, and nMP and dMP are the normal and direction vectors of the MP, respectively (Figure 5). Off-plane motion patterns and maximum deviations of the pendulum points from the FSP. To obtain the off-plane motion patterns of the clubhead and shoulder/arm points during the swing, deviations of these points from the FSP were computed throughout the entire swing (TA\u2013MF) phase using Equation (3). Ensemble averages were computed for the generalized off-plane motion patterns and the TA\u2013MF time was used as 100% for time normalization. The maximum deviations from the FSP were computed in the TA\u2013MF phase for the clubhead and the pendulum points using Equation (8)", " The shoulder/arm points revealed vastly different relative motion patterns to the FSP from each other. Substantially larger mean relative inclinations were observed in the right shoulder and elbow (30\u2013398) than in the left shoulder and hand (10\u2013158), meaning that the left-arm points were moving more parallel to the FSP than their right-arm counterparts. More importantly, the shoulder/arm points revealed completely different direction of inclination profiles with the MPs of the left-arm points inclined forward (uMP . 08; Figure 5) but those of the right-side points inclined backward (uMP , 08; Table IV). The MPs of the shoulders (juMPj , 908; inclined upward) were flatter than those of the left hand and right elbow (juMPj . 908; inclined downward). The orientations of the MPs formed by the shoulder/arm points clearly show that the arm and shoulder girdle motions are not a single-plane motion as depicted in the multi-pendulum models (Cochran & Stobbs, 1968; Jorgensen, 1994; Sprigings & Neal, 2000). The club effects on the orientations of the MPs were mainly observed in the left arm (Table IV)", ") differences in the X-factor/X-factor stretch (McLean, 1992; McTeigue et al., 1994; Cheetham et al., 2001), research has failed to demonstrate a direct causal relationship between the X-factor/X-factor stretch and the clubhead velocity. A forceful trunk rotation produced by pre-stretched trunk rotators due to a large X-factor may sound like a feasible cause of high impact velocity in the planar multi-pendulum perspective, but the findings of this study suggest otherwise. Since the MP of the left shoulder is inclined forward/upward (uMP , 908; Figure 5), a 10\u2013158 relative inclination to the FSP makes the shoulder plane flatter (Table IV; Figure 5). The trunk plane (transverse) is also flatter than the FSP as the trunk axis (longitudinal) is aligned more upright than the normal axis of the FSP (Figure 7). The trunk rotation and linear shoulder motion during the downswing/follow-through, therefore, tend to promote an off-plane motion of the clubhead (and a spiral swing) by pulling it down past the FSP. The relative orientations of the shoulder MP and trunk plane to the FSP and the curvature of the clubhead trajectory with respect to the FSP (in the semi-planar swing in particular) suggest that trunk rotation is not what drives the downswing and the arms move somewhat independently of the trunk in a fashion to secure a clean planar motion of the clubhead during the execution phase" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000748_153101-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000748_153101-Figure4-1.png", "caption": "Figure 4. (a) Schematics of an external magnetic forcing of magnetic colloidal dispersions; an alternating magnetic field is applied perpendicular to the interface. (b) Sketch view of the experimental setup for the external forcing of a magnetic colloidal dispersion at a liquid\u2013air interface.", "texts": [ " As a consequence, in most cases it is more energetically favorable for a ferromagnetic microparticle at a liquid interface (where the friction is low) to proceed with the mechanism (b) and mechanically adjust the orientation of the particle in question (\u2018magnetic shaking\u2019). Moreover, during this process we transfer the particle\u2019s torque to the local excitations of the liquid\u2013air interface (energy injection to the interface). A sketch of a typical experimental setup for a magnetic forcing of colloidal magnetic suspensions at a liquid\u2013air interface [56, 57] is shown in figure 4. Magnetic microspheres are suspended over the surface of the water\u2013air interface. The spheres are small enough to be supported by the surface tension. A cylindrical container with the floating magnetic microspheres is placed in a vertical alternating (ac) magnetic field, Hac = H0 sin(2\u03c0 f t), where H0 and f are the amplitude and frequency of the applied field, respectively. A driving alternating magnetic field is applied perpendicular to the water\u2013air interface. The magnetic field is produced by an electromagnetic coil capable of creating vertical magnetic fields up to 170 Oe", " An additional in-plane dc magnetic field, Hdc (up to 30 Oe), may be applied with a pair of Helmholtz coils to probe the magnetic properties of the self-assembled structures. Typically sets of nickel spherical particles with diameters from 20 to 100 \u03bcm were used in experiments. The saturated magnetic moment per 90 \u03bcm particle is 2\u00d710\u22124 emu at a saturation field of about 4 kOe. The magnetic moment per particle in the driving fields used in the experiments (\u223c120 Oe) is one order of magnitude smaller. The motion of the individual particles in the container is monitored with a high-speed camera (see a schematic view of the experimental setup in figure 4) mounted at a microscope stage. The inhomogeneity of the driving magnetic field in the setup is negligible since the magnetic force associated with the vertical field gradient per particle on the liquid surface in the container is less than 1% of its gravitational force. While the driving external magnetic field is uniform across the system, the energy injection to the interface might be highly non-uniform due to the fact that it strongly depends on the positions of magnetic particles at the interface and morphology of structures they might have dynamically self-assembled", " As one can see from figure 6, chains transfer the energy to the surrounding fluid at each driving cycle (field up and down), resulting in a doubled effective frequency of energy injection, resulting in a harmonic (with external driving field) response of the induced standing waves. There is a critical driving field amplitude below which no snake-like structures could be generated. The value of the critical field is strongly dependent on the external driving frequency and number of magnetic particles in the ensemble: higher field amplitude is required to create a \u2018snake\u2019 structure when working at a higher driving frequency or smaller number of particles in an ensemble. The critical field amplitude as a function of particle surface density is plotted in figure 4 for two different driving frequencies. The dashed lines in figure 4 are fits of the experimental data to the function H0 = A + B/ \u221a \u03c1 (A and B here are parameters) and provide a good description of the dependences observed in the experiments. A similar type of behavior has been reproduced within the theoretical model [57] describing dynamic self-assembly phenomena in these systems (see section 3.1). Far-from-equilibrium assembly in the colloidal dispersion suspended at the liquid\u2013air interface brings to light rather nontrivial magnetic ordering of the dynamically assembled structures", " The function \u03c6, which phenomenologically describes the dependence of the forcing term on the density of particles, is proportional to \u03c1 for small densities and saturates for larger densities. For simplicity, we took \u03c6 = \u03c1 \u2212 0.3\u03c12. This density dependence accounts for the fact that the effect of forcing vanishes for low particle densities (\u03c1 \u2192 0) and saturates for higher densities. It is consistent with our experimental observation of the dependence of the critical field H0 for a \u2018snake\u2019 formation on the number of particles, see figure 4. From the linear stability analysis of the trivial (nonoscillating) state \u03c8 = 0, \u03c1 = \u03c10 = const one obtains from equations (6) that parametric instability occurs at the optimal wavenumber k = k\u2217 = \u221a (\u03c9b \u2212 \u03b5)/(\u03b52 + b2) and at the critical driving amplitude \u03b3 = \u03b3c given by the expression (see for comparison [77]) \u03b3c\u03c6(\u03c10) = \u03c9\u03b5 + b\u221a \u03b52 + b2 . (7) Thus, for small densities \u03c1 = \u03c10 \u2192 0 we obtain from equation (7) that the critical value of \u03b3c for parametric instability behaves as \u03b3c \u223c 1/\u03c10. Since \u03b3 \u223c H 2 0 , we obtain from equation (7) H0 \u223c 1/ \u221a \u03c10, which is consistent with experimental observations (see figure 7)" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002721_j.mechmachtheory.2020.104164-Figure8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002721_j.mechmachtheory.2020.104164-Figure8-1.png", "caption": "Fig. 8. Measuring system of the decompressing condition.", "texts": [ " More importantly, higher preloading level introduces higher critical axial load to reach the decompression condition, and thus larger deformation of the screw shaft and nut body of the loading nut to offset the initial deformation in the unloading nut, leading to a decrease of F a,max / F p . Therefore, F a,max / F p decreases with increasing preloading levels in Fig. 7 . Case 2: Ball screws with additional elastic unit For the double-nut ball screws with additional elastic units ( F B /K \u2032 = 0 ), a measuring system was constructed to detect the decompression condition. As shown in Fig. 8 (a), one precision positioning nut ( 9 \u00a9), one disc ( 8 \u00a9), three fore sensors ( 7 \u00a9) (FUTEK MODEL LCM300), and one sleeve ( 6 \u00a9) are specially designed and mounted on a typical 4010 ball screw (parameters is shown in Table 1 ) with the slave nut machined with external threads, in which the preload can be adjusted and measured by rotating the precision positioning nut and force sensor, respectively. In the measuring system, as shown in Fig. 8 (b), the tested ball screw ( 4 \u00a9) is installed on the support unit ( 5 \u00a9) of the test bench. One end of the ball screw is connected with the anti-rotation unit ( 3 \u00a9) through a key, which ensures the screw shaft can only move in the axial direction without rotation. When the load unit ( 1 \u00a9) compresses the load cell ( 2 \u00a9), the exerting force acts on the anti-rotation unit, the screw shaft, the master nut and the sleeve in sequence; then the contact force as well as the deformation of the ball-raceway contact increases within the master nut" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000794_s0076-5392(08)62099-8-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000794_s0076-5392(08)62099-8-Figure2-1.png", "caption": "FIG. 2. Nomogram for orbital elements.", "texts": [ " The requirement that the three parameters (p, q , (t) should satisfy Eqs. (11.9) and (11.10) leaves these quantities one degree of freedom. The parameters will be specified completely when the magnitude of the impulse is given. A convenient graphical means of determining all those orbits ( p , q , 61) into which an orbiting body may be transferred by application of a single impulse in a given direction a t a given point is as follows: Construct the graph of the functional relationship y = x2 (see Fig. 2 ) . Fix the point A on the z-axis a t a distance from the origin 0 given by the equation S OA = ~ Z 2 tan cp and erect the perpendicular AB to OA such that S AB = 2* tan2 + Let P be a point (2, y) on the curve y = x2 and let (11.11) (11.12) PN be the perpendicular 11. Transfer Between Elliptical Orbits 327 from P on to AB. Denoting L PBA by a, we have by simple geometry PB cos a = A B - y (11.13) PB sin a = OA - x = OA - y1I2 (11.14) If, therefore, we interpret PB, a, and y thus, (11.15) P Z\u2019 tan2 4 a = O - & , " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002513_0954405418805653-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002513_0954405418805653-Figure5-1.png", "caption": "Figure 5. Schematic diagram of the interaction between the particles and the laser: (a) laser power attenuation and (b) interaction between particles.", "texts": [ " When the powder particles are injected from the nozzle, they pass through the laser beam and reach the molten pool; thus, the powder may cover the laser beam such that only a small part of the laser energy reaches the base.28 The laser power attenuation model has the following assumptions: 1. Powder particles are uniform and spherical with a radius of r; 2. Powder particles do not overlap in the laser beam; 3. Reflection, diffraction, and scattering of the pow- der particles are not considered; 4. Laser energy is uniformly distributed. The diagram of the laser power attenuation is shown in Figure 5(a) and a schematic diagram of the interaction between the particles and the laser is shown in Figure 5(b). The laser power attenuation is deduced using equations (7)\u2013(14). The time t required for the particles to eject from the nozzle to the substrate is as follows t= H vp sin u \u00f07\u00de The quality of the ejected powder of the nozzle is as follows Vpfrt= VpfrH vp sin u \u00f08\u00de The volume V of the powder flowing from the nozzle before reaching the substrate is as follows V=pr2jet H sin u \u00f09\u00de Assuming that the powder is uniformly distributed in space by volume, the powder quality per unit volume is as follows Vpfr pr2jetvp \u00f010\u00de The volume occupied by the powder particles involved in shading during the time t is as follows pr2l rjet cos u , rjet\u00f8rl \u00f011\u00de The powder quality involved in the laser power attenuation n is as follows n 4pr3prp 3 = Vpfr pr2jetvp pr2l rjet cos u \u00f012\u00de The area of the powder particles Sp and the laser spot Sl are defined as follows Sp = npr2p = 3vpfrr 2 l 4vprprjetrp cosq , Sl =pr2l \u00f013\u00de Therefore, the laser power attenuation is as follows Pat Pl = Sp Sl = 3Vf 4prprpvprjet cos ujet , rjet\u00f8rl \u00f014\u00de In these experiments, the particle radius rp, the carrier gas velocity vp, the angle between the powder flow and the horizontal direction u, and the radius of the powder particles formed on the substrate rjet were 120mm, 600mm/min, 558, and 8mm, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003252_tia.2020.3040142-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003252_tia.2020.3040142-Figure1-1.png", "caption": "Fig. 1. Configuration of a CMG.", "texts": [ " In this article, the HMM is applied to solve the magnetic field distribution of surface-mounted CMGs with the consideration of magnetic saturation. Then, the SDM, HMM, and FEA are compared when concerning the computation time and accuracy for the magnetic performances of CMGs. Finally, the nondominated sorting genetic algorithm II (NSGA-II) optimization method is developed based on the harmonic modeling of CMGs. The multiobjective optimization is carried out to achieve a CMG with low cost and high performance, and the optimal case is evaluated. A typical CMG structure is shown in Fig. 1, which contains three components. Two components have PMs mounted on their inner and outer surface, respectively, while the other one component is made of evenly distributed ferromagnetic bars. Actually, either one of three components can be fixed, while the other two rotate and transmit the torque similar to mechanical gearboxes. In this article, the outermost one is fixed, called as stator. The inner one is high-speed rotor and the outer one is low-speed rotor. CMGs satisfy a few structure requirements to produce a steady torque" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002893_tia.2020.3036328-Figure19-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002893_tia.2020.3036328-Figure19-1.png", "caption": "Fig. 19. Temperature distributions from top view at 600 rpm. (a) 6S16P CFRPM. (b) 12S16P CFRPM.", "texts": [], "surrounding_texts": [ "Although the proposed 6S16P CFRPM machine can produce much higher average torque compared with the 12S16P FRPM machine and its consequent pole type, it also exhibits much higher torque ripple. For a fair comparison, different techniques are employed to reduce the torque ripple of the proposed 6S16P CFRPM machine to a level comparable to the 12S16P FRPM machine and its consequent pole type. The cogging torque and back EMF harmonics are responsible for the torque ripple. As shown in Fig. 8(a), by changing the rotor width from 4 to 2.5 mm, the cogging torque can be effectively reduced without compromising too much torque. However, by this means, the torque ripple cannot be reduced because the 2nd harmonic in back EMF increases from 1.61 to 4.93 V, as reported in Table IV. Therefore, several other techniques are used to suppress the torque ripple. 1) Step Skewed Rotor: Stator or rotor skew is quite commonly used in electrical machines for minimizing torque ripple [33]\u2013[36]. Two-step to five-step skewed rotors are shown in Fig. 21. Fig. 22 compares the influence of step number and skew angle on the torque characteristics. Fig. 22(a) shows that for each step number, the average torque decreases when increasing the skew angle. Under the same skew angle, the average torque increases with the increase of the step number, which is due to that more rotor laminations move a smaller angle away from their original positions in axial direction. Besides, the torque difference between three-step and four-step is very small. Fig. 22(b) shows that for each step number, there exists an optimum skew angle to achieve minimum torque ripple. Increasing the step number can help to decrease the minimal torque ripple, and the five-step skewed rotor with 9\u00b0 has the lowest torque ripple of 3.7%. The two-step skewed rotor is preferable to decrease the torque ripple if the skew angle is smaller than 5\u00b0, while the five-step skewed rotor is better if the skew angle is larger than 7\u00b0. The three-step skewed rotor has similar capability with the four-step one in decreasing the torque ripple with less than 7\u00b0 skew angle, but if the skew angle increases further, the three-step one is better. Here, the two-step skewed rotor is employed to ease the manufacturing as well as to maintain the torque capability. Fig. 23 shows that for the two-step skewed rotor, there is an optimum skew angle for minimum torque ripple although the Authorized licensed use limited to: California State University Fresno. Downloaded on June 26,2021 at 14:21:53 UTC from IEEE Xplore. Restrictions apply. average torque decreases when increasing the skew angle. At this point, the torque ripple is decreased by about 70% with 20.7% reduced average torque. This is not a good tradeoff since too much average torque is sacrificed. On the other hand, the cost coefficient curve of the torque to the torque ripple reaches its maximum value with 5\u00b0 skew angle, which is slightly larger than that with 4\u00b0 skew angle. If the skew angle is 4\u00b0, the torque ripple can be reduced to as low as 16.5%, as shown in Fig. 24, which is already lower than that of the 12S16P FRPM machine. More importantly, the output torque is only compromised by 13%. It still has a big advantage over the 12S16P FRPM machine and its consequent pole type. Fig. 25 compares the back EMF waveforms and the corresponding harmonics under different skew angles. The fundamental harmonic decreases with the increase of the skew angle, which leads to the decrease of average torque. The 2nd harmonic is the main reason for the torque ripple. It reaches its minimum value when the skew angle is 5\u00b0, and hence the torque ripple also reaches its minimum value. The change period of the 4th harmonic with the skew angle is twice of the change period of the 2nd harmonic. When the 2nd harmonic is minimum, the 4th harmonic is maximum. Therefore, if the torque ripple needs to be further decreased, a step skewed rotor should be combined with other techniques such as rotor shaping, uneven tooth, shifted rotor tooth, etc., or the step number be increased. 2) Shifted Rotor Tooth: Shifted rotor tooth can be used to reduce the cogging torque, since the phase difference of cogging torque waveforms of two adjacent rotor teeth would make the peak to peak value much smaller [34], [37], as shown in Fig. 26. The torque ripple can be reduced in the same way. In Fig. 27, although there are two valleys with the change of rotor shift angle, the torque ripple cannot be reduced as low as the 12S16P FRPM machine or its consequent pole type. Naturally, this way would reduce output torque to 2.35 Nm with 34.3% torque ripple and 1.96 Nm with 28.5% torque ripple at two valley points. 3) Shaped Rotor Tooth: Stator tooth or rotor tooth can be shaped to reduce the rate of change of the airgap permeance [38]\u2013[40], as shown in Fig. 28. There is an optimum radius of Authorized licensed use limited to: California State University Fresno. Downloaded on June 26,2021 at 14:21:53 UTC from IEEE Xplore. Restrictions apply. curvature 3.6 mm when the torque ripple has a minimum value of 30.2%, as shown in Fig. 29. At this point, the average torque decreases by 10%. 4) Dummy Slot: The airgap permeance can also be changed by introducing axially partially dummy slots or unbalanced dummy slots on the rotor poles [41]\u2013[46]. Although the cogging torque decreases with the increase of the dummy slot number [45], the output torque will also decrease due to the increase of the equivalent airgap length. Besides, the space on the rotor tooth is limited. In this article, the dummy slot number is chosen as two, as shown in Fig. 30. The dimensional parameters wt, ht, and ws are the dummy slot width, the dummy slot depth, and the dummy slot distance from the tooth center. In this way, the equivalent airgap length is increased, which would compromise the output torque consequently. Fig. 31 demonstrates that the dummy slot dimensions will not help decrease the torque ripple to a low level. What is worse is that improper dummy slot dimensions may increase the torque ripple greatly. Authorized licensed use limited to: California State University Fresno. Downloaded on June 26,2021 at 14:21:53 UTC from IEEE Xplore. Restrictions apply. 5) Different Tooth Widths: Different tooth widths also help to diminish harmonics, and thus decrease the torque ripple [47]. Tw1 and Tw2 represent the tooth widths of two adjacent teeth, as shown in Fig. 32. The contour plot Fig. 33(a) shows that there are three minimum torque ripple areas. The contour plot, Fig. 33(b), shows when the tooth width is 3 or 4 mm, the average torque reaches its maximum value. When both the average torque and the torque ripple are taken into consideration, we should choose the two adjacent tooth width as 2 and 6 mm. The torque ripple is reduced to 30% and the torque decreased by 19%. In summary, several means can be used to reduce the torque ripple. Step skewed rotor, shifted rotor teeth, and different tooth widths share a similar way for the reduction of cogging torque. They introduce the phase differences of cogging torque waveforms of either two rotor modules or two adjacent teeth. Meanwhile, rotor tooth shaping and dummy slot decrease the torque ripple by suppressing the harmonics. However, there is always a tradeoff between the torque ripple and the average torque. Step skewed rotor is found to be more effective without too much compromising of the output torque when the step number is chosen as two and skew angle chosen to be 4\u00b0." ] }, { "image_filename": "designv10_9_0003046_j.simpat.2020.102080-Figure13-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003046_j.simpat.2020.102080-Figure13-1.png", "caption": "Fig. 13. Isometric view of Section I.", "texts": [ " In order to explore and optimize parameters (see Table 2a), the influence of three clearances on windage loss has been investigated in this paper, respectively. In this study, the gear rotational speed is set to 10,000 r/min in a counterclockwise direction. The toe clearance is set to 1.5 mm, 5 mm, 7.5 mm and 10 mm, respectively. The face clearance and the heel clearance are fixed at 5 mm (Groups 1\u20134 in Table 2a). All CFD simulation settings and geometric parameters are consistent with Section 3, except that the toe clearance is regarded as the only independent variable. The corresponding contours of static pressure on the section I (see Fig. 13) in the front viewpoint are depicted in Fig. 14. As pictures, the toe clearance has a significant effect on the static pressure on Section I, the maximum pressure occurs near the addendum at the toe and the heel of the bevel gear (see Fig. 14(b) and (d)). Along with the decrease of the toe clearance, the static pressure first decreases and then increases. As the clearance is nearby 7.5, the static pressure reaches the minimum, meaning that the shroud has the best windage-reduction performance. It was also found that the pressure is relatively low when the toe clearance is 1" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002956_tte.2020.2997607-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002956_tte.2020.2997607-Figure5-1.png", "caption": "Fig. 5. Three different flux paths in the stator: (a) half-tooth loop and half-tooth crossing; (b) whole-tooth loop; (c) whole-tooth crossing.", "texts": [ " 2332-7782 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. IEEE TRANSACTIONS ON TRANSPORTATION ELECTRIFICATION 7 Since there are various harmonics existing in the DRMWM, the flux path in the stator is no longer the same as conventional PM synchronous machines. For the DRMWM, there are three different types of fluxes within the stator teeth, as shown in Fig. 5. It can be observed that for the left and right side of the stator tooth, the flux path and saturation degree is different. Hence, the flux density are divided into 2P parts to take account of the different saturation degree of stator teeth. The saturation coefficient ksat2,j for each tooth part is defined as: 2, , , 0 1 \u02c6 1 ( / ) sat j stator j j g j k H l B g (62) where j refer to the jth stator tooth, , \u02c6 stator jH is the field strength at the narrowest section for the flux within this modulator piece. Besides, the length of the flux path can be calculated approximately as \u03c0htooth, (\u03c0+2)htooth and 0.5\u03c0htooth+hslot for (a), (b), (c) in Fig. 5, respectively. Similarly, ,g jB is the average radial component of air-gap flux density below this tooth part. Then, the permeance \u03bb of outer air gap can be expressed as: 0 , i sat igk (63) Since the flux density can be expressed as the product of magneto motive force F and permeance \u03bb: B F (64) It is acceptable to ignore the flux leakage within permanent magnets. Then, F can be regarded as a constant. Hence, for each tooth part, the specific order harmonic of the radial outer air gap flux density considering saturation can be expressed as: 1 2,( ) ( ) IV IV r r sat sat jB j B j k k (65) where 1satk is the average value of the saturation coefficient of different modulator pieces" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000415_978-3-642-37552-1-Figure10.3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000415_978-3-642-37552-1-Figure10.3-1.png", "caption": "Fig. 10.3 a Schematic of floating plate. Outer diameter, thickness, and the cog angle of floating plate correspond to 2, 20 or 50 \u00b5m, and 45\u25e6. SEM photographs of floating plates of b type 1 (L = 100 \u00b5m), c type 2 (L = 200 \u00b5m) and d type3 (L = 400 \u00b5m). [21]\u2014Reproduced by permission of the Royal Society of Chemistry", "texts": [ " We applied 60 V under the conditions in Fig. 10.2d. As seen in the figure, 60 V was adequate to make the edge of the droplet move to the outer edge of the electrode. By changing the voltage-applied electrodes, the edge of the droplet is tunable. The floating plates were made from silicon on insulator (SOI) wafer. First, the plates were formed on the top layer by deep reactive ion etching (DRIE). Then the plates were released by removing the back layer with DRIE and the glass layer with hydrofluoric acid, respectively. Figure 10.3a has a schematic of the plates. The floating plate has four cogs. We fabricated four types of floating plates. The cog length, L, and the thickness, t, of the plates we fabricated were: L = 100 \u00b5m and t = 20 \u00b5m (type 1), L = 200 \u00b5m and t = 20 \u00b5m (type 2), L = 400 \u00b5m and t = 20 \u00b5m (type 3) and L = 400 \u00b5m and t = 50 \u00b5m (type 4). The cog angle was 45\u25e6 and their outer diameter was 2 mm. The scanning electronic microscopy (SEM) images of three of the fabricated plates (types 1\u20133) are shown in Figs. 10", " The amplitude of the applied voltage was DC 60 V and its polarity was positive in the experimentsduring this session. The voltage was supplied by a piezo actuator (MESS-TEK M-2680, \u00b1300 V and \u00b150 mA at maximum). We set the time to 0 at the moment velocity in the floating plate was observed. The theoretical shift of the rotational position was 22.5\u25e6. Figure 10.5b shows the step response of the liquid motor with different volumes of liquid. We used a type-3 floating plate in this experiment, shown in Fig. 10.3d, and placed droplets of liquid of 2.5, 3.0 and 3.5 \u00b5L on the base plate. The times to reach the maximum displacement corresponded to 21, 33, and 48 ms. The rising speed was increased while the volume of the liquid was reduced. The step responses with different cog lengths are shown in Fig. 10.5c. In this experiment, types 1\u20133 floating plates were used and the volume of the liquid was 3 \u00b5L. With 100, 200 and 400 \u00b5m cog lengths, the times to reach the maximum displacement corresponded to 77, 46, and 33 ms" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002107_j.measurement.2018.07.031-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002107_j.measurement.2018.07.031-Figure2-1.png", "caption": "Fig. 2. Schematic representation for radial deflection of ball bearing.", "texts": [ " For ball-inner race contact stiffness (Kin) \u2211= \u2217 \u2217 \u2217\u2212 \u2217 \u2212\u03c1 \u03b4K 2.15 10 ( )in 5 in 1/2 in 3/2 (2) For ball-outer race contact stiffness (Kout) \u2211= \u2217 \u2217 \u2217\u2212 \u2217 \u2212\u03c1 \u03b4K 2.15 10 ( )out 5 out 1/2 out 3/2 (3) The position of any rolling element \u2018\u03b8i\u2019 at any time, \u2018t\u2019 with respect to its initial position \u2018\u03b80\u2032 depends on angular velocity of cage (\u03c9c) and number of rolling elements (Nb) in bearings: = + +\u03b8 \u03c0 i \u03c9 t \u03b82 * Ni b c 0 (4) Deflection of ith ball in radial direction is provided by the following expression. Refer Fig. 2. = \u2212 \u2217 \u2212\u03b4 X X cos\u03b8 C( )i in s b i ri (5) The total deflection of ith ball in radial direction has been computed through following equation: = + = \u2212 \u2217 + \u2212 \u2217 \u2212\u03b4 \u03b4 \u03b4 X X cos\u03b8 X X cos\u03b8 C( ) ( )i total i in i out s b i b h i ri i (6) The cantilever portion of the shaft (from left end support to the test bearing) has been considered for dynamic analysis as other portion of the shaft is mounted between two rollers and assumed to be rigid. The stiffness\u2019s of cantilever portion of the shaft and bearing housing has been computed through finite element analysis" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000198_s1672-6529(11)60094-2-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000198_s1672-6529(11)60094-2-Figure1-1.png", "caption": "Fig. 1 Hopping motion of the single-legged robot (a), and virtual muscles on single-legged robot (b).", "texts": [ " In this paper, we firstly analyze the single legged hopping mechanism, built the single-legged control unit; then we construct the biped control mechanism by combining two control units; finally we validate the proposed biped control mechanism by simulation. The planar single-legged robot has a hip joint with rotational degree of freedom and a knee joint with linear degree of freedom. A linear spring is set on the knee joint to store energy. The robot can only move in the sagital plane. Single-legged robot has the same hopping motions with animals such as kangaroo, as shown in Fig. 1a. Hopping motion is divided into stance phase and flight phase. During stance phase, an animal maintains balance with muscles and stores energy with tendons, while a robot maintains balance with drivers on the hip joint and stores energy with the spring on the leg. As the leg touches the ground, the robot moves downward and the spring is compressed to store energy; when the robot reaches bottom altitude, its vertical velocity changes to upward as the spring stretches to release energy. During flight phase, the animal adjusts the angle between leg and ground for next landing, and contracts leg in order to avoid collision with obstacles, hopping robot has the same motion", " Motions of animals are generated by nerve- muscle system. Once the hopping motion starts, CPGs coordinate and control the joint muscles according to feedback information, while extensors and flexors cooperate to generate the desired motion. Imitating animal\u2019s nerve-muscle control mechanism, virtual muscles are used to analyze the control mechanism of hopping robot. Virtual muscles refer to the drivers of robot joint, suppose the robot moves toward right, virtual muscles of the robot are shown in Fig. 1b. Motions of robot joints are generated by cooperation of extensors and flexors, the joint stretches when extensor acts, and withdraws if the flexor acts. Both the hopping animal and legged hopping robot move passively. During hopping, the perturbations and terrains are unknown to the robot, it is hard to predict when and where the robot touches ground, and to plan joint trajectory before the motion is disturbed. The control system needs to receive sensory feedbacks and control joint motion in real time according to feedback information" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003142_j.jallcom.2020.158529-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003142_j.jallcom.2020.158529-Figure3-1.png", "caption": "Fig. 3. Finite element (FE) model meshes: (a) diamond-type scaffold and (b) BCC-type scaffold.", "texts": [ " 2c and d). All porous alloy scaffolds (Fig. 2e and f) were manufactured using an SLM machine (Renishaw AM400, UK) with a layer thickness of 30 \u00b5m, laser power of 110 W, hatch spacing of 0.12 mm and scanning speed of 350 mm/s. A checkerboard scanning strategy with a rotation angle of 67\u00b0 was used. The 3D CAD scaffold models using an explicit solver were established in the DEFORM-3D software to generate the quasi-static deformation process, and the 3D models were meshed with a tetrahedral model (Fig. 3). Moreover, the geometrical dimensions of the 3D models in the simulation were identical to those in the compression test. Considering the actual compression conditions, the porous scaffolds were sandwiched between the upper and lower rigid circular plate, and the bottom of the circular plate was set as the fixed constraint; parallel to this, the top circular plate was set as the surface loading condition of the porous structure. Note that the TC4 alloy scaffolds were used in the experiment, the FE model had an elastic modulus of 110 GPa, and Poisson's ratio of 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003198_j.mechmachtheory.2020.103960-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003198_j.mechmachtheory.2020.103960-Figure3-1.png", "caption": "Fig. 3. Local coordinate systems of an RRlS limb.", "texts": [ " Stiffness matrix of the RRlS limb using MSA Since n(3RRlS) RSPMs are used in space as robotic manipulators and the operational speed of 3RRlS RPM is rather slow, the effect of acceleration and gravity can be neglected. Moreover, all actuators, platforms, and joints of 3RRlS RPM are regarded to be rigid. Since the links of 3RRlS RPM are slender, they are flexible and equivalent to beam models. The local coordinate systems of all links and limbs are successively established at the end of the links, as shown in Fig. 3 (a) and the end of the limbs, Please cite this article as: C. Zhao, H. Guo and D. Zhang et al., Stiffness modeling of n(3RRlS) reconfigurable series-parallel manipulators by combining virtual joint method and matrix structural analysis, Mechanism and Machine Theory, https: //doi.org/10.1016/j.mechmachtheory.2020.103960 6 C. Zhao, H. Guo and D. Zhang et al. / Mechanism and Machine Theory xxx (xxxx) xxx i.e., point C i . A single link can be regarded as a cantilever beam for stiffness analysis, and the compliance matrix of the link in its local coordinate system is as follows: C e = K e \u22121 = \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 l 3 3 EI y 0 0 0 l 2 2 EI y 0 0 l 3 3 EI x 0 \u2212 l 2 2 EI x 0 0 0 0 l EA 0 0 0 0 \u2212 l 2 2 EI x 0 l EI x 0 0 l 2 2 EI y 0 0 0 l EI y 0 0 0 0 0 0 l GI p \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 (11) where E and G denote the elastic modulus and shear modulus of the link, respectively", " For small deformations, the total deformation of the limb can be calculated as p Ci = G Bi p Be + G Ci p Ce = G Bi C Be F Be + G Ci C Ce F Ce = G Bi C Be G Bi T F Ci + G Ci C Ce G Ci T F Ci = ( G Bi C Be G Bi T + G Ci C Ce G Ci T ) F Ci (12) Where G Bi = [ R (\u03c0 \u2212 \u03b8i \u2212 \u03b8Bi ) \u0302 t BCi R (\u03c0 \u2212 \u03b8i \u2212 \u03b8Bi ) 0 R (\u03c0 \u2212 \u03b8i \u2212 \u03b8Bi ) ] ; t BCi = [ 0 0 \u2212l ] T ; G Ci = [ I 0 0 I ] . Since p Ci = C Ci F Ci , the compliance matrix of the RRlS limb can be obtained as C Ci = G Bi C Be G Bi T + G Ci C Ce G Ci T (13) 3.2.1. Stiffness matrix of RRlS 2 limb When the local coordinate system of the limb coincides with the axes of constraint forces, as shown in Fig. 3 (b), the equation p Ci = C Ci F Ci is expanded as \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 p ci p 1 i p ri p 2 i p 3 i p 4 i \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 = \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 C i 11 C i 12 C i 13 C i 14 C i 15 C i 16 C i 21 C i 22 C i 23 C i 24 C i 25 C i 26 C i 31 C i 32 C i 33 C i 34 C i 35 C i 36 C i 41 C i 42 C i 43 C i 44 C i 45 C i 46 C i 51 C i 52 C i 53 C i 54 C i 55 C i 56 C i 61 C i 62 C i 63 C i 64 C i 65 C i 66 \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 F ci 0 F ri 0 0 0 \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 (14) The dimension of Eq. (14) can be reduced to two, and hence, the stiffness equation of the constraint wrenches is expressed as [ p ci p ri ] = [ C i 11 C i 13 C i 31 C i 33 ][ F ci F ri ] (15) The compliance matrix of the RRlS 2 limb can be obtained as C Ci = K \u22121 Ci = [ C i 11 C i 13 C i 31 C i 33 ] (16) When the RRlS 2 limb does not have an actuator, its compliance matrix can be obtained as C Ci = K \u22121 Ci = [ C i 11 ] (17) 3.2.2. Stiffness matrix of RRlS 1 limb Let \u03c6\u2032 = \u03b8B 1 \u2212 \u03c6, and when the local coordinate system of the limb coincides with the axes of constraint forces, as shown in Fig. 3 (b), the equation p Ci = C Ci F Ci is expanded as \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 p ci p 1 i p ri p 2 i p 3 i p 4 i \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 = \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 C i 11 C i 12 C i 13 C i 14 C i 15 C i 16 C i 21 C i 22 C i 23 C i 24 C i 25 C i 26 C i 31 C i 32 C i 33 C i 34 C i 35 C i 36 C i 41 C i 42 C i 43 C i 44 C i 45 C i 46 C i 51 C i 52 C i 53 C i 54 C i 55 C i 56 C i 61 C i 62 C i 63 C i 64 C i 65 C i 66 \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 F ci 0 F ri 0 T ci s\u03c6 \u2032 T ci c\u03c6 \u2032 \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 (18) Please cite this article as: C. Zhao, H. Guo and D", ", Stiffness modeling of n(3RRlS) reconfigurable series-parallel manipulators by combining virtual joint method and matrix structural analysis, Mechanism and Machine Theory, https: //doi.org/10.1016/j.mechmachtheory.2020.103960 C. Zhao, H. Guo and D. Zhang et al. / Mechanism and Machine Theory xxx (xxxx) xxx 7 The dimension of Eq.(18) can be reduced to two, and thus the stiffness equation of the constraint forces is expressed as[ p ci p ri ] = [ C i 11 C i 13 C i 15 s\u03c6 \u2032 + C i 16 c\u03c6 \u2032 C i 31 C i 33 C i 25 s\u03c6 \u2032 + C i 26 c\u03c6 \u2032 ][ F ci F ri T ci ] (19) When the local coordinate system of the limb coincides with the axis of constraint couple, as shown in Fig. 3 (c), the compliance matrix of the RRlS 1 limb can be obtained as C \u2032 Ci = G \u2032 Ci C Ci G \u2032 Ci T (20) Where G \u2032 Ci = [ R (\u03c6\u2032 ) 0 0 R (\u03c6\u2032 ) ] . The equation p Ci = C Ci F Ci is expanded as \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 p ci p 1 i p ri p 2 i p 3 i p \u03d5i \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 = \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 C \u2032 i 11 C \u2032 i 12 C \u2032 i 13 C \u2032 i 14 C \u2032 i 15 C \u2032 i 16 C \u2032 i 21 C \u2032 i 22 C \u2032 i 23 C \u2032 i 24 C \u2032 i 25 C \u2032 i 26 C \u2032 i 31 C \u2032 i 32 C \u2032 i 33 C \u2032 i 34 C \u2032 i 35 C \u2032 i 36 C \u2032 i 41 C \u2032 i 42 C \u2032 i 43 C \u2032 i 44 C \u2032 i 45 C \u2032 i 46 C \u2032 i 51 C \u2032 i 52 C \u2032 i 53 C \u2032 i 54 C \u2032 i 55 C \u2032 i 56 C \u2032 i 61 C \u2032 i 62 C \u2032 i 63 C \u2032 i 64 C \u2032 i 65 C \u2032 i 66 \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 F ci \u2212 F ri s\u03c6 \u2032 F ri c\u03c6 \u2032 0 0 T ci \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 (21) The dimension of Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001144_j.mechmachtheory.2013.09.001-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001144_j.mechmachtheory.2013.09.001-Figure1-1.png", "caption": "Fig. 1. Surface parameters of the VTT rack cutter.", "texts": [ " By comparison of the TCA simulation results, the merits of the gear pairs generated by the proposed generation method with the modified VTT hob can be clearly verified. 2. Mathematical model of the modified hob with variable tooth thickness (VTT) Basically, the theoretical tooth profile of a hob is a helical gear that can be generated by a rack cutter. In this study, however, the proposed modified VTT hob can be generated by a modified rack cutter. The tooth thickness of the rack cutter is modified along its helix line as shown in Fig. 1, and along its profile line as shown in Fig. 2. The helix angle of the rack cutter is equal to the standard helix angle at the reference point P, which is located at the middle transverse section of the rack cutter. The helix line of the rack cutter is modified by a second order polynomial, as expressed in Eq. (17). A schematic relationship among coordinate systems for generation of the modified VTT hob is shown in Fig. 3. Coordinate systems S7(x7,y7,z7), Sp(xp,yp,zp), and Sq(xq,yq,zq) are rigidly connected to the rack cutter, hob, and frame, respectively", " sjki circular tooth thickness, j = b, o, p; k = t, n; i = 1, 2, 3. \u03b3 crossed angle \u03b2jki helix angle, j = b, o, p; k = t, n; i = 1, 2, 3. mjki module, j = b, o, p; k = t, n; i = 1, 2, 3. Ni number of teeth, i = 1, 2, 3. Eo operating center distance \u03b1jki pressure angle, j = b, o, p; k = t, n; i = 1, 2, 3. rjki radius of the cylinder, j = b, o, p; k = t, n; i = 1, 2,3. a center distance variation coefficient (refer to Eq. (15) and Fig. 4) b hob normal tooth thickness variation coefficient (refer to Eq. (4) and Fig. 1) c hob diagonal shifting coefficient (refer to Eq. (10) and Fig. 4) d tooth profile modification coefficient (refer to Eq. (1) and Fig. 2) subscripts n measured in the normal section t measured in the transverse section o operating pitch circle p pitch circle 1 hob 2 proposed work gear 3 standard involute gear The authors are grateful to the National Science Council of the R.O.C. for financial support. Part of this work was performed under Contract No. 101-2218-E-035-010. [1] F.L. Litvin, Gear Geometry and Applied Theory, PTR Prentice Hall, Englewood Cliffs, NJ, 1994" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000753_j.engfailanal.2011.11.004-Figure18-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000753_j.engfailanal.2011.11.004-Figure18-1.png", "caption": "Fig. 18. Fatigue safety factor with the application of the FEM method.", "texts": [ " All values of the corresponding component stresses (presented in Table 5) were obtained by the finite element method and they are below the line A\u2013B, which represents the fatigue boundary. However, as the line C\u2013D was chosen to be the relevant line of fatigue, the values of the corresponding component stresses at the point of fracture (item 1) are above this line, which leads to the conclusion that fatigue safety is not provided. The same results were also reached by fatigue analysis with the application of the finite element method. The value of fatigue safety factor is lower than 1 at the point of radius ending (Fig. 18), which corresponds to the analysis of the Goodman diagram. On the basis of the FEM results, it can be concluded that: The stress state for case II is less favorable than I and it covers the situations when the BWE turns while moving backward or forward and it frequently appears in operation. The level of the stress state in the zone of fracture of the drive shaft for loads II is very high; the levels of uniaxial stresses, at the point of support \u2018\u2018A\u2019\u2019 are 2.1 times higher than the stresses for load case I; The safety factor of the drive shaft in the characteristic section for load case I is: S \u00bc ry req;max;I \u00bc 745 324 \u00bc 2:3, for case II S \u00bc ry req;max;II \u00bc 745 680 \u00bc 1:1 The fatigue analysis showed that the stress value at point 1 exceeded the fatigue boundary line and that fatigue failure safety was not provided" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002430_tmag.2019.2941699-Figure9-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002430_tmag.2019.2941699-Figure9-1.png", "caption": "Fig. 9. Motor design for the model validation and winding configuration. (a) Motor design. (b) 2 \u00d7 3 phase winding configuration.", "texts": [ " After that, the total field can be found by using of a superposition principle as a sum of both components. The radial and tangential components of the flux density can be calculated as follows: Br = 1 r \u2202A \u2202\u03b8 , B\u03b8 = \u2212\u2202A \u2202r . (74) B. Comparison of Magnetic Field Distribution With FEA The comparison of the analytical and FEA results was done for the motor, which is currently being designed for E-bike [13]. The geometrical and input parameters of the motor are listed in Table I. The machine geometry is shown in Fig. 9(a). The labels A1, B1, and C1 denote the coils corresponding to an appropriate phase. The machine includes a 2 \u00d7 3 phase winding configuration, as depicted in Fig. 9(b). Each phase of the concentrated double-layer winding consists of four coils connected in series. Each three-phase winding system is localized within 180\u25e6 segment. Thereby, half of the machine belongs to the A1, B1, and C1 star, while another half to the A2, B2, and C2 star. The comparison of the flux density distribution for the radial and tangential components in the inner and outer air gaps for the no-load condition is given in Figs. 10 and 11, respectively. The comparison is presented for 90\u25e6 arc, since the machine topology has 90\u25e6 odd periodicity. The flux density was measured along the arc with the radii rprobe = (R1 + R2/2) and rprobe = (R5 + R6/2) for the internal and external air gaps, respectively. For the on-load condition at the current density of 14.9 A/mm2, the comparison is shown in Figs. 12 and 13 for the internal and external air gaps, respectively. The flux density was also compared with the one inside the slot and inside the internal and external slot openings along the dashed arcs (Fig. 9) for the no-load case. The results are presented in Figs. 14\u201316. The flux lines obtained from the FEA and analytical calculations are presented in Fig. 17(a)\u2013(f) for the no-load case, the flux lines produced by the current when the magnets are off, and the on-load case, respectively. The flux distribution is given for the PM region of the inner and outer rotors, the inner and outer air gaps, the inner and outer slot openings, and the slot subdomains. C. Comparison of Electromagnetic Parameters With FEA The computation of the bEMF has been performed by using the approach described in [2]" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003476_j.triboint.2021.106951-Figure13-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003476_j.triboint.2021.106951-Figure13-1.png", "caption": "Fig. 13. Oil flow fields inside the intermediate gearbox when circling.", "texts": [ " In the present work, the roll angle of the helicopter is set to 20\u25e6 and the angular velocity is \u03c0/3 rad/s, which Fig. 11. Churning losses at three speeds. Fig. 12. Force diagram of the helicopter when circling. X. Hu et al. results in a circling radius 3.25 m. The center of rotation and angular velocity of the intermediate gearbox are set in the non-inertial coordinate system of the Flow-3D software. The rotating speed of the driving gear is set to 3000 rpm and the simulation time is 1s. The oil distribution inside the gearbox and oil flow rate of oil guide holes are obtained as shown in Fig. 13 and Fig. 14. There is more lubricating oil at the No. 1 and No. 2 oil guide holes at 0.62s than that of 1s, as shown in Fig. 13(a) and (e), which is because the lubricating oil becomes more disordered with time. From Fig. 13(b), it is X. Hu et al. Tribology International 159 (2021) 106951 obvious that the oil is mainly distributed on the inner wall of the gearbox. Fig. 13(c) and (d) show the volume fraction of lubricating oil of No.3 and No.4 oil guide holes at 0.62s and 1s respectively. It can be seen that there is sufficient lubricating oil in the two oil guide holes and the amount of lubricating oil in No. 3 oil guide hole is more than that in No. 4. Fig. 13(e) and (f) show that the oil inside the gearbox inclines to one side due to centrifugal force. And the lubricating oil tilts more obviously as time goes by. Fig. 14 shows the oil flow rate in the No. 4 oil guide hole is the smallest when circling, with an average of 7.27 \u00d7 10\u2212 4kg/s which is obviously insufficient for lubricating bearings, while the rest of oil guide holes has sufficient lubricating oil. There is almost no lubricating oil passing through the oil guide holes in 0\u20130.2s, which is because that most of the oil is still at the bottom of the gearbox at this time" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001328_j.renene.2014.03.036-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001328_j.renene.2014.03.036-Figure2-1.png", "caption": "Fig. 2. Interface points for the FRF calculations.", "texts": [ " By changing the value of some of the most important design parameters, it can be shown that some parameters should be carefully chosen during design while other parameters have little influence on the overall reliability and N&V behavior of the gearbox. With regard to reliability the main excitation source is the connection between the rotor and the main shaft. Three main loading degrees of freedom (DOFs): radial, thrust and bending are investigated. The input for each of these FRFs is the forces at the rotor main shaft coupling. Fig. 2 shows the rotor-main shaft coupling and the corresponding forces. The main response of DOFs is the planet carrier displacements at the rear planet carrier (PLC) bearing location (PLC-B) and the gearbox bushing displacements. Fig. 1 shows the different bearings in the gearbox, whereas Fig. 2 shows the gearbox bushings. The planet carrier motion is investigated, since this parameter is significantly affected by the non-symmetric loading of the gearbox [6]. Fig. 3 illustrates this. Due to the planet carrier displacements the loading conditions in the planet-ring gear meshes can become unfavorable. This can potentially result in non-symmetric planet bearing loading and corresponding overloading of one of the planet bearings [10]. The planet-ring gear meshes displacements are not used in the FRF analysis in this paper since we want to make abstraction of the influence of the gear meshing stiffness on the behavior of the gearbox suspension" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002386_s12555-018-0741-2-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002386_s12555-018-0741-2-Figure1-1.png", "caption": "Fig. 1. Reference frames of a marine surface vehicle.", "texts": [ " (5) Definition 2 [31]: A barrier Lyapunov function is a scalar function V (x), defined with respect to the system x\u0307 = f (x) on an open region D containing the origin, that is continuous, positive definite, has continuous first-order partial derivatives at every point of D, has the property V (x)\u2192 \u221e as x approaches the boundary of D, and satisfies V (x (t))\u2264 b \u2200t \u2265 0 along the solution of x\u0307 = f (x) for x (0) \u2208 D and some positive constant b. Lemma 5 [32]: For any positive constant kb, positive integer p and z \u2208 R satisfying |z|< kb, there exists log k2p b k2p b \u2212 z2p < z2p k2p b \u2212 z2p (6) Lemma 6 [39]: The system z\u0307 = f (z,v) , z \u2208 Rn, v \u2208 Rm with f (0,0) = 0, is finite-time input-to-state stable (FTISS), if it has an FTISS-Lyapunov function. 2.2. Dynamic model of a MSV The MSV in horizontal plane is shown in Fig. 1. For motion control of a three degree-of-freedom (DOF) surface vehicle, we first define the earth-fixed frame (EF) OEXEYEZE and the body-fixed frame (BF) ObXbYbZb. The origin OE of the EF is fixed to the earth. OEXE -axis is directed to north, OEYE -axis is directed to east. The body axes ObXb is directed from aft to fore, ObYb is directed to right starboard, and ObZb is directed from vehicle top to bottom. Neglecting the heave, roll and pitch motion, the dynamic model of a 3-DOF surface vehicle subject to external disturbances can be described as follows: \u03b7\u0307 =R (\u03c8)\u03bd , M\u03bd\u0307 =\u2212C (\u03bd )\u03bd \u2212D (\u03bd )\u03bd +\u03c4 +MRT (\u03c8)\u03b4 (t) , y =\u03b7 , (7) where \u03b7 = [x,y,\u03c8]T represents the vehicle position (x,y) and the heading angle \u03c8 in EF" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002705_j.mechmachtheory.2020.104006-Figure9-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002705_j.mechmachtheory.2020.104006-Figure9-1.png", "caption": "Fig. 9. The distribution of limit points in the enclosed box.", "texts": [ " The schematic diagram of the enclosed box configuration is shown in Fig. 8 . The D-H parameters and dimensions of the redundant circular-sliding manipulator are the same as above. The origin of the circular-sliding rail base is taken as the coordinate origin. Due to the axisymmetric arrangement of the redundant circular-sliding manipulator and the enclosed box body, six limit points are selected in the enclosed box for accessibility analysis. The distribution of limit points in the enclosed box is shown in Fig. 9 . According to the size of the enclosed box, the coordinates of the six limit points are set as follows: (470, -376.5, 0) mm , (470, 251, 0) mm , (470, -376.5, 603) mm , (470, 251, 603) mm , (157, 376.5, 0) mm , (157, 376.5, 570) mm . According to the inverse kinematics solution of the redundant circular-sliding manipulator, each joint angle of the manipulator at the limit position points in the enclosed box can be obtained, as shown in Fig. 10 . According to the limit point test of the enclosed box manipulator workspace and the reachability analysis of the manipulator, the global reachability of the manipulator in the enclosed box can meet the work task requirements in the full space of the enclosed box" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001290_j.ces.2015.08.056-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001290_j.ces.2015.08.056-Figure4-1.png", "caption": "Fig. 4. Scheme of the particle movement during the free fall experiments.", "texts": [ "sasoltechdata. com/alumina_group.asp). The synthetic zeolite 4A granules (produced by Chemiewerk Bad K\u00f6stritz GmbH) consist of approximately 83 ma% zeolite primary particles (Na2O\u2219Al2O3\u22192SiO2\u2219nH2O) and 17 ma% attapulgite binder content (Mg,Al)2Si4O10(OH) 4(H2O) (Mueller et al., 2015). The measured (most relevant) physical and granulometric characteristics of the material samples in the dry state are summarized in Table 1. The free fall tests had been performed using a home-built test rig, see Fig. 3. Fig. 4 presents the schematic representation of the particle movement during the conducted tests. At the beginning of each free fall test, one single particle is fixed using vacuum tweezers before being dropped so that it starts to fall freely without any initial velocity v0\u00bc0 and rotation \u03c90\u00bc0. Different drop heights have been used to ensure different impact velocities in the range 0.3 m/sovAo2.5 m/s. The vacuum-held particle (granule or glass bead) was released from the desired drop height h1, such that it falls freely until impacting on the impact plate (glass plates of different thicknesses H, see Table 2) arranged orthogonal to the trajectory of the falling particle" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002664_tec.2020.2990914-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002664_tec.2020.2990914-Figure3-1.png", "caption": "Fig. 3. Geometry structure of the proposed switched reluctance motor.", "texts": [ " Optimization of Stator and Rotor This section presents the required equations for design optimization of the proposed motor based on flow-chart shown in Fig.2. According to this algorithm [18], the motor is designed based on a constant volume (fixed stack length and stator outer diameter. After specifying the stack length and stator outer diameter, other variables are determined. The geometry of the proposed SRM with the rotor at aligned position and the 1st phase of the stator have been shown in Fig. 3 and the specifications have been summarized in Table I. i. Stator Yoke Thickness, bsy The stator yoke of the SRM is determined based on its peak flux density. The major part of the stator pole flux in the aligned position passes through the yoke of the C-core which is on contrary to the conventional SRM. In the conventional SRM, half of the stator pole flux passes through the stator yoke. The stator pole flux has two flux paths consisting of the yoke in the C-core part and the yoke in parts between the two C-cores" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000426_tmag.2012.2197734-Figure9-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000426_tmag.2012.2197734-Figure9-1.png", "caption": "Fig. 9. Specifications of the typical SR motor.", "texts": [ " The excitation beginning angle and the excitation width are and , respectively. Fig. 8(a) indicates the observed and calculated waveforms of voltage and current of the trial SR motor. The figure clearly reveals that both waveforms are in almost good agreement. Fig. 8(b) shows the comparison of the voltage and current waveforms when the auxiliary winding currents are 0 and 3 A, respectively. A load torque is in the both cases. It is understood that the phase current is decreased by exciting the auxiliary windings. Fig. 9 shows the specifications of the typical 12/8-pole SR motor used for the comparison, which has the same dimensions, core material, and windings as the proposed SR motor shown in Fig. 2. Fig. 10 shows the current density versus torque characteristics. In the figure, the solid, broken, and dotted lines indicate the calculated values, while the symbols denote the measured ones. Only the calculated values are indicated in the case of the typical SR motor shown in Fig. 9 since an actual machine does not exist. It is seen from the figure that the close agreement between the calculated and measured values is obtained, and that the torque of the proposed SR motor is improved by exciting the auxiliary windings. Fig. 11 shows the efficiency characteristics of the trial SR motor. The efficiency of the proposed SR motor is also improved. When the auxiliary windings are excited by dc current, the fluxes generated from the magnets and auxiliary windings flow through the stator and rotor poles aligned with each other as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003529_s11071-021-06796-3-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003529_s11071-021-06796-3-Figure2-1.png", "caption": "Fig. 2 View of cross section", "texts": [ "1 Definition of coordinate system A global Cartesian coordinate system with an origin O at the symmetric center of top surface of carriage is defined as shown in Fig. 1. High-precision linear motion can be realized by recirculating balls between rail and carriage. When carriage is subjected to evenly distributed lateral and radial loads, and moments in rolling, pitching and yawing directions F = [Fy Fz Mx My Mz] T, the linear and angular displacements of carriage block relative to fixed rail are X = [uy uz hx hy hz] T as a result of the localized deformation between groove surface and balls. The cross sections of guide block shown in Fig. 2 indicate that carriage block can provide equal load capacity in all coordinate directions normal to motion direction due to the initial contact angle a0 of 45 . There are four rows of ball (j = 1, 2, 3, 4) inside linear guideway in a face-to-face arrangement which higher stiffness is exhibited than back-to-back ball arrangement [20]. Each ball groove has a contact profile of a circular arc forming a two-point contact mode. The ball arrangement of each row is assumed to be identical and same load ball number of each row is k" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000931_9781118703274.ch2-Figure2.62-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000931_9781118703274.ch2-Figure2.62-1.png", "caption": "Figure 2.62 Flow and forces on the rotor blade given the same wind speed for active-stall adjustment (a) Laminar flow (b) Stalling", "texts": [ "2, the rotor blades can be moved in the direction of the feathering pitch in order to reduce the power absorbed by a turbine. In contrast, active-stall-controlled machines require that the blades are rotated in the direction of the plane of rotation in order to move into the stall range and thus reduce the power drawn from the airstream. In general, a blade pitch-adjustment range of a few degrees is sufficient to protect the machine from overload, for example, or to adjust output to the desired levels. Figure 2.62(a) and (b) illustrates the change in the torque-producing tangential force Ft given the same wind conditions and only slightly changed blade pitch angle or angle of attack (\ud835\udefd or \ud835\udefc). On the other hand, stall-controlled machines with a synchronous generator and frequency controller or double-fed asynchronous generator permit variable-speed turbine operation. Such configurations mean that the peripheral speed of the blades and thus the angle of attack can be altered by adjusting the turbine speed (see Figure 2" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003155_s12555-019-0421-x-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003155_s12555-019-0421-x-Figure1-1.png", "caption": "Fig. 1. Mechanic structure of four-PMSM system.", "texts": [ " In Section 4 \u201cCharacteristic model-based adaptive control scheme with GAE\u201d, an adaptive discrete-time terminal sliding mode controller is proposed to achieve a good performance in our four-PMSM synchronization system. Besides, the close-loop stability is proved with Lyapunov theorem. Section 5 \u201cSimulation Results\u201d and Section 6 \u201cExperiment results\u201d show the simulation and experiment results respectively. Finally, some conclusions are given in Section 7 \u201cConclusion,\u201d 2.1. Dynamic model of four-PMSM system The mechanical structure of the four-PMSM synchronous system in this article is shown in Fig. 1. The PMSMs are controlled with id = 0 strategy. Similar as paper [19], the dynamical model of whole system in d \u2212 q coordinate system could be described as: Lsq j disq j(t) dt = usq j(t)\u2212Rs jisq j(t)\u2212Ce jw j(t) +d1 j, J j dw j(t) dt =CT jisq j(t)\u2212Tf j(t)\u2212Tc j/rc j +d2 j, Tc j(t) = kcm j[z jc(t)\u2212\u03b1 j], zc j(t)\u2265 \u03b1 j, 0, |zc j(t)|< \u03b1 j, kcm j[z jc(t)+\u03b1 j], zc j(t)\u2264\u2212\u03b1 j, zc j(t) = \u03b8c j(t)\u2212 rm\u03b8m(t), Jmw\u0307m(t)+bmwm(t) = 4 \u2211 j=1 rmTc j(t)\u2212TL +d3, \u03b8\u0307m(t) = wm(t), Tf j(t) = [ Fc j +(Fs j \u2212Fc j)e \u2212 ( w j (t) Vs j )2 ] , \u00d7 2 \u03c0 arctan(kv jw j(t))+b jw j(t), j = 1,2,3,4" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002795_j.oceaneng.2019.106429-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002795_j.oceaneng.2019.106429-Figure3-1.png", "caption": "Fig. 3. AUV-T and its coordinate system.", "texts": [ " However, the pool test showed that the ranging sonars could work with Fig. 1. AUV-T. Fig. 2. Ranging sonar. X. Wang et al. Ocean Engineering 190 (2019) 106429 satisfactory accuracy in the range of 0.2\u201320 m when they work in polling mode. The sonars of AUV-T work in polling mode so that the accuracy of sonar data can be guaranteed when following the wall. The main parameters of the AUV are shown in Table 1. Based on the ITTC and SNAME\u2019s offer, the submarine motion is described through a 6-DOF body coordinate frame of reference (Fig. 3), in which the origin is located at the center of gravity with the positive directions along the x-, y-, and z-axes, which denote forward, starboard, and vertically downward, respectively. The 6-DOF AUV kinematic and dynamic equations are as (Tanakitkorn et al., 2018): _\u03b7 \u00bc J\u00f0\u03b7\u00dev (1) where v \u00bc \u00bdu v w p q r\ufffdT, \u03b7 \u00bc \u00bdx y z \u03d5 \u03b8 \u03c8 \ufffdT, \u03c4 is a vector of external forces and moments, d is the external disturbance force and moment, J\u00f0\u03b7\u00de is a transformation matrix, is the rigid-body inertia matrix, C\u00f0v\u00de is a matrix of rigid-body Coriolis and centripetal forces, D\u00f0v\u00de is a damping matrix, and g\u00f0\u03b7\u00de is a vector of generalized gravitational and buoyancy forces (Mahapatra and Subudhi, 2018)" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003277_tmech.2021.3057898-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003277_tmech.2021.3057898-Figure4-1.png", "caption": "Fig. 4. Tracking errors in the Frenet frame.", "texts": [ " (22) According to (20), the original control input of driving force fd is achieved by (23) for the model with force measurements fd = (fv \u2212G0hy \u2212Gsfs)/Gd + hx = Rfv L2 0 cos 2 \u03b4 + (m0b 2 0 + J0)v0 tan \u03b4fs L2 0 cos 2 \u03b4 + c0 tan \u03b4hy L0 + hx (23) where R is defined in Appendix B. Similarly, according to (5), (24) then gives the calculation of fd for the dynamic model of the whole vehicle fd = (fv \u2212 gsfs \u2212 g0)/gd. (24) Note that due to the fact\u2212\u03c0/2 < \u03b4 < \u03c0/2 of the physical tractor, (23) and (24) always suffice the bijective mapping, which means fd can certainly be obtained once given fv . We first express the tracking errors with respect to the Frenet frame as follows (see Fig. 4): xe = (x0 \u2212 xr) cos \u03b8r + (y0 \u2212 yr) sin \u03b8r ye = \u2212(x0 \u2212 xr) sin \u03b8r + (y0 \u2212 yr) cos \u03b8r \u03b8e = \u03b80 \u2212 \u03b8r ve = v0 \u2212 vr. (25) Computing the time derivative and applying the dynamic equations with virtual control inputs, we have the following error dynamics: x\u0307e = v0 cos \u03b8e + \u03b8\u0307rye \u2212 vr (26) y\u0307e = v0 sin \u03b8e \u2212 \u03b8\u0307rxe (27) \u03b8\u0307e = v0C\u03b4 \u2212 \u03b8\u0307r (28) v\u0307e = fv \u2212 v\u0307r (29) C\u0307\u03b4 = ( 1 L0 + L0C 2 \u03b4 ) fs (30) where C\u03b4 = tan \u03b4 L0 is the curvature of the tractor and (30) is derived as follows: C\u0307\u03b4 = fs L0 cos2 \u03b4 = ( L0 sin 2 \u03b4 L2 0 cos 2 \u03b4 + L0 cos 2 \u03b4 L2 0 cos 2 \u03b4 ) fs = ( 1 L0 + L0C 2 \u03b4 ) fs" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003198_j.mechmachtheory.2020.103960-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003198_j.mechmachtheory.2020.103960-Figure7-1.png", "caption": "Fig. 7. Line drawing of n(3RRlS) RPM.", "texts": [ " Guo and D. Zhang et al., Stiffness modeling of n(3RRlS) reconfigurable series-parallel manipulators by combining virtual joint method and matrix structural analysis, Mechanism and Machine Theory, https: //doi.org/10.1016/j.mechmachtheory.2020.103960 10 C. Zhao, H. Guo and D. Zhang et al. / Mechanism and Machine Theory xxx (xxxx) xxx 4. Stiffness modeling of n(3RRlS) RSPM The n(3RRlS) RSPM proposed in [4-5] is composed of n identical 3RRlS RPMs connected in series, and a schematic diagram is shown in Fig. 7 . The j th 3RRlS RPM can be written as 3RRlS RPM j, whose static platform and moving platform are shared with the moving platform of 3RRlS RPM j -1 and the static platform of 3RRlS RPM j + 1 , respectively. 4.1. Deformation analysis of n(3RRlS) RSPM The velocity equation of a 2(3RRlS) RSPM, i.e. 3RRlS RPM j -1 and 3RRlS RPM j , is expressed as j\u22122 j v = j\u22122 j\u22121 v + j\u22122 j\u22121 R j\u22121 j v + j\u22122 j\u22121 \u03c9 \u00d7 ( j\u22122 j\u22121 R j\u22121 j t ) = j\u22122 j\u22121 v + j\u22122 j\u22121 R j\u22121 j v + T ( j\u22122 j\u22121 R j\u22121 j t ) j\u22122 j\u22121 \u03c9 (33) Where denotes the operation of the skew-symmetric matrix" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002629_s00170-019-04558-5-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002629_s00170-019-04558-5-Figure6-1.png", "caption": "Fig. 6 Path planning. a Schematic diagram of the filling path calculation. b Schematic diagram of cylindrical circumferential filling. c Schematic diagram of cylindrical axial filling", "texts": [ " For the complex curve of propeller cross section, it is impossible to get the internal filling path gradually according to a certain offset. Because the curvature at both ends of the propeller section curve is very large, the intersection point will be generated at both ends when the offset inward, which will affect the filling quality. In order to prevent this situation from occurring, the article proposes a method of the internal filling path of STL file surface slice: filling on the sliced cylinder with a uniform \u201cgrid,\u201d as shown in Fig. 6a. Unlike planar slices, the Z coordinates of data points of filling paths are not fixed values equal to the slice height, but a series of points distributed on the cylindrical surface when path planning of cylindrical surface slicing. Therefore, not only the X and Y coordinates of each filling path data point but also the Z coordinates of each point need to be calculated in the path planning. (1) Cylindrical circumferential filling method The offset of the cylindrical circumferential filling method is half the width of a single deposition, that is, 3", "5 mm each time until Xmax. The coordinates of the outline data points are obtained from the cylindrical surface slices, and the coordinate ranges of the propeller contour corresponding to each xfill in the Y direction are calculated respectively. They are recorded as y1 and y2; within the range of y1 and y2, mark every point every 3.5 mm and calculate corresponding Z coordinates for each point on the cylinder. Connect the dots with the same X coordinate in order, the circumferential filling path is set, as shown in Fig. 6b. (2) Cylindrical axial filling method Cylindrical axial filling is similar to cylindrical circumferential filling, the offset of which is 3.5 mm. According to the blade profile obtained from the cylindrical surface slicing, the Ymax and Ymin of the contour edge are calculated respectively. The filling path yfill begins with Ymin and increases by 3.5 mm each time until Ymax. The coordinates of the outline data points are obtained from the cylindrical surface slices, and the coordinate ranges of the propeller contour corresponding to each yfill in the X direction are calculated respectively. The intersections are marked with x1 and x2; similarly, within the range of x1 and x2, mark every point every 3.5 mm and calculate corresponding Z coordinates for each point on the cylinder. Connect the dots with the same Y coordinate in order to set the surface axial filling path as shown in Fig. 6c. In the actual calculation process, the point in the filling path that coincides with the contour path needs to indent to the inside of the contour by 3.5 mm to avoid interference from the filling path and contour. Meanwhile, the overlap ratio needs to be ensured during actual accumulation. Before the actual printing, the simulator needs to be divided into several regions: one for the hub and one for each blade for the complexity and symmetry of the blade. In the manufacturing process, the hub is first formed by plane slicing and offset filling, and the blade is formed piece by piece by cylindrical slice and cylindrical axial filling and cylindrical circumferential filling alternately", " Since the hub and the cylindrical surface are coaxial, the hub, in the paper, is manufactured first; the blades are later printed on the hub piece by piece. Kazanas et al. researched the fabrication of geometrical features using WAAM and described the dimensional error of component due to heat accumulation [22]. For reducing the effect of heat accumulation on the contour dimensional accuracy, the inner part is firstly formed and then the contour is printed layer by layer. The cylindrical axial filling is as shown in Fig. 6b, the cylindrical circumferential filling is as shown in Fig. 6c, and the actual deposition result is as shown in Fig. 7. Powerscan is a non-conducting 3D scanner based on surface structured light, whose measurement accuracy can reach \u00b1 0.05 mm and single plot cloud scan can reach 0.5 s. In the process of producing propeller simulator with WAAM, 8\u201310 photos of point cloud file are taken along the predetermined trajectory. These files are auto-stitched; then, high-precision point cloud files of propeller simulator are prepared. Post-processing is a necessary step to obtain the actual 3D model of the propeller" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000868_10402004.2015.1021944-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000868_10402004.2015.1021944-Figure3-1.png", "caption": "Fig. 3\u2014Schematics of the vertical bearing test rig employed in the present work.", "texts": [ " The roughness samples of steel roller, steel washer, and ceramic washer, scanned from real specimens and used as input data for the model, are presented in Fig. 2, including the corresponding values of root mean square roughness Rq and skewness Rsk for each surface pattern. It can be seen that the ceramic washer is much smoother than the steel one and has a much more negative skewness (i.e., deep valleys prevail over high summits). The experiments were conducted on a vertical bearing tester, schematically shown in Fig. 3, with a thrust SKF bearing 81108 TN (60 \u00a3 40 \u00a3 13 mm) inserted as a test element. The number of rolling elements in the thrust bearing was reduced to just three cylindrical rollers (6 \u00a3 6 mm) in order to obtain the following test conditions: (1) a precise and equally distributed load on the three rolling elements; (2) the maximum number of loading cycles affecting the rolling element rather than the bearing raceway; and (3) a maximum contact pressure of about 2 GPa per rolling element for the hybrid contact and 1" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002490_mnl.2018.5320-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002490_mnl.2018.5320-Figure1-1.png", "caption": "Fig. 1. (Top) Photograph and (bottom) mechanical drawing of MLA.", "texts": [ " The intense heat from the Sun requires the spacecraft to point its sunshade toward the Sun at all times; during noon\u2013midnight orbits, this requirement constrains the payload deck to point within \u223c10\u25e6 about the ecliptic south pole, with MLA ranging at a slant angle as high as 70\u25e6. The MLA measures the topography of Mercury via laser pulse time-of-flight and spacecraft orbit position data. The primary science measurement objectives for MLA are to provide a high-precision topographic map of the northern polar regions, to measure the long-wavelength topographic features of the mid-to-low latitude regions, and to detect and quantify the planet\u2019s forced librations. Fig. 1 shows a photograph and a mechanical drawing of MLA. Fig. 2 shows U.S. Government work not protected by U.S. copyright. the MESSENGER payload instruments and the location of MLA on the spacecraft. MLA operates under a harsh and highly dynamic thermal environment, due to the large variation in heat flux from the Mercury surface from daytime to nighttime and from deep space background. The transmitter and receiver optics undergo rapid and uneven swings in temperature during science measurement (tens of degrees per hour at the laser-beam expander and the receiver telescope)", " The calibration results are described here. The MLA coordinates, with respect to the spacecraft coordinate system, are obtained from a combination of the MLA measurements and spacecraft survey results after payload integration. The definitions of the MESSENGER spacecraft coordinate system are labeled in Fig. 2. The XY plane is the same as that defined by the launch vehicle separation plane, and the origin is at the center of the adapter ring. MLA orientation in the spacecraft coordinate system is shown in Fig. 1. All the MLA physical dimensions and angular directions can be referenced to the alignment reference cube attached to the side of the main housing, as shown in Fig. 1. The coordinates of the MLA alignment reference cube in the MESSENGER spacecraft coordinate system have been measured to be [\u221215.2, 63.5,\u221218.7] mm. The estimated spacecraft center of mass was at [0, 8,\u2212827] mm, with an uncertainty of [\u00b110,\u00b110,\u00b120] mm at launch. The center of mass during the mission is a function of propellant usage and distribution within the fuel tanks. The MLA range measurement is referenced to the XY plane that passes through the center of the reference cube. The MLA laser pointing angle was measured by focusing the beam with an off-axis parabola (OAP) to a reticle and measuring the angular offset between the reticle and the OAP optical axis" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003535_j.mechmachtheory.2021.104436-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003535_j.mechmachtheory.2021.104436-Figure3-1.png", "caption": "Fig. 3. Ankle motion fitting models.", "texts": [ " In Section 5, a module combination kinematic analysis method for GSPM is illustrated. Based on these 2 methods above, a class of 3-, 4- and 5-DOF GSPMs are synthesized and their kinematic characteristics are analyzed. Then 6 GSPMs matching the ankle motion fitting models are selected and modeled. Section 6 concludes the study as a whole. In order to improve the reasonableness of basic model for ankle rehabilitation robot design, 6 ankle motion fitting models are proposed based on the human ankle bone structure, which are U1R, U2R, U1U1, U1U2, U1S and U2S in Fig. 3. In these models, the tibiotalar joint is equivalent to universal (U) joint, which includes 2 forms: U1 and U2. The former mainly takes the tilt fluctuation of tibiotalar joint axis into account. The latter focuses on the internal/external rotation between the knee and tibiotalar joint. The subtalar joint can be equivalent to revolute (R), 2 universal (U1 / U2) and spherical (S) joint, respectively. Their abilities to match the subtalar joint increase sequentially, so that models with different matching abilities can be selected according to the requirements of different rehabilitation levels. All models composing of 2 equivalent tibiotalar and 4 equivalent subtalar joints can be used as candidates. For the limited length of the paper, only 6 most representative ankle motion fitting models are given in Fig. 3. Due to the limitation of the talus size, the distance between the tibiotalar and subtalar joint centers is relatively short. If the serial mechanism is directly used to be the rehabilitation robot body, the motor with sufficient torque cannot be arranged in such a small space. Therefore, an idea is proposed to use parallel mechanism to fit the motion of serial model. Since the human ankle is generally considered to be a generalized spherical joint in medical research, these parallel mechanisms are defined as \u2019generalized spherical parallel mechanisms (GSPM)\u2019, which should have the following basic properties: 1) The GSPM should have 2 generalized motion centers (\u2019fixed spherical center\u2019 and \u2019moving spherical center\u2019), which coincide with motion centers of the tibiotalar and subtalar joints, respectively", " In the PES-groups 2-UR [RRR], UR [RRR]&UR [RR] and UR [RRR]&URR, they can be expressed as \u23a7 \u23aa \u23aa \u23aa \u23aa \u23aa\u23a8 \u23aa \u23aa \u23aa \u23aa \u23aa\u23a9 m1 = \u2212 lcos\u03b81sin\u03b82 \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\u0305\u0305\u0305\u0305\u0305\u0305 1 \u2212 sin2\u03b81sin2\u03b82 \u221a m2 = \u2212 lsin\u03b81cos\u03b82 \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\u0305\u0305\u0305\u0305\u0305\u0305 1 \u2212 sin2\u03b81sin2\u03b82 \u221a m3 = lcos\u03b81cos\u03b82 \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\u0305\u0305\u0305\u0305\u0305\u0305 1 \u2212 sin2\u03b81sin2\u03b82 \u221a (12) In the PES-groups UR [RRR]&UP [RRR], UR [RRR]&UP [RR] and UR [RRR]&UPR, these parameters can be denoted as \u23a7 \u23aa \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23aa \u23a9 m1 = \u2212 lcos\u03b81sin\u03b82 \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\u0305\u0305\u0305\u0305\u0305\u0305\u0305 1 \u2212 sin2\u03b81cos2\u03b82 \u221a m2 = \u2212 lsin\u03b81sin\u03b82 \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\u0305\u0305\u0305\u0305\u0305\u0305\u0305 1 \u2212 sin2\u03b81cos2\u03b82 \u221a m3 = lcos\u03b81cos\u03b82 \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\u0305\u0305\u0305\u0305\u0305\u0305\u0305 1 \u2212 sin2\u03b81cos2\u03b82 \u221a (13) Eq. (12) shows the relationship between PSI parameters and input parameters (\u03b81/\u03b82) in groups UR [RRR]&UR [RR], UR [RRR]& URR and 2-UR [RRR]. Eq. (13) can represent the relationship between PSI parameters and input parameters (\u03b81/\u03b82) in groups UR [RRR]&UP [RRR], UR [RRR]&UP [RR] and UR [RRR]&UPR. Based on the equivalent tibiotalar joints (U1 and U2) shown in Fig. 3, 2 methods are proposed to describe the position of O2, which are respectively expressed as (m1, m2, m3, 0) = Rot(x, \u03b11) Rot(y, \u03b21) (0 , 0 , l, 0)T (14) J. Zhang et al. Mechanism and Machine Theory 166 (2021) 104436 (m1, m2, m3, 0) = Rot(z, \u03b11) Rot(y, \u03b21) (0 , 0 , l, 0)T (15) where \u03b11 and \u03b21 are position parameters, and l is constant. The x and y axes of tibia coordinate system are perpendicular to the coronal and sagittal planes, respectively. The z axis is vertical downward. The expansions of rotation transformation matrices Rot (x, \u03b11), Rot (y, \u03b21) and Rot (z, \u03b31) can be respectively written as Rot(x, \u03b11) = \u23a1 \u23a2 \u23a2 \u23a3 1 0 0 0 0 cos\u03b11 \u2212 sin\u03b11 0 0 sin\u03b11 cos\u03b11 0 0 0 0 1 \u23a4 \u23a5 \u23a5 \u23a6 , Rot(y, \u03b21) = \u23a1 \u23a2 \u23a2 \u23a3 cos\u03b21 0 sin\u03b21 0 0 1 0 0 \u2212 sin\u03b21 0 cos\u03b21 0 0 0 0 1 \u23a4 \u23a5 \u23a5 \u23a6 and Rot(z, \u03b31) = \u23a1 \u23a2 \u23a2 \u23a3 cos\u03b31 \u2212 sin\u03b31 0 0 sin\u03b31 cos\u03b31 0 0 0 0 1 0 0 0 0 1 \u23a4 \u23a5 \u23a5 \u23a6 The translation transformation matrix can be expressed as Tran (m1, m2, m3), which can be written as Tran(m1, m2, m3) = \u23a1 \u23a2 \u23a2 \u23a3 1 0 0 m1 0 1 0 m2 0 0 1 m3 0 0 0 1 \u23a4 \u23a5 \u23a5 \u23a6 After calculation, Eq", " As listed in Table 15, there are 32 3-DOF basic GSPMs. Among them, 4 species have 2 repeating limbs and 28 species have no repeating limbs. Based on the equivalent replacement method, there are totally 804 3-DOF GSPMs (28 \u00d7 33+4 \u00d7 3 \u00d7 3=804). Among them, there are 16 compact GSPMs composed of the PES-groups and OES-limbs, which are shown in Table 16. Based on the third kinematic analysis method, the kinematics of the 3-DOF GSPMs in Table 16 are analyzed. The GSPMs meeting the motion requirements of the models U1R and U2R (Fig. 3(a) and (b)) are selected, which are respectively mechanisms UR [RRR]& URR&SR [RR] and UR [RRR]&UPR&SR [RR] shown in Fig. 20. Their kinematic performances are listed in Table 17. The mechanism UR [RRR]&URR&SR [RR] is composed of PES-group UR [RRR]&URR and OES-limb SR [RR], and its transformation matrix TU1R is shown in Eq. (20). The mechanism UR [RRR]&UPR&SR [RR] is composed of PES-group UR [RRR]&UPR and OES-limb SR [RR], and its transformation matrix TU2R is shown in Eq. (24). The third kinematic analysis method is used to analyze the kinematic performances of 2 GSPMs" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000480_0022-2569(66)90017-6-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000480_0022-2569(66)90017-6-Figure6-1.png", "caption": "FIG. 6. The surfaces of inflection points for spatial motion showing the intersecting plane and the inflection circle applicable to planar motion and the special point F.", "texts": [ " The former assumption would unnecessarily eliminate terms such as Z(zl\u00a2Oo-roW1) which written in the form Z{o~o(T1 - Zo)- To(O91 - too)} becomes Z(aoOgo- ZoCto) an expression incorporating properties of acceleration of the axodes at the instant of the motion. When the second order small quantities in (3.5) are neglected the equations (3.5), (3.6) and (3.7) are written (Y2 +Z2)tolAd/l + XYwlAflo-Z(zlAflo+to:Abo)=O (3.11) Y2ogoogtAflo + Y(ziOgo-ZotOl)-Zzoo91A$t +Zoo91Abo+zozlAflo=O (3.12) YZogoogiAflo+ XzototAflo+ YzoogtA$t +Z(rtOJo-Zoogt)=O. (3.13) These second order surfaces are respectively a hyperboloid of one sheet, a parabolic cylinder, and a hyperbolic paraboloidt (Fig. 6). t The hyperbolic paraboloid is identified when reduced to the simplest form, YI2-Z12~: -(2~0/to0)X~, to which it is susceptible by the transformation of coordinates given by, 7l\" Where 0-----~, Xl 1 0 0 YI+M= 0 Z I + N 0 A A I//t (l\" 10\"M -- ~'0('O 1 ) t.O0tOl ABo2 1 M = x/(2)eaototAflo{(,ltm-r0tot)+r0tolAel }, and 1 N = X/(2)tootol A.8o{(rlt\u00b0\u00b0--'r\u00b0t'\u00b0l) -- r\u00b0t\u00b0l A ~1 }\" cos 0 sin 0 sin 0 cos 0 X--A Y Z Inflection points are located on the intersection of any two of these three surfaces. With the exception of two straight lines of intersection the lines along which pairs of surfaces intersect are twisted curves" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003023_978-3-030-55502-3-Figure14-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003023_978-3-030-55502-3-Figure14-1.png", "caption": "Fig. 14 Electrochemical QD-based paper devices. a Schematic diagram of an electrochemical LFA that integrates a screen-printed electrode underneath the test zone of the strip for QD detection. Reprinted from Lin et\u00a0 al. [134], copyright 2008, with permission from Elsevier. b Photographs of the front and back of an electrochemical paper device with the electrodes deposited directly onto the paper substrate. Microfluidic pattern is wax-printed on the front face of the paper and the electrodes are deposited by sputtering on the back side of the paper. Reprinted with permission from Kokkinos et\u00a0al. [135], copyright 2018, with permission from the American Chemical Society", "texts": [ " 156 Reprinted from the journal 1 3 Although optical sensing has been by far the dominant detection method applied in the field of paper microfluidics, examples of electrochemical QD-based paper devices for clinical diagnostics can also be found in literature [134\u2013136]. Electrochemical sensing offers an alternative detection system for quantitative analysis in paper devices due to its simplicity, portability and sensitivity. Small-sized electrodes can be easily integrated into the paper strip (Fig.\u00a014a) or fabricated directly onto the 157Reprinted from the journal 1 3 paper substrate (Fig.\u00a0 14b). These devices, combined with commercially available miniaturized \u201cpotentiostats\u201d appear to be a very interesting alternative to fluorescence-based paper devices. Barcode assays for POC applications are in high demand by modern healthcare systems [137]. Barcode assays are capable of simultaneously detecting multiple targets from patient samples, thereby increasing the speed of the analysis and improving the precision and accuracy of the diagnosis. As already mentioned, QDs can be used as barcoded probes by embedding them into polymeric particles [97]" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002819_ddf.398.34-Figure10-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002819_ddf.398.34-Figure10-1.png", "caption": "Fig. 10: The (S-N) for socket material. Fig. 11: Von-Mises stress for type Fig. 12: Safety factor for type K1(3R20). K1(3R20).", "texts": [], "surrounding_texts": [ "The (S-N) curve was drawn by the data obtained from the fatigue tests that were conducted on three specimens for six stress stages, and the resulted data are presented in fig. (10).These results were obtained from the fatigue testing, in which the no. of cycles is recorded on the \"fatigue testing apparatus (Table 4). The (S-N) curve that was obtained from this test presents a clue to when the fatigue failure will occur under the fatigue life conditions. From this curve, the stress endurance limit was found 34.5 MPafor the composite material that was used. Figures (11,and 12)represent the Vonmises stress and factor of safety for prosthetic knee For type K1(3R20)" ] }, { "image_filename": "designv10_9_0001165_tim.2013.2241534-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001165_tim.2013.2241534-Figure3-1.png", "caption": "Fig. 3. Geometrical drawing to show the relation \u0394D and \u03b8 for elbow flexion.", "texts": [ " 2 are given as the averaged value over 20 times. The optical loss was obtained using a light-emitting diode (LED) at the wavelength of 1.31 \u03bcm, which was coupled into a transmission fiber and an optical power meter (OP710, Opto Test Co.). It is confirmed from Fig. 2 that a standard deviation of 0.55% is obtained, which corresponds to 0.11 mm for the full scale of 2.1 dB for \u0394D = 20 mm. This result shows that the accuracy of the stretching module is sufficient to capture motions at a body joint or at trunk. TO CAPTURE THE FLEXION OF ELBOW Fig. 3 shows a schematic drawing for converting the angle of the elbow flexion to \u0394D. The thin sensor module was sewed under the upper arm portion of a sportswear so that the wear could be stretched when the elbow flexion is given. As shown in Fig. 3, \u0394D is approximated to the circular arc, which is given as \u0394D = ( h 2 ) \u00b7 ( \u03b8\u03c0 360 ) (1) where h and \u03b8 are the thickness of the arm and the angle of the bending elbow, respectively. The simple relation between \u03b8 and \u0394D given by (1) is plotted in Fig. 4 to ensure that the full range of elbow motion (typically \u03b8 = 145\u25e6) for healthy people could be covered with the maximum stretching \u0394D = 20 mm. The accuracy of the elbow flexion angle could be estimated to be 1.26\u25e6, which corresponds to the standard deviation of 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001710_j.cja.2015.03.003-Figure8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001710_j.cja.2015.03.003-Figure8-1.png", "caption": "Fig. 8 Cubic vertices within the workspace.", "texts": [ "003 grid step and its absolute position error meets the accuracy requirements, then it is selected as the optimum grid step of the given region. According to industrial robots performance criteria and related test methods up to China\u2019s national standard and professional standard (GB/T 12642\u2013\u20132001), 8 suitable positions must be determined within the cube of the working region to examine the pose accuracy of an industrial robot. As shown in Fig. 5, Ci\u00f0i \u00bc 1; 2; . . . ; 8\u00de are selected as the cubic vertices (see Fig. 8). There are 4 planes to be selected for a pose experiment based on the standard requirement. In this case, the planes are C1\u2013C2\u2013C7\u2013C8, C2\u2013C3\u2013C8\u2013C5, C3\u2013C4\u2013C5\u2013C6, and C4\u2013C1\u2013C6\u2013C7. 5 points (P1, P2, P3, P4, and P5) that must be measured are on the diagonals of the measuring planes in the standard requirement. P1 is the center of the cube. The positions of other point P2 to P5 are shown in Fig. 9. To describe the errors within the entire grid space as much as possible, the points on the other two diagonals are added" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001190_0954406215621098-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001190_0954406215621098-Figure1-1.png", "caption": "Figure 1. TRB loadings and displacements: (a) bearing external loads and corresponding displacements and (b) misaligned TRB geometry.", "texts": [ " The modeling and analysis assumptions are as follows: (1) all friction and cage forces are negligible; (2) bearing races remain circular under loading; (3) elastic deformation occurs only at the contact locations between the rollers and races; (4) smooth dry contact exists between the rollers and raceways, and the effect of the lubrication film is negligible. TRB model subjected to angular misalignment This study extends the five DOF roller bearing model outlined by de Mul et al.12 In de Mul\u2019s model, the inner ring is assumed to rotate freely around its axis, and thus the displacement vector with only five elements is considered as { }T\u00bc { x, y, z, y, z}. Figure 1(a) shows the bearing with external loads and displacements. With the external load vector {F}T\u00bc {Fx, Fy, Fz,My,Mz} given beforehand, the corresponding global displacement vector { } can be at Middle East Technical Univ on May 11, 2016pic.sagepub.comDownloaded from estimated using iterative techniques. Tong and Hong14 have detailed the calculation scheme for this model. To analyze the effect of angular misalignment on TRB dynamic characteristics, the inner ring is assumed to be permanently misaligned by an angle z (Figure 1(b)). Angular misalignment can exist in an arbitrary axis normal to the bearing axis. Summation of two orthogonal misalignment angles in the vertical and horizontal axes can represent the misalignment angle. For simplicity, the bearing model presented here considers only a single misalignment angle in the horizontal axis, but it can easily be extended to consider other misalignment angles in an arbitrary direction. Bearing angular misalignment caused by an out-ofline shaft, bearing geometric inaccuracy (cocked or tilted bearing outer race) often occurs independent of loading" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001645_tie.2017.2786205-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001645_tie.2017.2786205-Figure4-1.png", "caption": "Fig. 4. Schematic of operation principle of the proposed unaligned PP-HEFSLM with only PM excitation. (a) d-axis position. (b) q-axis position. (c) \u2013d-axis position. (d) \u2013q-axis position.", "texts": [ " 2, and definitions of corresponding variables to be optimized are listed in Table I, where \ud835\udc58\ud835\udc60 , \ud835\udc58\ud835\udc61 , \ud835\udc58\ud835\udc4f , \ud835\udc58\ud835\udc4e denote split ratio, top secondary width ratio, bottom secondary width ratio, armature teeth width ratio, respectively. Fig. 3 shows flux-regulation principle of the proposed PPHEFSLMs with unaligned structure at armature coil d-axis position. Clearly, PM flux and excitation flux are in parallel connection and resultant armature coil flux can be adjusted through the variation of magnitude or polarity of excitation current, which is the fundamental principle of hybrid-excited machine. The operation principle of the proposed PP-HEFSLMs is illustrated in Fig. 4. Similar to conventional flux-switching machines, the flux of each armature coil is periodically changed with the secondary position. When the secondary is at d-axis TABLE I KEY PARAMETERS FOR OPTIMIZATION OF THE PP-HEFSLMS Symbol Definition Initial value \ud835\udc58\ud835\udc60 (\u210e\ud835\udc5d2 + \ud835\udeff2 + \u210e\ud835\udc60 + \ud835\udeff1)/\u210e 0.50 \ud835\udc58\ud835\udc61 \ud835\udc64\ud835\udc60\ud835\udc61/\ud835\udf0f\ud835\udc5d 0.50 \ud835\udc58\ud835\udc4f \ud835\udc64\ud835\udc60\ud835\udc4f/\ud835\udf0f\ud835\udc5d 0.50 \ud835\udc58\ud835\udc4e \ud835\udc64\ud835\udc61/\ud835\udf0f\ud835\udc60 0.38 0278-0046 (c) 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001468_j.mechmachtheory.2018.09.005-Figure13-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001468_j.mechmachtheory.2018.09.005-Figure13-1.png", "caption": "Fig. 13. (a)\u2013(c) Motion sequences of a model of motion type AII-BII-DI according to Eq. (A.13b) .", "texts": [], "surrounding_texts": [ "there could be many solutions, which is difficult to be solved directly. So here we introduce the extra conditions in thick panel origami, and the obtained assembly will be transferred back to generating new thick-panel origami structures. One hand, for the flat-developability, \u03b112 + \u03b123 + \u03b134 = \u03c0 , considering\n\u03b1Br 12 = \u2212\u03b1Br 61 = \u03b1K = \u2212\u03b112 , \u03b1Br 23 = \u2212\u03b1Br 56 = \u03b2K = \u03b123 \u2212 \u03c0, (17) \u03b1Br 34 = \u2212\u03b1Br 45 = \u03b3 K = \u03b134 .\nwe have\n\u03b1K = \u03b2K + \u03b3 K . (18)\nOn the other hand, for the compact flat-foldability, we have t 12 + t 23 \u2212 t \u2032 23 = t 34 according to Eq. (3) , i.e., for a planesymmetric linkage\nu K + v K = w K . (19)\nSubstitute Eqs. (18) and (19) into Eqs. (11b) , (12b) and (15) , we get ( u A s \u03b3 A t \u03b8A 2\n2\nt \u03b8A 3\n2\n\u2212 w A s \u03b1A )( c \u03b3 A t \u03b8A 2\n2\nt \u03b8A 3\n2\n\u2212 c \u03b1A ) = 0 , (20a)\n( u B s \u03b3 B t \u03b8B 2\n2\nt \u03b8B 3\n2\n\u2212 w B s \u03b1B )( c \u03b3 B t \u03b8B 2\n2\nt \u03b8B 3\n2\n\u2212 c \u03b1B ) = 0 , (20b)\n( u D s \u03b3 D t \u03b8D 2\n2\nt \u03b8D 3\n2\n\u2212 w D s \u03b1D )( c \u03b3 D t \u03b8D 2\n2\nt \u03b8D 3\n2\n\u2212 c \u03b1D ) = 0 . (20c)\nThen the following solutions are obtained. In linkage A\nAI : t \u03b8A 2\n2\nt \u03b8A 3\n2\n=\nc \u03b1A c \u03b3 A , (21a)\nAII : t \u03b8A 2\n2\nt \u03b8A 3\n2\n=\nw A s \u03b1A\nu A s \u03b3 A . (21b)\nIn linkage B\nBI : t \u03b8B 2\n2\nt \u03b8B 3\n2\n=\nc \u03b1B c \u03b3 B , (22a)\nBII : t \u03b8B 2\n2\nt \u03b8B 3\n2\n=\nw B s \u03b1B\nu B s \u03b3 B . (22b)", "In linkage D\nDI : t \u03b8D 2\n2\nt \u03b8D 3\n2\n=\nc \u03b1D c \u03b3 D , (23a)\nDII : t \u03b8D 2\n2\nt \u03b8D 3\n2\n=\nw D s \u03b1D\nu D s \u03b3 D . (23b)\nEach linkage is a plane-symmetric Bricard linkage with six active joints, so t \u03b8K\n2 2 t \u03b8K 3 2 are not always zero or infinity.\nAs each linkage has two relationships between \u03b8K 2 and \u03b8K 3 , the assembly of the three linkages has eight types of the combination of the relationships, which are named motion types , i.e., AI-BI-DI, AI-BI-DII, AI-BII-DI, AII-BI-DI, AI-BII-DII, AIIBI-DII, AII-BII-DI, AII-BII-DII. Compatibility conditions on the red link should be analyzed under the motion types.\nFor motion type AI-BI-DI and considering Eqs. (16a) and ( 16b ), we have\nt \u03b8B 2\n2\nt \u03b8D 3\n2\n= 1 , t \u03b8B 3\n2\n=\nc \u03b1B c \u03b3 B t \u03b8D 3 2 ,\nt \u03b8A 2\n2\nt \u03b8D 3\n2\n=\nc \u03b1A c \u03b1D c \u03b3 A c \u03b3 D , t \u03b8A 3 2 = c \u03b3 D c \u03b1D t \u03b8D 3 2 .\n(24)\nBy substituting Eq. (24) into Eqs. (11a) and ( 12a ), we get\nt \u03b8A 4\n2\nt \u03b8D 3\n2\n=\nc \u03b1D\nc \u03b3 D c \u03b3 A , t\n\u03b8B 1\n2\nt \u03b8D 3\n2\n= \u2212 1\nc \u03b1B . (25)\nWith \u03b8A 4 + \u03b8B 1 = 2 \u03c0 in Eq. (16c) , we have\nc \u03b1D c \u03b1B = c \u03b3 D c \u03b3 A . (26)\nTwo solutions for the compatibility condition on the red link under motion type AI-BI-DI are obtained\n\u03b3 D = \u03b1D , \u03b3 A = \u03b1B , \u03b1K = \u03b2K + \u03b3 K ,\nu B + v D = w A , u K + v K = w K , (27a)\nand\n\u03b1D = \u2212\u03b3 A , \u03b3 D = \u2212 \u03b1B , \u03b1K = \u03b2K + \u03b3 K ,\nu B + v D = w A , u K + v K = w K . (27b)", "Similarly, compatibility conditions on the red link for the eight motion types are obtained and expressed in the Appendix A . With the comparison among the conditions of eight motion types, there are only five distinct motion types, as AI-BI-DI, AI-BI-DII, AI-BII-DII, AII-BI-DII, AII-BII-DI.\nTo ensure the mobility of the assembly in Fig. 4 , each of the links shared by three linkages should satisfy the compatibility condition under a specific motion type. When all links have same compatibility conditions to Eq. (27a) or ( 27b ), we can get the compatibility conditions on the other shared links as\nADE : \u03b1A = \u03b3 A , \u03b3 E = \u03b1D , u D + v A = w E ,\nDBA : \u03b1D = \u03b3 D , \u03b3 A = \u03b1B , u B + v D = w A ,\nBCD : \u03b1B = \u03b3 B , \u03b3 D = \u03b1C , u C + v B = w D ,\nF DE : \u03b1F = \u03b3 F , \u03b3 E = \u03b1D , u D + v F = w E ,\nDGF : \u03b1D = \u03b3 D , \u03b3 F = \u03b1G , u G + v D = w F ,\nGCD : \u03b1G = \u03b3 G , \u03b3 D = \u03b1C , u C + v G = w D ,\n(28a)\nand\nADE : \u03b1A = \u2212\u03b3 E , \u03b3 A = \u2212\u03b1D , u D + v A = w E ,\nDBA : \u03b1D = \u2212\u03b3 A , \u03b3 D = \u2212\u03b1B , u B + v D = w A ,\nBCD : \u03b1B = \u2212\u03b3 D , \u03b3 B = \u2212\u03b1C , u C + v B = w D ,\nF DE : \u03b1F = \u2212\u03b3 E , \u03b3 F = \u2212\u03b1D , u D + v F = w E ,\nDGF : \u03b1D = \u2212\u03b3 F , \u03b3 D = \u2212\u03b1G , u G + v D = w F ,\nGCD : \u03b1G = \u2212\u03b3 D , \u03b3 G = \u2212\u03b1C , u C + v G = w D ,\n(28b)\nwhere all the linkages satisfy Eqs. (18) and (19) . Simplifying Eqs. (28a) and ( 28b ), we obtain two cases, case I and case II assemblies, as\n\u03b1A = \u03b3 A = \u03b1B = \u03b3 B = \u03b5 j\u22121 , \u03b1C = \u03b3 C = \u03b1D = \u03b3 D = \u03b1E = \u03b3 E = \u03b5 j , \u03b1F = \u03b3 F = \u03b1G = \u03b3 G = \u03b5 j+1 , \u03b2K = 0 ,\nu K + v K = w K , v A = v F = w E \u2212 u D ,\nv B = v G = w D \u2212 u C , v D = w A \u2212 u B = w F \u2212 u G ,\n(29a)\nand\n\u03b1A = \u2212\u03b3 E = \u03b1F = \u03b4 j\u22122 , \u03b2A = \u03b2F = \u03b4 j\u22122 + \u03b4 j\u22121 , \u03b3 A = \u2212\u03b1D = \u03b3 F = \u2212\u03b4 j\u22121 , \u03b2D = \u03b4 j\u22121 + \u03b4 j , \u03b1B = \u2212\u03b3 D = \u03b1G = \u03b4 j , \u03b2B = \u03b2G = \u03b4 j + \u03b4 j+1 , \u03b3 B = \u2212\u03b1C = \u03b3 G = \u2212\u03b4 j+1 , \u03b2C = \u03b4 j+1 + \u03b4 j+2 ,\nu K + v K = w K , v A = v F = w E \u2212 u D ,\nv B = v G = w D \u2212 u C , v D = w A \u2212 u B = w F \u2212 u G .\n(29b)\nAs \u025b j \u2019s in Eq. (29a) can be different for case I assembly, all plane-symmetric Bricard linkages on the same guideline X j , such as linkage C, D, E are identical, but the linkages on different X-guidelines can be with different twists, as shown in Fig. 5 (a). Similarly, for case II assembly, in Fig. 5 (b), the linkages on the same guideline Y j are identical, while those on different Y-guidelines are of different twist \u03b4j . The prototypes of both cases are shown in Fig. 6 . However, those two cases cannot be combined together to have both X-guideline and Y-guideline at the same time, which will only lead to the assembly with all Bricard linkages identical rather than all of them are different.\n4. Variation of the diamond thick-panel origami patterns\nCases I and II extend the construct condition of mobile assembly of plane-symmetric Bricard linkages. Considering the kinematic equivalence between the mobile assembly and thick-panel origami, they should subsequently enhance the geometric variation in the diamond thick-panel origami.\nFor case I, X-guideline cannot apply to diamond thick-panel origami, as the twists of linkage lead to negative sector angles of origami from Eq. (17) . Meanwhile, applying X-guideline would destroy the plane-symmetric property of diamond thickpanel origami. For case II, twists of Bricard linkages on different Y-guidelines can be different ( Fig. 5 (b)). So correspondingly, in the diamond thick-panel pattern, sector angles can be different along different rows of vertices, see Fig. 5 (c), which is" ] }, { "image_filename": "designv10_9_0000001_marc.201000590-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000001_marc.201000590-Figure1-1.png", "caption": "Figure 1. a) Uniaxial true stress-strain (st vs. l) curves of a monodomain sample parallel (*) and perpendicular ( ) to the director, and of a polydomain sample (*) of the corresponding SmC MCLCE at 25 8C. The arrows indicate regions of changing slope; refer to text. The solid curves are the fits to the data points. b) Structure of a SmC MCLCE. The distances of the layers (d), length (l) between repeating units, and angles of monomers (90-w) and layers (f) with respect to the stretching direction z are shown.", "texts": [ " Chemical structures of the compounds used for the synthesis of the SmC MCLCE. well as between the field and the layers, was always observed. A sample of a polydomain of SmC MCLCE was uniaxially stretched and compared with the deformation of its corresponding monodomain \u2013 parallel and perpendicular deformations with respect to the director. The corresponding monodomain had a conical distribution of the smectic layers. A perfect monodomain (mesogens and layers present at the same time) can only be achieved by further shear experiments.[1] Figure 1a shows the uniaxial stress\u2013 strain experiments for all three deformations on a polydomain and its corresponding monodomain. The results clearly show that the deformation of a polydomain is softer than the deformation parallel to the director of a monodomain, but a little bit harder than the perpendicular deformation to the director of the monodomain. In order to reinforce in more detail this result, all three samples were evaluated following the expression for the description of the increase of true stress as function of the www", " The slope value (dst/dl) in this curve and the initial pre-stress component (Epre) of the Young\u2019s modulus (E) are lower than the uniaxial stress\u2013 strain parallel to the director of the monodomain sample, and resembles the stress\u2013strain behaviour of the uniaxial stress\u2013strain perpendicular to the director of the monodomain sample but with a rising of the stress at lower strain values. Thus, the three regions seen during the deformation of the polydomain sample can be explained by the breaking of the random distribution of the domains, the reorientation of those domains, and the stretching of the polymer backbones (Figure 1a). Several previous communications have reported the soft plateau region[5,12,13] and necking[10,11] during PM transformations, but have only used the mechanical response from the nominal stress (sn\u00bc F/A0) in nonequilibrium conditions. The present results use true stress (st\u00bc sn l) versus strain (l), and are thus closer to reality and to the existent theories. Polydomain\u2013Monodomain Structure Transformation As observed from the uniaxial stress\u2013 strain experiments, the mechanical properties of this elastomer strongly depend on the direction of the applied force and the initial orientational state of the mesogens", "5 0 20 40 60 80 100 120 -40 -20 0 20 40 60 80 \u03c6 (d eg ) \u03bb I II III SAXS 90 - \u03d5 (d eg ) WAXS b) 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0 Areas Intensities ISA X S /IW A X S ( \u00d70.17) A SA X S/A W A X S \u03bb II III S I Figure 3. a) Peak maxima in the WAXS (90-w) and SAXS (f) azimuthal intensity distributions as a function of uniaxial strain, l. b) Order parameter S, area ratio and intensity ratio between the SAXS and WAXS peak maxima as function of uniaxial strain, l. In the strain regime of 1.0 l 1.5 (Figure 1a), the polydomain sample assumes a weakly ordered conical mesogen distribution which resembles a SmCA phase (see Supporting Information, Figure SI-4), where the layer normal is around f\u00bc 908 (two broad azimuthal maxima) and the mesogens show an average strain dependent angle of 90-w\u00bc 60\u2013208 (four broad azimuthal maxima). This SmCA distribution of layers has the layer normal perpendicular to the applied mechanical field and looks like the slow motion deformation process already observed during the deformation of main-chain liquid-crystalline polymers.[40] The first steps during the orientational process are actually identified by the strong increase of the order parameter from S\u00bc 0.00 at l\u00bc 1.0 to S\u00bc 0.46 at l\u00bc 1.5 (Figure 3b), where S reflects the product of the orientational and director order parameter. In the strain regime of 1.6 l 2.4, where the stress\u2013 strain curve is almost linear (Figure 1a), the previous SmCA elastomer becomes SmC with an enhancement of the order of both mesogens and layers. A huge layer rotation of the layer normal occurs by 388 from f\u00bc 908 to 528 (four azimuthal maxima) \u2013 with a slope down of 58 of difference in the middle part \u2013 and the mesogens are distributed around an angle of 90-w\u00bc 08 (two azimuthal maxima). During this rotational process of the layers, the order parameter increases as function of the uniaxial strain from S\u00bc 0.47 to 0.66 gradually (Figure 3b), where this is an indication of ordering of the system. Finally, in the strain regime of 2.5 l 4.5 (Figure 1a), all mesogens align to the stretching direction (90-w\u00bc 08, with two azimuthal maxima) and the layers adopt the final conical distribution from f\u00bc 528 to 468 (four azimuthal www.MaterialsViews.com Macromol. Rapid Commu 2011 WILEY-VCH Verlag Gmb maxima), similar to the final optimisation of the packing of the mesogenic monomer units under strain in the stretching process for a conical layer distribution system under uniaxial stress parallel to the director.[1] The slope at break (dst/dlmax \u00bc 5.2 MPa), however, does not recover the value observed for the deformation parallel to the director (dst/dlmax \u00bc 30 MPa), but it is one order of magnitude higher than for the deformation perpendicular to the director (dst/dlmax \u00bc 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001328_j.renene.2014.03.036-Figure11-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001328_j.renene.2014.03.036-Figure11-1.png", "caption": "Fig. 11. Hydraulic suspension model.", "texts": [], "surrounding_texts": [ "In order to minimize the influence of the specific design of the GRC gearbox on the generality of the overall drive train behavior, it was chosen not to include the gear meshing stiffness in the models. In theory the forces and moments which are introduced in the gearbox should be transferred to the gearbox bushings through a path comprising of the planet carrier, planet carrier bearings and the gearbox housing, as shown in Fig. 12. Unless there is play in the bearings or the planet carrier and/or housing stiffness is insufficient the gear meshing stiffness does not play a role in this mechanism. In addition by excluding the gear meshing stiffnesses it is possible to assure that the housing is an important part of the transfer path. Since the gear meshing stiffness is needed to counteract the torque applied at the rotor, an equivalent total gear meshing stiffness is taken into account in the torsional DOF and superimposed on the stiffness values at both planet carrier bearings. More information on the assumptions that were made can be found on page 5." ] }, { "image_filename": "designv10_9_0000476_1.4007349-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000476_1.4007349-Figure3-1.png", "caption": "Fig. 3 Bearing hub models", "texts": [ " The ball-race contact force can be zero by reasonably setting the force-deflection parameters of the spring element. Three double-row four contact-point ball bearings are used in a 1.5 MW wind turbine to connect three blades with the hub. The frame of the pitch bearing is shown in Fig. 2. The main parameters of the pitch bearing are listed in Table 1. The outer diameter is 2677 mm. However, the minimum thickness of the outer ring is only 81 mm. The ratio of the thickness and outer diameter is up to 3%. The bearing supporting structure is the cast hub shown in Fig. 3. There are three holes required for the bearing installation, the left hole for the main shaft connection and access holes in the hub to allow for service. The outer diameter of the hub shell is 3450 mm. The shell thickness is 65 mm. The other bearing connection is the hollow blade root made of an anisotropic material. In the static analysis, extreme loads of the pitch bearing are taken into account. The corresponding load coordinate system and bearing circumference angle is defined in Fig. 4. Here z coincides with the bearing\u2019s center axis, x is perpendicular with y and parallel with the bearing plane, y is perpendicular to the x and z axes and parallel with the bearing plane" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002277_978-3-319-27131-6-Figure8.8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002277_978-3-319-27131-6-Figure8.8-1.png", "caption": "Fig. 8.8 Initiated and propagating surface cracks to flaking", "texts": [], "surrounding_texts": [ "The initiated subsurface microcracks are defined as the microcracks at about 150\u2013200 \u03bcm below the surface, as shown in Fig. 8.9. They result from the impurity of bearing steels in the production process. However, the bearing steel quality has been strongly improved in the last decades. The initiated microcracks are usually in the order of a few microns on the surface and in the subsurface of the bearings. They are considered as initial crack nuclei in the bearing material. The maximum shear stress of about one-third of the maximum Hertzian pressure occurs under the contact zone and causes the crack propagation toward the bearing surfaces, as shown in Fig. 8.10. The development of the initiated microcracks is further intensified by a large number of cyclic shock loads acting upon the contacting surfaces. As soon as the cracks reach near the surfaces, flaking (spalling) occurs on the surfaces of the rolling elements and raceways due to forced rupture (s. Fig. 8.11). 8.2 Failure Mechanisms in Rolling Bearings 179 The flaking-related failure occurred in the rolling element and raceway generates the formation of large and deep cavities by heavy loads or shock loads on the contacting surfaces. Additionally, the flaking induces intensive noises (NVH) and strongly reduces the bearing lifetime. The flaking (spalling) effect mostly leads to the fatal failure of the bearing in a few hundred km driving after loud noises take place in the electric or hybrid vehicles. 180 8 Bearing Friction and Failure Mechanisms" ] }, { "image_filename": "designv10_9_0002734_j.mechmachtheory.2020.104222-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002734_j.mechmachtheory.2020.104222-Figure1-1.png", "caption": "Fig. 1. Dynamics model of a valve train system with flexible camshaft and linkages.", "texts": [ " Section 3 describes the test rig of dynamic stress and engine housing vibration. In Section 4 , the natural frequency, mode shape, housing vibration, inlet pushrod stress and loss of valve lift are predicted through the proposed model. The predicted pushrod stress and housing vibration are compared with the measured results. The conclusions are summarised in Section 5 . 2. Dynamic model The valve train system, which consists of a camshaft, an inlet air valve train and an outlet air valve train, is illustrated in Fig. 1 . Inlet and outlet air cams are mounted on the camshaft to drive the inlet and outlet air valves, respectively. The camshaft is supported by two ball bearings at the end and driven by another gear shaft. The effect of gear meshing on the dynamics of the valve train system is excluded from this study. The structure of the inlet air valve train, which consists of a cam, a tappet, a pushrod, a rocker arm, a valve, a spring, and a valve seat, is the same as that of the outlet air valve train. As shown in Fig. 1 , an elastic dynamic model with 31 nodes and 94 DOFs is established using the finite element method. The gear and cam bodies are assumed to be rigid, and the contact flexibilities between the cams and tappets are represented by linear spring\u2013damper elements. The dynamic equations of the gear and cam rotor discs, the flexible camshaft and linkages with support bearings and the contact formula of the cam\u2013tappet are deduced. 2.1. Rotor disc The rotor configuration of the cam or gear disc is shown in Fig", " (1) The dynamic equation of the disc can be expressed in the following matrix form using the Lagrange equation: M d i q\u0308 d i + G d i \u02d9 q d i = F d i (2) where M d i and G d i are the mass and gyroscopic matrices, respectively, which are written as follows: M d i = diag ( m d m d m d J Dd J Dd J Pd ) (3) q s = [ x 1 y 1 z 1 \u03b8x 1 \u03b8y 1 \u03b8z1 x 2 y 2 z 2 \u03b8x 2 \u03b8y 2 \u03b8z2 ]T (8) The tappets, pushrods and valves are modelled as bar elements, whereas the rocker arms are divided into combined bar-beam elements, as shown in Fig. 4 . Similarly, motion equations of flexible linkages can be written as follows, and the detailed derivation is shown in our previous work [30] . M l i \u0308q l i + C l i \u0307 q l i + K l i q l i = F l i (9) where vector q i l ( i = 1, 2) is the DOF of the bar and beam elements in the inlet and outlet air valve trains. It can be written as follows: l [ ]T l [ ]T q 1 = u 55 , u 56 , u 57 , \u00b7 \u00b7 \u00b7 u 74 , q 2 = u 75 , u 76 , u 77 , \u00b7 \u00b7 \u00b7 u 94 (10) As shown in Fig. 1 , the camshaft is supported by two 7001AC ball bearings (#1 and #2), which can freely rotate around direction z . Bearings #1 and #2 are mounted on nodes 1 and 9 of the camshaft, respectively. The inlet and outlet rocker arms rotate around bearings #3 and #4, which are installed on nodes 16 and 27, respectively. The basic structure parameters of 7001AC bearing are shown in Table 1 . The working state of bearings has an effect on vibration intensity and uneven loading conditions of system [31] . Thus, the support stiffness of bearings should be considered in the dynamic analysis of valve trains", " q is the vector of the overall DOFs with 94 vector elements which can be expressed as follows: q = [ u 1 u 2 u 3 \u00b7 \u00b7 \u00b7 u 93 u 94 ] (22) 3. Experiment As shown in Fig. 7 , a test rig of the single-cylinder engine was built to measure the pushrod stress and housing vibration. To avoid the effects of the piston, crank shaft and connecting rod on the engine vibration, these components were disassembled from the engine. A servo motor was used to drive the camshaft by using a synchronous belt transmission. Four strain gauges were installed on element 11 ( Fig. 1 ) of inlet pushrod to constitute a full-bridge converter, and the installation position of these gauges is shown in Ref. [30] . The strain gauges were calibrated prior to measurement to avoid the influence of initial strain generated during the strain gauge installation. Engine vibration tests were conducted. The installation position of two acceleration sensors are presented in Fig. 7 . Sensor #1 is a tri-axis acceleration sensor used to acquire the engine housing acceleration near joint #3 ( Fig. 1 ). Sensor #2, which is also a tri-axis acceleration sensor, was used to obtain the three-directional acceleration of the engine housing. The three directions of sensor #2 differ from those of the coordinate system in Fig. 1 . Processing errors would occur if these test data were transformed from sensor #2 to the coordinate system in Fig. 1 by coordinate transformation. By contrast, the three directions of sensor #1 are exactly the same with the coordinate system in this study. Therefore, only the test data from sensor #1 were compared with the predicted acceleration in this study, and the test data acquired by sensor #2 will be used in other studies. 4. Results and discussions The structural parameters of the elements are listed in Table 2 . In this case, the stiffness of the valve spring is K s = 4.6 \u00d7 10 3 N/m, and its per-compression length is l 0 = 9 mm" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002207_icesi.2019.8863004-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002207_icesi.2019.8863004-Figure1-1.png", "caption": "Figure 1. Schematic process chain for the production of hairpin windings", "texts": [ " [1] After the insulated copper wire has been unwound from the coil, it is straightened and bent by a combination of different bending operations to form a hairpin. In the next step, the preformed conductors are inserted into the lamination before the free sides get bent to each other in a twist operation. After this bending step, the free conductor ends are mechanically and electrically connected to each other in a contacting process. [5] From the schematic representation of the manufacturing process in Figure 1 it can be concluded, that depending on the number of slots and conductors per slot, a high number of electrical contacts must be realized for the production of hairpin windings. For this purpose, the thermoplastic insulation needs to be removed in the joining area without any residues, before a connection can be made. [6] Since the failure of one contact point already leads to the loss of function of the electric drive, the contacting operation represents a crucial process in the process chain. In combination with the high number of contacts, it gets necessary to apply contacting technologies featuring short process times and especially high process reliabilities" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000211_s00227-010-1581-7-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000211_s00227-010-1581-7-Figure2-1.png", "caption": "Fig. 2 Experimental setup for the digital holographic PTV measurements", "texts": [ " Cells in their exponential growth phase were used, and the assay contained a natural population of solitary and chain-forming cells. The concentration of organisms in the culture was about 3,200 cells ml-1. The dimensions of the solitary and chain-forming cells tested in the present study are summarized in Table 1. Figure 1 shows microscopy photographs of the single cell and 8-cell chain of C. polykrikoides tested in the present study. Experimental setup for digital holographic PTV A single beam in-line holography system was employed. Figure 2 shows the experimental setup used to measure the 3D motion of the fast-swimming dinoflagellate C. polykrikoides. The sample chamber consisted of a BK7 glass window with dimensions of 15 9 15 9 5 mm3. The field of view (FoV) captured with a 9 4 objective lens was 4.3 9 4.3 9 5 mm3 in the center region of the sample chamber. The size of the sample chamber was relatively large compared with the FoV. Room and water temperatures were maintained at 22 C. All experiments were performed with background illumination to create an environment similar to daylight" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003046_j.simpat.2020.102080-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003046_j.simpat.2020.102080-Figure3-1.png", "caption": "Fig. 3. CFD model: (a) With a shroud; (b) Without shroud; (c) Cross-section of the shroud; (d) Mesh model with a shroud; (e) Partial enlarged detail of the mesh model; (f) Top view of the spiral bevel gear.", "texts": [ " (4), (6), (7) and (8), it is reasonable to believe that similar to a spur/helical gear, its windage power loss of the spiral bevel gear is also relative to the fluid properties, the structure parameters of the bevel gear, and the angular velocity, even though the spiral bevel gear is far more complex than a spur gear. Therefore, this paper attempts to carry on research from the above aspects. To avoid the interference by accessories in the internal gearbox, a single isolated spiral bevel gear instead of the whole gear transmission was used to investigate the windage power loss. The gear (the spiral gear in this paper is Gleason tooth as shown in Fig. 3(f)) and shroud geometry were developed using three-dimensional modeling software. Fig. 3(a) and (b) are isometric views of the CFD geometric model with and without a shroud, respectively. The initial baseline simulation was done with unshrouded bevel gear (see Fig. 3(b)) in pure air. Geometric data for this unshrouded gear is listed in Table 1. Referring to Fig. 3(c), shroud configurations can be identified by three basic parameters of interest: the toe clearance, the face clearance and the heel clearance (indicated by t, f, h). The windage power losses are the work the enclosed gear transmissions perform in order to drive the pure air or oil-air mixture surrounding the gears. On the basis of multi reference frame (MRF) theory, with the help of the CFD methodology established by Simmons [31,32] and Dai [43,44], a rotating reference frame is adapted to simulate the driving process of a high-speed bevel gear, namely, the bevel gear is rotating and walls stand still in the absolute coordinate system are seen to be rotating in relation to the relative coordinates (here refers to the rotating domain)", " 9, Cm is essentially constant over much of the speed range except for the highest measurement uncertainties at the speed of 4486 r/min and slightly increase at higher speed, so Cm at the speed of 4486 r/min is estimated as 0.0575, and the simulation value is 0.049 when the number of mesh elements exceeds 2240,836, the difference is less than 15%. Therefore, the number of total mesh elements in all simulations was approximately 2.6 million, where the minimum and maximum sizes of the meshes are 0.5 mm and 12 mm, respectively, and the max size, height and the num layers of the prismatic layer is 1 mm, 0.5 mm and 3, respectively. Fig. 3(d) and 3(e) illustrated the mesh model and partial enlarged detail of the gear tooth surface, where the maximum skewness, maximum aspect ratio, average orthogonal quality, and the mesh quality were 0.8491, 15.331, 0.7596, and 0.5306, respectively. Since the SST k-\u03c9 turbulence model was used in the simulation, the mesh criterion requirement y+ < 5 was necessary to adequately the latter turbulent model =+y yu \u00b5/ is a dimensionless wall parameter where y is the distance from the center of the first cells to the wall and us is the wall friction velocity given by =u | |/w where \u03c4w is the shear stress at the wall", " Benefited by the existence of the shroud, the static pressure rapidly dropped by an even more dramatic 80 percent (comparing Fig. 11 and Fig. 8(a)). It also can be concluded from Fig. 8(b) and Fig. 12 that the total windage moment appears a sharp decrease. This shows the shroud can contribute to decreasing the windage loss of the bevel gear. Therefore, to concern the influence of the shroud on the windage loss of bevel gears is not only of great theoretical significance but also of considerable practical significance. As defined previously in Fig. 3(c), the shroud structure mainly involves parameters in three directions, the toe clearance t, the face clearance f and the heel clearance h. In order to explore and optimize parameters (see Table 2a), the influence of three clearances on windage loss has been investigated in this paper, respectively. In this study, the gear rotational speed is set to 10,000 r/min in a counterclockwise direction. The toe clearance is set to 1.5 mm, 5 mm, 7.5 mm and 10 mm, respectively. The face clearance and the heel clearance are fixed at 5 mm (Groups 1\u20134 in Table 2a)" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000931_9781118703274.ch2-Figure2.50-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000931_9781118703274.ch2-Figure2.50-1.png", "caption": "Figure 2.50 Hydraulic blade pitch-regulation system with positioning cylinder and lever transmission (WKA 60, MAN)", "texts": [ " Four positioning cylinders acting directly upon the blade positioning rods bring the 80 metre-diameter blades of the teetered-hub rotor into the positions dictated by the control system. This positioning system thus makes it possible to control power in both directions. The hydraulic pressure supply with its pumps, fluid cooler and control computer are located at the rear of the nacelle. To provide a redundant backup supply for use during power outages, a hydraulic reservoir is located in front of the rotor hub. A similar idea for pitch setting is to be found in the WKA 60 1.2MW turbine shown in Figure 2.50. Here, too, the hydraulics unit and the cabinet with the electronics for control and regulation are located at the rear of the nacelle. Each of the three blades has its own direct-acting positioning cylinder. Double redundancy is thus afforded. Manufacturers of wind turbines prefer mass produced, reliable components for the hydraulic pitch adjustment systems, which are currently in use. The buckling load on the positioning cylinder can be kept low if the mechanism is designed such that positioning routes are kept short and direct (Figure 2" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002889_tmag.2020.3032648-Figure18-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002889_tmag.2020.3032648-Figure18-1.png", "caption": "Fig. 18. SPM motor with segmented PMs, a) prototyped model b) schematic.", "texts": [ " The prototyped models have identical stator/rotor sections with the only difference being the magnet type and the magnet arrangement in the rotor. The first prototyped model includes segmented high-energy rare-earth magnets (remanent flux density of 1.2 T) with 12 magnetic pieces per pole (i.e., 4 pieces along tangential direction and 3 pieces along axial direction), whereas the second model is made of the low-energy ferrite magnet (remanent flux density of 0.25 T) with single jointed magnet. Fig. 18 illustrates the schematic and the prototyped model of the segmented motor. The stator winding includes 50 turns per phase and the stator stack length is 60 mm. Fig. 19 depicts measured back-EMF waveforms of the two prototyped motors. As observed, the measured results are in a good agreement with the calculated and simulated waveforms. Similarly, the cogging torque and the electromagnetic torque of both prototyped models are measured and compared against the FE and analytical results (Figs 20 and 21)" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000193_j.cma.2011.04.006-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000193_j.cma.2011.04.006-Figure7-1.png", "caption": "Fig. 7. Towards application of longitudinal crowning.", "texts": [ " For definition of a skew imaginary crown-gear generating a skew bevel gear, the projection point Oh, origin of coordinate system Sh, for any given point M0, is not the center of the outer sphere but the tangent point with a circle defined on the pitch plane of the generating crown-gear as shown in Fig. 6(b), whose radius Rb is given by Rb \u00bc Ro sin\u00f0b\u00de; \u00f013\u00de where b is the skew angle of the bevel gear. The skew angle b is considered positive for a right-hand skew bevel gear (as shown in Fig. 6(b)) and negative for a left-hand skew bevel gear. A point P(u,h) on the imaginary generating crown-gear tooth surface (Fig. 7) is defined by profile parameter u of the blade (that defines the reference point M on the reference blade profile and corresponding point M0 on the outer sphere) and its longitudinal direction parameter h, measured from Oh on the projection line OhM0 (Fig. 6). For any given point M0 defined by profile parameter u of the reference blade profile, angles ab and aa can be determined (Fig. 5). Angle ab defines point M0 in coordinate system Sh. Then, by considering angle aa and skew angle b, point M0 might be determined in coordinate system Scg (Fig", " Longitudinal crowning is applied to the generating surfaces of the imaginary crown-gear by modifying angle aa with Daa, determined by Daa\u00f0h\u00de \u00bc ald\u00f0h h0\u00de2 h : \u00f016\u00de Here, ald is the parabola coefficient for longitudinal crowning, h is the longitudinal parameter, defined as mentioned above, and h0 is the value of parameter h where modifications of the generating surface start. By choosing appropriately different values for h0 and ald for the toe and heel areas of the crown-gear generating tooth surface, partial longitudinal crowning can be applied, as shown in Fig. 7. The upper sign in Eq. (16) is applied for generation of the driving side of the bevel gear (left side) and the lower sign is applied for generation of the coast side of the bevel gear (right side). The modified angle aa will be denoted as a a and is given by a a\u00f0u; h\u00de \u00bc aa\u00f0u\u00de \u00fe Daa\u00f0h\u00de \u00bc xc\u00f0u\u00de Ro ald\u00f0h h0\u00de2 h : \u00f017\u00de The following conditions have to be observed in Eq. (17) in order to provide longitudinal partial crowning to the surfaces of the imaginary generating crown-gear (Fig. 7). Three areas will be considered: If h < h0t , then ald \u00bc aldt and h0 \u00bc h0t (area D of zones 1, 4, and 7 in Fig. 3(a)). If h P h0t and h 6 h0h , then ald = 0 (area E of zones 2, 5, and 8 in Fig. 3(a)). If h > h0h , then ald \u00bc aldh and h0 \u00bc h0h (area F of zones 3, 6, and 9 in Fig. 3(a)). Parameters \u00f0aldt ; h0t \u00de and \u00f0aldh ; h0h \u00de control the crowning and position of areas D and F, respectively, for longitudinal crowning. By considering h0t \u00bc h0h \u00bc Ro Fw=2 and aldt \u00bc aldh we can take into account a conventional longitudinal parabolic crowned surface for the imaginary crown-gear" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000684_20131218-3-in-2045.00128-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000684_20131218-3-in-2045.00128-Figure1-1.png", "caption": "Fig. 1 Rotary Inverted Pendulum", "texts": [ " A mode-switching controller is designed to integrate swing up and stabilization control, which means that each time the pendulum reaches a certain location after it is swung up, the stabilizing controller is activated and \u2018catches\u2019 the pendulum allowing it to be balanced at the upright position. The paper is organized as follows. The mathematical model of the rotary inverted pendulum is presented in the Section II. Section III deals with the controller designs. Simulation results are presented in Section IV. Section V concludes the work. 978-3-902823-59-5/2013 \u00a9 IFAC 654 10.3182/20131218-3-IN-2045.00128 The Rotary inverted pendulum system is shown in Fig. 1. The system consists of two modules \u2013 a servo module and a rotary module. The servo module shown in Fig. 2 consists of a DC servomotor with built in gearbox ratio 70:1. The DC servomotor, whose input is +5 V, is mounted in a solid aluminium frame. The motor drives a built-in Swiss-made 14:1 gearbox whose output drives an external gear. The motor gear drives a gear attached to an independent output shaft that rotates in a precisely machined aluminium ball bearing block. The output shaft is equipped with a 1024 count quadrature encoder" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003479_0954407021999483-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003479_0954407021999483-Figure5-1.png", "caption": "Figure 5. Third order radial mode shapes without load for: (a) phase 1 (117.65 Hz) and (b) phase 2 (117.65 Hz).", "texts": [ " The results show that the natural frequencies of each order increase with the increase of inflation pressure, and when the tire is not restricted by the road, that is, when the load is 0, the vibration modes of tire can be divided into circumferential vibration, radial vibration and transverse vibration according to the vibration mode. In this paper, the radial 1\u20136 order vibration which is easy to distinguish modal shapes is selected as the research object. When there is only rim constraint, the radial modal frequency of the tire has a double root phenomenon, that is, the mode shape and frequency are the same, but the phase is different. Take the radial third order as an example, the modal vibration mode is shown in Figure 5. The stress of the steel belts under different pressure can be seen directly from Figure 6. As the main stress component of the tire, the belt can reflect the stress of the tire. When the tire increases from 0.18MPa to 0.24MPa, the stress on the belt increases, and the average stress is 112.983MPa, 123.474MPa, 134.094MPa, and 144.755MPa, respectively, and the greater the tension of the tire. Thus, the overall stiffness of the tire is increased, and the reason for the increase of vibration frequency is further explained" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002700_tmech.2020.3015133-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002700_tmech.2020.3015133-Figure4-1.png", "caption": "Fig. 4. Single-axis flexure hinge and coordinate system.", "texts": [ " Authorized licensed use limited to: Cornell University Library. Downloaded on August 24,2020 at 08:11:28 UTC from IEEE Xplore. Restrictions apply. 1083-4435 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Based on the above-simplified model, a coordinate system of the dynamic and kinematic design parameter of the elliptical flexible hinge [34] is established, as shown in Fig. 4. The force on the flexible hinge is defined as f = [Fx, Fy, Fz,Mx,My,Mz] (1) The corresponding deformation is defined as xh = [\u2206x,\u2206y,\u2206z,\u2206\u03b1x,\u2206\u03b2y,\u2206\u03b3z] T (2) The relationship between equations (1) and (2) can be defined as follows: xh = f Kh (3) where Kh is the stiffness of the flexible hinge. Unlike the work of Cao et al. [35], only the bending stiffness around the z axis is considered in this study. The twist of the bending moment around the z axis is obtained by the microelement method and is defined as \u2206\u03b3z = ax \u222b \u2212ax Mz(x) EIz(x) dx (4) where ax, ay is the long semi-axis and the short semi-axis of the ellipse, respectively; E is the elastic modulus of the Nitinol tube; Mz(x) is the bending moment experienced by the flexible unit around z axis; Iz(x) is the moment of inertia of the flexible unit. Based on the elliptical flexible hinge of the Fig. 4, the moment of inertia is calculated as follows: Iz(x) = w[t+ 2ay \u2212 2ay \u221a 1\u2212 x2/ax2] 3 12 (5) where w is the thickness of the Nitinol tube wall; t is the minimum width of the elliptical notch. The bending stiffness of the elliptical flexible hinge can be obtained by the above equation. Kbending = Mz \u2206\u03b3z = E \u00b7 w \u00b7 ay3 12 \u00b7 ax \u00b7 f1 (6) f1 = 12\u00b7s4\u00b7(2\u00b7s+1) (4\u00b7s+1)5/2 arctan \u221a 4 \u00b7 s+ 1+ 2\u00b7s3(16\u00b7s2+4\u00b7s+1) (4\u00b7s+1)2\u00b7(2\u00b7s+1) (7) where s = ay/t. Based on the mechanical model, the deformation of the flexible unit is analyzed" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002277_978-3-319-27131-6-Figure8.5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002277_978-3-319-27131-6-Figure8.5-1.png", "caption": "Fig. 8.5 Abrasive wear mechanism in rolling bearings", "texts": [ " It mostly occurs at the minimum oil-film thickness near the outflow of the Hertzian contact area. Under bearing loads and moments, the asperities of the bearing surface begin deforming plastically. When the tensile and shear stresses in the asperities exceed the ultimate tensile and critical shear stresses, some asperities of the rolling elements and raceways break up. Then, the broken bits together with the hard particles in lubricating oil cause the abrasive wear in the form of dents on the surfaces of the rolling elements and raceways, as shown in Fig. 8.5. 8.2 Failure Mechanisms in Rolling Bearings 175 In the point of view of the tribological mechanism of wears, contact fatigue and corrosive and tribochemical wears must be taken into account besides the adhesive and abrasive wear: 176 8 Bearing Friction and Failure Mechanisms \u2013 Contact fatigue is generated by the cyclic loads between two moving surfaces after a certain number of operating cycles (e.g., revolutions of the rotor). It causes contact fatigue where the yield stress of material strongly reduces at increasing the number of operating cycles according to the W\u20acohler curve" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002893_tia.2020.3036328-Figure35-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002893_tia.2020.3036328-Figure35-1.png", "caption": "Fig. 35. Prototype machines. (a) 12S16P FRPM. (b) 12S16P CFRPM. (c) Proposed 6S16P CFRPM with 2-step skewed rotor.", "texts": [ " Step skewed rotor is found to be more effective without too much compromising of the output torque when the step number is chosen as two and skew angle chosen to be 4\u00b0. After employing 4\u00b0 two-step skewed rotor, the torque ripple of the proposed 6S16P CFRPM machine is reduced to 16.5%, which is comparable to those of the 12S16P FRPM machine and its consequent pole type. The 6S16P CFRPM machine with two-step skewed rotor still exhibits 43% and 22% higher torque than the 12S16P FRPM machine and its consequent pole type, respectively, as shown in Fig. 34. To further verify the previous analyses, three prototype machines are manufactured, as shown in Fig. 35, and their parameters are listed in Table II. Fig. 36 shows the FEA calculated and measured back EMFs when the speed is 600 rpm. Under the same Authorized licensed use limited to: California State University Fresno. Downloaded on June 26,2021 at 14:21:53 UTC from IEEE Xplore. Restrictions apply. slot filling factor, the number of series turns per phase is 100 for the 12S16P FRPM machine and its consequent pole type, and 136 for the proposed 6S16P CFRPM machine. For the 12S16P FRPM machine, the FEA-predicted and measured back EMFs match well, and the latter is about 95% of the former" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003479_0954407021999483-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003479_0954407021999483-Figure6-1.png", "caption": "Figure 6. Stress of steel belts under different air pressure at: (a) 0.18 MPa, (b) 0.20 MPa, (c) 0.22 Mpa, and (d) 0.24 MPa.", "texts": [ " The results show that the natural frequencies of each order increase with the increase of inflation pressure, and when the tire is not restricted by the road, that is, when the load is 0, the vibration modes of tire can be divided into circumferential vibration, radial vibration and transverse vibration according to the vibration mode. In this paper, the radial 1\u20136 order vibration which is easy to distinguish modal shapes is selected as the research object. When there is only rim constraint, the radial modal frequency of the tire has a double root phenomenon, that is, the mode shape and frequency are the same, but the phase is different. Take the radial third order as an example, the modal vibration mode is shown in Figure 5. The stress of the steel belts under different pressure can be seen directly from Figure 6. As the main stress component of the tire, the belt can reflect the stress of the tire. When the tire increases from 0.18MPa to 0.24MPa, the stress on the belt increases, and the average stress is 112.983MPa, 123.474MPa, 134.094MPa, and 144.755MPa, respectively, and the greater the tension of the tire. Thus, the overall stiffness of the tire is increased, and the reason for the increase of vibration frequency is further explained. The influence of load on tire modal In this section, the tire inflation pressure is 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002460_j.mechmachtheory.2018.03.018-Figure17-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002460_j.mechmachtheory.2018.03.018-Figure17-1.png", "caption": "Fig. 17. Graphic simulator of the 7R 6-DOF robot and the trajectory.", "texts": [ " 16 . From Fig. 16 , the functional redundancy motion adjusts the robot out of the singularity region, even though the initial solution is illconditioned and the task required motion i.e. motion in the relevant task subspace moves the robot closer to the wrist interior singularity. In other words, the proposed method is effective for singularity avoidance with an ill-conditioned initial solution, as expressed in Section 4.2 . The robot is used to paint a vertical surface on the part as shown in Fig. 17 . A classical raster trajectory is defined. The orientation of EE is planned to be fixed throughout the trajectory (i.e. the Z axes parallel to X axes of the base frame and the X, Y axes opposite to Y, Z axes of the base frame respectively). The duration of the motion is determined as 20 s. At about t = 10 s , the wrist boundary singularity occurs, i.e. \u03b8 = 180 \u25e6. Here, we choose \u03b5 = 5 \u00d7 10 4 , \u03bbmax = 0 . 2 , \u03b3 = 0 . 2 , \u03b1 = 1 . The 5 joint positions planned by the DLS method and TWA with new criterion are shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003529_s11071-021-06796-3-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003529_s11071-021-06796-3-Figure1-1.png", "caption": "Fig. 1 Global coordinate system of linear guideway", "texts": [ " 4, experiment is conducted for dynamic parameter identification and the validations of calculation methodology and proposed model by a commercial linear guideway. Finally, several conclusions are drawn in Sect. 5. The proposed model can be used to identify the mechanism of time domain vibration response of linear guideway, understand the posture variation of carriage and develop new numerical model algorithms to determine the vibration characteristics. 2.1 Definition of coordinate system A global Cartesian coordinate system with an origin O at the symmetric center of top surface of carriage is defined as shown in Fig. 1. High-precision linear motion can be realized by recirculating balls between rail and carriage. When carriage is subjected to evenly distributed lateral and radial loads, and moments in rolling, pitching and yawing directions F = [Fy Fz Mx My Mz] T, the linear and angular displacements of carriage block relative to fixed rail are X = [uy uz hx hy hz] T as a result of the localized deformation between groove surface and balls. The cross sections of guide block shown in Fig. 2 indicate that carriage block can provide equal load capacity in all coordinate directions normal to motion direction due to the initial contact angle a0 of 45 " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002022_978-3-319-40036-5-Figure5.14-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002022_978-3-319-40036-5-Figure5.14-1.png", "caption": "Fig. 5.14 Example SolidWorks design", "texts": [ " Each layer contains a structural component which is created by cutting voids out of the material, when layered together this creates a three-dimensional network of chambers and channels for flow control. Once the disk design is complete it is important to ensure that all complex structures requiring the interconnection of multiple layers are perfectly aligned, this can be done by zooming and rotating around the central axis of the disc. If the quality of the design is assured the disk design can be separated into 2D layers which are compatible with the knife cutter and laser cutter (Fig. 5.14). 134 B. Henderson et al. Sheets of pressure sensitive adhesive are cut using a Graphtec automated knife cutter. This device is controlled by the programme \u201cRobo Master-Pro \u2122 Vision 4.6.0\u201d which accepts the previously attained DXF files (alternative hardware / software can be used) (Fig. 5.15). Dissolvable film tabs are used to restrict the flow of fluid from one microfluidic structure to the next by sealing the channel and creating a counteracting pressure which pushes back the liquid. These DF tabs can be wetted and dissolved by increasing the spin rate of the disc until the liquid comes in contact with the DF, this is known as the burst frequency (Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000684_20131218-3-in-2045.00128-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000684_20131218-3-in-2045.00128-Figure2-1.png", "caption": "Fig. 2 Servo Module", "texts": [ " A mode-switching controller is designed to integrate swing up and stabilization control, which means that each time the pendulum reaches a certain location after it is swung up, the stabilizing controller is activated and \u2018catches\u2019 the pendulum allowing it to be balanced at the upright position. The paper is organized as follows. The mathematical model of the rotary inverted pendulum is presented in the Section II. Section III deals with the controller designs. Simulation results are presented in Section IV. Section V concludes the work. 978-3-902823-59-5/2013 \u00a9 IFAC 654 10.3182/20131218-3-IN-2045.00128 The Rotary inverted pendulum system is shown in Fig. 1. The system consists of two modules \u2013 a servo module and a rotary module. The servo module shown in Fig. 2 consists of a DC servomotor with built in gearbox ratio 70:1. The DC servomotor, whose input is +5 V, is mounted in a solid aluminium frame. The motor drives a built-in Swiss-made 14:1 gearbox whose output drives an external gear. The motor gear drives a gear attached to an independent output shaft that rotates in a precisely machined aluminium ball bearing block. The output shaft is equipped with a 1024 count quadrature encoder. This gives the motor shaft position. A second gear on the output shaft drives an antibacklash gear connected to a precision potentiometer" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000931_9781118703274.ch2-Figure2.34-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000931_9781118703274.ch2-Figure2.34-1.png", "caption": "Figure 2.34 Side rotor yaw system (Allgaier): 1, side rotor; 2, pinion; 3, worm; 4, worm shaft", "texts": [ "33(b)) are established in the market. Their greater axial length, among other things, makes it easier to climb into the nacelle from the tower. Brake systems (Figure 2.33(c)) stop the yaw movement and thus protect the yaw gears and ring gears in particular. Side-rotor yaw systems were widespread in earlier times, also being found in Dutch windmills (Figure 1.7), but for cost reasons they are hardly used today. They are mostly limited to wind energy machines that are not connected to the public grid supply (Figure 2.34). Passive yaw systems are only used on small machines. The wind vane system (Figure 2.35(a)) was very popular, being used by the million on the American wind pumps known as the \u2018Western wheel\u2019 and similar machines (Figure 1.8). On the other hand, downwind turbines (Figure 2.35(b)), steered by wind pressure of the rotor blades, are not used so often. In these systems an azimuth drive is unnecessary, but Coriolis accelerations caused by changes in wind direction can exert considerable forces on the blades unless some damping or stabilizing system is provided" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001791_j.mechmachtheory.2016.05.001-Figure2.3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001791_j.mechmachtheory.2016.05.001-Figure2.3-1.png", "caption": "Fig. 2.3. Sketch of 3-SPR PM.", "texts": [ " (3c), a novel velocity transmission equation can be derived as following: Vr \u00bc J3 v\u03c9 ;Vr \u00bc vr1 vr2 vr3 0 0 0 0 0 2 66666666664 3 77777777775 ; J3 \u00bc \u03b4T1 e1 \u03b41\u00f0 \u00deT \u03b4T2 e2 \u03b42\u00f0 \u00deT \u03b4T3 e3 \u03b43\u00f0 \u00deT f T1 d1 f 1\u00f0 \u00deT 0T 3 1 0T 3 1 f T2 d2 f 2\u00f0 \u00deT f T3 d3 f 3\u00f0 \u00deT 0T 3 1 0T 3 1 2 66666666666664 3 77777777777775 : \u00f07a\u00de J0,5 and J0,8 denote the constrained torques in r1 and r3 in the Exechon PM, respectively. It can be seen from Eqs. (3c) and (7a) that J0,5 and J0,8 are converted into zero vectors. Since the constrained torques in r1 and r3 are eliminated, r1 and r3 are converted into a SPR-type legs, and then the third KIM (3-SPR PM) (see Fig. 2.3) for the Exechon PM can be obtained from Eq. (7a). Some geometric constraints are satisfied for this PM as follows: Ri1\u22a5ri;Ri1\u2551a2o i \u00bc 1;3\u00f0 \u00de;R21\u2551a1a3;R21\u22a5r2: \u00f07b\u00de Since f1 = R12, it leads to J0;4 \u00fe t1 J0;5 h i v\u03c9 \u00bc f T4 dT 4 f T4 h i v\u03c9 \u00bc 0; f 4 \u00bc f 1;d4 \u00bc d1 \u00fe t1R11 \u00f08a\u00de here t1 is a scalar quantity, d4 = d1 + t1R11 denotes the vector from o to c1, c1 is a point on line R11. (see Fig. 2.4). It is easy to determine that \u00bd f T4 dT 4 f T4 in Eq. (8a) represents one constrained force which is parallel with R12 and passes through c1" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002151_j.apm.2015.04.031-Figure12-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002151_j.apm.2015.04.031-Figure12-1.png", "caption": "Fig. 12(b). The whole system framework of VCM.", "texts": [ "2 Time(s) vo lta ge (v ) 0.02 0.021 0.022 0.023 0.024 -0.65 -0.6 -0.55 -0.5 The Estimate Disturbance Signal The Practical Disturbance Signal Fig. 15. The estimation of the disturbance. 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 x 10 -3 Time(s) P os iti on (m ) 0.02 0.022 0.024 0.026 1.2 1.4 1.6 1.8 x 10 -3 The reference signal The traditional PID control The ADRC control Fig. 16. The robust performance of ADRC and PID. An overview of the experimental platform is displayed in Fig. 12(a), the experimental control plant is the VCM, the resistor: R = 3.5 X, the inductance: L = 6.5 mH. The position signal is measured by the fiber-optic displacement sensors, the position range: 4 mm, the bandwidth: 150 kHz. The control panel using TMS320C28335 as the core chip can achieve position control based on ADRC algorithm. The HCHB seven-level inverter topology structure is used as power converter, the DC bus voltage U1 = 50 V; U2 = 25 V. The whole system framework includes DSP section and power amplify section. As shown in Fig. 12(b), the DSP is the core part of this control section. It can achieve the ADRC method and the design of FOS. It also can output PWM signals and gather position feedback signal. According to the feedback signal and reference signal, the ADRC controller can output the reference voltage, which is modulated based on the HFPWM method to output 8 PWM signals, which is used to drive HCHB inverter for power amplify. In order to test the availability of the proposed method. Firstly, according to formula (13), the algorithm of the ADRC is written by using S-function C language template, which is provided by MATLAB/Simulink" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002735_j.mtla.2020.100992-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002735_j.mtla.2020.100992-Figure1-1.png", "caption": "Fig. 1. \u03bcCT view of porosity within the printed cylinder. The three largest pores in the volume are highlighted with the arrow. In this particular cylinder, the three largest pores have effective diameter (in \u03bcm) of 1 (280 \u03bcm), 2 (270 \u03bcm), and 3 (260 \u03bcm).", "texts": [ " Build design and powder reuse The printing process was conducted with an ARCAM A2X Electron eam AM system. All printing was conducted according to the default arameters of the machine for Ti6Al4V, which includes a beam speed f 4530 mm/s, beam current of 15 mA, max current of 20 mA, focus ffset of 25 mA and speed function of 45. The influence of powder reuse n the printed metal porosity was evaluated using a simple cylindrical art with 6 mm diameter and 21 mm height. The geometry was choen to best serve the \u03bcCT analysis. The build design is shown in Fig. 1 a. s evident from this figure, the part was printed together with addiional specimens that were used for characterizing other aspects of the icrostructure and mechanical properties of the metal with reuse. Thirty consecutive builds were performed over a period of approxiately 6 months using the PBF-EB system. The total powder consumed n each build was approximately 0.16 kg, and roughly 12 kg of power was exposed to the electron beam during the pre- and post- heating tages. For consistency, part placement remained the same in all builds f the investigation", " Once reconstructed, the volume was then exported as a slice tack along the build height direction and then imported to VGSTUDIO AX (Volume Graphics Inc., Charlotte, NC, USA) where the surface was etermined using automatic determination due to the very distinct maerial and background intensity peaks. Pores were excluded during the urface determination so they could be included in the porosity calcuation. Porosity was then calculated with special care to exclude \ud835\udf07CT treak artifacts. A fully reconstructed porosity map from \ud835\udf07CT evaluaion is shown in Fig. 1 b. The three pores with largest effective diameter re highlighted in this figure along with the measured total porosity pore volume per cylinder volume). The porosity data was then analyzed to extract important characterstics related to the pores within the parts and trends with powder reuse. ost important for this analysis were the pore size and its distribution. he pore morphology was also analyzed due to its contribution to the ffective stress concentration posed by the pore. In addition, the spatial istribution of pores was evaluated in two ways", " 2 t c w t y b a t t a r t l l 3 o r v % p d a t d o l a p g d n t t i s w b s b r w P c t c w i [ i .3. Microscopy Optical Microcopy (OM; Olympus BX50 Microscope, Olympus Scienific Solutions America, Waltham, MA, USA) and Scanning Electron Miroscopy (SEM; JSM-6010PLUS/LA, JEOL USA Inc., Peabody, MA, USA) ere used to visually inspect voids within the specimens that were idenified in the microstructural analysis. In addition, a fractographic analsis was performed on the fracture surfaces of specimens from the same uilds that were subjected to tensile loading to failure ( Fig. 1 a). This nalysis included specimens with both vertical and horizontal orientaions to further assess qualities of the voids and their contributions to he initiation of failure. Detailed results concerning the microstructure nd mechanical properties of the metal as a function of powder reuse are eported elsewhere [ 29 , 32 ]. Nevertheless, relevant results of the tensile esting are provided in the supplemental data (S1) for review and correation with the porosity measurements along with characteristic of the arge pore are given in the Supplemental data and Figure A1 ", " Therefore, there is some inconsistency in he apparent mechanisms responsible for the development of LOF voids mong the published studies. Future work appears warranted to improve he current understanding. A primary concern in metal AM overall is the contribution of metal efects to the structural behavior of components. But surprisingly, only eak correlations were identified between the mechanical properties nd the various measures of porosity; the metal ductility showed the ost sensitivity to pores. Comparing the tensile properties of specimens ith horizontal and vertical orientation ( Fig. 1 a), those with vertical rientation underwent the largest decrease in ductility with increasing orosity. There was a 30% decrease in ductility of the Ti6Al4V speciens with vertical orientation over only 0.08% increase in overall porosty (from .06% to 0.14% by volume). For commercially pure titanium, inor increases in porosity can cause large reductions in ductility. Howver the effects of porosity are reportedly not as substantial for Ti6Al4V 47] . The substantial decrease in ductility with small rise in porosity is xpected to result primarily from the largest pores and the stress conentration they pose [48] " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001106_0278364914552112-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001106_0278364914552112-Figure1-1.png", "caption": "Fig. 1. (a) Illustration of the passive SLIP model and (b) the phases of motion.", "texts": [ " For simplification purposes, we chose to reduce the system to its dimensionless counterpart, normalizing with respect to the gravity acceleration constant g, the leg length at rest L0, and the mass M. Everything can then be written as a function of the leg length \u2018 = L/L0, the spring length \u2018k = Lk/L0, the dimensionless time t = ffiffiffiffiffiffiffiffiffiffi g=L0 p t, and the relative spring stiffness g = kL0/Mg. Also, let us define x and y as the horizontal and vertical coordinates of the point mass, as shown in Figure 1(a), such that x = \u2018 cos u and y = \u2018 sin u. The function ( ) : is the derivative with respect to the dimensionless time: ( ) = d dt ( ) The SLIP model can be considered a hybrid system with its motion divided into two parts: the flight phase and the stance phase. Flight phase is defined as the portion of the motion where there is no contact with the ground. The motion is governed by gravity only, where \u20acy = 1, \u20acx = 0 The stance phase is defined by the contact between the terminal point of the leg (the foot) and the ground" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001300_1350650115577402-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001300_1350650115577402-Figure1-1.png", "caption": "Figure 1. The schematic view of the bearing and cage. (a) Model of ball bearing, (b) model of cage with the force.", "texts": [ " Although many researches on cage stability have been developed, the attention of those studies has been to focus on steady working conditions. Cage stability under transient conditions, especially during the starting process, was not taken into account. This paper will develop the dynamic model of ball bearings under oil-lubricated conditions and, based on the model, will investigate the effect of external loads on cage stability both under steady conditions and during the starting process. A model of ball bearings and coordinate systems is shown in Figure 1. Cage motion can be divided into the translational motion of the mass center and the rotation motion around the mass center. The differential equations of the cage can be expressed using the system above as equation (1) Xn j\u00bc1 \u00f0 Fbpjx\u00de \u00bc mc \u20acxc \u00f01:a\u00de Fly \u00fe Xn j\u00bc1 \u00f0 Fbpjy cos j Fbpjz sin j\u00de \u00bc mc \u20acyc \u00f01:b\u00de Flz \u00fe Xn j\u00bc1 \u00f0 Fbpjy sin j Fbpjz cos j\u00de \u00bc mc \u20aczc \u00f01:c\u00de Xn j\u00bc1 Fbpjy Dc 2 \u00feMl \u00bc Ic \u20ac c \u00f01:d\u00de where n is the ball number, mc and Ic are cage mass and rotational inertia and Dc is the pitch diameter of bearings" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003476_j.triboint.2021.106951-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003476_j.triboint.2021.106951-Figure1-1.png", "caption": "Fig. 1. Simulation model of the intermediate gearbox.", "texts": [ " Finally, a test rig is specially made which can realize several typical dynamic motions of the gearbox, and experiments are performed to verify the feasibility of the simulation method. Results of this work can provide a reference for the enhancement of the splash lubrication X. Hu et al. property of the intermediate gearbox of a helicopter. The simplified structure diagram of the intermediate gearbox of a helicopter, which is principally composed of the housing, a pair of spiral bevel gears, bearings and two bearing caps both with two oil guild holes, is shown in Fig. 1. To simplify the model and improve the calculation efficiency, structures that have less influence on the splash lubrication performance have been omitted in the simplified model. The oil guide holes on the driving gear bearing cap are numbered 1 and 2, while those on the driven gear are numbered 3 and 4. The parameters of spiral bevel gears are illustrated in Table 1. The lubricating oil is stirred as the driving gear rotates to realize the lubrication and heat dissipation of gears, and part of the oil flows to the bearing through the four oil guide holes" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002894_tte.2020.3035180-Figure15-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002894_tte.2020.3035180-Figure15-1.png", "caption": "Fig. 15. 12-slot/10-pole FSCW PMSMs. (a) Stator. (b) Conventional rotor. (c) Bread-loaf rotor.", "texts": [ " Due to the low harmonics content of the bread-loaf PMSM, the 4pth-, 6pth-, 8pth-order radial force of the bread-loaf PMSM is smaller than that of the conventional PMSM. However, since the vibration at 4fe, 6fe, 8fe and later frequencies is insignificant, the reduction has little effect on the total vibration level. The predicted vibration results verify the previous theoretical analysis, namely the bread-loaf magnet has negative effect on the total vibration performance of FSCW PMSMs. V. EXPERIMENTAL VERIFICATION A. Prototypes and Modal Test Fig. 15 shows the prototypes of two 12-slot/10-pole FSCW PMSMs. The modal test of the entail motor is carried out to obtain the natural frequencies for the 12-slot/10-pole PMSM. The PMSM is suspended by elastic rope to simulate unconstrained state as shown in Fig. 16. The hammering method is used in the modal experiment. Since the difference between two 12-slot/10-pole PMSMs is just in magnet structure, the modal parameters of two PMSMs are considered as the same. The modal experiment of one 12-slot/10-pole PMSM is conducted to avoid repetition" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002067_tec.2017.2761787-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002067_tec.2017.2761787-Figure3-1.png", "caption": "Fig. 3. Schematic ECB symbol", "texts": [ " By applying the Ritz-Galerkin method, the weak form integral is taken as: ( ) ( ) ( ) \u222b\u222b\u222b \u222b\u222b \u222b\u222b \u0393\u2126\u0393 \u0393\u0393 \u2126\u2126 \u0393\u22c5\u22c5 \u2202 \u2202 +\u2126\u22c5\u22c5+\u0393\u22c5\u22c5\u22c5 =\u0393\u22c5\u22c5\u22c5+\u0393\u22c5\u22c5\u2212 +\u2126\u22c5\u2207\u22c5\u2207+\u2126\u22c5 \u2202 \u2202 Tea ahu dT n TkdTqdTTh dTThdTTTh dTTkdT t Tc aa auu ddd dd dd\u03c1 (7) The first and second items on the left side in (7) are used to generate the element mass matrix and the element stiffness matrix in \u03a9, respectively. The second term on the right side corresponds to the element load matrix in \u03a9. The fourth item on the left side and the first item on the right side are used to generate the boundary element stiffness matrix and boundary element load matrix on \u0413a. The discretization of the items cited is well established in the classical FEM for heat conduction equation [20]. The third item on the left side and the third item on the right side in (7) will be dealt with in next subsections. Fig. 3 shows the ECB symbol. The difference between the ECB and the conventional convective boundary condition expressed by (5) is that Ta is a given value but Tu is to be solved. Hence, Ta is on the right side in (7), while Tu is on the left. With an unknown ambient temperature Tu in the third item on the left side in (7), another equation is needed to make the system of the linear equations solvable, which is based on energy conservation and can be expressed as: It is assumed that the temperature in a surface element e on \u0413hu is expressed as: \u2211 = \u22c5= m j e j e j e NTT 1 )()()( (9) Then, (8) can be discretized as: u e u m j e ju e jeuu QQdNhTSTh huhu e == \u0393\u2212 \u2211\u2211 \u2211 \u222b \u0393\u0393 = \u0393 )( 1 )()( (10) According to (10), the energy conservation equation on element e can be expressed as: )( 1 )()( e u m j e ju e jeuu QdNhTSTh e = \u0393\u2212 \u2211 \u222b = \u0393 (11) On the other hand, if \u03b4T is assumed to be Ni (e), which is the interpolation function at node i in element e, then the discretization of the 3rd item on the left side in (7) on element e can be expressed as: ( ) ( ) \u222b\u222b \u2211 \u222b \u0393\u0393 = \u0393 \u0393\u2212\u0393=\u0393\u22c5\u22c5\u2212 ee e dNhTdNNhTdTTTh e iuu m j e j e iu e juu )( 1 )()(d (12) It can be seen from (11) and (12) that Tu can be considered as a unknown variable which is related to each element on \u0413hu" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002228_tcst.2019.2958015-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002228_tcst.2019.2958015-Figure1-1.png", "caption": "Fig. 1. Geometrically exact pose description of soft robots.", "texts": [ " These three parts together describe the relationship between the space configuration, internal strain, internal stress, and external load. 1) Kinematics of Deformation: Kinematics of deformation describe how the space configuration changes with respect to the internal strain along the robot body. The pose of any cross section on the body with respect to a reference configuration of soft robots can be described by a directing vector and the coordinate of the center E(s) = [d1, d2, d3, r](s). (1) As shown in Fig. 1, s is the arc length from the base of the soft robot. {dk(s), k = 1, 2, 3} here represents the orientation of the cross section and r(s) represents the position of the cross section. Deformation of the body from the reference configuration means that cross sections of the body undergo some motions such as rotations around the directing vectors which cause bend u1(s), u2(s) and torsion u3(s), or displacements along the directing vectors which cause shear v1(s), v2(s) and stretch v3(s). The effect of the strain on the poses of cross sections can be described as d\u0307k(s) = [u1(s), u2(s), u3(s)]T \u00d7 dk(s) (2) r\u0307(s) = [v1(s), v2(s), v3(s)]T " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002969_tmag.2020.3007439-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002969_tmag.2020.3007439-Figure2-1.png", "caption": "Fig. 2. MSO coil for high fill-factor. (a) Manufacturing process of the MSO coil, and (b) manufactured MSO coil for the specimen.", "texts": [ " This section describes the nature of mechanical loss and the prediction methods for mechanical loss. The conventional, experimental, and proposed methods are compared in this section. Table I shows the specifications of the specimen, which has 14-poles and 12-slots and an outer rotor, used for verifying the proposed method. The armature winding of a maximum slot occupation coil (MSO coil) is used to show the effect of the eddy current loss in conductors over its large conductor area as shown in Fig. 2(a) and Fig. 2(b), to verify the proposed method. An MSO coil is a winding technology that enables to increase the fill-factor extremely by machining a copper block into a coil that can be fit into the slot [6], [9]. The mechanical loss of the motor consists of bearing and windage losses. The bearing loss is caused by the friction occurring between the ball of the bearing and the lubricants as shown in Fig. 3(a), and the friction phenomenon is similar to viscous friction. The windage loss is caused by the friction between the fluids in the air-gap and the rotor as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000039_978-1-84996-220-9-Figure2.5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000039_978-1-84996-220-9-Figure2.5-1.png", "caption": "Figure 2.5 Decomposition of internal forces and moments. We decompose internal forces and moments into contact centers of pressure, internal tensions, and normal moments. Contact centers of pressure allow us to control contact rotational behavior while internal tensions and normal moments allow us to control the behavior of contact points with respect to surface friction properties.", "texts": [ " The task operator JkUNs in the above equation, behaves as a constrained Jacobian transformation mapping 2 Compliant Control of Whole-body Multi-contact Behaviors in Humanoid Robots 37 joint velocities into task velocities and we refer to it using the symbol J\u2217k JkUNs. (2.15) This expression is motivated by the dependency of base velocities on joint velocities, as shown in Figure 2.3. 38 L. Sentis We consider whole-body contact scenarios where multiple extremities of the robot are in stable contact against flat surfaces (see Figure 2.5). In this case, every contact imposes six constraints on the robot\u2019s mobility. We assume that each extremity in contact has enough joints with respect to the base link to enable the independent control of its position and orientation. This condition translates to the existence of six or more independent mechanical joints between the base link and the extremity in contact. We consider contact scenarios involving an arbitrary number of supporting extremities, represented by the number ns. Flat supporting contacts impose 6ns constraints on the robot\u2019s motion, where 6 of these constraints provide the support to maneuver the robot\u2019s center of mass and the other 6(ns \u2212 1) describe the internal forces and moments acting on the closed loops that exist between supporting extremities [63]", " Internal forces and moments play two different roles in characterizing the contact behavior of the robot: (1) contact centers of pressure define the behavior of the contact links with respect to edge or point rotations and (2) internal tensions and moments describe the behavior of the contact links with respect to the friction characteristics associated with the contact surfaces. For ns links in contact we associate ns contact CoPs. Each contact center of pressure is defined as the 2D point on the contact surface where tangential moments are equal to zero. Therefore, 2ns coordinates describe all contact pressure points. Figure 2.5 illustrates a multi-contact scenario involving three supporting contacts on the robot\u2019s feet and left hand and an operational task designed to interact with the robot\u2019s right hand. We focus on the analysis of the forces and moments taking place on a particular contact body, as shown in Figure 2.6. Based on [60], we abstract the influence of the robot\u2019s body above the kth supporting extremity by the inertial and gravity force fsk and the inertial and gravity moment msk acting on a sensor point Sk" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003369_j.mechmachtheory.2021.104386-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003369_j.mechmachtheory.2021.104386-Figure1-1.png", "caption": "Fig. 1. Contact pattern of helical gear.", "texts": [ " Furthermore, the root profile of a helical gear is not accurately considered in the TAM. To address this problem, an improved analytical model (IAM) is proposed in this study. The IAM accurately implements the trochoidal root fillet profile of a helical gear using cutter information and reflects the profile in the TVMS and LSTE calculations. The model is validated using an FE model, and the analysis results of the TAM and IAM are compared according to the helix angles. Unlike a spur gear, a helical gear has a helix angle and the contact line appears as shown in Fig. 1 . The gear mesh moves its operating location from the SAP at one end (point A) to the EAP at the other end (point E) along the face width. The figure also shows that the length of the contact line (blue line) increases as it starts from point A and becomes shorter when it reaches the maximum length, where the mesh ends (i.e., point E). Because the mesh stiffness of a gear changes according to the mesh position, it is essential to accurately predict the mesh position over time for accurate stiffness calculation" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000281_tmech.2012.2182777-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000281_tmech.2012.2182777-Figure5-1.png", "caption": "Fig. 5. Foot design structure with FSRs (\u00a91 , \u00a97 : covers, \u00a92 , \u00a95 : sensor housings, \u00a93 , \u00a96 : contact materials, and \u00a94 : FSRs).", "texts": [ " HSR has been in continual development and research by the Robot Intelligence Technology laboratory, KAIST [5]. Its height and weight are 52.8 cm and 5.5 kg, respectively. It consists of 12 dc motors with harmonic drives for the lower body and 16 RC servo motors for the upper body (two servo motors in each hand control). The on-board Pentium-III compatible PC, running RT-Linux, calculates the proposed algorithm every 5 ms in real time. To measure the ground reaction forces (GRFs) on the feet and the real ZMP trajectory while walking, as shown in Fig. 5, four FSRs are equipped on the sole of each foot, which are all sensors used in the experiment. Fig. 6 illustrates a free-body diagram of the foot structure for the ZMP measurement, where pli and pri (i = 1, 2, 3, and 4) are the 2 \u00d7 1 position vectors of the FSRs of the left and right feet, respectively. Note that since the ZMP is defined on the xy-plane, the position vectors are also defined on the xy-plane. In addition, fli and fri are the GRFs measured by FSRs of each foot, respectively. pzmp = [xzmp yzmp]T represents the ZMP position vector" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001144_j.mechmachtheory.2013.09.001-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001144_j.mechmachtheory.2013.09.001-Figure2-1.png", "caption": "Fig. 2. Profile and its parameters of the modified VTT rack cutter.", "texts": [ " By comparison of the TCA simulation results, the merits of the gear pairs generated by the proposed generation method with the modified VTT hob can be clearly verified. 2. Mathematical model of the modified hob with variable tooth thickness (VTT) Basically, the theoretical tooth profile of a hob is a helical gear that can be generated by a rack cutter. In this study, however, the proposed modified VTT hob can be generated by a modified rack cutter. The tooth thickness of the rack cutter is modified along its helix line as shown in Fig. 1, and along its profile line as shown in Fig. 2. The helix angle of the rack cutter is equal to the standard helix angle at the reference point P, which is located at the middle transverse section of the rack cutter. The helix line of the rack cutter is modified by a second order polynomial, as expressed in Eq. (17). A schematic relationship among coordinate systems for generation of the modified VTT hob is shown in Fig. 3. Coordinate systems S7(x7,y7,z7), Sp(xp,yp,zp), and Sq(xq,yq,zq) are rigidly connected to the rack cutter, hob, and frame, respectively", " When Case A is compared with Case B under the axial assembly errors, the contact point locations and contact ellipse distributions of the crowned gear generated by the proposed VTT hob with a hob diagonal feed (Case B) are much better than those of Case A. 3. Gear assembly misalignments will result in the contact zone of the gear pair shifted longitudinally. 4. When the gear pairs of Cases A and B are meshed under assembly error conditions, their transmission errors are still very small, since the work gears of both Cases A and B are crowned. This example investigates the influence of hob's profile modification coefficient d (expressed in Eq. (1) and Fig. 2) on the tooth contact ellipses and paths of the generated work pairs. The basic parameters for the gear sets are the same as those given in Example 1. Some additional basic coefficient parameters are shown in Table 3. There are three sets (Cases C, D, and E) of tooth profile modification coefficient d that apply to the generation of the crowned helical gear 2. The simulated contact ellipses and contact paths on gear 3 with vertical misaligned angle (\u0394\u03b3v = 0.1\u00b0) for these three cases are shown in Figs. 14\u201316, respectively. Comparing Figs. 14\u201316 reveals that the increase of tooth profile modification coefficient d will cause the contact point distribution to tend to the lead direction, and it can easily cause an edge contact in the presence of assembly errors. It is noted that the VTT hob in Case C is the hob without profile modification (i.e., d = 0 mm in Table 3 and also refer to Fig. 2) developed by Hsu and Fong [8]. The transmission errors of Case C show a jump contact condition which may induce a higher level of noise during the gear pair meshing. It is found that the transmission errors of Case D and Case E are much better than that of Case C with vertical misaligned angle assembly errors on gear drives. Therefore, a properly chosen smaller value of hob's modification coefficient d is very important. This study presents the mathematical models for the crowned work gears that are generated by a modified profile of VTT hob and by a conventional hob, respectively", " mjki module, j = b, o, p; k = t, n; i = 1, 2, 3. Ni number of teeth, i = 1, 2, 3. Eo operating center distance \u03b1jki pressure angle, j = b, o, p; k = t, n; i = 1, 2, 3. rjki radius of the cylinder, j = b, o, p; k = t, n; i = 1, 2,3. a center distance variation coefficient (refer to Eq. (15) and Fig. 4) b hob normal tooth thickness variation coefficient (refer to Eq. (4) and Fig. 1) c hob diagonal shifting coefficient (refer to Eq. (10) and Fig. 4) d tooth profile modification coefficient (refer to Eq. (1) and Fig. 2) subscripts n measured in the normal section t measured in the transverse section o operating pitch circle p pitch circle 1 hob 2 proposed work gear 3 standard involute gear The authors are grateful to the National Science Council of the R.O.C. for financial support. Part of this work was performed under Contract No. 101-2218-E-035-010. [1] F.L. Litvin, Gear Geometry and Applied Theory, PTR Prentice Hall, Englewood Cliffs, NJ, 1994. 412\u2013468. [2] J. Abler, et al., Gear Cutting Technology: Practice Handbook, Liebherr-Verzahntechnik GmbH, Kempten, 2004" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003535_j.mechmachtheory.2021.104436-Figure10-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003535_j.mechmachtheory.2021.104436-Figure10-1.png", "caption": "Fig. 10. Configuration principle and kinematic model of PES-group.", "texts": [ " The PES-group has the same motion and constraint performance as the PB-group. Based on Tables 1 and 2, it can be easily analyzed that PES-groups 2-UR [RRR] and UR [RRR]&UP [RRR] composed of pure PES-limbs can control the position of O2 exclusively, but not affect the orientation of moving platform. Thus, these PES-groups are defined as \u2019pure PES-groups\u2019. The groups UR [RRR]&UR [RR], UR [RRR]&URR, UR [RRR]&UP [RR] and UR [RRR]&UPR are composed of pure PES-limb UR [RRR] with other PES-limbs, which is shown in Fig. 10. Their 2 inputs determine the position of O2. However, when the 2 driving links are locked, PES-groups UR [RRR]&UR [RR] and UR [RRR]&UP [RR] still constrain 1 rotational DOF of the moving platform around O2, and PES-groups UR [RRR]&URR and UR [RRR]&UPR restrict 2 rotational DOFs of the moving platform around O2. In order to further quantitatively study their kinematic performance, the 6 PES-groups above were analyzed as examples. For the limited length of the paper, Fig. 10 only shows 4 PES-groups with more complex kinematics, which are groups UR [RRR]&UR [RR], UR [RRR]&URR, UR [RRR]&UP [RR] and UR [RRR]&UPR. As shown in Fig. 10, when 2 PES-limbs are combined, their lines O1O2 must coincide, and their v-planes are required to be perpendicular to each other. The origin of the fixed coordinate system (system {1}) coincides with O1. The x1 axis is located on the vplane of limb UR [RRR], the z1 axis is perpendicular upward to the base platform. Thus the y1 axis lies in the v-plane of the other limb. The origin of the moving coordinate system (system {2}) coincides with O2. The z2 axis coincides with axis O2E1, which is perpendicular upward to the moving platform. The y2 axis coincides with another rotating axis (O2D2 for Fig. 10(a); O2C3 for Fig. 10(b); O2D5 for Fig. 10(c); O2C6 for Fig. 10(d)) of the moving platform. The x2 axis is determined by the right-hand rule, so it is not marked in Fig. 10. The ai represents the vector of the driving link ai in the system {1}, (i=1, 2, 3, 4, 5, 6). The joint angles \u03b81 and \u03b82 between the 2 driving links of PES-group and the base platform are input parameters of the PES-group. The angle \u03b821 between the axis O1B1 and x1 is equal to the input angle \u03b82. The angle between the axis O1B (O1B2 for Fig. 10(a); O1B3 for Fig. 10(b); O1B4 for Fig. 10(c); O1B5 for Fig. 10 (d)) of the other limb and the y1 axis is \u03b811, which is equal to the input angle \u03b81. As shown in Fig. 10(a) and (b), the coordinates of 2 vectors a1 and ai (i=1, 2, 3) of the groups 2-UR [RRR], UR [RRR]&UR [RR] and UR [RRR]&URR in the system {1} are expressed as { a1 = ( cos\u03b82, 0, sin\u03b82 ) ai = ( 0, cos\u03b81, sin\u03b81 ) (10) As shown in Fig. 10(c) and (d), the coordinates of 2 vectors a1 and ai (i=4, 5, 6) of the groups UR [RRR]&UP [RRR], UR [RRR]&UP [RR] and UR [RRR]&UPR in the system {1} are expressed as { a1 = ( cos\u03b82, 0, sin\u03b82 ) ai = ( \u2212 sin\u03b81, cos\u03b81, 0 ) (11) The position of O2 in the base platform is only determined based on PES-group input parameters. The O2 coordinates in the system {1} are expressed as (m1, m2, m3) by rectangular coordinates. In fact, there are many ways to represent it, such as cylindrical and spherical coordinates", " The coordinates of the z2 axis (O2E1) of moving platform are set to (n1, n2, n3) in the system {1}, which are the crucial intermediate variable for establishing the relationship between the orientation parameters and input parameters. Thus, the coordinate parameters n1, n2, and n3 are defined as \u2019orientation solution intermediate parameters\u2019 of PES-group, which are expressed by \u2019OSI parameters\u2019. The equations describing the relationship between the OSI parameters (n1/n2/n3) and the orientation parameters (\u03b12/\u03b22/\u03b32) of moving platform are defined as \u2019orientation solution intermediate equations\u2019 of PES-group, which are represented by \u2019OSI equations\u2019. As shown in Fig. 10 (a), the posture transformation of the moving platform of PES-group UR [RRR]&UR [RR] is described as: 1). The system {1} rotates \u03b11 around its x1 axis to transform to the system {11}, so that the y11 axis coincides with O1B2. (In this case, the y11 axis is perpendicular to both O1O2 and z11 axis). 2). The system {11} rotates \u03b21 around its y11 axis to transform to the system {12}, so that the z12 axis coincides with O1O2. (In this case, the y12 axis is parallel to O2C2). 3) The system {12} translates a distance l along its z12 axis to transform to the system {13}, so that its coordinate origin coincides with O2", " Mechanism and Machine Theory 166 (2021) 104436 Because the coordinates of the z2 axis in the system {1} is (n1, n2, n3), it can be derived: 1 \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 n2 1 + n2 2 + n2 3 \u221a [n1, n2, n3, 0]T = Rot(x, \u03b11) Rot(y, \u03b21) Tran(0, 0, l) Rot(y, \u03b12) Rot ( z, \u03c0 2 ) Rot(y, \u03b22) [0, 0, 1, 0]T = [cos\u03b22sin(\u03b12 + \u03b21), cos\u03b11sin\u03b22 \u2212 cos\u03b22sin\u03b11cos(\u03b12 + \u03b21), sin\u03b11sin\u03b22 + cos\u03b22cos\u03b11cos(\u03b12 + \u03b21), 0]T After further calculation, the OSI equations of PES-group UR [RRR]&UR [RR] can be obtained as follows: The OSI parameters (n1/n2/n3) are expressed by the position parameters (\u03b11/\u03b21) and orientation parameters (\u03b12/\u03b22) as \u23a7 \u23aa \u23aa\u23a8 \u23aa \u23aa\u23a9 n2 n1 = tan\u03b22cos\u03b11 \u2212 cos(\u03b12 + \u03b21) sin\u03b11 sin(\u03b12 + \u03b21) n3 n1 = tan\u03b22sin\u03b11 + cos(\u03b12 + \u03b21) cos\u03b11 sin(\u03b12 + \u03b21) (19a) Eq. (16b) is substituted for Eq. (19a) and simplified. The orientation parameters (\u03b12/\u03b22) can be expressed by the input parameters (\u03b81/\u03b82) and OSI parameters (n1/n2/n3) as \u23a7 \u23aa \u23aa \u23a8 \u23aa \u23aa \u23a9 \u03b12 = arctan(tan\u03b82cos\u03b81) + arctan ( n1 n3cos\u03b81 \u2212 n2sin\u03b81 ) \u03b22 = arctan \u239b \u239c \u239d n2cos\u03b81 + n3sin\u03b81 \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\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 (n3cos\u03b81 \u2212 n2sin\u03b81) 2 + n2 1 \u221a \u239e \u239f \u23a0 (19b) As shown in Fig. 10 (b), the posture transformation of the moving platform of PES-group UR [RRR]&URR is described as: 1). The fixed coordinate system {1} rotates \u03b11 around its x1 axis to transform to system {11}, so that the y11 axis coincides with O1B3. 2). The system {11} rotates \u03b21 around its y11 axis to transform to system {12}, so that the z12 axis coincides with O1O2. 3) The system {12} translates a distance l along its z12 axis to transform to the system {13}, so that its coordinate origin coincides with O2", " The transformation matrix from the system {1} to system {2} in the PES-group UR [RRR]&URR can be written as T13 = Rot(x, \u03b11) Rot(y, \u03b21) Tran(0, 0, l) Rot(y, \u03b12) (20) According to the coordinates of the z2 axis in the system {1} is (n1, n2, n3), it can be derived: 1 \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 n2 1 + n2 2 + n2 3 \u221a [n1, n2, n3, 0]T = Rot(x, \u03b11) Rot(y, \u03b21) Tran(0, 0, l) Rot(y, \u03b12) [0, 0, 1, 0]T = [sin(\u03b12 + \u03b21) , \u2212 sin\u03b11cos(\u03b12 + \u03b21) , cos\u03b11cos(\u03b12 + \u03b21) , 0]T By further calculation, the OSI equations of PES-group UR [RRR]&URR can be obtained as follows: The OSI parameters (n1/n2/n3) are expressed by the position parameters (\u03b11/\u03b21) and orientation parameters \u03b12 as \u23a7 \u23aa \u23a8 \u23aa \u23a9 n2 n1 = \u2212 sin\u03b11 tan(\u03b12 + \u03b21) n3 n1 = cos\u03b11 tan(\u03b12 + \u03b21) (21a) Eq. (16b) is substituted for Eq. (21a) and simplified. The orientation parameters \u03b12 can be expressed by the input parameters (\u03b81/\u03b82) and OSI parameters (n1/n2/n3) as { \u03b12 = arctan(tan\u03b82cos\u03b81)+ arctan ( n1 \u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305 n2 2 + n2 3 \u221a ) (21b) As shown in Fig. 10 (c), the posture transformation of the moving platform of PES-group UR [RRR]&UP [RR] is described as: 1). The fixed coordinate system {1} rotates \u03b11 around its z1 axis to transform to the system {11}, so that y11 axis coincides with O1B5. 2). The system {11} rotates \u03b21 around its y11 axis to transform to the system {12}, so that z12 axis coincides with O1O2. 3) The system {12} translates a distance l along its z12 axis to transform to the system {13}, so that its coordinate origin coincides with O2", " Mechanism and Machine Theory 166 (2021) 104436 Because the coordinates of the z2 axis in the system {1} is (n1, n2, n3), it can be derived: 1 \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 n2 1 + n2 2 + n2 3 \u221a [n1, n2, n3, 0]T = Rot(z, \u03b11) Rot(y, \u03b21) Tran(0, 0, l) Rot(y, \u03b12) Rot ( z, \u03c0 2 ) Rot ( y, \u03b22 ) [0, 0, 1, 0]T = [cos\u03b22cos\u03b11sin(\u03b12 + \u03b21) \u2212 sin\u03b11sin\u03b22 , cos\u03b22sin\u03b11sin(\u03b12 + \u03b21) + cos\u03b11sin\u03b22 , cos\u03b22cos(\u03b12 + \u03b21) , 0]T After further calculation, the OSI equations of PES-group UR [RRR]&UP [RR] can be obtained as follows: The OSI parameters (n1/n2/n3) are expressed by the position parameters (\u03b11/\u03b21) and orientation parameters (\u03b12/\u03b22) as \u23a7 \u23aa \u23aa\u23a8 \u23aa \u23aa\u23a9 n1 n3 = sin(\u03b12 + \u03b21) cos\u03b11 \u2212 tan\u03b22sin\u03b11 cos(\u03b12 + \u03b21) n2 n3 = sin(\u03b12 + \u03b21) sin\u03b11 + tan\u03b22cos\u03b11 cos(\u03b12 + \u03b21) (23a) Eq. (17b) is substituted for Eq. (23a) and simplified. The orientation parameters (\u03b12/\u03b22) can be expressed by the input parameters (\u03b81/\u03b82) and OSI parameters (n1/n2/n3) as \u23a7 \u23aa \u23aa \u23a8 \u23aa \u23aa \u23a9 \u03b12 = arctan ( tan\u03b82 cos\u03b81 ) + arctan ( n1 n3 cos\u03b81 + n2 n3 sin\u03b81 ) \u03b22 = arctan \u239b \u239c \u239d n2cos\u03b81 \u2212 n1sin\u03b81 \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\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 (n1cos\u03b81 + n2sin\u03b81) 2 + n2 3 \u221a \u239e \u239f \u23a0 (23b) As shown in Fig. 10 (d), the posture transformation of the moving platform of PES-group UR [RRR]&UPR is described as: 1). The fixed coordinate system {1} rotates \u03b11 around its z1 axis to transform to the system {11}, so that the y11 axis coincides with O1B6. 2). The system {11} rotates \u03b21 around its y11 axis to transform to the system {12}, so that the z12 axis coincides with O1O2. 3) The system {12} translates a distance l along its z12 axis to transform to the system {13}, so that its coordinate origin coincides with O2", " The mechanism UR [RRR]&URR&SR [RR] is composed of PES-group UR [RRR]&URR and OES-limb SR [RR], and its transformation matrix TU1R is shown in Eq. (20). The mechanism UR [RRR]&UPR&SR [RR] is composed of PES-group UR [RRR]&UPR and OES-limb SR [RR], and its transformation matrix TU2R is shown in Eq. (24). The third kinematic analysis method is used to analyze the kinematic performances of 2 GSPMs. The angle between the v-planes of limbs SR [RR] and UR [RRR] is set as 180\u25e6. The input parameters (\u03b81/\u03b82) of PES-groups UR [RRR]&URR and UR [RRR]&UPR are shown in Fig. 10(b) and (d), respectively. The input parameter \u03b83 of the limb SR [RR] is the angle between the driving link a8 and the x1 axis negative direction of the fixed coordinate system, so the coordinates of vector a8 in the fixed coordinate system are (\u2014cos\u03b83, 0, sin\u03b83). Based on the basic properties of the limbs URR, UPR and SR [RR], these 3 limb driving links (a3 for Fig. 10(b); a6 for Fig. 10(d); a8 for Fig. 17) are perpendicular to the z2 axis of the moving coordinate system. Thus, the OSI parameters (n1/n2/n3) can be easily calculated as \u23a7 \u23a8 \u23a9 n1 = cos\u03b81sin\u03b83 n2 = \u2212 sin\u03b81cos\u03b83 n3 = cos\u03b81cos\u03b83 (49) \u23a7 \u23a8 \u23a9 n1 = cos\u03b81sin\u03b83 n2 = sin\u03b81sin\u03b83 n3 = cos\u03b81cos\u03b83 (50) Eqs. (46) and (47) being substituted into the OSI equations (21) and (25) respectively, the complete orientation kinematics of mechanisms UR [RRR]&URR&SR [RR] and UR [RRR]&UPR&SR [RR] can be obtained as \u03b12 = arctan(tan\u03b82cos\u03b81) + arctan(tan\u03b83cos\u03b81) \u21d4 \u03b83 = arctan ( tan(\u03b21 + \u03b12) cos\u03b11 ) (51) \u03b12 = arctan ( tan\u03b82 cos\u03b81 ) + arctan ( tan\u03b83 cos\u03b81 ) \u21d4 \u03b83 = arctan[tan(\u03b21 + \u03b12)cos\u03b11] (52) Obviously, 2 3-DOF GSPMs above have the same transformation matrices as the series mechanisms U1R and U2R" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002872_j.msea.2020.140099-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002872_j.msea.2020.140099-Figure1-1.png", "caption": "Fig. 1. (a) Selected laser scanning strategies; (b) Tensile model and specimens.", "texts": [ " The prepared powder mixture was stored in a sealed bag under vacuum for subsequent SLM. A renishaw AM 400 was used to build 10 mm cubes on stainless steel substrates at the layer thickness of 50 \u03bcm. The preheating temperature was 80 \u25e6C. The forming chamber was first evacuated to less than 10\u2212 4 Pa and then high purity argon (\u226599.999%) was introduced at the flow rate of 1.8 m/s as the protective gas. Laser power of 180 W and point exposure time of 110 \u03bcs were employed. The laser scan strategy was shown in Fig. 1(a). The hatching was rotated by 67\u25e6 in each layer prior to next exposure. The samples were removed from the stainless steel substrate after fabrication by wire cutting along the direction perpendicular to building direction. Samples for phase and microstructure characterization were ground and polished following standard procedures. They were etched using a mixed acid solution consisting of 15 ml HCl, 10 ml HNO3 and 10 ml CH3COOH. The phase constitution was analyzed by X-ray diffraction (XRD, RIGAKU D/max-RB)", " Electron backscatter diffraction (EBSD) was used to analyze the as-formed grain structure on a Hitachi S-3400 N SEM equipped with a HKL-EBSD system. The interface between the Gr and Inconel 625 in the samples were characterized using transmission electron microscope (TEM, JEM-F200) with an accelerating voltage of 200 kV. Vickers micro-hardness was measured using a microhardness tester (HVS-1000) at the applied load of 0.2 kg with a residence time of 15 s. The tensile samples were machined from the as-built coupons and are shown in Fig. 1(b). Tensile testing was carried out on an Instron 3382 universal tensile testing machine at a strain rate of 0.5 mm/min at room temperature. Three tensile tests were conducted for each sample X. Li et al. Materials Science & Engineering A 798 (2020) 140099 condition. The friction and wear properties were measured using an MFT-4000 friction tester (MFT-4000, Huahui, China). The coefficient of friction (COF) of each sample was recorded during wear test. Friction testing followed the ASTM G76 standard and was conducted at room temperature, under an applied normal load of 30 N, a friction speed of 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003479_0954407021999483-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003479_0954407021999483-Figure7-1.png", "caption": "Figure 7. The third-order radial mode shapes for a load of 2000 N for: (a) phase 1 (116.21 Hz) and (b) phase 2 (120.47 Hz).", "texts": [ " Tire road constraints are added, and the load is settled as 2000N, the first 6-order natural frequencies of the tire in the radial direction are shown in Table 1. It can be seen from Table 1 that when the tire is under load, the frequency values at the heavy roots mentioned in the previous section show a big and a small difference, and the degree of differentiation increases with the increase of the order. In order to compare with the no-load mode shape in the previous section, this section still takes the radial third-order modal shape as an example, and the modal vibration mode of the tire under 2000N load is shown in Figure 7. Figure 7 shows that when the tire is in the load state, compared with the tire without load, not only the vibration frequency of the tire has a big and a small differentiation, but also the phase of the tire modal shape has changed. For the convenience of research, the following takes the radial increase frequency as the research object to conduct a comparative study of the vibration frequency under different loads of 2000N, 3000N, 4000N, and 5000N. The results are shown in Figure 8. It can be seen from Figure 8 that with the increase of tire load, the frequency of tire radial increase gradually increases" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002022_978-3-319-40036-5-Figure8.2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002022_978-3-319-40036-5-Figure8.2-1.png", "caption": "Fig. 8.2 (A) (a) Schematic of microfluidic multi-electrode array (MMEA) device showing the different layers. (b) Photograph of MMEA during operation. [20]. (B) Schematic of device developed by Mauleon et al. (a) perfusion chamber having gas inlet and outlet. (b) different parts of the device: the perfusion chamber, the PDMS membrane, the PDMS microfluidic channel, and a glass slide and the alignment marks show how the gas is supplied to the device (c) top view of device [21]", "texts": [ " The separation of brain tissue specimens under in vitro conditions is a very complicated task as it requires exquisite control over experimental conditions and access to neural networks and synapses [19]. Scott et al. designed a MF chip for simultaneous recording of electrical signals and optical characterization of brain tissue slice preparations [20]. The device was utilized to record waves of spontaneous activity in developing cortical slices and to perform multisite extracellular recordings during simultaneous calcium imaging of activity. The device consists of an array of MF channels and a perfusion chamber (Fig. 8.2A). Each channel consists a well at one end, an aperture which is in contact with the perfusion chamber in the middle, and pressure and electronic controls at the other end is connected to port. The apertures are 20 or 50 \u03bcm in diameter with a spacing of 300 \u03bcm and are designed to probe an array of anatomically relevant sites. The relatively large aperture size and spacing were chosen because they are appropriate for the anatomical features in the particular study. The work paved a way to develop devices of different geometric configurations for other studies also", " The use of microchips may overcome the limitations of reduced oxygen and nutrient supply while using conventional interface and submerged slice chambers to the brain slices allow the neuroscientists to design complex experiments to have a better insight into neuroprocesses [15]. Mauleon et al. developed an MF system that allows diffusion of oxygen throughout a thin membrane and directly to the brain 196 S. Solanki and C.M. Pandey slice via MF gas channels [21]. The device consists of four independent parts: the perfusion chamber, the PDMS layer, the PDMS MF channel, and a glass slide (Fig. 8.2B). The designed microchannel provides rapid and efficient control of oxygen and can be further modified accordingly to allow the various regions of the slice to experience different oxygen conditions. Using this novel device, stable and homogeneous oxygen environment throughout the brain slice has been obtained, and the oxygen tension in a hippocampal slice can be altered rapidly. It was observed that the device allows more complete temporal control and can reach greater differences in oxygen concentration as compared to the standard perfusion method" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001330_amr.1020.66-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001330_amr.1020.66-Figure1-1.png", "caption": "Figure 1. Deformation in shear zone of reinforcement bar:", "texts": [ " Application of oscillation shaping compared to roller and drum shaping provided the following: increase the quality of shaping, make the service life of compression elements times longer, reduce drawing force and torque, reduce additional time used for filling and setting, make higher use of rated capacity due to simultaneous drawing of several bars, increase productivity per unit of equipment and per one worker, simplifying maintenance of filling tools and make work of machine operators easier, etc. Rotating knives, cutting the bar operate similar to parallel ones (figure 1) causing shearing stresses in the shear zone. Unlike parallel knives rotating ones access the bar at an angle and during cutting also turn at some angle. Due to this the knife which accesses the bar by the back edge demonstrates lower cutting force and lateral thrust force higher compared to the other one, which penetrates the bar much less. The rate of specific cutting forces for the knives is equal to 0.8\u20261.0. The experiments demonstrate that the cutting force, lateral force values, their rates, dependence of properties of steel cut by them as well as ( )\u03b3rez fP = ; ( )dfP \u03b4rez = for the discussed knives are the same as for parallel ones" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001723_s00170-015-7481-8-Figure12-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001723_s00170-015-7481-8-Figure12-1.png", "caption": "Fig. 12 Schematic of the top view of the interactions between powder flow and molten pool", "texts": [ " Referring to the deposition layer formation model in the previous study [20], the deposition height can be defined as the height of mid-longitudinal section of the deposition layer profile. Substituting the powder flow distribution obtained in this study (instead of the uniform powder distribution) into the deposition layer formation model in literature [20], and considering the obtained powders amount within the length of the molten pool along mid-longitudinal cross-section, the height of mid-point (deposition height) hc can be defined as hc \u00bc 1 \u03c1p Z B A vpc X ; 0; S\u00f0 \u00de dX vb \u00f023\u00de As shown in Fig. 12, (A,0,S) and (B,0,S) are the front end and back end of the molten pool, respectively. It can be obtained as A=\u22121.26 and B=0.86 with the processing parameters of laser power P=1850W, laser scan speed vb=5 mm s\u22121, powder feed rate mp=0.088 g s\u22121, and spot diameter Db= 2.5 mm (referring to literature [20]). So the layer height can be calculated from Eqs. (21) and (23). Figure 13 shows the calculated deposition layer height versus the distance between deposited surface and powder nozzle exit plane. It can be seen that the deposited layer height increases rapidly at first and then decreases slowly with the increase of the distance between the deposited surface and the nozzle exit plane" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001821_iet-epa.2016.0543-Figure9-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001821_iet-epa.2016.0543-Figure9-1.png", "caption": "Fig. 9 Experimental test equipment", "texts": [ " It should be mentioned that the simulation was not including also the start-up period due to the required very long simulation time. To validate the simulated results several experimental measurements were performed. The control algorithms were implemented into IET Electr. Power Appl., 2017, Vol. 11, Iss. 4, pp. 548\u2013556 & The Institution of Engineering and Technology 2017 Digital Signal Controller MC56F8346 from Freescale, which was used for the inverter control board. The experimental test equipment is shown in Fig. 9. The waveforms of the currents and torque of the healthy and one open phase condition were measured for the proposed current profiling control method. The speed was kept constant at 100 rpm by a dynamometer with power of 330 kW. To verify this method in a best way, a minimal speed ripple has to be achieved. This is the reason of using a dynamometer with very high moment of inertia (J = 1.9 kgm2). In Fig. 10a, there are depicted the phase currents for healthy SRM and SRM with one open phase. The total torque for these two conditions can be seen in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003608_s11665-021-05603-9-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003608_s11665-021-05603-9-Figure3-1.png", "caption": "Fig. 3 SP testing fixture mounted on the test machine with the extensometer for punch displacement measurement", "texts": [ " The combination of the rod and ball constitute the punch, which is driven through the specimen, encapsulated between the upper and lower die. The fixture is shown in Fig. 2 in both disassembled (a) and assembled (b) form. The fixture was mounted on a universal electro-mechanical test machine, equipped with a 5 kN capacity load cell and an extensometer. The extensometer was attached to one of the columns of the machine in order to measure the relative displacement between the machine actuator and the machine frame, in close proximity to the punch. Figure 3 shows the fixture mounted on the test machine and the positioning of the extensometer with respect to the machine actuator. All tests were performed at room temperature (21 C \u00b1 2 C) in actuator displacement control, at rates between 0.001 mm/s and 0.003 mm/s. Force, actuator displacement, and punch displacement (extensometer) data were recorded at a sampling frequency of 1 Hz. To account for the compliance of the test system on punch displacement, actuator and extensometer displacements were recorded without a specimen in place, and then subtracted from displacements measured during the tests" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003603_jestpe.2021.3065997-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003603_jestpe.2021.3065997-Figure3-1.png", "caption": "Fig. 3. (a) cross view of a spoke array rotor. (b) Rotor of the spoke array rotor with claw plates.", "texts": [ " The N-pole and S-pole are engaged with each other and the tangential excited permanent magnets are sandwiched between Authorized licensed use limited to: University of Technology Sydney. Downloaded on May 20,2021 at 04:22:13 UTC from IEEE Xplore. Restrictions apply. 2168-6777 (c) 2021 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. them. Its magnetic path is equivalent to a conventional spoke array rotor with plates on both ends. The basic idea of the machine can be revealed by Fig. 3. For convenience, the claw guiding flux out to the stator is defined as N-claws and other claws are S-claws. Unlike the traditional spoke array rotor, all the N-claws in the proposed topology are connected to the N-plate and it is the same for S-claws to S-plate. So, apart from the conventional magnetic path in the spoke array rotor, the claw plates provide an extra path for the other magnetic field harmonics. B.Working principle of the machine In the traditional claw-pole machine, the flux starts from the N-pole of PMs mounted on rotor claws" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003090_j.mechmachtheory.2020.104045-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003090_j.mechmachtheory.2020.104045-Figure5-1.png", "caption": "Fig. 5. (a) Distance along line of contact [26] . (b) Load sharing factor smooth mesh [26] . (c) Load sharing factor unmodified mesh [26] and (d) Load sharing factor high load carrying capacity [26] .", "texts": [ "30GHz frequency with 4 GB RAM was used on Windows 10 pro operating system to perform all the programming in MATLAB. Running simulations were done for approximately 1 h with scuffing constraint for one oil and one profile. However, without scuffing constraint, the time period was about half an hour. 5. Gear tooth profile To compute the gear tooths flash temperature, which has been used for the calculation of the probability of scuffing failure, one of the main requirement is to calculate the load sharing factor. All the three types of gear tooth profiles given in AGMA [26] are tested in this study. Fig. 5 (a) demonstrates the various distances along the line of contact for meshing gears. The highest and lowest points of tooth pair contact (HPSTC & LPSTC) are designated by distances CD and CB respectively. Distances CE and CA are the pinion end and start of the active profile (EAP & SAP) respectively. CF is the distance between two mating gear base circles, whereas CC is the operating pitch point distance. 5.1. Smooth meshing profile The variation in load sharing factor along the line of contact is given in Fig. 5 (b). The load sharing factors for the smooth meshing gear profile are given by the Eqs. (29) , (29a) and (29b) ; \u03be is the roll angle of pinion at any arbitrary point along the line of contact (i.e. from A to E). X (i ) = ( \u03be(i ) \u2212 \u03beA \u03beB \u2212 \u03beA ) f or \u03beA \u2264 \u03be(i ) < \u03beB (29) X (i ) = 1 f or \u03beB \u2264 \u03be(i ) < \u03beD (29a) X (i ) = ( \u03beE \u2212 \u03be(i ) \u03beE \u2212 \u03beD ) f or \u03beD \u2264 \u03be(i ) < \u03beE (29b) 5.2. Unmodified tooth profile The load sharing factors for the unmodified profile are given by the Eqs. (30) , (30a) and (30b) . Fig. 5 (c) show the graphic representation of load sharing factor for such a profile. X (i ) = 1 3 + 1 3 ( \u03be(i ) \u2212 \u03beA \u03beB \u2212 \u03beA ) f or \u03beA \u2264 \u03be(i ) < \u03beB (30) X (i ) = 1 f or \u03beB \u2264 \u03be(i ) < \u03beD (30a) X (i ) = 1 3 + 1 3 ( \u03beE \u2212 \u03be(i ) \u03beE \u2212 \u03beD ) f or \u03beD \u2264 \u03be(i ) < \u03beE (30b) 5.3. High load capacity tooth profile The graphic representation of this gear tooth profile, with pinion as driver, is shown in Fig. 5 (d). Eqs. (31) , (31a) and (31b) show the load sharing factors X ( i ) at any point of contact. MOO results were compared with the industrial gearbox provided in the AGMA standard [27] . This comparison was carried out for three different gear profiles such as, smooth meshing tooth profile (S), unmodified tooth profile (U), and high load capacity tooth profile (H). The oil used in the industrial gearbox was ISO VG 220 and the oil sump temperature was 95 \u25e6 C. The same oil and oil sump temperature were used in all the simulations" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000990_j.mechmachtheory.2013.05.006-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000990_j.mechmachtheory.2013.05.006-Figure1-1.png", "caption": "Fig. 1. Model of cylindrical roller bearing with external loads.", "texts": [ " The quasi-static analysis method uses raceway control theory [18]. Its computing accuracy is inadequate for high speed bearing analysis. Compared with other methods, the quasi-dynamic analysis method provides better calculating accuracy and efficiency, and it is widely used in practice [19]. In quasi-dynamic analysis model of bearings with external loads, distribution of internal loads is calculated based on equilibrium between external and internal loads and compatibility between relative displacement of inner and outer rings and deformation of rollers. Fig. 1 shows the model of cylindrical roller bearings with external loads and coordinate systems. OXYZ and O2X2Y2Z2 are coordinate systems of the fixed outer ring and the inner ring respectively. When external loads Fy Fz My Mz\u00bd are applied on the inner ring, relative displacement between inner and outer rings is \u0394y \u0394z \u03b8y \u03b8z\u00bd . Transformation matrix from the coordinate of the inner ring to the fixed coordinate of the outer ring is represented with relative angle between inner and out rings: Tir \u00bc cos \u03b8y 0 sin \u03b8y 0 1 0 \u2212 sin \u03b8y 0 cos \u03b8y 2 4 3 5 cos \u03b8z sin \u03b8z 0 \u2212 sin \u03b8z cos \u03b8z 0 0 0 1 2 4 3 5 \u00bc cos \u03b8y cos \u03b8z cos \u03b8y sin \u03b8z sin \u03b8y \u2212 sin\u03b8z cos \u03b8z 0 \u2212 sin \u03b8y cos \u03b8z \u2212 sin \u03b8y sin \u03b8z cos \u03b8y 2 4 3 5 \u00f01\u00de The transformation from fixed coordinate OXYZ to jth roller coordinate system objxajyajzaj is shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000259_j.cirp.2010.03.020-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000259_j.cirp.2010.03.020-Figure4-1.png", "caption": "Fig. 4. The 5-axis serial-type machine tool: the plane stiffness problem.", "texts": [ " At each height, surface jmin = jmin(xp, yp) is cut off at a level of jmin = 0.5. The areas lying in truncation planes satisfy requirement jmin 0.5 and show the sections of the TSV allowable working volume [V]tr. A vertical milling centre with double pivot spindle head is the typical representative of the 5-axis serial kinematics machine tools. Compliance of the drive systems and bending of the column present dominant compliance sources. For simplicity, the planar static problem is considered (Fig. 4). The minimal dimensionless TSV jmin = (ktr)min/kact, resulting in maximum load-induced dis- placement of the tool relative to the workpiece, takes place when three compliance values are added together: jmin \u00bc 1\u00fe H2kact krot \u00femkact km ! 1 ; with m \u00bc L3 3c pL\u00f0L c p\u00de \u00fe 3L\u00f0L 2c p\u00de\u00f0bPPz=Py bGGz=Py\u00de L3 m where kact is the stiffness value of the Y-axis translational servomotor considered as a tension-compression spring; krot is the stiffness value of the X-tilting drive considered as a torsion spring acting on the arm H; km = 3EI/(Lm)3 is the compliance value associated with the displacement of the column as a cantilever beam C0C (Fig. 4) when the milling head is located at the mean height Lm; and m is the dimensionless factor depending on structural dimensions in the desired configuration and the ratios of the active forces G/Py and Pz/Py. Numerical example. Structural dimensions: z0 = 400 mm, cP = 600 mm, bP = 500 mm, bG = 370 mm, Lm = 1050 mm, and H = 300 mm. Relations of the forces G/Py = 2.5 and Pz/Py = 0.4 (face milling). The stiffness values of the translational drives is kact = 2.5 107 N/m and stiffness of the column is km = 2" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003040_j.mechmachtheory.2020.103837-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003040_j.mechmachtheory.2020.103837-Figure1-1.png", "caption": "Fig. 1. Exechon hybrid manipulator. (a) CAD model of the Exechon hybrid manipulator. (b) Sketch of the Exechon hybrid manipulator.", "texts": [ " It is well-known that the Exechon PM(2UPR + SPR PM) has two rotational and one translational DOFs, when the RR-type SM is added onto the moving platform of the 2UPR + SPR PM, the mobility of the whole manipulator is 5. However, its explicit DOF property has been ignored in the previous works. In fact, there is a very interesting phenomenon that the terminal constraint of the whole hybrid manipulator is neither a pure constraint force nor a pure constraint torque as it has been commonly considered. The terminal constraint and mobility of the Exechon hybrid manipulator will be analyzed in what follows. Fig. 1 shows the schematic diagram of the Exechon hybrid manipulator which includes a 2UPR + SPR PM connected in series with a RR-type SM. The 2UPR + SPR PM (see Fig. 1 ) comprises a base n 0 , a moving platform n 1 , two identical U P Rtype limbs r i ( i = 1, 3) and one S P R-type limb r 2 . n 0 is a regular triangle with O 0 as its center and A i ( i = 1, 2, 3) as its three vertices. n 1 is a regular triangle with O 1 as its center and B i ( i = 1, 2, 3) as its three vertices. The terms R, P, U, and S represent revolute, prismatic, universal, and spherical joints, respectively, and the underlined P denotes an actuated prismatic joint. Let R 1 ij ( i = 1, 2, 3; j = 1, 2,\u2026) be the j th R joint in the i th leg r i from bottom to top for the 2UPR + SPR PM", " The 2UPR + SPR PM has the following geometric constraints: R 1 i 1 | A 1 A 3 , R 1 i 1 \u22a5 R 1 i 2 , R 1 i 2 \u22a5 r i , R 1 i 2 \u2016 R 1 i 3 , R 1 i 3 \u2016 B 2 O 1 ( i = 1 , 3 ) , R 121 \u2016 B 1 B 3 , R 121 \u22a5 r 2 (1) The RR SM has the following geometric constraints: d | R 21 , R 21 \u22a5 n 1 , R 21 \u22a5 R 22 (2) Let { n i } be the coordinate system at O i ( i = 0 , 1 ) with X i \u2016 A i 1 A i 3 , Y i \u22a5 A i 1 A i 3 , Z i \u22a5 n i are satisfied. Let { n 2 } be the terminal coordinate system at the intersection point ( O 2 ) of R 21 and R 22 with X 2 | R 22 is satisfied (see Fig. 1 b). 2.1. Mobility composition principle Let $ 0 and $ r 0 be the motion and the constraint screw systems of the end-effector of the 5-DOF hybrid manipulators, respectively. Here, the superscript r denotes reciprocal operation for screw systems [26] . Let $ i and $ r i ( i = 1 , 2 ) be the sub motion and the sub constraint screw systems of the i th manipulator, respectively. Let $ r i j ( i = 1, 2) be the j th independent constraint of the i th manipulator, respectively. Let \u222a be the union and \u2229 be the intersection operation symbols, respectively", " The constraint screw system of the 2UPR + SPR PM can be constructed by selecting 3 independent constraint wrenches, which are shown in { n 0 } as following: S r 1 j = [ f T 1 j ( d 1 j \u00d7 f 1 j )T ] T , f 1 j = R 1 j1 , d 1 j = A 1 j \u2212 O 2 ( j = 1 , 2 , 3 ) (9) Where, f 1 j is the unit vector of the j th constraint force and d 1 j is the position vector from O 2 to any point on F p 1 j expressed in { n 0 }. 2.3. Constraint of the RR SM From the geometric rules for determining the constraint wrenches [2] , it can be determined that there are three constraint forces F p 2 i ( i = 1, 2, 3) which pass through the intersection of R 21 and R 22 , and one constraint torque T p 2 which is perpendicular to R 21 and R 22 in the RR-type leg. The intersection of R 21 and R 22 is the center of the terminal coordinate system O 2 (see Fig. 1 b). The three independent constraint forces can be seen as three arbitrary orthogonal forces passing through O 2 . Thus, the four constraint screws S r 2 j can be expressed in { n 0 } as follows: S r 21 = [ 1 0 0 0 0 0 ]T , S r 22 = [ 0 1 0 0 0 0 ]T , S r 23 = [ 0 0 1 0 0 0 ]T , S r 24 = [ 0 0 0 ( R 21 \u00d7 R 21 ) T ] T (10) where, R 21 and R 22 are the unit vectors of R 21 and R 22 expressed in { n 0 }. 2.4. Constraint analysis of the integrated hybrid manipulator GCA is a powerful tool which has been successfully used in the kinematics and singularity of SMs and PMs [33\u201336] " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000152_j.aca.2011.01.051-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000152_j.aca.2011.01.051-Figure3-1.png", "caption": "Fig. 3. Cyclic voltammograms of 1.0 \u00d7 10\u22124 mmol L\u22121 DA recorded at (a) CPE, (b) CILE, (c) graphene/CPE, and (d) IL-graphene/CPE. Electrolyte: pH 7.0 B\u2013R buffer solution.", "texts": [ "0 mmol L\u22121 [Fe(CN)6]3\u2212/4\u2212 recorded at (a) CPE, b) CILE, (c) graphene/CPE, and (d) IL-graphene/CPE. Electrolyte: 0.1 mol L\u22121 KCl. bility toward various substrates, were helpful for promoting the electrochemical signals [10]. Above experimental results exhibited the superiority of IL-graphene/CPE to CILE and graphene/CPE, and the potential of IL-graphene as a new generation of electrochemical sensing platform. 3.2. Direct electrochemistry of DA The comparison of the electrochemical activities of different kinds of carbon electrodes was also made with DA as the redox probe, as displayed in Fig. 3. The corresponding peak-to-peak separation ( Ep) was 0.52 V for CPE (curve a), 0.12 V for CILE (curve b), 0.15 V for graphene/CPE (curve c), and 0.09 V for IL-graphene/CPE (curve d), respectively. ILgraphene/CPE showed a quasi-reversible redox couple for DA. In addition, largest redox peak currents of DA at the IL-graphene/CPE (ipc = 2.431 \u00d7 10\u22125 A and ipa = \u22123.141 \u00d7 10\u22125 A) appeared as compared to CILE (ipc = 5.563 \u00d7 10\u22126 A and ipa = \u22127.947 \u00d7 10\u22126 A) and graphene/CPE (ipc = 1.067 \u00d7 10\u22125 A and ipa = \u22121" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000193_j.cma.2011.04.006-Figure13-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000193_j.cma.2011.04.006-Figure13-1.png", "caption": "Fig. 13. (a) Contact pattern and (b) function of transmission errors for case A2a (straight(A) whole-crowned(2) aligned(a) bevel gear drive).", "texts": [ " However, function of transmission errors is very sensitive to the axial displacement of the pinion (misaligned condition d) and the axial displacement of the gear (not shown in this paper), having in these cases lineal functions of transmission errors that are the source of high levels of noise and vibration of the gear drive. In order to absorb the lineal functions of transmission errors caused by errors of alignment in general and the axial displacements of pinion or gear in particular, Designs 2 and 3 (see Table 3) are proposed with whole-crowned and partial-crowned bevel gear tooth surfaces, respectively. Figs. 13 and 14 shows the contact patterns and the predesigned functions of transmission errors for cases A2a and A3a corresponding to a straight whole-crowned and aligned bevel gear drive (Fig. 13) and to a straight partialcrowned and aligned bevel gear drive (Fig. 14). Parabolic functions of transmission errors have been predesigned with levels of 8.5 arcsec for whole-crowned surfaces (Design 2) and 5.5 arcsec for partial-crowned surfaces (Design 3). Design 3 (partial-crowning) allows the contact pattern to cover a larger area of the bevel gear contacting surfaces, by creating an area of no modification of the tooth surfaces. The main advantage of this geometry is that the lower the misalignment is, the bigger the contact pattern is obtained, allowing contact stresses to be reduced" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001833_j.engfailanal.2017.04.017-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001833_j.engfailanal.2017.04.017-Figure7-1.png", "caption": "Fig. 7. Breakage case b with \u03b8b > (\u03c0/2\u2212 \u03b2b).", "texts": [ " 6(b) is the projection of involute arc B1B2 (shown in Fig. 6(a)) into plane of action and specified in simulation. In addition, for simplification, the projection of edge B2B3 of the breakage into plane of action is assumed to be a straight line. hb denotes the length of breakage along tooth width and tb the thickness. The variable \u03b8b represents the angle between the hypotenuse and the transverse section of tooth, indicating relative position between the hypotenuse and contact line. And there're two situations here (see Fig. 7). a) \u03b8b < (\u03c0/2\u2212 \u03b2b) In this case, the actual length la(t) of contact line with local breakage can be calculated by \u23a7 \u23a8\u23aa \u23a9\u23aa l t l t t t l v t \u03b5p w sin \u03b8 sin \u03c0 \u03b8 \u03b2 t t t t t t ( ) = ( ) \u2264 (t) \u2212 ( \u22c5 \u2212 ( \u2212 )) ( 2 \u2212 \u2212 ) < \u2264 0 < \u2264 a bs t b bs be be total t t bt b b b (29) where t \u03b5p w v= ( \u2212 ) tbs bt b (30a) t \u03b5p h \u03b2 v= ( \u2212 tan )b tbe bt b (30b) t \u03b5p v=total tbt (30c) \u03b8 arc h w= tan( ).b b b (30d) b) \u03b8b > (\u03c0/2 \u2212 \u03b2b) In this case, the actual length of contact line could be obtained by \u23a7 \u23a8\u23aa \u23a9\u23aa l t l t t t w \u03b2 v t t sin \u03b2 \u03b2 \u03b8 \u03b2 \u03c0 t t t t t t ( ) = ( ) \u2264 sin \u2212 \u22c5( \u2212 )( + cos tan( + \u2212 2)) < \u2264 0 < \u2264 a bs b b t bs b b b bs be be total t b (31) The time instants tbs" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003006_j.triboint.2020.106806-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003006_j.triboint.2020.106806-Figure3-1.png", "caption": "Fig. 3. Schematics of sample with dimensions (a) and build and UNSM directions (b).", "texts": [ " The force is directly proportional to the surface hardness, the grain size, strain-hardened layer and CRS. The surface roughness is inversely proportional to the force, while it is directly proportional to the feed-rate. Tensile properties of the samples were evaluated by tensile tester (130\u201310, QMS, Korea) in accordance with ASTM E8 standard. The total length and thickness of the sample was 100 and 3 mm, respectively. Schematics of the sample with dimensions in mm and build along with UNSM treatment directions are depicted in Fig. 3(a and b), respectively. Dry tribological properties were assessed by ball-on-disk tester (Optimol SRV IV, Germany) in accordance with ASTM G99 standard up to 5000 cycles. Applied load was 10 N, frequency was 2 Hz, and stroke was 4 mm for 5000 cycles against a Cr steel ball. With the intention of having trustworthy results tests were carried out 2\u20133 times depending on their likeness. LSM (laser scanning microscope) was used to measure the surface roughness (VK-X100 Series, Keyence, Japan). Hardness data were collected using a MVK-E3, Mitutoyo, Japan) tester" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000347_j.triboint.2013.10.003-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000347_j.triboint.2013.10.003-Figure2-1.png", "caption": "Fig. 2. Schematic view of the FZG gear test rig.", "texts": [ "7382 0.5489 t @ 0.2 GPa [/] 0.1390 0.1360 0.1335 0.1335 0.1485 Piezoviscosity @ 40 1C \u00f0\u03b1 10 8\u00de [Pa 1] 2.207 1.437 1.590 1.600 1.278 Piezoviscosity @ 70 1C \u00f0\u03b1 10 8\u00de [Pa 1] 1.774 1.212 1.339 1.353 1.105 Piezoviscosity @ 100 1C \u00f0\u03b1 10 8\u00de [Pa 1] 1.527 1.071 1.182 1.197 0.988 VI [/] 85 140 150 163 230 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 650700750800850900950100010501100115012001250130013501400145015001550160016501700175018001850 A bs or va nc e Wavenumber (cm-1) MINR ESTR PAOR MINE PAGD Fig. 1. IR spectrum. Fig. 2 presents the FZG test machine used in this work. The FZG machine is a gear test rig with circulating power due to a static torque applied [35]. Test pinion (1) and wheel (2) are connected by two shafts to the drive gearbox (3). The shaft connected to test pinion (1) is divided into two parts by the load clutch (4). One-half of the clutch can be fixed with the locking pin (5), whereas the other can be twisted using the load lever and different weights (6). The torque loss (TL) was measured using a ETH Messtechnik DRDL II torque transducer assembled on the FZG test machine, as shown schematically in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002335_s11071-018-4204-3-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002335_s11071-018-4204-3-Figure1-1.png", "caption": "Fig. 1 a Gearbox of the urban rail vehicle, b topological graph of the wheelset-gear system of the urban rail vehicle", "texts": [ " In this paper, we focused on the nonlinear analysis of the gear system of an urban rail vehicle exported to Argentina under acceleration conditions. The paper is organized as follows. Section 2 presents the mathematical model of the gear model and all the excitation. Section 3 details quasi-static analysis and time\u2013 frequency analysis and discusses the results above. Section 4 presents the conclusions and suggestions for future work. 2.1 Gear model of railway vehicle All components are assumed to be rigid bodies. A sketch and a topological graph of the running gear of the urban rail vehicle are presented in Fig. 1. The gear is installed on the axle, and the pinion is connected to the motor, which is mounted on the frame of the running gear. The axle box suspension, which is installed between the axle and frame, filters vibration from the wheel set, thereby allowing the direct execution of vibration on the axle. We chose the frame as reference object, so the vibration of the gear system can be measured from the frame of running gear. Based on the structure, the pinion is directly influenced by the rail irregularity in the absence of a filter. The specifications of the presented gear system are listed in Table 1. Rail irregularity excitation is the most special factor in the gear system of urban rail vehicle, and in order to establish the torsional vibration gear system of urban rail vehicle, we need to transform the rail irregularity excitation into the torsional vibration model. Figure 1b describes the topological structure of the wheelset-gear system. Under the assumption of quasi-static condition, the damping force and inertia force are neglected, and the vertical movement of the wheelset is fixed. The wheel\u2013rail normal force is expressed bymeans of contact stiffness and vertical displacement, and the wheel\u2013rail friction force is a function of normal force and friction coefficient. Without considering other external excitation, the equilibrium equation of the gear is composed of wheel\u2013rail friction torque and meshing torque, which can be written as k (t) x\u0303ra = \u03bckczrw, (1) where x\u0303 is dynamic transmission error (DTE),\u03bc is friction coefficient, z is rail irregularity, ra is the base circle radius of the pinion, and rw is the wheel radius" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003046_j.simpat.2020.102080-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003046_j.simpat.2020.102080-Figure6-1.png", "caption": "Fig. 6. Static pressure of the single bevel gear: (a) 4486 r/min; (b) 6708 r/min; (c) 8203 r/min; (d) 10,031 r/min; (e) 12,286 r/min; (f) 15,000 r/ min.", "texts": [ " The simulations were run as parallel jobs on the High Performance Computing Center of Central South University, predominantly using a fat node including eight quad-core AMD Opteron processor, using all four cores. Simulations based on the control gear's mesh took around three hours each to complete. In order to analyze the change laws of windage power losses intuitively and clearly, the bevel gear surface is selected as the reference plane. In this analysis, the gear rotational speed is set to 4486 r/min, 6708 r/min, 8203 r/min, 10,031 r/min, 12,286 r/min and 15,000 r/min, respectively, the gear rotates counterclockwise (A) viewed from the toe. The calculated results of static pressure are shown in Fig. 6. Furthermore, the pressure distribution under different rotating speeds as it is generally preferred in fluid dynamics is also plotted in Fig. 7. It shows that the distribution of the pressure coefficient is similar to the static pressure. Referring to the existing public literature [1], the static pressure is chosen as an index to measure the windage power losses. As can be seen in Figs. 6 and 7, the pressure on the convex surface is higher than the concave side due to the counterclockwise rotation of the bevel gear" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000039_978-1-84996-220-9-Figure3.10-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000039_978-1-84996-220-9-Figure3.10-1.png", "caption": "Figure 3.10 Optimal stance poses for differently weighted collision cost", "texts": [ " The important aspect is to unconstrain the three stance dofs, simply by assigning zeros to the corresponding column of the task Jacobian. This results in the stance dofs not being employed in the task space of the movement. However, they are still being utilized in the null space. When assigning a target to the task vector, the controller equations will in each iteration make a step towards it, while shifting the stance coordinate system to a po- sition and orientation that leads to a (local) minimum with respect to the employed null space criteria. A minimum can be found with regression techniques. Figure 3.10 illustrates this for the task of grasping a basket from a table. The task vector is composed of the following elements: xtask = (xT f oot\u2212l \u03d5 T Euler, f oot\u2212l xT f oot\u2212r \u03d5T Euler, f oot\u2212r xT cog,xy xT hand\u2212l \u03d5 T Polar,hand\u2212l) T . (3.23) The tasks for the feet are chosen to be in a normal stance pose. The horizontal components of the center of gravity lie in the center of the stance polygon. The left hand position and orientation are aligned with the handle of the basket. The null space of the movement is characterized by a term to avoid joint limits (Equation 3.8), and another term to avoid collisions between the robot links and the table (Equation 3.16). The weight of the latter is increased in Figure 3.10 left to right. It can be seen that the resulting stance pose has a larger body-to-table distance for a higher collision weight. This scheme is very general as it can be applied to arbitrarily composed task vectors. The resulting stance pose will always be a local optimum with respect to the null space criterion. Upon convergence, the resulting stance dofs 80 M. Gienger, M. Toussaint and C. Goerick can be commanded to a step pattern generator which generates a sequence of steps to reach the desired stance" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002964_robosoft48309.2020.9116022-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002964_robosoft48309.2020.9116022-Figure2-1.png", "caption": "Fig. 2. Robophysical model of a centipede. (a) CAD diagram of the segment of the robot. The legs (blue) are out-of-phase and their up/down and for/aft positions are controlled by two different servos (XL-320). Body servo controls the lateral undulation of the body. Body angle and legs are coupled to each other. Inset shows the neutral angle (35o) of the leg. (b) Top view of the segment that shows body angle, \u03b2, and leg for/aft angle, \u03b1. (c) CAD diagram of a segmented 3D-printed multi-legged robot developed to model the locomotion of centipede.", "texts": [ " Coordinated with the retraction/protraction times of the limbs the body segments actively undulate in a transverse horizontal plane [8], [32], [38]. We designed the robophysical model of a centipede by considering three main DoFs: forward/backward and upward/downward motions of the legs and lateral undulation of the body. To simplify the mechanical system and reduce the number of actuators, which can be costly in terms of energy and fabrication time, we coupled the horizontal and vertical motion of two legs on a segment with rigid connectors. The leg to body connector (yellow part in Fig. 2a) has angled pivot joints for the legs and connects the leg up/down servo to the leg swing servo. The mechanism that controls the vertical 157 Authorized licensed use limited to: Macquarie University. Downloaded on June 24,2020 at 06:22:11 UTC from IEEE Xplore. Restrictions apply. motion of the legs is similar to the four-bar mechanism, the hip joints are hinged to each other using a rigid 1DoF revolute joint which is connected to the leg up/down servo whose rotation axis is parallel to the anteroposterior line. The legs can lift up to 35o from their neutral position which corresponded to maximum lift, about 4cm above the ground. The vertical distance of the pivot joints from the ground is chosen so that the leg with a vertical hip height, hleg = 8.5 cm, can provide enough leverage from the ground. The neutral angle of the leg (see inset of the Fig. 2a) can be modified according to desired body posture by changing the length of the rigid connector between legs. The lateral body angle, \u03b2, is actively controlled by a servo. The final design of a segment (length = 9 cm) with three servos is given in Fig. 2a. This modular design allows us to change the number of the segments (and legs) of the robot easily, which has important implications for the understanding of the locomotor mechanics and evolutionary morphology of multi-legged systems. There are many possible footfall patterns that legged animals could use during locomotion. Gaits are generally considered to be discrete patterns of footfalls and are divided into two categories, symmetrical and asymmetrical, according to relative contact duration of a pair of legs (fore or hind) [29], [39]", " cli(t) = \u03c3(t+ 2\u03c0iLFS) cri (t) = \u03c3(t+ 2\u03c0iLFS + \u03c0) (1) \u03c3(t) = { 1 (contact), if (t mod 2\u03c0) < \u03c0 0 (lifted), otherwise (2) where cli and cri are the contact state of i-th left and right legs respectively; LFS is the relative phase shift between adjacent legs. We prescribed the lateral body undulation as a traveling wave, such that j-th joint is prescribed as \u03b1j(t) = A\u03b1 sin (t+ 2\u03c0Lj + \u03c60), where A\u03b1 is the amplitude of leg movements and \u03c60 is the relative phase offset between body undulation and leg movements. \u03c60 is optimized by using geometric mechanics gait design framework ( [40]\u2013[42]). To systematically evaluate the performance impact of variation in body-leg coordination, we constructed a robophysical model of the centipede (Fig. 2c) from the eight segments given in Fig. 2a (total length = 72cm). All parts of the segments were 3D printed by ABS plastic. Fig. 3a shows snapshots from one of the experiments (LFS 15%, duty factor 50%) for a cycle (T). The red dots show the legs on the ground. At the beginning of each experiment, all the legs are positioned to their neutral position and the body angle is set to zero. The robot moved on a level, smooth hardboard (60\u00d7120 cm) for five trials of three steps each per condition. We explored all the gaits with a duty factor 50% (means all the legs are on the ground during half of the cycle) and LFS from 10 to 90% with an increment of 5%", " After the contact with the obstacle ended, the initial configuration was restored by a helical extension spring attached to the knee joint which rotated the lower part of the leg. The coupling of the leg movement on the vertical axis is broken by replacing the rigid connector with a non-extensible Kevlar thread (size 207) of the same size. The leg can freely rotate from the hip joint and returns to its neutral position by a helical extension spring attached between the leg and the rigid swing connector (the yellow part in Fig. 2a). The flexible connection between legs provides extra flexibility on the vertical plane and removes pairwise effects of external disturbances on the legs. Both the flexible leg and the flexible leg connector improves the robustness of the robot to uncertainty in the environment. From animal experiments, we observed that the portion of the body that is unsupported by the legs has a tendency to curve downwards passively under gravity (see Fig. 4a). This compliance distributes the forces on the body, reduces loss of foot contact, and provides shape adaptability to the environment" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001190_0954406215621098-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001190_0954406215621098-Figure2-1.png", "caption": "Figure 2. Schematic diagram of the TRB: (a) local coordinate system (r, , x), (b) local contact geometry with inner ring contact load, roller and inner ring displacements.", "texts": [ "2\u20137 The bearing misalignment angle may be inconstant because of time-varying applied loads, but such a loading condition is not considered here. The calculation procedure of TRB14 comprises two iterative loops based on the Newton\u2013Raphson method: the global loop for global equilibrium of the inner ring and the local loop for equilibrium of each roller. The global loop begins by assuming the inner ring displacement components xo, yo, zo and yo. Because z is given in this case, the initial guess vector for inner ring displacements becomes { o} T \u00bc { xo, yo, zo, yo, z}. From Figure 2, the displacement of the inner ring cross-section at a particular roller {u } T \u00bc {u , u , } can be obtained as u f g \u00bc K\u00bd R 0f g \u00f01\u00de where the transformation matrices12 are given as R \u00bc cos sin 0 xP sin xP cos 0 0 1 rP sin rP cos 0 0 0 sin cos 2 64 3 75 \u00f02\u00de and K\u00bd \u00bc cos sin 0 sin cos 0 0 0 1 2 64 3 75: \u00f03\u00de Next, the local loop is initiated by giving an initial guess vector of roller displacements, {v } T \u00bc {v , v , }. The roller\u2013raceway contact loads can be calculated from the obtained {u } and {v }", " Subsequently, the roller equilibrium equations are solved for a new roller displacement {v } (n) by the iterative Newton\u2013Raphson method. At the end of the local loop, differences between {v } (n) and {v } are evaluated against a designated tolerance {\"r}. After the equilibrium equations are solved for all z rollers, the global equilibrium equation of the inner ring is established by summing the equivalent contact load vector of the inner ring {f} and the external load vector {F}. Ff g \u00fe Xz j\u00bc1 f j \u00bc 0f g \u00f05\u00de where f \u00bc R T K\u00bd T Q \u00f06\u00de {Q }, the contact load vector of the inner ring at a particular roller of location angle (Figure 2(b)), is determined by Q \u00bc Q Q T 8>< >: 9>= >; \u00bc Qi cos \" Qf sin 0 Qi sin \" Qf cos 0 Mi Qflf sin 8>< >: 9>= >;: \u00f07\u00de Because the misalignment angle z is known, the other four unknowns x, y, z and y should be determined by solving four out of five global equations containing the corresponding load components. Similar to the local loop, the difference between the resultant displacement vector { } and the initial guess vector { o} is evaluated against a specific tolerance {\"b}. The iteration repeats until the difference between { } and { o} falls within {\"b}" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001488_s00332-015-9253-x-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001488_s00332-015-9253-x-Figure1-1.png", "caption": "Fig. 1 (Color online) Schematic of the system geometry. The red circle indicates the orientation of the squirmer\u2019s thrust", "texts": [ " In this study, a time-independent boundary condition at the swimmer\u2019s surface is used in order to compare the swimming dynamics and stability of the swimmer in Newtonian and viscoelastic fluids. The role of fluid elasticity on the near-wall residence time is quantified for a wide range of initial positions and orientations. We model the microorganism as a two-dimensional \u201csquirmer\u201d that propels itself via a tangential surface velocity (Blake 1971; Lighthill 1952), u\u0302s , described as u\u0302s = [B\u03021 sin(\u03b8 \u2212 \u03c6) + B\u03022 sin(2(\u03b8 \u2212 \u03c6))] e\u03b8 , (1) where \u03b8 is the polar angle and \u03c6 is the swimming direction (both measured from the x-direction along the wall, as shown in Fig. 1), e\u03b8 is the tangential unit vector, and \u201c .\u0302 \u201d denotes dimensional variables. The surface velocity described in (1), representing the truncated form of Blake\u2019s original boundary condition (Blake 1971), is commonly used in the literature to model the metachronal beating of ciliated microorganisms and Janus particles (Lauga and Powers 2009; Crowdy 2013). Here, B\u03021 and B\u03022 = \u03b2 B\u03021, respectively, represent the amplitudes of the first and second modes of Blake\u2019s surface velocity. For \u03b2 > 0 (< 0), thrust is generated in front of (behind) the microorganism, as in the case of bacteria (algae), and the squirmer is called a puller (pusher)" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002942_j.jmapro.2020.04.022-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002942_j.jmapro.2020.04.022-Figure7-1.png", "caption": "Fig. 7. Cutting area and locus of the cutting edge with to relative motion of tool and workpiece in pass 3.", "texts": [ " 6, =D x x y y z z e t1 tN t1 tN t1 tN (1) where [xti, yti, zti]T is the point Qi in cutting tool coordinate. The points on the tool cutting edge contour Ce at time t are defined by Eq. (2) according to the rotation angle about the zt axis \u03c6t(t), rotation angle about the z axis of the workpiece \u03c6w(t), displacement of the center of the cutting tool x-axis direction rx, and tilt angle about the x-axis of the tool rotation axis \u03b8. = +C R R R Dt t t r( ) ( ( )) ( ) ( ( )) 1 1 0 0 0 0 ee wz x zt t x (2) In Eq. (2), Rx, Rzt, and Rz represent rotation matrices about the x, zt, and z axes, respectively. Fig. 7 shows the relative movement of the cutting tool in the case where the workpiece is fixed. This figure describes an example of machining pass 3. The green colored area corresponds to the cutting area. Fig. 8 explains the analysis of the interference between the nodal points on the work surface and the tool cutting edge during the process. Qj,i(t) is the i-th point of j-th cutting edge contour Ce(t) at time t. Ej,i(t) is an element of discretized cutting edge, and it is expressed as = +E Q Qj,i j,i 1 j,i" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003479_0954407021999483-Figure13-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003479_0954407021999483-Figure13-1.png", "caption": "Figure 13. Influence of forward traveling wave on radial second-order mode shapes: (a) radial 2nd order unaffected by forward traveling waves (94.315 Hz) and (b) radial 2nd order affected by forward traveling wave at 30 km/h (99.88 Hz), the hollow arrow indicates the direction of rotation of the tire, and the solid arrow indicates the direction of propagation of the forward traveling wave.", "texts": [], "surrounding_texts": [ "Tire is a complex nonlinear system, it is difficult to establish the relationship expression between tire wear, tire pressure and other parameters. Therefore, this paper uses BP neural network to perform nonlinear fitting regression between each parameter. From the foregoing, it can be found that there is a certain regularity between tire pressure, load, vehicle speed, tread wear, and tire radial modal frequency, but the first-order radial natural frequency is not sensitive to vehicle speed, so radial 2\u20136 orders radial increase frequency is used as an input parameter. Therefor the number of neurons for input layer is eight, they are tire pressure, load, vehicle speed and radial 2\u20136 orders radial increase frequency. And the number of neurons for output layer is just a one called tread wear amount. BP neural network can be divided into single hidden layer and multiple hidden layers according to the hidden layer. The choice of the number of hidden layers should be considered in terms of network accuracy and training time. For simpler mapping relationships, when the network accuracy meets the requirements, a single hidden layer can be selected to speed up the speed; for complex mapping relationships, a multiple implicits can be selected to improve the prediction accuracy of the network. Considering the small number of neurons in the input layer and output layer, and the amount of data samples is not large, the number of hidden of the BP NN established in this paper is set to one. For the hidden layer structure, a suitable range of hidden layer nodes should be first calculated according to the empirical formula shown in formula (17), and then use mse (mean square error) which can represent the performance of BP neural network to determine an optimal number of hidden nodes. The smaller the value of mse, the better the BP neural network fitting effect.26 node= ffiffiffiffiffiffiffiffiffiffiffi g+s p +c \u00f017\u00de where node represents the number of hidden layer nodes, g is the number of input layer nodes, s is the number of output layer nodes, and c represents a constant from 1 to 10. Therefore, the number of hidden layer nodes of this paper will be determined within the range from 4 to 13, and the mean minimum error percentage which is getted by a loop algorithm developed in this paper is selected as the criterion for selecting the number of hidden layer nodes. Figures 14 and 15 show the basic flow of the estimation algorithm and relation between the mse and the number of hidden layer nodes respectively. It can be seen from the Figure 15 that, the value of mse reach a minimum when the number of hidden layer nodes is 11, therefor, the number of hidden layer nodes is settled to 11, and the neural network model of tire wear estimation is shown in Figure 16. The activation function of the hidden layer of the neural network designed in this paper is the tansig function, the activation function of the output layer is the purelin function, and the training method is the trainlm training method. The formula of the BP neural network in this paper is explained as formulas (18) and (19). Oj = tansig X11 l=1 wjlxi + uj ! \u00f018\u00de where Oj is the excitation of the corresponding hidden unit, and j(j=1, 2,. . .,11) is the number of hidden layer neurons; tansig is the transfer function of the hidden layer, and its mathematical expression is tansig(n)= 2 1+e n 1; wjl is the weight of neurons from the output layer to the hidden layer; xi(i=1, 2,. . ., 8) are input parameters, namely inflation pressure, load, speed, and 2\u20136 orders of radial increase frequency; uj is the neuron threshold of the hidden layer. M=purelin X1 j=0 w2 ijOj + um ! \u00f019\u00de where M is the output layer unit, representing tire wear; purelin is the excitation function of the output layer, and its mathematical expression can be expressed as purelin(n)=n; wij is the weight from the corresponding hidden layer to the output layer; Oj is the excitation of the hidden unit shown in equation (18), and it is worth noting that O0 =1; um is the neuron threshold of the output layer. Analysis of the estimation of tire wear results Based on the tire finite element model established above, through the controlled variable method, 324 sets of data samples between tire inflation pressure, load, speed, tread wear, and 2\u20136 radial increase vibration frequencies are uniformly obtained. Among them, 324 sets of data samples are used as the sample set of the neural network, are divided into training set, validation set and test set which are 70%, 20%, and 10% of the total sample respectively. The results are shown in Figures 17 to 19. Figure 17 shows the relation between the value of mse and the epoch, it can be seen that the train of neural network is terminated at 45th epoch, this moment, the value of mse is 7.0026e-4, but the value less than the performance goal 4e-5 because the maximum of validation reaches the set value, so the train of neural network is stopped to avoid overfitting. Figures 18 and 19 are results analysis of test set which are inputted into the neural network has been trained completely. It can be seen from Figure 18 that the prediction curve of the tire wear prediction BP neural network built in this article has a relatively high degree of overlap with the actual wear curve, and the tire wear error values predicted by the BP neural network are all within the range of 60.5mm, of which 96.88% of the prediction errors are within the range of plus or minus 0.25mm, and the average predicted error is 0.0874mm; it can be seen from Figure 19 that the error percentage is basically within 610%, and the average prediction error percentage is 2.78%. Therefore, the inflation pressure, vehicle speed, load, and radial 2\u20136 order increased vibration frequency are used as input parameters to build BP neural network has a certain feasibility for predicting tire wear." ] }, { "image_filename": "designv10_9_0000193_j.cma.2011.04.006-Figure20-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000193_j.cma.2011.04.006-Figure20-1.png", "caption": "Fig. 20. (a) Contact pattern and (b) function of transmission errors for case B3a (skew(B) partial-crowned(3) aligned(a) bevel gear drive).", "texts": [ " In order to absorb those lineal functions of transmission errors caused by errors of alignment for the skew bevel gear drive, Designs 2 and 3 (see Table 3) are proposed also for this transmission, with whole-crowned and partial-crowned bevel gear tooth surfaces, respectively. Figs. 19 and 20 shows the contact patterns and the predesigned functions of transmission errors for cases B2a and B3a corresponding to a skew whole-crowned and aligned bevel gear drive (Fig. 19) and to a skew partial-crowned and aligned bevel gear drive (Fig. 20). A parabolic function of transmission errors with maximum level of 7 arcsec has been predesigned for the whole-crowned skew bevel gear drive (Design 2). However, for the case of partial-crowned skew bevel gear drive (Design 3), a function of transmission error of 2 arcsec is obtained taking advantage of an area of non-modified tooth surface due to partial crowning. Again, Design 3 (partial-crowning) allows the contact pattern to cover a larger area of the bevel gear contacting surfaces. Fig. 21 shows the contact patterns for cases B2b (21(a)), B2c (21(b)), and B2d (21(c))" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002328_j.cirp.2018.04.061-Figure10-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002328_j.cirp.2018.04.061-Figure10-1.png", "caption": "Fig. 10 shows the developed metal crystal of a thin-w deposition using DED combined with the remelting process un", "texts": [], "surrounding_texts": [ "The elongated structure, as shown in Fig. 8, is a so-ca dendrite, which initiates anisotropic characteristics. For exam the hardness in the direction of growth of the dendrite is gener higher than in other directions. In the case of Inconel 625, the (2 surface is the hardest, and appears on the flat surface as show Fig. 3. Furthermore, the dendrite grows along with the ther gradient; thus, the hardest surface (200) could be oriented tow the surface of the deposited part by employing the remel process. From this viewpoint, the remelting process is conducte 3 mm pitch on the surface of the deposited part by using the AC-axes as shown in Fig. 9, and the crystal orientation and hardn are evaluated in comparison with conventional DED. Each tes conducted three times. Fig. 7. Summary of porosity rate reduction in remelting process (Average of 3 tests). rate is confirmed at the top of the deposited part. On the other hand, (b) shows the result of 70-layer deposition to which the remelting process has been applied. The local porosity rate certainly decreases particularly in the remolten area. The overall porosity rate can be calculated by counting and comparing the number of black pixels with all the pixels and these results are summarized in Fig. 7. The error bars represent maximum and minimum values of 3 times tests under each deposition condition. The all remolten depositions show a smaller porosity rate, as about 0.017%, than the conventional DED with same number of layers. Considering that the all error bars have only less than 20% width, R. Koike et al. / CIRP Annals - Manufacturing Technology xxx (2018) xxx\u2013xxx4 These results indicate that combining the remelting process with DED enables the metal structure of the deposited part to be controlled such that high density and high hardness can be obtained." ] }, { "image_filename": "designv10_9_0002022_978-3-319-40036-5-Figure2.18-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002022_978-3-319-40036-5-Figure2.18-1.png", "caption": "Fig. 2.18 (a) Fabrication flow chart for the process used (b) FESEM image of Al microcantilever 78 \u03bcm long and 28 \u03bcm width (c) Force displacement characterization on a nanoindenter", "texts": [ "16 Fabrication sequence of the nanomechanical oscillators; (a) Thermal oxidation and LPCVD deposition of the polycrystalline silicon device layer; (b) Lithographic definition of the oscillator; (c) Sacrificial silicon dioxide removal using HF; (d) Free standing cantilever (L\u00bc 6 \u03bcm, w\u00bc 0.5 \u03bcm, t\u00bc 150 nm) SEM image (Reproduced from Ilic et al. [52] with permission from the American Institute of Physics) 54 G. Bhatt et al. For releasing the Al micro-cantilever a second step of masking and anisotropic wet etching was done with TMAH etchant [55]. Figure 2.18a shows a detailed fabrication flowchart of the process used for etching of silicon cantilevers. Figure 2.18b shows the FESEM image of a thin film and Fig. 2.18c shows a force deflection characterization using a nano-indenter. Our studies have revealed a very high resilience (almost equal to that of natural rubber) of these metallic cantilever structures [56]. Our group has also been heavily involved in fabrication of polymeric cantilevers using the photosensitive epoxy based polymer SU-8. These SU8 cantilevers have been developed using a one-step lithography based process using maskless grayscale lithography (MGL). Generally in photolithographic process there are only two states \u20180\u2019 or \u20181\u2019 i" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003198_j.mechmachtheory.2020.103960-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003198_j.mechmachtheory.2020.103960-Figure2-1.png", "caption": "Fig. 2. Schematic diagram of three ADCs of 3RRlS RPM.", "texts": [ " The outer radiuses of the static and moving platforms and the lengths of the links are r and d , respectively. Since the lockable spherical joint can be switched between the spherical joint (lS 2 ) and the Hook joint (lS 1 ), the 3RRlS RPM has four configurations, i.e., 3RRlS 2 , 2RRlS 2 -RRlS 1 , 2RRlS 1 -RRlS 2 and 3RRlS 1 configurations [5] , which contain different actuation distribution configurations (ADCs) according to the number and positions of actuators. Specifically, the 3RRlS 2 configuration with three DOFs contains only one ADC, as shown in Fig. 2 (a); the 2RRlS 2 -RRlS 1 configuration with two DOFs contains two ADCs, as shown in Fig. 2 (b) and 2(c); the 2RRlS 1 -RRlS 2 configuration with one DOF contains five ADCs, and the 3RRlS 1 configuration with one DOF contains three ADCs, as shown in Appendix 1 . 2.2. Stiffness modeling method By considering the link flexibility, actuation constraints, and structural constraints, the stiffness modeling method for 3RRlS RPMs and n(3RRlS) RSPMs is proposed in this paper combines the screw theory, the principle of virtual work, VJM and MSA based on [ 20 , 26 ]. The proposed method is time-efficient since it yields a m \u00d7 m stiffness matrix which has a smaller dimension than MSA, which provides a reference for modeling the stiffness of overconstrained PMs and SPMs" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002680_tec.2020.3000753-Figure11-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002680_tec.2020.3000753-Figure11-1.png", "caption": "Fig. 11. Flux density map at rated operation state.", "texts": [ "org/publications_standards/publications/rights/index.html for more information. There are usually both d-axis and q-axis magnetic fields inside the motor. Since the cross-coupling effect has been taken into account in the above RMP models, by superimposing the d-axis RMP model shown in Fig. 3 and the q-axis RMP model shown in Fig. 9 directly, the total RMP model considering the interaction of multi-excitation sources can be obtained. When the motor is at the rated operation state, its flux density map is shown in Fig. 11. For synchronous motors, when the armature current is the fundamental current, the rotor magnetic field and the stator magnetic field rotate synchronously. The magnetic potential of each point on the rotor surface will remain unchanged, that is, the flux density map in Fig. 11 remains unchanged. Therefore, the proposed method does not need to consider the rotor rotation. Conversely, for the traditional EMN model, which needs to consider the connection between the stator and rotor, the relative position between the stator and rotor changes continuously due to the rotor rotation, hence it is necessary to re-solve air-gap reluctances according to the actual rotor position. As can be seen from Fig 11, when the motor is at the rated operation state, the stator teeth saturation cannot be neglected. In Fig 12, the MMF Fs1-Fs6 on the stator inner surface are not equal to F1-F6 in value due to the magnetic potential drop on the stator tooth reluctances Rt1-Rt6 (When the stator saturation is neglected, Fs1-Fs6=F1-F6). In this section, based on the above RMP models and MEC models, an iterative method is proposed. The magnetic potential drop on Rt1-Rt6 is calculated by using this iterative method, and then the MMF Fs1-Fs6 and the RMP model considering the influence of stator and rotor saturation are obtained" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000559_1.4731663-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000559_1.4731663-Figure3-1.png", "caption": "FIG. 3. Spatial orientation of a Kuhn segment with respect to the electric vector of the light E. \u03b8 , \u03d5, and \u03c8 are the three Euler angles, see text for details.", "texts": [ " The contribution to the free energy provided by a single network strand whose endto-end vector is b\u2032, can be written in the following form: Fstrand(b\u2032) = NkT \u222b d f ( , b\u2032) ln f ( , b\u2032) +N \u222b d U ( )f ( , b\u2032), (4) where k is the Boltzmann constant, T is the absolute temperature, and f( , b\u2032) is the orientation distribution function of Kuhn segments inside the network strand. The first term in Eq. (4) describes the entropic elasticity of a network strand and the second one reflects the influence of the lightinduced orientation potential. The solid angle \u2261 (\u03b8 , \u03d5, \u03c8) Downloaded 10 Aug 2012 to 128.148.252.35. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissions determines the orientation of a Kuhn segment in the space and is defined by the three Euler angles \u03b8 , \u03d5 and \u03c8 (Figure 3): \u03b8 is the angle between the long axis of the Kuhn segment and the vector E, \u03d5 is the angle between the y-axis and the projection of the long axis of the Kuhn segment on the yz-plane, \u03c8 is the angle between the plane of symmetry of the Kuhn segment and the plane formed by the long axis of the segment and the vector E. Thus, the angle \u03d5 determines the rotation of the Kuhn segment around the vector E and the angle \u03c8 defines the rotation of the segment around its long axis. The integral in Eq. (4) runs over the angles \u03b8 , \u03d5, and \u03c8 : \u03b8 \u2208 [0, \u03c0 ], \u03d5 \u2208 [0, 2\u03c0 ], \u03c8 \u2208 [0, 2\u03c0 ], and d = sin \u03b8d\u03b8d\u03d5d\u03c8 " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002154_j.measurement.2019.03.072-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002154_j.measurement.2019.03.072-Figure1-1.png", "caption": "Fig. 1. a) The structure of SCIM; b) The squirrel-cage rotor of SCIM.", "texts": [ " Along with the increasing expansion of electric motors in the various applications, it is essential to monitor their conditions and diagnose their unforeseen problems and faults which occur during their operation, such as the rotor and stator overheating, and also different types of the rotor and stator faults. Condition monitoring and fault diagnosis help engineers to make a diagnostic decision on the basis of obtained signals [7\u201315]. The structure of SCIM and its squirrel-cage rotor are shown in Fig. 1. In normal operation of SCIMs, the large part of generated heat by the losses is dissipated through heat transfer methods to the surrounding environment. However, different reasons including heavy overloading, prolonged starting and impairing in the cooling conditions during operation (due to broken cooling fan or clogged motor casing) change the SCIM\u2019s cooling capability [16,17]. Furthermore, it should be noted that state-of-the-art relays for SCIMs utilize a start inhibit algorithm. The SCIM acceleration time, the starting times per hour, and the time between two starts are monitored" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000931_9781118703274.ch2-Figure2.2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000931_9781118703274.ch2-Figure2.2-1.png", "caption": "Figure 2.2 Airstream around the turbine", "texts": [ " The best results might be obtained by considering the axial and radial momentum of the airstream, or of small-diameter infinite flow-tubes impinging on the rotor blades, or of elements thereof, thus allowing us to determine local flow conditions and the resulting forces or rotational action on the turbine blades. The following considers this briefly. Calculations based on circulation and vortex distribution over aerofoils [2.1], which allow the derivation of solutions by the Biot\u2013Savart theorem, are not taken into consideration here. Within its effective region, the rotor of a wind turbine absorbs energy from the airstream, and can therefore influence its velocity. Figure 2.2 represents the flow that develops around a converter in an unrestricted airstream in response to prevailing transmission conditions, whereby the airstream is decelerated axially and deviated tangentially in the opposite direction to the rotation of the rotor. From references [2.2, 2.3] and [2.4], the energy absorbed from an air volume Va of cross-section A1 and swirl-free speed of flow \ud835\udc631 far upstream of the turbine, which results in a downstream reduction of flow speed to \ud835\udc633 with a corresponding broadening of the cross-sectional area (wake decay) to A3, can be expressed as Ww = Va \ud835\udf0c 2 ( \ud835\udc632 1 \u2212 \ud835\udc632 3 ) (2", "17) The force thus depends on the radius and the axial and tangential airstream at the turbine. The air, according to equations (2.14) and (2.17), exerts identical forces on the rotor blades. For the sake of clarity, the physical processes will be shown for a single rotor blade. Multiblade arrangements for fast-running turbines (e.g. with z = 2, 3 or 4 lift-type blades) can be handled by extension of this system, considering conditions at a single blade of z-fold depth. Depending on blade radius, Figure 2.2 shows that there is different flow behavior at the profile for different blade angles (Figure 2.3). The combined effect of velocity components and the resultant forces are shown for a single blade element in Figure 2.4. Total values (forces, moments, power) are obtained by the integration of the corresponding values over the blade radius, or by summation of the components of individual blade sections. A segment at radius r of a blade rotating with angular velocity \ud835\udf14R experiences two airflows: that due to the wind deceleration across the swept area, v2 = v2ax + v2t (2", " Wind power machines for generating electricity are produced in horizontal and vertical axis format. The turbines are so constructed that they can utilize the force of lift. Lift originates in the flow of air past the rotor blade, which causes an overpressure on the underside of the blade and an underpressure on the top. The tangential component of the lifting forces causes the rotor blade to rotate. According to Betz [2.2], a lifting rotor can only extract 60% of the energy/power from an airstream. The remaining 40% of power must remain in the air flowing past (see Figure 2.2). Complete braking of themoving air mass to \ud835\udc633 = 0would result in air backing up at the turbine; the inflow of air would be halted and energy extractionwould no longer be possible. In practice, after conversion losses, lower levels in the order of 45% are achieved. Therefore, in contrast to water-driven turbines, for example, no efficiency levels are quoted for wind turbines \u2013 rather the performance coefficient cp is used. For operating machines, this figure gives the ratio of the power taken from the wind to that contained by it (Equation 2.8). A deceleration of the air as in Figure 2.2 can occur just as well with many blades moving slowly as with a few blades rotating at high speed. Simple wood and sheet metal constructions only allow slow rotation with high blade counts (e.g. more than six). The torques to be transmitted are correspondingly high, and the constructions must, in consequence, be massive. A few, swiftly spinning blades (e.g. one to three) attain higher power extraction levels and thus better performance coefficients (Figure 2.15). Such figures are, however, only possible using correctly formed aerofoil sections having a low structural area and low vortex creation and which generate little resistance to rotational movement", " In the machine shown in Figure 2.17 the blades are rigidly connected to the hub, while in Figure 2.18 the blades are attached to the hub such that they can rotate about their longitudinal axes. The single-blade rotor (Figure 2.19), on the other hand, is fitted with a cone-hinge hub. Multibladed arrangements are commonly found in small machines in the kilowatt range and below. When designing a machine to extract energy from the wind and to develop the resulting torque in the turbine, the airstream pattern shown in Figure 2.2 is the goal. It is then possible to achieve energy extraction using many blades at low speed or a few blades at high speed. Further, the optimal wind deceleration for the same speed of rotation can be attained using one very broad blade, or two or three blades of correspondingly smaller breadth. The optimal blade chord can be derived from the blade radius by the formula tB (r) = 2\ud835\udf0br z 8 9 1 ca \ud835\udc632 1 \ud835\udc63u (r) \ud835\udc63r (r) . (2.40) A rotor tip speed of \ud835\udc63u (r) = \ud835\udf14r = \ud835\udf06 r R \ud835\udc631, (2.41) a target wind deceleration at the turbine of \ud835\udc632 = 2 3 \ud835\udc631 (2" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002107_j.measurement.2018.07.031-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002107_j.measurement.2018.07.031-Figure1-1.png", "caption": "Fig. 1. (a) Schematic representation of experimental set up (b) Free body diagram of shaft \u2013 bearing system under study.", "texts": [ " The presented dynamic model is also capable to study the effect of governing parameters like radial load, shaft rotational speed and waviness order on amplitude of waviness defect frequency. In the present study, number of experiments have been performed for the validation of proposed dynamic model. Simulated and experimental results have been compared for different radial loads, shaft rotation speeds and waviness orders on either bearing race. Based on the work reported herein, a good correlation between theoretical and experimental results can be seen. The schematic representation of experimental set up for shaftbearing system under investigation is shown in Fig. 1(a). A polymeric cage deep groove ball bearing BB1B 420206 purchased from SKF (SKF India Ltd, Pune, India) is mounted on left end of the shaft. A split type test bearing housing is designed and developed for protection and rigid support to this test bearing. The Fig. 1(b) shows free body diagram of shaft-bearing system for vibration analysis. The following assumptions have been made to derive a dynamic model: \u2022 Masses of shaft including bearing inner race (Ms), mass of each rolling element (Mb) and mass of housing including bearing outer race (Mh) have been considered. \u2022 Friction between ball and races is neglected. \u2022 Effect of thermal aspect is neglected. \u2022 Force only in radial X direction has been considered. \u2022 Effects of centrifugal forces acting on balls are neglected", " = + \u2217A A \u03c6A sin(N )i out i out 0 m w (24) Contact angle \u03c6i out for outer raceway waviness for ith rolling element is given as follows. = \u2212 + \u2217\u03c6 \u03c0 i \u03c9 t2 *( 1) Ni out b c (25) The effect of waviness in the dynamic model has been incorporated by adding computed amplitude of waviness for inner race, \u2018Ai in\u2019 through Eq. (19) and outer race Ai out through Eq. (24) in total deflection for ith ball \u2018\u03b4i total\u2019 computed through Eq. (6). The following equations of motion (26\u201328) for each mass in radial X direction have been derived based on the assumptions made in Section 2. Refer Fig. 1(b). Equation of motion for shaft in radial (X) direction is as follows: \u2211 \u2211 + + + + + \u2212 = = = \u03b4 \u03b8 X \u03b8 M X\u0308 C X\u0307 K X K ( A ) cos C (X\u0307 \u0307 )cos 0 i s S s S S S i 1 N eq in i in i in 3/2 i 1 N in s bi i b b (26) Equation of motion for ith ball in radial (X) direction is as follows: \u2212 \u2212 \u2212 + + + + \u2212 = X \u03b8 \u03b4 cos\u03b8 \u03b4 \u03b8 \u03b8 K ( A ) cos C (X\u0307 X\u0307 )cos 0 bi bi in s bi i eq in i in i in 3/2 i eq out i out i out 3/2 i out bi h i (27) Equation of motion for test bearing housing in radial (X) direction is as follows; \u2211 \u2211 + + \u2212 \u2212 \u2212 + = = = X X \u03b8 \u03b4 \u03b8 K ( A ) cos Q h h h h h h i 1 N out bi h i i 1 N eq out i out i out 3/2 i b b (28) To find vibration response of shaft-bearing system in presence of defective raceways of deep groove ball bearing, the governing equations of motion (26\u201328) solved iteratively for each step of time" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002046_12.2263863-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002046_12.2263863-Figure1-1.png", "caption": "Figure 1. Schematic of the AMMT prototype system [8].", "texts": [ " Analysis is performed on a single scan track as a baseline experiment to maintain focus on the development of the methodology. While analysis techniques of the MPM signal are purposefully kept to simple mathematical operations, they are shown to be capable of highlighting variations due to key events, such as material ejecta. Finally, the relationship between the MPM signal and resultant scan track is discussed. 2. METHODOLOGY Experiments were performed in the Additive Manufacturing Metrology Testbed (AMMT) prototyping system [7,8], shown in Figure 1. The system uses a 500 W multimode Yb fiber laser at 1070 nm wavelength, which is delivered through two XY galvanometer scan mirrors, and focused onto a horizontal build platform within an inert gas chamber. This creates a nominally 100 \u03bcm full width at half maximum (FWHM) spot at the laser focus. Light emitted from the laser-heated region is passed back co-axially with the laser beam path, but transmitted through a beam splitter which reflects off the 1070 nm laser wavelength, and transmits wavelengths from 950 nm to 400 nm" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000820_j.cja.2013.02.027-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000820_j.cja.2013.02.027-Figure1-1.png", "caption": "Fig. 1 Schematic illustration of the laser deposition process for the hybrid fabricated 1Cr12Ni2WMoVNb steel sample.", "texts": [ " LMDwas carried out using a LMD system equipped with aGSTFL-8000 CO2 laser (maximum output power 8 kW), a BSF-2 powder feeder together with a co-axial powder delivery nozzle, aHNC-21M computer numerical control (CNC)multi-axismotion system, and an argon-purged processing chamber with oxygen content less than 100 \u00b7 10 6. A 1Cr12Ni2WMoVNb steel bar sample with dimensions of approximately \u00d855 mm \u00b7 30 mm was laser deposited on the wrought substrate. The processing parameters were as follows: laser beam power 4.5\u20135.0 kW, scanning speed 4\u20135 mm/s, beam diameter 5 mm, powder delivery rate 6.5\u20137.5 g/min, overlap ratio 30%\u201350%. The scanning mode was to-and-fro scanning. A schematic illustration of the laser deposition process for the hybrid fabricated 1Cr12Ni2WMoVNb steel sample was shown in Fig. 1. The newly laser deposited sample was tempered at 580 C for 2 h in order to eliminate residual stresses and obtain a tempered microstructure. Metallographic samples were prepared using standard practices and examined by an optical microscope (OM). The etchant is a mixture of 4 g picric acid, 5 ml hydrochloric acid, and 100 ml ethanol. Microhardness profile of the hybrid fabricated sample was measured by using a HXZ-1000 semi-automatic Vicker tester with a test load of 500 g and a dwell time of 10 s" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001524_s12206-014-0931-7-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001524_s12206-014-0931-7-Figure2-1.png", "caption": "Fig. 2. The 2(rT)2PS parallel mechanism.", "texts": [ " In this paper, the rTPS limb will be used by connecting the rT joint to the base and the spherical joint with the moving platform. The obtained new mechanisms will demonstrate different topologies by considering the numbers (2 to 6) of the rTPS limbs and the limb arrangement. The method is to use the constraint plane of the (rT)2PS limb to represent the limb configuration to investigate all possible assemblies. Then altering the limbs into the (rT)1PS phase will generate new mechanism phases with mobility change. A parallel mechanism consisting of two (rT)2PS limbs is shown in Fig. 2(a), in which the platform connects to limb 1 and limb 2 with their spherical joints centered at point A1 and A2, respectively. By fixing the two rT joints on the base with their centers at points B1 and B2, the two limbs are constrained in plane \u22111 and \u22112 with normal vectors n1 and n2, respectively as in Fig. 2(a). A fixed coordinate system oxyz is located on the base and a moving coordinate system Quvw is attached on the moving platform. Based on the constraint equations in Eq. (2) for the (rT)2PS limb, the geometric constraint of the 2(rT)2PS parallel mechanism can be given as: 1 1 1 2 2 2 ( ). ( ). d d \u00a2 + =\u00ec\u00ef \u00ed \u00a2 + =\u00ef\u00ee R R a q n a q n (3) where R = [u, v, w] is the rotational matrix from the local coordinate system to the fixed coordinate system oxyz, u, v, w and q are the unit vectors of the moving coordinate system axes and vector of the coordinate center Q expressed in the fixed coordinate system oxyz respectively", " Obviously, the platform can rotate about line A1A2 freely due to the local degree of freedom between two spherical joints. An additional constraint between the spherical joints can be added to control this mobility as analyzed in the analysis of parallel mechanisms with line platforms [36, 37]. By using normal vectors to represent planes, different topologies of the metamorphic parallel mechanism consisting of two reconfigurable (rT)2PS limbs can be demonstrated in the following sections. When the two constraint planes intersect with each other as in Fig. 2(a), there is 1 2. cosa=n n (4) where \u03b1\u2208[0, \u03c0] is the angle between normal n1 and n2. When \u03b1 = 0 or \u03c0, n1 = \u00b1 n2, the two planes are parallel to each other. A special topology exists when the two planes are coincident as in Fig. 2(b) in which the platform can be simplified by a line segment A1A2, from Eq. (3) there is: 1 2 1( ). 0\u00a2 \u00a2- =R a a n . (5) Thus, line A1A2 is perpendicular to normal n1 and located in the constraint plane \u22111 as in Fig. 2(b). The platform has a plane motion and a local rotation about A1A2. Another special topology of the mechanism is with angle \u03b1 = \u03c0/2 in which the two limbs work in two perpendicular planes. When two constraint planes are parallel to each other, there is n1 = n2 as in Fig. 3(a). Set the unit vector of line A1A2 as 12\u00a2m expressed in the moving coordinate system and locate the moving coordinate center Q on the line between A1 and A2. There is: 1 1 12 1 1 1 2 1 12 2 1 2 ( ). ( ). ( ). ( ). q q l d l d \u00a2 \u00a2+ = + =\u00ec\u00ef \u00ed \u00a2 \u00a2+ = + =\u00ef\u00ee R R R R a q n m q n a q n m q n (6) where l1q and l2q are the distances from points A1 and A2 to the moving coordinate center Q", " When fixing point A1, point A2 can only move along a circle with radius lsin \u03b2 and centered at the projection point A\u20191 of A1 as in Fig. 3(a). When point A1 moves, the circle moves. It follows the same rule when considering point A2 with respect to point A1. This describes the rotation motion rule of the platform A1A2. Two special cases occur when d1 and d2 are set particularly. When the distance between the two planes d1-d2 = 0, the two planes are coincident, which gives the same topology in Fig. 2(b). When the distance between the two planes || d1-d2|| = l12, then cos\u03b2 = 1 from Eq. (7) and A1A2 is perpendicular to the constraint planes as in Fig. 3(b) with geometric constraints: 12 1 1 1 1 2 2. q qd l d l \u00a2 =\u00ec\u00ef \u00ed = - = -\u00ef\u00ee Rm n q n . (9) Thus, the platform line A1A2 has fixed orientation and the moving coordinate center Q is determined by point A1 or A2 only. A1 and A2 are mutual projection points to each other along n1 on each other\u2019s plane. The mechanism has two translational degrees of freedom along the constraint plane and one local rotation about line A1A2" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001321_j.oceaneng.2015.02.006-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001321_j.oceaneng.2015.02.006-Figure3-1.png", "caption": "Fig. 3. Inertial fIg and body coordinate frame fBg.", "texts": [ " Section 6 concludes the paper with final remarks. Following notations are used throughout this paper. AT denotes transpose of matrix A, Lncosh\u00f0\u03be\u00de \u00bc \u00bdlncosh\u00f0\u03be1\u00de;\u2026lncosh\u00f0\u03ben\u00de T where \u03be\u00bc \u00bd\u03be1\u2026\u03ben T . The norm of vector x is defined as jxj \u00bc ffiffiffiffiffiffiffi xTx p and JAJ \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u03bbmax\u00f0ATA\u00de q is the norm of matrix A. The three dimensional equations of motion for AUV have been described by Fossen (1994) using inertial reference frame fIg and body fixed frame fBg as shown schematically in Fig. 3. As rotation of earth is having little effect on low speed underwater vehicles, earth fixed frame can be considered as inertial frame. The body fixed frame has velocity components in six directions with three linear velocities surge, sway, heave and three rotational velocities roll, pitch, yaw given by the vector \u03bd as \u03bd\u00bc \u00bd\u03bdT1 \u03bdT2 T \u00bc \u00bdu v w p q r T \u00f01\u00de The position of the vehicle can be expressed as \u03b71 \u00bc \u00bdx y z T . However for three dimensional underwater operational space Euler angle representation leads to singularity" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001525_cp.2014.0479-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001525_cp.2014.0479-Figure6-1.png", "caption": "Figure 6. Adapted stator yoke discretization to avoid dependent thermal resistor", "texts": [ " The accuracy benefit, however, also decreases with the discretization level. Since the heat flow inside a solid component is assumed to be independent in the radial, tangential and axial directions [3], the discretization level of the adjacent components of coil must be adapted accordingly, so that the thermal resistors remain parallel to the axes of the coordinate system. Otherwise, resistors depending on more directions will occur, which leads to an unrealistic thermal conductance of the component. In Fig. 6 the winding is discretized in 2 elements in tangential direction. In the left network all the resistors are independent. On the right hand, the stator yoke is not adapted to higher discretization, which causes two resistors to be dependent on both radial and tangential direction. Fig. 7 demonstrates the impact of dependent resistors. The negative resistors are neglected to simplify the network. The thermal potentials are defined as TL and TR on left- and righthand side. Only horizontal heat flow should take place in this thermal network" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002942_j.jmapro.2020.04.022-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002942_j.jmapro.2020.04.022-Figure5-1.png", "caption": "Fig. 5. Simulation model of power skiving.", "texts": [ " According to the results, the measured forces (particularly Fz) were significantly influenced by the noise during the non-cutting time, and the vibration caused by the machining process also affected the measurement waveform. The cutting force generally decreased in the following order: passes 1, 3, and 2. The radial depth of cut is 0.5 mm in pass 2 and pass 3. Although the radial depth of cut is the same, measured cutting forces are larger in pass3 since the tool immersion is large [14]. The simulation model is shown in Fig. 5. The cutting edges of the Fig. 1. Experimental setup. tool rotates clockwise with a speed of \u03c9t around the rotation axis zt, where \u03c6t(t) represents the angle from the x-axis at time t. The workpiece is a ring with an inner diameter of rw, and it also rotates clockwise with respect to the z-axis at a speed of \u03c9w. The rotation angle of a cutting edge from the x-axis at time t is \u03c6w(t). The tool rotation axis zt is assumed to be inclined by an angle \u03b8 to the x-axis of the work coordinate system. The center of the tool in the x-axis direction viewed from the center of the workpiece is rx", " For all the elements of cutting edge Ej,i(t), S\u2019j,i is expressed as follows; =S S S E E Et t t t ' ( ) ( ) \u00b7 ( ) | ( )|j,i j,i j,i j,i j,i 2 j,i (4) The angle between S\u2019j,i(t) and \u2013Hj,i(t) is the effective rake angle \u03b1j,i (t). = H S H S t t t t t ( ) cos ( ) ' ( ) | ( ) ' ( )|j,i 1 j,i j,i j,i j,i (5) In accordance with the foregoing method, the cutting area when the skiving tool rotates was simulated for pass 1 to pass 3. In the simulation, the rotation angle of the skiving tool with respect to the x-axis shown in Fig. 5 was divided into 100 steps in the range of \u221240\u00b0 to 40\u00b0 (\u22122\u03c0/ 9< \u03c6t(t)< 2\u03c0/9). Fig.10 shows the cutting area for pass 1 to pass 3. The areas of green and gray stripes in the figure correspond to the machined surface generated by the process; the color alternates between green and gray every five calculation steps. From this figure, it can be seen that in the first process pass 1, the cutting is started from the left side of the tooth surface, and the tool is detached from the material. However, in the third process (pass 3), the cutting is started from the right side and the tool is detached from the left side" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002207_icesi.2019.8863004-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002207_icesi.2019.8863004-Figure2-1.png", "caption": "Figure 2. Setup tensile shear test", "texts": [ " A common method for determining electrical resistances is to measure a voltage drop UM at a known current IM. In order to avoid a falsification of the measurement result by the resistances of the measuring leads, four-wire sensing can be used. This technology separates the current supply and the measuring of the voltage, which means that the resistance of the leads can be neglected. [13] In order to determine the mechanical strength of the joint, it is advisable to apply a tensile shear test. For this purpose, the specimens are bent as defined in Figure 2 followed by a tensile test to quantify the mechanical strength. [14] Measuring the electrical resistance RC of contacts of hairpin windings is challenging due to several reasons. On the one hand, the transition between the joining zone and the base material is fluent in the case of welded connections, which is why the contact cannot be precisely localised. For this reason, the contacting for the measurement of the voltage drop is always carried out in such a way that the resistance outside the joining zone is also partly measured", " To compare the initial strategy with the optimized feed movement, Figure 11 compares the resulting geometry of both cases. It can be seen, that the optimized strategy on the right side results in a broader joining area and reduced displacement due to the higher amount of molten material. Properties As the contact points have to resist the mechanical operating forces during vehicle operation, it is also necessary to be able to assess their mechanical properties. For this reason, shear tensile tests are carried out as shown in Figure 2. To examine if there is a relationship between the measured resistance and the mechanical strength, sample parts with different welding depths are produced. After the resistance RC has been determined, a shear tensile test is performed to measure the maximum tensile force FT. For the determination of the mathematical relationship, a regression analysis is performed in Minitab. The result is the quadratic relationship given in equation 2. FT (RC) = -1875 + 118.5 * RC \u2013 1.605 RC \u00b2. (2) The model quality can be rated as very high, since 97" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001476_j.ast.2018.12.019-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001476_j.ast.2018.12.019-Figure1-1.png", "caption": "Fig. 1. Helicopter frames.", "texts": [ " A practical way to deal with modeling of a helicopter is to establish a simplified 6-DOF rigid-body model by treating the other trivial factors affecting the helicopter system as uncertainties or disturbances [46,47]. In order to establish the model of the helicopter, two reference frames are defined. The first one is the inertial frame defined as I = {O e, Xe, Ye, Ze}, and the second is the body-fixed frame defined as B = {O b, Xb, Yb, Zb}, where the origin is located at the gravity center of the helicopter. The two frames are shown in Fig. 1. The 6-DOF rigid-body model of the unmanned helicopter is expressed as [37,41]\u23a7\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 P\u0307 = V , V\u0307 = ge3 + 1 m R( )(F + Fd), \u0307 = H( ) , \u0307 = \u2212 J\u22121 \u00d7 J + J\u22121( + ), (2) d where P = [x, y, z]T and V = [u, v, w]T are, respectively, positions and velocities in the inertial frame, = [\u03c6, \u03b8, \u03c8]T represents the vector of three Euler angles, which are roll angle, pitch angle, and yaw angle, respectively. = [p, q, r]T is the vector of angular velocities in the body-fixed frame, g is the acceleration of gravity, e3 = [0, 0, 1]T , m represents the mass of the helicopter, J = diag{ J xx, J yy, J zz} is the diagonal inertia matrix with respect to the body-fixed frame" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002889_tmag.2020.3032648-Figure8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002889_tmag.2020.3032648-Figure8-1.png", "caption": "Fig. 8. Surface-mounted PM Machine, a) circular rotor, regular arc-shape PM, b)octagon rotor, c) circular rotor,loaf-shape PM d)octagon rotor,loaf-shape PM.", "texts": [ " a ab ac aa ab ac a a a L L L I I I (22-a) 7 12 0 12 0 ( ) , 2 b c rem a s stk s rI r I I B g N L R B (r,\u03c6 ) .d\u03c6 (22-b) 6 0 6 0 ( ) , 2 b c rem ab s stk s rI r I I B g N L R B (r,\u03c6 ) .d\u03c6 (22-c) 5 12 0 12 0 ( ) , 2 b c rem ac s stk s rI r I I B g N L R B (r,\u03c6 ) .d\u03c6 (22-d) Next, the PM and armature flux density is inserted into the Maxwell\u2019s stress tensor to calculate the resultant motor torque: 2 0 0 2 , ., )( ).d\u03c6(r,\u03c6B)(r,\u03c6B rL T r\u03c6IrrI stk r (23) The schematics of four different machine topologies are presented in Fig. 8. The stator section, air-gap length, machine stack length and the angular length of the magnets are identical among all four machines, but each topology has a unique rotor frame and/or magnet shape. The shape of the magnets and the structure of rotor frames are chosen based on the existing topologies of surface mounted PM machines [21]. The motor specifications that are common among all four machines are listed in Table I. Each of the four motors is supplied with a balanced three-phase current source with the amplitude of 5 A" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002441_9781119509875-Figure16.3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002441_9781119509875-Figure16.3-1.png", "caption": "Figure 16.3 Necessary sensor element", "texts": [ " Each mechanical leg owns 3-DOF and contains hip joint, knee joint and ankle joint which are same as human joints shown in Figure 16.2. The mechanical leg could be divided into the thigh part and the shank part, and the length of each part could be changed electronically to meet the various legs length of patients from 1.5m to 1.9m. To satisfy the different shapes of patients, the width between two legs could be adjusted automatically. A separable chair with four universal wheels used for sitting/lying training and patients transfer was designed. The torque and pressure sensors equipped on LLRR are shown in Figure 16.3. Four torque sensors are installed in hip and knee joints which could receive torque data constantly from the joints. The joint torque data is the necessary judgment of the active training and the VR training. 206 Emerging Technologies for Health and Medicine Foot pressure data, which is collected by sensors equipped in the foot pedal, could transformed into the acceleration factor used for controlling training velocity of mechanical legs terminal. In order to obtain LLRR training trajectories smooth and flexibility, the velocity and the acceleration of the endpoint of the mechanical leg should be continuous" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002277_978-3-319-27131-6-Figure9.2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002277_978-3-319-27131-6-Figure9.2-1.png", "caption": "Fig. 9.2 Dynamic unbalance of the rotor", "texts": [ " The static unbalance is caused by the production mistakes, large eccentricity at mounting the iron-sheet packages on the rotor shaft, nonhomogeneous rotor materials, and asymmetric geometry of the iron sheets. On the contrary, the couple unbalance is created by misalignment of the iron-sheet packages to the rotor shaft. In practice, both static and couple unbalances occur in the production process of electric rotors. Both rotor unbalances lead to the dynamic unbalance of the rotor, as shown in Fig. 9.2. The dynamic unbalance is similar to the couple unbalance, but the mass center of the rotor does not lie on the rotation axis (s. Fig. 9.2). Therefore, the dynamic unbalance can be decomposed in the static and couple unbalances. The eccentricity \u03b5 of the static unbalance and the misalignment angle \u03b1 of the couple unbalance are combined together leading to the dynamic unbalance of the electric rotor. Considering the rotor with an unbalance mass mu at a radius ru, as shown in Fig. 9.3, the static unbalance of the rotor is written as U \u00bc muru \u00f09:1\u00de Due to unbalance mass mu, the resulting mass center G of the rotor locates at the unbalance radius \u03b5" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002664_tec.2020.2990914-Figure12-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002664_tec.2020.2990914-Figure12-1.png", "caption": "Fig. 12. Prototyped motor (a) final assembly stator, (b) rotor and shaft and (c) final assembly SRM.", "texts": [ " 11 shows the excitation current having hysteresis waveform for every phase with an overlapping at 5A excitation current; the electromagnetic torque of the both motors at 2000 rpm show less torque ripple in the proposed SRM. In Fig. 11 the conduction angle of the 12/8 SRM is 22.5 mechanical degrees of rotor rotation and the corresponding angle for the 12/14 SRM is 12.85 mechanical degrees. Both motors have conduction angle of 180 electrical degrees. To validate the predicted performance of the proposed 12/14 SRM, its prototype was built. Fig 12 presents the different parts of the motor including stator and its winding, rotor and the whole model of the motor. Fig. 13 illustrates the torque-rotor angle measurement setup in which a phase of the 12/14 SRM is fully excited until it TABLE VI Phase current (A) 12/14 SRM Tmean Tins( max ) Tins( min ) td Tr (%) T\ua78cr (%) 1 0.067 0.070 0.057 0.013 19.40 104.48 2 0.253 0.278 0.197 0.081 32.02 109.88 3 0.512 0.597 0.345 0.252 49.22 116.60 4 0.792 0.954 0.470 0.484 61.11 120.45 5 1.079 1.297 0.593 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003475_lra.2021.3060708-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003475_lra.2021.3060708-Figure6-1.png", "caption": "Fig. 6. Potential field force generation with active occupied points.", "texts": [ " The repulsive force Fi exerted by each cell pi and the total repulsive potential field U of all occupied cells can be written as Fi (x, xpi) = \u2212\u2207Uref (x, xpi) , (7) U = \u2211 pi\u2208C Uref (x, xpi) . (8) Therefore, the total repulsive force on the haptic probe by the 3D occupied cells can be calculated as F = \u2212 \u2211 pi\u2208C \u2207Uref (x, xpi) . (9) The center of mass of the occupied grid cells, within a searching boundary from the haptic probe, is used to compute the direction vector and magnitude for the potential field force. Fig. 6 shows the potential field force generation strategy. C. Virtual-Proxy Force The proxy-based haptic interaction is employed to generate a contact force from the surface of the objects that feels like a relatively stiff surface to the user. This approach, which uses a notion of the virtual proxy, is widely used in haptic interactions [40]\u2013[42]. The force response, ff , of the haptic device in 3D using the spring-damper model that connects the virtual proxy and the haptic probe can be written as: ff = k ( xproxy \u2212 xprobe) + d ( vproxy \u2212 vprobe) , (10) where xprobe and xproxy are the positions of the haptic probe and the virtual proxy in 3D while vprobe and vproxy are the velocities of the virtual proxy and the haptic probe in 3D, respectively", " To provide seamless haptic interaction (quality of service) while enhancing the networked teleoperation performances, a computational cost reduction strategy with efficient search algorithm was applied to achieve smooth operations and intuitive usability. Any environmental objects within a certain spherical boundary from the haptic probe are explored rather than searching the full range of the workspace to detect the objects. Moreover, a region-of-interest (ROI) based local computations are employed that utilizes only part of the 3D points of the active environmental objects (active points in Fig. 6) when they are within a searching boundary from the haptic probe. Those strategies reduce the computational complexity to ensure continuous operation. Dynamic path planning of the haptic-microrobot system produces an effective path adaptively in the realistic haptic environment. An instant target is created based on the dynamic movement of the haptic device so that the near-optimal path from the current haptic position to the instant target is dynamically generated by reflecting the user\u2019s intention of the haptic control" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000026_c1ay05103b-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000026_c1ay05103b-Figure1-1.png", "caption": "Fig. 1 Diagram of the FI-CL system. a: Water carrier; b: luminol; c: H2O2; d: Co3O4 nanoparticles; V: injection valve; P1 and P2: peristaltic pumps; F: flow cell; W: waste; D: detector; PC: personal computer.", "texts": [ " After further stirring for 10 min, the obtained suspension was trans- ferred into a Teflon-lined stainless steel autoclave with 100 mL capacity. After the autoclave was sealed and maintained in an electric oven at 150 C for 3 h, it was cooled down to room temperature. The product was separated by centrifugation and thoroughly washed several times with ultrapure water until the pH of the supernatant was approximately 7, then dried at 60 C for 4 h. The as-synthesized Co3O4 nanoparticles could be welldispersed in aqueous buffer. A diagram of the flow injection CL detection system is shown in Fig. 1. Two peristaltic pumps (30 r min 1, Longfang Instrument Factory, Wenzhou, China) were used to deliver all solutions (luminol, H2O2/glucose solutions, Co3O4 nanoparticles, and water carrier) at a flow rate of 3 mL min 1 (per tube). PTFE tubing (0.8 mm i.d.) was used to connect all components in the flow system. For CL measurement, flow lines were inserted into the luminol solution, water, and Co3O4 nanoparticles solution, respectively. Then the pumps were started until a stable baseline was recorded" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001882_icmimt.2018.8340426-Figure8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001882_icmimt.2018.8340426-Figure8-1.png", "caption": "Figure 8. Contour plot of temperature distribution at various distances.", "texts": [ " However, as the powder stream is focused coaxially to the laser beam, the leading edge of the pool receives a higher amount of powder as compared to the trailing edge. Thus, at different moments during cladding, a slight accumulation of mass can be observed at the front edge of the pool. This accumulation is redistributed to the trailing edge as the melt pool moves forward. Fig. 7 illustrates the 2D distribution of temperature and it indicates the heat affected zone, deposit and substrate. It can be observed that deposit, interface section as well as heat affected zone have the higher temperature as this was theoretically expected. Fig. 8 represents temperature distribution at various positions. It is evident that at the initial position as shown in Fig. 8(a) the temperature is below 700 \u00b0C and as it moves towards the middle, the temperature rises to above 700 \u00b0C as illustrated in Fig. 8(b) and 8(c). As it moves towards the end, the temperature starts to decrease as shown in Fig. 8(d). Cooling rates are smaller at the middle of the track than at the end because the laser beam moving ahead of the middle of the tack continues to provide heat into the track. Figs. 9-12 represent the graph of heat affected zone height, dilution, aspect ratio and powder efficiency for experimental and CFD results. Analysing HAZ, dilution and aspect ratio graphs, it can be observed that the CFD results for the composites resembles the results obtained from experimental investigation with only 6% difference" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003176_tia.2020.2983632-Figure13-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003176_tia.2020.2983632-Figure13-1.png", "caption": "Fig. 13. (a) Dissembled stator, coils (left) and core (right), of the single sided machines. The same stator is used for S1M and S2M prototype machines. (b) The YASA machine, segmented stator (left) and both rotors (right), employed for experimental validation of the study. Similar rotors are used for single sided machines, with magnet thickness of only one of the rotors in the YASA machine (S1M) and double that thickness (S2M).", "texts": [ " Therefore, it is expected that YASA outperforms single sided structure at even lower current densities when more space is permitted in the axial direction. Likewise, for axially shorter designs single sided machines outperform YASA machine in a wider range of current density. This is shown by a second study for a smaller frame with 20% reduction in the slot depth, Fig. 9, where the YASA structure only barely outperforms the single sided machine at very high current densities. The 3D FEA model is validated with experimental measurements for the single sided and YASA machine. The prototyped machines are shown in Fig. 13. The test setup for the YASA and single sided machine are shown in Fig. 14. Measurements are performed in order to test the comparative performance of the machines under study at different electric loadings, in addition to validate the FEA results. The favorable agreement between back EMF constant obtained from measurements and 3D FEA, presented in Table II, attest to the fidelity of the simulations. The measurement of the torque-current characteristics are obtained for all three machines ensuring identical temperature by allowing sufficient cooling time between each measure- Authorized licensed use limited to: UNIVERSITY OF BIRMINGHAM" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001871_s00170-018-1840-1-Figure19-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001871_s00170-018-1840-1-Figure19-1.png", "caption": "Fig. 19 Distortion results in a laser cladded gasket specimen with two different patterns of bead deposition using DEA technique (distortion values were scaled 10 times larger)", "texts": [ " The simulated hardness contours of the specimens with longitudinal, transverse, and spiral patterns of cladding are shown in Fig. 18 which indicates that the specimens with the spiral and transverse patterns of cladding have the highest and lowest maximum hardness values. In addition, the spiral pattern of cladding creates more uniform hardness contour in the clad area. The DEA technique was further employed to study the effect of bead deposition patterns on distortion distribution and values in a gasket part shown in Fig. 19 with a large number of cladding beads which reveals the effect of bead deposition pattern on values and distribution of distortions. Effect of bead deposition pattern was explored by comparing three different patterns including out-ward, in-ward, and diagonal filling (Fig. 20) with the bead geometry of 8 mm width, 1 mm height, and 50% overlap. The results from Table 6 indicate that the out-ward and diagonal patterns 150 \u00d7 35 0.000 [\u2212 3.401]: 3.401 0.000 [\u2212 2.540]: 2.540 0 1 2 3 4 0 2000 4000 6000 Fl at ne ss ( m m ) Surface area (sq" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001170_we.1656-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001170_we.1656-Figure5-1.png", "caption": "Figure 5. (a) Response of the model under a traction force Q (fine lines: undeformed; coarse lines: deformed). (b) Q-\u03b4 curve of the nonlinear spring.", "texts": [ " Figure 4 shows the model for the contact between the ball and the outer ring-upper raceway and the inner ring-lower raceway (the other identical model for the outer ring-lower raceway and inner ring-upper Wind Energ. (2013) \u00a9 2013 John Wiley & Sons, Ltd. DOI: 10.1002/we raceway contacts is not represented in the figure). The spring was modeled by a unique traction-only nonlinear spring element (COMBIN39 in ANSYS, ANSYS INC., Canonsburg, Pennsylvania, USA) with an initial length L equal to the raceway diameter minus the ball diameter. When a forceQ acts on the spring (Figure 5a), its deformation \u03b4 is obtained by means of5the following: \u03b4 \u00bc 8:97\u00b710 4 1 s\u00f0 \u00de0:1946 Q2=3 dw1=3 (15) Wind Energ. (2013) \u00a9 2013 John Wiley & Sons, Ltd. DOI: 10.1002/we The Q-\u03b4 curve is the one represented in Figure 5b (for dw=20mm and s=0.943). In order to include the influence of the preload of the balls, in the present work, the spring has been divided into three elements, each of them with a length equal to a third of the raceway diameter minus the ball diameter (L/3): two of the elements are the nonlinear spring elements (COMBIN39) and the third one is a linear spring element (COMBIN14) with infinite stiffness. Thus, when a force Q is acting Wind Energ. (2013) \u00a9 2013 John Wiley & Sons, Ltd. DOI: 10.1002/we on the spring, the linear spring remains undeformed (the element in the center in Figure 6a)" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000146_1.34476-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000146_1.34476-Figure1-1.png", "caption": "Fig. 1 Tripropeller VTOL UAV.", "texts": [ " However, they both employ complex rotormechanisms to achieve these capabilities. For small VTOL aircraft, such as a small UAV equipped with multiple propulsion units, it is possible to use differential thrust as attitude control effectors, due to the small inertia of the rotors. In this paper, the guidance, navigation, and control (GNC) system design for a tripropeller UAVis introduced, based on a 6 degree-of-freedom (6DOF) nonlinear dynamic model. The structure of the tripropeller UAV is shown in Fig. 1a, herein referred to as the Ohio University UFO (unique flying object) or OU UFO, which is based on a flight control research and education test bed developed by Quanser, Inc.\u2021 known as the Quanser UFO (see Fig. 1b). Both of them are installed with three propellers, which are driven by dc motors. The attitude control of the UFOs is achieved by differential thrust of the propellers. The difference between the OU UFO and theQuanser UFO is that the latter has only 3DOF rotational motion, with attitude angles measured by three optical encoders mounted on the gimbal axes;whereas, the former is capable of 6DOF flight, with an additional 2DOF of control actuation provided by the flaps mounted in the slipstream of the propellers, and the attitude and position of the vehicle measured by an onboard inertial navigation system and Global Positioning System (GPS)", " The moments and total thrust generated by the voltages applied to the three motors and the yaw trim flap deflection angle, respectively, are determined experimentally as Mx My Mz fz T L U1 U2 U3 U4 T where L @Mx @U1 @Mx @U2 @Mx @U3 @Mx @U4 @My @U1 @My @U2 @My @U3 @My @U4 @Mz @U1 @Mz @U2 @Mz @U3 @Mz @U4 @fz @U1 @fz @U2 @fz @U3 @fz @U4 2 66664 3 77775 0 0:991 0:991 0 0:569 0:582 0:582 0 0:106 0:106 0:106 0:1 1:120 1:120 1:120 0 2 664 3 775 Hence, the actuator commands are given by U1com U2com U3com U4com 2 664 3 775 L 1 Mxcom Mycom Mzcom fzcom 2 664 3 775 The 6DOF controller and the UFO model are implemented in MATLAB/SIMULINK as shown in Fig. 5. The UFO model is implemented based on Eqs. (5\u20138) and (11) with actuator dynamics for each motor-propeller modeled as a second-order lowpass filter with a damping coefficient 0:707 and !n 30. The system parameters are based on the OU UFO shown in Fig. 1a with m 6 kg, Ixx 0:04012 kg m2, Iyy 0:05288 kg m2, Izz 0:09014 kg m2, Ixz 0:0002 kg m2, and CDV 0:02. The controller is implemented according to the design in Sec. IV. There are four (three-channel) pseudodifferentiators in the nominal controllers, and four LTV tracking error regulators in the overall closed-loop systems, as shown in Fig. 4. For the present work, constant controller parameters ijk are used for i 1, 2, 3, 4, j 1, 2, 3, and k 1, 2, as defined in Eq. (10), which define linear time invariant closed-loop dynamics for each of the four TLC loops described by the characteristic equation 2 2 ", " With these biases removed from measurements, lower long-term drifts in state estimates will be produced, thus allowing for longer system stability in the event of loss of GPS lock. The main results of this paper are the 6DOF TLC flight controller design and simulation testing for the tripropeller VTOL UAV. It is the first time that TLC is applied to 6DOF flight control, and the performance and robustness of the designed controller without any tuning are satisfactory. Future work includes implementing the 6DOF controller presented herein integrated with the 6DOF navigation system on the OU UFO shown in Fig. 1a for 6DOF hardware-in-loop testing and flight testing. Fine tuning of the controller parameters will be needed to account for actuator dynamics, sampling delay, and modeling errors, such as propeller thrust change due to vertical and forward velocity of the vehicle. With the use of inertial sensors, nonlinear observers (estimators), such as the extended Kalman filter, trajectory linearization observer [28], etc., will be implemented to estimate position and attitude from sensed body velocity and angular velocity" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002460_j.mechmachtheory.2018.03.018-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002460_j.mechmachtheory.2018.03.018-Figure1-1.png", "caption": "Fig. 1. Prototype of the 7R 6-DOF painting robot.", "texts": [ " [9] and Zhang and Xu [10] identified all singularity configurations of a class of manipulators with non-spherical wrist by the elementary Jacobian transformation method and depicted exemplar implementations for modified Canadarm2 and 6R manipulators with non-spherical wrist (modified from Canadarm2). However, this method is effective only for the manipulators with the last three joint axes orthogonal one another. As shown \u2217 Corresponding author. E-mail address: zhaochen@tju.edu.cn (C. Zhao). https://doi.org/10.1016/j.mechmachtheory.2018.03.018 0094-114X/\u00a9 2018 Elsevier Ltd. All rights reserved. in Fig. 1 , the 7R 6-DOF robot with a 4R 3-DOF wrist does not meet this condition. To the best of the author\u2019s knowledge, the singularity analysis of the 7R 6-DOF robot is still imperfect, thus remaining an open issue to be investigated. In this paper, a rational transformation between the 7R 6-DOF robot and the well-known equivalent 6R robot is constructed on velocity level. All singularity conditions are identified based on this transformation. A redundant robot which has more than necessary degrees of freedom (DOF) is more dexterous and versatile than a non-redundant robot", " Section 2 introduces the configuration of a 7R 6-DOF painting robot, derives the differential kinematic equation, and decouples the singularities into the position singularities and the orientation singularities. In Section 3 , all singularity conditions are identified based on a rational transformation between the 7R 6-DOF robot and the well-known equivalent 6R robot. In Section 4 , the methods to deal with the position singularities and orientation singularities are proposed. In Section 5 , two numerical simulations are implemented to demonstrate the effectiveness of the proposed method. The conclusion is drawn in Section 6 . As shown in Fig. 1 , the 7R 6-DOF painting robot consists of 7 revolute joints. Configuration of the first three joints i.e. R \u22a5 R//R is widely used in industrial robots, and the latter four joints construct the non-spherical wrist with the second and third of which are coupled with the relation: \u03b8 = \u2212\u03b8 . Fig. 2 shows the D-H coordinate systems of the 7R 6-DOF robot. The 6 5 corresponding D-H parameters are listed in Table 1 . Then, the kinematic equation can be expressed as t = [ \u03bdT , \u03c9 T ] T = J (\u03b8) \u0307 \u03b8 (1) where t \u2208 2 \u00d7 R 3 is the EE velocity, \u03bd and \u03c9 respectively denote the linear and angular velocities of EE, \u02d9 \u03b8 = [ \u0307 \u03b81 , \u02d9 \u03b82 , \u02d9 \u03b83 , \u02d9 \u03b84 , \u02d9 \u03b85 , \u02d9 \u03b87 ] T is the independent joint rate vector, J ( \u03b8) \u2208 R 6 \u00d7 6 is the Jacobian matrix" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002254_j.ijnaoe.2015.09.003-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002254_j.ijnaoe.2015.09.003-Figure1-1.png", "caption": "Fig. 1. Coordinate systems.", "texts": [ " The proposed portable DP system consisting of thrusters, whose rotation speed is controlled by using a neuro-fuzzy algorithm, generates forces to counteract environmental forces. Because an appropriate and professional ship equipped with a DP system is rare and costly, identifying alternatives to a sophisticated DP system is necessary. Moreover, many ships may not have originally been equipped with a DP system, and therefore, the use of portable outboard thrusters as a DP system, as suggested by the present study, could be an effective alternative. The mathematical model can be described in three coordinate systems, as illustrated in Fig. 1: the earth-fixed coordinate system O X0Y0Z0, ship body coordinate system G xyz, and horizontal body coordinate system G x 0 y 0 z 0 . The coordinates of the center of gravity of the ship in the O X0Y0Z0 coordinate system are represented by XG, YG, and ZG, and Euler's angles are denoted by f, q, and j. In this study, nonlinear equations based on the mathematical model of Fang and Luo (2005) were used to describe dynamic ship motion responses to external forces in the ocean. The nonlinear equations describing six-DOF ship motions under DP control are as follows: m _u v _j \u00bc my Xv _j v _j mx _u mxzG\u20acq mzw _q\u00feXFK \u00feXWF R\u00feXD \u00feFcx \u00feFTx Fcable \u00f0surge motion\u00de \u00f01\u00de m _v\u00fe u _j \u00bc mxu _j my _v\u00femyzG\u20acf Yvv Y\u20acj \u20acj\u00fe Y _j _j \u00fe Yvjvjvjvj \u00fe Yvj _jjv _j \u00fe Y _jj _jj _j _j \u00fe YFK \u00fe YDF \u00fe YWF \u00fe YD \u00feFcy \u00feFTy \u00f0sway motion\u00de \u00f02\u00de m _w\u00bc mz _w Zww Z\u20acq \u20acq Z _q _q Zqq\u00fe ZFK \u00fe ZDF \u00femg \u00f0heave motion\u00de \u00f03\u00de Ixx\u20acf Ixx _q _j\u00bc Jxx _q _j Jxx\u20acf K _f _f\u00femyzG _v\u00fe Yvv Y _j _j zG \u00feKFK \u00feKDF \u00feKWF \u00feNTx \u00f0roll motion\u00de \u00f04\u00de Iyy\u20acq\u00fe Ixx _j _f\u00bc Jxx _f _j Jyy\u20acq M _q _q Mqq M _w _w Mww mxzG _u\u00feMFK \u00feMDF \u00feNTy \u00f0pitch motion\u00de \u00f05\u00de Izz\u20acj Ixx _q _f\u00bc Jxx _q _f Jzz\u20acj N _v _v Nvv N _j _j\u00feN _jj _jj _j _j \u00feNvv _jv 2 _j\u00feNv _j _jv _j 2 \u00feNff\u00feNvjfjvjfj \u00feN _jjfj _jjfj \u00fe Yvv\u00fe Y _j _j\u00fe Yvjvjvjvj \u00fe Yvj _jjv _j \u00fe Y _jj _jj _j _j xH \u00feNFK \u00feNDF \u00feNWF \u00feND \u00feNC \u00feNTz \u00f0yawmotion\u00de \u00f06\u00de where m is the ship mass; mx, my, and mz are the ship added masses in the directions of the x-, y- and z-axis; Ixx, Iyy, and Izz are the mass moments of inertia about the three rotation axes; Jxx, Jyy, and Jzz are the ship added mass moments of inertia about the three rotation axes; u, v, and w are the surge, sway, and heave velocities of the ship in coordinate system G x'y'z', respectively; f, q, and j are the roll, pitch, and yaw displacements, respectively; and g is the acceleration of gravity" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000618_ilt-11-2011-0098-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000618_ilt-11-2011-0098-Figure4-1.png", "caption": "Figure 4 Principle of measuring the bearing eccentricity ratio", "texts": [ " In this experiment the fluted rubber bearing in Figure 2 was superseded by the rubber bearing with two cavities used in numerical calculation. The measuring method of the friction coefficient of the hydrodynamic lubrication rubber bearing is the same as that of the fluted rubber bearing. Experimental and numerical study on water-lubricated rubber bearings You-Qiang Wang, Xiu-Jiang Shi and Li-Jing Zhang Volume 66 \u00b7 Number 2 \u00b7 2014 \u00b7 282\u2013288 Themeasurement of the eccentricity ratio of the hydrodynamic lubrication rubber bearing is based on the principle of relative displacement as illustrated in Figure 4. In the experiment, the shaft rotates around the centreOofFigure 4 and the shaft center cannot be changed and held by the two hybrid bearings in the apparatus. So when the shaft rotates, the free rubber bearing center will be changed from the static state center O1 to the quasi-stable state center O2. Two capacitive transducers were put on the bearing circumferential circles in horizontal and perpendicular direction, respectively, for measuring the bearing clearances when the shaft keeps static and rotating at the quasistable state. The eccentricity ratio 1 of the hydrodynamic lubrication rubber bearing can be calculated by: 1 \u00bc e C0 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d2x \u00fe \u00f0C0 2 dy\u00de2 q C0 \u00f02\u00de where,C0 \u00bc R 2 r is the gapbetween thebearing and the shaft,R is the inner radius of the bearing and r is the outer radius of the shaft, e is the eccentricity of the rubber bearing or the distance from O1 to O2 in Figure 4. The measuring system of the hydrodynamic lubrication rubber bearing experiment is illustrated in Figure 5. In the experiment, first adjust the original distance between the capacitive transducer and the rubber bearing shell by the capacitive minimeter. Then keep the rubber bearing inner bottom contact with the shaft bottom by loading, and at this moment the eccentricity ratio 1 \u00bc 1. Output the light beam oscillogragh signals and record the digital display value of the transducer minimeter. Thereafter keep the rubber bearing inner top contact with the shaft top by reverse direction loading, and at that moment 1 \u00bc 21" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000911_978-1-4939-0292-7-Figure10.1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000911_978-1-4939-0292-7-Figure10.1-1.png", "caption": "Fig. 10.1 Moving Poincar\u00e9 section for the periodic trajectory . ?; P ?/, where TS. / denotes the tangent space", "texts": [ " This motivation has brought into play new state variables decomposing the system dynamics into a scalar variable , which represents the position along a target orbit, and the remaining coordinates, which represent the dynamics transverse to the orbit. Since the local properties of the system dynamics around the orbit are independent of , this variable can be safely disregarded beyond the orbit, whereas the transverse coordinate defines a moving Poincar\u00e9 section [77]. A family of (2n 1)-dimensional C1-smooth surfaces fS.t/; t 2 \u01520; T g of class C1 (see Fig. 10.1) is said to be a moving Poincar\u00e9 section associated with the solution q?.t/, t 2 \u01520; T , if \u2022 Surfaces S. / are locally disjoint; that is, there exists a \" > 0 such that S. 1/ \\ S. 2/\\ O\" D ;, for all 1 2 \u01520; T /, 2 2 .0; T , 1 \u00a4 2. \u2022 Each of the surfaces S. / locally intersects the orbit only in one point; that is, there exists \" > 0 such that S. / \\ f.q?.t/; Pq?.t//; jt j < \"g \\ O\".q?/ D f.q?. /; Pq?. //g for each 2 \u01520; T . \u2022 The surfaces S. / are smoothly parameterized by time; that is, there exists s 2 C1" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003195_s10846-019-01129-4-Figure8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003195_s10846-019-01129-4-Figure8-1.png", "caption": "Fig. 8 Test T1. Mechanical connectors. a Versions of the male and female mechanical connectors of one and two planes; b male and female connectors together in a perfect fit", "texts": [ " We conducted six preliminary tests (T1-T6) as proof of concept of the proposed architecture: \u2013 T1. Mechanical connections preliminary test. To evaluate aspects regarding the mechanical design, mechanical robustness, gaps, and interference, we printed in plastic sectors of a standard module and a mechanical connector, in natural scale. Distinct versions of the connectors were produced until we obtained a perfect fit with considerable mechanical robustness in the connection. After small corrections due to interference, we considered the mechanical drawing approved (Fig. 8). The strategy of the grooves was considered suitable for connecting the modules; \u2022 T2. Boards electrical test. Several candidate plugs for power circuits were previously investigated, and the 2- ways Molex Mini-Fit (male and female) plug, which supports up to 50A and 600V, was selected. To assure high-quality interfaces between the connectors and the module devices, special electronics boards were designed (Fig. 9). All boards were visually inspected and passed in electrical continuity tests; \u2013 T3" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000879_1.4026264-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000879_1.4026264-Figure3-1.png", "caption": "Fig. 3 Relative position of the head-cutter to the imaginary generating crown gear", "texts": [ " Appropriate modifications of existing basic manufacturing parameters can significantly enhance the EHD performance characteristics of the gear drive. For this reason, the following manufacturing parameters are taken as the basis of the proposed optimization formulation: the radii of the head-cutter blade profile (rprof1 and rprof2, Fig. 1(b)), the difference in head-cutter radii for the manufacture of the contacting tooth flanks of the pinion and the gear (Drt0), the tilt (j) and swivel (l) angles of the cutter spindle with respect to the cradle rotation axis (Figs. 2 and 3), the tilt distance (hd , Fig. 3), the variation in the radial machine tool setting (De, Figs. 2 and 3), and the variation in the ratio of roll in the generation of the pinion tooth 071007-2 / Vol. 136, JULY 2014 Transactions of the ASME Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/27/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use surface (Dig1). Therefore, the EHD load-carrying capacity of the oil film and the friction factor due to shear stresses in the oil film depend on the eight manufacturing parameters: W mp\u00f0 \u00de \u00bc W rprof1; rprof2;Drt0;j;l; hd;De;Dig1 fT mp\u00f0 \u00de \u00bc fT rprof1; rprof2;Drt0; j; l; hd;De;Dig1 (1) 2" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001791_j.mechmachtheory.2016.05.001-Figure2.2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001791_j.mechmachtheory.2016.05.001-Figure2.2-1.png", "caption": "Fig. 2.2. Sketch of UPR + SPR + SPS PM.", "texts": [ " (4b) and (4c), a novel velocity transmission equation can be derived as following: Vr \u00bc J2 v\u03c9 ;Vr \u00bc vr1 vr2 vr3 0 0 0 0 0 2 66666666664 3 77777777775 ; J2 \u00bc \u03b4T1 e1 \u03b41\u00f0 \u00deT \u03b4T2 e2 \u03b42\u00f0 \u00deT \u03b4T3 e3 \u03b43\u00f0 \u00deT f T1 d1 f 1\u00f0 \u00deT 0T 3 1 R11 R12\u00f0 \u00deT f T2 d2 f 2\u00f0 \u00deT 0T 3 1 0T 3 1 0T 3 1 0T 3 1 2 66666666666664 3 77777777777775 : \u00f06a\u00de Eqs. (3c) and (6a) have identical solutions. It can be seen from Eqs. (3c) and (6a) that J0,7 and J0,8 are converted into zero vectors in the process of elementary row operations. Thus, the constrained forces and torques in r3 of the Exechon PM are eliminated, r3 is converted into a SPS type leg, and then the second KIM (UPR + SPR + SPS PM) (see Fig. 2.2) for the Exechon PM can be easily obtained from Eq. (6a). Some geometric constraints are satisfied for this PM as following: R11\u2551A1A3;R11\u22a5R12;R12\u22a5r1;R12\u2551R13;R13\u2551a2o;R21\u2551a1a3;R21\u22a5r2: \u00f06b\u00de By adding \u22121 times the fifth row to the eighth row of Eq. (3c), then by adding 1/A1A3 times the fourth row and \u22121/A1A3 times the seventh row to the fifth row of Eq. (3c), a novel velocity transmission equation can be derived as following: Vr \u00bc J3 v\u03c9 ;Vr \u00bc vr1 vr2 vr3 0 0 0 0 0 2 66666666664 3 77777777775 ; J3 \u00bc \u03b4T1 e1 \u03b41\u00f0 \u00deT \u03b4T2 e2 \u03b42\u00f0 \u00deT \u03b4T3 e3 \u03b43\u00f0 \u00deT f T1 d1 f 1\u00f0 \u00deT 0T 3 1 0T 3 1 f T2 d2 f 2\u00f0 \u00deT f T3 d3 f 3\u00f0 \u00deT 0T 3 1 0T 3 1 2 66666666666664 3 77777777777775 : \u00f07a\u00de J0,5 and J0,8 denote the constrained torques in r1 and r3 in the Exechon PM, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001655_j.mechmachtheory.2018.01.012-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001655_j.mechmachtheory.2018.01.012-Figure4-1.png", "caption": "Fig. 4. Coordinate systems and relative motion for investigating mesh of enveloping spiroid drive.", "texts": [ " (29) By virtue of the meshing theory for gear drives [27] , the curvature parameters of (S) 1 , including the normal curvatures, k (1) \u03be and k (1) \u03b7 , along g1 and g2 , respectively, and the geodesic torsion \u03c4 (1) \u03be along g1 , can be attained without differentiating its complex equation, i.e. Eq. (22) . The attained results can be expressed as k ( 1 ) = \u2212 g 2 2z , k ( 1 ) \u03b7 = k 2 \u2212 \u03bc2 , \u03c4 ( 1 ) = \u03bcg 2 z . (30) \u03be d d \u03be d 4. Mesh of enveloping spiroid gearing The hobbing process of the conical worm gear is completely the same as the working process of the enveloping spiroid drive. Therefore, no distinction between these two processes will be made in the current work. 4.1. Equation of generating conical helicoid family and relative motion As Fig. 4 shows, a fixed coordinate system \u03c3o2 { O 2 ; i o2 , j o2 , k o2 } is employed to indicate the original position of the conical worm gear and the unit vector k o2 is along its axial line. The positive direction of the axis k o2 points to the heel of the conical worm gear. The two unit vectors, k o1 and k o2 , are perpendicular with each other and the unit vector i o2 is along their common perpendicular line. The shortest distance between k o1 and k o2 is the length of the straight line segment \u2212\u2212\u2192 O 2 O \u2032 and | \u2212\u2212\u2192 O 2 O \u2032 | = a ", " The i flank of the enveloping spiroid generally is the main load-bearing surface. Therefore, the rotation direction of the conical worm gear should be determined on the basis of the action between such a flank and the related tooth surface of the conical worm gear. In line with the helical direction of the enveloping spiroid and its rotation direction, it is possible to detect the direction of the normal force, F n , acted on the tooth surface of the conical worm gear by the i flank of the enveloping spiroid, which are marked in Fig. 4 (a). The circumferential force, F t , acted on the conical worm gear can be obtained by decomposing the normal force, F n , in accordance with the parallelogram law. The direction of this circumferential force, F t , ascertains the rotary direction of the conical worm gear. From this, it is possible to discover the direction of the angular velocity vector, \u03c9 2 , is toward the negative direction of the axis k o2 . A rotating coordinate system \u03c32 { O 2 ; i 2 , j 2 , k 2 } is associated with the conical worm gear" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003481_j.optlastec.2020.106782-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003481_j.optlastec.2020.106782-Figure6-1.png", "caption": "Fig. 6. Temperature distribution when the heat source reaches the centre node (node 3) of the third layer.", "texts": [ " Under a certain deformation condition, when the equivalent stress of a point in the stressed object reaches a certain value, the point begins to enter the plastic state. The expression is as follows: \u03c3 = \u0305\u0305\u0305 2 \u221a 2 \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\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\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305 (\u03c31 \u2212 \u03c32) 2 + (\u03c32 \u2212 \u03c33) 2 + (\u03c33 \u2212 \u03c31) 2 \u221a = \u03c3s (19) Among them, \u03c31, \u03c32, and \u03c33 are the first, second, and third principal stresses, respectively. The mechanical property parameters used for the stress field analysis in this study are shown in Fig. 5 [25,26]. Fig. 6 shows the temperature distribution when the heat source was located at node 3. It can be clearly seen from the figure that the maximum temperature at this time was 2265.54 \u25e6C, the minimum temperature was 261.358 \u25e6C, and the shape of the heat affected zone around node 3 was similar to the ellipse spreading to the periphery, which was consistent with the other studies [13,16]. In addition, it can be obviously seen that the temperature line at the front of the molten pool was relatively dense, and the temperature gradient was greater than that at the end of the molten pool" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003025_bf02919918-Figure13-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003025_bf02919918-Figure13-1.png", "caption": "Fig. 13. =. Motor ; b. Pair of levers.", "texts": [ " I t is convenient to fix our coordinate system, supposed to be at rest, to the body considered as immobile. A single mass m as represented in fig. 1 2c is in principle equivalent to a bi-terminal system with inertance m of which the second member is connected to the immobile. M o t o r. A motor in general is some machine tha t moves one body with respect to another body. Often one of these bodies m a y be considered as immobile or connected to the immobile, but this is not s tr ict ly necessary. In fig. 13a we have represented a motor tha t moves a rod by means of a pinion. The motor itself m a y glide, not rotate, while friction and inertia are supposed to be negligible. Then the system m a y t ransmit a force, meanwhile giving a differential movement x 2 - - x l . The power delivered is W = F ( v 2 - - v l ) . There are also motors tha t produce oscillatory motions. P a i r o f l e v e r s . A pair of levers as indicated in fig. 13b operates according to the formulae F 1/ F 2 = (v12 - - %2) / (v l l - - v21) = =12/ l 1. This means tha t a small force and a great velocity difference m a y be t ransformed into a great force and a small velocity difference or conversely, the power remaining the same. R i g i d j o i n t . At a rigid and massless joint of two or more solid bodies all the bodies have the same movement and the sum of the forces working on the joint is zero (see fig. 3c): v l = v 2 = v 3 . . . . . ; F1 + F 2 + F a + ", " An illustration of the complete analogy is given in fig. 5b and c where we have also introduced schematic symbols for the mechanical impedances. As to the latter we may remark: The symbol for a mechanical resistance was introduced by H e c h t 1) and the symbol for a spring is selfevident. We have not adopted Hecht 's symbol for inertance as it rather represents a mechanically working hydraulic inertance than a pure mechanical inertance; so we adopted a symbol suggested by fig. 12d. The symbol for the motor was derived from fig. 13a. As a consequence of the view adopted, a system of parallel mechanical impedances corresponds to an electric system with the analogous electric impedances likewise parallel, and a mechanical series system corresponds to an electric series system. This is represented in fig. 6b and c, and fig. 7b and c. M e c h a n i c a l o s c i l l a t o r s . Fig. 14arepresentsan-oscillator formed by a mass m suspended by a spring with compliance c, and fig. 14b-e represent schemes of it. In the pendulum of fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000931_9781118703274.ch2-Figure2.3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000931_9781118703274.ch2-Figure2.3-1.png", "caption": "Figure 2.3 Definition of blade pitch angle", "texts": [ " The air, according to equations (2.14) and (2.17), exerts identical forces on the rotor blades. For the sake of clarity, the physical processes will be shown for a single rotor blade. Multiblade arrangements for fast-running turbines (e.g. with z = 2, 3 or 4 lift-type blades) can be handled by extension of this system, considering conditions at a single blade of z-fold depth. Depending on blade radius, Figure 2.2 shows that there is different flow behavior at the profile for different blade angles (Figure 2.3). The combined effect of velocity components and the resultant forces are shown for a single blade element in Figure 2.4. Total values (forces, moments, power) are obtained by the integration of the corresponding values over the blade radius, or by summation of the components of individual blade sections. A segment at radius r of a blade rotating with angular velocity \ud835\udf14R experiences two airflows: that due to the wind deceleration across the swept area, v2 = v2ax + v2t (2.18) and that due to the speed of the rotating element at the given radius, v = \u2212\ud835\udf14R \u00d7 r" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002555_j.jsv.2019.115117-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002555_j.jsv.2019.115117-Figure2-1.png", "caption": "Fig. 2. Force distribution in bearing.", "texts": [ " The variation of AE with clearance for different loads at 1000 rpm is shown in Fig. 19. The variation of AE with speed at load of 4.9 kN is shown in Fig. 16. From Figs. 19 and 20, it can be observed that the AE decreases as the clearance increases. Also, it can be seen that irrespective of clearance the variation of AE with load and speed is similar to what is observed in Figs. 14 and 16, respectively. The decrease in AE due to an increase in clearance, mainly due to the angle subtended by load zone (refer Fig. 2) at the inner race center is computed from the solution of the MBDmodel at different clearance values. Fig. 21 shows the variation of load zone subtended angle at different radial clearance values. It is observed from Fig. 21 that the load zone subtended angle decreases with an increase in radial clearance. This indicates that during rotation of the bearing, the net area of contact between the raceways and rolling element decreases. As a result of this, the net number of asperities in contact reduces; releasing less amount of energy" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000560_j.mechmachtheory.2013.06.001-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000560_j.mechmachtheory.2013.06.001-Figure3-1.png", "caption": "Fig. 3. Four bar mechanism.", "texts": [ " 1(a), motion of a link relative to another link connected by a joint i is represented by a screw $i and the associated transformation matrix Ai is determined as in Eq. (1) from the Rodrigues parameters of the joint. The displacement of the end-effector from a reference position to a target position can be considered as a resultant of n successive screw displacements. The resultant screw displacement can be obtained by pre-multiplying the associated transformation matrices [22] and the target position p from the reference position p0 can be obtained as: p \u00bc A1A2\u22efAnp0: \u00f04\u00de A planar four bar mechanism with link lengths r1, r2, r3, and r4, shown in Fig. 3 is taken as an example to illustrate the application of screw theory. It is to be noted that the angles are defined with reference to previous link in order to apply screw theory. Table 1 gives relevant details of the mechanisms and the Rodrigues parameters are given in Table 2. Link-2 and link-4 are taken as input and output links respectively. Link-1 is fixed to the ground and link-3 is the coupler with coupler point CP positioned at a specified distance from joint-2. For analysis purpose, the mechanism is considered to be made up of two open chains closing at joint-3. First chain is made up of link-2 and link-3, and associated screws of joint-1 and joint-2 (namely $1 and $2) are shown in Fig. 3. Link-1 and link-4 constitute the second open chain and associated screw is $4. Considering the first open chain and taking Rodrigues parameters from Table 2, the position of end-point 3 of link-3 is determined by 3p \u00bc A1A2 3p0 \u00bc c\u03b82 \u2212s\u03b82 0 0 s\u03b82 c\u03b82 0 0 0 0 1 0 0 0 0 1 0 BB@ 1 CCA c\u03b83 \u2212s\u03b83 0 r2 1\u2212c\u03b83\u00f0 \u00de s\u03b83 c\u03b83 0 \u2212r2s\u03b83 0 0 1 0 0 0 0 1 0 BB@ 1 CCA r2 \u00fe r3 0 0 1 0 BB@ 1 CCA: \u00f05\u00de For the second open chain, the appropriate Rodrigues parameters given in Table 2 are used and the position of end-point 3 of link-4 is obtained as 3p \u00bc A4 3p0 \u00bc c\u03b84 \u2212s\u03b84 0 r1 1\u2212c\u03b84\u00f0 \u00de s\u03b84 c\u03b84 0 \u2212r1s\u03b84 0 0 1 0 0 0 0 1 0 BB@ 1 CCA r1 \u00fe r4 0 0 1 0 BB@ 1 CCA: \u00f06\u00de Equating Eqs" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002890_tia.2020.3033505-Figure10-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002890_tia.2020.3033505-Figure10-1.png", "caption": "Fig. 10. Overall comparison of the 6 FMPM models.", "texts": [ " This is because on the one hand, the current angle between the phase current and phase back-EMF increases, so the power factor angle between the phase current and phase voltage decreases, thus leading to a higher power factor. On the other hand, with the increase of the speed, the flux weakening effect becomes stronger, and the synchronous inductance increases, so the power factor decreases afterwards. All in all, taking rated torque, power factor, torque smoothness, overload capability and flux weakening capability into consideration, the radar map of 6 FMPMs is plotted in Fig. 10. It can be seen the overall performances of Nr=13 is the optimal. Authorized licensed use limited to: University of Gothenburg. Downloaded on December 19,2020 at 20:34:12 UTC from IEEE Xplore. Restrictions apply. 0093-9994 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. In order to verify the superiority of the proposed FMPM, it is compared to two regular FMPMs which include a regular stator-PM FMPM, and a regular rotor-PM FMPM with the employment of FEA simulations" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000502_00207179.2011.627596-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000502_00207179.2011.627596-Figure1-1.png", "caption": "Figure 1. Vertical take-off and landing aircraft.", "texts": [ " (1992), we consider the following input-disturbed aircraft system moving in the vertical-lateral plane: _x1 _x2 _x3 _x4 _x5 _x6 0 BBBBBBBBBBBBB@ 1 CCCCCCCCCCCCCA \u00bc x2 0 x4 1 x6 0 0 BBBBBBBBBBBBB@ 1 CCCCCCCCCCCCCA \u00fe 0 0 sinx5 \" cos x5 0 0 cos x5 \" sin x5 0 0 0 1 0 BBBBBBBBBBBBB@ 1 CCCCCCCCCCCCCA u1 \u00fe 1 u2 \u00fe 2 ! \u00f075\u00de \u00bc f \u00f0x\u00de \u00fe g\u00f0x\u00de\u00f0u\u00fe \u00de \u00f076\u00de with the outputs y1 \u00bc x1, y2 \u00bc x3, \u00f077\u00de where x1 and x3 denote, respectively, the horizontal position y and vertical position z of the aircraft centre of mass in the body-fixed reference frame shown in Figure 1, x5 is the roll angle of the aircraft, x2, x4 and x6 are the corresponding velocities, respectively, and \" is a small coefficient that characterises the coupling between the rolling moment and the lateral force. \u2018 1\u2019 denotes the acceleration of gravity; the control inputs are the thrust (directed out the bottom of the aircraft), u1, and the rolling moment about the aircraft centre of mass, u2, and 1 and 2 are thrust and rolling moment disturbances, respectively. D ow nl oa de d by [ U ni ve rs ity o f L ou is vi lle ] at 1 2: 38 2 3 D ec em be r 20 14 By introducing the following error coordinates: e1 \u00bc y1 y1d \u00bc x1 y1d, e2 \u00bc _y1 _y1d \u00bc x2 _y1d, e3 \u00bc y2 y2d \u00bc x3 y2d, e4 \u00bc _y2 _y2d \u00bc x4 _y2d, 1 \u00bc x5, 2 \u00bc \"x6 e2 cos x5 e4 sin x5, \u00f078\u00de and by defining the new inputs v1 \u00bc u1 sin x5 \u00fe u2\" cos x5 \u20acy1d, v2 \u00bc u1 cos x5 \u00fe u2\" sinx5 1 \u20acy2d, \u00f079\u00de the system (75) can be transformed in the normal form as _e1 \u00bc e2, _e2 \u00bc v1 \u00fe d1, _e3 \u00bc e4, _e4 \u00bc v2 \u00fe d2, _ 1 \u00bc 1 \" \u00f0 2 \u00fe e2 cos 1 \u00fe e4 sin 1\u00de, _ 2 \u00bc 1 \" \u00f0 2 \u00fe e2 cos 1 \u00fe e4 sin 1\u00de\u00f0e2 sin 1 e4 cos 1\u00de \u00fe \u20acy1d cos 1 \u00fe \u00f01\u00fe \u20acy2d\u00de sin 1, \u00f080\u00de where the new disturbances d1 \u00bc 1 sin x5 \u00fe \" 2 cos x5, d2 \u00bc 1 cos x5 \u00fe \" 2 sin x5: \u00f081\u00de Rewriting the internal dynamics by separating its linear part from its non-linear part yields _ 1\u00bc 1 \" e2\u00fe 1 \" 2\u00fe 1 \" \u00f0e2 cos 1\u00fe e4 sin 1 e2\u00de, _ 2\u00bc 1\u00fe 1 \" \u00f0 2\u00fe e2 cos 1\u00fe e4 sin 1\u00de\u00f0e2 sin 1 e4 cos 1\u00de \u00fe \u20acy1d cos 1\u00fe\u00f01\u00fe \u20acy2d\u00desin 1 1 , \u00f082\u00de which can be described in a matrix form as _ 1 _ 2 \u00bc 0 1 \" 1 0 " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000426_tmag.2012.2197734-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000426_tmag.2012.2197734-Figure2-1.png", "caption": "Fig. 2. Specifications of the proposed SR motor.", "texts": [ " The A-phase torque is expressed in the following equation by using the magnetic co-energy : (2) If the magnetic nonlinearity is ignored, the magnetic co-energy is expressed as follows: (3) From (2) and (3), the following equation is obtained: (4) It is understood from (4) that the positive torque can be obtained when the A-phase winding is excited in Region I of Fig. 1(b). On the other hand, the negative torque is generated 0018-9464/$31.00 \u00a9 2012 IEEE when it is excited in Region II. Therefore, the SRmotor requires the position detection. Fig. 2 shows the specifications of the proposed SR motor. It has 12 stator and 8 rotor poles, respectively. Three-phase concentrated windings are arranged on each stator pole. On the other hand, the auxiliary windings are wound around the stator yoke, which are excited by a dc current. Exciting directions of each winding are indicated by the arrows. The core and magnet materials are nonoriented silicon steel with a thickness of 0.35 mm and ferrite magnet, respectively. The residual flux density and the coercive force of the magnet are 0", " It is clear that the flux linkage is increased in the low-MMF region by exciting the auxiliary windings. Fig. 4(b) shows the static torque when auxiliary winding currents are 0 and 3 A, respectively. It is understood that the torque is increased, especially in the low-current region, by exciting the auxiliary windings. In addition, the cogging torque of the proposed SR motor is very small as shown in Fig. 5 because almost the all magnet flux circulates in the stator yoke. The proposed SR motor shown in Fig. 2 was made on a trial basis as shown in Fig. 6. Fig. 7 illustrates a configuration of the experimental setup. The auxiliary winding current is provided by the independent dc power supply. In the experiment and FEM simulation, the dc voltage of the drive circuit is V. The excitation beginning angle and the excitation width are and , respectively. Fig. 8(a) indicates the observed and calculated waveforms of voltage and current of the trial SR motor. The figure clearly reveals that both waveforms are in almost good agreement. Fig. 8(b) shows the comparison of the voltage and current waveforms when the auxiliary winding currents are 0 and 3 A, respectively. A load torque is in the both cases. It is understood that the phase current is decreased by exciting the auxiliary windings. Fig. 9 shows the specifications of the typical 12/8-pole SR motor used for the comparison, which has the same dimensions, core material, and windings as the proposed SR motor shown in Fig. 2. Fig. 10 shows the current density versus torque characteristics. In the figure, the solid, broken, and dotted lines indicate the calculated values, while the symbols denote the measured ones. Only the calculated values are indicated in the case of the typical SR motor shown in Fig. 9 since an actual machine does not exist. It is seen from the figure that the close agreement between the calculated and measured values is obtained, and that the torque of the proposed SR motor is improved by exciting the auxiliary windings" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002970_s00773-020-00746-1-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002970_s00773-020-00746-1-Figure3-1.png", "caption": "Fig. 3 The LOS guidance principle", "texts": [ " = r r\u0307 = \u2212 1 T r \u2212 a T r3 + K T \ud835\udeff + f \ud835\udefd = arctan (v\u2215u) 1 3 In this paper, the path following control consists of the reference heading based on LOS algorithm and heading angle control by MPC methodology. The structure of the control design as shown in Fig.\u00a02. In this section, a LOS guidance law is used to produce the reference heading angle. The LOS guidance method is proposed by Fossen [3] to reduce the control objects from (x, y, \u03c6) to \u03c6, that is to say, the matter of the path following is converted into the problem of the heading control [4]. Figure\u00a03 shows the principle of the LOS guidance. Where ye is the cross-track error, \u0394 is the lookahead distance, \u03b8k is the current straight line angle, 0 < \u03b1 <\u03c0 is the angle between the successive straight paths, \u03c3 =\u03c0\u2212\u03b1 is the turning angle, Rm is the radius of the circle of acceptance for the current waypoint, namely the acceptable radius of choosing the next waypoint. Firstly, the path is composed by the successive straight lines that connect the current waypoint Pk and the next waypoint Pk+1. Then, the LOS position Plos is located in the current straight line, and selected as the point where a circle intersects this straight line and closest to the next waypoint", " In this section, the LESO is presented to approximate the f and r that are used in MPC design. The ESO is the key part of ADRC proposed by Han [27]. Then, the LESO was developed by Gao [39]. Considering the items 3 and 4 in Eq.\u00a03, the LESO may be built where l1, l2 and l3 are LESO positive parameters.?\u0302? , r\u0302 and f\u0302 are the estimations of \u03c6, r and f, respectively. The \u03c6 and \u03b4 are the inputs, the r\u0302 and f\u0302 are the outputs of the LESO. In this section, the stability analysis is provided. According to the point-line distance formula and the Fig.\u00a03, the crosstrack error ye can be computed (15) { \u0307\u0302y = \u0302\u0307y \u2212 ky1(y\u0302 \u2212 y) \u0307\u0307\u0302y = \u2212ky2tanh(y\u0302 \u2212 y) , (16) { u\u0302 = \u0302\u0307y sin\ud835\udf11 + \u0302\u0307x cos\ud835\udf11 v\u0302 = \u0302\u0307y cos\ud835\udf11 \u2212 \u0302\u0307x sin\ud835\udf11 , (17) \u23a7\u23aa\u23aa\u23a8\u23aa\u23aa\u23a9 \u0307\u0302\ud835\udf11 = r\u0302 \u2212 l1(?\u0302? \u2212 \ud835\udf11) \u0307\u0302r = f\u0302 \u2212 r\u0302 T \u2212 ar\u03023 T + K T \ud835\udeff \u2212 l2(?\u0302? \u2212 \ud835\udf11) \u0307\u0302 f = \u2212l3(?\u0302? \u2212 \ud835\udf11) , 1 3 where ak, bk and Ck are the parameters of the current straight line. And considering the nonlinear observer (15) and LESO design (17), the estimation errors could be built where A\u0303 = A\u0302 \u2212 A (A denote z, z\u0307 , \u03c6, r and f) are the estimation errors, z denote x and y" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000931_9781118703274.ch2-Figure2.12-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000931_9781118703274.ch2-Figure2.12-1.png", "caption": "Figure 2.12 Main turbine types", "texts": [ " This can be represented in ramp form or \u2013 closer to what actually happens \u2013 in cosine form (Figure 2.10(a) and (b)). Mechanical and electrical losses depend mostly on performance and rotor speed. Effects due to thermal changes, etc., cannot easily be handled mathematically. For simple modeling, machine-dependent losses Pv = f (P) can be handled using constants (Pvo) and a power-dependent component (PvN), as shown in Figure 2.11. The conversion of kinetic energy from the wind for technical applications is effected by means of a variety of turbine types [2.4] (Figure 2.12). Machine designs are divided into horizontal and vertical axis types. Depending on the way in which energy is extracted from the wind, wide variations are discernible between converters, depending on whether they use the drag developed at the surface of the moving parts or the lift exerted on the blades. In turbines that use drag only, e.g. cup types, board constructions and other surfaces set against the wind, the energy derived is lower than that developed by lift types. Because of lower speeds of rotation, the use of such machines is limited essentially to driving mechanical devices", " Independently moving blades with cone hinges allow a freely self-adjusting cone angle (Figure 2.16(c)). This corresponds with the direction of the resultant of wind thrust (due to lift on the blade) and centrifugal forces as a result of the rotating blade masses, such that the articulation is free of bending moment in the direction of the wind. However, the two last-mentioned systems require relatively complicated constructions and are thus susceptible to repairs. They have therefore been unable to establish themselves on the market. As shown in Figure 2.12, the rotor (seen from upwind) can be run in front of the tower (the upwind model, as in historical windmills) or behind the tower (downwind model). Three-bladed rotors (Figure 2.17) are by far the most widely used horizontal-axis types in all power ranges. Two-bladed rotors \u2013 widespread in the 1980s at the beginning of the modern development of wind turbines \u2013 today represent the exception (Figure 2.18). Turbines with a single blade (Figure 2.19), which also appeared in this phase of development, currently occupy an absolutely exceptional position" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000729_j.optlaseng.2011.01.007-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000729_j.optlaseng.2011.01.007-Figure2-1.png", "caption": "Fig. 2. (a) Macrostructure of the directionally solidified Al\u20131.5 wt%Fe alloy ingot and reg sample subjected to the LSR treatment.", "texts": [ " A directional solidification apparatus was used to obtain an Al\u20131.5 wt%Fe alloy cylindrical casting. Specific information about this experimental set-up can be found in a previous article [23]. The cylindrical ingots were subsequently sectioned along its vertical axis, ground and etched with an acid solution (Poulton\u2019s reagent: 5 mL H2O; 5 mL HF \u2013 48%; 30 mL HNO3; 60 mL HCl) to reveal the columnar macrostructure. A longitudinal sample, coincident with the columnar growth direction, was extracted to be used in the laser remelting experiments, as shown in Fig. 2. ion from where the sample to be laser treated was extracted. (b) Schematics of the Table 1 Thermophysical properties used in simulations [21,23]. Properties Symbol/unit Al\u20131.5 wt.%Fe Thermal conductivity kS (W m 1 K 1) 219.2 kL 91.2 Specific heat cS (J kg 1 K 1) 1247 cL 1166 Density rS (kg m 3) 2620 rL 2450 Latent heat of fusion L (J kg 1) 387,000 Liquidus temperature TLiq (1C) 653.4 Absorptivity A (%) 37 The laser equipment used in the surface treatment experiments was an Ytterbium fiber laser (IPG, YLR 2000S), which emits radiation at a wavelength of 1070 nm and has a maximum power of 2000 W" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000281_tmech.2012.2182777-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000281_tmech.2012.2182777-Figure6-1.png", "caption": "Fig. 6. Free-body diagram of foot structure.", "texts": [ "5 kg, respectively. It consists of 12 dc motors with harmonic drives for the lower body and 16 RC servo motors for the upper body (two servo motors in each hand control). The on-board Pentium-III compatible PC, running RT-Linux, calculates the proposed algorithm every 5 ms in real time. To measure the ground reaction forces (GRFs) on the feet and the real ZMP trajectory while walking, as shown in Fig. 5, four FSRs are equipped on the sole of each foot, which are all sensors used in the experiment. Fig. 6 illustrates a free-body diagram of the foot structure for the ZMP measurement, where pli and pri (i = 1, 2, 3, and 4) are the 2 \u00d7 1 position vectors of the FSRs of the left and right feet, respectively. Note that since the ZMP is defined on the xy-plane, the position vectors are also defined on the xy-plane. In addition, fli and fri are the GRFs measured by FSRs of each foot, respectively. pzmp = [xzmp yzmp]T represents the ZMP position vector. In this ZMP measurement model, it is assumed that each FSR is in the contact point with the ground" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002764_j.triboint.2019.04.041-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002764_j.triboint.2019.04.041-Figure1-1.png", "caption": "Fig. 1. (a) The semi tooth flank of crowned herringbone gears and (b) contact ellipse of EHL point contact.", "texts": [ " rt1 and rt2 are given by rt1= rb1tan\u03c6+s and rt2= rb2tan\u03c6+s, where rb1 and rb2 are the base radii of the driving and driven gears, respectively. \u03c6 is the normal pressure angle. s is the distance vector from pitch point to mesh point in the transverse plane, and the distance along LOA indicates the distance between the nominal approach point and mesh point in the transverse plane as well. Therefore, the effective radius in x direction is calculated by Rx= R1R2/(R1+R2). The crown modification is applied to herringbone gears as shown in Fig. 1 x and y coincide with the minor and major axes of the contact ellipse respectively, which denote the directions along involute profile and face width, respectively. It is noted that the effective radius Ry is larger than Rx. The semi major and semi minor axes are b and a, respectively. The effective radius in the y direction depends on the crown modification amount \u03b4 and the face width 2B of herringbone gear, which is expressed as [13]. =R B 8 cosy b 2 (17) The rolling speeds of two contacting solids at mesh point in the x direction can be written as = = u r u r 1 1 1 2 2 2 (18) where \u03c91 and \u03c92 are the angular velocities of driving and driven gears, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001876_j.mechmachtheory.2018.04.002-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001876_j.mechmachtheory.2018.04.002-Figure5-1.png", "caption": "Fig. 5. The instantaneous contact curve i 0 and its modified curve i 1 .", "texts": [ " At any given pinion angular position \u03d5 i 1 , given any discrete point p i j 0 (u j 2 ) on the instantaneous conjugate contact curve i 0 , the corresponding discrete point p i j 1 (u j 1 , v j 1 ) on the contact curve i 1 can be determined by solving the following system of nonlinear equations: x i j 1 ( u 1 , v 1 ) = L i j \u221a y i j 1 ( u 1 , v 1 ) 2 + z i j 1 ( u 1 , v 1 ) 2 = R i j (14) where [ x i j 1 , y i j 1 , z i j 1 ] T is the position v ect or of the discr ete point p i j 1 r epr esented in sy stem S 1 . The instantaneous conjugate contact curve i 0 and its modified curve i 1 at the pinion angular position \u03d5 i 1 are illustrated in Fig. 5 . As shown in Fig. 6 , for any pinion angular position \u03d5 i 1 , H ( j ) is the gap between the contact curve i 0 and its modified curve i 1 at the j th discrete point pair, p i j 0 and p i j 1 (u j 1 , v j 1 ) . So, the minimum gap ( i ) between the instantaneous conjugate contact curve i 0 and its modified curve i 1 represents the instantaneous unloaded transmission error, and can be defined as H ( j ) = \u221a (y i j 1 \u2212 y i j 0 ) 2 + (z i j 1 \u2212 z i j 0 ) 2 ( i ) = min H ( j ) j = 1 , \u00b7 \u00b7 \u00b7 , m (15) Here, m is the number of discrete point pairs, and is closely related to the precision of the TCA" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003535_j.mechmachtheory.2021.104436-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003535_j.mechmachtheory.2021.104436-Figure5-1.png", "caption": "Fig. 5. PB-limbs configuration.", "texts": [ " It consists of moving platform, base platform, links, R-joints and arcshaped prismatic (PR) joints. The origins of the fixed coordinate system (system {1}) and the moving coordinate system (system {2}) coincide with O1 and O2, respectively. The connection line between the 2 origins is defined as \u2019double center line\u2019 of the limb, which is represented by symbol O1O2. According to the basic properties of the GSPM, the length of O1O2 should always be equal to l. The link directly connected with the base platform is driving link of the PB-limb. As shown in Fig. 5, a series of PB-limbs meeting the requirements are listed, and their constraint performance is analyzed based on the screw theory. The constructed PB-limbs [RR] [RRR], [RR] [RR], [RR]R, [PRR] [RRR], [PRR] [RR] and [PRR]R are coded as limb-i (i=1, 2, 3, 4, 5, 6) in sequence. As shown in Fig. 5, rotating axes O1Ai and O1Bi in the limb-i are perpendicular to each other and intersect at O1. The rotating axis O2Ci is parallel to axis O1Bi, and both axes are perpendicular to O1O2. Specially, rotating axes O2C1, O2D1 and O2E1 in the J. Zhang et al. Mechanism and Machine Theory 166 (2021) 104436 limb-1 intersect at O2 (Fig. 5(a)); rotating axes O2C2 and O2D2 in the limb-2 intersect at O2 (Fig. 5(b)); rotating axes O2C4, O2D4 and O2E4 in the limb-4 intersect at O2 (Fig. 5(d)); and rotating axes O2C5 and O2D5 in the limb-5 intersect at O2 (Fig. 5(e)). The origin of the limb coordinate system is set to coincide with O2, and the z-axis is along the O1O2 direction, which is shown in Fig. 5. The $i1, $i2, $i3, $i4 and $i5 respectively represent the motion screws of rotating axes O1Ai, O1Bi, O2Ci, O2Di and O2Ei in the limb-i (i=1, 2, 3, 4, 5, 6). They form the motion screw system of the limb-i. By further calculating its reciprocal screw system, the constrained screw system of the limb is obtained, and the constraint characteristics of the limb are clarified. $r ijrepresents the jth constraint screw of the limb-i. As shown in Figs. 5(a) and (d), the motion screw systems of both limb-1 and 4 contain only 5 motion screws, and they have almost same expressions" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000399_icaccct.2012.6320804-FigureI-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000399_icaccct.2012.6320804-FigureI-1.png", "caption": "Fig I. TRMS phenomenological model", "texts": [ " SYSTEM DESCRIPTION The TRMS mechanical structure consists of two rotors placed on a beam together with a counterbalance whose arm with a weight at its end is fixed to the beam at ht e pivot and it determines a stable equilibrium position. The entire structure is attached to the tower allowing for safe helicopter control experiments. In normal helicopter, angle of attack is a control for controlling the aerodynamic force whereas in the laboratory ISBN No. 978-I-4673-2048-II12/$31.00\u00a920 12 IEEE setup as shown in Fig.I, the angle of attack is fixed. Hence, the speeds of rotors are varied to control the aerodynamic force. Therefore, supply voltages of dc motors are changes to control the rotation speed of the propeller which will change the corresponding position of the beam, where ([) and IjI are the corresponding horizontal and vertical positions of the beam [3]. Usually, the phenomenological models are nonlinear, that means at least one of the positions of the beam is an argument of a nonlinear function. In order to present such a model as a transfer function, it has to be linearised" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000137_s00422-011-0422-1-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000137_s00422-011-0422-1-Figure6-1.png", "caption": "Fig. 6 Single-leg simulator setup with three degrees of freedom (DOF) rail setup. Forward- and backward movement was unlimited but slightly damped, sidewards movement was restricted by a stiff spring-damper system and up- and downward movement was damped, unlimited in upwards direction and limited in downwards direction by a support platform. No rotational movements was allowed. Additionally segment names of the walking machine are given. For joint names see Fig. 1", "texts": [ " Similar to the setup described in von Twickel and Pasemann (2007), the torso of the single-legged walking machine was mounted on a rail system that allowed for forward and backward movements (damping constant 10 Ns m to stop movements during stance in a reasonable time interval) and up- and downward movements (damping constant of only 1 Ns m because ventral hard stop was always active). Additionally, it had a lateral spring-damper (damping constant 200 Ns m , spring constant 750 N m ) system to simulate lateral 2 The ODE library is a game physics engine geared toward speed, a prerequisite for employing evolutionary algorithms. Successful transfers of complex controllers from simulations to real robots are used as the criterion of sufficient precision. For details please see the cited literature. force influences of other legs (see Fig. 6). This allowed for small lateral movements similar to hexapod walking in stick insects (cp. Kindermann 2002). As an exception, the springdamper system was replaced by a simple damper (damping constant 50 Ns m ) in sidewards walking simulations. Up-down and sidewards rails included force sensors to measure forces exerted by the leg. The joint setup was similar to the one described in Ekeberg et al. (2004): each leg had three active hinge joints, namely Thorax-Coxa (ThC), Coxa-Trochanter (CTr), and Femur-Tibia (FTi)", " In both the parameter optimization cases (restricted and unrestricted, see above for details) lateral forces vanished with progressing optimization, becoming more similar to the in vivo example. The front-leg medio-lateral forces, though smaller in magnitude than in middle- and hind-legs, persisted. 50 [N ] Foreleg Middleleg Hindleg G0 G100 G1000 Foreleg Middleleg Hindleg a b 1 [m N ] 1 [s] G100 G1000 detcirtser detcirtsernu dorso-ventral forces (up increasing body support by leg) medio-lateral forces (up increasing medial force on body by leg) Fig. 15 Dorso-ventral and medio-lateral torso support forces (directions correspond to y- and z-axes in Fig. 6) by single legs: a in simulation (measured were forces between torso and rail suspension during forward walking) for hand tuned (G0) and parameter optimized controllers (G100 after 100 generations, G1000 after 1000 generations, restricted means optimization was only performed on a limited parameter set, cp. section 2.4.2) driving front-, middle-, and hind-legs. For each situation six independent parameter optimizations were run and for each best con- troller forces of five consecutive step cycles were averaged (gray lines)" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003340_j.addma.2021.101881-Figure14-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003340_j.addma.2021.101881-Figure14-1.png", "caption": "Fig. 14. Residual deformation in the (a) longitudinal and (b) vertical build direction before (BSR) and after support removal (ASR) simulated using 32 equivalent layers and 32 load steps (Benchmark no-lumping case).", "texts": [ " As a supplemental study, we have performed a simulation where 48 additional load steps are adopted since there are 4 elements in the thickness dimension of each block in the 16 mm-high cantilever beam (see Fig. 13). Compared with the simulation using 24 additional load steps, insignificant errors are found between the predicted residual deformations in the two cases. To save computational time, finally 24 additional load steps are employed consistently to simulate the support removal process in different scenarios including Section 3.1. The dominant shrinkage deformation occurs along the beam-support interface (see Fig. 13) in the length direction of the cantilever beam as shown in Fig. 14(a). Moreover, the dominant residual deformation occurs at the end of the beam in the vertical build direction as illustrated in Fig. 14(b). The simulation results are referred to as the benchmark no-lumping case in the following contents. For the purpose of validating the simulation results, the large cantilever beam was produced by L-PBF (EOS M290 DMLS printer) employing the same process parameters given in Section 3.1. After the fabrication process, W-EDM was employed to make a cut along the solidsupport interface to separate the teeth supports and cantilever beam. In addition, a 3D laser scanning device was used to measure the overall residual deformation before and after cutting", " MPM #2 is the artificial constitutive model used specifically to tune the inherent strains and yield stress for the low layer in the 2-layer ELLM case. Accordingly, the entire model is divided into two sections prepared to have two sets of material property parameters. The equivalent layerbased division is shown in Fig. 16. Certainly, it takes shorter time to finish running the 16-step simulation relative to the 32-step no-lumping case. The obtained residual deformation before and after separating the teeth support from the cantilever beam is shown in Fig. 17. Compared to those results in the benchmark no-lumping case (see Fig. 14), the prediction error is very small, thus demonstrating good accuracy of the 2-layer ELLM employing a tuned MPM to avoid stress and deformation overestimation. As a supplemental study, the computed residual deformation in vertical build direction after support removal using 2-layer LLM without the tuned MPM is shown in Fig. 18 as a comparison. It is seen that the prediction error for the maximum vertical deformation becomes larger compared to Fig. 17(b) with reference to the benchmark results in Fig. 14. This phenomenon strongly proves that material property tuning X. Liang et al. Additive Manufacturing 39 (2021) 101881 is necessary to improve the accuracy of the layer lumping method. As a further step, the 3-layer ELLM is studied in this example. Correspondingly, two more adjusted MPMs (#2 and #3) are needed in addition to the real MPM (#1) for IN718. Three adjacent equivalent layers are lumped into a super layer in the 3-layer ELLM case. As a benefit, only 11 load steps are needed for the 32-layer model", "1, the third MPM (#3) uses the specific material property parameters as seen in Table 2. Given the three MPMs above, the entire cantilever beam model is divided into three sections for layer-wise assignment of material properties accordingly. It takes much shorter time to finish the 11-step simulation than the 2- layer ELLM case and the 32-step benchmark case. The obtained residual deformation before and after removal of the support structures is shown in Fig. 19. Compared to those results in the benchmark case (see Fig. 14), the prediction error is acceptable though it increases slightly due to the lumping effect compared to the 2-layer ELLM case. Note the gray color near the arrow in Fig. 19(a) suggests shrinkage magnitude is beyond the maximum value of the legend color band. Another trial is to develop the 4-layer ELLM in order to accelerate the layer-wise simulation to a further extent. Correspondingly, three additional tuned MPMs (#2~#4) are needed in addition to the real MPM (#1) for IN718. Four adjacent equivalent layers are lumped into a super layer in the 4-layer ELLM case", " The computational time can be further reduced compared to the 2-layer and 3-layer ELLM case in Sections 4.1.1 and 4.1.2. Adjusted parameters of the involved fourth MPM (#4) in this example are already given in Table 2. It takes a lot shorter time to finish the 8-step simulation than the above two ELLM cases and the 32-step benchmark case. The obtained residual deformation before and after removal of the teeth-like structures is shown in Fig. 20. Compared to those results in the benchmark case (see Fig. 14), the overall trend of the residual deformation before and after removal of support structures matches well. However, the prediction error increases more significantly due to the lumping effect. The gray color area, which suggests residual deformation magnitude beyond the maximum value of the legend color band, becomes obviously larger in Fig. 20 compared with Fig. 19. One possible reason for the slightly increased prediction error is attributed to the geometry of the cantilever beam. The sudden transitional change of cross sections in the build direction, like the solid-support interface of the cantilever beam, is not considered in the meso-scale modeling", " Starting from the 23rd layer, four MPMs are sequentially assigned to the equivalent layers in the second section layer-wisely. Three more load steps are needed to finish the simulation while the two top layers (Layer #31 and #32) are activated in the last step. Due to TSD, computational time increases slightly compared with the previous 8-step simulation. However, the simulation accuracy is improved significantly as shown in Fig. 22. For example, the maximum X. Liang et al. Additive Manufacturing 39 (2021) 101881 vertical displacement of the selected point is 1.67 mm. Compared with the benchmark case (1.70 mm, see Fig. 14), the simulation error is reduced to 1.8%. In summary, the results have validated the necessity of the TSD or multi-section division (MSD) technique especially when some metal builds with transitional cross sections in the build direction are considered using the ELLM in the layer-wise simulation. The simulation times for all the cases are listed in Table 3 using the same desktop computer as in Section 3.1. It is shown that the simulation times using ELLM are reduced significantly. For example, if the 4-layer ELLM case with TSD is compared to the no-lumping case, the simulation time is decreased by 70%", ", in the 4-layer ELLM case, good accuracy can be obtained when a specific TSD technique is combined with the ELLM. However, upon closer examination of the results (see Figs. 20 and 22) obtained by the 4-layer ELLM cases in Section 4.1.3, it is found that the longitudinal shrinkage of the as-built cantilever beam shows incorrect distribution pattern, especially for those points on the outer surface nearby the solid-support interface. The shrinkage deformation does not look smooth enough compared with the simulated results in the benchmark no-lumping case (see Fig. 14(a)). This irregular shrinkage pattern is caused by lumping of too many layers. When more equivalent layers are merged into one super layer, they are activated and deformed simultaneously in one load step, which is inconsistent with the physical bottom-up nature of L-PBF process. As a result, when more and more equivalent layers are lumped into one super layer, the ELLM can have larger and larger error in the predicted residual deformation of the large as-built metal components. Therefore, the 4-layer ELLM case is suggested as the limiting case that may be employed to accelerate the simulation to the largest extent while good simulation accuracy can be ensured" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003469_jestpe.2021.3058261-Figure21-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003469_jestpe.2021.3058261-Figure21-1.png", "caption": "Fig. 21. Pictures of the prototype. (a) 18-slot stator core. (b) 15-slot stator. (c) Rotor. (d) Assembly and test bench.", "texts": [ " That is, there is the trade-off between the torque capability and power factor, which cannot be meet at the same time. Especially, for the model with slot/pole combination 18/12/6, namely pole ratio is 2, the torque capability of which is weaker than the 18/11/7 counterpart. And the reason is that the winding factor of 18/12/6 is 0.87, while the winding factor of 18/11/7 is 0.9. In order to validate the foregoing analysis, an 18/14/4 PMVM prototype and a 15/14/1 PMVM prototype with pole ratio of 3.5 and 14 have been built and tested, as shown in Fig. 21. Their major parameters have been listed in Table V. To investigate the influence of armature magnetic field on the machine performance, the two prototypes have the identical PM rotor, stack length and stator diameter. And the only difference between them is the stator slot number and winding pole-pair. In terms of the armature magnetic field, it is a \u201cmicroscopic\u201d viewpoint which is difficult to be verified by experiments. However, the influence of armature magnetic fields on machine \u201cmacroscopic\u201d performance, including torque, power factor and back-EMF, can be acquired by experiments" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003195_s10846-019-01129-4-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003195_s10846-019-01129-4-Figure1-1.png", "caption": "Fig. 1 Reconfigurable drones patents. a Drone with reconfigurable position of actuators from Elwha LLC; b Drones with interconnected structures from Amazon Technologies", "texts": [ " State-of-the-art works (academic, prototypes and patents) are exploring in different ways the concepts related to the physical reconfiguration or modularity in UAVs. Considering the physical disposition of the modules, at least four main strategies have been employed: 1. Moving parts. This class groups drones that can move its actuators [11, 12]. It refers to the simplest reconfiguration strategy where actuators can be rotated or even shifted (even during the flight) to allow more suitable movements (Fig. 1a); 2. Combined aircraft. This class groups full drones that can fly alone and that can also fly when connected [2, 18]. Although each robot is equipped with all onboard equipment (actuators, sensors, processor, battery and others), this strategy allows their combination into complex structures able to fly in distinct shapes (Fig. 1b); 3. Main body. This class groups drones with the main body in which multiple actuators can be attached [1, 34]. In this kind of aircraft, there is a central module which carries the main processor, battery, and control apparatus. Structures connected to this module allow the connection of actuators. This strategy has been employed mainly to allow the transportation of heavy and sometimes variable loads (Fig. 2a and b); 4. Modular. This class groups drones made of modules that are unable to fly alone but that are capable of flying when connected to each other" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002460_j.mechmachtheory.2018.03.018-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002460_j.mechmachtheory.2018.03.018-Figure4-1.png", "caption": "Fig. 4. Configuration of the equivalent 6R robot [6] .", "texts": [ " det ( J 11 ) = 0 (8) det ( J 22 ) = 0 (9) In Section 2 , the Jacobian matrix J is expressed in a block matrix form. However, for the 7R 6-DOF robot, the expression of J 22 is still complicated. In order to obtain the analytical expression of Eq. (9) , a rational transformation between the 7R 6-DOF robot and the well-known equivalent 6R robot is constructed on velocity level. Here, the equivalent 6R robot refers to a serial 6R robot with last three joints intersecting at one point and orthogonal one another, as shown in Fig. 4 . By comparing the two robots, configurations of the first three joints are the same and the wrists are different. Thus, the first three joint angles of the two robots are set to be equal, described by Eq. (10) . In order to derive the whole transformation, the orientation mechanism of the 7R 6-DOF robot and the equivalent 6R robot is respectively noted as 4R wrist and equivalent 3R wrist, as shown in Figs. 5 and 6 . Bruyninckx et al. [28] have made a comparison of the two wrists and presented an algorithm to derive the transformation between the two wrists" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001864_1.g002873-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001864_1.g002873-Figure3-1.png", "caption": "Fig. 3 With perfect symmetry vR can be 0.", "texts": [ " The vector vT can also be zero for other values of \u03c3B\u2215R. This situation is studied in the following section. It has been shown that the laws given by Eqs. (41) and (48) are Lyapunov stable but not necessarily asymptotically stable. Consider, for example, the special case in which vT 0 and \u03c3B\u2215R \u2260 0. Fortunately, it turns out that this occurs only with very specific symmetry conditions. To understand the geometric conditions that lead to this situation, consider the following regulation problem (\u03c3R\u2215N 0), depicted in Fig. 3. Let there only be one exclusion condition, given by n\u0302 y\u0302N. The boresight vector is in the body x\u0302 direction: b\u0302 x\u0302B. In this qualitative description, the angle \u03b8min is not relevant. The initial attitude is a rotation of 180\u00b0 about z\u0302N . Thus \u03c3B\u2215N tan 180\u00b0\u22154 z\u0302N . The vector vR will be vR \u2212\u03c3B\u2215N ln \u2212 CE 1 \u03c3B\u2215N \u03b11 \u2212 2 ln 1 \u03c3TB\u2215N \u03c3B\u2215N B ~b BN N n\u0302 CE 1 \u03c3B\u2215N (57) A necessary (but not sufficient) condition for vR to be zero with a nonzero \u03c3B\u2215N is \u03c3B\u2215N and B ~b BN N n\u0302 to be antiparallel. The latter is simply the vector b\u0302 \u00d7 n\u0302 written in the body frame" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003185_s00894-020-04395-4-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003185_s00894-020-04395-4-Figure1-1.png", "caption": "Fig. 1 AlSi10Mg nanoparticle pair. a Even-sized particles. b Uneven-sized particles", "texts": [ " Crystallographic orientation along X-, Y-, and Z-directions is set at < 100 >, < 010 >, and < 001 > with shrink-wrapped boundary conditions in all directions. Initially, the two-particle pairs are thermally equilibrated at 300 K for 20 ps to ensure the stability of atoms. Subsequently, different laser energy density, i.e., from 7 to 17 J/mm2, is applied in the MD simulation domain using the NVT ensemble. The laser energy density is incorporated in terms of temperature in this work. Sintering temperatures are extracted from a thermal model developed by Panda and Sahoo [36]. The time-step size in this work is taken 0.01 ps. Figure 1 shows the schematic diagram of particle arrangement and initial configuration of AlSi10Mg nanoparticle pair for both even and unevenly sized particles. Coalescence of pre-alloyed AlSi10Mg particles Classical molecular dynamics simulations are conducted to gain the fundamental insight of the necking and coalescence mechanism of pre-alloyed AlSi10Mg nanoparticles in the DMLS process at different laser energy density. The following relation is used to calculate the laser energy density [37]: Ed \u00bc PL hd:vs \u00f04\u00de where PL is the laser power in W, vs" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000193_j.cma.2011.04.006-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000193_j.cma.2011.04.006-Figure1-1.png", "caption": "Fig. 1. Pitch cones of bevel gears.", "texts": [ " The larger end of the pitch cone corresponds to the pitch diameter of the bevel gear. Given the module and the number of teeth of pinion and gear, their pitch radii are determined by rp1 \u00bc mN1 2 ; rp2 \u00bc mN2 2 : \u00f02\u00de Eq. (2) can be used for straight and skew bevel gears. Notice that the skew angle is not considered when determining the pitch radii for skew bevel gears. The pitch angles of pinion and gear for any given shaft angle R are determined by c1 \u00bc arctan sin R cos R\u00fem12 ; c2 \u00bc arctan sin R cos R\u00fem21 : \u00f03\u00de As shown in Fig. 1, the pitch cones are contained in a sphere of radius Ro, the outer pitch cone distance, determined by Ro \u00bc rp1 sin c1 \u00bc rp2 sin c2 : \u00f04\u00de The face and root angles of the pinion and gear tooth surfaces, cF and cR, will be determined by cF1;2 \u00bc c1;2 \u00fe ham Ro ; cR1;2 \u00bc c1;2 hf m Ro : \u00f05\u00de Here, ha and hf are the addendum and dedendum coefficients, usually chosen to be 1.0 and 1.25, respectively. According to typical design practice, the face width of a bevel gear is generally chosen as one third of the outer pitch cone distance, Fw Ro 3 : \u00f06\u00de 3", " (9)\u2013(11), the reference blade profiles are represented in coordinate system Sc as rc\u00f0u\u00de \u00bc a\u00f0i\u00depf \u00f0u u0\u00de2 cos ad u sinad pm 4 a\u00f0i\u00depf \u00f0u u0\u00de2 sin ad \u00fe u cos ad 0 1 2 66664 3 77775: \u00f012\u00de As mentioned above, the upper and lower signs correspond to the left and right blade profiles, respectively. 3.2. Geometry of the imaginary generating crown-gear The following ideas are applied for definition of the geometry of the generating crown-gear: The reference blade profile is developed over the outer sphere defined by the pitch cones of the to-be-generated pinion and gear, i.e., each point M of the reference blade profile has its corresponding point M0 on the sphere with radius Ro, the outer pitch cone distance, as shown in Fig. 1. The pitch plane of the generating crown-gear is defined by the pitch line of the reference blade profile and the center of the sphere. The geometry of the imaginary generating crown-gear will be obtained in coordinate system Scg, with origin in the center of the outer sphere and axis zcg containing the origin Oc of the reference blade profile coordinate system Sc, and axes xcg and ycg parallel to axes xc and yc of the reference blade profile, respectively (Fig. 5). of the imaginary generating crown-gear" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000259_j.cirp.2010.03.020-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000259_j.cirp.2010.03.020-Figure6-1.png", "caption": "Fig. 6. Tripod-based mechanism.", "texts": [ " vertical displacement of the milling head in the range h = 175 mm and angle of rotation around the horizontal axis in the range ux = 0\u2013458, for the stiffness value of the rotational drives krot = 6 106 N-m/rad, is shown. The minimal TSV lies in the within very narrow limits 0.70\u20130.72, i.e., has only a weak dependence on specific values of parameters h and ux. The dominant factor is compliance of the rotational drives. In Fig. 5b, the TSV j vs. vertical displacement h and ratio n = kact/krot, for ux = 0, is shown. Value j > 0.5 is provide when krot > 2.31 106 N-m. In the 5-axis tripod-based machine tool (Fig. 6), translations along the X- and Y-axes are actuated by machine table and saddle, while vertical position zp of platform 1 and angles ux and uy of the platform orientation result from active motions of sliders 2, 3, 4 along three vertical guideways. Connecting rods 5, 6, 7 are attached to the platform and sliders through spherical and revolute joints, respectively. The ith rod (i = 1, 2, 3) moves in its vertical plane. Platform-mounted spindle carries out the rotation of the cutting tool. The columns with the guideways are attached to fixed bed 8" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003476_j.triboint.2021.106951-Figure16-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003476_j.triboint.2021.106951-Figure16-1.png", "caption": "Fig. 16. Oil flow fields at three accelerations.", "texts": [ " Similarly, the churning losses show a decreasing trend from a certain value in 0\u20130.05s. The presence of acceleration will cause the oil level in the intermediate gearbox to tilt, which will also affect the lubrication performance. The acceleration of the intermediate gearbox is set to 3 m/s2 and 5 m/s2 respectively and the rotating speed of the driving gear is 5000 rpm. The oil flow fields inside the gearbox and oil flow rate of four oil guide holes make a comparison with those when the gearbox is at rest. Fig. 16 and Fig. 17 show the flow rate of each oil guide hole greatly fluctuates under acceleration attitude, and the greater the acceleration is, the more obvious the fluctuation is. Compared with the situation at a = 3 m/s2, the oil flow is more turbulent at a = 5 m/s2 and more oil is distributed on the internal wall of the gearbox and the surfaces of gears. Besides, the oil flow rate of No. 3 and No. 4 oil guide holes significantly increases under the acceleration attitude, which is because that the oil inside the gearbox tilts backwards due to inertia and thus the oil level near the bearings of the driven gear becomes higher so that more lubricating oil can enter the oil guide holes No" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003185_s00894-020-04395-4-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003185_s00894-020-04395-4-Figure2-1.png", "caption": "Fig. 2 a Computational domain used for thermal simulation and b thermal profile of AlSi10Mg powder bed", "texts": [ " Along with the physical assumptions, the governing equation for heat transfer in DMLS process is as follows: \u03c1\u2201 \u2202T \u2202t \u00bc \u2202T \u2202x K \u2202T \u2202x \u00fe \u2202 \u2202y K \u2202T \u2202y \u00fe \u2202 \u2202z K \u2202T \u2202z \u00fe Q \u00f05\u00de where \u03c1 is the density of the material (kg/m3),C is the specific heat capacity (J/kg K), T is the temperature of the laser spot on the powder bed, t is the interaction time, K is thermal conductivity (W/mK), and Q (x, y, z, t) is the volumetric heat generation (W/m3). A three-dimensional transient thermal model is developed by ANSYS 17.0 platform to find the sintering temperature with respect to applied laser power. The laser beam is considered to be a moving Gaussian heat source that scans the powder layer with a constant scan speed along X-direction. Figure 2a shows the schematic of the computational domain used for thermal simulation. The applied laser power affects the top surface of powder bed as well as on the substrate. The simulations are carried out at different laser power at a constant scan speed. To measure the sintering temperature attained with respect to laser power on the top surface of the powder bed, the temperature distribution on the powder bed as well as the substrate for the case (laser power of 70Wand scan speed of 100 mm/s) is shown in Fig. 2b. The thermal simulations and material property information is given with detail in work published by the authors [36, 38]. From the thermal simulation, it is observed that, at 70 W laser power, the temperature of the powder bed reached around 803 K. This temperature is considered to be the sintering temperature. Similarly, the thermal simulations are carried out by varying the laser power from 70 to 170 W by keeping a constant scan speed, i.e., 100 mm/s. Different set of temperatures which are extracted from a thermal model are used to study the sintering phenomena for varying laser energy densities" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002853_tnsre.2020.3003860-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002853_tnsre.2020.3003860-Figure3-1.png", "caption": "Fig. 3 The active ankle foot orthosis (AFO) with key components.", "texts": [ "9 kg and the transmission line is 0.15 kg. The total mass of the system is 2.6 kg excluding the battery pack. The pneumatic circuit and diagram of the electrical system of the proposed system are as shown in Fig. 2. A. Unilateral AFO hardware design The unilateral AFO consists an output pneumatic cylinder, a metallic slider crank mechanism, custom thermoplastic braces, two 2-way solenoid valves, a pressure sensor, a magnetic encoder, two custom optical type ground reaction force (GRF) sensors and a slave board as shown in Fig. 3. The weight of each component is summarized in Table 1. A slider crank mechanism was implemented to transform the linear motion of the output cylinder to rotational motion at the ankle (see Fig. 4-(a)). Such mechanism was selected for mechanical simplicity, compact size, and more importantly for user safety. The mechanical parameters of the slider crank mechanism were selected to structurally constrain the full range of motion (ROM) to 65\u00b0 (45\u00b0 for plantarflexion and 20\u00b0 for dorsiflexion) in the sagittal plane" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000834_s11661-015-2838-z-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000834_s11661-015-2838-z-Figure1-1.png", "caption": "Fig. 1\u2014Physical setup of processing head and laser beam with respect to the substrate.", "texts": [ " The macrostructure (Section III\u2013A), microstructure (Section III\u2013B), and indentation hardness profiles (Section III\u2013C) of each are compared and contrasted to understand the effects of laser-beam pulsing. An Optomec LENS MR-7, laser-based, directedenergy-deposition system was used for deposition. The system was equipped with a 500-watt Ytterbium-doped fiber laser (IPG YLR-500-SM) which was focused to a second-moment spot diameter of 0.62 mm at a distance of 20.7 mm above the substrate. Beam size measurements were made using a PRIMES GmbH FocusMonitor. As shown in Figure 1, the laser spot size was 1.24 mm at the working distance, which corresponded to a space of 9.27 mm between the substrate and four, radially symmetrically powder-delivery nozzles. Nozzles had an exit orifice diameter of 1.2 mm and were oriented at 18.25 deg with respect to the laserbeam propagation direction. Centered among the powder nozzles was a 6.35 mm diameter, center-purge nozzle, through which 30 lpm of argon flowed. During deposition, the substrate was in the X-Y plane while the laser processing head remained stationary" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002277_978-3-319-27131-6-Figure8.10-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002277_978-3-319-27131-6-Figure8.10-1.png", "caption": "Fig. 8.10 Initiated and propagated subsurface cracks", "texts": [ " They result from the impurity of bearing steels in the production process. However, the bearing steel quality has been strongly improved in the last decades. The initiated microcracks are usually in the order of a few microns on the surface and in the subsurface of the bearings. They are considered as initial crack nuclei in the bearing material. The maximum shear stress of about one-third of the maximum Hertzian pressure occurs under the contact zone and causes the crack propagation toward the bearing surfaces, as shown in Fig. 8.10. The development of the initiated microcracks is further intensified by a large number of cyclic shock loads acting upon the contacting surfaces. As soon as the cracks reach near the surfaces, flaking (spalling) occurs on the surfaces of the rolling elements and raceways due to forced rupture (s. Fig. 8.11). 8.2 Failure Mechanisms in Rolling Bearings 179 The flaking-related failure occurred in the rolling element and raceway generates the formation of large and deep cavities by heavy loads or shock loads on the contacting surfaces" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003340_j.addma.2021.101881-Figure17-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003340_j.addma.2021.101881-Figure17-1.png", "caption": "Fig. 17. The (a) longitudinal and (b) vertical residual deformation before (BSR) and after support removal (ASR) using 2-layer ELLM involving one tuned MPM.", "texts": [ " MPM #2 is the artificial constitutive model used specifically to tune the inherent strains and yield stress for the low layer in the 2-layer ELLM case. Accordingly, the entire model is divided into two sections prepared to have two sets of material property parameters. The equivalent layerbased division is shown in Fig. 16. Certainly, it takes shorter time to finish running the 16-step simulation relative to the 32-step no-lumping case. The obtained residual deformation before and after separating the teeth support from the cantilever beam is shown in Fig. 17. Compared to those results in the benchmark no-lumping case (see Fig. 14), the prediction error is very small, thus demonstrating good accuracy of the 2-layer ELLM employing a tuned MPM to avoid stress and deformation overestimation. As a supplemental study, the computed residual deformation in vertical build direction after support removal using 2-layer LLM without the tuned MPM is shown in Fig. 18 as a comparison. It is seen that the prediction error for the maximum vertical deformation becomes larger compared to Fig. 17(b) with reference to the benchmark results in Fig. 14. This phenomenon strongly proves that material property tuning X. Liang et al. Additive Manufacturing 39 (2021) 101881 is necessary to improve the accuracy of the layer lumping method. As a further step, the 3-layer ELLM is studied in this example. Correspondingly, two more adjusted MPMs (#2 and #3) are needed in addition to the real MPM (#1) for IN718. Three adjacent equivalent layers are lumped into a super layer in the 3-layer ELLM case. As a benefit, only 11 load steps are needed for the 32-layer model" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002022_978-3-319-40036-5-Figure6.1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002022_978-3-319-40036-5-Figure6.1-1.png", "caption": "Fig. 6.1 Idealized POC device [5] reproduced with permission from John Wiley & Sons, Inc. The POC device consists of a disposable part, with a loading port for sample introduction, a sample preparation and metering unit (for pre-concentration, amplification, cell lysis), a microfluidic processing unit (for splitting, moving, and mixing samples and reagents), a sensor unit (to target recognition receptors) for labeled or label-free detection, and a signal transduction unit with electronic readout circuit", "texts": [ " The only way to achieve this device goal and out-compete the need for cumbersome lab techniques that require culture bottles, petri dishes, and microtiter plates is to employ microfluidics. Analysis rates for POC devices integrated with microfluidic channels are usually shorter and several assays can be integrated in a single system without extending the size and complexity of the device. In addition to this, several steps of the analytical procedure can be integrated and automated within the system. An idealized concept of a POC device [5] is shown in Fig. 6.1. Based on George Whitesides\u2019 definition [6], microfluidics is \u201cthe science and technology of systems that process or manipulate a small volume of fluids, typically (10 9\u201310 18 L), using channels with dimensions of tens to hundreds of micrometers\u201d. The high surface-area-to-volume ratio of microfluidic devices leads to enhanced heat and mass transfer. In addition to the latter, interfacial phenomena that are not usually observable at the macroscale, such as the domination of surface forces instead of inertial and body forces can be elucidated" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000353_14763141.2012.660799-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000353_14763141.2012.660799-Figure1-1.png", "caption": "Figure 1. The position (ro) and orientation (n) of the best-fit trajectory plane can be described by a point on the plane (P) whose position vector is perpendicular to the plane. n is the unit vector of ro. Ri is the foot of trajectory point Qi on the plane.", "texts": [ "0 (two 3-handicappers and 12 scratch-or-betters; plus handicaps were entered as negative numbers), respectively. Participants were free of serious muscular or joint/ligament problems within 6 months prior to the study. Ethics approval was secured from the Texas Woman\u2019s University Institutional Review Board and informed consents were obtained from the participants prior to data collection. A new trajectory-plane fitting method was developed and used in this study. The trajectory of a point of interest (clubhead, hand, or shoulder; Q in Figure 1) can be fit to a plane defined by a point (P) whose position vector (ro) is normal to the plane (Figure 1) ro \u00bc \u00bdxo; yo; zo ; \u00f01\u00de n \u00bc ro roj j ; \u00f02\u00de where n is the unit vector of ro. Random deviation of a given trajectory point from the plane (1i) can then be expressed as a function of n 1i \u00bc \u00f0ri-ro\u00de\u00b7n; \u00f03\u00de where ri is the position of Qi. Three trajectory points or more provide a sufficiently determined nonlinear system of equations F \u00bc w111 wi1i wm1m 2 666666664 3 777777775 < 0; \u00f04\u00de where wi is the scalar weight and m is the point count ($3); m is a function of the sampling frequency and the phase of swing from which the trajectory is extracted" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000000_s1560354709060069-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000000_s1560354709060069-Figure3-1.png", "caption": "Fig. 3. Schema of four-wheel vehicle model with rear-wheel drive at regular cornering.", "texts": [ " Handling characteristics are discussed in section 3, and compared with field measurements in section 4. As the equations of motion have been linearized with respect to the trim states, a basic linear stability analysis of the steady-state motion including the powerslide condition is given in section 5. Some remarks on continuing research will conclude the paper. For analytical investigation of the motion of an automobile with rear-wheel drive at high lateral accelerations, at least a basic nonlinear four-wheel vehicle model has to be considered, see Fig. 3. Thus, the main effects of wheel load transfer during cornering and the nonlinear effects of large steering angles \u03b41 and \u03b42 of the front wheels and large side slip angle \u03b2 of the vehicle on the handling behaviour are included. Consequently, also the side slip angles \u03b1i (i = 1 \u2212 4) of the wheels may be large. From geometric and kinematic considerations, the relations tan(\u03b41 \u2212 \u03b11) = v sin \u03b2 + lf \u03c8\u0307 v cos \u03b2 + \u03c8\u0307s/2 , tan(\u03b42 \u2212 \u03b12) = v sin \u03b2 + lf \u03c8\u0307 v cos \u03b2 \u2212 \u03c8\u0307s/2 , tan \u03b13 = lr\u03c8\u0307 \u2212 v sin \u03b2 v cos \u03b2 + \u03c8\u0307s/2 , tan \u03b14 = lr\u03c8\u0307 \u2212 v sin\u03b2 v cos \u03b2 \u2212 \u03c8\u0307s/2 , (2", " With these simplifications, the equations of motion are found with Newton\u2019s and Euler\u2019s law: mv\u0307 cos \u03b2 \u2212 mv(\u03b2\u0307 + \u03c8\u0307) sin \u03b2 = Fx3 + Fx4 \u2212 Fy1 sin \u03b41 \u2212 Fy2 sin \u03b42, mv\u0307 sin \u03b2 + mv(\u03b2\u0307 + \u03c8\u0307) cos \u03b2 = Fy1 cos \u03b41 + Fy2 cos \u03b42 + Fy3 + Fy4, 0 = Fz1 + Fz2 + Fz3 + Fz4 \u2212 mg, (2.3) REGULAR AND CHAOTIC DYNAMICS Vol. 14 No. 6 2009 0 = (Fz1 \u2212 Fz2 + Fz3 \u2212 Fz4)s/2 \u2212 (Fy1 cos \u03b41 + Fy2 cos \u03b42 + Fy3 + Fy4)h, 0 = \u2212(Fz1 + Fz2)lf + (Fz3 + Fz4)lr + (Fy1 sin \u03b41 + Fy2 sin \u03b42 \u2212 Fx3 \u2212 Fx4)h, Iz\u03c8\u0308 = (\u2212Fy1 sin \u03b41 + Fy2 sin \u03b42 + Fx3 \u2212 Fx4)s/2 + (Fy1 cos \u03b41 + Fy2 cos \u03b42)lf \u2212 (Fy3 + Fy4)lr. (2.4) Fxi are the rear longitudinal tyre forces, Fyi the lateral and Fzi the vertical tyre forces, which are not depicted in Fig. 3. The total vehicle mass is denoted m, the vertical moment of inertia Iz, and the height of the centre of gravity (CG) above ground h. As this study focuses on the handling behaviour at lower velocities, the aerodynamic properties are neglected, as well as the tyre rolling resistance at the front tyres. Assuming both a linear relation between the vertical tyre forces Fzi and the corresponding vertical deflections zi and the geometric constraint (z1 + z4) = (z2 + z3) results in the relationship (Fz1 \u2212 Fz2)cr = (Fz3 \u2212 Fz4)cf " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002661_tia.2020.2987897-Figure26-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002661_tia.2020.2987897-Figure26-1.png", "caption": "Fig. 26. Optimal machine with unequal rotor teeth.", "texts": [ " 24 that a smaller Authorized licensed use limited to: University of Exeter. Downloaded on May 03,2020 at 21:22:58 UTC from IEEE Xplore. Restrictions apply. 0093-9994 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. EPP_OL can be achieved by designing the rotor with unequal teeth. It is found that the combination of \u03b8r1=19o and \u03b8r2=20o shown in Fig. 26 has the highest EPP_OL reduction, i.e., 0.51V and 0.06V for the HESFPM machines without and with unequal rotor teeth, respectively, as shown in Fig. 27(a). Consequently, EPP_OL reduction ratio is 89.05% by unequal rotor teeth, which is mainly due to the reduction of the 6th and 12th harmonics as shown in Fig. 27(b). As shown in Fig. 28, Tave of the optimal machine with unequal rotor teeth is slightly decreased, i.e., 1.13Nm due to a lower phase fundamental back-EMF compared with the original machine" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002700_tmech.2020.3015133-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002700_tmech.2020.3015133-Figure3-1.png", "caption": "Fig. 3. Simplification of the elastic skeleton: (a) the model of the elastic skeleton and (b) Simplified cross-section of flexible unit.", "texts": [ " The normal pressure applied to the middle of the angle between the tension vector of the wires. 3. The clearance between the wires and the guidewire discs is ignored. 4. The axial force cannot be transmitted through the guidewire discs to the elastic skeleton. The manipulator cannot stretch or contract in the longitudinal direction. 5. The constant curvature is adopted in a single flexible unit. The friction is considered in the mechanical model. Therefore, the curvature between flexible units is different. The flexible unit of the notch continuum manipulator is shown in Fig.3. The deformation of the continuum manipulator is mainly concentrated at the elliptical notches. Since the size of the flexible units (w = 0.3mm, t = 0.6mm) is small, it can be simplified to a rectangle as shown in Fig.3(b). Therefore, the deformation area of the flexible unit can be simplified to two elliptical flexible hinges. Authorized licensed use limited to: Cornell University Library. Downloaded on August 24,2020 at 08:11:28 UTC from IEEE Xplore. Restrictions apply. 1083-4435 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Based on the above-simplified model, a coordinate system of the dynamic and kinematic design parameter of the elliptical flexible hinge [34] is established, as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000806_j.mechmachtheory.2012.08.011-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000806_j.mechmachtheory.2012.08.011-Figure6-1.png", "caption": "Fig. 6. Image of the thin-rimmed gears deformed by the centrifugal loads. (a) Left inclined web. (b) Center inclined web. (c) Right inclined web. (d) Right straight web [5].", "texts": [ " 5, the FEMmodels for the other thin-rimmed gears can bemade automaticallywith the developed softwarewhen gearing parameters, engagement position parameters, structural dimension parameters and web angle are given. (a) Left straight web & 0min-1 (b) Left inclined web & 0min-1 Deformation and stress analyses are conducted for all the three types of the thin-rimmed inclined web gears shown in Fig. 2(a), (b) and (c) when the centrifugal loads are applied. In order to understand the centrifugal deformation of these gears, the calculated centrifugal deformation of all the gears is increased by 2000 times and images of the gears deformed by the centrifugal loads are illustrated in Fig. 6. Fig. 6(a), (b) and (c) are the images of the left, the center and the right inclined web gears deformed by the centrifugal loads. Fig. 6(d) is the image of the thin-rimmed right straightweb gear deformed by the centrifugal load. Fig. 6(d) was the result reported in the previous research [5]. From Fig. 6(a), (b) and (c), it is found that all the three types of the thin-rimmed gears have very similar deformation shapes under the centrifugal loads regardless of the longitudinal position difference of the inclined webs. It is also found that the deformation shapes of the inclined web gears are completely different from that of the straight web gear by comparing Fig. 6(a), (b) and (c) with Fig. 6(d). In Fig. 6(a), (b) and (c), the teeth of the inclinedweb gears have only a small inclination angle while the teeth of the straight web gear have a large inclination angle as shown in Fig. 6(d). It is very clear that a small inclination of the contact teeth shall have a little effect on tooth contact pattern and contact stress distributionwhile a large inclination of the contact teeth shall havemuch effect on the tooth contact pattern and contact stress distribution. This is confirmed in Section 6 by LTCA. Tooth radial deformation (in the direction of Y axis as shown in Fig. 5) of the inclined web gears under the centrifugal loads is calculatedwhen gear speed is 5000, 10,000, 20,000 and 40,000 min\u22121 respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000844_bf00251591-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000844_bf00251591-Figure1-1.png", "caption": "Fig. 1. Watt-I mechanism", "texts": [ " Apart from some general investigations of plane linked motion [19] and certain conjectures in this area [22], relatively little is known about the three general six-bar curves (except for Stephenson-1), although material on kinematic analysis [4, 10] and synthesis [8, 12] is available. It is the purpose of this investigation to study the mathematical properties of the three basic six-bar curves and to develop an analysis of six-bar motion in a general and uniform manner. HI. The Watt-1 Mechanism (Fig. 1) 1. The Mechanism This is an inversion of the Watt chain in which a binary link is held fixed. The six-bar curve is generated by point G. We take the origin at A and let AE coincide with the positive x-axis. 2. The Watt-1 Six-Bar Curve hence we write X = x + iy and Y = x - i y . From the figure, we have I X - r e i (~ +~)] [ Y - r e -~ (~'+~)] -- 12. Letting t = e ~ ~', we obtain where A t 2 - p t + A = O A = r e - i ~ X , P= X Y + r 2 - 12, and the bar denotes complex conjugation. (1) Since B-B--~=D-D--~---ff~=efa(n-n' e~), we have also (X_peiq '_se*a)(Y_pe-*~'_~e- i~)=(l ' ) 2, where s = n - n ' e i~", " 24 It can be shown via an examination of the range equation that if ABDE folds at tp'= 0 ~ ( r '+ m =n ' +p) and there are to be two positions at which CFmi n = I f - l ' [ and one position at which CFmax=l+l', the parameters of the mechanism must satisfy the equations r' + m = n ' +p, 2r 'm = n 'p [1 - cos(81 + e2)], where 90~ +e2)<270 ~ One such Watt-1 curve, is shown in curve W-001. 10. Kinematic Properties The vector polygon construction for the velocity and acceleration of point G (as a function of crank motion) is straightforward, since the velocity and acceleration of points C and F involve only the regular four-bar constructions. Analytically, it is convenient to perform these calculations (and also, for instance, the determination of the path curvature of G) by means of a parametric formulation of the locus equation and its time derivatives. Referring to Fig. 1 and using subscripts to identify point coordinates, we have XB=pcosq~, Yn=psin tp, YBq + (m-- Xn) Vr' 2[ y2 @(m- Xs)2-q 2] yD= y2 -t- (m - XB) 2 where q= 89 2 - n ' 2 + (m-Xs)2 + y2] , XD__ P 2 + r' 2 - n ' 2 - m 2 - 2 YB Yo 2(Xn-m) X n F = XD + ~-7 [(Xo-XB) ( - c o s y ) - ( r D - YB) sin ~] Yr = Y/~ +~7, [ ( X o - X a ) s i n ~ - ( Y o - YB)cosy], X c = p (XB cos a-- Yn sin ct), Yc=-~ (XB sin a + Yn cos ct). Let ma=12-1' 2 + X2 + y 2 - r 2, A = [(Ye- rc) 2 + ( X r - Xc)2], B= - m a ( Y ~ - Yc)+ 2 (XF-Xc) (YrXc-Xp Yc), C = 88 m 2 - rn a Xc(X F -Xc ) + (Xr -Xc ) 2 (r 2 --/2), y _ -B+-]/B2-4A C 2A S i x - B a r M o t i o n " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003281_j.jmatprotec.2021.117139-Figure20-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003281_j.jmatprotec.2021.117139-Figure20-1.png", "caption": "Fig. 20. Schematic of LMD tensile specimens under tension for (a) long unidirectional raster scan specimen undergoing longitudinal fracture effect and, (b) short unidirectional raster scan specimen undergoing transverse fracture effect.", "texts": [ " These findings are also consistent with the anisotropic behaviour in mechanical properties, like a lower UTS and yield strength for the short unidirectional than the long unidirectional raster scan build strategies seen from Fig. 12. Yu et al. (2013) found that crack propagation tends to occur at the interdendritic regions of LMD Stainless Steel 316 L due to the differences in the material constitutions. Since, the array of fusion zones within the LMD builds are distributed differently for each build strategy, the mechanical properties would hence reflect this difference due to the fracture propagation that occurs across the different arrays of fusion zones as illustrated in Fig. 20. In this study, the effects of Additive Manufacturing build strategies using LMD fabrication of Stainless Steel 316 L specimens provided a framework for characterizing the anisotropic properties and behaviour arising from build strategy pattern effects. In-situ process control was used to investigate the build strategy effects on the laser power control required to achieve consistent melt pool characteristics. A series of tensile tests were used to characterise the mechanical anisotropy of LMD specimens that were produced using long unidirectional, bidirectional, and short unidirectional raster scan build strategies" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002667_j.sna.2020.112034-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002667_j.sna.2020.112034-Figure3-1.png", "caption": "Fig. 3. Design of the soft fiber-reinforced bending finger with three chambers. (a) ECF jet generator. (b) Flexible tube and wrapped fibers. (c) Cap. (d) Assembled bending finger.", "texts": [ "), AR-S30 epoxy glue (Araldite standard, Hunts- an International LLC.) and 118-15A/B (electrically conductive poxy adhesive, Creative Materials Inc.). Other rigid parts were ade of PEI (Polyetherimide). Copper wire was used for connectng the electrodes to the voltage amplifier in our work. The LMT-55 ygon tube (inner diameter: \u00d82 mm, outer diameter: \u00d84 mm, Saintobain K.K.) was used for fabricating the bottom gap. .2. Design The soft fiber-reinforced bending finger reported in this aper consisted of three elemental components: an ECF jet enerator(Fig. 3a), a cap (Fig. 3b), and a fiber-reinforced tube with hree chambers (Fig. 3c). The ECF jet generator had three ECF umps. In the previous decades, we had developed three types of CF pumps: (a) thin planar electrode pairs, (b) triangular prism and lit electrode pairs, and (c) needle-ring electrode pairs. From the hree types of ECF jet generators, we chose the needle-ring pair as he electrode pattern of a power source to drive the bending finger ue to the smaller size. The needle-ring electrode pair consisted f two parts: a tungsten-made needle electrode and a brass-made ing needle (Fig. 3a). In each pair, the center of the needle electrode as exactly aligned with the hole of the ring electrode. The strucural parameters of the ECF pumps were designed according to the ptimized results in the previously reported papers [13,27]. The iameters of the electrodes were decided by two factors: (a) presure increases as the ring electrode becomes small; (b) pressure eneration is irrelevant to the needle diameter [13]. In addition, he tip angle of the needle had little influence on the pressure genration", "2 mm; (b) the pressure generated by the CF pump reduced when the gap increases. Considering the fabriation process, we set the design values as follows. The needle-type d bending finger with three chambers. (a) Initial position and components. (b)\u2013(g) ains the same. (h) Working area of the bending finger. C1, C2, and C3 are chamber electrodes had a diameter of 130 m and a tip angle of 180\u25e6, respectively. The ring electrode-type had a thickness of 200 m and a hole diameter of 300 m. The distance between these two electrodes was set to 0.2 mm. In Fig. 3a, we showed the fixation and a base to mount the needle electrodes. In the base, a hole was designed to fill the ECF from the tank and would be tightly sealed by using the bottom gap if the experiments were carried out. The ring electrodes were fixed to the cover having three holes, which were used to connect to the chambers of the flexible tube. The flexible tube was assembled by connecting each chamber with one ECF pump. Note that, the holes of the fixation were drilled after the assembling process. This process ensured an accurate alignment between the needle electrodes and the ring electrodes. Also, a tiny orifice was fabricated along the side of the cover and provides space to link the electrodes to the wires via conductive glue. The flexible tube (\u00d85 mm) was wrapped by several reinforced fibers, which were distributed at a gap of 1.5 mm along the axis of the soft tube (Fig. 3b). The cross-section of the flexible tube was composed of three partitions (forming the three chambers) and one periphery. We designed a PEI-made cap (Fig. 3c) to seal the flexible tube with the silicon glue instead of SU-8 material [36,37]. The final assembled device was shown in Fig. 3d. The overall sizes of the soft fiber-reinforced finger were 7.0 \u00d7 8.1 \u00d7 27.0 mm3. 3.3. Fabrication The fabrication process is shown in Fig. 4. To fabricate the flexible tube, two types of weight mixing ratios were prepared, which were 10: 1: 3 and 10: 1: 2.5 (KE-1316: CAT-1316: RTV thinner), respectively. To prepare the molds, we manufactured three pieces of fan-shaped brass with the angle of 120\u25e6, 5 mm in diameter and 18 mm in length, and then used a thin brass plate (0.20 mm in thickness) to ensure the clearances separating the three pieces of brass (Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003535_j.mechmachtheory.2021.104436-Figure19-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003535_j.mechmachtheory.2021.104436-Figure19-1.png", "caption": "Fig. 19. 4-DOF mechanisms corresponding to the ankle motion fitting models U1U1 and U1U2.", "texts": [ " Based on the equivalent replacement method, there are totally 3429 4-DOF GSPMs (33 \u00d7 34+28 \u00d7 33=3429). Among them, there are 15 compact GSPMs composed of the PES and OES-groups, which are shown in Table 13. Based on the first and second kinematic analysis methods, the kinematics of 4-DOF GSPMs in Table 13 are analyzed. The GSPMs meeting the motion requirements of the models U1U1 and U1U2 (Figs. 3(c) and (d)) are selected, which are respectively mechanisms 2- UR [RRR]&SR [RR]&SRR and 2-UR [RRR]&SR [RR] &SPR shown in Fig. 19. Their kinematic performances are listed in Table 14. The mechanism 2-UR [RRR]&SR [RR]&SRR is composed of a pure OES-group SR [RR]&SRR and a pure PES-group 2-UR [RRR]. The mechanism 2-UR [RRR]&SR [RR]&SPR consists of a pure PES-group 2-UR [RRR] and a pure OES-group SR [RR]&SPR. In order to avoid limb interference, the fixed coordinate system of the PES-group is rotated 180\u25e6 around its own z axis, and the obtained new coordinate system is set as the fixed coordinate system of the OES-group. Therefore, by multiplying a matrix Rot(z, \u03c0) behind the matrices Tran (m1, m2, m3) of Eqs" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000060_13506501jet578-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000060_13506501jet578-Figure4-1.png", "caption": "Fig. 4 Equivalent sphere for a bump", "texts": [ " Note that the material properties and overlap between elastic bodies for both Figs 2 and 3 are identical, except for the presence of a bump in Fig. 3, thus it can be concluded that the change to the pressure profile is solely due to the bump. Consequently, the total pressure in this case is given by Pt = P + Pb (3) As the contact area remains constant, increase in pressure invariably results in an increase in the force. Hence, the total force will be Ft = F + Fb (4) A closer examination reveals that the bump can be considered as a sphere of radius \u2018R\u2019 (Fig. 4), on the bearing race R = ( d2/4 + h2 ) 2h (5) Consider a contact between a ball and a bump represented by an equivalent hemisphere. The contact pressure (Fig. 5) can be expressed as Pb = Pbmax [ 1 \u2212 ( 2x\u2032 d )2 \u2212 ( 2y \u2032 d )2 ]1/2 (6) JET578 \u00a9 IMechE 2010 Proc. IMechE Vol. 224 Part J: J. Engineering Tribology at PORTLAND STATE UNIV on October 18, 2014pij.sagepub.comDownloaded from where \u2212d/2 x\u2032 d/2 and \u2212d/2 y \u2032 d/2. \u2018Pb max\u2019 is the maximum pressure in the ball\u2013bump contact. The force\u2013deflection relationship in this case is given by Fb = Kb\u03b4 3/2 b (7) For conditions when the bump is completely flattened, deformation \u2018\u03b4b\u2019 is assumed to be equal to the height, \u2018h\u2019 of the bump and \u2018Kb\u2019 is the equivalent stiffness between the bump and the ball" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000182_j.mechmachtheory.2011.04.011-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000182_j.mechmachtheory.2011.04.011-Figure2-1.png", "caption": "Fig. 2. Planar four-bars: (a) general, (b) foldable, and (c) degenerate.", "texts": [ " We take this familiar example as an introductory illustration of the local dimension finding technique, testing a generic four-bar, a four-bar in a singular position, and a degenerate four-bar. A pose of a planar four-bar with coupler point can be specified as the (x, y)-coordinates of five points, A0, B0, C0, D0, P0, two of which, say A0 and B0 are the stationary ground pivots, while C0 and D0 are initial positions of the joints on the coupler link and P0 is the initial position of the coupler point (see Fig. 2). After the linkage moves, the homologous points to C0, D0, P0 are C, D, P and the six coordinates of these are the variables in the assembly conditions. These conditions simply state that the links must have constant length, that is, f(x)=0, where f x\u00f0 \u00de = f1 = jC\u2212A0 j2\u2212 jC0\u2212A0 j2 f2 = jD\u2212B0 j2\u2212 jD0\u2212B0 j2 f3 = jC\u2212D j2\u2212 jC0\u2212D0 j2 f4 = jP\u2212C j2\u2212 jP0\u2212C0 j2 f5 = jP\u2212D j2\u2212 jP0\u2212D0 j2 8>>>< >>>: \u00f016\u00de x = C;D; P\u00f0 \u00de = cx; cy;dx; dy;px; py : \u00f017\u00de The \u201cpoint of construction,\u201d as we shall call z=(C0, D0, P0), is on VC f\u00f0 \u00de, so we may check the dimension at that point" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002277_978-3-319-27131-6-Figure9.1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002277_978-3-319-27131-6-Figure9.1-1.png", "caption": "Fig. 9.1 (a) Static unbalance; (b) couple unbalance of the rotor", "texts": [ " As a result, electric rotors are only balanced using the low-speed balancing at two balancing planes. The production of electric rotors induces the static, couple, and dynamic unbalances. The static unbalance occurs when the polar mass-inertia axis Ip differs from the rotation axis by an eccentricity \u03b5. On the contrary, the couple unbalance occurs when the polar mass-inertia axis Ip differs from the rotation axis by a misalignment angle \u03b1; however, they intersect at the mass center G of the rotor on the rotation axis. to the gravity at the equilibrium position (s. Fig. 9.1a). That means the rotor component moves from any initial position to the equilibrium due to its weight. Hence, it is also called the static unbalance since the rotor moves itself to the equilibrium position in the static unbalance. On the contrary, in the couple 186 9 Rotor Balancing and NVH in Rolling Bearings unbalance, the rotor does not move itself to the equilibrium position because the mass center G is always in the rotation axis. The couple unbalance is only recognized in the rotating condition in which an unbalance moment acts upon the rotor although the static unbalance equals zero, as shown in Fig. 9.1b. The static unbalance is caused by the production mistakes, large eccentricity at mounting the iron-sheet packages on the rotor shaft, nonhomogeneous rotor materials, and asymmetric geometry of the iron sheets. On the contrary, the couple unbalance is created by misalignment of the iron-sheet packages to the rotor shaft. In practice, both static and couple unbalances occur in the production process of electric rotors. Both rotor unbalances lead to the dynamic unbalance of the rotor, as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002646_j.jelechem.2020.113895-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002646_j.jelechem.2020.113895-Figure1-1.png", "caption": "Fig. 1. Miyata et al.", "texts": [ " Fabrication of porous Au microelectrodes Jo ur na l P re -p ro of Au and Cu wires were embedded in a mold filled with epoxy resin sealant and then cured at 65 C. Au and Cu wires were connected with conductive adhesive and dried at 25 C. Conductive adhesive and the epoxy resin sealant embedded with Au and Cu wires were sealed with epoxy resin adhesive and cured at 25 C. The fabricated electrode was cut crosswise using an abrasive cutter (RC-120, As One Co., Ltd., Japan) to expose the embedded Au wire. A schematic view of the electrode is shown in Fig. 1. The electrode was sequentially polished using a grinding wheel and washed with ultrapure water with sonication using an ultrasonic disperser (Bransonic-5210J, Emerson, Ltd., Japan) for 10 min at 25 C. In order to construct the pore at the surface, the polished Au electrode was anodized in 0.1 M (M = mol dm \u22123 ) phosphate buffer (pH 7.0) containing 0.5 M D-(+)-glucose at 1.9 V vs. Ag/AgCl/sat. KCl for 90 min (to modify CueO) or 2.0 V vs. Ag/AgCl/sat. KCl for 120 min (to modify BOD) with stirring", "), Rotating Electrode Methods Oxygen Reduction Electrocatalysts, Elsevier, Amsterdam, Oxford, , 2014: pp. 1\u201331. doi:10.1016/b978-0-444-63278-4.00001-x. [52] S. Tsujimura, H. Tatsumi, J. Ogawa, S. Shimizu, K. Kano, T. Ikeda, Bioelectrocatalytic reduction Jo ur na l P re -p ro of of dioxygen to water at neutral pH using bilirubin oxidase as an enzyme and 2,2\u2032-azinobis (3-ethylbenzothiazolin-6-sulfonate) as an electron transfer mediator, J. Electroanal. Chem. 496 (2001) 69\u201375. doi:10.1016/s0022-0728(00)00239-4. Jo ur na l P re -p ro of Figure captions Fig. 1. Schematic view of a Au microelectrode; (A) Cu lead wire, (B) epoxy resin adhesive, (C) Au wire, and (D) epoxy resin sealant. Fig. 2. Cyclic voltammograms recorded at (A and B) bare and (C and D) CueO modified (A and C) planar and (B and D) porous Au microelectrodes. Insets in A and B show microscopic images of each electrode surface. Solid and dotted lines indicate voltammograms recorded under O2-saturated and Ar-saturated McIlvaine buffer (pH 5.0), respectively, at r = 20 \u00b5m and v = 30 mV s \u22121 " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002277_978-3-319-27131-6-Figure5.21-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002277_978-3-319-27131-6-Figure5.21-1.png", "caption": "Fig. 5.21 Stress-strain diagram of a ductile material", "texts": [ " To study the wear mechanism in the bearings, some backgrounds of the elastic and plastic deformations of material are required [8, 9]. First, a small load acts upon the material that begins deforming; as soon as the load is removed, its form returns to the initial condition. This deformation is defined as elastic deformation. On the contrary, in case of plastic deformation, a heavy load acts upon the material. As a result, the resulting stress in the material exceeds the yield stress \u03c3o, the deformed material remains and does not return to the initial condition although the acting load is removed from it (s. Fig. 5.21). At further increasing the acting load at the plastic deformation, the material suddenly breaks up (material fracture) shortly after the ultimate tensile stress \u03c3u. 106 5 Tribology of Rolling Bearings Therefore, the wear process begins with the loss of the surface asperities (roughness peaks) that abrade the moving surfaces and cause wear paths on the surfaces. Applying the tensile force F on a cylindrical specimen with the initial crosssectional area A0 and length l0, the body begins deforming in the axial direction", " At further increasing the acting force, the normal stress increases larger than the yield stress \u03c3o; hence, the deformation of the body becomes plastic where the Hooke\u2019s law has been no longer valid. With a plastic stress of 0.2%, the strain remains at \u03b5\u00bc 0.2% after removing the acting force. The deformation is plastic up to the ultimate tensile stress \u03c3u. After exceeding the ultimate tensile stress, the normal stress sharply increases in a very short time, and the material breaks up. Shortly before the fracture occurs, the real cross-sectional area Ar significantly reduces due to material contraction at a constant load F, as shown in Fig. 5.21. Therefore, the normal stress sharply increases before the material fracture happens according to Eq. 5.29. Applying the force F acting on a specimen in the tangential direction, the body form deforms at a shear strain t. The shear rate _\u03b3 is defined as the ratio of the shear strain t to the specimen height h (s. Fig. 5.22). The shear stress is written at the contact surface A as \u03c4 \u00bc F A \u00bc G t h G _\u03b3: \u00f05:31\u00de where G is the shear modulus of the material. The shear modulus is calculated from the elasticity modulus E and the Poisson ratio v as E \u00bc 2G 1\u00fe v\u00f0 \u00de \u00f05:32\u00de where v equals 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003650_j.microc.2021.106585-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003650_j.microc.2021.106585-Figure1-1.png", "caption": "Fig. 1. Structure and principle of the GFET. (a) Structural representation of the SF hydrogel encapsulated GFET, (b) Schematic diagram of the equivalent capacitive circuit.", "texts": [ " For the preparation of the HRP cross-linked SF hydrogel, the preparation method is based on previous research [16]. Briefly, the raw SF was dissolved in PBS solution to get SF solution with a concentration of 5 wt%. Then the desirable amount of HRP (200 U/ml) and glucose oxidase (100 U/ml) were mixed with the SF solution and 50 \u00b5L H2O2 (0.5 %v/v) were added to 1 mL mixed solution. After incubation of the mixtures at ambient temperature for 1 min, the functionalized SF hydrogel was formed. The schematic structure of the hydrogel encapsulated GFET is shown in Fig. 1a. Au (~100 nm)/Cr (~10 nm) were deposited on the glass substrate by thermal evaporation to form source, drain and gate electrodes through a shadow mask. Single-layer graphene was grown on copper foils by chemical vapor deposition (CVD) method and transferred on the substrate. The graphene transfer process was adopted previous method [17]. Briefly, PMMA film (~500 nm) was spin-coated on graphene/copper foil and then annealed at about 100 \u25e6C for 30 min. Then, it was immersed in an aqueous solution of iron chloride to etch the Cu substrate to get PMMA/graphene film", " Furthermore, the change of color is not obvious when the Z. Wang et al. Microchemical Journal 169 (2021) 106585 concentration of glucose solution is lower than 100 \u00b5M. However, compared with the existing colorimetric detection method [20], this method still shows a good response performance to the glucose. GOx D-glucose + H2O + O2 D-gluconic acid + H2O2(1) HRP H2O2 + 2e\u2212 + 2H+ 2H2O(2) For detailed investigation of the sensing mechanism, a simple model is used here to describe the characteristic of the GFET (Fig. 1b). As the biosensor consists of graphene channel and gate electrode to constitute the conduction circuit on the interface of the SF hydrogel, the equivalent capacitive circuit could be calculated as: 1 Ctot = 1 Cg + 1 CG + 1 CH (3) Cg, CG and CH are the equivalent capacitance of graphene, gate electrode and hydrogel, respectively. Due to CG and CH could be regarded as constant, Cg is the main variable in the model. The Cg is calculated as: Cg = CQCdl/(CQ + Cdl), where Cdl is the double\u2011layer capacitance on the graphene, CQ is the quantum capacitance of graphene which could be described as [21]: CQ = Cdl ( V , gs \u2212 Vch ) Vch (4) where Vch is the channel potential and V\u2019 gs is the real voltage on the graphene" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001144_j.mechmachtheory.2013.09.001-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001144_j.mechmachtheory.2013.09.001-Figure7-1.png", "caption": "Fig. 7. Simulated topography for the work gear: Case B.", "texts": [ " This study presents the mathematical models for the crowned work gears that are generated by a modified profile of VTT hob and by a conventional hob, respectively. Transmission errors and tooth contact analysis of gear pair meshing simulations are also investigated for the gear sets that are composed of a crowned work gear and a standard involute gear. The simulation results of three numeral examples lead to the following conclusions: 1. The tooth surface twist of the crowned gear generated by the proposed method (Case B) is very small, as shown in Fig. 7. 2. When the gear pair is meshed under assembly errors, the distributions of contact point locations and contact ellipses of the crowned gear generated by the modified profile of VTT hob with a hob diagonal feed (Case B) are much better than those of the crowned gear generated by a conventional hob with center distance variation between the hob and the work gear and a diagonally shifted hob (Case A), as shown in Figs. 10 and 11. 3. The crowned work gear 2 generated by a conventional hob can easily cause contact points on the edge of the gear 3 during the gear pair meshing under assembly errors of vertical misaligned angle \u0394\u03b3v, horizontal misaligned angle \u0394\u03b3h, and center distance assembly error as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003063_s11071-020-05666-8-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003063_s11071-020-05666-8-Figure2-1.png", "caption": "Fig. 2 A generic mesh model that is applicable to all types of gears", "texts": [ " The stiffness matrix of each individual bearing is located in the complete bearing stiffness matrix,Kb, in accordance with the node number to which the corresponding bearing is attached and the remaining elements of Kb are zero. Consequently, the overall stiffness matrix of whole FEM model is obtained as K \u00bc Ks \u00feKb. Furthermore, assuming proportional damping, a set of damping ratio, fs, is used for the shaft-bearing assembly. A generic mesh model, which is applicable to all types of gears in the drivetrain considered in this study, i.e., spur, helical and spiral bevel gears, is formulated. The mesh model is illustrated in Fig. 2, which shows a three-dimensional dynamic model of a spiral bevel gear pair. The gears are connected to each other by a time-varying mesh stiffness and a timeinvariant mesh damping in the direction of tooth normal, i.e., along the line of action (LOA). Moreover, a displacement excitation in the form of static transmission error is connected in series with the stiffness and damping elements in the same direction. There is also backlash between the gears, which causes nonlinearity in the dynamics of the system", ", LOA vector and the position of mesh point, is much smaller compared to time variation of mesh stiffness [24], a constant LOA vector with an effective mesh point is utilized. Mesh couplings for spur and helical gears are exactly the same as the one for spiral bevel gear shown in the figure. The effective mesh nodes in the threedimensional discrete mesh model, which are coincident for pinion and gear, are connected to the Timoshenko beam finite element model of shaft- bearing structures by using rigid links as shown in Fig. 3. Since the mesh node of each gear has 3 translational and 3 rotational DOFs as illustrated in Fig. 2, a total of 12 DOFs defines the mesh coupling. Since some shafts have multiple gears forming multiple mesh couplings with the other shafts, the generalized coordinates are expressed relative to the local reference frames of the gear shafts, Ssi, rather than the local reference frames of the gears, Si. Thus, the displacement vectors of the gears can be written as xsi \u00bc xsi ysi zsi hxsi hysi hzsi\u00f0 \u00deT and subscript i \u00bc p; g represents pinion and gear, respectively. Transforming the displacement vectors of the gears to the LOA direction by using the coordinate transformation vectors, di, the relative dynamic displacement along the LOA, i" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002433_978-3-030-35699-6_1-Figure17-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002433_978-3-030-35699-6_1-Figure17-1.png", "caption": "Fig. 17. 3D diagram of a system with multiple coils [3]", "texts": [ " Moreover, in case of a non-deformable contact, the non-magnetic object would have to be very resistant to the very important instantaneous acceleration during the shock. In a further work, the structure of our coil gun will be optimized dividing the coil in several smaller coils activated sequentially. For example, scenarios using 2, 3 or 4 coils (each one having a half, a third or a quarter of the total turns of the initial coil), triggered sequentially by software or using a position sensor instead of a single coil as shown in Fig. 17 will be evaluated as in [2,7]. This will lead to have successively a maximum current on each coil when the rod is optimally placed in the coil, leading to a increased projectile speed. Eighteenth International Middle East Power Systems Conference (MEPCON), pp. 506\u2013511, December 2016. https://doi.org/10.1109/MEPCON.2016.7836938 2. Bencheikh, Y., Ouazir, Y., Ibtiouen, R.: Analysis of capacitively driven electromagnetic coil guns. In: The XIX International Conference on Electrical Machines - ICEM 2010, pp" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003594_j.asej.2021.01.009-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003594_j.asej.2021.01.009-Figure2-1.png", "caption": "Fig. 2. Photograph rotor and stator of SRG.", "texts": [ " As the rotor pole leaves the aligned position, the stator windings current decreases and the inductance reaches its minimum value. Torque generation in SRG depends on the magnetic field which tends to bring the poles to the minimum reluctance position. The SRG produces torque through excitation that is synchronized to rotor position [30]. As the poles are separated, the reluctance begins to increase, creating a negative torque. The photograph of SRG having eight poles in the stator and six poles in the rotor is shown in Fig. 2. In SRG, the torque generated by a phase under linear operating conditions is calculated as in (4). Te \u00bc 1 2 i2 dL dh \u00f04\u00de Where, Te,i, L and h refers to the electromagnetic torque, phase current, phase inductance, and rotor position, respectively. Since the SRG operates in the range where the inductance value decreases (dL/dh < 0), the resulting torque is negative. The total torque generated by the 4-phase generator used in this study is equal to the sum of the torques produced separately by the phases" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003373_j.mechmachtheory.2021.104348-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003373_j.mechmachtheory.2021.104348-Figure3-1.png", "caption": "Fig. 3. The leg-wheel module in this work. (a) Configuration of the module in wheeled mode ( \u03b8 = \u03b80 ). (b) Configuration of the module in legged mode ( \u03b80 < \u03b8 \u2264 \u03b8l max , \u03b8 = 90 \u25e6 in figure). (c) Notation related to the derivation of virtual work.", "texts": [ " According to Gruebler\u2019s equation [24] , the mechanism has four DOFs: DOF = 3 ( N bar \u2212 N joint \u2212 1 ) + N joint = 4 (1) The two additional DOFs result from free rotation between the upper and lower rims in the given motor bar configuration. In the design process, two methods were utilized to search for possible solutions to reduce the extra 2 DOFs. One is to constrain the relative motions of links (i.e., adding gears or slots), and the other is to adapt Gruebler\u2019s equation (i.e., adding links and joints). Several designs considered during the design process are shown in Table 2 . Fig. 3 shows the final design of the leg-wheel module utilized in this work; Fig. 3 (a) and 3(b) illustrate the wheeled and legged modes, respectively. By adding four linkages connecting the motor bars and the upper rims, the motions of the upper rims can be precisely defined and controlled. The motions of the upper rims further define the motions of the lower left/right rims. Specifically, the motors directly drive the inner five-bar linkage, which is formed by OAE and its mirror linkages. Then, the five-bar linkage further drives the upper rims through the four-bar linkages formed by ABCD and its mirror. Finally, two four-bar linkages drive the lower rims. The mechanism has 11 linkages and 14 joints, so it has two DOFs, which satisfy criterion 2: DOF = 3 ( 11 \u2212 14 \u2212 1 ) + 14 = 2 (2) The forward/inverse kinematics of the leg-wheel module between the actuator space and the foot configuration space are required for the robot\u2019s operation. The hip joint offers two rotational and coaxial DOFs, which are driven by two motors through the mechanism, as shown in Fig. 2 (a). As shown in Fig. 3 (b), these two DOFs directly drive the two upper inner linkages ( \u03c6R , \u03c6L ) . Because the leg-wheel mechanism is symmetrical, it is more convenient to express the leg-wheel configuration using coordinates ( \u03b2, \u03b8 ) . The symbol \u03b2 represents the relative orientation between the body and the symmetric line OG of the leg-wheel module, \u2212180 < \u03b2 \u2264 180 . The symbol \u03b8 represents the angle included by the upper-right inner linkage and the symmetrical line OG. This parameter also represents the leg-wheel configuration level, so \u03b8 is denoted as the leg-wheel configuration parameter", " Mapping between two coordinates is performed as follows: [ \u03b8 \u03b2 ] = 1 2 [ 1 \u22121 1 1 ][ \u03c6R \u03c6L ] (3) [ \u03c6R \u03c6L ] = [ 1 1 \u22121 1 ][ \u03b8 \u03b2 ] (4) When the leg-wheel is operated in wheeled mode, two driving linkages ( \u03c6R , \u03c6L ) move at the same speed. In this case, \u03b2 increases, but \u03b8 remains unchanged. Following the defined coordinate system ( \u03b2, \u03b8 ) , the foot configuration (i.e., point G) represented in the xy-coordinate, which originates at the hip joint O, is derived based on the trigonometric relationships of the linkages and through the sequential computations of the configurations of joints A\u2013E of the leg-wheel mechanism. As shown in Fig. 3 (b), the positions of joints A and B are as follows: A = ( l 1 sin\u03b8, l 1 cos\u03b8 ) (5) B = ( Rsin\u03b8, Rcos\u03b8 ) (6) where R is the radius of the wheel. The lengths of the linkages are calculated as follows: l 3 = BC = 2 R sin ( \u03c0 2 n BC ) (7) l 7 = CF = 2 R sin ( ( n HF \u2212 m ) \u03c0 \u2212 \u03b80 ) (8) where the symbols n BC = \u0302 BC /\u03c0 and n HF = \u0302 HF /\u03c0 represent the normalized arc length of the arc \u0302 BC and upper rim \u0302 HF . The positions of joints E and D are calculated as follows: E = ( 0 , l 1 cos\u03b8 \u2212 \u221a l 1 2 co s 2 \u03b8 \u2212 ( l 1 2 \u2212 ( l 5 + l 6 ) 2 )) (9) ( l 5 + l 6 ) 2 = l 1 2 + E y 2 + 2 l 1 E y cos ( \u03c0 \u2212 \u03b8 ) (10) D = ( l 1 l 6 l 5 + l 6 sin\u03b8, l 5 l 5 + l 6 E y + l 1 l 6 l 5 + l 6 cos\u03b8 ) (11) The intermediate states were computed using the following trigonometric formula: BD = \u221a l 2 2 + l 5 2 \u2212 2 l 2 l 5 cos ( \u03c0 \u2212 \u03b8 \u2212 \u2220 OEA ) (12) \u03c8 = \u2220 CBD + \u2220 ABD \u2212 \u03b8 (13) the position of C is C = ( Rsin\u03b8 + l 3 sin\u03c8, Rcos\u03b8 \u2212 l 3 cos\u03c8 ) (14) Next, using the following intermediate states of lengths and angles: AC = \u221a l 2 2 + l 3 2 \u2212 2 l 2 l 3 cos ( \u03b8 + \u2220 OEA ) (15) EC = \u221a l 4 2 + l 6 2 \u2212 2 l 4 l 6 cos ( \u2220 DAC + \u2220 DCA ) (16) EF = \u221a EC 2 + l 7 2 \u2212 2 EC l 7 cos ( \u2220 ECF ) (17) the position of F is F = ( EF sin \u2220 F E G, E y \u2212 E F cos \u2220 F E G ) (18) l 8 = F G = 2 R sin ( ( 1 \u2212 n HF ) \u03c0 2 ) (19) EG = EF cos \u2220 FEG + \u221a l 8 2 \u2212 ( EF sin \u2220 FEG )2 (20) Finally, the position of G is calculated as follows: G = G ( \u03b8 ) = ( 0 , E y \u2212 EG ) (21) The position of G represents the foot configuration of the leg-wheel module, so G (\u03b8 ) represents the module\u2019s forward kinematics. Eqs. (5) \u2013(21) also reveal that although only trigonometric relationships are involved, the expanded expression of G (\u03b8 ) is messy due to multi-layer substitution. Thus, the expanded expression is omitted here. Fig. 3 reveals the rough configuration and kinematics of the proposed leg-wheel module, but the precise configuration of the module requires further investigation. The six variables need to be quantitatively defined, including \u03b80 , l 1 , l 5 , l 5 + l 6 , n HF , and n BC . The remaining parameters of the leg-wheel module are passively determined by these six variables. These six variables are crucial because they determine the configuration of the leg-wheel module, including the configuration of the fully extended leg and configurations in the middle of the transformation", " This process was related to empirical realization, so some empirical considerations, such as the sizes of linkages and joints, needed to be set a priori . This process involved the geometrical settings of the linkages and joints, and the details are omitted here. After screening, 188 feasible combinations satisfied the requirement. In the third stage of the selection, the power/torque transmission condition was utilized as the cost. The leg-wheel mechanism transmitted the actuator power at the inputs ( \u03b2, \u03b8 ) to the foot configuration at the output ( G x , G y ), as shown in Fig. 3 . The preferred condition was that while the input provided constant torque at a constant speed, the output similarly delivered constant force at a constant speed. Any variation in this mapping would increase the control effort. The formal analysis required use of the mechanism\u2019s dynamics. The equations of motion using the Lagrangian method were explored. However, as shown in (5)\u2013(21), the geometric relationship between the hip joint and foot was already complicated, not to mention the derivations of these position vectors and the required matrix inverse. The equations could not be successfully solved with any of the numerical methods we explored. Thus, a simpler method, virtual work, was utilized, where the torque required by the motor when the mechanism is in a static balance was derived. The scenario was set to be the vertical hop of the leg-wheel module ( \u03b2 = 0 ), where the input power is utilized to lift the leg-wheel module up with point contact on the ground at point G , as shown in Fig. 3 (c). When the leg-wheel module was installed on the robot body, the body mass was much heavier than the leg-wheel mass. Thus, the analysis assumed that the leg-wheel module only had a point mass located at the hip (point O ), and the leg-wheel mechanism itself was massless. The virtual work of the leg-wheel is as follows: 2 \u03c4m \u03b4\u03b8 = mg\u03b4G y (22) or \u03c4m = mg\u03b4G y 2 \u03b4\u03b8 (23) where \u03c4m is the torque applied by the actuator. The results satisfying the constraints listed in Table 4 were then inspected visually" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000121_j.mechmachtheory.2009.05.003-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000121_j.mechmachtheory.2009.05.003-Figure2-1.png", "caption": "Fig. 2. Phases of the gait cycle (sagittal plane view): (a) single support finite motion phase, and (b) impulsive motion of heel strike.", "texts": [ " For example, in the case of walkers with curved feet, these points denote the point of the foot which is instantaneously in contact with the ground. This represents different physical points of the foot during motion when rolling takes place. The gait cycle has in general two characteristic phases: the single support phase with finite motion dynamics, and the impulsive motion phase that takes place when the swing foot collides the ground at heel strike and the topology changes. These phases are represented from a sagittal plane view in Fig. 2. During the finite motion single support phase, one of the feet (namely, the stance foot) is in contact with the ground without slipping, Fig. 2a. This can be modeled by bilateral constraints AS _q \u00bc 0; \u00f02\u00de where S is either R or L depending on which of the feet is the stance foot. This contact condition will give rise to constraint forces acting on the foot. The non-slipping condition of the foot will have to be checked during the analysis of this phase of motion. This will be discussed in further sections of this work. Note that in the case of 2-dimensional motion, the velocity level constraints in Eq. (2) are always holonomic, hence they can also be reduced for each step to configuration level constraints in the form of U\u00f0q; ki\u00de \u00bc 0, where ki is a constant associated with step i, representing a different offset along the direction of walking. In 3-dimensional motion these constraints can also become non-holonomic, for example for curved-feet walkers [28]. The instantaneous phase of heel strike represents impulsive motion. The topology of the system changes in this phase (Fig. 2b). The swing foot impacts the ground at ti. This impact is required to be inelastic, i.e., the colliding point of the swing foot must stay in contact with the ground after heel strike. This is a reasonable and widely used assumption when studying walking systems [9,10,12,13,23\u201325]. Hence, this event can be characterized by inert constraints which represent a class of impulsive constraints [29,30]. Let us consider that ti represents the time of the impulsive event and \u00bdt i ; t\u00fei is an interval representing the pre- and postimpact instants" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003482_tia.2021.3066955-Figure8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003482_tia.2021.3066955-Figure8-1.png", "caption": "Fig. 8. Mechanical analysis of the 18/12 SRM (a) with the frame and (b) without the frame.", "texts": [ " Rms current value in FrsumI, FrsumII, FrsumIII, and FrsumIV currents are quite similar around 10 Arms. After completing Maxwell analysis, the next step is performing mechanical analysis to investigate the vibration in the 18/12 SRM. In the mechanical analysis, the result from Maxwell analysis is imported. Mechanical analysis is continuation of Maxwell analysis when investigating vibration in electrical machine. In the mechanical analysis, rotor and coil parts are suppressed; thus, only stator and frame are remained. Fig. 8(a) and (b) shows the stator body of the 18/12 SRM with and without the frame, respectively. Fixed point is set at the surface of the frame attached to the wall and vibration acceleration is evaluated in the surface of the stator. This condition is similar with the actual experimental setup. Vibration at the stator surface is investigated. The 18/12 SRM is rotated at 1000 r/min so that fundamental frequency is 200 Hz. Fig. 9 shows comparison of the vibration at the stator surface excited by the square and the four proposed currents" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002795_j.oceaneng.2019.106429-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002795_j.oceaneng.2019.106429-Figure4-1.png", "caption": "Fig. 4. Schematic of the AUV-T working in the tunnel.", "texts": [ " The hydrodynamic coefficients are calculated by CFD numerical simulation calculations. When the heave (z) motion, pitch (\u03b8) and roll (\u03c6) angles of the AUV are ignored, the horizontal motion model can be expressed as 2 6 6 4 m X _u 0 0 0 m Y _v 0 0 0 Iz N _r 3 7 7 5 2 6 6 4 _u _v _r 3 7 7 5\u00fe 2 6 6 4 0 0 \u00f0Y _v m\u00dev 0 0 \u00f0m X _u\u00deu \u00f0m Y _v\u00dev \u00f0X _u m\u00deu 0 3 7 7 5 2 6 6 4 u v r 3 7 7 5 2 6 6 4 Xu\u00feXujujjuj 0 0 0 Yv\u00feYvjvj jvj 0 0 0 Nr\u00feNrjrjjrj 3 7 7 5 2 6 6 4 u v r 3 7 7 5\u00fe 2 6 6 4 fX fY fN 3 7 7 5\u00bc \u03c4 (3) As shown in Fig. 4, the AUV-T performs the voyage observation in the tunnel. If the distance between the AUV and the wall is adjusted by the traverse movement, then the heading of the AUV will be seriously disturbed, and the video cannot be collected clearly. Therefore, in this study, the distance between the AUV and the wall is changed by adjusting the heading of the AUV to ensure the stability of the heading. Assume that the distance between the AUV center and the wall is H, and the ratio of the distance from the wall to the diameter of the AUV is e (e \u00bcH/D) (Bhattacharyya et al" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001687_s11665-018-3520-6-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001687_s11665-018-3520-6-Figure3-1.png", "caption": "Fig. 3 Process that formed the fish-scale structure SLM in (a) diagram of the Marangoni effect caused by the laser. (b) Diagram of the molding process of the horizontal plane", "texts": [ " The obtained polarization curves were analyzed using the curve-fitting routine of the ZView2 software to obtain the corrosion potential (Ecorr), and the corrosion current (Icorr). The MM images of SG and CG are shown in Fig. 2. Figure 2(a) is the morphology of SG on horizontal surfaces, exhibiting fish-scale-likeness tracks. The vertical direction of the metallographic organization is shown in Fig. 2(b). The fishscale-likeness tracks can be explained by the Marangoni effect (Ref 27). As the laser is a Gaussian light source, the temperature field of the laser possesses a Gaussian distribution, as shown in Fig. 3(a). Through Eq 1, the surface tension in the center of the metal pool is lower than that of the edge. Thus, the molten metal has a tendency to flow out and cover the previously solidified part, forming fish-scale-like tracks shown in Fig. 3(b). Additionally, an MM image of the CG is shown in Fig. 2(c), which indicates that the CG microstructure possesses a dendritic texture, and the pattern of CG growth is dendritic (Ref 22). cV 2=3 m \u00bc k TC T\u00f0 \u00de \u00f0Eq 1\u00de Among these: c liquid surface tension, Vm liquid molar volume, K universal constant, Tc critical temperature. Deeper microstructural features are revealed via highmagnification of SEM images, as shown in Fig. 4. Uniform cellular structures can be observed in Fig. 4(a). At the edge of the pools, pool boundaries and columnar structures can be Journal of Materials Engineering and Performance observed, as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000931_9781118703274.ch2-Figure2.56-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000931_9781118703274.ch2-Figure2.56-1.png", "caption": "Figure 2.56 Aerodynamic brakes", "texts": [ " The above paragraphs have looked at a few of the most important blade positioning systems out of the wide spectrum available, some of which also bring the blades into active stall (see the systems shown in Figures 1.23(c) and (d) and Figure 1.26(g)). Fixed-speed machines without pitch variation, which will be described in Section 2.3.3, do not allow the manipulations described here. Such machines must be protected against overspeeding as a result of power outages (during which the generator develops no load torque and so cannot dictate the speed of rotation) by a so-called \u2018passive control\u2019 system. This may take the form of braking flaps in the blade profile (see Figure 2.56(a)) or the blade tips (Figure 2.56(b)). In addition, rotor brakes, usually in the form of disc brakes (see Figures 1.2 and 2.48 to 2.50), afford the possibility of bringing the rotor to a standstill in most machines. Blade positioning drives \u2013 as control and safety systems \u2013 must guarantee the controlled operation of wind power units in all conditions. They must therefore ensure that in critical conditions the rotor blades can reduce the energy extracted by the turbine as quickly as possible to protect the machine from possible damage" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002508_j.triboint.2019.03.048-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002508_j.triboint.2019.03.048-Figure7-1.png", "caption": "Fig. 7. Oil guide device.", "texts": [ " [12] and Concli and Gorla [11,36] to obtain other methods to solve this problem. Besides, according to investigations by [8,36\u201339], squeezing losses, which the separation method can't capture, are parts of churning losses; however, because squeezing losses are excluded from churning losses by all simulations in this paper, the change tendency of churning losses with different structures of oil guide device would not be affected. The simplified model of the intermediate gearbox and parameters of the spiral bevel gears are illustrated in Fig. 6 and Table 2, respectively. Fig. 7 shows the reference geometric model of the oil guide device, where the oil guiding tank capacity is 13.34ml and the diameter of the oil guiding pipe is 5mm. Table 3 gives main physical parameters used in simulations. The mesh inside the gearbox is discretized with unstructured tetrahedron elements which can undergo a certain degree of mesh deformation so that the mesh can adapt better to the complex geometric shape of the spiral bevel gear pair. Besides, mesh surrounding gears and the oil guide device is locally refined while that of other positions is sparser and coarser than the former, aiming to guarantee simulation precision and improve calculation efficiency at the same time" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001170_we.1656-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001170_we.1656-Figure1-1.png", "caption": "Figure 1. Frame of reference and nomenclature.", "texts": [ " First, the geometrical interference model is formulated where axial, radial, and angular displacements are imposed to one of the rings. Next, the interference combinations are assessed for which the statically allowable elastic deflection is reached in order to define the acceptance surface in the interference space. Finally, the force and moment equilibrium equations are derived to obtain the load combinations that define the acceptance surface in the load space. The basic nomenclature, illustrated in Figure 1, is as follows: \u03a8 is the azimuthal angle that indicates the position of a ball within the bearing; c1 is the contact direction between the upper raceway of the inner ring and the lower raceway of the Wind Energ. (2013) \u00a9 2013 John Wiley & Sons, Ltd. DOI: 10.1002/we outer ring; c2 is the contact direction between the lower raceway of the inner ring and the upper raceway of the outer ring; dw and dpw are, respectively, the ball diameter and ball center diameter; and rc is the raceway radius, identical for the four raceways" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002329_s11771-018-3765-0-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002329_s11771-018-3765-0-Figure3-1.png", "caption": "Figure 3 Quadrotor UAVs and flow simulation", "texts": [ " To better analyze the effect of the external disturbance for quadrotor UAVs, the wind tunnel test in SolidWorks is imitated for quadrotor UAVs fluid dynamics analysis to obtain the parameters of actual flight UAV under the wind disturbance. The specific parameters of the airframe in the fluid analysis are set according to the experimental aircraft model. The speed of four motors is set to 3100 r/min which is measured by the hover status of aircraft model. Then a 2 level wind (wind speed is 3 m/s) disturbance is added through Y-axis along the airframe coordinate frame, as shown in Figure 3. The two wind curves from the flow simulation results which pass through the centroid of aircraft are extracted. In curve 2 and curve 9, the data are extracted from the two curves to get the actual static pressure distribution of UAVs surface as follows. From Figure 4, we can see that the distribution about 2 level wind in the static pressure (it is perpendicular to the direction of the fluid motion) of UAVs surface is a sine wave curve, which are 101325.1895 Pa, 101325.1664 Pa respectively. While the area of UAVs along the y-axis is 4" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001170_we.1656-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001170_we.1656-Figure2-1.png", "caption": "Figure 2. Geometrical interference model.", "texts": [ " The basic nomenclature, illustrated in Figure 1, is as follows: \u03a8 is the azimuthal angle that indicates the position of a ball within the bearing; c1 is the contact direction between the upper raceway of the inner ring and the lower raceway of the Wind Energ. (2013) \u00a9 2013 John Wiley & Sons, Ltd. DOI: 10.1002/we outer ring; c2 is the contact direction between the lower raceway of the inner ring and the upper raceway of the outer ring; dw and dpw are, respectively, the ball diameter and ball center diameter; and rc is the raceway radius, identical for the four raceways. The osculation ratio s is defined as follows: s \u00bc dw 2rc (1) Figure 2 shows the geometrical interference between the rings and a ball whose azimuthal angle is \u03a8, but in this case, preload term has been introduced. Then, preload and displacements that are plotted represent the relative displacement between the inner and outer rings. When a given \u03b4a, \u03b4r, and \u03b4\u03b8 combination of axial, radial, and angular displacements (\u03b4\u03b8= \u03b8dpw/2, where \u03b8 is the tilt angle) is applied on the inner ring of the bearing, the actual contact angles \u03b11 and \u03b12 and the ball-raceway interferences \u03b41 and \u03b42 for contact directions c1 and c2, are arranged according to expressions (2\u20135) for a ball with azimuthal angle \u03a8 and initial contact angle \u03b10" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001372_s11465-016-0389-7-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001372_s11465-016-0389-7-Figure1-1.png", "caption": "Fig. 1 CAD model of the spatial parallel robot: (a) Overview and (b) bottom view", "texts": [ " In Section 3, the singularity of the proposed PKM is investigated both qualitatively and quantitatively, and the results are provided. Section 4 concludes the study. In this section, we first introduce a four-DoF spatial PKM with a single-platform structure in detail. Then, we analyze the mobility of this PKM using a line graph method based on Grassmann line geometry. Finally, the inverse kinematic modeling for this PKM is presented. 2.1 Description of the mechanism The CAD model of the PKM presented in this study is shown in Fig. 1, the kinematic scheme is presented in Fig. 2, and a global frame \u211c: o-xyz is established. As shown in Figs. 1 and 2, this PKM consists of four identical kinematic limbs and a single platform. The kinematic chain for each limb can be represented by RR(Pa)RR (R: Active revolute joint; R: Revolute joint; Pa: Parallelogram mechanism composed of four links connected end to end by four revolute joints). The four limbs are in 180\u00b0 symmetry (Fig. 2). The axes of revolute joints B1 and B3 as well as B2 and B4 are coaxial, and B1B3 (which is coaxial with the x-axis) is perpendicular to B2B4 (which is coaxial with the y-axis)" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000162_detc2009-86548-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000162_detc2009-86548-Figure1-1.png", "caption": "Figure 1: Indexing motion of Face-Hobbing", "texts": [ "asmedigitalcollection.asme.org/ on 02/01/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use 2 Copyright \u00a9 2009 by ASME tooth surface errors for face-hobbed spiral bevel and hypoid gears using the universal motions. Unlike face-milling process, face-hobbing is a continuous indexing process in which the concave and convex tooth surfaces are generated simultaneously under a single set of machine tool settings. During the hobbing process, two sets of independent motions are provided. As shown in Figure 1, the first set of related motion is called indexing which is the relative rotation between the cutter head and the virtual generating gear under the following relationship, c t t c N N = \u03c9 \u03c9 (1) Here, t\u03c9 and c\u03c9 denote the angular velocity of the tool and the generating gear; tN and cN denote the numbers of the blade groups and of the teeth of the generating gears respectively. The indexing motion generates the lengthwise trace of the teeth, which is called the extended epicycloid. The second set of related motion is the relative rotation between the virtual generating gear and the work, which is called rolling or generating motion and is represented as, a w c c w R N N == \u03c9 \u03c9 (2) Here w\u03c9 denotes the angular velocity of the work; wN denotes the number of teeth of the work; aR is called the ratio of roll" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003177_mra.2020.2979954-Figure10-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003177_mra.2020.2979954-Figure10-1.png", "caption": "FIGURE 10. (a) State space of modified Bernoulli shift map, (b) Inverted modified Bernoulli shift map.", "texts": [ " The state space I of the chaotic map f (\u00b7) is partitioned into N disjoint regions, I = {I }Ni=1, such that Ii \u2229 Ij = 0 for i 6= j and \u222aNi=1Ii = I . Note that this partition is not unique. For any sequence generated by iterating (3), if we can assign N alphabets (s = [s1; . . . ; sN ]) to each of the disjoint regions, the dynamics of the system can be represented by a sequence of finite alphabet S. This sequence is called the symbolic dynamics of the system. Bernoulli shift map is used as an example to explain the principle of this modulation. Therefore, many other maps can achieve the similar goal. As shown in Fig. 10, by partitioning a chaotic phase space to arbitrary regions, and labeling each region with a specific symbol, the trajectories can be converted to a symbolic sequence. The parameter shown in Fig. 10, (0 \u2264 p < 1), controls the width of the middle region of the map and the chaotic behaviour of the generated sequences. On the other hand, because of the sensitivity to the initial conditions of the chaotic map, the sequence diverges rapidly, making the demodulation a real challenge. By iterating from a final condition x[N ] onto the inverse function of (3) (f \u22121), the initial condition is contained in the set\u2229N\u22121n=0 f \u2212n(Ii) [128]. When N tends to infinity, the set contains a single initial condition which shows a direct relation between the chaotic sequence and an infinite symbolic sequence" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000244_978-3-642-13377-0-Figure4.4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000244_978-3-642-13377-0-Figure4.4-1.png", "caption": "Fig. 4.4 Probability density \u03c1 in (one-dimensional) space computed by the Fokker\u2013Planck equation for drift A = 0.1, diffusion B = 0.6, and an initialization close to a \u03b4 -function at r = 0. The line (r = At = 0.1t) indicates the trajectory of highest probability.", "texts": [ " We restrict ourselves to the two-dimensional case but the step to a three-dimensional model would be straight forward. Note that for A = 0 and B = \u221a 2 Equation 4.51 is reduced to Fick\u2019s second law \u2202\u03c1(r, t) \u2202 t = Q\u22072\u03c1(r, t), (4.52) which describes a standard diffusion process. In Figure 4.3 on the next page the temporal evolution of an initial peak \u03c1(0,0) \u2192 \u221e using the one-dimensional Fokker\u2013Planck equation and four sample trajectories of the corresponding Langevin equation are shown (see the Figure caption for details). The C-program, that was used, is given in Appendix B on page 129. In Figure 4.4 on the next page a similar situation for higher diffusion and the trajectory of highest probability, which is in this case just a line with slope A, are shown. In Figure 4.5 on page 53 we compare the numerical solution of the onedimensional Fokker\u2013Planck equation to a histogram obtained by sampling trajectories using the corresponding Langevin equation (Monte Carlo method). The Fokker\u2013Planck equation belongs to the class of partial differential equations (PDE). In general, PDE are hard to solve if they are not of a standard type, which is 52 4 A Framework of Models for Swarm Robotic Systems not the case here" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003479_0954407021999483-Figure12-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003479_0954407021999483-Figure12-1.png", "caption": "Figure 12. Influence of backward traveling wave on radial second-order mode shapes: (a) radial 2nd order unaffected by backward traveling waves (94.315 Hz) and (b) radial 2nd order affected by backward traveling wave at 30 km/h (89.324 Hz), the hollow arrow indicates the direction of rotation of the tire, and the solid arrow indicates the direction of propagation of the backward traveling wave.", "texts": [], "surrounding_texts": [ "The contact settings in this model mainly include the contact between rim and bead, tread and road surface. The rim and pavement are very hard compared with the tire, and the object of this study is the modal frequency of the tire. Therefore, the rim and the road surface can be simplified as analytical rigid bodies. Both of the above contact pairs are defined by penalty function formula which allows elastic sliding, and their contact form all is surface to surface contact. Among them, there is interference assembly condition between the rim and the tire. The rim is set with the main contact surface, and the corresponding tire contact part is set as the contact slave surface. The interference assembly of the rim is completed by gradually removing the tire surface node and applying the rim displacement. Figure 3 shows the 2-D cross-section diagram of rim assembly structure before and after the rim assembly. It is worth noting that after the rim is assembled, the bead is the main stress component. Analysis of finite element simulation results Influence of inflation pressure on tire modal In this section, the tire has no road limit, that is, the load is 0, but considering the restraint effect of the rim on the tire and constraining the degrees of freedom in six directions of the rim reference point, then the modal analysis of the tire under different tire pressures of 0.24MPa, 0.22MPa, 0.20MPa, and 0.18MPa is carried out respectively. The first 10 modal data are analyzed, and the results are shown in Figure 4 below. It can be seen from Figure 4 that the higher the inflation pressure, the higher the frequency of each order of the tire. This is because the higher the inflation pressure and the greater the tension on the tire, the greater the overall stiffness of the tire and the corresponding natural frequency of each order. The results show that the natural frequencies of each order increase with the increase of inflation pressure, and when the tire is not restricted by the road, that is, when the load is 0, the vibration modes of tire can be divided into circumferential vibration, radial vibration and transverse vibration according to the vibration mode. In this paper, the radial 1\u20136 order vibration which is easy to distinguish modal shapes is selected as the research object. When there is only rim constraint, the radial modal frequency of the tire has a double root phenomenon, that is, the mode shape and frequency are the same, but the phase is different. Take the radial third order as an example, the modal vibration mode is shown in Figure 5. The stress of the steel belts under different pressure can be seen directly from Figure 6. As the main stress component of the tire, the belt can reflect the stress of the tire. When the tire increases from 0.18MPa to 0.24MPa, the stress on the belt increases, and the average stress is 112.983MPa, 123.474MPa, 134.094MPa, and 144.755MPa, respectively, and the greater the tension of the tire. Thus, the overall stiffness of the tire is increased, and the reason for the increase of vibration frequency is further explained. The influence of load on tire modal In this section, the tire inflation pressure is 0.24MPa, and the radial mode of the tire is still taken as the research object. Tire road constraints are added, and the load is settled as 2000N, the first 6-order natural frequencies of the tire in the radial direction are shown in Table 1. It can be seen from Table 1 that when the tire is under load, the frequency values at the heavy roots mentioned in the previous section show a big and a small difference, and the degree of differentiation increases with the increase of the order. In order to compare with the no-load mode shape in the previous section, this section still takes the radial third-order modal shape as an example, and the modal vibration mode of the tire under 2000N load is shown in Figure 7. Figure 7 shows that when the tire is in the load state, compared with the tire without load, not only the vibration frequency of the tire has a big and a small differentiation, but also the phase of the tire modal shape has changed. For the convenience of research, the following takes the radial increase frequency as the research object to conduct a comparative study of the vibration frequency under different loads of 2000N, 3000N, 4000N, and 5000N. The results are shown in Figure 8. It can be seen from Figure 8 that with the increase of tire load, the frequency of tire radial increase gradually increases. This is because the increase of load will increase the degree of deformation of the tire when squeezed by the ground, which will increase the overall rigidity of the tire, thereby increasing the natural frequency, but the influence of load on frequency is small. It is worth noting that the frequency curves of 4000N and 5000N are almost overlapped, and the frequency difference of each order is very small. The reason is that as the load gradually increases, the amplitude of the increase in vibration frequency gradually decreases, and when the load increases to a certain value, the stiffness of the tire increases and decreases, or even no longer increases. Influence of tread wear on tire modal In this section, the tire inflation pressure is 0.24MPa and the load is 0N. The tread thickness of the tire used in the simulation in this paper is 8mm. Assuming that the tire is uniformly worn, the wear simulations are no wear, 2mm, 4mm, and 6mm, respectively. The details of the model tread with no wear and 2mm wear are shown in Figure 9, and the other two wear amount tread details are not given. As in the previous section, this time only the influence of tread wear on the tire radial increase frequency is analyzed. The results are shown in Figure 10. It can be seen from Figure 10 that the radial increase frequency of the tire increases with the increase of the tire wear amount, and the natural frequency discrimination between different wear amounts is obvious. This is because the wear of the tire tread causes the total mass of the tire to decrease, and therefore the natural frequency of the tire increases. In addition, in the daily use of tires, the rubber will be aged due to the stimulation of external environment, and the aging effect of rubber will cause the hardness of rubber materials to increase, which will lead to the increase of the overall stiffness of the tire. This aging phenomenon will make the discrimination of tire natural frequency between different wear amounts greater. Influence of speed on tire modal In this section, the tire inflation pressure is 0.24MPa, the load is 2000N, and the tread wear is 0. The tire rolling simulation condition in this paper is steady state free rolling, the tire is not accelerating or braking, that is, the torque received by the tire when it is rolling freely is zero. The tire\u2019s free rolling simulation is completed by the steady-state transport analysis in the ABAQUS software, but the steady-state transmission analysis only makes the material flow inside the grid. At this time, the natural frequency of the tire cannot be correctly simulated by the speed, so it is necessary to open the inertia switch button for steady-state transmission analysis applies the inertial force during rolling to the tire model. The keyword of ABAQUS steadystate transport is *STEADY STATE TRANSPORT, INERTIA=YES. In this section, the first six-order natural frequencies in the tire radial direction are still taken as the research object, and the radial natural frequencies of the tires at a speed of 0 to 60km/h with interval of 10 are studied. The results are shown in Figure 11. When the speed is 0, it corresponds to the radial mode when the load is 2000N in the preceding paragraph, that is, the natural frequency multiple root value of the tire in the free state has an increase and a decrease. It can be seen from Figure 11 that, except that the natural frequencies of the first order at various speeds are basically unchanged, the radial natural frequencies of order 2\u20136 show more obvious differentiation with the increase of speed, and the higher the order, the more obvious the differentiation phenomenon. Traveling wave vibration theory can explain the influence mechanism of speed on radial natural frequency of tire. The tire in rolling can be abstracted as a ring or shell. The vibration generated by the contact part of tire with the ground will be divided into forward traveling wave and back traveling wave in traveling wave vibration theory. The forward traveling wave will increase the vibration frequency of tire, while the backward wave will reduce the vibration frequency of tire, and the influence of forward traveling wave and backward traveling wave on radial vibration frequency of tire is proportional to the speed. Figures 12 and 13 show the effects of forward and backward traveling waves on the radial second-order mode shapes. Tire wear estimation algorithm Basic principle of BP neural network BP (Back Propagation) neural network is a multi-layer feedforward network, including input layer, hidden layer and output layer, but the learning algorithm of BP neural network is reversed, and the weight correction is performed by gradient descent method, so BP neural network is a tutor-type learning algorithm.24 Before the BP network training, the sample data needs to be divided into training set, validation set and verification set, generally 70%, 20%, and 10% of the total number of data samples. Training set are used to train the neural network to generate the objective function, the validation set is used to determine when to stop the training to avoid overfitting and the test set is finally used to evaluate the best NN obtained during the training. The input and expected output of the training sample of the BP neural network are paired. The network will calculate the error between the expected output and the actual output according to the output results of each neuron in the hidden layer and the output layer, and the error will be transmitted layer by layer through back propagation for the input layer and the hidden layer, combined with the principle of gradient descent, the positive and negative connection weights of the output layer and the hidden layer and the thresholds of the hidden layer and the output layer are modified. With the repeated iterative operation of the BP neural network, the calculated error value will continue to decrease.25 When the error value falls within the required accuracy range, the operation stops. BP neural network is very suitable for processing nonlinear or linear fitting regression problems and classification problems." ] }, { "image_filename": "designv10_9_0002864_s40430-020-02510-3-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002864_s40430-020-02510-3-Figure1-1.png", "caption": "Fig. 1 The 3[P2(US)] architecture of delta robot", "texts": [ "\u00a05, the proposed control strategy is described, and Sect.\u00a06 contains an FTC based on AST-NITSMC. Stability analysis of the proposed controller is discussed in Sect.\u00a07, and the desired path planning is addressed in Sect.\u00a08. Section\u00a09 is devoted to numerical simulation and the conclusion is drawn in Sect.\u00a010. The 3[P2(US)] parallel manipulator under study consists of a moving platform termed the end-effector and a fixed platform named the base, joined together via three identical limbs as depicted in Fig.\u00a01. Each limb is comprised of an active prismatic joint, installed at an inclination relative to the base and a parallelogram linkage. As the name implies, each parallelogram consists of two parallel rods with universal and spherical joints at their both extremities. Geometric parameters and variables of one of the limbs are illustrated in Fig.\u00a02. Three limbs are connected to the base through points Ai , which are located on an imaginary circle with radius R and centered at the origin of reference frame" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000931_9781118703274.ch2-Figure2.37-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000931_9781118703274.ch2-Figure2.37-1.png", "caption": "Figure 2.37 Propeller moment", "texts": [ " The following design characteristics of a rotor blade: \u2022 lateral and longitudinal geometry, \u2022 stiffness, \u2022 mass distribution, dictated by the choice of constructional materials, \u2022 possible degrees of freedom in the directions of teeter and wind thrust and in the rotational direction of the rotor and \u2022 bearings, can, depending on the operating conditions of a machine, give rise to the torsional moments described in what follows. Propeller moments Propeller moments arise as a result of the unequal mass distribution of the rotor blade (shown in Figure 2.37 as an aerofoil element) with respect to the axis of rotation of the blade due to the centrifugal force Fz acting on every partial centre of mass. Breaking this down into its normal and transverse components FN and FQ yields the quantity FPr, which is largely dependent on the speed of rotation and blade pitch angle. Multiplying FPr by aP, which is the offset from the blade axis at which FPr applies and integrating the product over the length of the blade yields the propeller momentMPr. For the usual operating blade angle of approximately 90\u2218 and the always-small blade angle with respect to the vertical axis (\ud835\udefe < 10\u2218), aP can be approximated for the moment-building offset, so that the propeller moment can be expressed as dMPr \u2248 dFPrap" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000193_j.cma.2011.04.006-Figure21-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000193_j.cma.2011.04.006-Figure21-1.png", "caption": "Fig. 21. Contact patterns for: (a) case B2b, (b) case B2c, (c) case B2d and (d) functions of transmission errors for previous cases of design.", "texts": [ " 19) and to a skew partial-crowned and aligned bevel gear drive (Fig. 20). A parabolic function of transmission errors with maximum level of 7 arcsec has been predesigned for the whole-crowned skew bevel gear drive (Design 2). However, for the case of partial-crowned skew bevel gear drive (Design 3), a function of transmission error of 2 arcsec is obtained taking advantage of an area of non-modified tooth surface due to partial crowning. Again, Design 3 (partial-crowning) allows the contact pattern to cover a larger area of the bevel gear contacting surfaces. Fig. 21 shows the contact patterns for cases B2b (21(a)), B2c (21(b)), and B2d (21(c)). Fig. (21(d)) shows the obtained functions of transmission errors for previous cases of design. Although for cases of design B2b and B2c the contact pattern is localized inside the contacting surfaces, avoiding undesirable edge contacts, when an axial displacement of the pinion occurs, the contact pattern is shifted towards the edge of the gear as shown in Fig. 21(c). All functions of transmission errors are obtained with parabolic shape, absorbing efficiently the lineal functions of transmission errors caused by errors of alignment for non-modified bevel gear tooth surfaces. Fig. 22 shows the contact patterns for cases B3b (22(a)), B3c (22(b)), and B3d (22(c)). Fig. (22(d)) shows the obtained functions of transmission errors for previous cases of design. For this design, the contact patterns are also localized inside the contacting surfaces, avoiding edge contacts, and the predesigned function of transmission errors is able to absorb the lineal functions of transmission errors caused by errors of alignment" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001753_tia.2014.2301862-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001753_tia.2014.2301862-Figure6-1.png", "caption": "Fig. 6. Flex-PCB winding description and specification.", "texts": [ " 5, the general principle consists first in printing on both sides of a double-sided copper clad flexible PCB the tracks corresponding respectively to the go-and-back conductors of the winding loops and in connecting these tracks with vias. The flex-PCB can be then wrapped to give the winding its final shape before its insertion into the air gap. In addition to greatly simplifying the manufacturing process, this technology gives a lot of freedom on the winding shape and on its section width. Unlike traditional technology, it is therefore possible to fully exploit the space between consecutive loops, particularly in the general case shown in Fig. 6 where the segments forming the coils do not have the same slope. Two parameters essentially determine the performance of dc motors, i.e., torque constant kT and phase resistance Rph. This section derives their analytical expressions both for the two kinds of winding shape and the two kinds of winding technology. Considering that: \u2022 the PM recoil permeability is close to one; \u2022 the dimensions Rr and Re\u2212Rs are sufficient to accept the necessary flux and therefore to assume the iron ideal; \u2022 the end effects are negligible; the r-component of the magnetic flux density produced by the PMs can be approached in the air gap by [10] Br,a(r, \u03d5) = B\u0302r,a(r) cos(\u03d5\u2212 \u03b8) (2) with \u03b8 as the rotor position and B\u0302r,a(r) = Br R2 m \u2212R2 r 2 (R2 s \u2212R2 r) ( 1 + R2 s r2 ) ", " Considering the conductor radius rc as a dependent parameter, it can be linked to the minimum distance separating adjacent loops through the following relation: rc = \u03b1 2 min ( w\u00a91 , w\u00a92 ) (25) with \u03b1 as a factor \u2208 [0, 1] that takes into account the thickness of the insulation, assuming that it is proportional to the wire diameter. On this basis, the phase resistance of a classical winding is given by Rph = Nt Nl \u03c1 4 l\u00a91 + 2 l\u00a92 \u03c0 r2c (26) where lengths l\u00a91 and l\u00a92 are taken from (17) and (18) or from (21) and (22) depending on whether the winding is a skewed or a rhombic winding. 2) Flex-PCB: As explained in Section II, flex-PCB windings are made from rectangular wires of constant thickness but of variable width. This implies, as illustrated in Fig. 6, that these wires can be adjacent to each other on each segment of the winding. Considering the conductor thickness tc and widths wc,\u00a91 and wc,\u00a92 as dependent parameters, they can be linked to the distances separating adjacent loops w\u00a91 and w\u00a92 and the thickness of one layer tl through the following relations: w c,\u00a91 =\u03b1w\u00a91 wc,\u00a92 =\u03b1w\u00a92 tc = \u03b1 2 tl. (27) On this basis, the phase resistance of a flex-PCB winding is given by Rph = Nt Nl \u03c1 [ 4 l\u00a91 w c,\u00a91 tc + 2 l\u00a92 w c,\u00a92 tc ] (28) where lengths l\u00a91 and l\u00a92 are taken from (17) and (18) or from (21) and (22) depending on whether the winding is a skewed or a rhombic winding", " This flexible circuit material is an adhesiveless laminate whose copper layers are 35 \u03bcm thick and polyimide substrate is 50 \u03bcm thick. To get a better filling factor, an additional layer of copper has been added by electroplating to reach a total thickness of 50-\u03bcm copper on both sides of the substrate. The additional layer used to ensure the electrical insulation between the copper tracks of the winding successive layers is a double-sided adhesive tape of 50 \u03bcm thick. In accordance with the notations given in Fig. 6, the total thickness of a winding layer tl is therefore equal to 200 \u03bcm, whereas the thickness of the copper layers tc is 50 \u03bcm. The distance between copper tracks was set to 100 \u03bcm and the electrical connection between go-and-back conductors of each winding loop across the substrate was realized using a line of 6 microvias of 75-\u03bcm diameter. The flex-PCB winding was sized to be inserted into the motor considered for theoretical study and whose characteristic parameters are listed in Table I. Considering the total thickness of a winding layer tl and the space available for the winding in the air gap Rs \u2212Rw, the number of winding layers Nl was set to 6. The number of turns per layer and per phase Nt was arbitrarily set at 9. The winding shape, characterized by parameters fr and frL introduced in Fig. 6, was optimized in order to maximize the coefficient kp. The resulting flex-PCB winding is shown in Fig. 9 before and after being wrapped. All its dimensional characteristics, including the reduction factors fr and frL, are synthesized in Table III. In order to validate the model presented in Section III, we measured the phase resistance Rph and the torque constant kt of the flex-PCB winding described above. The measurement of the resistance was performed with a four-terminal ohmmeter. The torque constant was obtained by coupling the prototype with a drive dc motor, as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000498_tec.2012.2185826-Figure10-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000498_tec.2012.2185826-Figure10-1.png", "caption": "Fig. 10. Calculation process of stator flux linkage vector difference in DTLC.", "texts": [ " As can be seen from (2), Te is strictly linear related to sin \u03b4, and then close loop control of the voltage based on PI controller is developed, as shown in Fig. 8, where the output of PI controller is defined as the sine value of the given torque angle, sin \u03b4\u2217. Compared with the equivalent system in Fig. 7, the torque loop is omitted and the torque can be controlled directly and linearly by the output of the voltage loop (sin \u03b4\u2217). The DTLC scheme for PHEFS generator based on the sine value of the torque angle is shown in Fig. 9. Fig. 10 shows the calculation diagram of the stator flux linkage vector difference. TABLE II COMPARISON OF DTC AND DTLC SCHEMES FOR PHEFS GENERATOR SYSTEM In Fig. 10, \u03b8s(k) is the angle of the stator flux linkage vector of period k ( \u21c0 \u03c8s(k)), \u03b8r(k) is the angle of the PM flux linkage vector and the excitation flux linkage vector of period k ( \u21c0 \u03c8pm(k) + \u21c0 \u03c8e(k)). Since the mechanical time constant is greater than the electrical time constant during an interrupt period, the speed \u03c9r can be taken as constant, hence the change of the excitation flux linkage vector angle is \u03c9T ( 1). Then the PM flux linkage vector and the excitation flux linkage vector of period k + 1 ( \u21c0 \u03c8pm(k+1) + \u21c0 \u03c8e(k+1)) can be obtained" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000476_1.4007349-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000476_1.4007349-Figure5-1.png", "caption": "Fig. 5 An assembly of bearing, hub, and blade", "texts": [ " That is, the pitch bearing should mainly overcome the overturning moment. The material parameters of all parts are listed in Table 3. It is noted here that the material of the blade root is anisotropic. Fig. 2 Sectional view of a pitch bearing 041105-2 / Vol. 134, OCTOBER 2012 Transactions of the ASME Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use A solid model consisting of the bearing, the hub, and the blade is shown in Fig. 5. The bolts\u2019 pretightening forces are assumed to be large enough so that there are no contact opening and sliding between the bearing ring and its connection. Thus, the hub and the blade are \u201cglued\u201d to the rings directly in the FE model, which is somewhat different from the fact that bolts are used. The bolt holes in the hub, the blade and the rings, which are shown in Fig. 5, are reserved to partially consider the effect of bolt connections. One pitch bearing is built in the model. In order to simulate the actual condition of the pitch bearing as much as possible, the other two simplified pitch bearings are used in the model shown as Fig. 5(a). In the simplified pitch bearings, the balls are ignored and the rings are glued together. The plane ribs and blade roots connected to the simplified pitch bearings are kept. Because there are plane ribs connected to the inner ring, the influences of the stiffness of the other two pitch bearings on the overall model are relatively less. Thus, the simplified method of the pitch bearing has certain rationality. The downwind torus is the flange for connecting the main shaft. The balls inside the bearing are not directly modeled; their load transfer and deformation characteristics are modeled using the traction spring elements in the FE model", " Figure 17 shows the radial displacement of the first raceway of the outer ring in the whole hub case. The displacement scale is 100 times. The raceway has been shifted entirely. The maximal radial displacement is 2.814 mm relative to the original raceway. Hence, the maximal radial deformation is about 1.407 mm, which is 0.124% of the radius (1126.2 mm) of the original raceway. The variation of the principal curvature at the contact point is less. It indicates that the uniform assumption of coefficient C for the ballrace contacts is reasonable. The plane ribs in Fig. 5 are used to strengthen the hub. In order to study how the plane ribs affect the load distribution in the pitch bearing, the cases about the plane ribs with different center holes are analyzed. The diameter d of center hole are 0 mm (whole hub case mentioned above), 426 mm, 1326 mm, and 2226 mm (no plane rib), respectively. Also, the case that there is only one pitch bearing connected with the hub is analyzed. Figures 18 and 19 show the ball-race contact forces in the first and second raceway. In all of the cases, the load distribution is the worst when there is only one pitch bearing in the hub" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003338_taes.2021.3053134-Figure12-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003338_taes.2021.3053134-Figure12-1.png", "caption": "Fig. 12. 3-D motion trajectory in T under the PD+ controller.", "texts": [ " In addition, the boresight of the vision sensor remains pointing towards the target after a short period of time, and in particular, the target is always in sight. As a consequence, the proposed I&I adaptive controller successfully accomplishes the proximity operations mission, whilst complying with both path and FOV constraints. However, even though the PD+ controller can also enable the pursuer to arrive at the anchoring point with the vision sensor\u2019s boresight pointing towards the target, two kinds of kinematic constraints are transgressed, as clearly seen in Fig. 12. Finally, we depict the time histories of \u2016ve\u2016\u221e and \u2016\u03c9e\u2016\u221e in Fig. 13, from which it is evident that, under the PD+ controller, both the velocity and angular velocity errors exceed the maximum allowable values, thus violating the dynamic constraints. In this subsection, a practical simulation scenario is considered to testify the effectiveness of the proposed control method in a (close to) realistic environment. Several practical aspects including thruster modulation, installation deviation, parameter variations, and external disturbances are taken into account in the simulation" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000039_978-1-84996-220-9-Figure3.8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000039_978-1-84996-220-9-Figure3.8-1.png", "caption": "Figure 3.8 (a) Position and (b) attitude intervals", "texts": [ " The cuboid can be conceived as a virtual box around the reference point, in which the effector is allowed to move (see Figure 3.7). If one dimension of this box is set to zero, the effector may move on a plane. Similarly, setting two box-dimensions to zero, the effector may move on a straight line in the third, free direction. Setting all interval dimensions to zero leads to the standard motion control tracking the reference trajectory exactly. Therefore, the proposed approach can be seen as an extension to common trajectory generation methods. Figure 3.8 left illustrates the computation of the linear displacement in each iteration. It computes as \u03b4xdisp = \u2212\u03b1pos ( \u2202H \u2202x )T . (3.21) Displacement xdisp is superposed with the reference trajectory, and it is checked if the updated effector command lies within the permitted boundary. If the boundary is exceeded, the displacement vector xdisp is clipped to stay within the permitted region. Figure 3.8 (a) illustrates this for a 2D example. An interval formulation for the effector axis direction is depicted in Figure 3.8 (b). The commanded effector axis acmd is allowed to move within a cone with symmetry axis being the reference axis and opening angle \u03d5 being the displacement boundary. The cone edge is of unit length, so that the depicted circumference is the intersection of the cone and a unit sphere. The tangential displacement on the unit sphere results from the gradients \u2202H \u2202\u03c9x and \u2202H \u2202\u03c9y : \u03b4a = \u2212\u03b1att \u239b\u239c\u239c\u239d \u2202H \u2202\u03c9x \u2202H \u2202\u03c9y 0 \u239e\u239f\u239f\u23a0\u00d7acmd . (3.22) If the propagated command axis acmd = are f + adisp lies within the tolerance cone, no clipping has to be carried out. Otherwise, the command axis has to be clipped according to the lower parts of Figure 3.8. 78 M. Gienger, M. Toussaint and C. Goerick When carrying out a task with a humanoid robot, it is crucial to determine a good stance position with respect to the object to grasp or manipulate. There exist some interesting approaches, which sample and evaluate a reachable space for feasible solutions [24, 25, 64]. In this section, we will explain a potential-field-based method to determine an optimal stance. The underlying kinematic model is depicted in Figure 3.9. We introduce a stance coordinate system that is described by the translation and rotation in the ground plane, corresponding to the stance poses the robot can reach" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000751_tmag.2013.2274747-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000751_tmag.2013.2274747-Figure5-1.png", "caption": "Fig. 5 Simulation model of 500 kV overhead HVTL. Red squares with \u201cs\u201d denote the MR sensor array.", "texts": [ " The error of the reconstructed system frequency to the actual value is less than 0.3%. These experiments performed with the testbed proved the principle of the current monitoring technology based on magnetic field measurement and current source reconstruction. The technology can function properly regardless of whether the transmission lines are in normal operation state or in abnormal conditions. This reconstruction method was tested with the simulation model of the 500 kV transmission lines in Fig. 5. A typical HVTL emanates magnetic field in the amplitude of several hundred microTesla at the top level of the transmission tower. The magnetic field can be accurately measured by commercially available MR sensors which can provide sensitivity down to around 10- Tesla and spatial resolution of 0.9 mm [3]. Fig. 5 shows a transmission tower with three-phase 50 Hz 500 kV (maximum load current is 3.75 kA per phase) transmission lines [4]. The configuration of the three phase conductors is flat formation, as shown on the right side of the figure. A magnetic sensor array is installed on the top level of the tower and used to measure the magnetic field emanated by the phase conductors. The array is composed of 11 MR sensors with 1.0 m spacing among each other. FEA simulation was conducted to investigate the influence of the steel structure of the transmission tower on the magnetic field measurement", " Thus in this work we only need to consider the effects of transmission-line conductor sagging and image current in the conducting ground when calculating the magnetic field distribution. The magnetic field from the transmission lines can be accurately calculated by analytical method [6], [7]. The resulting magnetic field of multi-conductor power lines can be evaluated by superimposing the contribution from each phase current flowing in the conductors and the image currents. The detailed calculation of the magnetic field of the transmission line with sagging is described in [6]. Fig. 7(a) shows the magnetic field distribution of the 500 kV transmission lines in Fig. 5 on the top level of the tower. The magnetic field is simulated with conductor sag of 10 m. We assume that every conductor suffers the same sag. The maximum magnetic flux density of the resulting magnetic field is T obtained at the center sensor position. Fig. 7(b) shows the phase current reconstruction results from the measured magnetic field. It is found that the amplitudes of phase currents are reconstructed with an average error of 0.13% to the actual value. The current cycle is found to be 20" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001791_j.mechmachtheory.2016.05.001-Figure2.5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001791_j.mechmachtheory.2016.05.001-Figure2.5-1.png", "caption": "Fig. 2.5. Sketch of 2-UPU + SPR PM.", "texts": [ " (4b) and (8a), a novel velocity transmission equation can be derived as following: Vr \u00bc J4 v\u03c9 ;Vr \u00bc vr1 vr2 vr3 0 0 0 0 0 2 66666666664 3 77777777775 ; J4 \u00bc \u03b4T1 e1 \u03b41\u00f0 \u00deT \u03b4T2 e2 \u03b42\u00f0 \u00deT \u03b4T3 e3 \u03b43\u00f0 \u00deT f T4 d4 f 4\u00f0 \u00deT 0T 3 1 0T 3 1 f T2 d2 f 2\u00f0 \u00deT f T3 d3 f 3\u00f0 \u00deT 0T 3 1 R31 R32\u00f0 \u00deT 2 66666666666664 3 77777777777775 : \u00f08c\u00de From J4 and the properties of constrained wrenches, the fourth KIM (UPU + SPR + UPR PM) for the Exechon PM can be derived (see Fig. 2.4). Some geometric constraints are satisfied for this PM as follows: Ri1\u2551A1A3;Ri1\u22a5Ri2;Ri2\u22a5ri;Ri2\u2551Ri3 i \u00bc 1;3\u00f0 \u00de;R13\u22a5R14;R14\u22a5m;R33\u2551a2o;R21\u2551a1a3;R21\u22a5r2: \u00f08d\u00de 3.6. The fifth KIM for the Exechon PM: 2-UPU + SPR PM Using the same method for deriving Eq. (8a), it leads to J0;7 \u00fe t2 J0;8 h i v\u03c9 \u00bc f T5 dT 5 f T5 h i v\u03c9 \u00bc 0; f 5 \u00bc f 3;d5 \u00bc d3 \u00fe t2R31 \u00f09a\u00de here t2 is a scalar quantity, d5 = d3 + t2R31 denotes the vector from o to c2, c2 is a point on line R31(see Fig. 2.5). It is easy to determine that \u00bd f T5 dT 5 f T5 in Eq. (9a) represents one constrained force which is parallel with R32 and passes through c2. As determining the UPU leg in the UPU + SPR + UPR PM, one UPU type leg (see Fig. 2.5) which connects A3 to a3 can be determined from Eq. (9a). The geometrical constraints in this leg are symmetrical to the UPU leg in the UPU + SPR + UPR PM. By adding t2 times the eighth row of Eq. (8c) to the seventh row, then by adding 1/c1c2 times the fourth row and \u22121/c1c2 times the seventh row to the eighth row of Eq. (8c), and combining with Eqs. (8a) and (9a), a novel velocity transmission equation can be derived as following: Vr \u00bc J5 v\u03c9 ;Vr \u00bc vr1 vr2 vr3 0 0 0 0 0 2 66666666664 3 77777777775 ; J5 \u00bc \u03b4T1 e1 \u03b41\u00f0 \u00deT \u03b4T2 e2 \u03b42\u00f0 \u00deT \u03b4T3 e3 \u03b43\u00f0 \u00deT f T4 d4 f 4\u00f0 \u00deT 0T 3 1 0T 3 1 f T2 d2 f 2\u00f0 \u00deT f T5 d3 f 5\u00f0 \u00deT 0T 3 1 0T 3 1 2 66666666666664 3 77777777777775 : \u00f09b\u00de From J5 and the properties of constrained wrenches, by substituting one UPR leg in UPU + SPR + UPR PM with one UPU leg, the fifth KIM (2-UPU + SPR PM) for the Exechon PM can be derived (see Fig. 2.5). Some geometric constraints are satisfied for this PM as follows: Ri1\u2551A1A3;Ri1\u22a5Ri2; ri\u22a5Ri2;Ri2\u2551Ri3;Ri3\u22a5Ri4;Ri4\u22a5m i \u00bc 1;3\u00f0 \u00de;R21\u2551a1a3;R21\u22a5r2: \u00f09c\u00de From Eq. (8c), it can be seen that J4,4, J4,7 and J4,8 are linearly dependent. By firstly adding 1/c1A3 times the fourth row and then adding \u22121/c1A3 times the seventh row to the eighth row of Eq. (8c), a novel velocity transmission equation can be derived as following: Vr \u00bc J6 v\u03c9 ;Vr \u00bc vr1 vr2 vr3 0 0 0 0 0 2 66666666664 3 77777777775 ; J6 \u00bc \u03b4T1 e1 \u03b41\u00f0 \u00deT \u03b4T2 e2 \u03b42\u00f0 \u00deT \u03b4T3 e3 \u03b43\u00f0 \u00deT f T4 d4 f 4\u00f0 \u00deT 0T 3 1 0T 3 1 f T2 d2 f 2\u00f0 \u00deT f T3 d3 f 3\u00f0 \u00deT 0T 3 1 0T 3 1 2 66666666666664 3 77777777777775 : \u00f010a\u00de Eqs" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003169_j.mechmachtheory.2020.103844-Figure14-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003169_j.mechmachtheory.2020.103844-Figure14-1.png", "caption": "Fig. 14. The 3- P ( S S ) S PM with closed-loop passive limbs: (a) kinematic structure; (b) kinematic scheme.", "texts": [ " As is well known, the zero-torsion parallel mechanism, which has two orientational DOF and one translational DOF, has attracted much attention due to the increasing demand of A/B-axis tool heads in the manufacture of structural aircraft parts with thin walls [43] . The 3- P RS parallel mechanism is a very typical zero-torsion parallel mechanism since it has successfully been used in the development of the Sprint Z3. To provide an alternative scheme, the 3- P ( S S ) S PM with three closed-loop passive limbs is presented here as shown in Fig. 14 . The mobile platform is connected to three limbs by means of spherical joints (i.e., C i ) that are equally spaced at a nominal angle of 120 \u00b0. The passive limb of each limb contains two passive chains, i.e., bar B i ,1 C i and bar B i ,2 C i , of constant length with two spherical joints, respectively. The lower ends of the two passive chains in each limb are linked to one actuated joint with two spherical joints (i.e., B i ,1 and B i ,2 ). Each actuated joint is a slider and can move up and down along its vertical slideway, and the actuated joints are also spaced at a nominal angle of 120 \u00b0 from one another", " (21) The physical meanings of these three actual proximal twists are three independent velocities along the Z-axis. By using the actuating strategy, as presented in section 2.2.2, three proximal wrenches are identified as 1 S PW = ( B 1 C 1 ; c 1 \u00d7 B 1 C 1 ) , 2 S PW = ( B 2 C 2 ; c 2 \u00d7 B 2 C 2 ) , 3 S PW = ( B 3 C 3 ; c 3 \u00d7 B 3 C 3 ) . (22) The parameters utilized for this analysis were selected to demonstrate the loci of singularities and motion-force interaction performance of the 3- P ( S S ) S PM and, as such, may not be optimal in terms of workspace and performance. The parameters in Fig. 14 (b) are presented in Table 1 , where L is the length of the passive limb, R is the radius of the base, r is the radius of the mobile platform, and K = B i 1 B i 2 is the structural parameter of the closed-loop passive limb in the 3- P ( S S ) S PM. The distributions of the values of the PII, DII, and LII in the orientation workspace of the 3- P ( S ) S PM are illustrated S Fig. 16. Distributions of index values in the orientation workspace of the 3- P ( S S ) S PM: (a) PII; (b) DII; (c) LII. Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003369_j.mechmachtheory.2021.104386-Figure8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003369_j.mechmachtheory.2021.104386-Figure8-1.png", "caption": "Fig. 8. Line of action in the transverse plane of helical gear pair.", "texts": [ " \u03beH is the central angle for the deviation length on the base circle of the j th slice from the slice at the end and is calculated using Eq. (20) . \u03beT = ( t \u2212 1 ) \u00d7 2 \u03c0 z p , (19) \u03beH = b j \u00d7 tan \u03b2b r , (20) b where t denotes t th tooth pair in the mesh and has a value from 1 to a rounded integer of the contact ratio; b i represents the distance from the end of the gear to the j th slice; and \u03b2b is the base helix angle, which is defined as \u03b2b = \u23a7 \u23a8 \u23a9 + \u03b2b 0 \u2212 \u03b2b if a gear pair has left \u2212 hand helix angle if a gear pair is a spur gear pair if a gear pair has right \u2212 hand helix angle . (21) As shown in Fig. 8 , T 1 and T 2 are the contact points of the action line (red line) on the base circle of the pinion and gear in the transverse plane of a helical gear pair. Point A on the action line is the starting point of the mesh, where it meets the active addendum circle of the gear. Point E on the action line is the end point of the mesh where it meets the active addendum circle of the pinion. The instantaneous pressure angle of the gear mesh has a value between \u03b1min and \u03b1max and is calculated as \u23a7 \u23a8 \u23a9 \u03b1min = arctan ( T 1 A r b,p ) \u03b1max = arctan ( T 1 A + AE r b,p )" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000312_1.4002447-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000312_1.4002447-Figure3-1.png", "caption": "Fig. 3 Nonspherical \u201esatelliting\u2026 particles", "texts": [ " The powder dynamic equations 21,23 are given by dx dt = up 4 dup dt = 18 pdp 2 CDRe 24 u \u2212 up + g p \u2212 p 5 Re = dp u \u2212 up 6 CD = 24 Re 1 + a1Rea2 + a3Re a4 + Re 7 a1 = exp 2.3288 \u2212 6.4581 + 2.4486 2 a2 = 0.0964 + 0.5565 a3 = exp 4.905 \u2212 13.8944 + 18.4222 2 \u2212 10.2599 3 a4 = exp 1.4681 + 12.2584 \u2212 20.7322 2 + 15.8855 3 8 where p, dp, and up are the density, diameter, and velocity of each particle, respectively. Basically, the particles are driven by the forces of gas flow drag and gravity. is the shape factor for nonspherical particles. As shown in Fig. 3, the powder has a satelliting shape and a shape factor value of 0.8 is chosen 18,24 . Particle temperature is governed by the laser heating, ambient gas convection, and latent heat of its phase change rate, and is described by 18 mpcp dTp dt = hcAp T \u2212 Tp + I Ap 4 \u2212 mpLf df dt 9 Nu = hcdp = 2 + 0.6 Re0.5 Pr0.33 10 where is the thermal conductivity of the surrounding gases and Pr =cp / is the Prandtl number. f is the liquid fraction, which is expressed as MARCH 2011, Vol. 133 / 031007-3 ms of Use: http://www" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001379_978-3-319-22056-7-Figure3.6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001379_978-3-319-22056-7-Figure3.6-1.png", "caption": "Fig. 3.6 Planar separation of a beam", "texts": [ "145) radial velocity of the remainder body is not higher than the initial velocity and v\u2217 S1r vS1r . For 2\u03c1S1 ( k M \u2212 m \u2212 2 1 ) (rS10 \u2212 rS1) + k M \u2212 m (r2S10 \u2212 r2S1) + 2v2S1c ln rS10 rS1 > 0, (3.146) radial velocity (3.143) is after mass separation, higher than initial one. Besides, the boundary value for 1 depends on separated mass m: If separated mass is larger, the limit value of the angular velocity of rotation is higher. In this section an example of in-plane mass separation of an initial beam into a separated and a remainder part is considered. Mass of the homogenous initial beam (Fig. 3.6) is 3.8 In-Plane Separation of a Beam 51 and its moment of inertia is IS = 1 12 \u03c1AL3, (3.148) where \u03c1 is density, L is length, A = hs = const. is constant cross section, h L is width of the beam and s L is thickness of the beam. Beam moves in x Oy plane and has three degrees of freedom. Velocity and angular velocity of the remainder beam are determined using the previously suggested analytical procedure. Let us assume generalized velocities of motion: components of mass centre velocity x\u0307S , y\u0307S and angular velocity of the beam \u03c8\u0307 = ", " Using position coordinates of S1 xS1 = xS \u2212 \u03c1S1 cos\u03c8, yS1 = yS \u2212 \u03c1S1 sin\u03c8, (3.159) and \u03c1S1 = l/2, velocity projections and angular velocity are in general x\u0307S1 = x\u0307S + l 2 \u03c8\u0307 sin\u03c8 + x\u0307\u2217 S1, y\u0307S1 = y\u0307S \u2212 l 2 \u03c8\u0307 cos\u03c8 + y\u0307\u2217 S1, \u03c8\u03071 = \u03c8\u0307 + \u03c8\u0307\u2217 1 , (3.160) where x\u0307\u2217 S1, y\u0307\u2217 S1 and \u03c8\u0307\u2217 1 are perturbed values of velocity and angular velocity. Substituting (3.160) into (3.158), we have T\u0303a1 = 1 2 1 12 \u03c1A(L \u2212 l)3(\u03c8\u0307 + \u03c8\u0307\u2217 1) 2 + 1 2 \u03c1(L \u2212 l)A (( x\u0307S + l 2 \u03c8\u0307 sin\u03c8 + x\u0307\u2217 S1 )2 + ( y\u0307S \u2212 l 2 \u03c8\u0307 cos\u03c8 + y\u0307\u2217 S1 )2 ) . (3.161) For impulse shown in Fig. 3.6, it is J = \u2212J sin(\u03c8 + \u03b1)i + J cos(\u03c8 + \u03b1)j, (3.162) 3.8 In-Plane Separation of a Beam 53 where \u03b1 = const. and J is intensity of impulse of the impact force. As impulse acts on the end of the beam (see Fig. 3.6) and its component normal on beam has the same direction as angular velocity of the beam, the virtual work of the impulse is according to (3.106) \u03b4A = \u2212J sin(\u03c8 + \u03b1)\u03b4x\u0307S + J cos(\u03c8 + \u03b1)\u03b4 y\u0307S + J ( L 2 cos\u03b1\u03b4\u03c8\u0307 ) . (3.163) Due to (3.109) and (3.163), generalized impulses are Qx\u0307 S = \u2202 A \u2202 x\u0307S = \u2212J sin(\u03c8 + \u03b1), Qy\u0307S = \u2202 A \u2202 y\u0307S = J cos(\u03c8 + \u03b1), (3.164) Q\u03c8\u0307 = \u2202 A \u2202\u03c8\u0307 = J L 2 cos\u03b1. Velocity and angular velocity of the remainder beam are calculated according to \u2202 \u2202 x\u0307S (T\u0303a \u2212 T\u0303b) = Qx\u0307 S, \u2202 \u2202 y\u0307S (T\u0303a \u2212 T\u0303b) = Qy\u0307S, \u2202 \u2202\u03c8\u0307 (T\u0303a \u2212 T\u0303b) = Q\u03c8\u0307S, (3" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002624_j.compstruct.2019.111561-Figure9-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002624_j.compstruct.2019.111561-Figure9-1.png", "caption": "Fig. 9. Tests on a 3U CubeSat prototype. (a) Release tests of solar arrays, (b) temperature curves of thermal cycling tests, (c) setup and control curves of vibration tests.", "texts": [ " The free recovery of the release device was monitored by a camera to record the recovery trajectory and a thermal infrared imager (Jenoptik InfraTec, Dresden, Germany) to record the heat field distribution. The shapes and angles measured by camera during the recovery were referred as Sr and \u03b8r , and the original ones were denoted by S0 and \u03b80 in Fig. 8. The shape recovery ratio (Rr) quantifying the shape memory effect was calculated as follows: = \u2212 \u2212 \u00d7\u00b0R \u03b8 \u03b8 \u03b8180 100%r r 0 0 (3) To investigate the feasibility of this ultra-light release device on CubeSats, experiments including release, thermal cycles and vibration were done with a 3U prototype in Fig. 9. The deployable panel was latched by the curved release device, and the packaged configuration was obtained. For deployable configuration, the release device was heated by the screen-printed heaters with 3V DC voltage, recovering to its original flat state, and the panel was deployed. Reusability is another characteristic which makes SMPC release device superior to explosive actuators and burn wire non-explosive actuators. These tests were conducted by repeating the molding and release process, during which the release times were obtained and morphologies of the release device were observed. Since the temperature was used as the mechanism to release the deployable panel, premature deployment must be avoided. However, unwanted heating and cooling were inevitable for spacecraft during the storage, launch and flight stages. Therefore, thermal cycling tests were used to simulate this temperature variation process. It consisted of 4.5 cycles and was performed in a Zwick temperature chamber with a temperature variation from \u221225 \u00b0C to 55 \u00b0C and changing rate of 3 \u00b0C/ min in Fig. 9 (b). The tested release device was printed with the heater named \u2018Type B-IO-IO\u2019. It is significant to find a way to verify the locking property after these thermal cycles for two reasons. On the one hand, as mentioned before, the drastic change in temperature might cause crack propagation and fracture of the SMPC. On the other, the viscoelastic property of SMPC makes the creep more obvious at high temperatures, thus the interference will be diminished as well as the locking force. Therefore, to justify whether the deployable panel could be latched reliably by the release device after thermal cycles, vibration tests were conducted on an electro-dynamic vibration system", " However, these structures are flexible and need to be latched by HRMs to raise their vibration frequency during the launch process. Thus, the mechanical properties of the release device are critical in the vibration. It needs to provide enough locking force to maintain the packaged configuration. Therefore, to investigate whether the CubeSat packaged by the release device after thermal cycles could withstand this harsh mechanical environment, sinusoidal and random vibration tests were conducted. The test conditions were shown in Fig. 9(c) where the red lines represented the upper and bottom limitations and black lines characterized actual plot recorded by the acceleration sensor on the vibration table. Due to the miniaturization of the release device, no data was collected. The results were evaluated by test phenomenon, morphology and release time. The curves of the stress versus strain from tensile tests of SMP and SMPC-77.8dtex and SMPC-141.4dtex have been shown in Fig. 10. As predicted by the classical lamination theory, the elastic modulus is decreased from 980MPa for pure SMP to 945MPa for SMPC-77" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001408_iet-epa.2016.0739-Figure10-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001408_iet-epa.2016.0739-Figure10-1.png", "caption": "Fig. 10 9S/10P prototype PM machine", "texts": [ " Overall, the improved superposition method is proved to be effective for the UMF prediction under rotor eccentricity conditions. The experiments are also adopted to verify the proposed method. The experiment appliances and the principle have been introduced in [2], which will be used in this paper as well. In order to easily measure the UMF of the prototype machine, three phase currents are excited with Ia = 0 and Ib =\u2212Ic = Idc for q-axis current. The stator and rotor of the prototype 9S/10P PM machine and the measured results are shown in Fig. 10, together with those obtained by the improved superposition method, direct linear FEA and direct non-linear FEA. Fig. 10c shows that the results obtained by the proposed method and the linear FEA match well as previously described. Both of them predict the slightly higher UMF than those by the non-linear FEA and measurements. It can be seen that the measurement results are more close to those obtained by the non-linear FEA, which accounts for the magnetic saturation of stator and rotor cores. Since the accurate measurement of UMF is also quite hard, it can be considered that both magnitude and tendency are in good agreement" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002460_j.mechmachtheory.2018.03.018-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002460_j.mechmachtheory.2018.03.018-Figure2-1.png", "caption": "Fig. 2. D-H coordinate systems of the 7R 6-DOF robot.", "texts": [ " In Section 4 , the methods to deal with the position singularities and orientation singularities are proposed. In Section 5 , two numerical simulations are implemented to demonstrate the effectiveness of the proposed method. The conclusion is drawn in Section 6 . As shown in Fig. 1 , the 7R 6-DOF painting robot consists of 7 revolute joints. Configuration of the first three joints i.e. R \u22a5 R//R is widely used in industrial robots, and the latter four joints construct the non-spherical wrist with the second and third of which are coupled with the relation: \u03b8 = \u2212\u03b8 . Fig. 2 shows the D-H coordinate systems of the 7R 6-DOF robot. The 6 5 corresponding D-H parameters are listed in Table 1 . Then, the kinematic equation can be expressed as t = [ \u03bdT , \u03c9 T ] T = J (\u03b8) \u0307 \u03b8 (1) where t \u2208 2 \u00d7 R 3 is the EE velocity, \u03bd and \u03c9 respectively denote the linear and angular velocities of EE, \u02d9 \u03b8 = [ \u0307 \u03b81 , \u02d9 \u03b82 , \u02d9 \u03b83 , \u02d9 \u03b84 , \u02d9 \u03b85 , \u02d9 \u03b87 ] T is the independent joint rate vector, J ( \u03b8) \u2208 R 6 \u00d7 6 is the Jacobian matrix. A configuration is singular when the rank of the Jacobian matrix decreases", " 11 (b), when an initial solution is at or in the vicinity of a singular configuration, the functional redundancy motion could also adjust the robot away from the corresponding singularity. In other words, the new proposed method is effective for the general case and when the initial solution is ill-conditioned, which is a main improvement. In order to demonstrate the effectiveness of the proposed singularity avoidance method, a 7R 6-DOF painting robot is used as the example mechanism to perform painting operations. The configuration and D-H parameters of the robot have been respectively shown in Fig. 2 and Table 1 . As the end-effector (EE), an electrostatic spray gun is added to the end of the robot as shown in Fig. 12 . The transformation matrix from the link frame {X 7 , Y 7 , Z 7 } to the tool frame {X t , Y t , Z t } is expressed as Eq. (37) . In this section, two examples are tested with the TWA with new criterion. The first example deals with the wrist interior singularity, while the second one handles the wrist boundary singularity. For comparison, the DLS method is also utilized to solve the two singularity avoidance problems" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002952_tbme.2020.2994152-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002952_tbme.2020.2994152-Figure3-1.png", "caption": "Fig. 3. Method used to estimate ground slope, combining knowledge of shank pitch and ankle angle to achieve the most accurate possible estimate. Estimation involved averaging the value \u03b1\u2212 \u03b2 during a time when the foot was detected to be flat on the terrain.", "texts": [ " Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. b) Estimation of ground slope: We employed the footflat detection algorithm described above for estimating the ground slope by calculating a running average of the difference between ankle angle and estimated shank pitch while the foot was detected to be flat on the ground. This can be shown through simple geometry to yield the ground slope, a relationship illustrated in Figure 3. We validated our foot flat detection algorithm by quantifying its accuracy in measuring three different ground slopes, including level ground and an ascending and descending 9- degree ramp. c) Development of the heuristic: Once we were convinced that we could estimate these heuristic signals accurately enough, we developed a heuristic classifier with manually tuned coefficients to distinguish between terrains based on a direct, dynamic measurement of terrain geometry across all subjects. The heuristic architecture is shown in Figure 4" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002098_j.ijheatmasstransfer.2018.05.030-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002098_j.ijheatmasstransfer.2018.05.030-Figure1-1.png", "caption": "Fig. 1. The main forces affecting on the algae [11].", "texts": [ " Many certain species of micro-organisms such as Chlamydomonas nivalis and Euglena viridis are structurally featured to be bottom-heavy. This has the consequence that a viscous torque is applied to the micro-organisms. There are a number of forces acting on the algae, the gravitational torque orienting the direction of cell and viscous torque originating from the shear flow, which leads to \u2018gyrotaxis\u2019 [7]. The effect of gyrotaxis is to tip the bottom-heavy cells away from regions of upflow and make the downflow regions denser than the upflow regions. The main forces affecting the cell are described in Fig. 1, assuming that the method of swimming has no effect on the flow field or the cell itself [8]. For the micro-organisms with asymmetric mass distributions in dilute suspensions, a new continuum model was formulated by Pedley [9]. It assumed that the cells swimming is random with direction, hpi, which satisfies the Fokker-Planck equation. Therefore, the mean cell orientation and the related translational diffusivity can be observed in a statistical manner. A good agreement with the results observed in the experiment by Bees [10], which shows that this new continuum model is reasonable" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003373_j.mechmachtheory.2021.104348-Figure9-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003373_j.mechmachtheory.2021.104348-Figure9-1.png", "caption": "Fig. 9. Wheel-to-leap transition of the leg-wheel module: (a) illustrated configurations of the module and (b) corresponding screenshots of an experiment.", "texts": [ " The moment of phase transition does not need to be specified because it is passively determined by the input trajectory. The module then enters the flight phase, where the leg-wheel transforms into wheel mode to avoid a higher obstacle. The leg-wheel remains in wheel mode until touch down. In summary, the boundaries of the wheel-to-leap behavior are defined by two leg-wheel orientation configurations: \u03b2T R and \u03b2LO . Several key motion moments of the leg-wheel module were quantitatively defined in the first planning step, as shown in Fig. 9 . Assume that at the very beginning, the leg-wheel module is rolling on the ground continuously. The transition begins after the rolling wheel enters the lower rim (i.e., method 2). At this moment, the leg-wheel orientation is denoted as \u03b2T R , and the leg-wheel configuration parameter \u03b8 starts to increase. At a certain moment, the module switches its phase from the lower rim phase to the point-contact phase. Then, the leg reaches its maximum length, \u03b8l max , and the leg-wheel poses at the lift-off configuration, \u03b2LO " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000670_j.spinee.2013.09.019-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000670_j.spinee.2013.09.019-Figure2-1.png", "caption": "Fig. 2. The defined trunk segment and the resulting trunk angle as viewed from the oblique frontal and transverse planes.", "texts": [ " For the purposes of this study, the axial angular trunk velocity was calculated as the change in hip to trunk differential angle over a designated time increment. The hip angle was considered to be the angle formed between the line joining the hip joint centers and a theoretical line parallel to the yaxis between the tee and the target (transverse plane). Similarly, the trunk angle was calculated as the angle formed between this theoretical line and the line between two virtual markers located bilaterally midway between the hip and the shoulder joint markers (Fig. 2). For both the hip and trunk angles, a positive value was indicative of rotation from the neutral position away from the target (closed position; clockwise rotation), whereas rotation from the neutral position toward the target (open position; counterclockwise rotation) was represented by a negative value. The lateral flexion angle of the spine required two virtual points to be calculated based on the location of the hip and shoulder markers. The mid-hip virtual point was calculated as the half distance between the left and right hip markers, while the mid-shoulder virtual point was calculated in a similar fashion for the left and right shoulder markers" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001710_j.cja.2015.03.003-Figure9-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001710_j.cja.2015.03.003-Figure9-1.png", "caption": "Fig. 9 Schematic for the selection of experimental points within a grid.", "texts": [ " According to industrial robots performance criteria and related test methods up to China\u2019s national standard and professional standard (GB/T 12642\u2013\u20132001), 8 suitable positions must be determined within the cube of the working region to examine the pose accuracy of an industrial robot. As shown in Fig. 5, Ci\u00f0i \u00bc 1; 2; . . . ; 8\u00de are selected as the cubic vertices (see Fig. 8). There are 4 planes to be selected for a pose experiment based on the standard requirement. In this case, the planes are C1\u2013C2\u2013C7\u2013C8, C2\u2013C3\u2013C8\u2013C5, C3\u2013C4\u2013C5\u2013C6, and C4\u2013C1\u2013C6\u2013C7. 5 points (P1, P2, P3, P4, and P5) that must be measured are on the diagonals of the measuring planes in the standard requirement. P1 is the center of the cube. The positions of other point P2 to P5 are shown in Fig. 9. To describe the errors within the entire grid space as much as possible, the points on the other two diagonals are added. 9 points \u00f0P1;P2; . . . ;P9\u00de within each grid are selected as measurement points. In Fig. 9, L represents the length of the diagonal. for robot calibration based on error similarity, Chin J Aeronaut (2015), http:// When the cube is small enough to be close to a point, the predictive accuracy of the error model is close to the point\u2019s repeat accuracy. With increasing of the grid size, the predictive ability of the error model decreases. The maximum error and the standard deviation of the measurements are used as the criteria. The largest grid that meets the accuracy requirements is selected as the optimum compensation grid step in the region" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001653_j.measurement.2018.02.067-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001653_j.measurement.2018.02.067-Figure5-1.png", "caption": "Fig. 5. Typical displacement measurement configuration [62].", "texts": [ " Therefore, the components measured by strain gauges during ship operation can be divided into vertical and horizontal components in the form of orbits with which the trends in shaft bending direction can be identified as a function of engine load during operation by comparison with static conditions. In addition to the time-domain and rotation angle-domain plots, an orbit plot is useful for the analysis of vibration and behavior, especially to investigate the influence of the ship operation on the shaft motion. To obtain the orbit plot, two non-contact displacement sensors are installed at 90\u00b0 intervals from the shaft center and an additional displacement sensor is installed to record the rotational speed as shown in Fig. 5. In this case, the signal generated by one sensor becomes the input of the horizontal axis and the signal of the other sensor becomes the input of the vertical axis. Signals for two intersecting directions can be displayed simultaneously with a time-domain waveform, or they can be combined and displayed as a single piece of information. In reality, in order to measure the accurate displacement and shaft orbit, a non-contact displacement sensor is to be installed in the vicinity of the propeller or the aft stern tube seal which is expected to be directly affected by the hydrodynamic propeller force" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001880_j.mechmachtheory.2018.04.001-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001880_j.mechmachtheory.2018.04.001-Figure2-1.png", "caption": "Fig. 2. Predesigned transmission error curve.", "texts": [ " The goal of function-oriented design is to generate the pinion target surface meeting the desired function requirements. We obtained the target surface of HCR spiral bevel gears with seventh-order TE based on function-oriented design in our previous work [25] . The principal is that the pinion target tooth surface is acquired by correcting the conjugated tooth surface derived from the mating gear with the design HTE and contact path. To obtain a gear set meeting the design requirements, we designed the HTE curve ( Fig. 2 ). The equation for this curve is: \u03b4( \u03d5 1 ) = c 0 + c 1 \u03d5 1 + c 2 \u03d5 1 2 + c 3 \u03d5 1 3 + ... + c 10 \u03d5 1 10 + c 11 \u03d5 1 11 (1) where c i (i = 0 , 1 , 2 , ..., 10 , 11) are polynomial coefficients and \u03d51 is the pinion meshing angle. The locus of the tool surface is given by the following equations: r p ( s p , \u03b8p ) = \u23a1 \u23a2 \u23a3 ( R p + s p sin \u03b11 ) cos \u03b8p ( R p + s p sin \u03b11 ) sin \u03b8p \u2212s p cos \u03b11 1 \u23a4 \u23a5 \u23a6 (2) n p ( \u03b8p ) = [ cos \u03b11 cos \u03b8p cos \u03b11 sin \u03b8p \u2212 sin \u03b11 ] (3) where s p , \u03b8p are tool surface parameters, R p is the cutter radius, and \u03b11 is the profile angle" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000180_j.mechmachtheory.2010.07.003-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000180_j.mechmachtheory.2010.07.003-Figure3-1.png", "caption": "Fig. 3. Reaction forces Fri applied at the spherical joint Ti.", "texts": [ " The dynamic equations for each of the legs could be expressed as: Mi\u00f0qi\u00deq :: i + Ci\u00f0qi;q\u0307i\u00deq\u0307i + Ni = Q i + JTi Fri; i = 1\u223c3 \u00f04\u00de Mi = \u00f0ms + mL\u00deb \u2202 \u2202Si ; \u2202 \u2202Si N 1 2 mLb \u2202 \u2202Si ; \u2202 \u2202\u03b8i N 1 2 mLb \u2202 \u2202\u03b8i ; \u2202 \u2202Si N 1 3 mLb \u2202 \u2202\u03b8i ; \u2202 \u2202\u03b8i N 2 6664 3 7775 2\u00d72 is the inertial matrix of leg i and b:;:N denotes the inner product of the where corresponding bases. ms andmL denote the mass of the slider and connecting rod, respectively. Ci\u00f0qi;q\u0307 i\u00deq\u0307i denotes the centrifugal and Coriolis forces of the leg iwhile Ni denotes the gravitational force. Fri = \u00bd frix friy friz T denotes the reaction forces applied at the spherical joint Ti in the Cartesian space as shown in Fig. 3. JiT is the 2\u00d73 transformation matrix which transforms the reaction forces Fri from the Cartesian space into the joint space and given as [21]: JTi = \u2202 \u2202Si T \u2202 \u2202\u03b8i T 2 66664 3 77775 \u00f05\u00de It is shown in Eqs. (4) and (5) that the formulation of the dynamic model for each leg is straightforward and simple under the joint coordinates. where bases Gi = where Ry\u00f0\u03b2\u00deR skew- To describe the motion of the moving platform, let P = px py pz\u00bd T denotes the position of its mass center Tc with respect to the Cartesian coordinate system", " Gi is a 3\u00d76 matrix whose columns consist of the of the task space coordinates frame and it could be determined as: I3\u00d73 \u2202R \u2202\u03b1 \u22c5pti \u2202R \u2202\u03b2 \u22c5pti \u2202R \u2202\u03b3 \u22c5pti 3\u00d76 \u00f08\u00de I3\u00d73 is a 3\u00d73 identity matrix and the partial derivatives of general matrix R have the expressions: \u2202R \u2202\u03b1 = x\u00f0\u03b1\u00deU1Rz\u00f0\u03b3\u00de,\u2202R\u2202\u03b2 = Ry\u00f0\u03b2\u00deU2Rx\u00f0\u03b1\u00deRz\u00f0\u03b3\u00de, \u2202R \u2202\u03b3 = Ry\u00f0\u03b2\u00deRx\u00f0\u03b1\u00deRz\u00f0\u03b3\u00deU3 with the operators U1, U2 and U3 expressed by three symmetric matrices associated to unit vectors U1 = 1 0 0\u00bd T , U2 = 0 1 0\u00bd T andU3 = 0 0 1\u00bd T . With the matrix Gi in Eq. (8), the reaction forces applied at the spherical joint Ti could be transformed from the Cartesian space into the task space by nspose Gi T. its tra Since the reaction forces Fri applied at the spherical joint Ti as shown in Fig. 3 could be regarded as the externally applied forces for the moving platform, the dynamic equations of the moving platform could be expressed as: Mo\u00f0X\u00deX :: + Co\u00f0X;X\u0307\u00deX\u0307 + No = \u2212 \u2211 3 i=1 GT i Fri = \u2212GTFr \u00f09\u00de Mo = mT \u22c5I3\u00d73 03\u00d73 03\u00d73 Mr\u00f0\u03b1;\u03b2;\u03b3\u00de 6\u00d76 is the inertial matrix of the moving platform.mT is the mass of the moving platform, 03\u00d73 where denotes a 3\u00d73 zero matrix and Mr is the inertial matrix for rotation of the moving platform. The complete formulation of the matrixMr is derived in Appendix A. Co\u00f0X;X\u0307\u00deX\u0307 denotes the centrifugal and Coriolis forces of the moving platformwhile No denotes its gravitational force", " To avoid the complex calculation of the reaction forces due to the augmented coordinates, a special decomposition of the reaction forces Fri is proposed in the following section based on the analysis of geometric constraints. Besides, since the spherical joints connect the legs and the moving platform, the applied reaction forces Fri have great impact on dynamics of the parallel manipulator. The dynamic coupling between each of legs and dynamic interaction with the moving platform could also be analyzed by decomposing the reaction forces. In this section, the 9 reaction forces shown in Fig. 3 are decomposed into the constraint forces and the driving forces of the moving platform. Three constraint forces are identified as the internal forces of the moving platform such that they would not appear in the equations of the moving platform. The other components of the reaction forces can thus be computed directly from the moving platform. In order to perform such a task, the constraint equations by considering the geometric conditions for the parallel mechanism are derived first. Physically, without connection to the moving platform, the joint coordinates Si; \u03b8if g corresponding to each leg i are linearly independent", " On the other hand, since the constraint forces -FCTi are the internal forces for the moving platform as shown in Eq. (17), they would not appear in its dynamic equations and only six unknowns, FTiz and \u03bbmini, exist in Eq. (21-2) as comparing to the nine reaction forces Fri in Eq. (9). That is, they can be directly computed without considering the dynamics of the legs which provide a different approach to calculate the reaction forces. The decomposition shown in Fig. 8 also used nine variables to represent the reaction forces as those in Fig. 3. However, based on the special decomposition, one part of the reaction forces can be calculated directly from the dynamics of the moving platform while the other part of the reaction forces can be obtained from the dynamics of the three legs. The process to calculate the reaction forces could be more efficient and the detailed algorithm is described in the following section. In this section, the step by step procedures are summarized to solve the inverse dynamics problem of the 3-PRS parallel manipulator and given as follows: 3", " Since the gravity force of the connecting rod is 588 N, the resultant oscillating moment is much larger than that resulted from fTiz and the oscillating amplitudes of the constraint forces \u03bbci become large correspondingly. Once the constraint forces \u03bbci are obtained, the externally applied forces QSi are calculated by Eq. (23) and determined to vary within a wide range from \u2212879 N to \u22121166 N as shown in Fig. 9f. To verify the proposed decomposition algorithm, the resultant of the reaction forces \u03bbci, \u03bbmi and fTiz in Fig. 8 applied at the spherical joints are compared with those in Fig. 3 obtained by direct calculation of Eq. (10). Due to the limited space, only the reaction force Fr1 is demonstrated in Fig. 10 and it is clear that the X, Y and Z-axis components of the reaction force Fr1 = Fr1x Fr1y Fr1z T are exactly identical by the two different approaches. The decomposition of the reaction forces as shown in Eq. (20) could not only reduce the computational effort but also could be used to analyze the effects of different force components upon the reaction forces. Fig. 11a\u2013c shows the different forces components along the Z-axis" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000492_j.cnsns.2012.11.008-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000492_j.cnsns.2012.11.008-Figure4-1.png", "caption": "Fig. 4. Cart\u2013pole system.", "texts": [ " 0 which implies that S2 ? 0. Therefore, it can be concluded that the stabilization of both subsystems can be achieved. This completes the proof. h In order to verify the theoretical considerations and show the correct operation of the proposed control method, a cart\u2013 pole system is simulated and comparisons between the proposed method and the existing decoupled methods (DSMC and TVSSS) are demonstrated. All simulations were carried out by Matlab/Simulink. The dynamic behavior of the cart\u2013pole system shown in Fig. 4 can be described by the following nonlinear equations _x1\u00f0t\u00de \u00bc x2\u00f0t\u00de \u00f030\u00de _x2\u00f0t\u00de \u00bc f1\u00f0x; t\u00de \u00fe b1\u00f0x; t\u00deu\u00f0t\u00de \u00fe d1\u00f0t\u00de \u00f031\u00de _x3\u00f0t\u00de \u00bc x4\u00f0t\u00de \u00f032\u00de _x4\u00f0t\u00de \u00bc f2\u00f0x; t\u00de \u00fe b2\u00f0x; t\u00deu\u00f0t\u00de \u00fe d2\u00f0t\u00de \u00f033\u00de where f1\u00f0x; t\u00de \u00bc mtg sin\u00f0x1\u00de mpL sin\u00f0x1\u00de cos\u00f0x1\u00dex2 2 L\u00f043 mt mp cos2\u00f0x1\u00de\u00de \u00f034\u00de b1\u00f0x; t\u00de \u00bc cos\u00f0x1\u00de L\u00f043 mt mp cos2\u00f0x1\u00de\u00de \u00f035\u00de f2\u00f0x; t\u00de \u00bc 4 3 mpLx2 2 sin\u00f0x1\u00de \u00fempg sin\u00f0x1\u00de cos\u00f0x1\u00de 4 3 mt mp cos2\u00f0x1\u00de \u00f036\u00de b2\u00f0x; t\u00de \u00bc 4 3\u00f043 mt mp cos2\u00f0x1\u00de\u00de \u00f037\u00de where x1(t) is the angular position of the pole from the vertical axis, x2(t) is the angular velocity of the pole with respect to the vertical axis, x3(t) is the position of the cart, x4(t) is the velocity of the cart, mt is the total mass of the system (which includes the mass of the pole, mp, and the mass of the cart, mc), and L is the half-length of the pole" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002508_j.triboint.2019.03.048-Figure12-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002508_j.triboint.2019.03.048-Figure12-1.png", "caption": "Fig. 12. Velocity streamlines; R=10r.", "texts": [ " 11 reveals that the curves of the oil flow rate in the oil guide tubes fluctuate obviously. From the fourth rotation of the driving gear, there is continuous oil flowing through the monitoring surface of oil guide tubes, and the value of flow rate fluctuates up and down at a certain fixed value and maintains the trend, the calculation can be considered to be converged. Both the flow rate of the oil guide tube 1 and 2 are about 2.5 L/min. To visually reflect the oil flow regime inside oil guide device, the velocity streamlines when rotations R=10r is illustrated in Fig. 12. As can be observed from Fig. 9 (d) and 12, only a small portion of the oil which flows into oil guide device enters the oil guide tubes, while most of it flows out the oil tank and back to the area between the gear pair and bottom face of the gearbox's housing; besides, the circular sections of the oil guide tubes are fully occupied by oil, which indicates that oil supply of them is sufficient. Fig. 12 also shows that from the moment when the oil begins to flow from the oil tank to the oil guide tubes to when it eventually comes out from the oil guide tubes, its speed drops drastically, which is from about 10m/s to about 2.5m/s. From the above observations, it can be inferred that the structure of the oil guide device is the key factor affecting the oil flow rate of the oil guide tubes which indirectly determines the oil supply for the bearings. Therefore, without changing the shape and overall size of the oil guide device, three parameters including the oil tank capacity, the hole diameter and fillet radius of oil tubes are determined as the structural influence parameters" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002606_s00170-019-04141-y-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002606_s00170-019-04141-y-Figure7-1.png", "caption": "Fig. 7 Schematic representation of cross section", "texts": [ " With this set-up, experimental trails were conducted to investigate the influences of process parameters on the attributes of the unit block by fabricating thin-wall parts. Totally, 40-layered thin-wall part was deposited layer by layer for each experiment groups. After deposition, the cross-section samples were intercepted from the thin-wall and the variables were measured according to the following measurement method. The schematic representation of cross-section measurement system and parameter abbreviation were shown in Fig. 7 and Table 3, respectively. Area A is the effective region and areas B and C are the regions containing surface ripples that need to be machined by post-processing. It should be noted that the former 4 layers were subtracted from the measured results to prevent the thermal effect of the base plate [23]. Generally, the surface quality is represented by surface waviness. To measure the surface waviness of the side of the thinwall, an infrared range finder was adopted, which can give a quantitative description of undulate surface of the thin-wall", " Regarding the effective deposition rate, it is defined as the ratio of the volume of deposited block (Vblock) to unit time (t) as follows: EDR \u00bc \u03c1Vblock t \u00bc \u03c1\u22c5EWW\u22c5Hblock\u22c5TS \u00f011\u00de where \u03c1 is the density of aluminum welding wire, which was set to 2.7 kg/m3 in this present test. To measure the effective wall width, cross sections were intercepted from the middle of the thin-wall specimen. After the process of grinding, polishing, and corroding, the morphology photos was taken by OLMPUS laser scanning confocal microscopy. The EWW was obtained by measuring effective area with the aid of Adobe Photoshop CS4, as shown in Fig. 7b. The Hblock can be calculated as follows: HI \u00bc TWH\u2212EAH 36 \u00f012\u00de Table 3 Parameter abbreviation TWW Total wall width EWW Effective wall width TWH Total wall height EAH Excluded area height Fig. 8 Morphology of thin-wall under the same number of layers. TS = 8 mm/s: a, WFS = 3 m/min, b WFS = 4 m/min, c WFS = 5 m/min The material utilization that evaluating the cost of AM process is defined as the ratio of the effective area to total area as follows: MU \u00bc A A\u00fe B\u00fe C \u00f013\u00de where both area of A, B, and C can be obtained by microscope and analyzed with the aid of Adobe Photoshop CS4" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001170_we.1656-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001170_we.1656-Figure4-1.png", "caption": "Figure 4. Schematic representation of the model for the ball and the ball-raceway contact.8,15", "texts": [ " In the FE model built in previous work,8 the balls were simulated by a traction-only nonlinear springs, whereas the ball-raceway contacts were reproduced by rigid shells elements, in accordance with the model developed and validated by Daidi\u00e9.15 Two rigid beams were arranged in each contact zone, their confluence point (located in the curvature centers of the raceways) being the anchorage of the traction-only nonlinear spring; this geometrical feature enables to simulate appropriately the contact angle variation. Figure 4 shows the model for the contact between the ball and the outer ring-upper raceway and the inner ring-lower raceway (the other identical model for the outer ring-lower raceway and inner ring-upper Wind Energ. (2013) \u00a9 2013 John Wiley & Sons, Ltd. DOI: 10.1002/we raceway contacts is not represented in the figure). The spring was modeled by a unique traction-only nonlinear spring element (COMBIN39 in ANSYS, ANSYS INC., Canonsburg, Pennsylvania, USA) with an initial length L equal to the raceway diameter minus the ball diameter" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002676_j.mechmachtheory.2020.103955-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002676_j.mechmachtheory.2020.103955-Figure7-1.png", "caption": "Fig. 7. Gear mesh model.", "texts": [ ", Investigation of nonlinear dynamics and load sharing characteristics of a two-path split torque transmission system, Mechanism and Machine Theory, https://doi.org/10.1016/ j.mechmachtheory.2020.103955 12 Z. Hu, J. Tang and Q. Wang et al. / Mechanism and Machine Theory xxx (xxxx) xxx Z. Hu, J. Tang and Q. Wang et al. / Mechanism and Machine Theory xxx (xxxx) xxx 13 G d = \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I dP 0 0 0 0 \u2212I dP 0 0 0 0 0 0 0 0 \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 (8) here, m is the mass of gears; I dD and I dP are the diametral and polar moment of inertia. As illustrated in Fig. 7 , the mesh effect is simplified as time varying mesh stiffness effect combing mesh damping effect and excited by static transmission error. The relative displacement of the gear mesh pair in the direction normal to the tooth surface along the plane of action is represented as \u03b4ih = [(x p \u2212 x g ) sin\u03b1m + (y p \u2212 y g ) cos\u03b1m + \u03b8pz r p + \u03b8gz r g ] cos\u03b2t +[(r p \u03b8py + r g \u03b8gy ) cos\u03b1m + (r p \u03b8px + r g \u03b8gx ) sin\u03b1m + (z g \u2212 z p )] sin\u03b2t \u2212 e i (t) (9) where, \u03b4ih (i = 1 , 2 , 3 , 4) is the relative displacement of the i pair of gears, i = 1 , 2 refers to the spur gear engagement at the first stage and i = 3 , 4 stands for the double-helical gear pair at the second stage" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003480_lra.2021.3061388-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003480_lra.2021.3061388-Figure2-1.png", "caption": "Fig. 2. Based on robot-assisted craniotomy modeling and surgical planning, the surgeon guides the handle of the robot system to drill on the skull of the patient; (a) Overview of the robot-assisted craniotomy; (b) Definition of frames fixed on the robotic tool for craniotomy; (c) Aligning step with an isotropic admittance; (d) Drilling step with an anisotropic admittance.", "texts": [ " In this study, the \u201clow-stiffness\u201d control adopts the zero-force control, and the \u201chigh-stiffness\u201d control adopts velocity tracking based on the admittance method. The switched VF based on intention recognition can be equivalent to a \u201cbang-bang control\u201d created by an experienced surgeon\u2019s intelligence. Moreover, the intention recognition-based controller using the surgeon\u2019s intelligence is more intuitive and efficient than the fixed VFs. The frames of human-robot interaction (HRI) and environment-robot interaction (ERI) are represented in Fig. 2(b). The frame of the robotic tool center point (TCP) is also presented in Fig. 2(b). The feedback controller controls an admittance loop during the aligning and drilling process. The admittance controller achieves both anisotropic and isotropic admittance control for drilling and aligning through a switching condition. The overview of the control system is represented in Fig. 3. The resultant controller is explained as Equation (1). q\u0307d = J+((S\u0304Cali + SCdri)( env h Ahh +Whhenv) +Kh(pd \u2212 pa)) (1) whereJ+ is determined as the pseudo-Jacobian of frame HRI for the robot. Wh is defined as the weight matrix from the surgeon to the robot" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001248_s1003-6326(17)60121-3-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001248_s1003-6326(17)60121-3-Figure1-1.png", "caption": "Fig. 1 Horizontal view and vertical view", "texts": [ " Before microstructural examination, the samples were polished as indicated in the following steps, first with SiC grinding paper up to 3000 grit size, then with diamond powder and polishing solution. To reveal the microstructure, all samples were etched with a 1 mL HF, 2 mL HNO3 and 7 mL H2O solution. Microstructural anisotropy might exist in SLM specimens, therefore two cross sections were examined: vertical view along the building direction (vertical section) and top view (horizontal section) perpendicular to the building direction, as shown in (Fig. 1). A Nikon optical microscope (OM) LV150N and a Hitachi scanning electron microscope (SEM) SU8010 were used for metallography examinations. The phase composition was examined by a Brukers D8 ADVANCE X-ray diffraction. The Vikers micro-hardness tests were performed on a TIME6610A micro-hardness tester and at least five readings were taken for each sample. Qi ZHANG, et al/Trans. Nonferrous Met. Soc. China 27(2017) 1036\u22121042 1038 Both the horizontal and vertical views of sample A presented very similar microstructures, as shown in Figs" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003535_j.mechmachtheory.2021.104436-Figure9-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003535_j.mechmachtheory.2021.104436-Figure9-1.png", "caption": "Fig. 9. Schematic of PES-limbs.", "texts": [ " They are 6 PB-limbs and 12 PE-limbs, which are listed in Table 3. In this table, [RR] and [RRR] represent that axes of the R-joints intersect at a point (O1 or O2). [PRR] represents that the axis of the R-joint passes through the center (O1) of PR-joint. [TPR] and [TRR] represent that the axis of the Rjoint passes through the remote motion center (O1) of TR and TP-joint. The PE-limbs constructed in Table 3 include 6 PES-limbs, which are PES-limbs UR [RRR], UP [RRR], UR [RR], UP [RR], URR and UPR. The structures of PES-limbs are shown in Fig. 9. The PES-limb has the same motion and constraint screws as the PB-limb, so all of them contain a constraint force $F1 along the O1O2 direction. Among them, the limbs UR [RRR] and UP [RRR] are equivalent to the limbs [RR] [RRR] and [PRR] [RRR] respectively. They do not affect the orientation of moving platform, so they are defined as \u2019pure PESlimbs\u2019. Based on 18 PB-groups, 150 position groups can be synthesized by the equivalent replacement method. There are 18 PES-groups, of which 6 are representative and research significance" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000340_978-3-642-30976-2_68-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000340_978-3-642-30976-2_68-Figure4-1.png", "caption": "Fig. 4. The symmetric double-bridge model", "texts": [ " The wireless sensor network with the advantages of high robustness and self-organization is applied to network platform of swarm robotics. The self-organizing of ant colony in nature have attracted the attention of entomologist long time ago, Deneubourg [23] et al. developed a study on the foraging behavior of ant colony by \u201cdouble bridge experiment\u201d. The symmetric double-bridge (the two bridges have same length) A, B will be separated from the nest and food source, ants can moved from the nest to the food source freely, shown in Fig. 4. In the early stage, there is no pheromone in two bridges, every ant will choose bridge A and bridge B at the same probability, so the pheromone left in two bridges is equal. After a period of time, the most ants choose bridge A for some random fluctuations, resulting bridge A attracts more ants with more pheromone left on it. As time goes by, the number of ants who choose bridge A will be more and more, and bridge B just the opposite. Based on the symmetric double-bridge model, the asymmetric double-bridge experiment has been developed in the Player/Stage, as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002833_j.ymssp.2020.106778-Figure8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002833_j.ymssp.2020.106778-Figure8-1.png", "caption": "Fig. 8. Equivalent modeling of stator core and winding.", "texts": [ " Therefore, it is necessary to establish the equivalent stator core model, and assign it the equivalent orthotropic material parameters [17]. Similarly, the equivalent modeling of the winding is the same as the stator core. To sum up, to accurately obtain the modal parameters of SRMs, it is necessary to comprehensively consider the equivalent modeling of the stator core and the winding, and the contact conditions between parts. First, the equivalent modeling of the stator core and the winding has been carried out. The stator core and the winding are established in ANSYS, respectively, as shown in Fig. 8. The winding in the stator slotting is equivalent to twelve straight conductors, and the end winding is built into two rings. The equivalent orthotropic material parameters should be assigned to the stator core and the winding, mainly including the density, the Poisson ratio, the elasticity modulus, and the shear modulus. The density can be determined by the ratio of the actual mass to the volume of the equivalent model. Because the Poisson ratio change has a small effect on the modal parameters of the motor [11], the Poisson ratio is unchanged" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002721_j.mechmachtheory.2020.104164-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002721_j.mechmachtheory.2020.104164-Figure1-1.png", "caption": "Fig. 1. Double-nut ball screws without additional elastic unit.", "texts": [ " When the axial load reaches a certain level, the preload vanishes and the balls will roll in an undefined manner, which is called the decompressing condition [ 6 , 7 ]. This is an undesirable mode of operation and can cause a sudden change in the contact conditions, possible disruptions of the oil film, and an excessive increase in wear [ 8 , 9 ]. Therefore, more attention should be directed toward precisely predicting the critical axial load for avoiding the decompressing condition. Generally, the most commonly used double-nut ball screw mainly comprises one screw shaft, two nuts, and one gasket [10] , as shown in Fig. 1 . In such a system, the preload is hard to be adjusted and cannot be directly measured. Therefore, additional elastic units are widely used in existing studies for adjusting and detecting the preload in ball screws [ 4 , 11\u201313 ]. \u2217 Corresponding author. E-mail address: zhoucg@njust.edu.cn (C.-G. Zhou). https://doi.org/10.1016/j.mechmachtheory.2020.104164 0094-114X/\u00a9 2020 Elsevier Ltd. All rights reserved. Nomenclature F a the axial load applied on the ball screw F A the load applied on nut A due to F a F Ani the axial load applied on the i th part of nut A F Asi the axial load applied to the i th part of screw within nut A L Ani the axial length of nut A between the (i-1) th ball and i th ball L Asi the axial length of the screw between the (i-1) th ball and i th ball within nut A Q Ani the normal contact load on the ball-nut contact of the i th ball in nut A Q Asi the normal contact load on the ball-screw contact of the i th ball in nut A \u03b1Ani the contact angle of the i th ball relative to nut A \u03b1Bni the contact angle of the i th ball relative to nut B \u03b4Ani the Hertz deformation on the ball-nut contact of the i th ball in nut A \u03b4\u2032 Ai the axial component of ( \u03b4Ani + \u03b4Asi ) \u03b4\u2032 Ai \u22121 the axial component of ( \u03b4Ani \u22121 + \u03b4Asi \u22121 ) e rsi the radius error of the i th ball relative to the screw e Ani the profile error of the raceway of nut A relative to the i th ball e \u2032 Ani the axial component of ( e rni + e Ani ) n Ai the axial deformation of the i th part of nut A c Kn the structural constant of the nut c K the structural constant with c K = c Kn + c Ks K Ani the rigidity of nut A between the (i-1) th ball and i th ball \u03b1Ai the contact angle of the i th ball in nut A with \u03b1Ai = \u03b1Ani = \u03b1Asi \u03b3 the helix angle \u03b4A the axial deformation of the first ball in nut A K \u2032 the equivalent rigidity of the gasket and other elastic units F p the preload of the ball screw F B the load applied on nut B due to F a F Bni the axial load applied on the i th part of nut B F Bsi the axial load applied to the i th part of screw within nut B L Bni the axial length of nut B between the (i-1) th ball and i th ball L Bsi the axial length of the screw between the (i-1) th ball and i th ball within nut B Q Bni the normal contact load on the ball-nut contact of the i th ball in nut B Q Bsi the normal contact load on the ball-screw contact of the i th ball in nut B \u03b1Asi the contact angle of the i th ball in nut A relative to the screw \u03b1Bsi the contact angle of the i th ball in nut B relative to the screw \u03b4Asi the Hertz deformation on the ball-screw contact of the i th ball in nut A \u03b4\u2032 Bi the axial component of ( \u03b4Bni + \u03b4Bsi ) e rni the radius error of the i th ball relative to the nut e ri the radius error of the i th ball, with e ri = e rni = e rsi e Asi the profile error of the screw-raceway within nut A relative to the i th ball e \u2032 Asi the axial component of ( e rsi + e Asi ) s Ai the axial deformation of the i th part of the screw within nut A c Ks the structural constant of the screw c E the material constant K A si the rigidity of screw within nut A between the (i-1) th ball and i th ball \u03b1Bi the contact angle of the i th ball in nut B with \u03b1Bi = \u03b1Bni = \u03b1Bsi l Os \u2212Ani the distance of curvature center between screw-raceway and nut-raceway \u03b4B the axial deformation of the first ball in nut B \u03b4\u2032 the compensation for the axial displacement of nuts A and B Namely, besides the screw shaft, nut, and gasket, another most commonly used double-nut ball screw contains additional elastic units, e" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001144_j.mechmachtheory.2013.09.001-Figure14-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001144_j.mechmachtheory.2013.09.001-Figure14-1.png", "caption": "Fig. 14. Simulated tooth contact ellipses, contact points, and transmission errors: Case C.", "texts": [], "surrounding_texts": [ "This example illustrates the tooth contact ellipses and contact points on gear 3, and transmission errors of the gear pair meshing under gear assembly error conditions. The basic parameters for the gear pair are the same as those given in Tables 1 and 2. The influence on the vertical misaligned angle (\u0394\u03b3v = 0.1\u00b0) assembly error for Cases A and B are shown in Figs. 10(a) and 11(a), and the horizontal misaligned angle (\u0394\u03b3h = 0.1\u00b0) assembly error is shown in Figs. 10(b) and 11(b), respectively. The shift of bearing contacts caused by the center distance error (\u0394E = 1 mm i.e., 0.83% operating center distance) for Cases A and B are shown in Figs. 10(c) and 11(c), respectively. The corresponding transmission errors for Cases A and B with assembly errors are revealed in Figs. 12 and 13, respectively. Based on the simulation results shown in Figs. 10 to 13, the following conclusions can be made: 1. When gear pairs are meshed under axial assembly errors of, the crowned work gear generated by a conventional hob with center distance variation (i.e., with parameter a of Case A) may easily cause an edge contact on gear 3. 2. When Case A is compared with Case B under the axial assembly errors, the contact point locations and contact ellipse distributions of the crowned gear generated by the proposed VTT hob with a hob diagonal feed (Case B) are much better than those of Case A. 3. Gear assembly misalignments will result in the contact zone of the gear pair shifted longitudinally. 4. When the gear pairs of Cases A and B are meshed under assembly error conditions, their transmission errors are still very small, since the work gears of both Cases A and B are crowned." ] }, { "image_filename": "designv10_9_0003310_j.mechmachtheory.2021.104428-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003310_j.mechmachtheory.2021.104428-Figure5-1.png", "caption": "Fig. 5. Transmission paths from meshing points to A4.", "texts": [ " Because path 7 is consist of N (the number of planets) branch transmission paths, the AM function caused by the transmission path is denoted by w2,n(t) and can be given by the following expression w2, n(t) = \u03b12wrpn 1 (t) = \u03b12 \u2211Q q\u2208\u2212 Q Wqejqwcte\u2212 jq\u03c6n . (12) Similarly, path 8 is composed of two parts: one time-invariant part from the g3-g4 meshing point to the r-p1 meshing point and one time-varying part, that is, path 1. The transmission path function w3,n(t) of path 8 can be expressed as Y. Nie et al. Mechanism and Machine Theory 167 (2022) 104428 w3, n(t) = \u03b13wrpn 1 (t) = \u03b13 \u2211Q q\u2208\u2212 Q Wqejqwcte\u2212 jq\u03c6n , (13) where, \u03b13 present the attenuation effect of the time-invariant part in path 8, \u03b13 \u2208 (0,1), and \u03b13 < \u03b12 < \u03b11. Fig. 5 illustrates the main transmission paths from each meshing point to A4. As can be seen in Fig. 5, paths 9\u201312 are all time-invariant, and their length only affects the amplitude attenuation of the vibration signal received by A4. they cannot introduce the AM effects on the meshing vibration. Accordingly, under the healthy condition, the Y. Nie et al. Mechanism and Machine Theory 167 (2022) 104428 vibration signal received by A4 is at the gear mesh frequency harmonics and is unmodulated. The vibration signal received by A5 is similar to that of A4, which are all free from the AM effects of the time-invariant vibration transmission paths" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002794_j.addma.2019.100847-Figure8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002794_j.addma.2019.100847-Figure8-1.png", "caption": "Fig. 8. (a) Relative dimensions of channels of diameter 0.2, 0.6, and 1.6 mm. (b) Example of determination of the deviations (shown by blue line segments) between simulations results and experimental data in twelve points across channel cross section. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)", "texts": [ " 7 showed a good agreement between the modeling results and experimental data for the channels with diameters 0.4\u20132mm (Fig. 7b\u2013f). To quantify the errors of the simulations we estimated the standard deviation between predicted and experimental contours of the channels cross section. Absolute values of deviations \u0394rk were estimated in n=12, \u2026, 24 points across each experimental contour as \u0394rk= rk\u2212 rexp,k, where rk and rexp,k are the measured distance between center of the channel and its estimated and experimental boundary in the kth direction, respectively (Fig. 8b). Found standard deviation = \u2211 =S r\u0394n k n k 1 1 2 and relative standard deviation = \u00d7S S d\u00af ( / ) 100% for different channels are presented in Table 1. It is seen that standard deviation is of the order of layer thickness for the all channels and its relative value is reduced with increase of the channels diameters that is natural consequence of the definition of S\u0304 in the case of almost constant value of S. As mentioned above, the channel of diameter 0.2mm was totally closed during fabrication due to the high value of the laser power that was used in the SLM process. In the simulations, we discovered that a small open area may exist inside the channel (Fig. 7a). This deviation between the modeling and experimental results shows the limitations of the model, and possibly the lack of accuracy in the model parameters. The coarsened approach employed may not be applicable for accurate predictions of small geometric features, whose size is of the order of a single layer (relative dimensions of the channels without scaling is presented in Fig. 8). Some deviations between simulation and experimental measurements are also seen in Fig. 7b\u2013f. Non-symmetric cross sections with respect to the z-axis may be explained by the different placement of the laser action points during processing of the channels upper surface. As far as the simulations are concerned, we used the coarsened heat source model and expected the predicted channels geometry to be always symmetric with respect to z-axis and that the real contours of the channels vary around these theoretical predictions" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003469_jestpe.2021.3058261-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003469_jestpe.2021.3058261-Figure2-1.png", "caption": "Fig. 2. Machine model. (a) The cross-section of halbach PMVM with 12-stator-slot 10-PM-pole-pair. (b) Conventional torque production mechanism based on PM air-gap magnetic field and armature current. (c) Proposed torque production mechanism based on armature magnetic field and PM equivalent magnetizing current.", "texts": [ " Furthermore, the influence of armature fields on power factor is investigated in Section IV. In Section V, the relationship between torque capability and power factor has been established. And the prototype has been manufactured to verify the effectiveness of the analysis in Section VI. Based on ampere\u2019s law, the torque production of permanent magnet machine is generally treated as the interaction between PM magnetic field and armature current [16], [17]. Take the 12-stator-slot 10-PM-pole-pair PMVM as an example, as shown in Fig. 2(a). The torque of which is actually acting on the stator, as depicted in Fig. 2 (b). In other words, it is the reaction torque of real torque. However, in this paper, by swapping the roles of rotor PMs and armature windings, the torque is based on the force of PM rotor carrying the equivalent magnetizing current under armature magnetic fields. As shown in Fig. 2(c), the torque is acting on the PM rotor. And the corresponding torque expressions have been given as follows: 2 0 2 2 0 = , , , , co n c g s t PM a g s t PM T N r l B t d I t r l B t A t d (1) , , , = =a c a g g dF t dN I t A t r d r d (2) 2 0 = , , ,pro PM st a PMT r l B r t dI t (3) where Tcon and Tpro are the torque acquired by the conventional and proposed torque analysis method, respectively. BPM(\u03b8,t), Ba(r,\u03b8,t), IPM(\u03b8,t), Ia(\u03b8,t), Fa(\u03b8,t), Nc, rg, rPM and lst are the PM magnetic field, armature magnetic field, PM equivalent magnetizing current, armature winding current, armature magneto-motive force (MMF), winding series turns per phase, air-gap radius, PM radius and stack length, respectively", " 1, , sin 1, sin r ri i r r ir i r r ir J r t ip M M ip i t r K t M ip i t (4) 0 4 sin 2 r ri B iM i (5) 0 4 cos 2 r i B iM i (6) r r p r t W W W W W (7) where Mri and M\u03b8i are the ith harmonic magnitudes of radial and tangential magnetization, and both of which are given as the Fourier series; i is a positive odd integer; pr is the PM pole-pair; \u03c9r, Br and \u03b1 are the rotor electrical angular velocity, magnet remanence and the ratio of the radial magnetized segment pole-arc to the pole pitch, respectively. \u03bcr, \u03bc0, r and \u03b8 represent relative permeability, vacuum permeability, radial and tangential position. And the position with \u03b8=0 is corresponding to the centre of radial magnetized PM, as shown in Fig. 2(a). It can be observed in (4) that both the radial and tangential magnetized PMs contribute the volume current density, while the surface current density is only related with the tangential magnetized components. For the regular surface-mounted permanent magnets, the equivalent surface current is zero. To verify the analysis mentioned above, the magnetic fields produced by the PMs and equivalent magnetizing currents are compared in Appendix A, where the good agreement can be achieved. And the main harmonic components of volume/surface magnetizing current are listed in Table I" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002680_tec.2020.3000753-Figure31-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002680_tec.2020.3000753-Figure31-1.png", "caption": "Fig. 31. Experimental platform.", "texts": [ " It can be seen from the comparison results that the maximum error of the air-gap flux density fundamental amplitude does not exceed 6%, the maximum difference of the air-gap flux density THD does not exceed 10%, and the maximum error of the average torque does not exceed 3%. The FEA software used in this paper is Maxwell 17.2, and the number of meshes of the V-type, U-type, and I-type motors is 14856, 15528, and 15504, respectively. The average solution time of FEA is 299 seconds, and that of the proposed method is 198 seconds [i5-6500 @ 3.20GHz CPU, 8.00GB RAM]. The 8-pole/48-slot V-type IPM motor used in this paper is built and tested, as shown in Fig. 31. In order to fix the PMs, the edges of the flux barriers on both sides of the PM are concave in 0.5mm respectively (as shown in Fig. 31), which has a negligible influence. In the no-load test, the motor is dragged by the dynamometer to rated speed, and the no-load back EMF is measured. In the load test, the rated speed is maintained, and the torque is measured using the torque sensor HBM T40B. The control unit in the experimental system is composed of DSP (TMS320F28335) and FPGA (EP1C6Q240C8). The measured waveform of three-phase line no-load back EMF, the no-load back EMF waveforms of phase A obtained by the three methods, and the harmonic spectra are shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000160_acc.2009.5160136-Figure10-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000160_acc.2009.5160136-Figure10-1.png", "caption": "Fig. 10. Spring model with five mass points and six stiffnesses.", "texts": [ " In the plots showing experiments done at speed levels of 2000 lfmin and 3000 lfOlin one can even see that the torque stays constant for a wide range of angles and suddenly jumps at about 'PoMF == 0\u00b0. The reason for this behavior are sLicLion effecLs: AL sInail displaceInenl angles lhe elaslic spring forces are so small that they cannot overcome the friction due to centrifugal force. This results in cOlnpressed It is not sufficient to have a homogeneous spring Inodel as it would not show a changing stiffness (see section III-B). Therefore~ lhe spring is fragrnenled inlo six elaslic segrnenlS and five lumped masses [1] (see Fig. 10). Applying the law of angular 1110lnenlulU conservation to these masses returns In equation (1) and (2)~ Teng and Tclu are the torques of the engine and the clutch respectively. TS,l and TS ,6 are the spring torques (see section IV-B). Those contribute angular mOlnentum to the flywheels according to the switching functions u1, aj, u~ and a~. The torque tenns Tfrie.pri and Tfrie.sec describe all friction forces that act on the flywheels. The four switching functions u: E {O, I} are a: = 1 if the spring is in contact with one of the stoppers of the ftywheels" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000468_20110828-6-it-1002.01876-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000468_20110828-6-it-1002.01876-Figure1-1.png", "caption": "Fig. 1. Definition of forces, moments and angles.", "texts": [ " The equations of motion of the aircraft longitudinal dynamics from (Stevens and Lewis (2003)) read V\u0307a = 1 m (\u2212D + FT cos\u03b1\u2212mg sin \u03b3) , (1) \u03b3\u0307 = 1 mVa (L+ FT sin\u03b1\u2212mg cos \u03b3) , (2) \u03b8\u0307= q, (3) q\u0307 = M(\u03b4e) Iy , (4) where m and Iy are the mass and the inertia; Va is the aerodynamic velocity; \u03b3 is the flight path angle; \u03b8 is the pitch angle; q is the pitch angular velocity; FT is the engine thrust and, finally, L, D and M(\u03b4e) are the aerodynamics forces lift, drag and pitching moment, respectively. In Fig. 1 a detailed definition of the forces, moments, and velocities are shown. Note that \u03b1 = \u03b8 \u2212 \u03b3, where \u03b1 is the angle of attack. As usual in aerodynamic modeling, the aerodynamic forces and moments are computed through their non-dimensional coefficients, as follows: L = 1 2 \u03c1V 2 a SCL, D = 1 2 \u03c1V 2 a SCD, M = 1 2 \u03c1V 2 a Sc\u0304Cm, (5) where \u03c1 is the air density, S is the reference wing surface, c\u0304 is the mean chord and CL, CD and Cm are the lift, drag and pitching moment coefficients. Moreover, we consider the following models for the drag and moment coefficients (see for instance Etkin and Reid (1996); Pamadi (2004) and Schmidt (1998)): CD =CD0 + k1CL + k2C 2 L, (6) Cm =Cm0 + Cm\u03b1\u03b1+ Cmqq + Cm\u03b4e \u03b4e, (7) where CD0 , k1, k2, Cm0 , Cm\u03b1 , Cmq and Cm\u03b4e are aircraft aerodynamic coefficients, and \u03b4e is the elevator angle" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003110_j.mechmachtheory.2020.104122-Figure20-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003110_j.mechmachtheory.2020.104122-Figure20-1.png", "caption": "Fig. 20. View of the harmonic drive test apparatus.", "texts": [ " The increase of \u201ccontact ratio\u201d may improve the load-carrying capacity, but as shown in Table 4 , the improvement of kinematic error is very limited. In addition, the simulation results with three different WG shapes show that the bending stress is more sensitive than the \u201ccontact ratio\u201d to the shape of the WG. Therefore, for the WG shape, its influence on bending stress should be paid more attention to. A specialized harmonic drive test device is designed to measure kinematic error, efficiency, and stiffness. As depicted in Fig. 20 , it is an electromechanical system that includes a servo drive motor, a load motor, rotary encoder, torque sensor, a HD unit, and a digital control module. The concentricity is adjusted by an Easy-Laser shaft alignment instrument. The encoder with resolution 0.00439 \u00b0 is selected at the input end. A higher-precision encoder (resolution = 0.0 0 056 \u00b0) is used for the load position, considering that the rotation speed of the output end is obviously slower than the input speed. In order to measure the stiffness of reducer and transmission efficiency, the torque sensors are installed at the input and output sides respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002814_j.apor.2019.102002-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002814_j.apor.2019.102002-Figure2-1.png", "caption": "Fig. 2. Coordinate system of AUV in horizontal plane.", "texts": [ " The \u201cWL-3\u2033 AUV studied in this paper was developed by the Science and Technology on Underwater Vehicles Laboratory affiliated to Harbin Engineering University, China. As shown in Fig. 1, \u201cWL-3\u2033 AUV is an underactuated autonomous underwater vehicles. \u201cWL-3\u2033 AUV belongs to a propeller-rudder-driven AUV, and the velocity can reach 2 kn in design and 4 kn at maximum. The main parameters of \u201cWL-3\u2033 AUV are shown in Table 1. The inertial reference coordinate system {I} is established with the Earth defined as the origin, and the body-fixed reference {B} with origin chosen to coincide with the center of mass of the AUV, as shown in Fig. 2. The kinematic model of the AUV in the horizontal plane can be described as follows [30]. = R v( ) (1) = = = uvrv R [ ] [ ] ( ) cos sin 0 sin cos 0 0 0 1 T T (2) Where, \u03be and \u03b7 are the Cartesian coordinates of the center of mass of the AUV in {I}, \u03c8 denotes the yaw angle in {I}, u, v, and r denotes the surge, sway, and yaw velocities, respectively, expressed in {B}. Based on the following assumptions: 1) The center of gravity is in the origin of the body-fixed coordinate system; 2) The elements corresponding to heave, roll and pitch are neglected, the equation of motion for underactuated AUV can be divided into two noninteracting subsystems: the horizontal subsystem, the vertical subsystem [31]" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000180_j.mechmachtheory.2010.07.003-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000180_j.mechmachtheory.2010.07.003-Figure1-1.png", "caption": "Fig. 1. The schematic representation of a 3-PRS parallel manipulator.", "texts": [ " One is to combine both sets of equations by eliminating the corresponding Lagrange multipliers [14\u201316]. The other is to calculate Lagrange multipliers directly by the inversion of augmented matrix [8] and [13]. The first approach does not obtain the information about the reaction forces which could have significant impact on the dynamic behavior of parallel manipulator. The second approach could require large computational effort in calculating the reaction forces due to the augmented coordinates. In this paper, the 3-PRS (Prismatic, Revolute, Spherical) parallel manipulator shown in Fig. 1 is the target mechanism and a novel approach is proposed to formulate its dynamic equations in the bi-coordinates system. Based on the development and analysis of the geometric constraints, the reaction forces applied at the spherical joints are decomposed and each component could thus be calculated sequentially. The complex calculation of the reaction forces due to the augmented coordinates could be avoided by applying the proposed decomposition and it could be utilized to analyze the complicated dynamic behavior of the parallel mechanism", " A novel algorithm based on the decomposition is proposed to calculate the reaction forces and solve the inverse dynamics problem. In Section 4, simulations of circular trajectory are performed to demonstrate the proposed algorithm. In this section, the dynamic model of the legs and the moving platform of the 3-PRS parallel manipulator are formulated in the joint and task spaces, respectively. It will be shown that the resultant symbolic expression of the dynamic model is simple. Then the integration of the whole equations through the reaction forces is discussed. As shown in Fig. 1, the 3-PRS manipulator can be regarded as three legs manipulating a moving platform. Each leg consists of a ball screw, a slider, and a connecting rod. Three ball screws are perpendicularly connected to the base platform at points A1, A2 and A3. Bi is the location of the slider for i=1,2,3. Prismatic joints are assumed in between the sliders and the corresponding ball screws. The rod BiTi connects the slider Bi with a revolute joint. Because the motions of the connecting rods are constrained by the revolute joints, the rods B1T1, B2T2 and B3T3 can only rotate on their corresponding fixed planes AcA1B1T1, AcA2B2T2, and AcA3B3T3, respectively", " Concerning the mobility of the moving platform, we remark that three of six variables giving its position are parameters of parasitic motions. The configuration of the overall system allows the moving platform to have three degrees of freedom [20]. For each of leg i, a set of generalized local coordinates qi = Si \u03b8i\u00bd T in the joint space is adopted to specify the position of each joint. Si corresponds to the translation of the slider while \u03b8i corresponds to the rotation angle of the connecting rod. Under the Cartesian coordinate system O(X, Y, Z) attached on the fixed base at point O as shown in Fig. 1, the position of the spherical joint Ti for each of leg i can be expressed as: where OTi qi\u00f0 \u00de = fix qi\u00f0 \u00de\u21c0i + giy qi\u00f0 \u00de\u21c0j + hiz qi\u00f0 \u00de\u21c0k \u00f01\u00de fix\u00f0qi\u00de, giy\u00f0qi\u00de and hiz\u00f0qi\u00de denote the coordinate functions of the joint Ti under the Cartesian coordinate system. By Eq. (1), the where velocity of each spherical joint Ti is determined as: VTi qi;q\u0307i\u00f0 \u00de = d dt OTi\u00f0 \u00de = S\u0307i \u2202 \u2202Si + \u03b8\u0307i \u2202 \u2202\u03b8i \u00f02\u00de the bases of each local coordinate frame are given as [21]: \u2202 \u2202Si = \u2202fix\u00f0qi\u00de \u2202Si \u21c0 i + \u2202giy\u00f0qi\u00de \u2202Si \u21c0 j + \u2202hiz\u00f0qi\u00de \u2202Si \u21c0 k \u00f03 1\u00de \u2202 \u2202\u03b8i = \u2202fix\u00f0qi\u00de \u2202\u03b8i \u21c0 i + \u2202giy\u00f0qi\u00de \u2202\u03b8i \u21c0 j + \u2202hiz\u00f0qi\u00de \u2202\u03b8i \u21c0 k \u00f03 2\u00de The two bases \u2202 \u2202Si and \u2202 \u2202\u03b8i for each of leg i are attached to the joint Ti where \u2202 \u2202Si is downward parallel to the Z-axis and \u2202 \u2202\u03b8i is perpendicular to the connecting rod BiTi as shown in Fig", " JiT is the 2\u00d73 transformation matrix which transforms the reaction forces Fri from the Cartesian space into the joint space and given as [21]: JTi = \u2202 \u2202Si T \u2202 \u2202\u03b8i T 2 66664 3 77775 \u00f05\u00de It is shown in Eqs. (4) and (5) that the formulation of the dynamic model for each leg is straightforward and simple under the joint coordinates. where bases Gi = where Ry\u00f0\u03b2\u00deR skew- To describe the motion of the moving platform, let P = px py pz\u00bd T denotes the position of its mass center Tc with respect to the Cartesian coordinate system. Assume a body-fixed coordinate o x; y; z\u00f0 \u00de is attached at Tc as shown in Fig. 1. The orientation of the body-fixed coordinate relative to the Cartesian coordinate could be determined by three Euler angles \u03b1, \u03b2 and \u03b3. The corresponding rotation matrix of three Euler angles is determined as product of three known rotation matrices R \u03b1;\u03b2;\u03b3\u00f0 \u00de = Ry \u03b2\u00f0 \u00deRx \u03b1\u00f0 \u00deRz \u03b3\u00f0 \u00de as follows: R \u03b2;\u03b1;\u03b3\u00f0 \u00de = c\u03b2c\u03b3 + s\u03b1s\u03b2s\u03b3 \u2212c\u03b2s\u03b3 + s\u03b1s\u03b2c\u03b3 s\u03b2c\u03b1 c\u03b1s\u03b3 c\u03b1c\u03b3 \u2212s\u03b1 \u2212s\u03b2c\u03b3 + s\u03b1c\u03b2s\u03b3 s\u03b2s\u03b3 + s\u03b1c\u03b2c\u03b3 c\u03b1c\u03b2 2 4 3 5 \u00f06\u00de s\u03b1, c\u03b1 are the abbreviations for sin \u03b1 and cos \u03b1, respectively. Similar abbreviations are also for the other Euler angles \u03b2 and \u03b3 where in Eq", " In order to perform such a task, the constraint equations by considering the geometric conditions for the parallel mechanism are derived first. Physically, without connection to the moving platform, the joint coordinates Si; \u03b8if g corresponding to each leg i are linearly independent. However, as the three legs cooperatively manipulate the moving platform, these joint coordinates would be dependent. Under the assumption that the moving platform is rigid, the dependency could be described by the constraints which specify the distance between each of the spherical joint Ti to be constant. As shown in Fig. 1, three holonomic constraint equations are thus determined as: where found corres AT c1 = where as sho the joi in Eq. \u03d51 = jOT1 S1; \u03b81\u00f0 \u00de\u2212OT2 S2; \u03b82\u00f0 \u00dej\u2212c = 0 \u00f011 1\u00de \u03d52 = jOT2 S2; \u03b82\u00f0 \u00de\u2212OT3 S3; \u03b83\u00f0 \u00dej\u2212c = 0 \u00f011 2\u00de \u03d53 = jOT3 S3; \u03b83\u00f0 \u00de\u2212OT1 S1; \u03b81\u00f0 \u00dej\u2212c = 0 \u00f011 3\u00de Let the constraint force corresponding to the constraint /i=0 be denoted as Aci T\u03bbci where Aci T is the basis of the constraint force in the joint space and \u03bbci is the corresponding magnitude. The basis Aci T could be obtained by the partial derivative of the constraint equation /i=0 with respect to q and given as: AT ci = \u2202\u03d5i \u2202q T \u2208 R6\u00d71 ; i = 1\u20133 \u00f012\u00de However, the expression of the basis Aci T in Eq", " If the reaction forces Fri are decomposed into the constraint forces FCTi and the other components, the constraint forces FCTi will not appear in the dynamic equations of the moving platform. After deriving the first set of the constraint equations as shown in Eqs. (11-1)\u2013(11-3), the second constraints based on the coordinates in the task space are derived in this section. In Eq. (7-2), the position vectors pti of the spherical joints Ti under the body-fixed coordinate system have satisfied the constraints set in Eqs. (11-1)\u2013(11-3). However, the expression of the velocity in Eq. (7-2) did not consider the allowable motion of the spherical joint Ti. As shown in Fig. 1, each of the joint Ti is constrained to move on its corresponding plane AcAiBiTi because of the revolute joint at the slider. Therefore, the velocities of the three joints Ti perpendicular to their corresponding planes AcAiBiTi are constrained to be zero and they are given as: nT i \u22c5GiX\u0307 = 0; i = 1\u223c3 \u21d2 nT 1\u22c5G1 nT 2\u22c5G2 nT 3\u22c5G3 2 64 3 75X\u0307 = 03\u00d71 \u21d2 Am1 Am2 Am3 2 4 3 5X\u0307 = 03\u00d71\u21d2AmX\u0307 = 03\u00d71 \u00f018\u00de ni is the unit normal vector of the plane AcAiBiTi in the Cartesian space. Am = Am1 Am2 Am3 2 4 3 5 is a 3\u00d76 matrix whose rows are the where bases of the constraint forces in the task space", " To determine the angular velocity of the moving platform by the rotation matrix R, the derivative R\u0307 should be determined first. The derivative of the column RCi with respect to time t is given as: R\u0307Ci = \u2202RCi \u2202\u03b1 \u2202RCi \u2202\u03b2 \u2202RCi \u2202\u03b3 3\u00d73 \u03b1\u0307 \u03b2\u0307 \u03b3\u0307 2 4 3 5 3\u00d71 = dRCiX\u0307r \u00f0A1\u00de where \u03b1\u0307 2 3 where dRCi denotes \u2202RCi \u2202\u03b1 \u2202RCi \u2202\u03b2 \u2202RCi \u2202\u03b3 3\u00d73 and X\u0307r denotes \u03b2\u0307 \u03b3\u0307 4 5 3\u00d71 : The derivative R\u0307 could thus be obtained as R\u0307 = R\u0307C1 R\u0307C2 R\u0307C3 . Let the angular velocity of the moving platform under the body-fixed coordinate o x; y; z\u00f0 \u00de in Fig. 1 be denoted as \u03c9b T = \u03c9b Tx \u03c9b Ty \u03c9b Tz h iT . The velocities \u03c9TX b , \u03c9TY b and \u03c9TZ b are the 3-2, 1-3 and 2-1 entries of the matrix RT R\u0307 , respectively [7] and they are given as: \u03c9b T = RT C3R\u0307C2 RT C1R\u0307C3 RT C2R\u0307C1 T = RT C3dRC2 T RT C1dRC3 T RT C2dRC1 Th iT X\u0307r = R\u03c9X\u0307r \u00f0A2\u00de R\u03c9 is a 3\u00d73 matrix having following elements: R\u03c9 = cos\u03b3 cos\u03b1 sin\u03b3 0 \u2212sin\u03b3 cos\u03b1 cos\u03b3 0 0 \u2212sin\u03b1 1 2 6664 3 7775 \u00f0A3\u00de With the obtained body angular velocity\u03c9T b in Eq. (A2), the rotational kinetic energy of themoving platform could be expressed as: TR = 1 2 \u03c9b T T IT \u03c9b T = 1 2 X\u0307T rMrX\u0307r \u00f0A4\u00de IT is the constant moment inertia of the moving platform with respect to the body-fixed frame o x; y; z\u00f0 \u00de and the inertial where matrix Mr = RT \u03c9ITR\u03c9" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002277_978-3-319-27131-6-Figure4.7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002277_978-3-319-27131-6-Figure4.7-1.png", "caption": "Fig. 4.7 Two-phase oil flow at the contact-area outflow A-A", "texts": [ " The oil wakes spread out into the outflow area in the rolling direction x like the Ka\u0301rman vortex sheet flowing behind a spherical object. Between the oil wakes is the two-phase oil flow that contains the gas bubbles and liquid oil ribs. The wake flows could excite the next behind ball in radial and axial vibrations in the raceways. Due to air releasing and cavitation [6, 8], gas bubbles (i.e., bubbles of air and oil vapor) are generated in the lubricating oil at the outflow and transported into the next ball in the raceways. The two-phase oil outflow behind the ball at the section A-A is displayed in Fig. 4.7. 70 4 Oil-Film Thickness in Rolling Bearings The oil-film thickness at the Hertzian region is based on the theory of Hamrock and Dowson [3] that is implemented in program COMRABE using the MATLAB code [9]. There are two oil-film thicknesses of hc and hmin at the center and outflow of the contact area, as shown in Figs. 4.3 and 4.4. Generally, the oil-film thickness between the balls and raceways depends on the speed parameter of the balls, material parameter of the balls and raceways, load parameter of the ball, and ellipticity parameter of the Hertzian contact area" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000121_j.mechmachtheory.2009.05.003-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000121_j.mechmachtheory.2009.05.003-Figure1-1.png", "caption": "Fig. 1. Schematic of a general 3-dimensional bipedal walking system whose configuration is described by n generalized coordinates q1; . . . ; qn . Inclination / indicates that we consider the general case of walking, either on a slope \u00f0/ \u2013 0\u00de or on level ground \u00f0/ \u00bc 0\u00de.", "texts": [ " It will be seen that such a decomposition is a useful tool for the analysis of velocity change and kinetic energy redistribution at heel strike. As an example, the method will be applied to the compass-gait biped and detailed analysis and discussions on how the parameters and the impact configuration affect the dynamics of impacts will be reported. We consider a bipedal walking system whose general configuration can be described by n generalized coordinates that are represented by the n 1 dimensional array q \u00bc q1 qn\u00bd T , Fig. 1. Step i is considered to take place between time points ti 1 and ti. This is a variable topology system, where PR and PL represent the two points of the feet which are subjected to physical constraints during the various phases of motion (i.e., ground contact). The subscripts R and L denote that the point belongs to the right or the left foot, respectively. The velocities of points PR and PL can be respectively expressed as vR \u00bc AR _q and vL \u00bc AL _q; \u00f01\u00de where AR and AL are the related Jacobian matrices (which are functions of the system configuration), and _q is the n 1 dimensional array of generalized velocities" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002380_b978-0-444-64114-4.00009-1-Figure9.2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002380_b978-0-444-64114-4.00009-1-Figure9.2-1.png", "caption": "FIG. 9.2 Historical developments of enzymatic biosensors.", "texts": [ " In order to achieve this, a transducer is used to convert the chemical signal into an electronic one, which can be processed in some way, usually with a microprocessor. Over the years, a variety of enzyme-based biosensors have been developed, but only a few of them are commercialized. Most of the published work on enzymatic biosensors focuses on targeted blood glucose monitoring based on amperometric techniques. The amperometric biosensors have been divided into three generations, based on their working principle (Fig. 9.2). The first generation biosensors were projected by Clark and Lyons [116], and implemented by Updike and Hicks [122], who denoted the term \u201cenzyme electrode.\u201d The enzyme electrode described by them was comprised of an oxidase enzyme, that is, glucose oxidase, immobilized onto a dialysis membrane on a platinum electrode. The depletion of O2, or the formation of H2O2, is subsequently measured by the platinum electrode. The second generation biosensors have been commercialized, mostly in a one-time use testing platform" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003169_j.mechmachtheory.2020.103844-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003169_j.mechmachtheory.2020.103844-Figure3-1.png", "caption": "Fig. 3. The distal part of PMs: (a) with 6-dimension wrenches; (b) when one of the wrenches is removed.", "texts": [ " From this perspective, the entanglement of the influences of transmission or constraint wrenches seems less important. Therefore, the effect of transmission or constraint wrenches is considered comprehensively in this study. Blocking means letting all the actuated joints of the investigated PM be blocked. Under this condition, the investigated PM is converted into a static structure rather than a mechanism. Therefore, there are six-dimension wrenches applied on the mobile platform from all the limbs. Fig. 3 (a) focuses on the local area of the mobile platform and point d A j , which is the connection between the limb and the mobile platform. This local area is referred to as the distal part in the PMs. The point d A j is therefore called the distal application point. The wrenches applied on the mobile platform are called the distal wrenches. Obviously, the transmission-and-constraint capacity of the mechanism is effective when all the distal wrenches are linearly independent. Then let one of the distal wrenches be removed hypothetically as shown in Fig. 3 (b). Under this assumption, a unique and instantaneous virtual distal twist j S VDT will be generated. Note that the virtual distal twist is uniquely determined by the other five distal wrenches and only related to the current configuration of the investigated PM. It is worth mentioning that this idea is inspired by the works in [35 , 38] , in which the mobile platform of the PM with six supporting SS links gets six wrenches along the SS link when all the actuators are blocked. The investigated PM has n limbs, and the passive limb of the i th ( i = 1 , \u00b7 \u00b7 \u00b7 , n ) limb contains m i passive chains", " Finally, these 3 wrench spaces form a total wrench space 1 WS = { 1, 1 WS , 1, 2 WS , 1, 3 WS } = { 1 S DW , 2 S DW , 3 S DW } exerted on the mobile platform. \u2666 A total wrench system WS = { 1 WS , . . . , i WS , . . . , n WS } is obtained, which is exerted on the mobile platform from all the n limbs. Of note is that the number of wrench elements in the system WS is six in this paper. The total wrench system WS is rewritten as WS = { 1 S DW , . . . , j S DW , . . . , 6 S DW } ( j = 1 , . . . , 6 ), as shown in Fig. 3 (a), where j S DW represents the j th distal wrench. To measure the effect of the removed distal wrench on the mobile platform, that is, the motion/force transmission-and- constraint capacity, the power coefficient [20] of the removed unit distal wrench j S u DW and its corresponding unit virtual distal twist j S u VDT is defined as \u03bb j = | j S u DW \u25e6 j S u VDT | | j S u DW \u25e6 j S u VDT | max , (1) where | j S u DW \u25e6 j S u VDT | max = \u221a (h DW + h VDT ) 2 + d 2 max . h DW and h VDT are the pitches of j S u DW and j S u VDT , respectively", " In PMs with closed-loop passive limbs, the distal wrenches inside the closed-loop passive limbs are distinct from the pure transmission and pure constraint wrenches. The proposed DII can be adopted to evaluate the distal motion-force interactability of PMs with closed-loop passive limbs. The value of d max in | j S u DW \u25e6 j S u VDT | max is equal to the distance from the distal application point d A j to the axis of the unit virtual distal twist j S u VDT when the distal application point d A j lies on the axis of the unit distal wrench j S u DW . As shown in Fig. 3 (b), d max = d A j d C j . Its physical interpretation is the maximal length of the common perpendicular of the axes of the virtual distal twist j S VDT and any wrench which rotates freely around the distal application point d A j . Note that distal motion-force interactability is worst or distal interaction singularity occurs when the distal wrenches are linearly dependent. The minimum of the reciprocal products of the distal wrenches and its corresponding virtual distal twists is defined as \u03bc = min j { j S DW \u25e6 j S VDT } ( j = 1 , 2 , ", "2, six distal wrenches of the 3- P ( S S ) S PM are identified as { 1 S DW = ( B 1 , 1 C 1 ; c 1 \u00d7 B 1 , 1 C 1 ) 2 S DW = ( B 1 , 2 C 1 ; c 1 \u00d7 B 1 , 2 C 1 ) , { 3 S DW = ( B 2 , 1 C 2 ; c 2 \u00d7 B 2 , 1 C 2 ) 4 S DW = ( B 2 , 2 C 2 ; c 2 \u00d7 B 2 , 2 C 2 ) , { 5 S DW = ( B 3 , 1 C 3 ; c 3 \u00d7 B 3 , 1 C 3 ) 6 S DW = ( B 3 , 2 C 3 ; c 3 \u00d7 B 3 , 2 C 3 ) . (18) Without loss of generality, the i th virtual distal twist can be expressed by i S VDT = ( i s VDT ;i s 0 VDT ) = ( i L VDT , i M VDT , i N VDT ;i P VDT , i Q VDT , i R VDT ) . (19) As shown in Fig. 3 (b), the i S VDT can be identified by i S VDT \u25e6 j S DW = 0 , ( i = j ) . (20) The detailed calculation of the virtual distal twist is actually the nullspace construction of a five-screw system which was introduced in [17] . The actual proximal twists of the 3- P ( S S ) S PM are actually the input twists of three actuated joints and can be repre- sented as 1 S APT = ( 0 ; z ) , 2 S APT = ( 0 ; z ) , 3 S APT = ( 0 ; z ) . (21) The physical meanings of these three actual proximal twists are three independent velocities along the Z-axis" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000039_978-1-84996-220-9-Figure3.5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000039_978-1-84996-220-9-Figure3.5-1.png", "caption": "Figure 3.5 Zones for the collision cost function determination: (a) distance terms; and (b) cost zones", "texts": [ "8) The contribution of each individual joint is normalized with respect to its joint range. To avoid collisions, we use the formulation in [62] and loop through all collisionrelevant pairs of bodies, summing up their cost contributions. Each body is represented as a rigid primitive shape. Currently we use capped cylinders and sphere swept rectangles [61]. The cost associated with a pair of bodies is composed of two terms, one related to the distance between the closest points dp = |P1 \u2212P2| and one related to the distance between their centers dc = |C1 \u2212C2|, see Figure 3.5 (a). To compute the closest point cost gp, we set up three zones that are defined by the closest point distance dp between two collision primitives. Figure 3.5 (b) shows the linear, the parabolic and the zero cost zones, respectively. In the region between contact (dp = 0) and a given distance boundary dB, the closest point cost gp is determined as a parabolic function, being zero at dp = dB and having the slope s for dp = 0. It progresses linearly for dp < 0, and for dp > dB, it is zero. Similarly, the center point cost gc shall only be active if the link distance has dropped below the distance dB. The cost function will be scaled continuously with a factor zero at dp = dB and one if dp = 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001833_j.engfailanal.2017.04.017-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001833_j.engfailanal.2017.04.017-Figure1-1.png", "caption": "Fig. 1. Calculation model of spur gear tooth.", "texts": [ " It's not difficult to find that the work about calculation of TVMS for helical gears with tooth faults is not enough and thorough, which is the motivation of this work. The organization of this work is as follows: method for calculating TVMS of helical gear with both healthy tooth and fault defects (spalling & local breakage) is presented in Section 2. Then simulation and discussion are given in Section 3. Finally, conclusions are arrived. According to elastic mechanics, the tooth of spur gear could be modeled as a non-uniform cantilever beam shown in Fig. 1(a) and bending Ub, axial compressive Ua and shear energies Us of the tooth can be expressed by \u222bU F k F d x F h EI dx= 2 = [ ( \u2212 ) \u2212 ] 2b b d b a x 2 0 2 (1) \u222bU F k F EA dx= 2 = 2a a d a x 2 0 2 (2) \u222bU F k F GA dx= 2 = 1.2 2s s d b x 2 0 2 (3) A h b= 2x x (4) I h b= 1 12 (2 )x x 3 (5) where F denotes the meshing forces between mating gear teeth of pinion and gear, Fa and Fb are the radial and tangential components of F. G, E, b represent shear modulus, Young's modulus and tooth width, respectively. Ix, Ax are the area moment of inertia and area of the section where the distance from the dedendum circle is x, the other parameters are shown in Fig. 1(a). Then the total potential energy stored in a pair of spur gears in mesh can be expressed by ( ) U U U U U U U U= = + + + + + + = + + + + + + F k h a b s a b s F k k k k k k k 2 1 1 1 2 2 2 2 1 1 1 1 1 1 1 h a b s a b s 2 2 1 1 1 2 2 2 (6) where k denotes the total mesh stiffness of the gear pair, subscripts 1 and 2 represent pinion and gear respectively. kh is Hertzian contact stiffness and takes following form k \u03c0Eb v = 4(1 \u2212 )h 2 (7) where v represents Poisson's ratio. In addition, the fillet-foundation deflection was found also affecting the stiffness of gear tooth and the deflection can be calculated by [5,21] \u23aa \u23aa \u23aa \u23aa \u23a7 \u23a8 \u23a9 \u239b \u239d\u239c \u239e \u23a0\u239f \u239b \u239d\u239c \u239e \u23a0\u239f \u23ab \u23ac \u23ad \u03b4 F k F \u03b1 Eb L u S M u S P \u03b1= = cos \u2217 + \u2217 + \u2217(1 + Q\u2217tan )f f m f f f f m 2 2 2 (8) The details for the parameters in above equation could be found in Fig. 1(b) and reference [5]. Then if there are totally n = ceil(\u03b5) (\u03b5 denotes total contact ratio of gear pair, and the function ceil(x) means getting the minimum integer bigger than x.) pairs of teeth in simultaneous contact, the resultant mesh stiffness can be calculated by \u2211k = 1 + + + + + + + +i n k k k k k k k k k=1 1 1 1 1 1 1 1 1 1 h i b i s i f i a i b i s i f i a i, 1, 1, 1, 1, 2, 2, 2, 2, (9) Different from spur gears that tooth surface comes into and exits from meshing in sudden, length of contact line of helical gears changes gradually which results in a smooth variation of TVMS" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001187_physreve.87.032712-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001187_physreve.87.032712-Figure1-1.png", "caption": "FIG. 1. (Color online) Sketch of a pair of rodlike circle swimmers with n = 11 repulsive Yukawa segments and aspect ratio p = /\u03bb. Self-propulsion is provided by a constant force F acting along the main rod axis u\u0302. The circular motion is brought about by an additional torque M perpendicular to the plane of motion. The total rod pair potential is obtained by a sum over all Yukawa segment pairs with distance r \u03b1\u03b2 ij and is a function of the center of mass distance vector r\u03b1\u03b2 and orientations (1). The circular swimming path of radius R of the center of mass coordinates is also indicated.", "texts": [ " The segments are distributed equidistantly along the rod axis with a fixed distance d = /[(n + 1)(n \u2212 1)]1/2 \u03bb. The total pair potential between a rod pair \u03b1 and \u03b2 with orientational unit vectors {u\u0302\u03b1,u\u0302\u03b2} and center of mass distance r\u03b1\u03b2 = r\u03b1 \u2212 r\u03b2 is given by U\u03b1\u03b2 = U0 n2 n\u2211 i=1 n\u2211 j=1 exp [\u2212( r \u03b1\u03b2 ij / \u03bb )] r \u03b1\u03b2 ij , (1) where U0 is an amplitude and r \u03b1\u03b2 ij = | r\u03b1\u03b2 + (li u\u0302\u03b1 \u2212 lj u\u0302\u03b2)| (2) is the distance between the ith segment of rod \u03b1 and the j th segment of rod \u03b2, with li \u2208 [\u2212( \u2212 \u03bb)/2,( \u2212 \u03bb)/2] denoting the position of segment i along the symmetry axis of the rod \u03b1 (see Fig. 1). We introduce an aspect ratio p = /\u03bb to quantify the effective anisotropy of the rod-shaped particles. The number of segments per rod is defined by n = 9p/8 , with \u00b7 denoting the nearest integer. We focus on the overdamped regime in the low-Reynoldsnumber limit, which is the relevant one for micro-organisms and artificial self-propelled colloidal mesogens. The resulting 032712-2 VORTEX ARRAYS AS EMERGENT COLLECTIVE . . . PHYSICAL REVIEW E 87, 032712 (2013) equations of motion for the center of mass position r\u03b1(t) and orientation u\u0302\u03b1(t) = [cos \u03d5\u03b1(t), sin \u03d5\u03b1(t)] of the circle swimmer emerge from a balance of the forces and torques acting on each rod \u03b1 and are similar to those described in Ref. [25]: fT \u00b7 \u2202tr\u03b1 = \u2212\u2207r\u03b1 U + F u\u0302\u03b1, (3) fR \u00b7 \u2202t u\u0302\u03b1 = \u2212\u2207u\u0302\u03b1 U + M. (4) Here F is the constant self-motility force acting along the longitudinal axis of each rod (Fig. 1), U = (1/2) \u2211 \u03b2,\u03b1:\u03b2 =\u03b1 U\u03b1\u03b2 is the total potential energy, \u2207u\u0302 denotes the gradient on the unit circle, and fT = f0[f\u2016u\u0302\u03b1u\u0302\u03b1 + f\u22a5(I \u2212 u\u0302\u03b1u\u0302\u03b1)], (5) fR = f0fRI (6) are the translational and rotational friction tensors (I is the twodimensional unit tensor) with a Stokesian friction coefficient f0. The dimensionless geometric factors {f\u2016,f\u22a5,fR} depend solely on the aspect ratio p and we adopt the standard expressions for rodlike macromolecules, as given in Ref. [89], 2\u03c0 f|| = ln p \u2212 0.207 + 0.980p\u22121 \u2212 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003535_j.mechmachtheory.2021.104436-Figure12-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003535_j.mechmachtheory.2021.104436-Figure12-1.png", "caption": "Fig. 12. Configuration principle of OB-group.", "texts": [ " The double-limb group can be composed of 2 of 6 types of OB-limbs, while the triple-limb group can exclusively be composed of 3 of 4 types of limb-i (i=7, 8, A, B). As shown in Table 4, the limb-7 and limb-A have the same constraint screws with the limb-8 and limb-B, respectively. Therefore, in the performance study of the OB-group, the analyses of limb-7 and limb-A are omitted. With OB-groups RU^ [RR]&PU^R, RU^ [RR]&RU^R and RU^ [RR]&RU^ [RR]&PRU^ [RR] being an example, the motion and constraint characteristics of OB-limbs in the group are analyzed based on the screw theory, which is shown in Fig. 12. As shown in Fig. 12(a), the motion screw axis $85 is perpendicular to $82 and $92, and motion screw axes $84 and $94 are parallel to $82 and $92 respectively. Therefore, when 2 driving links are locked, $82 and $92 are fixed. Thus the directions of $84, $94 and $85 are determined, so that the orientation of moving platform is fixed. As shown in Fig. 12(b), groups RU^ [RR]&PRU^R and RU^ [RR]&PU^R have the same analysis method. The 2 limb inputs control completely the orientation of moving platform. Similarly, as shown in Fig. 12 (c), the 2 limb-8 driving links control directly the $85 direction, and $B5 is perpendicular to $85 and $B4. When the driving link of limb-B is also locked, the $B4 direction is determined. Therefore, when inputs of 3 limbs are fixed, $B5 and $85 directions are determined. Thus the orientation of moving platform is fixed. The analysis shows that input parameters of the OB-group control directly the orientation of moving platform. The inputs of the OB-group are the motions of the driving links relative to the base platform" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000426_tmag.2012.2197734-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000426_tmag.2012.2197734-Figure3-1.png", "caption": "Fig. 3. Analytical model of the proposed SR motor. (a) Three-dimensional FEM model. (b) Electric circuit model.", "texts": [ " The core and magnet materials are nonoriented silicon steel with a thickness of 0.35 mm and ferrite magnet, respectively. The residual flux density and the coercive force of the magnet are 0.47 T and 325 kA/m, respectively. The outer shape of the proposed SR motor is square, which provide the larger space for the magnets and auxiliary windings. The length and width of the magnets are 10 and 28.7 mm, respectively. The width of the stator yoke wound by the auxiliary windings is almost half that of the stator pole. Fig. 3(a) shows the FEM model of the proposed SR motor. The three-dimensional electromagnetic field analysis is necessary so that flux leakage in the axial direction is taken into consideration because the diameter of the proposed motor is threetimes longer than the stack length. Fig. 3(b) shows the electric circuit model coupled with the FEM model. In this paper, the auxiliary windings are excited by the constant current source . Fig. 4(a) indicates the flux linkage of the A-phase winding when the dc current flows only in the A-phase winding. The A-phase magnetomotive force (MMF) is given by the product of the number of winding turns and current. It is clear that the flux linkage is increased in the low-MMF region by exciting the auxiliary windings. Fig. 4(b) shows the static torque when auxiliary winding currents are 0 and 3 A, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001871_s00170-018-1840-1-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001871_s00170-018-1840-1-Figure3-1.png", "caption": "Fig. 3 a Geometry of a single bead specimen. b Melt pool region simulated by MHS technique and the nodes on the section which were used for temperature profiles to be used in ITC technique [16]", "texts": [ " In the first methodology, the 3D conical Gaussian moving heat source model was adopted which represents the actual laser cladding condition and can model the energy with transient thermal solution [7, 10, 13\u201315, 25\u201328]. Figure 2 depicts the view of the Gaussian moving heat source model and the way that the heat source is placed on the cladding path. The equations and needed parameters to define this heat source have been discussed in detail by the authors in Nazemi et al. [7, 13\u201315]. The second technique, ITC, results in much less computation time. An example of a single-track bead specimen is shown in Fig. 3a with the geometric data and process parameters presented in Table 1. The melt pool provided by the MHS technique is depicted in Fig. 3b which is used to acquire temperature profiles for the ITC technique. The temperature profiles and their average were drawn from the nodes on the cross-section of the melt pool (Fig. 4). In Fig. 5, the resulted temperature distribution in a single-track bead specimen from ITC and MHS techniques are compared while the clad bead is heating up showing the difference between their heat distribu- Fig. 4 Temperature profiles in the single-track specimen (a) on the nodes in cross-section of the melt pool (b) average of the profiles in the melt pool Table 1 Compositions of the actual and simulations materials (wt" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002721_j.mechmachtheory.2020.104164-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002721_j.mechmachtheory.2020.104164-Figure5-1.png", "caption": "Fig. 5. The contact angle of the preload double-nut ball screw.", "texts": [ " (2) \u2013(7) , we can obtain the following relationship ( F p + F A ) = 1 K QAi [ ( \u2211 i \u22121 j=1 Q An j sin \u03b1An j cos \u03b3 K Ani + \u2211 i \u22121 j=1 Q As j sin \u03b1As j cos \u03b3 K Asi ) + ( c Kn \u00b7 c 2 E Q 2 / 3 Ani \u22121 sin \u03b1Ani \u22121 cos \u03b3 + c Ks \u00b7 c 2 E Q 2 / 3 Asi \u22121 sin \u03b1Asi \u22121 cos \u03b3 \u2212 c Kn \u00b7 c 2 E Q 2 3 Ani sin \u03b1Ani cos \u03b3 \u2212 c Ks \u00b7 c E 2 Q 2 / 3 Asi sin \u03b1Asi cos \u03b3 ) + ( e \u2032 Ani \u22121 + e \u2032 Asi \u22121 \u2212e \u2032 Ani \u2212e \u2032 Asi )] (8) where, K QAi = 1 K + 1 K (9) Ani Asi The two typical working conditions of ball screws are the heavy load and low speed, and the light load and high speed, respectively. In decompression condition, the axial load is usually very high, i.e., only the low-speed condition is considered in this study, in which the friction and sliding effects are neglected. According to Refs. [ 5 , 18 ], the contact angles of the ball-nut contact and ball-screw contact can be assumed to be the same under the low-speed condition. Therefore, we have Q Ai = Q Ani = Q Asi , \u03b1Ai = \u03b1Ani = \u03b1Asi . The contact angle of the i th ball in the two nuts can thus be obtained according to Fig. 5 and Eq. (10) , in which the parameters are defined in the Nomenclature. \u23a7 \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23a9 sin \u03b1Ai = l O s \u2212Ani sin \u03b1A 0 + \u03b4\u2032 Ai \u221a ( l O s \u2212Ani cos \u03b1A 0 ) 2 + ( l O s \u2212Ani sin \u03b1A 0 + \u03b4\u2032 Ai ) 2 sin \u03b1Bi = l O s \u2212Bni sin \u03b1B 0 + \u03b4\u2032 Bi \u221a ( l O s \u2212Bni cos \u03b1B 0 ) 2 + ( l O s \u2212Bni sin \u03b1B 0 + \u03b4\u2032 Bi )2 (10) Therefore, Eq. (8) can be simplified as F p + F A = i \u22121 \u2211 j=1 Q A j sin \u03b1A j cos \u03b3 + c K \u00b7 c E 2 K QAi cos \u03b3 \u00b7 ( Q 2 / 3 Ai \u22121 sin \u03b1Ai \u22121 \u2212 Q 2 3 Ai sin \u03b1Ai ) + E \u2032 A K QAi (11) where, E \u2032 A = 2 e ri \u22121 + e Ani \u22121 + e Asi \u22121 sin \u03b1Ai \u22121 cos \u03b3 \u2212 2 e ri + e Ani + e Asi sin \u03b1Ai cos \u03b3 (12) Similarly, the following relationship for nut B can be obtained F p \u2212 F B = M \u2211 i =1 Q Bi sin \u03b1Bi cos \u03b3 (13) F p \u2212 F B = i \u22121 \u2211 j=1 Q B j sin \u03b1B j cos \u03b3 + c K \u00b7 c E 2 K QBi cos \u03b3 \u00b7 ( Q 2 / 3 Bi \u22121 sin \u03b1Bi \u22121 \u2212 Q 2 3 Bi sin \u03b1Bi ) + E \u2032 B K QBi (14) where, E \u2032 B = 2 e ri \u22121 + e Bni \u22121 + e Bsi \u22121 sin \u03b1Bi \u22121 cos \u03b3 \u2212 2 e ri + e Bni + e Bsi sin \u03b1Bi cos \u03b3 (15) K QBi = 1 K Bni + 1 K Bsi (16) When the axial load F a is applied, the relationship between the axial displacements of nut A and nut B can be expressed as \u03b4A \u2212 e \u2032 An 1 \u2212 e \u2032 As 1 = \u03b4B \u2212 e \u2032 Bn 1 \u2212 e \u2032 Bs 1 + \u03b4\u2032 (17) where \u03b4A and \u03b4B denote the axial deformation of the first ball in nut A and nut B, respectively, \u03b4\u2032 denotes the compensation for the axial displacement of the two nuts, including the deformation of the gasket and other elastic units, which can be expressed as \u03b4\u2032 = \u00b1 F B K \u2032 (18) where K \u2032 denotes the equivalent rigidity of the gasket and other elastic units, \u201c+ \u201d and \u201c-\u201d correspond to the condition when the slave nut (nut B) and the master nut (nut A) are the unloading nut, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000353_14763141.2012.660799-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000353_14763141.2012.660799-Figure7-1.png", "caption": "Figure 7. The downswing styles: (A) \u2018semi-planar\u2019 and (B) \u2018spiral\u2019. The trajectory of the clubhead was projected to the FSP to visualize the direction and magnitude of the clubhead deviation from the FSP.", "texts": [ " Complete body models that can incorporate a full array of trunk (including lateral flexion), shoulder (including elevation/depression and winging), and arm (including elbow flexion/extension) motions must bedeveloped, and these motions mustbe the centerfoldof future in-depth 3D golf swing studies. A further analysis of the deviation patterns of the clubhead from the FSP revealed two different swing styles used by skilled golfers: semi-planar and spiral swing. The majority (12/14) of the participants were classified as \u2018semi-planar\u2019 swingers (Figure 7A) and two as \u2018spiral\u2019 swingers (Figure 7B). In the semi-planar swing, the FSP served as the lower boundary of the clubhead motion as golfers moved the clubhead down quickly toward the FSP during the transition phase (TB\u2013MD) and executed a clean planar swing in the execution phase (MD\u2013MF) before moving the clubhead back up in the late follow-through phase (Figure 7A). In the spiral swing style, however, the clubhead showed a helical trajectory in the execution phase. Golfers in this category moved the clubhead down gradually toward the FSP during the transition phase, but the clubhead crossed the FSP and moved further down during the execution phase and late follow-through. The spiral swing style was characterized by large clubhead deviations from the FSP at the beginning and end of the MD\u2013MF phase (Figure 7B) and, as a result, the plane fitting errors of the spiral swingers (n \u00bc 2, RMS \u00bc 0.7 ^ 0.1 cm, maximum \u00bc 2.1 ^ 0.2 cm) were substantially larger than those of the semi-planar swingers (n \u00bc 12, RMS \u00bc 0.2 ^0.1 cm, maximum \u00bc 0.7 ^ 0.3 cm). One notable difference between the two styles is the direction of the clubhead motion at the beginning of the downswing. While the clubhead accelerates moving toward the FSP from the very beginning in the semi-planar swing, the clubhead initially moves slightly away from or parallel to the FSP in the spiral swing (Figure 7). This initial clubhead motion in the spiral swing style can make it more difficult to bring the clubhead down toward the FSP before the shaft reaches the MD position. It appears that the initial motion of the clubhead toward the FSP is an important prerequisite of a clean planar swing during the execution phase, but further investigations are necessary. A spiral trajectory is essentially caused by a rotation around an axis and a translation along the axis, which means that two different forces act on the clubhead simultaneously: the onplane force parallel to the FSP (such as the centripetal force) and the off-plane force perpendicular to the FSP", " A forceful trunk rotation produced by pre-stretched trunk rotators due to a large X-factor may sound like a feasible cause of high impact velocity in the planar multi-pendulum perspective, but the findings of this study suggest otherwise. Since the MP of the left shoulder is inclined forward/upward (uMP , 908; Figure 5), a 10\u2013158 relative inclination to the FSP makes the shoulder plane flatter (Table IV; Figure 5). The trunk plane (transverse) is also flatter than the FSP as the trunk axis (longitudinal) is aligned more upright than the normal axis of the FSP (Figure 7). The trunk rotation and linear shoulder motion during the downswing/follow-through, therefore, tend to promote an off-plane motion of the clubhead (and a spiral swing) by pulling it down past the FSP. The relative orientations of the shoulder MP and trunk plane to the FSP and the curvature of the clubhead trajectory with respect to the FSP (in the semi-planar swing in particular) suggest that trunk rotation is not what drives the downswing and the arms move somewhat independently of the trunk in a fashion to secure a clean planar motion of the clubhead during the execution phase", " In the One-Plane swing, a golfer swings the arms and the club around the bent-over spine to the same plane (shoulder line) during the backswing. In the Two-Plane swing, the trunk is positioned more upright than the One-Plane swing and the leading arm is positioned more upright than the shoulder line at TB. First, Hardy\u2019s fundamental view of the swing (the combination of a circular motion about the trunk axis and an up-and-down motion along the trunk axis of the arms and club) generates a helical trajectory, not a plane. As shown in Figure 7, the clubhead motion is fairly independent of the trunk rotation, forming a clean planar trajectory in the execution phase. Second, due to the 2D perspective, the same relative position of the arm to the shoulder line at TB can be perceived differently depending on the amount of trunk rotation during the backswing. Therefore, the alignment/misalignment of the arm to the shoulder line at TB may not mean any fundamentally different backswing motions (one plane vs. two planes). Third, a downswing can be divided into the transition and execution phases and alignment/ misalignment of the arm to the shoulder line may affect the transition phase, but not the execution phase" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003376_j.jelechem.2021.115391-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003376_j.jelechem.2021.115391-Figure5-1.png", "caption": "Fig. 5. (a) CV responses of bare GCE, GA/GCE, Mo-W-O/GCE, and Mo-W-O/GA/GCE in the presence of 100 \u00b5M DA with N2 gas saturated 0.1 M PB (pH 7.0) at a scan rate 50 mV s\u22121, (b) the dependence bar diagram for Ipa response for DA over different modified GCEs, (c) CV responses of bare GCE, GA/GCE, Mo-W-O/GCE, and Mo-W-O/GA/GCE in the presence of 100 \u00b5M Tyr with N2 gas saturated 0.1 M PB (pH 7.0) at a scan rate 50 mV s\u22121, (d) the dependence bar diagram for Ipa response for Tyr over different modified GCEs.", "texts": [ " The EASA value of bare and modified electrodes was calculated from the obtained slopes of Ipa vs scan rate1/2 (mV s\u22121) 1/2 in Fig. 4d. The calculated EASA values were 0.78, 0.102, 0.157, and 0.274 cm2 for the bare GCE, GA/ GCE, Mo-W-O/GCE, and Mo-W-O/GA/GCE respectively. The higher EASA value of Mo-W-O/GA/GCE is expected to afford benefits for the electrochemical oxidation of DA and Tyr. To find the mass ratio of the active material in the electrochemical performance, Mo-W-O/GA/GCE was analysed using cyclic voltammetry (CV) for DA and Tyr respectively. Fig. 5a shows the CV response of different modified electrodes namely Mo-W-O/GA/GCE, Mo-W-O/ GCE, GA/GCE, and bare GCE under N2 gas saturated in 0.1 M PB (pH 7) containing 100 \u00b5M of DA at a scan rate of 50 mVs\u22121. The other modified electrodes and bare GCE shows significant redox peaks under the presence of DA. The obtained oxidation peak is corresponding to the DA oxidation to dopamine-o-quinone and the reduction peak is corresponding to the reduction of dopamine-o-quinone to DA. Scheme 2 shows the DA electro-redox mechanism as equation (2)", " Next, for the Mo-W-O modified GCE, DA shows well-defined little enhanced anodic peak current and lower anodic peak potential compared to GA modified GCE, because Mo-WO has large catalytic sites and nanowire structure. Moreover, Mo-W-O intercalated GA nanocomposite shows lower potential and higher + 2e- + 2H+ Dopamine Dopamine-quinone Electro-redox reaction of dopamine (2) Scheme 2. Electro-redox reaction mechanism of dopamine. current compared to other modified and bare GCE. This is due to the synergic effect of Mo-W-O nanowire and GA. The corresponding bar diagram (Fig. 5b) shows the enhanced current for Mo-W-O/GA/GCE compared with bare GCE, Mo-W-O/GCE, and GA/GCE. Fig. 5c shows the CV response of different modified electrodes namely Mo-W-O/ GA/GCE, Mo-W-O/GCE, GA/GCE, and bare GCE under N2 gas saturated in 0.1 M PB (pH 7) containing 100 \u00b5M of Tyr at a scan rate of 50 mVs\u22121. It shows a broad and small oxidation peak potential with a weak peak current response for the bare GCE. After modification of GCE with GA, the oxidation peak potential of Tyr was shifted to the less positive peak potential with the enhanced current response. This can be attributed to the higher electrical conductivity of GA/ GCE, this is due to the high surface area of GA", " The reason for improved electrochemical property is based on the more interfacial interactions and electrical contacts between GA and Mo-W-O nanowires and its synergistic effects of Mo-W-O nanowires and GA afford some novel and unique functionalities to the MoW-O/GA composite. It has been confirmed that the introduction of MoW-O into the GA provides more surface area of the Mo-W-O/GA nanocomposite to adsorbed more DA and Tyr molecules [46]. The combining properties of the Mo-W-O with GA can offer the synergic effect to the oxidation of DA and Try. The corresponding bar diagram (Fig. 5d) shows the enhanced current for Mo-W-O/GA /GCE compared with bare GCE, Mo-W-O/GCE, and GA/GCE. The electrochemical oxidation peak of Tyr corresponding to the hydroxyl groups involving the transfer of two protons and two electrons, resulting in the formation of quinone-type products. Scheme 3 shows the electrochemical oxidation mechanism of L-tyrosine in equation (3). 2e-,2H+ L-tyrosine Electrochemical oxidat Scheme 3. Electrochemical oxida Fig. 6a shows the electrochemical reaction of Mo-W-O/GA/GCE for the electro-redox reaction of DA was studied under various concentrations (10\u2013100 \u00b5M) in N2 gas saturated 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002715_j.neunet.2020.10.005-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002715_j.neunet.2020.10.005-Figure2-1.png", "caption": "Fig. 2. The illustrative elements and parameters of the ith section of the ontinuum robot.", "texts": [ " In this case, u = [u11, u12, u13, u21, u22, u23] T can be used to represent the robot in actuator space, where uij represent the length of the jth bellow of the ith section. Arc parameters denoted by a triplet (\u03d5i, ki, li) can be used to define the ith section of the robot in configuration space. The items of (\u03d5i, ki, li) represent the orientation of the deformation, the section\u2019s curvature and its backbone length respectively. We can have a more intuitive understanding of the arc parameters in Fig. 2. The position of the end-effector in Cartesian coordinate frame, which can be represented by p = [x, y, z]T, needs to be considered in task space. Besides, the orientation of the end-effector may be considered in some problems. In this case, we only need to add two variables to p indicating the orientation. As shown in Fig. 3, the unit vector n = [nx, ny, nz] represents the orientation of the end-effector and nxy is the projection of n on the x\u2013y plane of the world coordination system Cw . \u03b11 = arctan(ny/nx) is the angle between nxy and x axis", " 1 2 Since different robots have different designs and correspond to different methods to actuate them, the mapping fspecific from actuator space to configuration space is robot-specific. A two-section bellows-driven continuum robot is considered in this paper. The relationship between the actuator space and the configuration space of the ith section of the robot can be formulated as: \u03d5i = arctan (\u221a 3(ui2 + ui3 \u2212 2ui1) 3(ui2 \u2212 ui3) ) (1) i = 2 \u221a u2 i1 + u2 i2 + u2 i3 \u2212 ui1ui2 \u2212 ui1ui3 \u2212 ui2ui3 d(ui1 + ui2 + ui3) (2) i = ui1 + ui2 + ui3 3 (3) where d is the distance from the center of a section to the center of the actuator as illustrated in Fig. 2. The mapping findependent from configuration space to task space s independent of the designs of robots and the methods to ctuate them. It is applicable to all robots that can be approxmated as piecewise constant curvature arcs. In task space, a orld coordinate system Cw and some local coordinate systems are introduced as shown in Fig. 4. The position of the end-effector, which can be represented by a column vector pe \u2208 R3, is fixed and known relative to the coordinate system C3. However, we need to know the position relative to the world coordinate system in order to control the motion of the end-effector" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000931_9781118703274.ch2-Figure2.55-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000931_9781118703274.ch2-Figure2.55-1.png", "caption": "Figure 2.55 Electromechanical blade pitch adjustment with power transmission by means of toothed belts", "texts": [ "54(b) shows two positioning drives for a single blade of the 500 kW Enercon E40 turbine. Figure 2.54(c) shows the arrangement in the 1.5 or 1.8MW E66 turbine. The motors, rotating with the turbine, always act with the same gear ratio during positioning. Electric blade pitch adjustment drives predominate for turbines in the megawatt class. However, in contrast to the systems shown in Figure 2.54(a) and (b), these are usually fitted within the hub (Figure 1.2). The blade pitch adjustment system shown in Figure 2.55 is based upon a fundamentally different functional principle. In the 1.2MWVENSYS turbine with a permanently excited synchronous generator a safety and blade pitch adjustment system is used that requires no batteries, pressure reservoir or other energy storage devices for redundant operation and makes slip ring transmission superfluous. This is possible because the electromechanical safety system uses the rotor energy to bring the rotor blades into feathered pitch, e.g. in the event of an emergency stop [2" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000352_j.isatra.2012.10.005-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000352_j.isatra.2012.10.005-Figure2-1.png", "caption": "Fig. 2. Schematic of a two links manipulator.", "texts": [ " The results of simulation are shown in Fig. 1. It is hard to say which one of the three is better; however it seems that the exact solution approach results more precisely in expressing the status of the states. As it was introduced any constraint can be added in weighting matrix Q. The distance between the end-effector and an obstacle can be set as a constraint and be fitted in the right position in weighting matrix Q. This example was selected as simply as possible to show the details, a two links fix manipulator, presented in Fig. 2 and the states are chosen as x\u00bc \u00bdy1 y2 o1 o2 T . The state-space representation of the system is _x \u00bc x3 x4 D 1 U C G\u00f0 \u00de \" # 4 1 \u00f016\u00de where D is the inertia matrix, U is the input control vector, C is the vector which represents the terms of the Coriolis and Centrifugal forces and G is the gravity vector, all of which can be given as D\u00bc d11 d12 d12 d22 \" # ,U \u00bc u1 u2 \" # ,C \u00bc c1 c2 \" # ,G\u00bc g1 g2 \" # : \u00f017\u00de The details of the matrix and vectors are presented in Appendix. Weighting matrices R and Q are considered as R\u00bc 0:01 1 0 0 1 \u00f018\u00de Q \u00bc 10 L\u00fe1 0 0 0 0 1 0 0 0 0 10 0 0 0 0 10 2 6664 3 7775 \u00f019\u00de where L\u00bc Wffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi xe xob\u00f0 \u00de 2 \u00fe ye yob 2 q in which W is the weighting factor for the distance between an obstacle and the end-effector, xe, ye are the end-effector positions, and xob, yob are the positions of an obstacle" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003255_icem49940.2020.9271026-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003255_icem49940.2020.9271026-Figure2-1.png", "caption": "Fig. 2. Machine slot view (left) and winding pattern (right)", "texts": [ " In Section II the initial machine design is presented, including dimensions, specifications, electromagnetic and thermal performance using a housing water jacket. In Section III, the slot water jacket is introduced, and four different ducts placement are considered, carrying out electromagnetic and thermal comparisons. An interior permanent magnet (IPM) synchronous machine with a V-shape rotor magnets configuration is considered. The main machine specifications are listed in Table I. Radial and axial machine sections are shown in Fig.1. Sintered Neodymium-Iron-Boron (NdFeB) magnets are utilized. In Fig.2 and Fig. 3 the slot view along with the winding layout is reported. M. Villani is with University of L\u2019Aquila, L\u2019Aquila, Italy (marco.villani@univaq.it) M. Popescu is with Motor Design Ltd, LL13 7YT Wrexham, U.K. (Mircea.Popescu@motor-design.com) P Authorized licensed use limited to: Western Sydney University. Downloaded on June 14,2021 at 15:24:14 UTC from IEEE Xplore. Restrictions apply. The proposed design makes use of a hairpin stator winding. A double layer pattern with 4 conductors per slot is selected" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002277_978-3-319-27131-6-Figure2.4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002277_978-3-319-27131-6-Figure2.4-1.png", "caption": "Fig. 2.4 Normal load distribution Qi on Z balls", "texts": [ "22 is approximately calculated as [10] 2K t\u00f0 \u00de \u03c0\u03be 1 1:1419366F \u03c1\u00f0 \u00de 0:41126766F2 \u03c1\u00f0 \u00de \u00fe 0:55517131F3 \u03c1\u00f0 \u00de 1 1:1335601F \u03c1\u00f0 \u00de 0:23480198F2 \u03c1\u00f0 \u00de \u00fe 0:37695522F3 \u03c1\u00f0 \u00de in which F(\u03c1) is the curvature differences at the ball/roller and raceways that are given in Eqs. 1.23 and 1.24. The equivalent radial load Pm on the bearing is equal to the loads Qi on the balls in the load direction. Hence, the force balance in the load direction on the bearing is written as Pm \u00bc XZ 1 i\u00bc0 Qi cos i\u03b3\u00f0 \u00de with Qi 6\u00bc 0 for \u03b4i \u00bc \u03b40 \u00fe e=2\u00f0 \u00de cos i\u03b3 e=2 > 0; Qi \u00bc 0 for \u03b4i \u00bc \u03b40 \u00fe e=2\u00f0 \u00de cos i\u03b3 e=2 0 The load zone for Qi 6\u00bc 0 in the bearing is limited between the load angles +\u03b3L and \u03b3L (s. Fig. 2.4): 32 2 Design of Rolling Bearings Qi 6\u00bc 0 for \u03b3L < i\u03b3 < \u00fe\u03b3L with \u03b4i > 0 The freeload zone for Qi\u00bc 0 in the bearing is outside the load zone: Qi \u00bc 0 for \u00fe \u03b3L i\u03b3 2\u03c0 \u03b3L\u00f0 \u00de with \u03b4i 0 The limit load angle \u03b3L is calculated as \u03b4L \u00bc \u03b40 \u00fe e=2\u00f0 \u00de cos \u03b3L e=2 \u00bc 0 ) \u03b3L \u00bc cos 1 e 2\u03b40 \u00fe e This result shows that the load zone depends on the bearing diametral clearance and the maximum elastic deformation of the lowest ball (i\u00bc 0). and the freeload zone in the upper half part of the bearing: Qi 6\u00bc 0 for \u03c0 2 < i\u03b3 < \u00fe\u03c0 2 with \u03b4i > 0; Qi \u00bc 0 for \u00fe \u03c0 2 i\u03b3 \u00fe 3\u03c0 2 with \u03b4i 0 Due to symmetry of loads on the balls about the axis of Q0, the load distribution on the balls is written using Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000193_j.cma.2011.04.006-Figure17-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000193_j.cma.2011.04.006-Figure17-1.png", "caption": "Fig. 17. (a) Contact pattern and (b) function of transmission errors for case B1a (skew(B) non-modified(1) aligned(a) bevel gear drive).", "texts": [ " For cases of design A3b and A3c, the contact patterns are localized inside the contacting surfaces, avoiding edge contacts, although for case of design A3d the contact pattern is slightly shifted towards the top edge of the pinion. The lineal function of transmission errors caused by the axial displacement of the pinion (misaligned condition c) is not completely absorbed, so that the partial profile crowning is not working properly for this geometry. The skew bevel gear transmission with main design parameters shown in Table 2 is also designed using parameters shown in Table 3 for three different cases of design. Fig. 17 shows the contact pattern and the obtained function of transmission errors for case B1a corresponding to a skew non-modified and aligned bevel gear drive. The skew bevel gear drive with the proposed geometry, under aligned conditions, has no transmission errors, and the contact pattern covers the whole surface of the teeth as shown in Fig. 17(a). Fig. 18 shows the contact patterns for cases B1b (18(a)), B1c (18(b)), and B1d (18(c)). Fig. (18(d)) shows the obtained functions of transmission errors for previous cases of design. All misaligned conditions (from b to d) cause lineal functions of transmission errors. The skew bevel gear drive is very sensitive to the change of shaft angle DR (misaligned condition c) and the axial displacement of pinion (misaligned condition d) and the axial displacement of the gear (not shown in this paper)" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003277_tmech.2021.3057898-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003277_tmech.2021.3057898-Figure3-1.png", "caption": "Fig. 3. Nonholonomic tractor model with force measurements.", "texts": [ " To design feedback controllers based on (1)\u2013(5), we need to approximately identify all the kinematic and dynamic parameters of the trailers before running and online estimate the configurations of the trailers during the running. These are doable only in laboratory experiments (as indicated in Section IV) but still require significant efforts and suffer from, besides the estimation inaccuracy of the tractor states, the additional much higher level of inaccuracy of estimations for configurations and inertial parameters of the trailers. To eliminate the uncertainties associated with the trailers, we propose to install a 2-D force sensor at the hitch joint connecting the tractor and the very first trailer (see Fig. 3). This joint is the only point via which all the trailers behind exert effects on the tractor. With the force measurements, the dynamics of the tractor can be separately considered without the necessity of taking care of the trailers. The dynamic motion effects brought by trailing units are all precisely captured in the force readings. By including the force measurements, the tractor model can accurately account for the trailers without requiring any knowledge of the trailers. Applying the Newton\u2013Euler approach, the following dynamic equations are obtained: m0v\u0307x = fd \u2212 ff sin \u03b4 \u2212 hx +m0vy \u03b8\u03070 (7) m0v\u0307y = fr + ff cos \u03b4 + hy \u2212m0vx\u03b8\u03070 (8) J0\u03b8\u03080 = a0ff cos \u03b4 \u2212 b0fr \u2212 (b0 + c0)hy (9) where hx and hy are the two measurable forces exerted on the tractor by the trailers behind", " To implement CFC derived from the model (16)\u2013(20), the three-axis force sensor ME K3D160 with a measurement range of \u00b150KN in each axis is adopted. Only two forces parallel to the ground measured at 100 Hz are considered. The force sensor is installed on the tractor and is connected to the first trailer via a short intermediate link, as shown in Fig. 5. Due to the ignorable dimension of the link, we can assume that the force sensor is mounted right at the first off-axle hitch joint connecting the tractor and the first trailer, as depicted in Fig. 3. The position, orientation, and other states of the tractor are provided by our localization system, which consists of a 3-D LiDAR Velodyne VLP-16, a PointGrey side-looking camera, an Xsens MTi-300 IMU, two HEIN LANZ encoders on two rear wheels, and one encoder on the steering wheel, as shown in Figs. 1 and 5. The point cloud map of the environment is also utilized, as shown in Fig. 7. To implement CWV derived from (1)\u2013(5), the parameters and real-time configurations of the trailers are also required" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003481_j.optlastec.2020.106782-Figure15-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003481_j.optlastec.2020.106782-Figure15-1.png", "caption": "Fig. 15. Comparison of finite element simulation and experiment.", "texts": [ " In this study, because the established finite element model was small and the cutting of the substrate can cause the release of residual stress, the measurement of residual stress was difficult and uncertain. Therefore, this article mainly verified the reliability of the temperature field by the size of the molten pool, and verified the accuracy of the stress field by comparing with the results of other scholars. For the temperature field, the width and depth of the molten pool obtained from the experiment were compared with the numerical calculation results. The gray area in Fig. 15 indicates that the temperature was greater than 1400 \u25e6C, representing the shape of the molten pool. The width and depth of the molten pool obtained by experiments were 148 \u00b5m and 66 \u00b5m (Fig. 15), respectively. The error between simulation and experiment was less than 10%, which proved the validity of the temperature field. For the stress field, the research results show that the maximum von Mises stress appeared at the end of the first track of the first layer where it was connected to the substrate, and there was a larger von Mises stress around the part where it was connected to the substrate. This is consistent with the results of Gu et al., Bian et al., and Zhao et al [10,18,33]. Large residual stress occurred at the connection between the substrate and the part" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003017_j.addma.2020.101822-Figure24-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003017_j.addma.2020.101822-Figure24-1.png", "caption": "Fig. 24. Case 2 sample that contains partitions 5\u20138.", "texts": [ " This severe alteration of deposition angle is more than the maximum recommended overhang angle (10\u25e6) which causes a little material collapse. The percentage of the layer height increase is 2.5% in each partition which is negligible. However, the overhang angle is zero for the middle layer within a partition and 11.25\u25e6 at the bottom and top layers of each partition. The surface roughness variation can be affected by both overhang angle and heating/ cooling of partitions during dome fabrication. As Fig. 24 shows, there are inconsistencies at the points between partitions 5\u20138 as well. There is no obvious dependency between the layer height increase /tilted overhang angle and surface roughness. Fig. 25 depicts the Ra results for the partition 5\u20138 set. The FFT analysis of the 2 + 1 + 1-dome (Fig. 26) shows a dominant frequency of 0.1102. If the frequency is converted to wavelength, it results in a value of 9.07 mm. this value is near the partition lengths (8.83 mm); there is a 9% difference. Here the equation between the frequency and wavelength is: wavelenth = 1 frequency (13) The frequency is the number of waves in 1 mm length and wavelength is the length of the repetitive wave" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000066_0278364909101786-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000066_0278364909101786-Figure6-1.png", "caption": "Fig. 6. Models of the interaction between the needle and tissue. Here VN T is the instantaneous velocity of the needle with respect to the tissue expressed in point N . Left: With friction forces transverse deformations arise. Right: Without friction forces, only longitudinal deformations occur.", "texts": [ " The deformation caused by the needle around one of these points can be represented by the distance of the point of the tissue with respect to its original rest position and can be decomposed along two directions: tangential to the surface of the tissue, which will be called longitudinal deformation (d ), and normal to the tissue, called transverse deformation (d ). The transverse deformation depends on the dynamical behavior of the tissues through multiple parameters such as elasticity and stiffness, on the contacts between the needle and the tissue and also on the dynamical motion of the needle. Most of these parameters cannot be controlled directly. However, in a quasi-static model, if friction forces between the needle and the tissue are null there is no transverse deformations during step 3 (see Figure 6). However, transverse deformations do arise during piercing (steps 2 and 4), but they can be limited if the tangent to the tip of the needle is along the normal to the tissue at the entry point. Hence, to reduce tissue deformations during step 2 (piercing), the tangent to the tip of the needle at the end of the approach step must be as close as possible to the normal to the tissue. Under the quasi-static assumption, the point of the surface where the needle enters the tissues follows the motion of the needle while remaining on the same surface" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003642_s42835-021-00807-4-Figure10-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003642_s42835-021-00807-4-Figure10-1.png", "caption": "Fig. 10 Meshed model of a 12 slot BLDC motor", "texts": [ "\u00a0(2) and (3) in Eq.\u00a0(1) In the solution \u03a6 is the ith mode shape and \u2018\u03c9i\u2019 is the corresponding natural frequency. The FEA model of the BLDC motor developed in ANSYS 17.5 environment is shown in Fig.\u00a09. The mass density, (1)[M]x\u0308(t) + [K]x\u0307(t) = 0 (2){x(t)} = ej t{ }i (3)x\u0308(t) = \u2212\ud835\udf142 i ej\ud835\udf14t{\u03a6}i (4) ( [K]\u2212 i[M] ) {\u03a6}i ej t = 0 1 3 Poisson\u2019s ratio and Young\u2019s modulus material properties are duly chosen for the stator copper coil and steel areas. The meshed model with boundary conditions is shown in Fig.\u00a010. The mode shapes obtained from the 3-D analysis of a 12 slot 4 poles Spoke type motor and their corresponding displacement magnitudes along with the modal frequencies are shown in Fig.\u00a011 and Table\u00a05 respectively. From Table\u00a05, it is evident that mode 5 has the maximum displacement and mode 2 has the least. Similarly, the natural frequencies of the 6, 15 and 18, 24 and 30 slot stators are predicted using FEA analysis and compared in Fig.\u00a012. From Fig.\u00a012, it is evident that the spoke type BLDC motor with 12 slots operates at a higher natural frequency with reduced effects of structural resonances, including high levels of noise and vibration [6, 7]" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002695_j.addma.2020.101439-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002695_j.addma.2020.101439-Figure5-1.png", "caption": "Fig. 5. Dimensions of the hollow cubes used for measuring the powder-bed density in the current recycling study. After fabrication, the tabs were removed to measure the weight of the powder and the internal volume of the specimens for determination of the powder-bed density.", "texts": [ " Changes in the morphological, chemical, and microstructural powder properties collectively manifest as differences in the powder flowability with reuse, which may impact the part properties. Although many tests exist for assessing flowability including the Hausner ratio [43], angle of repose [44], and avalanche angle [45], this study used the density of the powder bed to determine the evolution in the powderbed quality with reuse. In order to measure the powder-bed density, 3 hollow cubes with the geometry shown in Fig. 5 were fabricated at the back and front of the build area (Fig. 2) for entrapping powder during the spreading process in a similar manner to the work conducted by Jacob et al. [46]. The powder within the cubes was emptied by removing tabs attached to 250 \u03bcm thick walls for determination of the powder mass. Measurement of the internal volume was performed by weighing each cube before and after filling with 91 % isopropyl alcohol. The density was then determined through division of the powder mass by the internal volume" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002451_s12555-016-0771-6-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002451_s12555-016-0771-6-Figure2-1.png", "caption": "Fig. 2. Quadrotor aircraft behavior against wind gusts which causes a rotational movement.", "texts": [], "surrounding_texts": [ "Knowing that:\nJ=W T \u03b7 IW\u03b7 , (3)\nwhere W\u03b7 is given by:\nW\u03b7 = \u2212sin(\u03b8) 0 1 cos(\u03b8)sin(\u03b8) cos(\u03d5) 0 cos(\u03b8)cos(\u03d5) \u2212sin(\u03d5) 0 . (4)\nThe attitude dynamic can be written in the general form as:\nI\u03b7\u0308 +C(\u03b7 , \u03b7\u0307)\u03b7\u0307 = \u03c4\u03b7 , (5)\nwhere\nI =\n m11 m12 m13\nm21 m22 m23 m31 m32 m33\n ,\nC(\u03b7 , \u03b7\u0307) =\n c11 c12 c13\nc21 c22 c23 c31 c32 c33 with\nm11 = (Ixxs2 \u03b8 )+(Iyyc2 \u03b8 s2 \u03d5 )+(Izzc2 \u03b8 c2 \u03d5 ),\nm12 = c\u03b8 c\u03d5 s\u03d5 (Iyy \u2212 Izz),\nm13 =\u2212Ixxs\u03b8 ,\nm21 = c\u03b8 c\u03d5 s\u03d5 (Iyy \u2212 Izz), m22 = (Iyyc2 \u03d5 )+(Izzs2 \u03d5 ),\nm23 = 0,\nm31 =\u2212Ixxs\u03b8 ,\nm32 = 0,\nm33 = Ixx,\nand\nc11 = Ixx\u03b8\u0307s\u03b8 c\u03b8 + Iyy(\u2212\u03b8\u0307s\u03b8 c\u03b8 s2 \u03b8 + \u03d5\u0307c2 \u03b8 s\u03d5 c\u03b8 )\n\u2212 Izz(\u03b8\u0307s\u03b8 c\u03b8 c2 \u03d5 + \u03d5\u0307c2 \u03b8 s\u03d5 c\u03d5 ),\nc12 = Ixx\u03c8\u0307s\u03b8 c\u03b8 \u2212 Iyy(\u03b8\u0307s\u03b8 s\u03d5 c\u03d5 + \u03d5\u0307c\u03b8 s2 \u03d5\n\u2212 \u03d5\u0307c\u03b8 c2 \u03d5 + \u03c8\u0307s\u03b8 c\u03b8 s2 \u03d5 )+ Izz(\u03d5\u0307c\u03b8 s2 \u03d5 \u2212 \u03d5\u0307c\u03b8 c2 \u03d5 \u2212 \u03c8\u0307s\u03b8 c\u03b8 c2 \u03d5 + \u03b8\u0307s\u03b8 s\u03d5 c\u03d5 ),\nc13 =\u2212Ixx\u03b8\u0307c\u03b8 + Iyy\u03c8\u0307c2 \u03b8 s\u03d5 c\u03d5 \u2212 Izz\u03c8\u0307c2 \u03b8 s\u03d5 c\u03d5 , c21 =\u2212Ixx\u03c8\u0307s\u03b8 c\u03b8 + Iyy\u03c8\u0307s\u03b8 c\u03b8 s2 \u03d5 + Izz\u03c8\u0307s\u03b8 c\u03b8 c2 \u03d5 ,\nc22 =\u2212Iyy\u03d5\u0307s\u03d5 c\u03d5 + Izz\u03d5\u0307s\u03d5 c\u03d5 , c23 = Ixx\u03c8\u0307c\u03b8 + Iyy(\u2212\u03b8\u0307s\u03d5 c\u03d5 + \u03c8\u0307c\u03b8 c2 \u03d5 \u2212 \u03c8\u0307c\u03b8 s2 \u03d5 )\n+ Izz(\u03c8\u0307c\u03b8 s2 \u03d5 \u2212 \u03c8\u0307c\u03b8 c2 \u03d5 + \u03b8\u0307s\u03d5 c\u03d5 ),\nc31 =\u2212Iyy\u03c8\u0307c2 \u03b8 s\u03d5 c\u03d5 + Izz\u03c8\u0307c2 \u03b8 s\u03d5 c\u03d5 , c32 =\u2212Ixx\u03c8\u0307c\u03b8 + Iyy(\u03b8\u0307s\u03d5 c\u03d5 + \u03c8\u0307c\u03b8 s2 \u03d5 \u2212 \u03c8\u0307c\u03b8 c2 \u03d5 ),\n\u2212 Izz(\u03c8\u0307c\u03b8 s2 \u03d5 \u2212 \u03c8\u0307c\u03b8 c2 \u03d5 + \u03b8\u0307s\u03d5 c\u03d5 ),\nc33 = 0.\n3. PROBLEM STATEMENT AND EMBEDDED ROBUST CONTROLLER DESIGN\nWind produces a strong distortion on the flight system of a mini-Quadrotor. Some applications of these robots require to carry out activities at a fixed point (tasks where the vehicle must be kept fixed at a specified point). Examples of these tasks could be: digital photogrammetry, high-precision search of objects and objects manipulation. Therefore if a fine task is required, an unwanted wind torque on the vehicle must be avoided.\nThe following system describes the translation of the system as a function of the dynamics in the orientation of the system [23]:\n\u03be\u0308 \u2243 tan\u03b7(t), (6)\n\u03b7\u0308 \u2243 u(t)+w(t).\nA remarkable term w(t) represents the disturbance vector due to the modeling and a bounded wind perturbation, which is rejected through a real time fine output control embedded on the system. In order to compare the performance of such control, the displacement of the vehicle on a longitudinal plane \u03be (t) was measured. Control performance experiments are shown in results section.\n3.1. Reduced wind math model A state space mathematical model was needed to develop a robust control of the vehicle orientation. This is described as follow:\nI\u03b7\u0308 +C(\u03b7(t), \u03b7\u0307)\u03b7\u0307 = u(t)+w(t). (7)\nGiven the complexity of the flight dynamics, certain assumptions about the model and the behavior of the vehicle in hover-mode were made. The obtaining of a reduced model depends strongly on the complexity of the system represented by a mathematical model. Some remarkable works have tried to obtain reduced models for", "stochastic modeled systems, with delays and incomplete statistics of mode information, see for instance [24] and [25]. These previous works can be used for models with a much higher complexity degree, such as UAV disturbance problems. In this work the reduction depended only on the Lipschitz conditions, where the main goal was to obtain a simple model needed to validate the algorithms developed of this paper.\nUsing the conditions of Lipschitz functions observed in the previous model, it was possible to somehow limit the dynamics of the systems. The matrix functions of the previous model (7) were simplified to a single nonlinear term with dynamic uncertain bounded. For this simplification, the following assumptions were considered:\nAssumption 1: The inertial matrix I is known. Gyroscopic and drag torques are neglected. The rotational dynamic model (7) has useful properties which will be used in the control design.\nAssumption 2: Let w(t) be a bounded vector for disturbance as following:\n\u2225w(t)\u2225 \u2264 wmax.\nAssumption 3: The effect of wind on the vehicle produces a torque on the mini air vehicle in such a degree that this effect is unknown, but it is bounded to a nonlinear function. Due that the Lipschtz function exists as \u03b4 (\u03b7\u0307 ,\u03b7 , t) = w(t)\u2212C(\u03b7(t), \u03b7\u0307)\u03b7\u0307 , then:\n\u2225\u03b4 (\u03b7\u0307 \u2032,\u03b7(t)\u2032, t,z)\u2212\u03b4 (\u03b7\u0307 ,\u03b7(t), t,z)\u2225 = \u2225\u2225\u2225\u03b4\u0303 \u2225\u2225\u2225 \u03b7(t)\u2032,\u03b7(t) .\nThrough previous assumptions, it was possible to build a reduced mathematical model. Since I\u22121, the rotational dynamics is:\n\u03b7\u0308 = I\u22121(u(t)+\u03b4 (\u03b7\u0307 ,\u03b7(t), t)). (8)\nThen, the following coordinate change is proposed:\n\u03b7\u03071 = \u03b72(t), \u03b7\u03072 = I\u22121(u(t)+\u03b4 (\u03b7\u0307 ,\u03b7(t), t)) (9)\nsuch that the following strict triangular system is obtained:\nx\u0307A = A0xA +G(u(t)+\u03b4 (\u00b7)), (10)\ny =CxA,\nwhere \u03b4 (\u00b7) = \u03b4 (\u03b7\u0307 ,\u03b7 , t)\u2208 R3x1,xA = [\u03b71 \u03b72] T \u2208 R6x1, G = [03x3 I\u22121]T \u2208 R6x3, with \u03b71 = [\u03d5 \u03b8 \u03c8] and \u03b72 = [\u03d5\u0307 \u03b8\u0307 \u03c8\u0307], as shown below:\nAo =\n[ 03x3 I3x3\n03x3 03x3\n] \u2208 R6x6,\nC \u2208 R1x6.\nGiven the properties of this system (8), it was easy to observe that the dynamics of the Euler\u2019s angles were decoupled, based on the assumption that there was a global nonlinear vectorial function \u03b4 (\u00b7). Therefore, a triangular system was built for each angular dynamic. Three dynamics were grouped in one general system without losing its observability properties. In this study, all states were measured. Since the technology provides relatively good and economic sensors, measurements of velocity and angular position with lowpass filter for the Quadrotor aircraft system were taken.\n3.2. Robust observer algorithm design In this work, the need to design a control technique to solve the above mentioned problem was met. A wind gust estimator was designed through a high gain state observer and such feedback is compensated over a nonlinear PD controller. First, advanced compensating techniques using a non-linear high gain observer are presented, with a robust control embedded on vehicle. Therefore, the following Residual High Gain observer is proposed:\n\u00b7 x\u0302A = A0x\u0302A +G(u(t)+ \u03b4\u0302 )\u2212S\u22121\n\u221e eo, (11) \u02d9\u0302\u03b4 =\u2212\u2126e0, \u2126(h) = \u0393\u22121GT S\u221e,\neo = x\u0302A \u2212 xA.\nAssumption 4: From the Lipschitz function \u03b4 (\u00b7), the following bounded properties were held:\n1) Let estimating error \u03b4\u0303 = \u03b4\u0302 \u2212\u03b4 (\u00b7) be:\u2225\u2225\u2225\u03b4\u0303 \u2225\u2225\u2225 \u2264 a1 \u2200 a1 > 0.\nThis assumption is not difficult to be fulfilled in practice, since it requires only that the distortion is not greater than a constant in the model.\n2) The matrix S\u221e is a positive matrix defined as:\n0 =\u2212hS\u221e \u2212AT c S\u221e \u2212S\u221eAc +CTC,\nand it has the following structure:\n(S\u221e(h))i, j = (S\u221e(1))i, j 1\nhi+ j\u22121", "for any h positive gain (it was proved in one of the most important estimation theory paper [9]).\n3) First derivative is bounded such that:\u2225\u2225\u2225\u03b4\u0307 (\u00b7) \u2225\u2225\u2225 \u2264 bS\u221e \u2225eo\u2225 \u2264 b\u2225eo\u2225\u221e .\nWith b > 0, the last and perhaps most important assumption is that the dynamics produced by the wind on the vehicle does not exceed the power limit expressed on the high gain h. This means that the magnitude of the maximum wind rate will not exceed the limit to reject it. In practice, this situation is naturally fulfilled. This situation is directly related to the controller performance: as the embedded controller output injection reach its natural limit, it will show a good performance.\nTheorem 1: (Nonlinear Residual High Gain Wind Estimator) Let (11) be a robust observer of the (10). While the above main analytical assumptions are held, the error estimation is bounded to obtain the practical stability in presence of disturbance wind and the unknown modeling part for any gain h.\nProof: Estimated error and its first derivative are as follows:\neo = x\u0302\u2212 x, e\u0307o = \u00b7 x\u0302\u2212 x\u0307.\nThen, the dynamic of (11) and (10) are substituted with Ac = (A0 \u2212S\u22121 \u221e ):\ne\u0307o = Aceo +G\u03b4\u0303 . (12)\nThe following Lyapunov function is proposed and its first derivative trajectories are then calculated:\nV (t) = eT o S\u221eeo + \u03b4\u0303 T \u0393\u03b4\u0303 ,\nV\u0307 (t) = e\u0307T o S\u221eeo + eT o S\u221ee\u0307o +2\u03b4\u0303 T \u0393 \u00b7 \u03b4\u0302 \u22122\u03b4\u0303 T \u0393\u03b4\u0307 .\nIt is possible to replace the estimate error from Assumption 4 by using:\nV\u0307 (t) =\u2212heT o S\u221eeo +2\u03b4\u0303 T \u0393\n\u00b7 \u03b4\u0302 \u22122\u03b4\u0303 T \u0393\u03b4\u0307 (13)\n\u2212 eT o eo +2\u03b4\u0303 T GT S\u221eeo.\nIn order to obtain 2\u03b4\u0303 T \u0393 \u00b7 \u03b4\u0302 +2\u03b4\u0303 T GT S\u221eeo = 0, the follow-\ning array must be held:\n2\u03b4\u0303 T (\u0393 \u00b7 \u03b4\u0302 +GT S\u221eeo) = 0.\nIn such a way that it is obtained the same disturbance estimation like (11) :\n\u00b7 \u03b4\u0302 =\u2212\u2126eo with \u2126 = \u0393\u22121GT S\u221e,\nif the above array is held, equation (13) is modified as follows:\nV\u0307 (t) =\u2212heT 0 S\u221eeo \u22122\u03b4\u0303 T \u0393\u03b4\u0307 + eT o eo. (14)\nUsing the triangle inequality and the property shown in Assumption 5, it is obtained:\nV\u0307 (t)\u2264\u2212h\u2225eo\u22252 \u221e +4a1b\u03bbmax(\u0393)\u2225e0\u2225\u221e +\u2225eo\u22252 .\nGiven the \u2225eo\u22252 > 0, it is held as [9] :\nV\u0307 (t)\u2264\u2212h\u2225eo\u2225\u221e (\u2225eo\u2225\u221e \u2212 4a1b\u03bbmax(\u0393) h ).\nFor any h \u226b 4\u03bbmax(\u0393), the system has a convergence ball as follows:\nBeo = \u2225eo\u2225\u221e \u2208 Rn : \u2225eo\u2225\u221e < 4a1b\u03bbmax(\u0393)\nh , (15)\nwhere the error of observation is bounded.\nDesign of control: Performing tasks in real time is often a challenge for embedded control. Usually, the PD control is the most commonly used in these cases, but this control usually has problems with robustness tuning and with different types of distortions during the flight. The main result of this work is the combination of an output control and an advanced estimator of distortions. An improvement of the classic PD control with a nonlinear compensation is proposed by using the residual high gain observer, which was discussed above. Theoretical and experimental real-time tests will be shown in the following sections.\nSince the uncertain term \u03b4 (\u03b7\u0307 ,\u03b7 , t)) is unknown, the estimator \u03b4\u0302 (\u03b7\u0307 ,\u03b7 , t)) of control law reject the predicted wind on the orientation of the vehicle. This estimator is used to compensate the wind effect. Therefore, control design" ] }, { "image_filename": "designv10_9_0000753_j.engfailanal.2011.11.004-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000753_j.engfailanal.2011.11.004-Figure2-1.png", "caption": "Fig. 2. Drive elements of the BWE SchRs630/6x25.", "texts": [ " The user unsuccessfully tried to eliminate this weakness by repair welding of the shaft. 2011 Elsevier Ltd. All rights reserved. The BWE SchRs630/6x25 (Fig. 1) is placed in the open pit mine in \u2018\u2018Kolubara\u2019\u2019 \u2013 Serbia and it is used for excavating and depositing of layers of slag and coal. Its motion is realized through three pairs of caterpillar tracks, each having its own drive. The BWE SchRs630/6x25 is driven by means of the 45 kW electromotor, the cardan shaft and the 55 kW planetary gearbox (Fig. 2). For the mentioned BWE, the largest diameter of the shaft is 250 mm at the point of supports, i.e. 570 mm at the point of connection with the planetary gearbox. The length of the shaft is 1290 mm, the mass is 525 kg and the frequency of rotation 1.878 min 1. The planetary gearbox of the mass ffi3100 kg has a cantilever type of connection, through a clutch, with the shaft (Fig. 3). Bucket wheel excavators mainly perform heavy duty operations and their loads are dynamic and stochastic, which is the frequent cause of their failures that can have catastrophic consequences [1\u20133]" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000931_9781118703274.ch2-Figure2.38-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000931_9781118703274.ch2-Figure2.38-1.png", "caption": "Figure 2.38 Moments arising from lift forces and aerodynamic restoration", "texts": [ " For the usual operating blade angle of approximately 90\u2218 and the always-small blade angle with respect to the vertical axis (\ud835\udefe < 10\u2218), aP can be approximated for the moment-building offset, so that the propeller moment can be expressed as dMPr \u2248 dFPrap. (2.59) The corresponding worked examples will be further detailed in Section 5.5. Equation (5.11) shows, for example, the entire propeller moment of a blade. The lifting force FA, acting to one side of the axis of the blade, develops momentsMlift as in Figure 2.38, which are largely dependent on the resultant wind velocity, the blade pitch angle, the blade profile and the offset at tB\u22154 between the point of action of the lifting force and the axis of the blade. For a single profile element the following is approximately true: dMlift = ca (\ud835\udefc) \ud835\udc632r \ud835\udf0c 2 aa cos \ud835\udefcdAB. (2.60) The total moment resulting from lift forces on the blade is found in accordance with Equation (5.12). The restoring torquesMT cause, among other effects, a twisting of the profile into the direction of flow and are dependent on the resultant wind velocity \ud835\udc63r, the blade area A, the chord of the blade tB and the airstream angle and blade profile, with the associated moment coefficient ct" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003727_1.1707742-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003727_1.1707742-Figure6-1.png", "caption": "FIG. 6. Effect of temperature on fatigue life.", "texts": [ " The air supplied to the testers for these temperature coefficient studies contained 60 percent relative humidity at 23 .. 9\u00b0C with other conditions as in Test Cor 13 percent relative humidity at 23.9\u00b0C with other conditions as in Test B. As the temperature of the test is lowered, the moisture content of the cord will increase. Only below 80\u00b0C will sufficient moisture be present to affect the life with other conditions as in Test B. The results of these temperature-coefficient measurements are given in Fig. 6. The lives in both the creep and fatigue tests are exponential functions of the reciprocal of the absolute temperature. For each fatigue test, the tempera ture coefficient is nearly the same for the two types of high-tenacity rayon yarns. It follows from the Arrhenius equation giving the activation energy of a physical or chemical molecular rate processB that loge L= (E/RT)+C, (2) 8 S. Glasstone, K. J. Laidler, and H. Eyring, Theory of Rate Processes (McGraw-Hill Book Company, Inc., New York, 1941). JOURNAL OF ApPLIED PHYSICS [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 128.59.222.12 On: Sun, 30 Nov 2014 01:57:34 where L is the time required for a selected amount of change to take place, E is the activa tion energy for the process, and C is a constant. Table V gives the activation energies determined from the slopes of the straight lines in Fig. 6. The value of the activation energy reported in the table for the fatigue test of Busse and others4 is a corrected value calculated from the original data. 9 This test approaches the conditions of Test C, and the activation energies of these two tests are in reasonable agreement. Table V also gives a rough activation energy determined in our laboratorylO for the degradp. tion of Cord 2 in an oven containing air. This activation energy was calculated using the times for equal loss in strength on heating rayon cord at 160aC and 18SaC in an oven", ") Thermal degrada tion of tire cord Activation energy in calories/kinetic unit 7800 23000 19000 22000 19000 25000 L. Larrick, J. App. Phys. 16, 120 (1945). . 10 E. A. Tippetts and A. W. Powell, unpublIshed data. VOLUME 17, JUNE, 1946 temperature, since the temperature coefficient for this test is the same as that for heat-aging and for creep. On the other hand, the effects of heat-aging and the creep under static load for Test B become relatively less important as the temperature is lowered. Since straight lines are obtained. for the Test B conditions of Fig. 6, it appears that neither of these factors is important for this test even at the highest temperature studied. Considerable heat degradation is in evidence in cords fatigued in air under the Test C condi tions. This is indicated by discoloration of the test sampks. Under the conditions of tempera ture, moisture, and time in the Type C fatigue test, an unloaded cord may lose 2S percent of its strength because of heat degradation in a normal failure time. Fatigue life is particularly sensitive to previous heat degradation, as shown by the data in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000806_j.mechmachtheory.2012.08.011-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000806_j.mechmachtheory.2012.08.011-Figure3-1.png", "caption": "Fig. 3. FEMmodels of the thin-rimmed inclinedweb gears used for centrifugal deformation and stress analyses. (a) Left inclinedweb gear. (b) Center inclinedweb gear. (c) Right inclined web gear.", "texts": [ " Web inclination angles are 45\u00b0 for all the three types of the gears as shown in Fig. 2(a), (b) and (c). Fig. 2(d) is the solid gear used as the mating gear of these thin-rimmed gears when they are engaged together. Tooth numbers, modules, the pressure angles and the profile shift coefficients of all the gears in Fig. 2 are z1=z2=z3=z4=50, m=4, \u03b1=20\u00b0 and x1=x2=x3=x4=0. Structural dimensions of these gears are also shown in Fig. 2. Torque load is 294 Nm and this condition is used for all the calculations in this paper. Fig. 3 is the FEM models used for deformation and stress analyses of the thin-rimmed inclined web gears under the centrifugal load conditions. Fig. 3(a), (b) and (c) are used for the left, the center and the right inclined web gears respectively. Joint circles of the webs with the bosses are fixed as FEM boundary conditions as shown in Fig. 3. Fig. 4 is the FEMmodels used for the deformation and stress analyses of the thin-rimmed straight web gears under the centrifugal load conditions. Fig. 4(a), (b) and (c) are used for the left, the center and the right straight web gears respectively. Also, the joint circles of the webs with the bosses are fixed as the FEM boundary conditions. Fig. 5 is the FEMmodel used for LTCA of the thin-rimmed gears deformed by the centrifugal loads when these deformed gears are engagedwith the solid mating gear shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001379_978-3-319-22056-7-Figure3.5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001379_978-3-319-22056-7-Figure3.5-1.png", "caption": "Fig. 3.5 a Rotor separation, b Remainder rotor", "texts": [ "126) and (3.131) values of radial velocity, circular velocity and angular velocity at a moment t = t1 are calculated vr (t1) = vSr = \u221a v2r0 + 2v2c0 ln \u03c1S \u03c10 \u2212 k1 M (\u03c12S \u2212 \u03c120), vc(t1) = vSc = vc0, (t1) = , (3.132) where \u03c1S = \u03c1(t1). Relations (3.132) correspond to velocity of mass centre S and angular velocity of the initial rotor at the moment of separation when t = t1. If distance between rotor and stator is zero, rotor touches thefixed stator. In the contact point an impulse force J Fr occurs (Fig. 3.5). It causes a part of the rotor to separate. Mass of the separated part is m and its moment of inertia, according to mass centre S2 of the separated body, is IS2. Mass of the remainder body is M \u2212 m and moment of inertia, according to mass centre S1, is IS1. If velocity of the remainder body and its angular velocity are known, velocity and angular velocity of the separated body can be calculated. Thus, if velocity of the remainder body is vS1 = vS + \u00d7 \u03c1S1 + v\u2217, (3.133) 48 3 Discontinual Mass Variation the radial and circular velocity components are vS1r = vsr \u2212 \u03c1S1c + v\u2217 r , vS1c = vsc + \u03c1S1r + v\u2217 c , (3", " As is previously mentioned, velocity of the separated body is vS2 = vS + \u00d7 \u03c1S2 + u, (3.137) 3.7 Separation of a Part of the Rotor 49 giving projections of the relative separation velocity in radial and circular directions ur = vS2r \u2212 vsr + \u03c1S2c, uc = vS2c \u2212 vsc \u2212 \u03c1S2r . (3.138) where \u03c1S2r and \u03c1S2c are projections of the position vector of S2 to S in radial and circular direction. It is of interest to analyze motion of the rotor after mass separation. Model of the remainder rotor after mass separation is shown in Fig. 3.5b. Following is assumed: rotor has an in-plane motion with initial velocity of mass centre (3.134) and initial angle velocity (3.135). On disc two forces act: elastic force in shaft and unbalance force. It is supposed that both forces are in SS1 direction. For such assumption, when rotation centre S and mass centre of the remainder body S1 are in-line in radial direction, differential equations of motion of the mass centre S1 and rotation around S1 are given as (M \u2212 m)ar + k\u03c1S = (M \u2212 m)\u03c1S1 2, (M \u2212 m)ac = 0, IS1\u0307 = 0. (3.139) Integrating (3.139)3 we obtain the constant angular velocity = 1 = const. (3.140) Solving (3.139)2, we obtain the constant circular velocity v\u2217 S1c v\u2217 S1c = vS1c = (\u03c1S \u2212 \u03c1S1)\u03d5\u0307 = \u03c1\u2217 S1\u03d5\u0307 = const, (3.141) where rS1 is distance of S1 to fixed point O (see Fig. 3.5b). Substituting (3.140) and (3.141) into (3.139)1, it follows vr dvr drS1 = \u03c1S1 2 1 \u2212 k M \u2212 m r \u2212 v2S1c rS1 , (3.142) where distance between mass centres S and S1 is \u03c1S1 = const. Integrating equation and using initial values radial velocity is v\u2217 S1r = \u221a v2S1r + 2\u03c1S1 ( k M \u2212 m \u2212 2 1 ) (rS10 \u2212 rS1) + k(r2S10 \u2212 r2S1) M \u2212 m + 2v2S1c ln rS10 rS1 , (3.143) 50 3 Discontinual Mass Variation where rS10 is initial position of S1 according to O aftermass variation. Radial velocity depends on angular velocity of rotation after mass separation", "10, damaged wind turbine and in Fig. 3.11, positions of the shovel after separation are shown. Our aim is to calculate angular velocity of the remainder rotor after shovel separation and to determine motion of the shovel after its separation. Dynamics of motion of the system is divided into three intervals: 1. Motion of the initial rotor 2. Dynamics of rotor separation 3. Motion of the separated shovel. Motion of the Initial Rotor As is previously mentioned, rotor of wind turbine represents a three-shovel system (Fig. 3.5) which rotates with angular velocity . Each shovel of the rotor is modeled as a beam with mass m, length l and moment of inertia 80 3 Discontinual Mass Variation Iz = ml2 3 . (3.284) Moment of inertia of the rotor is IS = ml2. (3.285) Angular momentum of the rotor is Lb = L = ml2 . (3.286) Dynamics of Rotor Separation Let us consider the case when a shovel is separated from the rotor. In Fig. 3.10, final body and model of the shovel separation is shown. If angular velocity of the separated shovel is 2 and velocity of mass centre is vS2, the angular momentum of the separated shovel is L2 = IS2 2 + l 2 mvS2" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000039_978-1-84996-220-9-Figure2.9-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000039_978-1-84996-220-9-Figure2.9-1.png", "caption": "Figure 2.9 Obstacle avoidance illustration. When an incoming obstacle approaches the robot\u2019s body a repulsion field is applied to the closest point on the robot\u2019s body. As a result, a safety distance is enforced to avoid the obstacle", "texts": [ " Projecting operational tasks into the null space of the constraints is not only used to prevent constraint violations but also provides a metric to measure task feasibility under the constraints. Monitoring task feasibility is used as a mechanism to change behavior at runtime in response to dynamic constraints. Similar control structures to the one shown in the above proposition can be used to handle obstacle constraints as priority tasks. To handle obstacles we apply repulsion fields in the direction of the approaching objects as shown in Figure 2.9. 52 L. Sentis Task feasibility can be measured by evaluating the condition number of prioritized Jacobians, i.e., \u03ba(J\u2217k|prec(k)) \u03c31(J\u2217k|prec(k)) \u03c3dim(k)(J\u2217k|prec(k)) , (2.45) where \u03ba(.) represents the condition number and \u03c3i(.) corresponds to the ith singular value of the prioritized Jacobian. Let\u2019s look at the example of Figure 2.10. The robot stretches the arm and body to move toward the object. Joint limits at the hip and arm, and balance constraints take up the available movement redundancy" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003169_j.mechmachtheory.2020.103844-Figure15-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003169_j.mechmachtheory.2020.103844-Figure15-1.png", "caption": "Fig. 15. The 3- P RS PM: (a) kinematic structure; (b) kinematic scheme.", "texts": [ " The lower ends of the two passive chains in each limb are linked to one actuated joint with two spherical joints (i.e., B i ,1 and B i ,2 ). Each actuated joint is a slider and can move up and down along its vertical slideway, and the actuated joints are also spaced at a nominal angle of 120 \u00b0 from one another. The motion-force interaction performance analysis of this kind of PM with closed-loop passive limbs is still a challenging work. A seemingly simple solution is to treat the 3- P ( S S ) S PM as the 3- P RS PM based on the strategy of kinematic equivalence, as shown in Fig. 15 . Then performance evaluation of the 3- P ( S S ) S PM is achieved by analyzing the motion/force transmissibility and constrainability of the 3- P RS PM [29] . However, 3- P ( S S ) S PM with different structural parameters, e.g. B i ,1 B i ,2 = K 1 and B i ,1 B i ,2 = K 2 (K 1 = K 2 ), will be regarded as a 3- P RS PM with constant parameters. That is to say, the structural parameter B i 1 B i 2 inside each passive limb cannot be taken into account by using the above solution. In addition, since their kinematics are equivalent, Jacobian-based method is also difficult to be used to distinguish the differences of performance between 3- P ( S S ) S PMs with different structural parameters", " By adopting the approach of ITI, OTI and CTI and their minimum value local singularity index (LSI) proposed in [29 ], a transmission wrench and a constraint wrench are identified in each limb of the 3- P ( S S ) S PM. The identified transmission wrench is applied on the point C i and follows line B i C i , whereas the identified constraint wrench is applied on the point C i and is parallel to line B i ,1 B i ,2 . Under this condition, the investigated 3- P ( S S ) S PM is actually converted into the 3-PRS PM as shown in Fig. 15 . The distributions of the values of ITI, min {OTI, CTI}, and LSI in the orientation workspace of the converted 3- P RS PM are illustrated in Fig. 20 . Some comparisons can be obtained as follows: (1) It is not difficult to find that the ITI distribution of the 3-PRS PM in Fig. 20 (a) is consistent with the PII distribution of the 3- P ( S S ) S PM in Fig. 16 (a). The reason is that the two kinds of PMs have the same input motions of the actuated joints and the same motion related wrenches. (2) The min {OTI, CTI} distribution of the 3- P RS PM in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000877_j.triboint.2015.03.011-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000877_j.triboint.2015.03.011-Figure1-1.png", "caption": "Fig. 1. Relative coordinate system and contact motion state of balls and inner race.", "texts": [ " In this paper, the research work will be carried out on the basis of Cui's research [28], and the spinning\u2013sliding\u2013rolling motion will be taken into account in quasi-dynamics further, based on the mechanical characteristics and motion obtained from quasi-dynamics, TEHL analysis with spinning will be carried out to complete the whole coupled theoretical analysis of lubricated problems on engineering bearings from whole to local. In this research, the quasi-dynamic model with high accuracy and applicability is adopted, the force analysis and equations solving of the balls, races and cage are revealed in Ref. [28]. Assuming that the outer race is fixed and the inner race rotates, the relative coordinate system and contact motion state between inner race and balls are shown in Fig. 1. Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/triboint Tribology International http://dx.doi.org/10.1016/j.triboint.2015.03.011 0301-679X/& 2015 Elsevier Ltd. All rights reserved. n Corresponding author. Tel./fax: \u00fe8645186402012. E-mail address: lqwanghit@163.com (L.-Q. Wang). Taking balls and inner race conjunctions as example, in the rolling direction, the velocities with spinning of the points in the ball and inner race at the contact region are given in the following formulas: U2bj \u00bc \u00f0\u03c9x0 j cos \u03b12j\u00fe\u03c9z0j sin \u03b12j\u00de\u00bdDm=\u00f02 cos \u03b12j\u00de \u00f0 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 2 y22j q O0M\u00de \u00fe\u03c9s2y2j \u00f01\u00de U2rj \u00bc \u00f0\u03c92 \u03c9o0j\u00de cos \u03b12j\u00bdDm=\u00f02 cos \u03b12j\u00de \u00f0 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 2 y22j q O0M\u00de \u00f02\u00de where the spinning angular velocity \u03c9s2 \u00bc\u03c9x'j sin \u03b12j\u00fe\u00f0\u03c92j \u03c9o0 j\u00de sin \u03b12j \u03c9z0 j cos \u03b12j, the entrainment velocity U2j\u00bc(U2rj\u00feU2bj)/2, O0M \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 2 a22j q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0DW=2\u00de2 a22j q , the sliding velocity U2sj\u00bcU2bj U2rj, the slide ratio is defined as the ratio of sliding velocity to entrainment velocity at the contact center, S2xj \u00bcU2sj=Uo2 j, the Nomenclature XYZ bearing fixed coordinate system x0jy 0 jz 0 j follow-up coordinate system of the jth ball \u03c8j azimuth angle of the jth ball (1) \u03c92, \u03c9m, \u03c9oj revolution angular velocities of inner race, cage and balls (rad/s) \u03c9Rj;\u03c9x0j;\u03c9y0j;\u03c9z0j rotation angular velocity and components of the jth ball \u03c92m relative angular velocity of inner race and cage \u03b2, \u03b20 pitching angle and yaw angle (1) Dm, Dw diameters of pitch-circle and balls (m) R2, Rx, Ry inner raceway radius and radii in x and y directions (m) \u03b12j contact angle of balls and inner race (1) a2j, b2j semi-major axis and semi-minor axis of the contact ellipse of ball and inner race (m) \u03c9s2, \u03c9r2 spinning angular velocity and rolling angular velocity of ball and inner race (rad/s) U2bj, U2rj, V2bj velocities of the points in the ball and inner race in the rolling direction and perpendicular to the rolling axis (m/s) U2sj, U2j, V2sj, V2j sliding and entrainment velocities of the ball and inner race in the rolling direction and perpendicular to the rolling axis (m/s) S2xj, S2yj slide ratios in the rolling direction and perpendicular to the rolling axis Uo2j entrainment velocity at the contact center in the rolling direction (m/s) p, pH film pressure and maximum Hertzian pressure (Pa) h, h0, hmin film thickness, reference parameter for dimension- less film and minimum film thickness, h0\u00bca2j 2 /Rx (m) T, T0 film temperature and inlet temperature (1C) p;h; T dimensionless film pressure, thickness and tempera- ture, p\u00bc p=pH ;h\u00bc h=h0; T \u00bc T=T0 xin, xout, yin, yout coordinates of the boundaries (m) \u03b7 viscosity of lubricant (Pa s) \u03c1, \u03c11, \u03c12 densities of lubricant, balls and inner race (kg m 3) x, y, z, z1, z2 coordinates along film thickness direction (m) x; y dimensionless coordinates, x\u00bc x=a2j; y\u00bc y=a2j c, c1, c2 specific heats of lubricant, balls and inner race (J/ (kg 1C)) k,k1, k2 thermal conductivities of lubricant, balls and inner race (W/(m 1C)) q flow of the lubricant (m3/s) u,v flow velocities along x axis and y axis (m/s) FX, FZ axial and radial loads of bearing (N) MZ, MY bending moments along X and Y directions (N m) f2 inner curvature coefficient \u03bb, \u03bbmax, \u03bbmin film thickness ratio, maximum film thickness ratio, and minimum film thickness ratio, respectively entrainment velocity at the contact center is written as follows: Uo2 j \u00bc \u00bd\u03c9x0j cos \u03b12j\u00fe\u03c9z0 j sin \u03b12j\u00fe\u00f0\u03c92 \u03c9o0 j\u00de cos \u03b12j \u00bdDm=\u00f02 cos \u03b12j\u00de\u00fe\u00f0R2 O0M\u00de =2 \u00f03\u00de In the direction perpendicular to the rolling axis, as the spinning is taken into consideration, the velocity of the point in the ball at the contact region V2bj \u00bc\u03c9s2x2j, the entrainment velocity V2j\u00bcV2bj/2, the sliding velocity V2sj \u00bc V2bj \u00bc\u03c9s2x2j, the additional sliding with gyratory motion will also generate, and the sliding velocity is given as formula (4), the sliding ratio S2yj \u00bc V2sj==Uo2j" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002966_012083-Figure9-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002966_012083-Figure9-1.png", "caption": "Figure 9. (a) The A-A cross section on the top view of WAAM model. The residual stress distribution along longitudinal direction with contour band setting view after separation technique applied (b) rectangular heat source (c) Goldak\u2019s double ellipsoidal heat source", "texts": [ " After a long cooling down period, the residual stress changes from tensile to compressive at the interfaces of the successive layers, meanwhile on the base plate the longitudinal stresses go into tension as indicated in the Figure 8 (b) and (d). Thus, in WAAM, residual stresses can be as high as the yield strength of the ICAME 2019 IOP Conf. Series: Materials Science and Engineering 834 (2020) 012083 IOP Publishing doi:10.1088/1757-899X/834/1/012083 material, the mechanical properties can be negatively affected with leading to distortions and decreased tolerances [20]. For a better understanding of the deviations of these stresses, the residual stress was plotted along x-direction along the line shown in Figure 9 (a). As expected, Figure 10 (a) shows the highly non-uniform distributed of all three residual stresses components. These stresses induce repetitive expansion and contraction of the material simultaneously. As shown in Figure 10 (a), mostly compressive residual stresses occur on the longitudinal direction of the substrate due the contractions of the materials as getting farther from the heat input. The significant drop in the residual stress which is lower than the yield strength after the substrate removal which the separation technique applied, is also shown in Figure 10 (b). This is due to the residual stresses are relieved as well when the substrate is detached from the deposited weld fillers. Hence, the reducing these residual stresses give a massive impact to its mechanical behaviour in terms of distortions particularly. However, figure 9 (c) demonstrate the WAAM model applied Goldak\u2019s double ellipsoidal heat source has higher deformations compared to the rectangular heat source model, where the residual stress at the edge deposited walls changes from compressive to tensile as getting farther to the centre of the deposited weld fillers. ICAME 2019 IOP Conf. Series: Materials Science and Engineering 834 (2020) 012083 IOP Publishing doi:10.1088/1757-899X/834/1/012083 (a) ICAME 2019 IOP Conf. Series: Materials Science and Engineering 834 (2020) 012083 IOP Publishing doi:10" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003655_j.jhazmat.2021.126509-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003655_j.jhazmat.2021.126509-Figure1-1.png", "caption": "Fig. 1. Opto-electrochemical cell set-up: a.) disassembled; and b.) assembled.", "texts": [ " Journal of Hazardous Materials 419 (2021) 126509 of Cl\u2212 and SO4 2\u2212 were at the levels of 86.6 \u00b1 1.2 mg\u22c5L\u2212 1 and 37.9 \u00b1 3.4 mg\u22c5L\u2212 1, respectively. CBZ in the non-spiked MFTWW samples was determined at the level of 6.0 \u00b1 0.3 \u00b5g\u22c5L\u2212 1. For comparison, during the winter, in Pomerania (northern Poland), the CBZ level in TWW obtained from four municipal wastewater treatment plants was at the level of: 2.33 \u00b5g\u22c5L\u2212 1 (Gdansk Wscho\u0301d WWTP), 2.03 \u00b5g\u22c5L\u2212 1 (Gdynia Debogorze D\u0119bogo\u0301rze WWTP), 1.82 \u00b5g\u22c5L\u2212 1 (Swarzewo WWTP), and 1.21 \u00b5g\u22c5L\u2212 1 (Jastrz\u0119bia Go\u0301ra WWTP) (Luczkiewicz et al., 2019). Fig. 1 illustrates the disassembled opto-electrochemical cell. The cell consists of three 3D-printed parts, a quartz optical window, four silicon gaskets, one copper contact, the transparent working electrode, a platinum wire as a counter electrode, and an Ag/AgCl electrode as reference. All the components are held together by two screws and bolts. The reactor volume is 280 \u00b5L, the electrode area in contact with the electrolyte is 1 cm2, and the optical depth is 2.8 mm. UV\u2013visible spectra were acquired with a double beam spectrophotometer (UV-9000 Metash) in the 200\u2013350-nm range with a scan step of 1 nm and a scan filter of 10, using a deuterium light source" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002441_9781119509875-Figure16.2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002441_9781119509875-Figure16.2-1.png", "caption": "Figure 16.2 Left mechanical leg", "texts": [ "1 Lower Limb Rehabilitation Robot Training System Design of Lower Limb Rehabilitation Robot 205 The LLRR (Lower Limb Rehabilitation Robot), presented in Figure 16.1, was designed as a modular structure, and it consist of the left mechanical leg, the right mechanical leg, the separable chair and the electric box. User could control the robot through the touchscreen equipped on the right mechanical leg. Each mechanical leg owns 3-DOF and contains hip joint, knee joint and ankle joint which are same as human joints shown in Figure 16.2. The mechanical leg could be divided into the thigh part and the shank part, and the length of each part could be changed electronically to meet the various legs length of patients from 1.5m to 1.9m. To satisfy the different shapes of patients, the width between two legs could be adjusted automatically. A separable chair with four universal wheels used for sitting/lying training and patients transfer was designed. The torque and pressure sensors equipped on LLRR are shown in Figure 16.3. Four torque sensors are installed in hip and knee joints which could receive torque data constantly from the joints" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003195_s10846-019-01129-4-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003195_s10846-019-01129-4-Figure6-1.png", "caption": "Fig. 6 Common Computational Architecture. a Detail of the Communication board (Arduino Pro Mini); b Placement of the communication board in the modules", "texts": [ " The communication between modules has been set to TTL full-duplex serial N:8:1 with 115.200 bps. The 2 additional ways of the 4-ways pins provided Tx and Rx lines to allow the communication. We defined as mandatory for each module to have an embedded device with any technology able to provide communication according to the defined protocol and that could store a unique ID. An Arduino PRO Mini was selected as this embedded device. A board setting place (max dimensions 18 x 33mm) was designed in the module. The common computational specifications are shown in Fig. 6. 3.2.2 Part Models (PM) In this section we define three distinct part models (PM1, PM2 and PM3) of the DRA-MR1 that are required to build a multirotor drone. All three parts follow the common architecture (C) specified for the DRA-MR1 in previous section. PM1 is a central module responsible for the command, computation and instrumentation of the UAV. PM2 is a propulsion module, that accommodate a single actuator. Finally, PM3 is a single layer multipurpose connector. Tables 1, 2 and 3 concentrate the implementation details to build the multirotor drone according to DRAMR1" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002789_j.jmatprotec.2019.116355-Figure20-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002789_j.jmatprotec.2019.116355-Figure20-1.png", "caption": "Fig. 20. Force analysis.", "texts": [ " The authors thought the objective of the research was to understand the effects of various forces that lead to the detachment of a droplet. Even under different parameters, the types of force were consistent. Fig. 19 showed the clear detachment process of the droplet, from which we could see the detaching tendency of the droplet. It was clearly seen that the droplets were subject to a significant rightward force when they were detached from the wire. The authors analyzed the force of the molten droplet, as shown in Fig. 20. FG was the weight of the droplet (mass\u00d7 gravity), FE was the radial pressure caused by the electromagnetic pinch effect, FE\u2019 was the axial pressure caused by the radial pressure FE, which was described by Wang et al. (2013) and FC was mainly the reactive force generated by the arc and plasma gas flow on the droplet, FM was the force of the magnetic field generated by the closed loop current on the droplet. Because the surface tension exists at any position on the surface of the metal droplet, we consider it to be approximately 0 due to the offset effect. In the end, the resultant force F pointed to the lower right, and that was the reason why the droplet transferred to the right, which we could conclude from Fig. 20. 1 Based on the captured droplets and arc behaviors, the generation process of the arc and droplets without the constraint of the ceramic nozzle was understood. As the electrical parameters increased, the droplet transfer frequencies continued to increase to 300 Hz with the droplet diameters decreasing continuously to 0.8 mm. A series of complex arc phenomena were created due to the instability of the droplet transfer at low-level electrical parameters before 200 A. Under high-level electrical parameters, the arc shape and droplet transfer were more stable" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001621_j.isatra.2017.05.005-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001621_j.isatra.2017.05.005-Figure3-1.png", "caption": "Fig. 3. A schematic description of TRMS [2].", "texts": [ " 2 comprises of a helicopter model with only pitch and yaw motions, referred to as twin rotor MIMO system (TRMS). TRMS is developed by Feedback Instruments Limited for laboratory aero-dynamical control system experiments. The TRMS model is interfaced using PCI card to a PC having Matlab/simulink. Two encoders attached to two rotors communicate the pitch and yaw angle measurements to the PC. The digital signal generated by the controller is converted to analog signal as two voltages and are sent to the two motors attached to the rotors. A more descriptive diagram of the TRMS is shown in Fig. 3. As can be observed in Figs. 2 and 3, the TRMS has two propellers attached at both ends of a beam pivoting on its base and driven by a DC motor. The two propellers are perpendicular to each other, designed such that it can rotate freely both in the horizontal and vertical planes. A counterbalance arm with a weight at its end is fixed to the horizontal beam. The rotor generating the vertical movement enables pitch is called main rotor. Similarly, the rotor generating the horizontal movement enabling yaw is called tail rotor" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001203_j.jfranklin.2016.07.017-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001203_j.jfranklin.2016.07.017-Figure1-1.png", "caption": "Fig. 1. TRMS Schematic diagram [17].", "texts": [ " This analysis will take into consideration the effects of the disturbance estimation errors and the errors due to the command filters. It is worth mentioning that a simpler version of this control scheme has been previously applied in [9] on an autonomous aerial vehicle. However, it neither included a disturbance observer nor the formal stability analysis presented herein. To validate the proposed approach, it is applied on an aerodynamical experimental setup known as the twin rotor MIMO system (TRMS). The TRMS is a laboratory setup which resembles a helicopter prototype designed for flight control experiments as shown in Fig. 1. The control system design of the TRMS is challenging since its mathematical model is a high order nonlinear system with heavy cross-coupling effects between the two propellers [10]. In the literature, several research studies have been carried out for to design control systems for the TRMS test bed. Fuzzy logic control has been used for the design of tracking controllers in several studies as in [11\u201314] which included also experimental validation of the presented controllers. Moreover, sliding mode control (SMC) has been utilized for the control of the TRMS to increase the robustness of the system to parametric uncertainties and external disturbances such as [10,15,16]", " Based on the stability proof presented, by increasing the gains \u03b3 and \u03bci, the tracking error bound can be reduced. Moreover, the solution to the disturbance observer-based closed loop system can be made arbitrarily close to the system (57) which was proved to be globally exponentially stable. However, in practice increasing these gains have other consequences discussed in Section 3.4. Thus, a compromise has to be performed by the designer to yield the most satisfactory performance. The TRMS is a laboratory setup designed for flight control experiments as shown in Fig. 1. It is perceived as a static test rig for a helicopter with several control challenges [21]. It consists of two rotors, the tail rotor and main rotor, driven by DC motors perpendicular to each other. The two rotors are connected by a beam pivoted on its base such that it can rotate in both the horizontal and vertical planes. The motion of the beam is damped by a counterbalance arm with a weight at its end hanging from the central pivot point. The input to the TRMS is the supply voltages of the DC motors which consequently change the aerodynamic forces generated by the propellers through the speeds of the two rotors" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002563_tsmc.2019.2956806-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002563_tsmc.2019.2956806-Figure1-1.png", "caption": "Fig. 1. Definition of reference frames: {n} and {b} frames, waves, current, and wind directions.", "texts": [ " 0 and I denote the zero matrix and the identity matrix with proper dimensions, respectively. AT stands for the transpose of the matrix A, and the block-diagonal matrix with matrices X1,X2, . . . ,Xn on its main diagonal is denoted as diag(X1,X2, . . . ,Xn). tr(X) denotes the trace of the square matrix X. In order to describe dynamical motion of the DP vessel, the local geographical inertial North-East-Down reference frame {n} which is fixed to the Earth and the noninertial body-fixed reference frame {b} which is fixed to the vessel are employed as shown in Fig. 1 according to [34]. The origin of frame {n} is defined relative to the Earth\u2019s reference ellipsoid, and the axis OEXE, OEYE, and OEZE point toward true North, true East, and downward normal to the Earth\u2019s surface, respectively. The origin O of the body-fixed frame {b} is chosen to coincide with the center of vessel gravity and the axis OX, OY , and OZ are directed from aft to fore, to starboard, and from top to bottom separately. Then the kinematic and kinetic models for the DP vessel can be described as follows [34]: \u03b7\u0307 = R(\u03c8)v (1) Mv\u0307 = \u2212Dv + \u03c4 + RT(\u03c8)b (2) where \u03b7 [x, y, \u03c8]T \u2208 3 is the generalized position vector in the frame {n}; \u03bd = [u, v, r]T \u2208 3 is the velocity vector in the frame {b}; M \u2208 3\u00d73 and D \u2208 3\u00d73 are inertia matrix and damping matrix of the vessel, respectively; \u03c4 = [\u03c4x, \u03c4y, \u03c4z]T is the vector of total forces and moments acting on the vessel\u2019s hull generated by the propellers and thrusters, which are projected onto the axis OX, OY , and OZ separately; b \u2208 3 is the unknown environmental disturbances induced by the waves (in the direction of \u03b2wave), wind (with the speed of Vw in the direction of \u03b2w), and current (with the speed of Vc in the direction of \u03b2c); and R(\u03c8) \u2208 3\u00d73 is the transformation matrix from the {b} to {n} frame which is defined as R(\u03c8) = \u23a1 \u23a3 cos(\u03c8) \u2212 sin(\u03c8) 0 sin(\u03c8) cos(\u03c8) 0 0 0 1 \u23a4 \u23a6 and has the following property that: R(\u03c8)RT(\u03c8) = RT(\u03c8)R(\u03c8) = I" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001790_j.mechmachtheory.2016.04.010-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001790_j.mechmachtheory.2016.04.010-Figure5-1.png", "caption": "Fig. 5. Schematic diagram of cage forces.", "texts": [ " Q c j \u00bc 0 \u03b4cmj \u22640 XNP j\u00bc1 \u03b4cmj 1:11 w ls 0:11A1:11 \u03b4cmjN0 8>< >: \u00f08\u00de The friction force Fcj between the jth roller and cage's cross beam is expressed as follows: Fc j \u00bc XNP j\u00bc1 \u03bcc jQ c j: \u00f09\u00de In Eq.(9), \u03bccj is friction coefficient [16]. \u03bcc j \u00bc \u22120:1\u00fe 22:28s j\u00dee\u2212181:46s j \u00fe 0:1: \u00f010\u00de The additional moment Mcj of the jth roller caused by Fcj is shown in Eq.(11). Mc j \u00bc XNP i\u00bc1 qc j \u03bcc j l 2 \u2212 m\u2212 1 2 W lc : \u00f011\u00de When bearing is working, cage is simultaneously acted by collision force of rollers, guiding force of outer ring and combined resistance of oil/air mixture to both cage ends and its surface, the cage forces are shown in Fig. 5. In Fig. 5, {oc;yc,zc} is coordinate system of cage center; {o;y,z}is reference coordinate system of cage;e is offset of cage center; \u0394yc, \u0394zc are components of e along y axis and z axis, respectively; \u03a8c is angle between {oc;yc,zc} and {o;y,z}. Infinitely short bearing theory is applied in this paper to determine forces and moment caused by hydrodynamic action between cage centering surface and outer ring guiding surface, where Fcy 0, Fcz0and Mcx 0 are expressed in Eqs.(12)\u2013(14), respectively [17]. Fcy 0 \u00bc \u2212\u03b70u1L 3\u03b52= C2 1 1\u2212\u03b52 2 \u00f012\u00de Fcz 0 \u00bc \u03c0\u03b70u1L 3\u03b5= 4C2 1 1\u2212\u03b52 3=2 \u00f013\u00de Mcx 0 \u00bc 2\u03c0\u03b70V1R 2 1L= C1 ffiffiffiffiffiffiffiffiffiffiffiffi 1\u2212\u03b52 p : \u00f014\u00de In Eqs" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002116_itec.2018.8450250-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002116_itec.2018.8450250-Figure5-1.png", "caption": "Fig. 5: Basic principle of the rotor with short-circuited rotor coils [19]", "texts": [ " The only exception was an additional feature, the functional models were equipped with, which underlines the three-dimensional freedom of design using additive manufacturing. To be more specific, additional rotor slots right underneath the magnets were added during the manufacturing process. Inserting short-circuited copper wires into these slots influences the magnetic anisotropy which improves the selfsensing performance of the machine. The basic theory of using short-circuited rotor coils for improving self-sensing machine characteristics is also described in [19] and [20]. Fig. 5 shows the concept which is an alternative to a meandering wire directly positioned in the q-axis. Regarding surface-mounted PMSM with usually Ld < Lq, (1) the aim is a decrease of Ld and/or an increase of Lq. By means of flux barriers or additional teeth in the q-axis, the magnetic anisotropy can only be influenced to a limited extend and this would furthermore affect the saturation behavior of the machine. Regarding the predefined boundary conditions, the presented approach just influences the differential inductances L\u2032 = [ L\u2032dd L\u2032dq L\u2032qd L\u2032qq ] = [ d\u03c8d/did,hf d\u03c8d/diq,hf d\u03c8q/did,hf d\u03c8q/diq,hf ] (2) by observing the current response of a superimposed highfrequency voltage signal" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002260_0954406216640572-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002260_0954406216640572-Figure3-1.png", "caption": "Figure 3. Torsional vibration model of gear drive train of wind turbine.", "texts": [ " According to the SV model, the 600-s speed time history curve has been obtained utilizing MATLAB program developed by the authors as shown in Figure 1. Gear transmission system dynamic model and equation This paper studies the gear transmission system of a 1.5MW wind turbine, which contains one level of at University of Birmingham on May 8, 2016pic.sagepub.comDownloaded from NGW planetary gear and two levels of parallel shaft gear. The structure diagram is shown in Figure 2. Torsional vibration model of gear transmission system is built using centralized parameter method, as shown in Figure 3. Modeling the meshing stiffness between gear pair as time-varying spring, and variation of meshing stiffness, comprehensive transmission error, backlash and other factors are taken into consideration in this model. The planet gears are assumed to be uniformly distributed and have the same physical and geometrical parameters. In Figure 3, OXYZ is a fixed coordinate system. The coordinate system of sun gear, planet gear and planet carrier is a moving coordinate system, which is referred to the coordinate system of planet carrier, rotating with the planet carrier. uc, us, upi, uj (i \u00bc 1, 2, 3, j \u00bc 1, 2, 3, 4) represent the torsion displacement of planet carrier, sun gear, planetary gears and medium and high level speed gears, respectively. kspi, krpi represent the meshing stiffness of sun gear and planetary gear i and the meshing stiffness of annular gear and planetary gear i; ks1 represents the torsional stiffness of the connecting shaft between the sun gear and gear 1; k23 represents the torsional stiffness of the connecting shaft between gear 2 and gear 3; k12, k34 represent the meshing stiffness of the medium speed gears and the high speed gears; cspi, crpi represent the meshing damping of sun gear, annular gear and planetary gear i; cs1 represents the torsional damper of connecting shaft between the sun gear and gear 1; c23 represents the torsional damper of connecting shaft between gear 2 and gear 3; c12, c34 represent the meshing damping of the medium level speed gears and the high level speed gears; espi, erpi represent the transmission error of sun gear, annular gear and planetary gear i; e12, e34 represent the comprehensive transmission error of the medium speed and high level speed gears" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002388_ab1534-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002388_ab1534-Figure1-1.png", "caption": "Fig 1. The main dimensions of the sample for welding.", "texts": [ " The authors hope that the results of this study can be applied for the development and improvement of welding and increasing the laser welding science of GTD-111 superalloy. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 A cc ep te d M nu sc rip t 5 2. Experimental Procedure The metal used in this study was GTD-111 nickel-based superalloy with a thickness of 1mm and dimensions of 50X50mm2, which had totally even edges cut by a wire cut from a cylindrical ingot with a diameter of 750 mm (Figure 1). The chemical composition of this alloy has been presented in Table 1. Welding operation was performed autogenously and by a pulsed Nd:YAG laser source, model IQL-10 with a maximum power of 400W. This laser is capable of producing square pulses with a width of 2-20ms and a frequency of 1-1000Hz with intended energies up to 40J. In order to measure the power and laser pulse energy, a power meter model 500 W-Lp and a Joulemeter, model LA300w-Lp made in Ophire, were used. In order to precisely set the specimen and avoid warpage during welding, the sample was tied to a fixture", " 35- Egbewande A T, Buckson R A and Ojo O A 2010 Analysis of laser beam weldability of Inconel 738 superalloy Materials Characterization 61 569\u2013574. 36- Wang C, Cai1 Y, Hu C, Zhang X, Yan F and Hu X 2018 Morphology microstructure and mechanical properties of laser-welded joints in GH909 alloy Journal of Mechanical Science and Technology 31 2497-2504. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 A cc ep te d M an us cr ip t 17 Figure captions Fig 1. The main dimensions of the sample for welding. Fig 2. Figure of (a) the experimental setup and (b) the schematic diagram of the welding machine and the work piece. Fig 3. Schematic diagram showing the dimensions of laser-welded specimens used in tensile tests. Fig 4. Microstructure of as-cast alloy. Fig 5. (a) Schematic mechanism of hot solidification crack formation during welding (b) SEM micrograph showing the formation of hot solidification cracks during welding of GTD-111. Fig 6. Changes in Weld Pool Size as a Function of Frequency" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000931_9781118703274.ch2-Figure2.22-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000931_9781118703274.ch2-Figure2.22-1.png", "caption": "Figure 2.22 Twist of the rotor blade", "texts": [], "surrounding_texts": [ "When designing a machine to extract energy from the wind and to develop the resulting torque in the turbine, the airstream pattern shown in Figure 2.2 is the goal. It is then possible to achieve energy extraction using many blades at low speed or a few blades at high speed. Further, the optimal wind deceleration for the same speed of rotation can be attained using one very broad blade, or two or three blades of correspondingly smaller breadth. The optimal blade chord can be derived from the blade radius by the formula tB (r) = 2\ud835\udf0br z 8 9 1 ca \ud835\udc632 1 \ud835\udc63u (r) \ud835\udc63r (r) . (2.40) A rotor tip speed of \ud835\udc63u (r) = \ud835\udf14r = \ud835\udf06 r R \ud835\udc631, (2.41) a target wind deceleration at the turbine of \ud835\udc632 = 2 3 \ud835\udc631 (2.42) and the resultant relative wind speed of \ud835\udc63r (r) = \u221a \ud835\udc632u + \ud835\udc632 2 = \ud835\udc631 \u221a( \ud835\udf06 R r )2 + 4 9 (2.43) yield a blade chord of tB (r) = 16\ud835\udf0bR 9ca\ud835\udf06z 1\u221a( \ud835\udf06 R r )2 + 4 9 . (2.44) According to this, hyperbolic blade contours are to be expected. These, however, differ widely for different (design) tip speed ratios and numbers of rotor blades [2.13]. Figure 2.20 shows the relative blade contours for one-, two- and three-bladed machines having design tip speed ratios \ud835\udf06A of 5, 8 and 12. This presentation makes it absolutely clear that single-bladed turbines are best for high-speed and multibladed turbines for low-speed machines. When producing rotor blades, the optimal blade contour is approximated, mostly in trapezoidal or even in rectangular form (Figure 2.21). Trapezoidal blades, by far the most widely used, reach performance coefficients approaching those of optimally shaped blades. Rectangular outlines, in contrast, yield a markedly lower maximum performance coefficient at the design tip speed ratio. Outside the design area, however, extensive ranges of operation exist, some with even better performance ratios. In addition to blade outline, the position of the rotor blades relative to the wind direction or to the rotor plane is decisive in extracting energy from the wind. The peripheral speed of the turbine is high at the blade tip and relatively low at the hub. This results, for the same airstream effect, in a low blade chord at the tip and a larger blade area near the hub. To obtain similar flow conditions over the entire length of the blade when running, similar flow directions relative to the aerofoil section must be achieved at all points between the tip and the hub. This is attained when the relative airspeed at design performance (i.e. nominal operation conditions) is the same at all radii (Figure 2.20). Following Figures 2.4 and 2.22, the angle of attack \ud835\udefc is the difference between the pitch angle \ud835\udf17 and the resultant relative airflow direction. This is the vector sum of the wind deceleration (\ud835\udc632 = 2 3 \ud835\udc63w = 2 3 \ud835\udc631) and the peripheral speed resulting from blade rotation. Hence the blade pitch angle \ud835\udf17 (r) = arctan 2\ud835\udc631 3\ud835\udc63u \u2212 \ud835\udefc (2.45) and its equivalent power complement \ud835\udefd (r) = \ud835\udf0b 2 \u2212 \ud835\udf17 (r) . (2.46) For electricity-generating machines, high-speed turbines are usually used. The rotor blades must exhibit the lowest possible moving mass and must be very strong. Further, glass-fibre-reinforced polyester and epoxy resin composite materials are mostly used to yield aerodynamically correct blade profiles and high strength. Even greater strength may be achieved using carbon fibre materials and the use of such materials is on the increase, in spite of the higher costs involved. Figure 2.23 shows the manufacture of rotor blades in the megawatt range. In large turbines, in particular, the necessary distance from the tower can be achieved even in operation at high wind speeds with bent blades (Figure 2.24). Figure 2.25 shows the complete rotor being lifted for fitting to the rotor shaft. Rotor blades are currently manufactured in two shells and put together into a single unit in the production halls for transporting and fitting. Figure 2.26 illustrates the dimensions of the rotor blades and the demands this places upon manufacture, logistics and fitting. Furthermore, it becomes evident that the limits of transportability can easily be exceeded in many regions. The importance of factories in harbour areas will therefore increase as the size of turbines \u2013 particularly those for offshore use \u2013 increases. The construction and the fitting of rotor blades and turbines, which are discussed in more detail in references [2.3, 2.4] and [2.13], will not be considered further here." ] }, { "image_filename": "designv10_9_0001791_j.mechmachtheory.2016.05.001-Figure2.6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001791_j.mechmachtheory.2016.05.001-Figure2.6-1.png", "caption": "Fig. 2.6. Sketch of UPU + 2-SPR PM.", "texts": [ " (8c), a novel velocity transmission equation can be derived as following: Vr \u00bc J6 v\u03c9 ;Vr \u00bc vr1 vr2 vr3 0 0 0 0 0 2 66666666664 3 77777777775 ; J6 \u00bc \u03b4T1 e1 \u03b41\u00f0 \u00deT \u03b4T2 e2 \u03b42\u00f0 \u00deT \u03b4T3 e3 \u03b43\u00f0 \u00deT f T4 d4 f 4\u00f0 \u00deT 0T 3 1 0T 3 1 f T2 d2 f 2\u00f0 \u00deT f T3 d3 f 3\u00f0 \u00deT 0T 3 1 0T 3 1 2 66666666666664 3 77777777777775 : \u00f010a\u00de Eqs. (8c) and (10a) have identical solutions. It can be seen from Eqs. (8c) and (10a) that J4,8 is converted into a zero vector. J4,8 denotes one constrained torque in r3 of the UPU + SPR + UPR PM. Since the constrained torque in r3 is eliminated, r3 is converted into a SPR-type leg. From J6 and the properties of constrained wrenches, by substituting the UPR-type leg in UPU + SPR + UPR PM with one SPR-type leg, the sixth KIM (UPU + 2-SPR PM) for the Exechon PM can be derived (see Fig. 2.6). Some geometric constraints are satisfied for this PM as follows: R11\u2551A1A3;R11\u22a5R12; r1\u22a5R12;R12\u2551R13;R13\u22a5R14;R14\u22a5m;R21\u2551a1a3;R21\u22a5r2;R31\u22a5r3;R31\u2551a2o: \u00f010b\u00de The Exechon PM and its KIMs have identical kinematics. However, different constraint wrenches produce different force combinations on the manipulator and therefore produce different stiffness. In what follows, the differences among them are analyzed in detail. 4. Unified force and stiffness model of the seven PMs The Exechon PM is an overconstrained PM with two overconstraints, it has various KIMs including overconstrained and nonoverconstrained PMs" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002088_j.mechmachtheory.2018.01.015-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002088_j.mechmachtheory.2018.01.015-Figure4-1.png", "caption": "Fig. 4. Link coordinate systems of the instrument arms.", "texts": [ " The adjacent transformation matrix between the frame x L y L z L of the laparoscopic visual window and frame O la 8 can be expressed as la T L 8 = \u23a1 \u23a2 \u23a3 cos ( \u03b8L ) 0 sin ( \u03b8L ) 0 0 1 0 0 \u2212 sin ( \u03b8L ) 0 cos ( \u03b8L ) 0 0 0 0 1 \u23a4 \u23a5 \u23a6 (2) Combining Eqs. (1) and (2) , with respect to the global coordinate system X 0 Y 0 Z 0 , the pose matrix of the visual coordinate system x L y L z L is given as la T L N0 = la T 8 N0 \u00b7 la T L 8 (3) The link coordinate systems of the 11-DOF instrument arms are shown in Fig. 4 . The adjacent transformation matrices between the base frame O in 0 to the tool frame O in 10 are assumed to be in T 1 0 , in T 2 1 , in T 3 2 , in T 4 3 , in T 5 4 , in T 5 4 , in T 7 6 , in T 8 7 , in T 9 8 , in T 10 9 , respectively. The instrument has 3 DOFs and it completes surgical operations directly. Moreover, the poses of the instrument forceps have drastic change characteristics. This makes the motion trail of the tool frame O in 10 quite complex. In case the coordinate points of the tool frames are used as the coordinates of the marked points, the motion trails of the marked points are too complex to be used in the tracking algorithm. In order to simplify the motion trails of the marked points, the coordinate points of frames O in 8 are chosen to be those of the marked points A and B, as shown in Fig. 4 . Therefore, the pose amplitude of variation can be much less than that for the instrument\u2019s forceps; the position vectors of the marked points are the best selections in these algorithms. The matrices \u03bb in T 8 N0 and \u03bb in P 8 N0 represent the pose matrix and the position vector of a typical marked point, respectively. \u03bb in T 8 N0 = T \u03bbN0 \u00b7 in T 1 0 \u00b7 in T 2 1 \u00b7 in T 3 2 \u00b7 in T 4 3 \u00b7 in T 5 4 \u00b7 in T 6 5 \u00b7 in T 7 6 \u00b7 in T 8 7 = \u23a1 \u23a2 \u23a2 \u23a2 \u23a3 \u03bb in n x \u03bb in o x \u03bb in a x \u03bb in p x \u03bb in n y \u03bb in o y \u03bb in a y \u03bb in p y \u03bb in n z \u03bb in o z \u03bb in a z \u03bb in p z 0 0 0 1 \u23a4 \u23a5 \u23a5 \u23a5 \u23a6 (4) \u03bb in P 8 N0 = [ \u03bb in p x \u03bb in p y \u03bb in p z ]T (5) When \u03bb = 1 , the vector 1 in P 8 N0 denotes the position vector of mark point A" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001379_978-3-319-22056-7-Figure4.1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001379_978-3-319-22056-7-Figure4.1-1.png", "caption": "Fig. 4.1 The model of the rotor on which the band is winding up", "texts": [ "38), equation of motion is M dv dt = Fr + , (4.48) where = d M dt (u \u2212 v). (4.49) Comparing (4.46a) and (4.48), it can be concluded that differential equations have the same form, where the reactive force for the translator motion corresponds to the reactive torque \u03b6 . Remark 10 Using the principle of solidification Cveticanin and Kovacic 2007, obtained differential equations of free motion of the body. Bessonov does not take the reactive torque into consideration. Let us consider in-plane motion of a drum onwhich the band is winding up (Fig. 4.1). Equations of the motion are according to (4.27) and (4.29) d dt (Mx\u0307S1) = Fx + d M dt vxb, d dt (M y\u0307S1) = Fy + d M dt vyb, d dt (IS1\u03d5\u0307) = MS1 + M S1 + d IS1 dt b, (4.50) 4.2 Band is Winding up on a Drum 93 where M S1 = d M dt [\u03c1\u2032 S2x (vyb \u2212 y\u0307S1) \u2212 \u03c1\u2032 S2y(vxb \u2212 x\u0307S1)], (4.51) \u03c1\u2032 S2x and \u03c1\u2032 S2y are projections of the position vector \u03c1\u2032 S2 due to mass centre S1, b is angular velocity of the winding band, vxb and vyb are projections of velocity of the winding band, M is mass of the drum with band, IS1 is moment of inertia of the drum with band, x\u0307S1 and y\u0307S1 are projections of the velocity of mass centre of drum with band and \u03d5\u0307 is angular velocity of the drum with band (Cveticanin and Kovacic 2007). Technical requirement for winding up of band is the absolute velocity of the band vb to be constant. This condition provides accurate rolling up of the band on drum, without crumpling of the band or its plucking. Band is moving translatory with velocity v horizontally, parallel to y-axle (Fig. 4.1). Projections of band velocity are vxb = 0, vyb = v. (4.52) In this section, rolling up of one band layer is discussed. Angle of rolling up of the band is in the interval from \u03d5 = 0 to \u03d5 = 2\u03c0. If mass of the drum with unrolled band is M0 and the rolling mass is Mr Mr = \u03bc\u03d5, (4.53) drum\u2019s mass variation M is a linear function of the angle \u03d5 M = M0 + Mr = M0 + \u03bc\u03d5, (4.54) 94 4 Continual Mass Variation where unrolled mass unit is \u03bc = Rhb\u03c1, (4.55) h is thickness, b is width and \u03c1 is density of band. Position of mass centre of the drum with unrolled mass \u03c1S1 = SS1 is \u03c1S1 = Mr M (SS\u2032), (4" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001307_1.3663042-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001307_1.3663042-Figure1-1.png", "caption": "Fig. 1 The moment-image method", "texts": [ " Now assuming that the plate is cut along the central plane 1-1 and that the load is now applied at the corner of the left-hand portion of the plate. Therefore the moment distribution at its fixed edge has to be changed to accommodate for the fixation moment which was carried by the right-hand part of the plate. By assuming that this extra moment is superimposed on the original part of the moment diagram ab as the exact image of the nonexisting part (be in this case), therefore the moment distribution due to a corner load can be easily obtained, Fig. 1(6). This procedure of moment images can be used to obtain the moment distribution when the load P is at any finite distance y from the corner of the plate as shown in Fig. 1(c). Although this approach may disturb the orthodox mathematician, the experimental agreement makes it a very simple empirical solution which can be used with enough accuracy for practical engineering purposes. Knowing that the cantilever-plate problem is a linear problem where superposition can be applied, the moment distribution at the fixed edge due to any type of transverse loading on a finite length of the plate can be readily obtained. Examples. The case of a load uniformly distributed along the free edge of a finite plate is first considered as a check to the validity of the method" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002441_9781119509875-Figure16.4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002441_9781119509875-Figure16.4-1.png", "caption": "Figure 16.4 Linkage model of LLRR mechanical leg", "texts": [ " In order to obtain LLRR training trajectories smooth and flexibility, the velocity and the acceleration of the endpoint of the mechanical leg should be continuous. However, the realization of the endpoint motion is through the control of the LLRR mechanism leg joints. It is necessary to map movement of the end point in the Cartesian coordinate into joints space to get each joint angular velocity, angular position and angular acceleration. The linkage model of LLR-Ro mechanism leg is built as shown in Figure 16.4. Hip joint axis, knee joint axis and ankle joint axis are placed at point O, A and B, respectively. Besides, P represents end point of mechanical leg; li (i = 1, 2, 3) expresses length of thigh, calf and foot; \u03b8i (i = 1, 2, 3) represents the angular position of three joints; the joint axis of hip joint is located at the base coordinate system. x0 represents the horizontal direction. y0 represents the vertical direction. In the below trajectory planning, as the coordinate of the end point P is almost same with the point B", "17) \u03b8 represents the angular position of the joints; \u03c4 represents the joint torque;H(\u03b8) represents the inertia matrix; C(\u03b8, \u03b8\u0307) represents the centrifugal force and Coriolis force related term matrix;G(\u03b8) represents the gravity terms matrix. To achieve active rehabilitation training for patients, it must be considered that the impact of lower limb gravity on the mechanical leg joint torque. In this chapter, referring to the study of robotic statics, the patient\u2019s lower limb is reduced to a two-bar linkage model. The gravity of foots is concentrated at the ankle joint, and the direction of force is vertical. Refer to linkage model of the mechanical legs in Figure 16.4, the equation could be obtained according to the principle of leverage, m1gR1 cos \u03b81+m2g [l1 cos \u03b81 +R2 cos(\u03b81 + \u03b82)] = (F0\u2212m3g) [l1 cos \u03b81 + l2 cos(\u03b81 + \u03b82)] (16.18) mi represents the quality of the patient\u2019s leg; li represents the length of the patient\u2019s leg; \u03b8i represents the angular position of the joints; Ri represents the distance from the center of the patient\u2019s leg to the joint; F0 represents the end force when the patient relaxes. Training System Design of Lower Limb Rehabilitation Robot 215 And the force vector F of lower limb to the leg end could be obtained: F = [ 0 m3g + m1gR1 cos \u03b81+m2g[l1 cos \u03b81+R2 cos(\u03b81+\u03b82)] [l1 cos \u03b81+l2 cos(\u03b81+\u03b82)] ] (16" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001328_j.renene.2014.03.036-Figure8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001328_j.renene.2014.03.036-Figure8-1.png", "caption": "Fig. 8. NREL GRC turbine drive train SET-UP.", "texts": [ " Therefore the gearbox is allowed to move freely in upward and downward direction while being constrained in the torque DOF. Figs. 6 and 7 illustrate the principle of the HS [18]. A full nacellemodel includingmain shaft, gearbox and generator is needed to investigate the influence of the drive train layout and mounting conditions. It is opted to start from the wind turbine available in the Gearbox Reliability Collaborative (GRC) of NREL [10,11], since there has been extensive validation on the system. A model of the GRC drive train is shown in Fig. 8. The drive train features a TPM configuration typical of modular MW class wind turbine drive trains today. A single spherical roller main bearing and two elastomeric trunnions support the gearbox and main shaft assembly. The 2 speed synchronous generator mounts to the end of the bedplate and flexibly couples to the gearbox. The gearbox has a three planet low speed stage followed by two parallel stages with an overall ratio of 1:81.491. A flexible multibody model of the GRC drive train was built and is shown in Fig. 8. The model used in this paper was defined according to the validatedmodeling described in Ref. [15] and bearing and gear forces during constant gearbox loading were validated against other models used in the GRC to improve confidence in the results. The GRC uses a TPM configuration. Two other investigated concepts were created based on the model of this initial model by adding an additional bearing for the TBC and an additional bearing and hydraulic system for the HS. Figs. 9e11 show the different models" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000618_ilt-11-2011-0098-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000618_ilt-11-2011-0098-Figure6-1.png", "caption": "Figure 6 The spreadout graph of the new structure rubber bearing", "texts": [ " The dimensionless force balance equation of the rubber bearing read as: W \u00bc h2 6huR2B w \u00f07\u00de where, W \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi W 2 x \u00feW 2 y q , Wx \u00bc R 1 0 R 2p=3 0 pcoswdwd z and Wy \u00bc R 1 0 R 2p=3 0 psinwdwd z, h is film thickness, B is the width of the bearing, R is the inner radius of the bearing, u is the rotating speed of shaft and h is the viscosity of water, w is the load capacity of the bearing. The hydrodynamic lubrication rubber bearing cylinder can be spreaded out into a rectangular domain along the bearing cylinder generatrix as illustrated in Figure 6. We suppose the pressure of the water cavity would be the same as the circumference pressure. The domain of ABCD is symmetric about the dash dot line in the figure. Sowe can only calculate the pressure of the domainABCD.TheABCD rectangular domain can be meshed into grids along circumferential and axial directions. If w1 \u00bc 0, then w2 \u00bc 2p/3. So the ABCD region can be meshed into m grids along the circumferential directions as 0 # p # 2p/3, meshed into n grids along the axial directions as 0 # Z # 1" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002414_j.carbon.2019.08.039-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002414_j.carbon.2019.08.039-Figure6-1.png", "caption": "Fig. 6. Schematic of a CNC/TiO2 nanomotors with radius R; pitch l; axial length L; filament radius a; contour length L \u00bc L=cosq; and pitch angle q, where tanq \u00bc 2pR= l. (A colour version of this figure can be viewed online.)", "texts": [ " As the carbon phase of the CNCs accepts photogenerated electrons [35], the photogenerated electrons will transfer to the CNCs and react with hydrogen ions, as described by Reaction 2, and the remaining photogenerated holes will engage in the water oxidation (Reactions 3 and/or 4) [36,37]. Thus, H\u00fe is highly concentrated on the TiO2 side, and a local electric field pointing from the TiO2 end to the CNCs end is formed to propel the movement of the CNC/TiO2 nanomotors. Based upon a qualitative analysis (Fig. 6), we see that the movement of CNC/TiO2 nanomotors in the solution are resulted from a combination of the driving force (F), torque (T) and viscous drag (D). Therefore, CNC/ TiO2 nanomotors with different sizes may have different stress conditions and different motion modes, which is consistent with our experimental results. The microscopic images (Fig. 7) illustrate the CNC/TiO2 nanomotors in deionized water with different movement patterns associated with the different screw lengths. In the observation, we /TiO2 nanomotors and the \u201con the fly\u201d degradation of Phenol" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003144_302-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003144_302-Figure3-1.png", "caption": "Figure 3. Figure 4;", "texts": [ " Now If a1>1/1/2, then u1 must be greater than either a2 or a3, and u12 + x22 + a32= 1. ...... (3) f(a1) = 1 (E1>1/2/2). ...... (4) f(4 =o (at 4/1 /31 . ...... (5) If a1 <1/2/3, at least one of the cosines a2 or cc3 must be greater than al, and If 1/2/2>aI>l/.\\/3, f ( a l ) lies between 0 and 1 and is calculated as follows from (1) ...... (6) aZ2 + a32 = 1 - aI2. The Cause of Anisotropy in Permanent Magnet Alloys 169 plot a point P whose Cartesian coordinates are a2, aa. From (6 ) P lies on the circumference of a circle of radius (1 -a1,)* as shown in Figure 3. By symmetry only one quadrant need be considered. f(al) =arc BC/arc ABCD = [n/2 - 2 cos-l{al/( 1 - a12)*}]/(n/2) If P lies between B and C, al>a2 and u1>a3, and = I -(4/n)cos-l {al(l -a1,)-*). (1/2/2>a1>1/1/3). . . . . . . (7) . .. * . . (8) From ( 1 ) and (2) , remembering that NAY= 1, 0 J, = - 3 ~ , j alf(al> dal, and from (4), (S), (7 ) and ( 8 ) The first term of (9) gives 0.75, and the second term was integrated graphically and gave 0.087, so that Gans (1932) using a more precise method not involving graphical integration, obtained Jr=@831J," ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000312_1.4002447-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000312_1.4002447-Figure2-1.png", "caption": "Fig. 2 Schematic 3D calculation d", "texts": [ " A powder model is first introduced in Sec. 2.1 to reveal the distinct powder flow behavior below the flat nozzle. Then a three-dimensional selfconsistent cladding model, which is discussed in Sec. 2.2, is developed with the incorporation of the distributed powder properties and rectangular laser profile as input to address multiphysics such as mass addition, heat transfer, fluid flow, melting, and solidification during the off-axis HPDL cladding process. 2.1 Off-Axis Powder Flow 2.1.1 Calculation Domain. Figure 2 describes the threedimensional calculation domain used in the powder flow model. The dimensions of the conical nozzle and flat powder nozzle and their relative positions are from the real configurations. The diameter of the conical nozzle is 47.00 mm and the flat nozzle slot opening is 4 14 mm2. The nozzle angle in Fig. 2 is set at 38 deg from the horizontal plane. The ambient space below the nozzle is L cladding process omain for powder flow model Transactions of the ASME ms of Use: http://www.asme.org/about-asme/terms-of-use c m s s m r p t o S L p t d o a u fl w d v \u2212 o c s t w t a t R p d t t E M x y z k J Downloaded Fr hosen to be 100 100.9 60 mm3, which is large enough to ake the boundaries not affected by the powder stream. The grid ystem is designed using tetrahedral meshes to fit the irregular hape domain except in the laser spot region, where fine cubic eshes were used to resolve the strong beam intensity for accuate calculation in the laser material interaction area" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002930_j.mechmachtheory.2020.103824-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002930_j.mechmachtheory.2020.103824-Figure3-1.png", "caption": "Fig. 3. Forces and moments acting on crank train.", "texts": [ " x r and y r are the displacements at the center of gravity of connecting rod in the horizontal and vertical directions. \u03c6r is the angular position of connecting rod according to the central line of cylinder liner. x pin and y pin are the displacements of piston pin in the horizontal and vertical directions. l 1 is the distance between the center of big end bearing and the center of gravity of connecting rod. l 2 is the distance between the center of small end bearing and the center of gravity of connecting rod. l is the sum of l 1 plus l 2 . Fig. 3 shows the forces and moments acting on crank train. F gas is the gas force. F xnall and F yfall are the total normal force and friction force between piston skirt and cylinder liner, respectively. They can be determined with the help of the piston secondary model. F xpr and F ypr are the components of the small end bearing forces in x direction and y direction, respectively. F xrc and F yrc are the components of big end bearing forces in x direction and y direction, respectively. These components of hydrodynamic forces are calculated using the Reynold\u2019s equation for infinitely short journal-bearing. T load is the external load on the engine. T fric is the friction and pumping torque of the engine. The piston moves in three directions: vertical, lateral and rotation about an axis perpendicular to the x \u2013y plane. The motion in the vertical direction is called reciprocating motion or primary motion and the motions in both lateral and rotational directions are called piston secondary motion. According to Fig. 3 , the equation of piston primary (vertical) motion can be established as [25 , 29 , 30] : F y fall + F yipin + F yipis \u2212 F gas cos \u03b8p \u2212 m p g + F ypr = 0 (1) where F gas is the force due to cylinder gas pressure that is measured from an internal combustion engine. F yipin and F yipis are the inertial forces of piston pin and piston body. They are given as: F yipin = \u2212m pin \u0308y pin (2) F yipis = \u2212m pis \u0308y pis (3) where m pin and m pis are the masses of piston pin and piston body, respectively. Thus, m p = m pin + m pis " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001871_s00170-018-1840-1-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001871_s00170-018-1840-1-Figure5-1.png", "caption": "Fig. 5 Temperature contours in a single-track specimen. a MHS. b ITC", "texts": [ " The equations and needed parameters to define this heat source have been discussed in detail by the authors in Nazemi et al. [7, 13\u201315]. The second technique, ITC, results in much less computation time. An example of a single-track bead specimen is shown in Fig. 3a with the geometric data and process parameters presented in Table 1. The melt pool provided by the MHS technique is depicted in Fig. 3b which is used to acquire temperature profiles for the ITC technique. The temperature profiles and their average were drawn from the nodes on the cross-section of the melt pool (Fig. 4). In Fig. 5, the resulted temperature distribution in a single-track bead specimen from ITC and MHS techniques are compared while the clad bead is heating up showing the difference between their heat distribu- Fig. 4 Temperature profiles in the single-track specimen (a) on the nodes in cross-section of the melt pool (b) average of the profiles in the melt pool Table 1 Compositions of the actual and simulations materials (wt.%) Element C P S Si Cr AISI 1018 0.15\u20130.2 0.04 0.05 \u2013 \u2013 S355J2G3 (0.18) 0.035 0.035\u2264 \u2264 1" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002943_ab8ea4-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002943_ab8ea4-Figure3-1.png", "caption": "Figure 3 (a) Photograph of electric and magnetic field integration system. (b) The structure of the electric and magnetic field integrated systems, which combines an electric field system that can generate an electric field by applying a voltage to an electrode, and an EMA system that generates a magnetic field by applying an electric current to a coil.", "texts": [ " After placing in the EMA system ROI, the hydrogel millirobot is aligned and propelled in a certain direction by using the intensity and gradient of the magnetic field generated in the EMA system. When the magnetic field is applied in the 0\u00b0, 30\u00b0, 60\u00b0, and 90\u00b0 directions with respect to the hydrogel millirobot in the ROI, whether it is aligned and propelled in the direction of the applied magnetic field is evaluated. The driving results of the hydrogel millirobot using the EMA system are observed using a CCD camera (Photonfocus, Germany). To verify the gripping motion and locomotion of the hydrogel millirobot, the electric and magnetic field integrated systems shown in Fig. 3(a) is employed. As shown in Fig. 3(b), the integrated system consists of an electric actuation system with a pair of electrodes, and an EMA system with two pairs of coils. The electric actuation system can generate an electric field by applying a voltage to the electrodes, while the EMA system can generate a magnetic field by applying current to the coils. Therefore, the electric actuation system can apply an electric field to the hydrogel millirobot to perform open and close motions, and the EMA system can apply a magnetic field to the hydrogel millirobot to locomote", " 6 shows that the hydrogel millirobot is aligned and locomoted along the magnetic field when the magnetic field and the magnetic gradient field are applied at a constant angle (0\u00b0, 30\u00b0, 60\u00b0, and 90\u00b0). As shown in Fig. 6(a)-(d), the millirobot was aligned within the average error range of 1\u00b0 along the magnetic field angle and locomoted within the average error range of 3\u00b0 according to the magnetic gradient field angle. As a result, through the locomotion investigation using the EMA system, the hydrogel millirobot was confirmed to be well aligned and locomoted in the expected direction. Using the electric and magnetic field integrated system of Fig. 3, the hydrogel millirobot demonstrates the gripping motion and the locomotion simultaneously, as shown in Fig. 7. First, when the cathodic electroactive hydrogel side of the hydrogel millirobot faces the cathode while the anodic side faces the anode, as shown in Fig. 7(b), the hydrogel millirobot exhibited the open motion. Second, when the magnetic field is applied, the opened hydrogel millirobot was advanced in the desired direction that is parallel to the electrode for generating the electric field, as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002329_s11771-018-3765-0-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002329_s11771-018-3765-0-Figure1-1.png", "caption": "Figure 1 Structure of quadrotor UAVs", "texts": [ " For the complex kinetic model, these assumptions based on the bionics principle are as follows: 1) The UAVs is regarded as the rigid body and completely symmetrical. Its mass is unevenly distributed. 2) The center of the mass of UAVs is superposition with the origin of aircraft coordinate frame. 3) It is regarded the earth coordinate frame as inertial coordinate and neglects the curvature and autobiography. In order to obtain a mathematical model of UAVs, the ground coordinate frame OXYZ and the airframe coordinates oxyz frame firstly are established, as shown in Figure 1. Then the position coordinates \u03be and attitude coordinate \u03b7 are defined where \u03be=(x, y, z) represents the airframe position vector; \u03b7=(, \u03b8, \u03c6) are roll angle, pitch angle and yaw angles respectively. The displacement and velocity vector V=(vx, vy, vz) of ground coordinate frame and the rotation angular velocity \u03c9=(p, q, r) have following relationship [42]: 1B VA (1) where A(, \u03b8, \u03c6) is the transformation matrix from the earth coordinate frame to the airframe coordinates; B(, \u03b8, \u03c6) is the transformation matrix with respect to the rotation for the airframe around the center of the mass" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001675_tia.2018.2847620-Figure16-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001675_tia.2018.2847620-Figure16-1.png", "caption": "Fig. 16. Spatial mode measured by experiment.", "texts": [ " The voltage reference update timing is 1/fc to reduce the microcomputer load. Fig. 12 shows a photograph of the measuring system. The test motor is fed by a test inverter. Thirteen asymmetric accelerometers (PCB, 0.5 Hz to 10 kHz, 10.2 mV/Pa) are installed asymmetrically with respect to one round of the motor case, and it is verified whether the spatial 0th mode or the other mode occurred. TABLE V. DRIVE CONDITIONS. Motor bench Load Load motor and inverter DC voltage 300 V Motor torque 20 Nm Motor rotation speed (1) Fig. 15, Fig. 16 500 and 5000 rev/min (Constant speed) (2) Fig. 17 100 rev/min/s acceleration to 6000 rev/min Test vehicle Load Test vehicle DC voltage 300 V Motor torque 20 Nm Motor rotation speed 100 rev/min/s acceleration to 6000 rev/min 0093-9994 (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. It is difficult to separate the electromagnetic noise on the test motor from the electromagnetic noise on the load motor in Fig", " The brake is a prototype made by Hitachi Automotive Systems, Ltd. with an electric boost type corresponding to a vehicle with no engine negative pressure and having a cooperative regenerative function. As shown Fig. 14, a microphone (PCB, 3.75 Hz to 20 kHz, 50 mV/Pa) is installed near the engine room to evaluate the electromagnetic noise. The resulting vibration FFTs of 500 and 5000 rev/min motor rotation speeds are presented in Fig. 15. As Fig. 15 indicates, the frequencies (fc+/-3f1, fc, 2fc) of PWM carrier harmonics vibration are determined. Fig. 16 shows the deflection plots of the motor case when the motor rotates at 500 and 5000 rev/min. The frequencies 12f1 are the spatial 1st mode. It can be presumed that the deformation was displaced from the axis center. It is assumed that axis misalignment of the test motor and the test bench occurs. Fig. 16 clearly shows that the spatial 0th mode is the dominant mode in a distributed winding PMSM of more than 8 poles. To determine the frequency of the electromagnetic vibration and noise on a given PWM pulse voltage, we have plotted the motor case acceleration with motor rotation speed. Fig. 17 shows the FFT results for motor case vibration when the motor rotation speed changes. It is apparent from Fig. 17 that fc+/-3f1, fc+/-f1, fc, and 2fc are the dominant frequencies in a distributed winding PMSM of more than eight poles" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003176_tia.2020.2983632-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003176_tia.2020.2983632-Figure1-1.png", "caption": "Fig. 1. The 3D FEA parametric model of three topologies to be studied; (a) the YASA structure, (b) the single sided machine with half the total magnet volume as the YASA (S1M), and (c) the single sided machine with the same total magnet volume as the YASA (S2M).", "texts": [ " The performance of the machines under typical loadings is discussed in Section V. The overload capability and experimental results are presented in detail in section VI and VII. The last section summarizes the outcomes of this study. The comparative study is conducted between three topologies: 1) a YASA structure, 2) a single sided machine with half the total magnet volume of the YASA machine (S1M), and 3) a single sided machine with the same total magnet volume as the YASA structure (S2M). The parametric models are presented in Fig. 1. They all have 10 poles and 12 open slots. The axial length, active diameter, slot depths and copper volume are maintained constant for all three machines. The rotor back iron lengths are identical while the stator yoke thickness is adjusted based on mechanical limitations and a constrained total axial length. The stator employs SMC in all cases. Most of the geometrical specifications were kept unchanged throughout the current study, in order to provide engineering insights on whether the difference in performance can be attributed, in principle, to the design configuration itself, i" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000994_icra.2014.6907574-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000994_icra.2014.6907574-Figure3-1.png", "caption": "Fig. 3. The US and needle coordinate systems. (a) Angle \u03b8 is shown. (b) Possible \u03b1 angles are shown for the quadrants.", "texts": [ " When frame sequences are used prior knowledge is available for the frames; when a single frame is used such data are not available. Two different techniques are proposed below to estimate the needle insertion angles for both cases. 1) Estimation of the Needle Insertion Angle from a single US image: Estimating insertion angle value in an image is quite complicated unless the angle is known a priori. We developed a method based on the quadrants of cartesian coordinate system to estimate the needle insertion angle in 2D US images. With this method, a rough estimate of the insertion angle, \u03b1, is chosen first as shown in Fig. 3(b). If the needle trajectory is similar to the trajectories as shown in quadrants I and III, we choose the initial insertion angle, \u03b1, as 135\u25e6, and for the quadrants II and IV, we choose \u03b1 as 225\u25e6. After the initial assignment, the Gabor filter is applied with the estimated insertion angle. The needle trajectory becomes more clear and in the next step the RANSAC line estimator is applied, and slope of the line, m, is found. The exact insertion angle in terms of the Gabor filter coordinate system, \u03b8, can be found more precisely at this point and then it can be used in the Gabor filter again to localize the biopsy needle. Due to the nature of how US images are collected, the coordinate frames of the needle axis and the Gabor filter are not positioned in the same direction, as shown in Fig. 3(a). Using (5), the exact insertion angle value is expressed in terms of the Gabor filter coordinate system. \u03b8 = \u03b1+ | tan\u22121(m) | \u221245\u25e6 (5) Steps of the needle insertion angle estimation is depicted in Fig. 5 for two different types of gel phantom. First, raw images are collected ((a) and (f)). Second, a rough estimate of the insertion angle is chosen and the Gabor filter is applied ((b) and (g)). Next, the RANSAC line estimator is applied to get the exact insertion angle, \u03b8 ((c) and (h)). Finally, the Gabor and the RANSAC are repeated to localize the needle and its tip ((d-e) and (i-j))" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002664_tec.2020.2990914-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002664_tec.2020.2990914-Figure1-1.png", "caption": "Fig. 1. Topology of the proposed SRM.", "texts": [ " The importance and impact of this configuration with C-cores upon increasing the mean torque and reducing the torque ripple are also presented. Also, summary of this new configurations of stator and rotor teeth for C-core three-phase proposed SRMs are briefly described in the following sub-sections. C-core Three-phase SRMs: The proposed SRMs include 12/14; 18/21; 24/28; 30/35 SRM. Meanwhile, if the outer diameter of the motor is enlarged, it is better to use the larger factors at a fixed volume for more output power and mean torque. As shown in Fig. 1a, there are two C-core for each phase. To minimize the axial forces exerted on the rotor and to hold the symmetry of forces applied to the rotor, the C-cores are placed opposite to each other. For a three-phase motor, six Ccores are required. Also, the magnetic flux passing one tooth of C-core must pass the next tooth of the same C-core. Therefore, to create this path, the magnetic flux must be placed opposite to any stator C-core tooth of one tooth of the motor. The rotor pole pitch is: \u03b8rp=360 \u0366 /Nr. So, the angle between the two teeth of C-core is as follows: 360 /rp rP\u03b1 \u03b8= = (1) Since the number of C-cores for a three-phase motor is 6, and distance from the center of one tooth of C-core and center of the adjacent tooth close to C-core is \u03b3, then we have: ( ) ( )6 360 60\u03b1 \u03b3 \u03b1 \u03b3+ = \u21d2 + = (2) In three-phase motors, there are always two choices: Nr=Ns\u00b12 [17] leading to 12/10 (Fig. 1e) and 12/14 (Fig. 1f) SRM respectively. On the other hand, the closer value of \u03b1 and \u03b3 means more suitable windings available space which is related to the smallest stator angle: \u03b1 or \u03b3. Here, two cases are studied. In the 1st case, \u03b1=36\u00ba and \u03b3=24\u00ba leading to 12/10 SRM. In the 2nd case, \u03b1=25.71\u00ba and \u03b3=34.29\u00ba leading to 12/14 SRM. Therefore, the minimum angle for 12/10 SRM is 24\u00ba and for 12/14 SRM is 25.71\u00ba. Thus, 12/14 SRM has more available winding space. Referring to Fig. 1c and Fig. 1d, assume the available windings space in the 12/10 SRM is A, and in the 12/14 SRM is B, so Area A 0, neutral steer, if KUS = 0, and oversteer, if KUS < 0. For a linear two-wheel vehicle and tyre model, assuming small slip and steering angles, the understeer gradient KUS can be derived straight forward, e.g. [2]. Therewith the required steering angle for steady-state cornering becomes \u03b4H is = l \u03c1 + KUSay . (1.2) Basic stability analysis reveals a stable steady-state motion for vehicles with understeer characteristics, while for vehicles with oversteer, stability is lost for v > \u221a \u2212l/KUS . *E-mail: johannes.edelmann@tuwien.ac.at **E-mail: manfred.ploechl@tuwien.ac.at 682 By including simple nonlinear tyre characteristics, but assuming still small angles, it turns out in [3], that different steady-state operating points for neutral steer (and the related definitions of over-/understeer) result from Eq. (1.1) dependent on the test conditions, i.e. on a specified constraint on the relationship between v and l/\u03c1. In particular, v = constant or \u03c1 = constant are discussed in [3], and for the later, d(\u03b4 \u2212 l/\u03c1) day \u2223 \u2223\u2223 \u2223 \u03c1=const = \u03c1 2v \u2202\u03b4 \u2202v , (1.3) with steering angle \u03b4 = \u03b4H/is of the front tyre(s), is derived. In accordance with [2], \u2202\u03b4/\u2202v = 0 then defines the boundary between over- and understeer, which is often used from a practical point of view. Also in this context, steady-state cornering test manoeuvres have been performed for various speeds, but constant cornering radius \u03c1. Stable, steady-state cornering requires that \u2202\u03b4 \u2202(l/\u03c1) \u2223\u2223 \u2223\u2223 v=const > 0 (1.4) for most regular driving conditions, see [2]. At regular steady-state cornering manoeuvres both steering angles of the front wheels and all side slip angles will remain small up to moderate lateral accelerations. Only small traction forces are required for constant speed there. However, steady-state cornering can also be performed with a very high side slip angle of the vehicle, considerably large traction forces and also large, negative steering angles of the front wheels, which are directed towards the outside of the curve. As a consequence, the constraint of small angles needs to be abandoned in this paper, and in addition, the mutual influence of the traction force on the lateral tyre force needs to be considered. For obvious reasons this manoeuvre may be called powerslide, and occurs most often in a transient way, e.g. on gravel roads at Rallye sports. In Figs. 1 and 2, the driving conditions for a two-wheel vehicle model with rear wheel-drive at regular and powerslide steady-state cornering are illustrated. Both vehicles perform the same right-hand turn (radius \u03c1) at the same velocity v. Note the negative steering angle \u03b4 and the large side slip angle of the rear tyre and of the vehicle, \u03b1r and \u03b2 respectively, in the powerslide condition, compared with a typical regular cornering condition. Other quantities are mentioned in the subsequent section. While regular steady-state cornering has fundamentally been covered e.g. in [3\u20137], the powerslide motion has hardly been addressed in literature. Early, but rudimentary contributions to the powerslide can be found in [4, 8], more recent ones in [9\u201312]. REGULAR AND CHAOTIC DYNAMICS Vol. 14 No. 6 2009 In section 2 the applied nonlinear vehicle and tyre model is presented and the equations of motion are derived. Handling characteristics are discussed in section 3, and compared with field measurements in section 4. As the equations of motion have been linearized with respect to the trim states, a basic linear stability analysis of the steady-state motion including the powerslide condition is given in section 5. Some remarks on continuing research will conclude the paper." ] }, { "image_filename": "designv10_9_0002893_tia.2020.3036328-Figure10-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002893_tia.2020.3036328-Figure10-1.png", "caption": "Fig. 10. Flux density distributions at open circuit condition. (a) 6S16P CFRPM. (b) 12S16P CFRPM. (c) 12S16P FRPM. (d) 6S4P SPM.", "texts": [ " It should be noted that during the optimization process the total winding length changes as well, which will also influence the output torque. For the distributed windings, the end winding length lend is calculated as lend = 2 sin(y\u03c0/Ns) (r3 \u2212 yk \u2212 0.5sh) . (9) For the concentrated windings, the winding length is calculated as lend = \u03c0 (r3 \u2212 yk \u2212 0.5sh) /Ns + 0.5tw (10) in which y is the slot pitch, r3 the stator outer radius, Ns the stator slot number, yk the stator yoke width, tw the stator tooth width, sh slot height. Fig. 10 shows the flux density distributions of the four machines at open circuit condition. The 6S4P SPM machine shows the highest flux density both in the stator tooth and stator yoke, and the flux density is over 1.6 T. For the other three machines, the flux path is much less saturated. Fig. 11 compares the back EMFs of the four machines. The back EMF waveforms of the 12S16P FRPM machine and its consequent pole type are more sinusoidal than those of the 6S16P CFRPM and 6S4P SPM machines. The 6S16P CFRPM shows the highest back EMF while the other three machines are of similar amplitude" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003340_j.addma.2021.101881-Figure24-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003340_j.addma.2021.101881-Figure24-1.png", "caption": "Fig. 24. Canonical part: (a) L-PBF processed IN718 deposition; (b) Geometrical profile of cross section.", "texts": [ " As a result, when more and more equivalent layers are lumped into one super layer, the ELLM can have larger and larger error in the predicted residual deformation of the large as-built metal components. Therefore, the 4-layer ELLM case is suggested as the limiting case that may be employed to accelerate the simulation to the largest extent while good simulation accuracy can be ensured. In order to check scalability of the methodology, the proposed ELLM is applied to a DMLS-processed IN718 canonical part as shown in Fig. 24 (a). In fact, residual deformation of this complex part has been investigated in our previous works regarding IN718 [18] and Ti6Al4V [28], indicating good robustness of the MISM. However, the laying lumping X. Liang et al. Additive Manufacturing 39 (2021) 101881 effect was not thoroughly studied in our previous papers. The dimensions of this canonical part are 81.6 \u00d7 81.6 \u00d7 64.5 mm3. A block void with a size of 29.8 \u00d7 29.8 \u00d7 64.5 mm3 is created including four fillet corners in the center of the part along the build direction. There is a chamber surrounded by an external and internal wall. The thickness is 2.91 and 1.05 mm for the external and internal wall, respectively, as shown in Fig. 24(b). A small overhang feature is also observed at a height of 51.8 mm. To avoid metal powders being trapped in the enclosed chamber during the L-PBF process, a small triangle is opened in the lower end of the part (see Fig. 24(a)). Moreover, for the purpose of preventing detaching, a thin reinforcement strip is added to the lower end of the part to enhance connection to the large build plate (see Fig. 24 (a) and also Ref. [18]). Note this base reinforcement was not included in the Ti6Al4V canonical part reported in Ref. [28]. Regardless of the small triangle opening, at least bi-plane geometrical symmetry can be observed for the canonical part. In order to save computational time, the small triangle opening and the cone belt are neglected in the simulation. Thus, only a quarter of the canonical part as shown in Fig. 25 is modeled in the layer-wise simulation. Considering the overhang feature, the canonical part is divided into two sections in the build direction for mesh generation" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000844_bf00251591-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000844_bf00251591-Figure2-1.png", "caption": "Fig. 2. Symmetrical Watt-1 mechanism in cusp position", "texts": [ " Cusps A cusp occurs when G is the instant center of link CG, in which case it is also the instant center of link GF. Geometrically, this means that G lies at the intersection of AC (extended, if necessary) and the line joining F and the point of intersection of cranks AB and DE. relations amongst the nine parameters of the mechanism. Due to the complexity of the general case, we shall limit the discussion of cusps to the special case of the symmetrical Watt-1 curve obtained when the hinge pivots of the triangular links are collinear (Fig. 2). Equating cosfl from triangles FBG and GBD of Fig. 2, we have b2 h 2 + bo = 0 (i) where b2=s; b o = - n ' E s 2 + ( s ' - l ) 2 - l ' 2 ] - s [ n ' 2 + ( s ' - l ) 2 ] . (ii) Equating cos2 from triangles GBD and GAE, we have aaha+a2h2+al h + a 0 = 0 where (iii) Eliminating h from (i) and (ii), we obtain the cusp condition in the form bo(a3 bo- al b2) 2 + b2(a2 b o - a o b2) 2--0. (v) Substituting the expressions for ao, a~, a2, a3, bo, b2 of equations (ii) and (iv) into equation (v), we obtain Q~ l+ Q2 =0 (vi) where Q1 and Q2 are functions of the mechanism parameters in which l and l' appear only in even powers", " A mechanism obtained graphically in this fashion describes curve W-005. The basic cusp condition in the form of equation (v) expresses the requirement that equations (i) and (iii), regarded as equations in h, have one root in common. We may double the number of cusps by requiring that equations (i) and (iii) have two roots in common. The conditions for two common roots are a3 bo = al b2, (viii) a2 bo =ao b2. (ix) Geometrically this means that we can change the sign of h, and this is equivalent to saying G in Fig. 2 can lie on either side of D. We can again change the sign of l (in equation (viii) and (ix), this time) and obtain two further equations, say (x) and (xi). The simultaneous subsistence of equation (viii) to (xi) then expresses the condition necessary for the existence of 8 cusps. This can happen only when l=l', s=s', p =n', r' = m - a very special case in which the motion of one branch possesses two degrees of freedom. 8. Circuits of circuits is p + 1. So for the Watt-1 curve this upper limit is six" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000525_j.proeng.2012.07.198-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000525_j.proeng.2012.07.198-Figure1-1.png", "caption": "Fig. 1 The six degrees of freedom of a quadcopter at (a) Bird\u2019s eye view, (b) Frontal view", "texts": [ " Selection and/or peer-review under responsibility of the Centre of Humanoid Robots and Bio-Sensor (HuRoBs), Faculty of Mechanical Engineering, Universiti Teknologi MARA. Keywords: hover control; quadcopter; microcontroller. The hover stability of a quadcopter is important for many of its applications such as security surveillance, crop monitoring and on-board imaging to allow clear still images to be taken in surveillance operations [1]. It also prevents the quadcopter from crashing in the event of strong wind or due to its weight. Fig. 1 shows the six degrees of freedom of the quadcopter. In Fig. 1(a), x and y represents the translational motion along the x- and y-axes respectively and represents yaw, the rotational motion about the z-axis, while in Fig. 1(b), represents roll, the rotational motion about the x-axis, represents pitch, the rotational motion about the y-axis and z represents the translational motion in the direction perpendicular to ground. The label \u20181\u2019 signifies the front propeller. With a hover control unit, the quadcopter will hover at a constant height z (see Fig. 1(b)), with its roll and pitch angles stabilised by the gyroscope. The person at the command base will only need to control the quadcopter\u2019s motion along the xand y-axes and also its rotation about the z-axis (to turn corners), reducing the degree of complexity from six to only three. This defines the purpose and aim of this paper, which is to obtain a stable quadcopter hover that will last for at least 5 minutes with an acceptable error of within of the hover altitude. * Corresponding author. Tel" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002977_s40194-020-00970-8-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002977_s40194-020-00970-8-Figure5-1.png", "caption": "Fig. 5 Modelling of WAAM cylinder and a cross-sectional view showing the weld layup with coloured weld beads (inset)", "texts": [ " The average height of each layer is measured from the macrograph using a Struer\u2019s welding expert [30] and is incorporated in the FEmodel (refer Table 3), and the average thickness is 7 mm (before machining). Abaquswelding interface (AWI) plug-in is utilised to aid in building the setup of additive layers and weld pre-processing, i.e. building the weld model. Each layer is partitioned 16 number of times to generate weld beads (totalling 144 beads throughout the model) from the viewport, as shown in Fig. 5. It is essential to set a custom weld pass sequence to lay each bead in its destined location. Along the clockwise direction, the plug-in automatically defines the passes from pass-1 to pass-144. Furthermore, the plug-in then completely builds the necessary analysis steps with apt data, creates energy transport boundary conditions for each individual step, outputs requests, and builds the complete thermal model proceeded by the automatic generation of the corresponding mechanical model for thermal stress analysis [31]" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001370_0954406215621097-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001370_0954406215621097-Figure1-1.png", "caption": "Figure 1. Components of a harmonic drive system.", "texts": [ " Various models have been proposed to explain the harmonic drive mechanism,4\u201317 but these models are developed based on various macroscopic properties, such as total stiffness and total friction torque, and do not provide designers and manufacturers with the knowledge to change their design and process parameters to improve the performance of their systems. To offer a theoretical basis for the dynamic design of a harmonic drive system, it is necessary to construct a harmonic drive model that can consider the geometry and the interactions of the internal parts and can elucidate the motion and force transmission process. As shown in Figure 1, a harmonic drive system is composed of three key components: a wave generator, a flexspline with outer teeth and a circular spline with inner teeth. The wave generator is an assembly of a thin-walled ball bearing fitted onto the periphery of an elliptical cam. Different configurations of these three components could play different roles in transmission, including as a reducer, speed increaser and differential. In most circumstances, a harmonic drive is used as a reducer in which the wave generator is 1School of Mechanical Engineering, Xi\u2019an Jiaotong University, Xi\u2019an, P" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002022_978-3-319-40036-5-Figure5.21-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002022_978-3-319-40036-5-Figure5.21-1.png", "caption": "Fig. 5.21 A PSA layer (Left) is bonded to a PMMA layer using a pressurised roller", "texts": [ " It is necessary to carefully remove all segments of PSA and PMMA that have been cut from the main disk layer, this is done by hand prior to entering the clean room. If left in place these small pieces of PSA and PMMA may interfere with the flow of fluid through the microchannels of the disk during testing (Fig. 5.20). A custom built alignment housing is used to ensure that that the disks are aligned accurately when assembled, due to the microfluidic nature of the Lab-on-a-disk platform even the smallest deviation during assembly can destroy the functionality of the device. Figure 5.21 shows how this custom assembly jig is used to guide the assembly of the disk. It is for this same reason that assembly is completed within a clean room environment as small particles of dust may inhibit the flow within the device. As previously stated the PSA serves a dual purpose in the construction and functionality of the disk, it provides channels of narrow dimensions for fluid to pass from one chamber to the next however it also acts as the adhesive that bonds the layers of PMMA together. This requires a great deal of pressure which is provided by a Hot Roll Laminator, or similar device" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002859_tmag.2020.3012193-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002859_tmag.2020.3012193-Figure2-1.png", "caption": "Fig. 2. Combination of Machine I and Machine II. To induce the back electromotive force (EMF) in the armature winding, it should satisfy [11]", "texts": [], "surrounding_texts": [ "0018-9464 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.\n0018-9464 \u00a9 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.\nSee http://www.ieee.org/publications_standards/publications/rights/index.html for more information. (Inserted by IEEE.)\nA Novel Dual Stator Hybrid Excited Permanent Magnet Vernier\nMachine with Halbach-Array PMs\nLiangliang Wei, and Taketsune Nakamura, Member, IEEE\nDepartment of Electrical Engineering, Kyoto University, Kyoto 615-8510, Japan\nPermanent magnet vernier machine has received more and more attention, due to its high torque density at low rotation speed. This paper proposes a dual-stator hybrid excited permanent magnet vernier machine with Halbach-array permanent magnets. The proposed machine can achieve high torque density with consequent-pole Halbach-array permanent magnets in the rotor, has good flux regulation capability and high power factor. Firstly, the basic principle of the proposed machine is discussed, and the proposed machine can be regarded as a combination of two machines. Finite Element Analysis simulations are performed to verify the performance. And the influence of different parameters on the torque density, flux regulation capability and power factor are analyzed. The results demonstrate the effectiveness of the proposed machine.\nIndex Terms\u2014Permanent magnet vernier machines, finite element analysis, torque, Halbach-array permanent magnets, flux\nregulation capability.\nI. INTRODUCTION\nN DIRECT drive industrial applications of motors, such as wind-power generation and ship propulsion, it is necessary to have high torque density at low rotation speed [1]. The torque density of conventional direct drive permanent magnet synchronous machine is not enough at low rotation speed. Various high torque density machines are being studied, such as switching flux machine [2-3], flux modulated machine [4], and vernier machine [5-6], etc. Especially, permanent magnet vernier machines (PMVM) have the merit of high torque density at low rotation speed, due to magnetic gear effect [7- 9]. And then, the PMVM has been proposed as a promising option for the direct-drive applications.\nMany topologies of the PMVM have been proposed. However, the existed PMVM suffers from three main problems: insufficient torque density, poor flux regulation capability and low power factor. Firstly, some research works have been presented to improve the torque density. For example, a dual-magnet PMVM in [10], a spoke-type PMVM by utilizing the flux focusing effect in [11], and a dual-stator vernier permanent magnet machine with rotor-PM in [12]. However, the magnetic flux generated by the PMs in the aforementioned machines is constant. The air-gap flux regulation capability for variable speed control is limited. Secondly, traditional flux regulation methods mainly include the negative d-axis flux weakening current and additional field winding. However, the negative d-axis flux weakening current suffers from the capacity limitation of the inverter at high speed region [13], although this effect can be mitigated by using a square wave switching pattern [14]. The additional field windings, PMs and armature winding are put on the same\nstator side; it will cause serious space conflicts and reduce the efficiency [15-16]. A dual stator switched flux machine with unequal length teeth is proposed to eliminate the space conflicts in [17], but it is complicated. In addition, The PMVM also suffers from low power factor because of high winding reactance [18].\nTo improve the torque density and the flux regulation capability of the PMVM, this paper proposes a novel dual stator hybrid excited permanent magnet vernier machine with Halbach-array PMs (DS-HPMVM). The proposed DSHPMVM can achieve high torque density with consequentpole Halbach-array PMs in the rotor, has excellent flux regulation capability and high power factor. Firstly, the principle of the DS-HPMVM is analyzed, and the DSHPMVM can be regarded as a combination of two machines. Then various Finite Element Analysis (FEA) simulation and optimization are performed to verify the performance of the DS-HPMVM. The results demonstrate the effectiveness of the proposed DS-HPMVM.\nII. TOPOLOGY AND WORKING PRINCIPLE OF DS-HPMVM\nFig. 1 shows the configuration of the proposed DSHPMVM. It includes two stators and a sandwiched rotor. The outer stator has 6 slots with 4-pole-pair non-overlapping concentrated armature windings, which have the short end winding length, resulting in reducing the copper loss. The inner stator has 12 slots with 6-pole-pair field windings, and the rotor has a consequent-pole Halbach-array PMs. The magnetization direction of Halbach-array PMs is also shown in Fig. 1.\nI\nManuscript received May 8, 2020. Corresponding author: L. Wei (e-mail: wei.liangliang.6x@kyoto-u.ac.jp). This work was supported by Grant-in-Aid for Early-Career Scientists (20K14718) in Japan.\nColor versions of one or more of the figures in this paper are available\nonline at http://ieeexplore.ieee.org.\nDigital Object Identifier (inserted by IEEE).\nAuthorized licensed use limited to: Middlesex University. Downloaded on August 05,2020 at 06:25:17 UTC from IEEE Xplore. Restrictions apply.", "0018-9464 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.\nr is sp p p (1)\ns r sZ p p (2)\nwhere Zs is the number of the outer stator slot, ps is the pole pair of the armature winding, pr is the pole pair of the rotor, and pis is the pole pair of the inner stator.\nBased on the principle of magnetic gear effect [11], the fundamental magnetic flux density of outer air gap of Machine I can be expressed as\n 10.5\u039b cosIm r ism r is r rB F p p p t (3)\nwhere Fism is the MMF amplitude produced by the field winding in the inner stator, \u039br1 is the first-order permeance amplitude of the rotor, \u03b8 is the rotor position with respect to the phase A winding axis, \u03c9r is the rotational angular velocity of the rotor.\nThe rotational angular velocity of the rotor \u03c9r can be\nexpressed as\n2 e\nr\nr\nf\nP\n (4)\nwhere fe is the electrical frequency of the armature current.\nFor machine I, according to Eq. (3), the magneto motive force (MMF) produced by field winding has pis-pole-pair component. After the flux modulation of pr iron-piece rotor, the outer air-gap magnetic flux density has (pr\u00b1pis)-pole-pair component. To induce the back EMF, Eq. (1) should be satisfied.\nThe fundamental magnetic flux density of outer air gap of\nMachine II can be expressed as\n \n 0\n1\n\u039b cos\n0.5\u039b cos\nIIm s rm r r r\ns rm s r r r\nB F p p t\nF Z p p t\n \n \n \n (5)\nWhere Frm is the MMF amplitude produced by the rotor-PMs, \u039bs0 and \u039bs1 are the constant and first-order permeance amplitudes of the stator teeth, respectively.\nHence, according to Eq. (5), the PM MMF in Machine II has pr-pole-pair component. After the flux modulation of stator teeth Zs, the outer air-gap magnetic flux density has (Zs\u00b1pr)-pole-pair component, and Eq. (2) should be satisfied.\nThere are some possible slot-pole combinations of the DSHPMVM which are based on Eq. (1) and Eq. (2). To facilitate the manufacturing, the number of teeth of the inner stator should be smaller. Hence, the DS-HPMVM with Zs=6, pr=7, pis=6, and ps=1 is chosen in this study.\nIII. SIMULATION AND OPTIMIZATION METHODS\nThe performance of the 6-slot / 7-rotor DS-HPMVM is studied by means of the commercial software JMAG\u00ae, in which the field-circuit transient method is adopted. The material of the permanent magnet is NdFeB (Coercive force Hc= 1060 kA/m, Remanence Br = 1.4 T), and that of iron core is silicon steel 50A1000. Nonlinear magnetic characteristics of iron core are also considered. The parameters of the DSHPMVM are shown in TABLE. I. The pole arc ratio of PMs in the rotor is 0.5, and the ratio of the length of side magnet to main magnet is 1:2.\nTo verify the operating principle of the proposed DSHPMVM, the analysis results of outer air gap magnetic flux density distribution of Machine I and Machine II at no load are shown in Fig. 3. The 6-pole-pair magnetic flux density produced by Machine I is modulated by 7 iron piece. Then the air gap magnetic flux density of Machine I has 1-pole-pair component, resulting in inducing back EMFs in the armature winding. The Halbach-array PMs of the rotor in Machine II has 7 pole pairs, the outer air gap magnetic flux density of Machine II has 7-pole-pair component. After the flux modulating by the outer stator slots (pr-ps=Zs), the outer air gap magnetic flux density of Machine II has 1-pole-pair component, resulting in inducing back EMFs in the armature winding.\nAuthorized licensed use limited to: Middlesex University. Downloaded on August 05,2020 at 06:25:17 UTC from IEEE Xplore. Restrictions apply.", "0018-9464 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.\nFig. 4 shows the no-load EMFs of the DS-HPMVM, Machine I and Machine II. As shown, the amplitude of the noload EMF of the DS-HPMVM, Machine I and Machine II is 19.8 V, 15.9 V and 7.8V, respectively. In addition, the no-load EMFs produced by Machine I and Machine II have the same spatial phase as each other. Hence, the no-load EMF generated by the proposed DS-HPMVM is the sum of that of Machine I and Machine II.\nFig. 5 shows the comparison results of the output torque and flux regulation capability. The input current is 15.0 A, input frequency is 35.0 Hz. For machine I (+10A), the average torque is 8.07 Nm. When applying the Halbach-array PMs on the rotor, the average torque of the proposed DS-HPMVM (+10A) can be increased to 11.54 Nm. Hence, compared with traditional wound field flux modulated machine, the torque of the proposed DS-HPMVM can be improved by 43.0%. In addition, for machine II, the average torque is 4.08 Nm.\nFurthermore, Fig. 5 also shows the flux regulation capability of the DS-HPMVM. By controlling the DC current of the field winding with -3 A, 0 A and +10 A, respectively, the corresponding average torque of the DS-HPMVM can be regulated to 2.21 Nm, 4.08 Nm and 11.54 Nm, respectively. It demonstrates the DS-HPMVM has good flux regulation capability.\nThe magnetic field distributions for different field currents are shown in Fig. 6. The armature winding is open-circuit. It shows the magnetic field distribution clearly varies when applying different DC currents of the field winding. For the case of flux weakening (-3A), the magnetic flux linkage in the stator is less. On the other hand, the magnetic flux linkage in the stator is much larger for the case of flux enhancing (+5 A), Hence, the results show that the flux regulation can be realized by controlling different DC currents of the filed winding.\nFig. 7 shows the input voltage and current waveforms of phase A of the DS-HPMVM, Machine I and Machine II. The input currents of three machines are the same. It shows the power factor of Machine I, Machine II, and DS-HPMVM is\nAuthorized licensed use limited to: Middlesex University. Downloaded on August 05,2020 at 06:25:17 UTC from IEEE Xplore. Restrictions apply." ] }, { "image_filename": "designv10_9_0001106_0278364914552112-Figure15-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001106_0278364914552112-Figure15-1.png", "caption": "Fig. 15. Reachability sets computed for different delay values. As expected, increasing dt reduces the reachable space.", "texts": [ " When implementing a control action, the time delay of such a controller is usually a concern that requires consideration. In the case of the algorithm proposed here, each time interval Dtn is dedicated to plan the desired actuation value at the next interval, \u2018act(Dtn + 1). This implies that at the initial time interval Dt1 there will be no actuation; namely, the actuator will begin its motion from the second time-step. We want here to investigate how this will affect the performance of our algorithm. As one would expect, increasing time delay reduces the reachable space (Figure 15) by limiting the maximum achievable actuator movement. The delay depends on the time interval chosen to perform our algorithm, dt, which in turn depends on the computational velocity of our computer. While the delay may seem a limitation, it is important to point out the following: on an average computer, the required (dimensional) time step is dt\u2019 0.01 s. In these circumstances, we can compare the reachable space with delay with the reachable spaces obtained with other control strategies (see Section 3), as shown in Figure 16" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001014_wcica.2012.6358437-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001014_wcica.2012.6358437-Figure5-1.png", "caption": "Fig. 5. Thrust decomposition for rotor 2 along x- and z-axis", "texts": [ " Since the aerodynamic coefficients is almost constant for small propellers, the equations can be simplified to Tn = kT \u03a92 n, (12) Qn = kQ\u03a92 n, (13) where kT and kQ can be obtained easily through some experiments. Differing from the conventional quadrotor, the total thrust of the 4SP quadrotor is formulated as the summation of the thrust components in z-direction of each rotor. More specifically, since rotor 2 and rotor 4 are installed slanted towards the positive and negative x-direction (see Fig. 5), we have Frotor = \u23a1 \u23a3 \u2212s\u03b1T2 + s\u03b1T4 0 \u2212(T1 + c\u03b1T2 + T3 + c\u03b1T4) \u23a4 \u23a6 . (14) Next, pitch and roll moments will be generated by the component thrust difference of the opposing rotors, with roll moments consist also the component moments by rotor 2 and rotor 4 at x-axis, while the yaw moments is generated based on the total component moments of each rotors at z-axis. The moment vector will then be Mrotor = \u23a1 \u23a3 c\u03b1l(T2 \u2212 T4) + s\u03b1(Q2 \u2212 Q4) l(T1 \u2212 T3) Q1 + Q3 + c\u03b1(Q2 + Q4) \u2212 s\u03b1l(T2 + T4) \u23a4 \u23a6 . (15) Note that in the final equation, thrust Tn and moments Qn should be written as kT \u03a92 n and kQ\u03a92 n respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000039_978-1-84996-220-9-Figure10.8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000039_978-1-84996-220-9-Figure10.8-1.png", "caption": "Figure 10.8 Example of sequencing of stepping, balance and reaching skills. Image (d) shows the generated exploration tree which was able to find the collision-free motion produced by the reaching skill", "texts": [ " return NOT YET FOUND Note also that the planner will request many sample motions from the available skills in order to progress with the search for a solution. Figure 10.7 illustrates some of the motion samples obtained from each of the skills. In summary, the overall algorithm is able to integrate discrete skill expansion of mobility skills with configuration space exploration of manipulation skills in a single framework. The approach is able to naturally solve the trade-off between performing difficult manipulations or re-adjusting the body placement with mobility skills. 290 M. Kallmann and X. Jiang Figure 10.8 shows the coordination obtained by the algorithm for solving a given reaching problem. The first image (a) shows that the goal is not in the reachable range of the arm. The next two images (b,c) show the initial and final postures produced by the balance skill from the initial standing posture to a (non-explorative) sampled body posture favoring approximation to the hand target. The reaching skill is then recruited and instantiated at this posture and a bidirectional exploration tree is expanded (image (d)) to connect the current posture to a posture reaching the target" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001720_jjap.54.06fp12-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001720_jjap.54.06fp12-Figure1-1.png", "caption": "Fig. 1. (Color online) Schematic of asymmetric movement of cilium, effective and recovery strokes.", "texts": [ " There are two characteristics of the proposed actuation system; one is that it can work similarly to natural cilia by a simple operation of an applied magnetic field, and the other is that a number of cilia work differently even under the same applied magnetic field. To realize artificial cilia, we have to consider how natural cilia work. Direct observation of natural cilia is most important to understand the mechanism of cilia motion. Studies using a high-speed motion camera attached to an optical microscope have been reported.8\u201311) First, we focus on the motion of each cilium. A natural cilium\u2019s motion is asymmetric, as shown in Fig. 1, which consists of two phases; an effective stroke and a recovery stroke. A natural cilium keeps it linear shape during the effective stroke, and the stroke produces a flow, while the cilium returns to its original position through a curved shape during the recovery stroke. This recovery stroke shows less flow obstruction. Repetition of this ciliary movement can produce a flow toward a constant direction. For micro-fluidic devices, actuators should follow the small-Reynolds-number regime, and generating an effective and recovery stroke is one of the best solutions" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002695_j.addma.2020.101439-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002695_j.addma.2020.101439-Figure3-1.png", "caption": "Fig. 3. Illustration of the scan strategy used for fabrication of all parts in a Renishaw AM250 using the parameters in Table 1 (adapted with permission from Sutton et al. [18]).", "texts": [ " However, too large of an area would cause more material consumption and lessen the number of times the powder can be reused. Consideration of all these factors led to our design of a part layout comprising nearly 35 % of the build area at each layer. Fig. 2 shows the build layout chosen for fabrication with a Renishaw AM250 L-PBF system. The Renishaw AM250 contains a 200 W Yb: Fiber pulsed laser, which operates at a wavelength of 1070 nm. The process parameters used for fabrication of all parts are shown in Table 1 using the stripe scan strategy illustrated in Fig. 3 with a layer thickness of 50 \u03bcm. The stripe strategy divides the parts into sections corresponding to the specified stripe width in Table 1 that are each processed individually with the laser. When rastering, the laser delivers energy to the powder bed in the form of pulses whose duration is the denoted as the exposure time. The distance between consecutive pulses is known as the point distance, while the distance between two neighboring rasters is referred to as the hatch distance. After completion of each layer, the stripes are rotated 67\u00b0 counterclockwise before subsequent processing", " The location dependency may stem from unoptimized argon gas flow resulting in spatter deposition onto previously solidified layers that have the potential to induce porosity in the final part if the particles are unable to melt due to their large size, as shown by Tonelli et al. [63]. Moreover, spatter deposition is also heavily influenced by the scan pattern utilized during processing [24]. If the scan pattern is not optimized to minimize spatter deposition onto parts, defects can be introduced into the parts. In this study, a stripe scan pattern was utilized (Fig. 3) that rotated counterclockwise by 67\u00b0 after each layer. Unoptimized gas flow at the edges of the build area coupled with a rotating scan pattern could cause excessive spatter deposition leading to the observed location differences. Porosity at the edges of the build area may also be due to unequal beam travel length between the middle and edges of the build area, although the optics in L-PBF systems generally correct for these variations. An additional source of the porosity may be due to differences in the powder-bed density at various locations where lower packing efficiencies of the powder bed have been correlated to a decrease in the part density [64]" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003535_j.mechmachtheory.2021.104436-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003535_j.mechmachtheory.2021.104436-Figure7-1.png", "caption": "Fig. 7. The construction principle of chain [RR]R and its equivalent chain.", "texts": [ " The line B1B2 is parallel to the vector a, its extension line always passes through O1, and its length is always a fixed value l2 which is equal to l1. In the cooperation of the SRS-link and the RCM, the motion of the SRS-link is described as the rotation about the axis O1B (line B1B2), and the axis O1B is the moving axis that rotates about the plane normal O1A in the v-plane. Obviously, the movement effect of this cooperation is similar to the U-joint, so it is defined as the \u2019UR and Up-joint\u2019. The link a is set as the driving link of this chain. The vector a is always perpendicular to O1O2. Obviously, the motion axes in Fig. 7(a), (b) and (c) have exactly the same relative positional relationship, and their v-planes are perpendicular to the base platforms. The motion axes in Fig. 8(a), (b) and (c) have exactly the same relative positional relationship, and their v-planes are parallel to the base platform. In detail, all axes O1A in the 2 figures always pass through O1 and are perpendicular to vplane, all axis O1B always passes through O1 and rotates around axis O1A in v-plane. The axis O2C is parallel to axis O1B, and both of them are perpendicular to O1O2" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001981_s11431-015-5808-1-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001981_s11431-015-5808-1-Figure6-1.png", "caption": "Figure 6 (Color online) Static load distribution for a ball bearing with constant vertical force acting on the inner ring.", "texts": [ " In the following, the peak-to-peak (P-P) VC periodic response of the system is traced by the Arc-length continuation with the cage speed as the controlled parameter (see eq. (7)). For 0 = 1.0 m and c = 200 Ns/m, Figure 5 shows the Tvc-1 and Tvc-2 branches of the displacement response. When vc approaches the vertical resonant frequency around x = 238.97 rad/s, according with refs. [16\u201318], soft hysteresis occurs in vertical direction because the weight acting on the inner race leads the balls and the raceways nearly always in contact in the bottom (for example the balls 2, 3 and 4 in Figure 6). As far as the phenomenon of bifurcation is concerned, we have calculated the whole Floquet multipliers of the periodic solutions by the Hsu\u2019s strategy, and the calculations are effective. For example, we find the turning point A in Figure 5 is indeed a cyclic fold bifurcation point, where the leading Floquet multiplier leaves the unit circle through +1 for of 235.256, 235.258, 235.257 and 235.250 rad/s as the Tvc-1 branch sweep counterclockwise (see Table 2), and the branch point B is a period doubling point, where the leading Floquet multiplier crosses the unit circle at 1 (see Table 3)", " On the contrary, the system displays a swallow-tail structure in the horizontal resonant range (around y = 170.93 rad/s), where the Tvc-1 branch would jump downward to small Tvc-1 attractors at the cyclic fold bifurcation points D and E when sweeps down and up respectively, which means soft and hard spring types co-exist at the horizontal resonant frequency. This is because that the bearing clearance and the weight can lead the balls and bearing raceways losing contact on the lateral sides (for example the balls 1 and 5 in Figure 6). The hysteresis induces fast dynamic jump of the motions, which is undesirable to the bearing systems, and then we will evaluate the relationship between some system parameters and the hysteretic behaviors. For 0 = 1.0 m, Figure 8 shows influence on the Tvc-1 resonant characteristics for different damping factors. One can see that the soft hysteresis in vertical resonant range noticeably depends on the damping coefficients, and this hysteresis disappears for a larger damping, while the typical swallow-tail structure in the horizontal resonant range still exists when the damping factors increase to the same level" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002004_tmech.2016.2578311-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002004_tmech.2016.2578311-Figure1-1.png", "caption": "Fig. 1. Aircraft Axis.", "texts": [ " The aircraft equations of motion can be developed based on the strap-down system. The body axis is described by Euler angles. However, Euler angles can be combined in different sequence of orientations. As a result, the same attitude can be described by multiple Euler angles representations. Direction Cosine Matrix (DCM) is a fixed representation of Euler angles. The system coordinate frame is first rotated about Z-axis, then Y-axis, followed by X-axis [6]. This aircraft body axis coordinate system is shown in Fig. 1. Aircraft dynamics equations are well developed [6], [8]. The dynamics equations are developed using rigid body equations of motion. The equation are subsequently linearised and decoupled into longitudinal and lateral components [7]. The longitudinal equations of motion for the experimental aerial vehicle may be written as follow, u\u0307 = (q1S) MU1 (\u2212CDu \u2212 2CD1 )u+ (q1S) M (CL1 \u2212 CD\u03b1)\u03b1 \u2212 g\u03b8 cos \u03b81 + (q1S) M (\u2212CD\u03b4e )\u03b4e (1) U1\u03b1\u0307\u2212 U1\u03b8\u0307 = (q1S) MU1 (\u2212CLu \u2212 2CL1 )u \u2212 (q1S) M (CD1 + CL\u03b1)\u03b1+ (q1Sc) 2MU1 (\u2212CL\u03b1\u0307)\u03b1\u0307 + (q1Sc) 2MU1 \u03b8\u0307 + (q1S) M (\u2212CL\u03b4e )\u03b4e (2) \u03b8\u0308 = (q1S) IyyU1 (Cmu + 2Cm1)u+ (q1Sc) Iyy (Cm\u03b1)\u03b1 + (Cm\u03b1\u0307q1Sc 2) 2IyyU1 \u03b1\u0307+ (Cmqq1Sc) Iyy \u03b8\u0307 + (q1Sc) Iyy (\u2212Cm\u03b4e )\u03b4e (3) where q1 is the dynamic pressure; S is the wing area; b is the wingspan; c is the chord length; M is the mass; Iyy is the moment of inertia; u is the x-direction velocity; \u03b1 is the angle of attack; \u03b2 is the side slip angle; \u03c6, \u03b8 and \u03c8 are Euler angles; p, q and r are angular velocities; and \u03b4e, \u03b4a and \u03b4r are elevator, aileron and rudder deflection angles, respectively", " In this section, the result shows that the Phugoid mode SMC is stable with a small amount of steady state error. Subsequently, it follows the desired trajectory. Thus, utilising Phugoid mode to control the longitudinal motion can be experimentally implemented. Throttle is another longitudinal mode control input. During the data acquisition period under human pilot control, the Experiments have been conducted to verify the performance of the proposed control methodologies. The experimental platform is a Boomerang 60, as shown in Fig. 1. The wingspan of Boomerang 60 is 1.9m. This experimental AAV platform weight 4.5kg, including all electronic and avionic equipment, and power sources (batteries). This platform is a high-wing model. High-wing models are more stable than low-wing models; hence, during the controller tuning process, the response of the experimental platform is more stable. The airfoil shape of Boomerang 60 is non-symmetric. Therefore, this experimental AAV platform can carry more payload and fly with a slower airspeed" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001510_j.mechmachtheory.2014.01.014-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001510_j.mechmachtheory.2014.01.014-Figure1-1.png", "caption": "Fig. 1. Four kinds of diagram of conventional mechanical WG.", "texts": [ " A FS always deforms under the assembly force exerted by theWG, where the shape of the deformation depends on the type of the WG. The best oval shape of the WG cam would generate the optimum stress in the FS cup after the insertion of the cam while keeping the required major axis and the periphery of the pitch curve. How to analytically express the shape of WG, and keep the periphery of the pitch curve equal to that of the original pitch circle of the unflexed FS is the main task of our research. Four kinds of diagram of conventional mechanical WG are shown in Fig. 1. TheWGwith four rollers are symmetrically placing at axial of FS and deforms the FS tooth rim to amaximum radial displacement u0 as shown in Fig. 2. The FS is a thin-walled cylindrical cupwith external teeth on its open side, whereas the closed side of the cup is a thick wall connected to the shaft of the assembly, and the CS is a rigid rimwith internal teeth. Dp is the roller diameter, rm is the radius of the neutral line of the tooth rim of the undeformed FS, \u03b2 is the polar angle between the contact point of the roller and themaximum radius, and \u03c1 and u are the radius vector and the radial displacement, respectively, of the neutral line of the tooth rim that is deformed under the action of the WG. As shown in Fig. 1b, two-roller WG can be regarded as a special case of four-roller WG when \u03b2 = 0\u00b0. The two-disk WG can be regarded as a two-roller WG which has a bigger roller diameter. Here, R is the radius of the disk, e is the eccentric distance of the disk axis relative theWG axis. \u03b3 is the angle of contact between the FS and the disk, as shown in Fig. 1c. However, the tooth rim of FS under the action of the two-disk WG suffers distributed force, which is same as the cam WG as shown in Fig. 1d. Based on the above analysis, compared with the conventional cam WG, the contact force of the tooth rim from the rollers can be regarded as a concentrated force at the contact position. Therefore, the four-roller WG is considered here to illustrate the principles of analysis and calculation process of the deformation curves and the internal forces of FS without loss of generality. As mentioned above, the FS is a thin-walled cylindrical cup; therefore, the FS structure is usually described by the cylindrical shell model, as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002955_j.jmatprotec.2020.116782-Figure10-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002955_j.jmatprotec.2020.116782-Figure10-1.png", "caption": "Fig. 10. Optical micrographs of different areas of cylindrical laser cladding.", "texts": [ " Overlapping ratios range from 30% to 40% was proven to be a better parameter to obtain the flat deposit according to the results. Fig. 9a presents a cross section of three passes laser cladding layer prepared with an overlapping ratio of 35%. The top part of this cladding layer was quite flat. Based on these results, a large area single crystal with five-passes and four-layers was successfully achieved, as shown in Fig. 9b. The dendrites in the multi-layer cladding structure displayed a uniform growth direction parallel to the [001] direction and the stray grains in the overlapping region was remelted completely. Fig. 10 shows a cross section of an annular laser cladding layer on the cylindrical sample, and typical cladding microstructures from \u03b2=0\u00b0 to \u03b2=90\u00b0 are exhibited. Note that the cladding layer had a similar microstructure every 90\u00b0 since the substrate crystal structure belonged to a cubic system. Optical micrographs display that the growth direction of cladding dendrites are always parallel to the< 001> orientation regardless of the angle \u03b2. The dendritic growth direction was [001] when \u03b2 was below 45\u00b0, and it turned to [100] while \u03b2 was above 45\u00b0" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002942_j.jmapro.2020.04.022-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002942_j.jmapro.2020.04.022-Figure2-1.png", "caption": "Fig. 2. Measurement of cutting forces.", "texts": [ "848 mm, 35 teeth, and a rake angle of 20\u00b0. As shown in the figure, the shank of the power skiving tool was attached to the tool holder. The workpiece was made of the JIS-SCM415 material and had outer and inner diameters of 100 and 58 mm, respectively. Internal involute gears of module 1 with 42 teeth were machined, and the cutting forces induced by the aforementioned power skiving tool were measured. The cutting forces were measured using a tool holder with a built-in sensor promicron SPIKE\u00ae unit. As shown in Fig. 2, it is possible to detect the bending moment, rotational torque, and axial force acting on the cutting tool. The detected bending moment, rotational torque, and axial force in xt-yt-zt that is the cutting tool coordinate are transmitted wirelessly, and converted to machine tool coordinate using a personal computer (PC). In this research, cutting tests of the internal gear were performed under the following conditions: a cutting tool rotation speed of 1311.0 min\u22121, a workpiece rotation speed of 764" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000143_j.jsv.2009.11.003-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000143_j.jsv.2009.11.003-Figure2-1.png", "caption": "Fig. 2. Load distribution angle.", "texts": [ " (3) and (4) and summing the forces in the X and Y directions, the governing equations of motion of the bearing system can be expressed as follows: m \u20acx\u00fec _x\u00fek XNc 1 i \u00bc 0 x cos ot\u00fe 2pi N \u00fey sin ot\u00fe 2pi N e 1:5 cos ot\u00fe 2pi N \u00bc 0; m \u20acy\u00fec _y\u00fek XNc 1 i \u00bc 0 x cos ot\u00fe 2pi N \u00fey sin ot\u00fe 2pi N e 1:5 sin ot\u00fe 2pi N \u00bcW ; (5) where x(t) and y(t) are the coordinates of the shaft mass, Nc(t) is the number of balls in the loading zone, W is the weight of the rotor and shaft, and c is the overall damping coefficient. The balls are compressed as they transmit the radial load from the inner ring to the outer ring. For bearings with nonzero radial clearance, the radial load is distributed over a subset of the balls, Fig. 2, inside a load-carrying zone. The number of those balls Nc is a function of the load, radial clearance, and the dynamic state of the bearing. The radial deformation of the balls is positive only for those balls within the loading zone di40 ith ball inside the load zone: dir0 ith ball outside the load zone: ( (6) Applying the polar transformation x=rt cos at, y=rt sin at to Eq. (4) and using condition (6), we find that the balls in the load zone must satisfy the following condition cos ot\u00fe 2pi N at Z e rt : (7) The extreme excursion ext(rt) occurs when a single ball is carrying the weight of the rotor and shaft" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000476_1.4007349-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000476_1.4007349-Figure1-1.png", "caption": "Fig. 1 Contact between raceway and ball", "texts": [ " Editor: Xiaolan Ai. Journal of Tribology OCTOBER 2012, Vol. 134 / 041105-1Copyright VC 2012 by ASME Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use raceways increase to some extent, the calculation time is so long that simulation is hardly accomplished even using the workstation with good performance. Therefore, traction springs with the same contact stiffness are used instead of balls to save the calculation cost. Figure 1 shows the simplification course of the contact between the raceway and one ball in a single-row four contactpoint ball bearing, which is referenced from Daidie\u0301 [3]. Although only one ball and single row are shown, the method is applicable to other rolling element bearing. In a four contact-point bearing, each raceway has two arcs which contact the ball. In Fig. 1(a), arcs 1 and 2 are in the outer raceway. Arcs 3 and 4 are in the inner raceway. C1, C2, C3, C4 are the centers of curvature of arcs 1\u20134, respectively. Cb is the ball center. When the bearing is in the static equilibrium, the contact forces between the ball and arcs 1 and 4 are through C1, C4, and Cb. The contact forces between the ball and arcs 2 and 3 are through C2, C3, and Cb. Thus, as illustrated in Fig. 1(b), contacts between the ball and arcs can be simulated by two traction springs with the same contact stiffness. Spring C1C4 simulates the contact between the ball and arcs 1 and 4. Spring C2C3 simulates the contact between the ball and arcs 2 and 3. In order to make spring forces directing along the normal to the arcs all the time, the arc center must move with its arc. Hence, two rigid beams are used to join centers with the corresponding arcs, which are shown in Fig. 1(c). In this way, the contact force always passes through the curvature center of each arc. In other words, the intersection angle between the spring and the bearing radial plane is the contact angle. This simplification method is used for all balls and raceways contacting in the bearing. When the raceway is pressed on the ball, the curvature center of inner ring is pushed away from that of outer ring. Thus, the traction spring is tense because of the rigid beam. The ball-race contact force can be calculated by the spring traction because the spring element with the same contact stiffness" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003535_j.mechmachtheory.2021.104436-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003535_j.mechmachtheory.2021.104436-Figure2-1.png", "caption": "Fig. 2. Spatial RR model.", "texts": [ " All the dorsiflexion/plantarflexion in the sagittal plane, inversion/eversion in the coronal plane, and internal/external rotation around the human longitudinal axis are combined movements of the tibiotalar and subtalar joint. The 3 rotating axes are not intersected [13]. If it is equivalent to a spherical joint, it will inevitably affect human-machine compatibility and cause interaction forces. Although the general RR model in anatomy [14] considers the influence from the talus onto the ankle movement, its both tibiotalar and subtalar joints are equivalent to revolute (R) joint (shown in Fig. 2), and its DOFs are less than human ankle. In fact, neither tibiotalar nor subtalar joint is a standard R-joint. The tibiotalar joint, being mainly responsible for dorsiflexion/plantarflexion, has a little inversion/eversion and internal/external rotation, and the subtalar joint has more complex rotation and axis fluctuation [33]. Therefore, in order to effectively improve the human-machine compatibility of rehabilitation robots, it is necessary to construct more advanced robotic mechanisms based on more reasonable ankle motion fitting models" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002859_tmag.2020.3012193-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002859_tmag.2020.3012193-Figure1-1.png", "caption": "Fig. 1. Configuration of the proposed DS-HPMVM. The DS-HPMVM can be regarded as a combination of a dual-stator flux modulated wound field machine (Machine I), and a single stator permanent magnet vernier machine with Halbach-array PMs (Machine II), as shown in Fig. 2.", "texts": [ " The proposed DSHPMVM can achieve high torque density with consequentpole Halbach-array PMs in the rotor, has excellent flux regulation capability and high power factor. Firstly, the principle of the DS-HPMVM is analyzed, and the DSHPMVM can be regarded as a combination of two machines. Then various Finite Element Analysis (FEA) simulation and optimization are performed to verify the performance of the DS-HPMVM. The results demonstrate the effectiveness of the proposed DS-HPMVM. II. TOPOLOGY AND WORKING PRINCIPLE OF DS-HPMVM Fig. 1 shows the configuration of the proposed DSHPMVM. It includes two stators and a sandwiched rotor. The outer stator has 6 slots with 4-pole-pair non-overlapping concentrated armature windings, which have the short end winding length, resulting in reducing the copper loss. The inner stator has 12 slots with 6-pole-pair field windings, and the rotor has a consequent-pole Halbach-array PMs. The magnetization direction of Halbach-array PMs is also shown in Fig. 1. I Manuscript received May 8, 2020. Corresponding author: L. Wei (e-mail: wei.liangliang.6x@kyoto-u.ac.jp). This work was supported by Grant-in-Aid for Early-Career Scientists (20K14718) in Japan. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier (inserted by IEEE). Authorized licensed use limited to: Middlesex University. Downloaded on August 05,2020 at 06:25:17 UTC from IEEE Xplore. Restrictions apply. 0018-9464 (c) 2020 IEEE" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000498_tec.2012.2185826-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000498_tec.2012.2185826-Figure3-1.png", "caption": "Fig. 3. PHEFS machine (PHEFSM): (a) cross section; (b) configuration.", "texts": [ " From the aforementioned analysis, it can be concluded that 1) the series hybrid excitation topologies without iron flux bridge have simple structure, but their excitation current utilization ratio is low, and there is a risk of demagnetization, 2) the series hybrid excitation topologies with iron flux bridge can increase the excitation current utilization ratio to some extent and has no risk of demagnetization; however, high-excitation current utilization ratio and high-PM utilization ratio are contradictory. Therefore, in order to further enhance the effectiveness of the excitation windings and avoid PM magnetic shortcircuit and possible demagnetization, the topology of PHEFS machine is investigated based on parallel hybrid excitation approach, as shown in Fig. 3. Diagrams of the series hybrid excitation topology with the iron bridge and that of the parallel hybrid excitation topology are shown in Fig. 4(a) and (b), respectively. As can be seen, the series hybrid excitation topology consists of an excitation winding, a PM and an iron bridge located in the same plane, whereas in the parallel hybrid excitation topology, an electrical excitation flux-switching machine and an FSPM machine are located in parallel planes, which can avoid demagnetization and shortcircuiting the PM flux" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003617_tec.2021.3070039-Figure15-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003617_tec.2021.3070039-Figure15-1.png", "caption": "Fig. 15. Photos of DA-Halbach prototype. (a) Stator. (b) Halbach array PMs. (c) Rotor core. (d) Rotor with armature windings. (e) Laminations. (f) Assembled machine with slip ring. (g) Test bench.", "texts": [ " Besides, all three SPM machines exhibit larger average torque than Halbach machine. More importantly, among the five machines, the proposed DAHalbach machine exhibits the largest average torque and the largest average torque per magnet volume, which makes it a strong competitor to SPM machines in some applications. A 12-stator-slot/14-rotor-slot DA-Halbach prototype with aforementioned optimized parameters has been built and tested to verify the above analyses. The stator and rotor structures as well as the photos of Halbach array PMs and test bench are shown in Fig.15. The simple cogging torque measurement method introduced in [20] is adopted and the comparison of tested and FE predicted cogging torque waveforms of DA-Halbach machine is shown in Fig.16. As can be seen, the measured cogging torque matches well with the FE predicted results with 16% discrepancy due to the manufacturing tolerance. The FE predicted and tested stator and rotor phase back EMFs are compared in Fig. 17, where great agreement can be observed. The cogging torque measurement method is also applicable for measuring the static torque characteristics" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000606_j.mechmachtheory.2014.12.001-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000606_j.mechmachtheory.2014.12.001-Figure4-1.png", "caption": "Fig. 4. Elastic half-space loaded by a normal pressure.", "texts": [ " The two-dimensional distribution of normal contact pressure in a line contact area is shown in Fig. 3 and determined as [13] p x\u00f0 \u00de \u00bc 2w \u03c0a ffiffiffiffiffiffiffiffiffiffiffiffiffi 1\u2212 x2 a2 s : \u00f012\u00de Provided the dimensions of the contact bodies are very large compared with the dimensions of the contact area, the stresses may be calculated to good approximation by considering each body as an elastic half-space. According to an elastic half-space loaded over the strip (e b x b f) by a normal pressure p(s) distributed as in Fig. 4, the stress components at point A(x, z) are [13]: \u03c3 x \u00bc \u22122z \u03c0 Z f \u2212e p s\u00f0 \u00de x\u2212s\u00f0 \u00de2ds x\u2212s\u00f0 \u00de2 \u00fe z2 2 \u03c3 z \u00bc \u22122z3 \u03c0 Z f \u2212e p s\u00f0 \u00deds x\u2212s\u00f0 \u00de2 \u00fe z2 2 \u03c4xy \u00bc \u22122z2 \u03c0 Z f \u2212e p s\u00f0 \u00de x\u2212s\u00f0 \u00deds x\u2212s\u00f0 \u00de2 \u00fe z2 2 : 8>>>>>< >>>>>: \u00f013\u00de When p(s) is a Hertzian distribution asp s\u00f0 \u00de \u00bc pH a ffiffiffiffiffiffiffiffiffiffiffiffiffiffi a2\u2212s2 p , the stresses of pointD at a depth d below the center of a Hertzian contact pressure can be calculated as \u03c3 x \u00bc \u2212pH a a2 \u00fe 2z2 a2 \u00fe z2 1=2 \u22122z 2 4 3 5 \u03c3 z \u00bc \u2212pHaffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a2 \u00fe z2 p 8>>< >>: : \u00f014\u00de From Hook's law in plane strain, \u03b5z \u00bc \u2202uz \u2202z \u00bc 1 E 1\u2212\u03c52 \u03c3 z\u2212\u03c5 1\u00fe \u03c5\u00f0 \u00de\u03c3 x n o : \u00f015\u00de Supposing thedisplacement of thepoint (0, L) is zero, as\u03c5 1\u00fe\u03c5\u00f0 \u00de\u03c3 x E \u226a 1\u2212\u03c52\u00f0 \u00de\u03c3 z E , the displacement of any point on z axis is approximated as [14] uz\u2248 Z z L 1\u2212\u03c52 \u03c3 z E ds \u00bc Z z L \u2212pHa 1\u2212\u03c52 E ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a2 \u00fe s2 p ds \u00bc \u2212pHa 1\u2212\u03c52 E sinh\u22121 z a \u00fe sinh\u22121 L a : \u00f016\u00de The displacement of point O on the surface of the half-space is determined as uzjz\u00bc0 \u00bc pHa 1\u2212\u03c52 E sinh\u22121 L a : \u00f017\u00de When R \u226b a, the deformation of the bodies on the contact center can be calculated approximately as \u03b4 \u00bc pHa E0 sinh\u22121 L a \u2248pHa E0 ln 2 L a : \u00f018\u00de Using the elastic half-space theory, the total deformation of the two contact bodies under hydrodynamic pressure p(s) can be calculated by [10] where \u03b4 x\u00f0 \u00de \u00bc \u2212 2 \u03c0E0 Z xo xi p s\u00f0 \u00de ln x\u2212s\u00f0 \u00de2ds\u00fe c ; \u00f019\u00de where xi and xo are the inlet and outlet locations of the lubricant, and c is the integral constant" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003535_j.mechmachtheory.2021.104436-Figure14-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003535_j.mechmachtheory.2021.104436-Figure14-1.png", "caption": "Fig. 14. The construction principle of chain RU^R and its equivalent chain.", "texts": [ " Since the input chains of OB-limbs [RRR] [RR] and [PRRR] [RR] are chains [RR] and [PRR] respectively, the equivalent chain [TRR] (or chain UR) and chain [TPR] (or chain UP) given in Section 3.3 are used to replace them, which can directly construct the compact OElimb. The typical examples [TRRR] [RR] and [TPRR] [RR] are shown in Fig. 13. For the OB-limbs RU^ [RR], PRU^ [RR], RU^R and PRU^R, 2 types of the equivalent chains are proposed below: The first equivalent chain of OB-limbs also concerns the RCM. As shown in Fig. 14(a) / (b) and Fig. 15(a) / (b), the equivalent chains TRU^R and TPU^R are obtained by using the RCM to replace the driving links of chains RU^R and PRU^R. According to the RCM properties, the axis O1B of the R-joint is always located in the v-plane and rotates around the plane normal O1A. The axis O1B is parallel J. Zhang et al. to vectors a, b and c (links a, b and c). The parallel link a is set as the driving link of this chain. The vector a is always parallel to axis O2D. Compared with this first equivalent chain, the second equivalent chain of OB-limbs has simpler structure", " This makes the two SR-links always parallel to O1O2 during the movement. The axis O2D has 2 DOFs relative to the axis O2B and is always parallel to O2B, which is equivalent to U^joint. The axis O1B is a moving axis that rotates around plane normal O1A in the v-plane. Obviously, the motion effect of this combination is similar to S-joint, so this cooperation is defined as \u2019SR and Sp-joint\u2019. The parallel link a is set as the driving link of this chain. The vector a is always parallel to the axis O2D. Obviously, the motion axes in Fig. 14(a), (b) and (c) have exactly the same relative positional relationship, and their v-planes are perpendicular to the base platforms. The motion axes in Fig.15(a), (b) and (c) have exactly the same relative positional relationship, their v-planes are parallel to the base platform. In detail, all axes O1A in the 2 figures always pass through O1 and are perpendicular to the v-plane. For each subfigure, the axis O1B always passes through O1 and rotates around axis O1A in the v-plane. The axis O2D is always parallel to O1B" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002833_j.ymssp.2020.106778-Figure10-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002833_j.ymssp.2020.106778-Figure10-1.png", "caption": "Fig. 10. Finite-element model of whole motor.", "texts": [ " The outer ring is fixed in the end cover, and the inner ring is fixed in the spindle, so the contact conditions should also be set as bonded. However, there is a degree of freedom of rotation between the inner ring and the outer ring, so the revolute joint should be applied. Besides, there is a rough frictional contact and no sliding between the end cover and the bolt, so the contact condition can be set as rough. Finally, the finite-element modal analysis of the whole machine is carried out, and verified by the modal test shown in Fig. 9(c). The finite-element model of the whole motor is shown in Fig. 10. The hexahedral mesh with an average of four millimeters has been applied to ensure the accuracy of the modal analysis. Besides, the number of elements and nodes is 228218 and 892642, respectively. Then, the measured and simulated modal shapes and frequencies of the whole machine are shown in Table 7. The relative errors of the first three symmetric modes are all within 5%, which further verifies the rationality and correctness of the finite-element modal analysis of the whole machine considering the orthotropy" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000220_j.asoc.2012.05.031-Figure20-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000220_j.asoc.2012.05.031-Figure20-1.png", "caption": "Fig. 20. Rapid prototyping of cylindrical shape.", "texts": [ " The integration of LSFF technology with a three dimensional computer-aided design (CAD) system, provides the ability 1518 A. Mozaffari et al. / Applied Soft Com t s d b r l s s u t t a w t P c t m f t t e t p 4 fi u s a o c m c t m t [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ o fabricate complex functional components with no intermediate teps. In rapid prototyping, the machine reads in data from a CAD rawing, deposits down successive layers of powder and finally uilds up the model from a series of cross sections. Fig. 20 illustrates apid prototyping of a cylindrical shape. One of the main drawbacks of the prototyping techniques is their ong manufacturing time. The manufacturing time depends on the canning speed and the layer height. With increasing the scanning peed and the layer height this time decreases and vice versa. But nfortunately, in LSFF process the layer height has an inverse relaion with the scanning speed in such a way that with increasing he scanning speed the clad height decreases. Therefore in a real pplication it is so important to find the best process parameters in hich the manufacturing time is the minimum value. At the same ime the dilution should be within the acceptable range. In this study, using the identified ANFIS models, and the optimal areto front, the minimum manufacturing time for prototyping a ylinder shape has been calculated. As Fig. 20 shows, the protoype part is a cylinder with radios 15 mm and height 30 mm. The anufacturing time and the related process parameters are as: Manufacturing time = 2 h : 48 min V = 4.6009 m\u0307 = 1.4975 P = 4.5053 This solution lies on the region number 2 in the obtained Pareto ront. It can be seen that after some hierarchical interactive steps, he solution that suggests an acceptable manufacturing time, diluion, powder flow rate, laser energy and scanning velocity was xtracted from the obtained archive" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001029_tmag.2015.2435156-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001029_tmag.2015.2435156-Figure1-1.png", "caption": "Fig. 1. Topology of a 12/10 poles HAFFSPMM.", "texts": [ " Chan proposed a fuzzy control for hybrid excitation brushless DC motor, which incorporated a fuzzy controller into the vector control (VC) system [5], and it cannot be used for the HESM. A novel fuzzy flux-weakening control for the HESM was proposed in [6], however, the method is only proved by simulation. The hybrid axial field flux-switching permanent magnet machine (HAFFSMM) is a novel HEFSPMM with both the PMs and winding in stator, which combines the advantages of the AFFSPMM [7] and HESM, as shown in Fig.1. In this paper, based on the VC method, the operating performance of the HAFFSPMM is investigated. To improve the robustness of the control system, a PSO-PI controller for the HAFFSPMM system is proposed. In section II, the topology and characteristics of the HAFFSPMM are analyzed. The control strategy for the HAFFSPMM drive system in whole operating region is presented in section III. The simulation and experiment research are also given in section IV. A 12/10 poles HAFFSPMM is illustrated in Fig.1, which is composed of two outer stators and one inner rotor. The stator has 6 \u201cE\u201d-shaped laminated segments, PMs and excitation windings, respectively. The PMs are sandwiched in the \u201cE\u201dshaped laminated segments, and the excitation windings are coiled around the middle teeth of the stator E-core. The structure, which both the excitation windings and PMs are in stator, is favored to avoid sliding contacts. Two outer stators have same structures, and the polarity of the opposite magnet in two stators is reversed" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000917_9781782421955.670-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000917_9781782421955.670-Figure3-1.png", "caption": "Figure 3: Characteristic features of tooth flank fracture (19)", "texts": [ " Figure 2 shows two example gears, a test and a turbine gear, with tooth flank fracture. These are only two examples, among many others, showing that subsurface fatigue failures, such as tooth flank fracture, can occur in almost every field application. Failures due to tooth flank fracture are reported in wind and steam turbines, truck gearboxes, bevel gears for heavy machinery and test gearboxes. Typical for the failure mode of tooth flank fracture is that the crack initiation is normally located below the flank surface in an approximate depth of the case-core transition (see Figure 3a) and b)) in the active flank area. The primary crack is often initiated at non-metallic inclusions that have significantly different Young\u2019s modulus compared to the normal material structure. Such imperfections below Figure 1: Typical surface gear failure examples \u2013 pitting (left) and tooth root breakage (right) the surface act as stress risers during the roll off of the flank because of the notch effect. If the material strength is locally exceeded, a crack with growth potential could be initiated in the material which can lead to tooth flank fracture later", " The primary crack propagates from the crack starter towards the surface of the loaded flank and into the tooth core towards the opposite tooth root section. The crack propagation rate towards the loaded flank is smaller in comparison to the core due to the higher hardness. After the primary crack has grown enough so the tooth stiffness is reduced, secondary cracks may occur under load. Distinctive feature of these cracks is that they normally start at the flank surface and propagate parallel to the tooth tip into the material. As shown in Figure 3a) and b) after the secondary crack meets the primary one, particles from the active flank may breakout. As the main crack reaches the loaded flank surface the remaining cross section of the tooth that carries the load is rapidly decreased. When a critical cross section is reached, the upper tooth piece is separated from the gear. The final breakage of the tooth is due to overload breakage as shown in Figure 3c). On the fracture area a typical shiny crack lens around the crack starter and a zone of rough overload breakage can be observed (see Figure 3c) and d)). Due to the given characteristics the failure type of tooth flank fracture can be differentiated from other failure types such as tooth root breakage and tooth interior fatigue fracture (TIFF) which show a crack progression over the tooth cross section as well. The failure type of tooth root breakage is characterized by a crack in the 30\u00b0-tangent area on the tooth root fillet. According to (3) the load on the tooth leads to a complex, multi-axial stress condition. The bending stress in the tooth root changes over time when the load on the flank moves towards the tooth tip or the tooth root respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000161_tmag.2010.2044043-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000161_tmag.2010.2044043-Figure1-1.png", "caption": "Fig. 1. The 3-D electromagnetic model (with part of the surface of the frame and without the air region) and the 3-D mechanical model incorporated into the electromagnetic model.", "texts": [ " The diamond winding consisted of form-wound multiturn coils, the detailed description of which can be found in some books and papers, such as [23]\u2013[25]. Inside the stator winding, each coil was made up of three turns in series and each turn consisted of three conductors in parallel. However, in both of the models, the multiturn coils were modeled as single turn coils, and the cross-sectional area of a single turn coil was equal to that of a multiturn coil. Because it was not possible to test the motor under full load in the laboratory, the rotor was removed and only the stator was tested. Table I lists the main parameters of the machine. Fig. 1 shows the electromagnetic model, which incorporated the mechanical model. A. 3-D Electromagnetic Model The 3-D electromagnetic model included mainly the end winding and its support structures as well as the air region. Moreover, the core end was included because it could be affected by the stator end-winding leakage [26]. The end shield and the frame were not modeled but they were replaced by standard impedance boundary condition (SIBC) on their inner surface [27], as shown in Fig. 1. B. 3-D Mechanical Model The 3-D mechanical model only comprised the end winding and its support structures. The support structures comprised support blocks, strapping tapes, and support rings, as shown in Fig. 4. The support blocks were fixed between two neighboring coil ends to mainly decrease their relative motion in the - and the -direction, where and denote the axial and the circumferential coordinate. The strapping tapes were capable of fastening two neighboring coil ends in the -direction to mainly de- crease their relative motion in the - and the -direction, where denotes the radial coordinate. The support rings, surrounding all the coil ends, could restrict their motion in the -direction. The material of the support structures was glass fiber. All the support structures were installed at three different levels in the -direction, as indicated in Fig. 1. On level 2 are just the support blocks, and on levels 1 and 3 are all the three kinds of support structures. It was quite difficult to model the support structures exactly as they were in the machine because of the limited computer resources. In view of their positions, two solid rings were built to model those support structures on levels 1 and 3. The axial length of the ring was equal to that of the support blocks, and the radial length covered both the inner and the outer layer of the winding. Such rings could, to a large extent, possess the same mechanical properties as the support structures in the machine. The support blocks on level 2 were modeled as they were in the machine. Fig. 1 shows clearly the model of those support structures. Besides, the multiturn coils exhibited anisotropic mechanical properties, but the anisotropic properties were supposed to be isotropic in the model because it was difficult to enforce the anisotropic properties in the model. First, the 3-D electromagnetic model was solved, and the magnetic forces on the end winding were calculated. Next, the calculated forces were used as excitation forces in the 3-D mechanical model, and the end-winding vibrations and the deformation were analyzed" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003353_jestpe.2021.3062833-Figure15-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003353_jestpe.2021.3062833-Figure15-1.png", "caption": "Fig. 15. Experimental setup of PMSM drive system used in this paper.", "texts": [ " 13-14, that although the parameters change rapidly, the harmonic currents are wellcontrolled and quickly converge to the references computed by the DHCC in steady state and during transients. The ESO can also effectively observe the disturbances when the inductances change. The proposed method has also been verified on a PMSM with large cogging torque. The parameters of this machinedrive system are summarized in Appendix B. This machine was initially designed for a vehicular application. The exper- imental setup is shown in Fig. 15, which includes a PMSM, a two-level inverter, a torque transducer, and a dynamometer. The DSP TMS320F28377D has been utilized in the experiment to carry out all control functions, and both the switching frequency and the sampling frequency of 10 kHz have been implemented. Since the bandwidth of the torque transducer is very limited, the instantaneous values of the measured torque under load have been calculated using the measured currents in dr, qr axis and applying (6)-(8). Before conducting other studies, the torque ripples are first estimated using the proposed method described in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000606_j.mechmachtheory.2014.12.001-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000606_j.mechmachtheory.2014.12.001-Figure3-1.png", "caption": "Fig. 3. Contact pressure distribution in a line contact area.", "texts": [ " Yagi and Sugimura presented that even in the isoviscous and elastic (IE) lubricant regimes, the fluid pressure might be insufficient to change the viscosity of the fluid but could be enough to significantly deform the surfaces [12]. In highly loaded cases, the deformation of elastic body may be approximated by that under the Hertzian pressure because the elastohydrodynamic line pressure distribution is similar to the Hertzian pressure distribution. In lightly loaded cases, the deformation of elastic body should be calculated by numerical method. The two-dimensional distribution of normal contact pressure in a line contact area is shown in Fig. 3 and determined as [13] p x\u00f0 \u00de \u00bc 2w \u03c0a ffiffiffiffiffiffiffiffiffiffiffiffiffi 1\u2212 x2 a2 s : \u00f012\u00de Provided the dimensions of the contact bodies are very large compared with the dimensions of the contact area, the stresses may be calculated to good approximation by considering each body as an elastic half-space. According to an elastic half-space loaded over the strip (e b x b f) by a normal pressure p(s) distributed as in Fig. 4, the stress components at point A(x, z) are [13]: \u03c3 x \u00bc \u22122z \u03c0 Z f \u2212e p s\u00f0 \u00de x\u2212s\u00f0 \u00de2ds x\u2212s\u00f0 \u00de2 \u00fe z2 2 \u03c3 z \u00bc \u22122z3 \u03c0 Z f \u2212e p s\u00f0 \u00deds x\u2212s\u00f0 \u00de2 \u00fe z2 2 \u03c4xy \u00bc \u22122z2 \u03c0 Z f \u2212e p s\u00f0 \u00de x\u2212s\u00f0 \u00deds x\u2212s\u00f0 \u00de2 \u00fe z2 2 : 8>>>>>< >>>>>: \u00f013\u00de When p(s) is a Hertzian distribution asp s\u00f0 \u00de \u00bc pH a ffiffiffiffiffiffiffiffiffiffiffiffiffiffi a2\u2212s2 p , the stresses of pointD at a depth d below the center of a Hertzian contact pressure can be calculated as \u03c3 x \u00bc \u2212pH a a2 \u00fe 2z2 a2 \u00fe z2 1=2 \u22122z 2 4 3 5 \u03c3 z \u00bc \u2212pHaffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a2 \u00fe z2 p 8>>< >>: : \u00f014\u00de From Hook's law in plane strain, \u03b5z \u00bc \u2202uz \u2202z \u00bc 1 E 1\u2212\u03c52 \u03c3 z\u2212\u03c5 1\u00fe \u03c5\u00f0 \u00de\u03c3 x n o : \u00f015\u00de Supposing thedisplacement of thepoint (0, L) is zero, as\u03c5 1\u00fe\u03c5\u00f0 \u00de\u03c3 x E \u226a 1\u2212\u03c52\u00f0 \u00de\u03c3 z E , the displacement of any point on z axis is approximated as [14] uz\u2248 Z z L 1\u2212\u03c52 \u03c3 z E ds \u00bc Z z L \u2212pHa 1\u2212\u03c52 E ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a2 \u00fe s2 p ds \u00bc \u2212pHa 1\u2212\u03c52 E sinh\u22121 z a \u00fe sinh\u22121 L a : \u00f016\u00de The displacement of point O on the surface of the half-space is determined as uzjz\u00bc0 \u00bc pHa 1\u2212\u03c52 E sinh\u22121 L a : \u00f017\u00de When R \u226b a, the deformation of the bodies on the contact center can be calculated approximately as \u03b4 \u00bc pHa E0 sinh\u22121 L a \u2248pHa E0 ln 2 L a : \u00f018\u00de Using the elastic half-space theory, the total deformation of the two contact bodies under hydrodynamic pressure p(s) can be calculated by [10] where \u03b4 x\u00f0 \u00de \u00bc \u2212 2 \u03c0E0 Z xo xi p s\u00f0 \u00de ln x\u2212s\u00f0 \u00de2ds\u00fe c ; \u00f019\u00de where xi and xo are the inlet and outlet locations of the lubricant, and c is the integral constant" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001241_j.jclepro.2017.02.167-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001241_j.jclepro.2017.02.167-Figure2-1.png", "caption": "Fig. 2. Research outline of plastic deformation in machining of laser cladded workpiece.", "texts": [ " 1(b), stresses induced by the cutting tool may reach and interact with the interface between the cladding and substrate materials. Such an interaction may weaken or at least change the interfacial characteristics, and then may lead to premature degradation of the cladding material. It is meaningful to understand the critical conditions in machining of workpiece with laser cladding layer material onto conventional engineering materials. In the present study, plastic deformation and critical condition for two-layered cutting mode in orthogonal machining of laser cladded workpiece are addressed. Fig. 2 shows the outline of this research. Machining-induced thermal and mechanical stresses can result in plastic deformation just into the cladding or tied with the substrate. A coupled thermo-mechanical model is established and utilized to predict the plastic deformation under various cutting parameters. This model is validated by using orthogonal machining experiments under different uncut chip thicknesses. The ratio of uncut chip thickness to critical cladded thickness is determined. The research result can be applied to guide the determination of process planning for re-manufacturing industrial worn parts" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001753_tia.2014.2301862-Figure10-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001753_tia.2014.2301862-Figure10-1.png", "caption": "Fig. 10. Test bench.", "texts": [ " The resulting flex-PCB winding is shown in Fig. 9 before and after being wrapped. All its dimensional characteristics, including the reduction factors fr and frL, are synthesized in Table III. In order to validate the model presented in Section III, we measured the phase resistance Rph and the torque constant kt of the flex-PCB winding described above. The measurement of the resistance was performed with a four-terminal ohmmeter. The torque constant was obtained by coupling the prototype with a drive dc motor, as shown in Fig. 10, and by measuring the phase back EMFs at different speeds, up to 70 Hz. The values obtained for these two parameters are listed in Table IV and compared with those predicted by the analytical model. 1) Phase Resistance: A relative difference of 20% between the analytical model and the experimental measurement is observed on the phase resistance. This can be explained by the fact that the model does not take some effects into account. The end winding, which provides the interconnection of the winding loops belonging to the same phase, and the microvias, which ensure the connection between go-and-back conductors of each winding loop across the substrate, introduce both an additional resistance" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002890_tia.2020.3033505-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002890_tia.2020.3033505-Figure7-1.png", "caption": "Fig. 7. Flux lines of the 18-stator-slot/13-rotor-slot FMPM: (a) \u03b8=0deg. (b) \u03b8=90deg. (c) \u03b8=180deg. (d) \u03b8=270deg.", "texts": [ " Hence, when the saturation effect is considered, the FMPM cannot be simply regarded as the superposition of a stator-PM and a rotor-PM FMPM. In other words, the decomposition method is only applicable for qualitative analysis, which does not demand high calculation accuracy. Second, as we know, the operation principle can be analyzed by the flux lines with respect to different rotor positions. We take the phase A winding as an example. Since the FMPM has 18 stator slots and 8 winding poles, there are 3 winding groups (A1, A2 and A3) for phase A, and each winding group has 2 coils, as shown in Fig. 7. It can be seen that when the rotor position \u03b8 is 0 electrical degree, the flux linkage of group A2 reaches the negative maximum, and group A1 and A3 are close to but not equal to the negative maximum. When \u03b8 is 90 or 270 electrical degrees, the flux linkage of group A2 is 0, and group A1 and A3 are close to 0. When \u03b8 is 180 electrical degrees, the flux linkage of group A1 gets the positive maximum, and group A1 and A3 are close to but not equal to the positive maximum. As shown in Fig. 8, the flux linkages of the phase A winding and group A2 are completely in phase" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001180_s11071-015-2505-3-Figure9-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001180_s11071-015-2505-3-Figure9-1.png", "caption": "Fig. 9 The gear faults in the experimental tests", "texts": [ " The hybrid faults were posed to Gear Z40 and Gear Z26. Four accelerometers were mounted on the gearbox body close to the shafts. The vibration signals were collected under 500 rpm (i.e., the driving frequency of DC motor fd is 8.33 Hz) in the experiment. The faulty frequency of the gear Z40 is f40 = 0.4 fd = 3.38Hz, and the faulty frequency of the gear Z26 is f26 = fd = 8.33Hz. The meshing frequency of the gear Z40 is fm40 = 135.28Hz, and the meshing frequency of the gear Z26 is fm26 = 216.58Hz. The sample sampling frequency was 10,000 Hz. Figure 9 shows the gear faults in the experiments. The vibration signals of the gearbox were recorded under four different conditions, including (1) normal condition, (2) hybrid faults of worn gear Z26 tooth and Fig. 8 The configuration of the experiment platform spalled gear Z40 tooth, (3) hybrid faults of cracked gear Z26 tooth and broken gear Z40 tooth and (4) hybrid faults of worn gear Z40 tooth and broken gear Z26 tooth. Here the condition of hybrid faults of cracked gear Z26 tooth and broken gear Z40 tooth was used to illustrate the mode extraction of VMD" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003310_j.mechmachtheory.2021.104428-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003310_j.mechmachtheory.2021.104428-Figure4-1.png", "caption": "Fig. 4. Transmission paths from the meshing points of g1-g2 and g3-g4 to A3.", "texts": [ " r-p meshing point\u2192 planet gear\u2192 sun gear\u2192 sun gear shaft\u2192 gear 1\u2192 gear 2\u2192 intermediate-speed shaft\u2192 intermediate-speed shaft bearing\u2192 gearbox casing\u2192 A3). However, since these paths are too long, resulting in large energy loss to vibration, they are neglected in this study. For the vibration generated by the meshing of the gear pairs in the ISS and HSS, on the one hand, it can be directly transferred successively through the gear in ISS/HSS, shaft, bearing and casing to A3, and these paths are usually time-invariant. On the other hand, they can be transferred through the low-speed shaft to PS and then to A3, and Fig. 4 draws the time-varying transmission paths from the g1-g2 and g3-g4 meshing points to A3. For g1-g2 gear pair, it can be seen from Fig. 4, there is a time-varying transmission path from the meshing point to A3, which is shown as Path 7. The vibration can be transferred successively through gear 1, bearing, and low-speed shaft to the sun gear, and then through path 4 to A3. Path 7: g1-g2 meshing point \u2192gear 1 \u2192 gear 1 bearing\u2192 low-speed shaft\u2192 sun gear\u2192 planet gear\u2192 ring gear\u2192 gearbox casing\u2192 A3. It is worth noting that when the vibration generated by the meshing of g1-g2 gear pair is transferred to the sun gear, the transmission path 7 divides into N (the number of planets) branch transmission paths, which are shown in Fig. 4 as paths 7i, 7ii, and 7iii, then the vibration is transmitted through the planet gears 1, 2, and 3 to A3 respectively. For g3-g4 gear pair, there is also a time-varying transmission path from the meshing point to A3, which is shown as path 8 in Fig. 4. The vibration can be transferred successively through gear 3, bearing, and intermediate-speed shaft to gear 2, and then through path 7 to A3. Path 8: g3-g4 meshing point\u2192 gear 3 \u2192 gear 3 bearing\u2192 intermediate-speed shaft\u2192 gear 2\u2192 gear 1\u2192 gear 1 bearing\u2192 low-speed shaft\u2192 sun gear\u2192 planet gear\u2192 ring gear\u2192 gearbox casing\u2192 A3. Similarly, the transmission path 8 also divide into three branch transmission paths, which are shown in Fig. 4 as paths 8i, 8ii, and 8iii. From the detailed analysis of transmission paths from the meshing points in ISS and HSS to A3, it can be seen that although the position between the g1-g2/g3-g4 meshing point and A3 is unchanged, there are still time-varying transmission paths that cannot be ignored. This has not been paid attention to the studies on single-stage planetary gearboxes. Assuming that the time delay caused by the change in the length of the vibration propagation is considered to be small enough to be neglected", " Between them, the first part has a constant length, while the latter part has a time-varying length (i.e. path 1). The first time-invariant transmission leads to amplitude attenuation on the vibration. We introduce a constant coefficient \u03b11 to present this attenuation effect, and \u03b11 \u2208 (0,1). Therefore, the AM function wspn 1 (t) of the vibration generated by the meshing of the s-pn gear pair can be expressed as wspn 1 (t) = \u03b11wrpn 1 (t) = \u03b11 \u2211Q q\u2208\u2212 Q Wqejqwcte\u2212 jq\u03c6n . (11) Then, we analyze paths 7 and 8. From Fig. 4, take the path 7i for example, it can also be divided into two parts: one time-invariant part from the g1-g2 meshing point to the r-p1 meshing point and one time-varying part, that is, path 1. Another constant-coefficient \u03b12 is used to present the attenuation effect of the time-invariant part, and \u03b12 \u2208 (0,1). Path 7 is longer than path 4, hence, \u03b12 < \u03b11. Because path 7 is consist of N (the number of planets) branch transmission paths, the AM function caused by the transmission path is denoted by w2,n(t) and can be given by the following expression w2, n(t) = \u03b12wrpn 1 (t) = \u03b12 \u2211Q q\u2208\u2212 Q Wqejqwcte\u2212 jq\u03c6n " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001328_j.renene.2014.03.036-Figure12-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001328_j.renene.2014.03.036-Figure12-1.png", "caption": "Fig. 12. Illustration of the reasoning corresponding to the assumption of not including the gear mesh stiffnesses in the models.", "texts": [ " Diagonal 6 6 stiffness and damping matrices are used, which results in the following equations to represent the bearings: FBody;1 FBody;2 \u00bc KBearing, qBody;1 qBody;2 \u00fe CBearing, _qBody;1 _qBody;2 (1) with: Kbearing \u00bc 2 6666664 kax;ax 0 0 0 0 0 0 krad1;rad1 0 0 0 0 0 0 krad2;rad2 0 0 0 0 0 0 0 0 0 0 0 0 0 ktilt1;tilt1 0 0 0 0 0 0 ktilt2;tilt2 3 7777775 (2) In order to minimize the influence of the specific design of the GRC gearbox on the generality of the overall drive train behavior, it was chosen not to include the gear meshing stiffness in the models. In theory the forces and moments which are introduced in the gearbox should be transferred to the gearbox bushings through a path comprising of the planet carrier, planet carrier bearings and the gearbox housing, as shown in Fig. 12. Unless there is play in the bearings or the planet carrier and/or housing stiffness is insufficient the gear meshing stiffness does not play a role in this mechanism. In addition by excluding the gear meshing stiffnesses it is possible to assure that the housing is an important part of the transfer path. Since the gear meshing stiffness is needed to counteract the torque applied at the rotor, an equivalent total gear meshing stiffness is taken into account in the torsional DOF and superimposed on the stiffness values at both planet carrier bearings" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000438_icra.2012.6225307-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000438_icra.2012.6225307-Figure5-1.png", "caption": "Fig. 5. Segment dynamics in three phases of walking including (a) leg loading, (b) midstance, and (c) swing initiation. Solid arrows denote active torques exerted muscle. dashed arrows mark reaction torques. Fg and Fi indicate trunk weight and impact force, \u03b8hip is the hip angle and \u03c4h/a represents the active hip/ankle torque.", "texts": [ " This muscle stimulation is determined mainly by the proportional-derivative terms kp(\u03b8 \u2212 \u03b8ref ) + kd\u03b8\u0307, where \u03b8 and \u03b8\u0307 are time delayed (\u2206t = 5ms) signals of the trunk angle and angular velocity. If the sum is positive, the terms add to the stimulation of the hip extensors GLU and HAM; for negative values, the amount adds to the stimulation of the hip flexor HFL. The trends in figure 4a suggest that trunk forward lean is a major contributor to fast walking. Intuition about the segment dynamics helps to understand the contribution of trunk lean to fast walking (Fig. 5a). Forward propulsion in legged locomotion can be created either by lengthening the leg after midstance or by rotating it about the hip. Hip rotation requires extension moments at that joint which accelerate the trunk backward. Trunk forward lean compensates for these moments as gravity and leg impacts create counter moments when the trunk\u2019s center of mass is located forward. As a result, faster walking can be generated by increasing hip extension moments during stance if the trunk leans more forward", " The other two stance control parameters, k\u03d5 and \u03d5k,off , belong to a proportional control that prevents knee overextension by suppressing the major knee extensor muscle VAS according to \u2212k\u03d5(\u03d5k \u2212 \u03d5k,off )(\u03d5\u0307k > 0), where \u03d5k and \u03d5\u0307 are time delayed (\u2206t = 10ms) sensory signals of the knee angle and angular velocity, and \u03d5k,off is a threshold below which no signal is generated. While the actual trend of this control with speed is less clear, the increased hip and ankle extension torques due to trunk lean and push-off tend to overextend the knee (Fig. 5b), which the suppression of VAS can compensate. Finally, the three swing-leg control parameters \u2206S , loff,HAM and GHAMHFL influence swing initiation and termination (Fig. 4c). In the neuromuscular model, swing is initiated during the double support phase in which the hip muscles receive a stimulation offset that increases the activity of HFL by \u2206S and decreases that of GLU by the same amount. The net effect is a forward propulsion of the swing leg that, due to passive inertial coupling, also tends to flex the knee (Fig. 5c). Thus increasing the single parameter \u2206S suffices to account for accelerated swing motions in fast walking. The contribution of the other two swing control parameters is less clear. Although HFL activity continues during swing, it is modulated by feedback from other muscles. In particular, the HFL stimulation is reduced by a negative feedback of the HAM position, GHAMHFL [lCE,HAM \u2212 loff,HAM ], where lCE,HAM is the time delayed (\u2206t = 5ms) signal of HAM\u2019s contractile element length, loff,HAM represents the signal threshold of the HAM muscle spindle sensors, and GHAMHFL is the feedback gain", " While the trunk reference lean \u03b8ref is similar during and after transition, the proportional and derivative gains, kp and kd, of the trunk balance sharply increase during the transition stride (Fig. 7a). This increase is required to stop the trunk around its new reference lean after it gets accelerated forward due to the large jump in \u03b8ref . The reverse change of kp and kd is not necessary during deceleration from fast to slow walking, because the trunk returns to a near upright position against the hip flexion torques created by the impact and gravity (Fig. 5a). The deviation suggests either a simple speed transition control that increases the trunk balance gains with the change \u2206\u03b8ref of the reference lean, or a more complex control that compensates for the asymmetric effects of leg impact and gravity on trunk balance. Both alternatives can be embedded with sensory feedbacks. Connected to the large change in trunk lean, the gain GSOL of the positive force feedback of the SOL sharply drops during the transition stride from slow to fast walking. The drop reduces the ankle extensor moment, which ensures that knee overextension by exaggerated hip extension torques is avoided during the stopping of the trunk (Fig. 5b). An automated regulation of GSOL the SOL could originate directly from the control that increases the gains of the trunk balance. However, more careful analysis will be required to clarify if such a control would compromise reactions to other disturbances and to explore alternative implementations. (Note that the other two stance parameters did not show a clear pattern that suggests controls.) The three parameters of the swing control show either similar values during and after transition (\u2206S) or do not show a clear pattern that suggests controls" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002894_tte.2020.3035180-Figure13-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002894_tte.2020.3035180-Figure13-1.png", "caption": "Fig. 13. Vibration deformation caused by 10th-order tangential force. (a) Conventional. (b) Bread-loaf.", "texts": [], "surrounding_texts": [ "In section 2, the initial phase relationship between each flux density harmonics has been identified. This Section will begin with the derivation of electromagnetic force, in which the force modulation effect is considered. Then, the effect of eccentric magnet on 2pth-order electromagnetic force will be clarified. A. Electromagnetic Force According to Maxwell Stress Tensor method, the radial and tangential force density can be expressed as 2 2 2 0 0 0 ( , ) ( , ) ( , ) ( , ) 2 2 ( , ) ( , ) ( , ) = r r r r B t B t B t p t B t B t p t (5) where pr and p\u03c4 are radial and tangential force (N/m2), \u03bc0 is the vacuum permeability. When calculating the radial force, the tangential flux density is generally ignored due to the small amplitude [35]. The air-gap magnetic field of PMSM is composed of PM radial and tangential magnetic field under no-load condition. The Fourier series expansion of the PM magnetomotive force in radial and tangential direction are expressed as 1,3,5... 1,3,5... ( , ) cos( 2 ) ( , ) cos( 2 ) r r r r mag r r e v v mag e v v F t F v p v f t F t F v p v f t (6) where Fr and F\u03c4 are the radial and tangential magnetomotive force (A/m2), Fr-mag and F\u03c4-mag are the magnitudes (A/m2), vr and v\u03c4 are spatial orders, \u03c6vr and \u03c6v\u03c4 are initial phases (rad). Due to the effect of stator slotting, the air-gap permeance is no longer a constant. The air-gap permeance can be expressed by a relatively permeance function, and its Fourier series is given as 0 1,2,3 ( ) cosk k kQ (7) where \u03bb is the air-gap permeance (H), \u03bbk is the k-order air-gap permeance (H), \u03bb0 is the DC component of the air-gap permeance (H), Q is the slot number. Thus, the PM flux density in the radial and tangential direction can be expressed as 0 =1,2,3... 1 cos( 2 )[ cos( )] cos( 2 ) cos[( ) 2 ] r r r r r r r r e r k v k r r r e r v rk r r e r k v B F F v p v f t kQ B v p v f t B v p kQ v f t (8) 0 =1,2,3... 1 cos( 2 )[ cos( )] cos( 2 ) cos[( ) 2 ] e k v k e v k e k v B F F v p v f t kQ B v p v f t B v p kQ v f t (9) where Br and B\u03c4 are the radial and tangential flux density (T). The spatial order, frequency and initial phase of radial and tangential force can be obtained by substituting (8) and (9) into (5). Both radial and tangential force harmonics are generated by the interaction of flux density harmonics. According to the multiplication rules of trigonometric functions, the spatial order, frequency and initial phase of electromagnetic force harmonics are determined by that of flux density harmonics. The low-order electromagnetic forces in FSCW PMSM are mainly generated by the tooth harmonics, which has relatively small amplitude under no-load condition. The high-order electromagnetic force harmonics have large amplitude because they are generated by the fundamental flux density and flux density harmonics with relatively large amplitude. Therefore, if the high-order electromagnetic force is neglected, the vibration analysis of FSCW PMSM will have a large deviation. B. Considering Force Modulation Effect This Section will investigate the modulation process of high-order electromagnetic forces to low-order ones in FSCW PMSM. Since radial and tangential force have same modulation process. Therefore, this paper only introduces the radial force modulation process. Firstly, the Fourier Transformation of the air-gap radial force density harmonic is conducted, which can be expressed as 2 0 ( ) ( , ) jv r rP v p t de (10) Authorized licensed use limited to: Carleton University. Downloaded on May 26,2021 at 11:29:26 UTC from IEEE Xplore. Restrictions apply. 2332-7782 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. where v is the spatial order of radial force. Since the sampled signal is periodic, the Fourier series of stator teeth sampling signal can be expressed as 1 2 ( ) ( ) Q k z k Q (11) The sampled signal is then subjected to a Fourier decomposition, which can be expressed as 1 ( ) [ ( )] ( ) Q k Q v kQZ v F z (12) Therefore, the output signal of the modulated radial force density can be expressed as ( , ) ( ) ( ),rmp t p t z (13) By using the frequency domain convolution theorem, (5) can be expressed as 1 ( ) ( ) ( ) 2 mP v P v Z v (14) Substituting (10) and (12) into (14), the modulated radial force density can be expressed as 1 1 ( )* ( 1 ( ) = [ ( )] 2 = ) 2 Q k Q k m Q v kQ Q P v k v P v Q P (15) According to the Nyquist-Shannon sampling theorem, the aliasing occurs when vr>Q/2. Therefore, the modulated radial force density can be expressed as cos( ) 2 cos(( ) ) ( > 2 , ) ( , ) v v v r v m m rv v Q p v t v Q p v kQ t v t t (16) where pm is the modulated radial force (N/m2), \u03c3v, \u03c9v and \u03c6v are the magnitude (N/m2), angular velocity (rad/s) and initial phase (rad) of the modulated radial force. The radial force on stator teeth can be equivalent to the concentration force, which can be obtained by circumferential integration of the force harmonics as shown in Fig. 2. Therefore, the modulated radial force on the stator teeth can be expressed as 2 , - 2 2 2 2 2 cos + , 2 = cos ( ( ) ( , ) + , 2 ) q q q q q q r q is r v v is r v v mF d Q LR v t d v Q LR v kQ t d v t p t (17) where Fr,q is the concentration force (N), \u03b8q is the angle of the qth stator tooth (rad), \u0394\u03b8 is the tooth pitch (rad), L is the stack length (m), and Ris is the inner radius of stator (m). Due to the limitation of the motor stator teeth number, the high-order radial forces acting on the stator teeth surface will be modulated to the low-order ones. The 2nd-order and 10th-order radial force harmonics of a 12-slots PMSM are taken as examples to investigate the modulation process. Fig. 3 shows the modulation process of the 2nd- and 10th-order radial force harmonics of the 12-slots PMSM. The 2nd- and 10th-order radial force harmonics are uniformly and continuously distributed in the air-gap. However, when the force acts on the stator teeth surface, the radial force is discretised due to the slotted structure. It can be seen that no aliasing occurs after the 2nd-order radial force is modulated by 12 stator slots. However, when the 10th-order radial force is modulated by 12 stator slots, it exhibits a 2nd-order distribution state in space. For FSCW PMSMs under no-load condition, the 2pth-, 4pth-, 6pth-, 8pth-order radial and tangential forces have relatively large amplitude. Among them, the 2pth-order radial and tangential force has the biggest amplitude. Due to the characteristics of the near number of slots and poles in FSCW PMSM, the 2pth-order radial and tangential force will be modulated to (Q-2p)th-order ones. Therefore, the 2pth-order radial and tangential forces are the most dominate components to the motor vibration performance. C. 2pth-order Electromagnetic Force The 2pth-order electromagnetic force harmonics are mainly generated by the PM flux density fundamental component and harmonics. Table \u2161 list the initial phase angles and frequencies of 2pth-order radial and tangential force. Also, the spatial orders, frequencies and initial phase angles of the radial and tangential flux density are also listed in Table \u2161. The red numbers represent radial flux density harmonics, and green numbers represent tangential flux density harmonics. The colors of the radial and tangential force indicate the source of the flux density harmonics. The main flux density sources of the 2pth-order radial and tangential force are (p, p), (p, 3p), (3p, 5p) and (5p, 7p) and the like. As analyzed in Section 2, the initial phase difference of (4k3)th-order and (4k-1)th-order PM flux density harmonics are always \u03c0 rad. It can be seen in Table \u2161 that the initial phases of radial and tangential force harmonics generated by flux density harmonics are all opposite to that generated by the fundamental flux density. This means that all PM flux density harmonics are able to suppress the total 2pth-order radial and tangential force. The eccentric magnet reduce the amplitude of PM flux density harmonics. As a result, the bread-loaf FSCW PMSMs with low harmonics content cannot reduce the amplitude of the total 2pth-order radial force and tangential force. Instead, it increases the amplitude of the total 2pth-order radial force and tangential force. It is worth emphasizing that these 2pth-order radial and tangential force components have Authorized licensed use limited to: Carleton University. Downloaded on May 26,2021 at 11:29:26 UTC from IEEE Xplore. Restrictions apply. 2332-7782 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. the same frequency, which is the premise of their vector superposition. In this Section, two 12-slot/10-pole FSCW PMSMs are used to evaluate the effects of bread-loaf magnet on electromagnetic force and vibration performance. Fig. 4 shows the finite-element models of the 12-slot/10-pole FSCW PMSMs with conventional and bread-loaf magnet. The main parameters of the 12-slot/10-pole FSCW PMSM are listed in Table 3. It should be emphasized that the aim of this paper is to study the effect of flux density harmonics on the radial force and vibration performance of the 12-slot/10-pole FSCW PMSM. Due to reduced usage of the bread-loaf magnet, when the conventional and bread-loaf PMSM use same magnet material, the working harmonic of the bread-loaf PMSM is smaller than that of the conventional PMSM. In order to keep the fundamental flux density consistent for a fair comparison, the remanence of the magnet material of the bread-loaf PMSM is higher than that of the conventional one. (a) (b) Fig. 4. Finite-element models of 12-slot/10-pole FSCW PMSMs. (a) Conventional. (b) Bread-loaf. TABLE \u2162 MAIN PARAMETERS OF TWO PMSMS Items Symbols Conventional Bread-loaf Stator outer dia. (mm) Do 125 125 Stator inner dia. (mm) Di 80 80 Stack length (mm) L 50 50 Air-gap length (mm) l 1.0 1.0 Slot opening (mm) so 2 2 Thickness of PM (mm) hpm 5 5 Pole embrace emb 1 1 Eccentricity (mm) hecc 0 20 PM materials - N30 N42 A. Electromagnetic Force The PM radial flux density spectrum of the 12-slot/10-pole PMSMs with conventional and eccentric magnet are shown in Fig. 5. The flux density wave of the bread-loaf PMSM is more Figs. 7 and 8 show the initial phase of radial and tangential flux density harmonics, and the initial phase of the 2pth-order radial and tangential forces produced by these flux density harmonics are also presented. The initial phase of radial flux density advances \u03c0/2 rad than that of tangential flux density. In addition, the phase difference of both (4k-3)th- and (4k-1)thorder radial and tangential flux are \u03c0 rad. The finite-element results are in good agreement with that listed in Table \u2160. Also, Figs. 7 and 8 clearly exhibit the phase relationship between the 2pth-order electromagnetic force harmonics. The spatial order and initial phase of the radial force are marked in red, and the spatial order and initial phase of the tangential force are marked in green. The blue number represent spatial order of flux density harmonics. The 2pth-order radial and tangential forces generated by fundamental flux density are marked as bold font. It can be clearly seen that there is a \u03c0 rad phase difference between the 2pth-order electromagnetic force generated by the fundamental flux density and generated by the flux density harmonics. Consequently, this means that both 2pth-order radial and tangential force harmonics generated by flux density harmonics decrease the total amplitude of radial and tangential force. The bread-loaf PMSM with low harmonics content has negative effect on reducing the total 2pth-order radial and tangential forces. Authorized licensed use limited to: Carleton University. Downloaded on May 26,2021 at 11:29:26 UTC from IEEE Xplore. Restrictions apply. 2332-7782 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Fig. 9 gives the two-dimensional (2-D) radial force spatial spectrums of the 12-slot/10-pole FSCW PMSMs with conventional and bread-loaf magnet. Spatial orders, frequencies and amplitudes of main radial and tangential force have been marked. The most remarkable feature is that the 10th-order (2pth-order) radial force amplitude of the 12-slot/10pole PMSM with conventional magnet is only 54.6% of that with bread-loaf magnet. In addition, due to the low harmonic content in bread-loaf FSCW PMSM, the 20th-, 30th- and 40thorder radial force are reduced by 58.2%, 78.3% and 87.8%, respectively. Fig. 10 gives the 2-D tangential force spatial spectrums of the 12-slot/10-pole FSCW PMSMs with conventional and bread-loaf magnet. Due to the bread-loaf magnet, the amplitude of the 10th-order tangential force has increased by 68.5%, and the 20th-, 30th- and 40th-order tangential forces have decreased by 80.0%, 78.8% and 87.3%, respectively. The FSCW PMSMs with bread-loaf magnet have less harmonic content. However, it has been verified to have negative effect on reducing the 2pth-order radial and tangential force. B. Vibration Simulations The bread-loaf magnet increases the 2pth-order radial and tangential force of the 12-slot/10-pole FSCW PMSM. In this Section, the effect of bread-loaf magnet on vibration performance will be further evaluated. Fig 11 shows the multiphysics vibration prediction model. The structural FEA model with mechanical mesh is shown in Fig. 11(b). Also, the location of the accelerometer has been pointed out in the structural FEA model. The structural FEA model contains the housing, end cover, stator core and equivalent winding of the 12-slot/10-pole FSCW PMSM. 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. Authorized licensed use limited to: Carleton University. Downloaded on May 26,2021 at 11:29:26 UTC from IEEE Xplore. Restrictions apply. 2332-7782 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Figs. 12 and 13 show the vibration responses caused by 10th-order radial and tangential force of 12-slot/10-pole FSCW PMSMs with conventional and bread-loaf magnet. The vibration responses are produced by the 10th-order electromagnetic force, but they both show the 2nd-order vibration mode. It verifies the correctness of force modulation effect. In addition, the 12-slot/10-pole FSCW PMSM with bread-loaf magnet reduces the amplitude of PM flux density harmonics, but the vibration deformation of the 12-slot/10pole FSCW PMSM with bread-loaf magnet is obviously higher than that with conventional magnet. Similarly, Fig. 12 gives the vibration responses caused by 10th-order tangential force of 12-slot/10-pole FSCW PMSMs with conventional and bread-loaf magnet. The vibration deformation of the 12-slot/10-pole FSCW PMSM with breadloaf magnet is obviously higher than that with conventional magnet. Due to the amplitude of 10th-order tangential force is smaller than that of 10th-order radial force, the vibration deformation cause by 10th-order tangential force is also smaller than that caused by 10th-order radial force. Fig. 14 shows the predicted results of vibration acceleration spectrum of 12-slot/10-pole FSCW PMSMs with conventional and bread-loaf magnet under no-load condition, and they both operate at 600 r/min. Hence, the corresponding electrical frequency is 50 Hz. It can be seen from Fig. 14 that the peaks of vibration acceleration mainly appear at even times of motor electric frequency. More importantly, the bread-loaf magnet significantly increase the vibration acceleration at 2fe. The vibration acceleration of the 12-slot/10-pole FSCW PMSM with conventional magnet is only 36.2% of that with the bread-loaf magnet at 2fe. In addition, the vibration acceleration of the 12-slot/10-pole FSCW PMSM with bread-loaf magnet has decreased correspondingly at. Different from the radial force at 2fe, the 4fe, 6fe, 8fe and later frequencies of radial force are mainly generated by the flux density harmonics. Due to the low harmonics content of the bread-loaf PMSM, the 4pth-, 6pth-, 8pth-order radial force of the bread-loaf PMSM is smaller than that of the conventional PMSM. However, since the vibration at 4fe, 6fe, 8fe and later frequencies is insignificant, the reduction has little effect on the total vibration level. The predicted vibration results verify the previous theoretical analysis, namely the bread-loaf magnet has negative effect on the total vibration performance of FSCW PMSMs. V. EXPERIMENTAL VERIFICATION A. Prototypes and Modal Test Fig. 15 shows the prototypes of two 12-slot/10-pole FSCW PMSMs. The modal test of the entail motor is carried out to obtain the natural frequencies for the 12-slot/10-pole PMSM. The PMSM is suspended by elastic rope to simulate unconstrained state as shown in Fig. 16. The hammering method is used in the modal experiment. Since the difference between two 12-slot/10-pole PMSMs is just in magnet structure, the modal parameters of two PMSMs are considered as the same. The modal experiment of one 12-slot/10-pole PMSM is conducted to avoid repetition. By hammering multiple positions on the motor surface and picking up the corresponding vibration data, multiple frequency response function curves of the motor structure are obtained. Then, the modal parameters are obtained by fitting multiple frequency response function curves in modal analysis software. The modal parameters including modal shapes, frequencies and damping ratio are listed in Table \u2163. It should be noted that the parameters of anisotropic materials in modal simulation are obtained from modal experiments. The equivalent material parameters can be obtained by adjusting the parameters in the finite-element model to approximate the modal test results. Authorized licensed use limited to: Carleton University. Downloaded on May 26,2021 at 11:29:26 UTC from IEEE Xplore. Restrictions apply. 2332-7782 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. The equivalent material parameters of the stator core, windings, and housing are given in Table \u2164. The back-EMF waveforms and harmonics analysis of the 12-slot/10-pole FSCW PMSM with conventional and breadloaf magnet are measured and compared as shown in Fig. 17, and the rotating speed is 600 r/min. The wave of the breadloaf PMSM is more sinusoidal than that of the conventional one. Also, it can be seen in Fig. 17(b) that the back-EMF harmonic content of the bread-loaf PMSM is smaller than of the conventional one. Although the bread-loaf PMSM has better back-EMF performance, it does not means that the bread-loaf PMSM has lower vibration response than the conventional one. In order to validate the theoretical vibration analysis of the 12-slot/10-pole FSCW PMSMs, the vibration and acoustic noise experiments of two 12-slot/10-pole FSCW PMSMs with conventional and bread-loaf magnet are conducted. The vibration and acoustic noise experiment setup of 12-slot/10pole FSCW PMSMs are shown in Fig. 18. It should be pointed out that due to the constraints of the platform, the vibration acceleration measured by the top accelerometer is smaller than that measured by the lateral accelerometers. Here, the vibration acceleration data collected by lateral accelerometers of both conventional and bread-loaf 12-slot/10-pole FSCW PMSMs are used for fair comparison. Fig. 19 shows the experimental results of vibration acceleration and sound pressure level of 12-slot/10-pole PMSMs with conventional and bread-loaf magnet structures. The motor rotates at 600 r/min. Hence, the electrical frequency is 50 Hz. The peaks of vibration and sound pressure level acceleration mainly appear at even times of the electric frequency, which are the frequencies of the main radial and tangential force harmonics. For the 12-slot/10-pole FSCW PMSMs, the most significant factor on vibration performance is the 2nd-order radial and tangential force, which is modulated from the 10th-order radial and tangential force. The frequencies of both 10th-order radial and tangential force are 2fe. As analyzed above, the amplitude of the 2pth-order electromagnetic force harmonics is significantly increased by the bread-loaf magnet. Compared to that of the conventional Hammer Accelerometer FSCW PMSM Data acquisition Authorized licensed use limited to: Carleton University. Downloaded on May 26,2021 at 11:29:26 UTC from IEEE Xplore. Restrictions apply. 2332-7782 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. one, the vibration acceleration of the PMSM with bread-loaf magnet has been significantly increased at 2fe. Meanwhile, the sound pressure level of the bread-loaf PMSM is 59.4 dB(A) at 2fe, which is larger than that of the conventional one. Since the sound pressure level at 2fe is far greater than that at other frequencies, the contribution of sound pressure level at this frequency to the overall noise is dominant. In addition, since the bread-loaf magnet reduce the radial and tangential force at 4fe, 6fe, 8fe and later frequencies, the amplitude of vibration and acoustic noise are decreased correspondingly. However, the vibration and acoustic noise decrease at 4fe, 6fe, 8fe and later frequencies have insignificant effect on the total performance. Consequently, the bread-loaf magnet has negative effect on the total vibration and acoustic noise performance of the 12-slot/10-pole FSCW PMSMs. The experimental results well verify above theoretical analyses. Fig. 20 gives the vibration acceleration of 12-slot/10-pole FSCW PMSMs with 5 Nm load, and the rotate speed is 600 r/min. The conventional and bread-loaf 12-slot/10-pole FSCW PMSMs have same stator structure, and they have same armature magnetic field in the air-gap. Therefore, the effects of armature magnetic field on vibration and acoustic noise of the conventional and bread-loaf 12-slot/10-pole FSCW PMSMs are consistent. Compared with the PMSM under noload condition, the amplitudes of vibration and acoustic noise of both conventional and bread-loaf PMSMs are increased. However, this does not affect the conclusion of the negative effect of bread-loaf magnet on vibration and acoustic noise in FSCW PMSMs. (a) VI. CONCLUSION In this paper, the effect of bread-loaf magnet on electromagnetic force and vibration performance of FSCW PMSMs have been investigated in depth. Firstly, the initial phase relationship of PM radial and tangential flux density has been clarified, which directly affect the phase relationship among electromagnetic force harmonics. Then, the effect of bread-loaf magnet on radial force and tangential force has been investigated, in which the force modulation effect has been considered. It has found that the bread-loaf magnet has negative effect on reducing the dominated electromagnetic force component. The magnet bread-loaf greatly weakens PM flux density harmonics. However, these weakened PM flux density harmonics are the sources of electromagnetic forces, which have opposite phase angle to that of the synthetic one. Afterwards, two 12-slot/10-pole FSCW PMSMs with conventional and bread-loaf magnet have been used to analyse the electromagnetic force and vibration response. The results disclose that the bread-loaf magnet has significantly negative effect on vibration performance in the FSCW PMSMs. Finally, the 12-slot/10-pole FSCW PMSMs with conventional and bread-loaf magnet have been manufactured, and the experiment results validate the theoretical analyses. According to the research of this paper, the bread-loaf magnet should be avoided in the design stage of FSCW PMSM with low vibration demand." ] }, { "image_filename": "designv10_9_0000167_robot.2010.5509701-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000167_robot.2010.5509701-Figure2-1.png", "caption": "Fig. 2: Section of rod from s to the free end ` subject to distributed forces and moments. The internal force and moment are also shown.", "texts": [ " The Bernoulli-Euler constitutive law can then be used to describe the relationship of the strain variables to the internal moment at s: M i(s) = Ki(s)\u2206ui(s), (6) where Ki(s) = diag{Ei(s)Ii(s) Ei(s)Ii(s) Gi(s)Ji(s)}, and M i(s) is the moment expressed in the local frame. We consider a single tube extending from arc length s = 0 to s = ` and subject to an arbitrary combination of distributed forces f(s) and moments l(s) along its length. We then cut a section of this tube at an arbitrary arc length location s, as shown in Fig. 2. By convention, we denote the internal force which the material of [s, `] exerts on the material of [0, s) as n(s), expressed in the global frame. Similarly, the internal moment which the material of [s, `] exerts on the material of [0, s) is m(s), expressed in the global frame. Summing the forces on the portion [s, `] we have, \u222b ` s f(\u03c3)d\u03c3 \u2212 n(s) = 0. (7) Similarly, summing the moments on the portion [s, `] about the world frame origin, we obtain\u222b ` s (r(\u03c3)\u00d7 f(\u03c3) + l(\u03c3)) d\u03c3 \u2212m(s)\u2212 r(s)\u00d7 n(s) = 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003535_j.mechmachtheory.2021.104436-Figure18-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003535_j.mechmachtheory.2021.104436-Figure18-1.png", "caption": "Fig. 18. 5-DOF mechanisms corresponding to the ankle motion fitting models U1S and U1S.", "texts": [ ") Based on the equivalent replacement method, there are totally 3072 5-DOF GSPMs (16 \u00d7 3 \u00d7 33+4 \u00d7 10 \u00d7 32 +12 \u00d7 3 \u00d7 3 \u00d7 3+4 \u00d7 3 \u00d7 10+4 \u00d7 35=3072). Among them, there are 8 compact GSPMs composed of the PES and OESgroups, which are shown in Table 10. Based on the first module combination kinematic analysis method, the kinematics of 5-DOF GSPMs in Table 10 are analyzed. The GSPMs meeting the motion requirements of the models U1S and U2S (Figs. 3(e) and (f)) are selected, which are respectively mechanisms 2-UR [RRR]&3-SR [RR] and UR [RRR]&UP [RRR]&3-SR [RR] shown in Fig. 18. Their kinematic performances are listed in Table 11. The mechanism 2-UR [RRR]&2-SR [RR]&SP [RR] is composed of the pure OES-group 2-SR [RR]&SP [RR] and pure PES-group 2-UR [RRR], and the mechanism UR [RRR]&UP [RRR]&2-SR [RR]&SP [RR] is composed of the pure PES-group UR [RRR]&UP [RRR] and pure OES-group 2-SR [RR]&SP [RR]. In order to avoid groups interference, the fixed coordinate system of the PES-group is rotated 180\u25e6 around its own z axis, and the obtained new coordinate system is set as the fixed coordinate system of the OES-group", " The correct transformation matrix above can be expressed as TUS = Tran(m1, m2 , m3) Rot(z, \u03c0) Rot(x, \u03b12) Rot(y, \u03b22)Rot(z, \u03b32) (46) where the O2 coordinates (m1, m2, m3) of UR [RRR]&2-SR [RR]&SP [RR] and UR [RRR]&UP [RRR]&2-SR [RR]&SP [RR] are respectively expressed as Eq. (14) and (15). In order to further solve the limb interference problem, the OES-limb SP [RR] of the OES-group shown in Fig. 17(c) as a whole is rotated clockwise around the z1 axis by 135\u25e6 to the middle of 2 limbs SR [RR], which is shown in Fig. 18. Obviously, the input parameter \u03b85 of the limb SP [RR] at the equilibrium position is \u20141.5\u03c0. Obviously, 2 GSPMs above have the same transformation matrices as the series mechanisms U1S and U2S. They have the same kinematic characteristics as the 5-DOF ankle motion fitting models, and achieve complete decoupling between position and orientation. Table 12 shows the 4-DOF basic GSPM configurations. They are composed of 2 PB-limbs and 2 OB-limbs. According to Tables 1, 2, 5 and 6, it can be comprehensively analyzed that line O1O2 rotates around origin O1 with 2 DOFs, which is equivalent to the U-joint motion" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002254_j.ijnaoe.2015.09.003-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002254_j.ijnaoe.2015.09.003-Figure3-1.png", "caption": "Fig. 3. Modified LOS guidance and a way-point.", "texts": [ " Furthermore, Ipp and Jpp are the moment of inertia of the propeller shaft and added moment of inertia of the propeller, respectively, and AE is the propeller expanded area. Both the blade area ratio Ae/Ao and pitch diameter ratio P/D of the propeller were set to 0.7. In the proposed DP system, ship control can be achieved by setting the desired way-points. The desired heading angle that is used to determine the ship heading is obtained using the line-of-sight (LOS) concept and the way-points. The LOS position can be calculated using LOS guidance (Fossen, 2002; Healey and Lienard, 1993). In Fig. 3, the modified LOS position (Xlos(t),Ylos(t)) and desired heading angle jd(t) required for heading control are obtained using the following equations: \u00f0Ylos\u00f0t\u00de YG\u00f0t\u00de\u00de2 \u00fe \u00f0Xlos\u00f0t\u00de XG\u00f0t\u00de\u00de2 \u00bc nLpp 2 \u00f032\u00de Ylos\u00f0t\u00de Yk 1\u00f0t\u00de Xlos\u00f0t\u00de Xk 1\u00f0t\u00de \u00bc Yk\u00f0t\u00de Yk 1\u00f0t\u00de Xk\u00f0t\u00de Xk 1\u00f0t\u00de \u00bc constant: \u00f033\u00de jd\u00f0t\u00de \u00bc tan 1\u00bd\u00f0Ylos\u00f0t\u00de YG\u00f0t\u00de\u00de; \u00f0Xlos\u00f0t\u00de XG\u00f0t\u00de\u00de \u00f034\u00de p tan 1\u00bd\u00f0Ylos\u00f0t\u00de YG\u00f0t\u00de\u00de; \u00f0Xlos\u00f0t\u00de XG\u00f0t\u00de\u00de p \u00f035\u00de \u00bdYk YG\u00f0t\u00de 2 \u00fe \u00bdXk XG\u00f0t\u00de 2 nLpp 2 \u00f036\u00de where nLpp is the permitted radius (i.e., n times the ship length), (Xk,Yk) is the present way-point, and (XG(t),YG(t)) is the ship position" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001791_j.mechmachtheory.2016.05.001-Figure3.1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001791_j.mechmachtheory.2016.05.001-Figure3.1-1.png", "caption": "Fig. 3.1. The force decomposition situation of SPR leg.", "texts": [ " For the SPS leg, only Fai produces longitudinal deformation along ri, it leads to Fri \u00bc WiFei ;Wi \u00bc 1\u00bd : \u00f012\u00de For the SPR type leg, there are two possible deformations produced by the active force Fai and the constraint force Fpi respectively. The active force Fai produces longitudinal deformation along ri, the constrained forces Fpi at S joint can be equivalent to one force Fpi,1 at ai, which produces a flexibility deformation in the SPR leg. Fpi,1 is parallel with Fpi and active in the opposite direction (see Fig. 3.1). Thus, Fri for the SPR leg can be expressed as following Fri \u00bc Fai Fpi;1 \u00bc Wi Fei ;Wi \u00bc 1 0 0 \u22121 : \u00f013\u00de For the UPR type leg, there are four possible decomposed force components which produce four possible deformations. The active force Fai produces longitudinal deformation along ri. The constrained forces Fpi at U joint can be equivalent to one force Fpi,1 at ai, which produces a flexibility deformation. Fpi,1 is parallel with Fpi and active in the opposite direction. The constrained torque Tpi in the UPR leg can be decomposed into two elements Tpi,1 and Tpi,2 which produce a torsional deformation and a bending deformation, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003137_j.mechmachtheory.2020.104180-Figure10-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003137_j.mechmachtheory.2020.104180-Figure10-1.png", "caption": "Fig. 10. Testing trajectory: (a) front view, (b) left view, (c) top view, (d) one pose of ABB IRB5400 on testing trajectory.", "texts": [ " (2) The initial solution obviously affects the performance of NR algorithm and the improper initial solution may result in the failure of NR algorithm. However, the results of proposed algorithm are very stable which are not sensitive to the given joint angles. To further prove the practicability of the proposed algorithm, it is applied to solve the inverse solutions of a series of end poses which forms a continuous trajectory of spray robot ABB IRB5400. A testing trajectory is firstly taught in robot simulation software RobotStudio as shown in Fig. 10 . Obviously, the orientation and position of the end of robot keep changing and the change of orientation is particularly dramatic at the corner of the trajectory. Fig. 11 shows the angle change of each joint on testing trajectory. 729 groups of joint angles are taken as testing samples from testing trajectory in a time interval of 0.024 s through the simulation function of RobotStudio. The inverse solution of the starting end pose is firstly determined automatically by finding the nearest group of inverse solution according to the given approximate angle value of each joint" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002212_icstcc.2019.8885596-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002212_icstcc.2019.8885596-Figure4-1.png", "caption": "Fig. 4. Quadrotor body coordinate system [1]. Fi are the sum forces for every motor and Mi are the torque vectors", "texts": [ " The control process uses three PID controllers for altitude and attitude control and preforms path generation as well almost all necessary processing for realizing a safe flight. The position corrections of the UAV are transmitted to FC using the MAVLink protocol. The control process also sends the current body position in local and global coordinates to the communication process which relays them to the ground station. For sake of clarity the quadrotor coordinate system Ob and the world coordinate system On are shown in Fig. 4. At the beginning of the inspection process the vehicle is navigated to the subject of inspection tower by using GPS measurements in world coordinate system, but during the tower and wire inspection their positions are converted to body coordinates in Ob. The wire following is performed using three PID controllers for altitude z, lateral position y, and yaw angle \u03c8 control respectively as shown in Fig. 5. The altitude loop controls the relative height of the quadrotor respective to the wire during inspection", " The yaw controller reference signal is the estimated relative angle of the wire. The angle estimation is performed by the vison system. The three PID controllers are realized on the control computer mounted on the vehicle. The computer sends the control commands to FC by means of MAVLink commands. To confirm the reliability and safety of the proposed autonomous inspection system numerous flight experiments were conducted. In this section some results are presented. Fig. 6(a) shows the error in y and z directions (see Fig. 4) during autonomous flight for inspection of 8mm thick ground wire over three transmission towers situated in straight line. The distance travelled is about 120m at low forward speed of 0.4 m/s. The peak in y direction of 0.4m occurred during overpassing the second tower where the wire position is lost for few seconds. It can be seen from same figure that the error in y direction is about \u00b10.15m and the altitude (z direction) error is approximately \u00b10.1m. The trajectory traveled in local coordinate system is shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001893_0142331218775477-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001893_0142331218775477-Figure1-1.png", "caption": "Figure 1. Reference frames of a medium-scale unmanned autonomous helicopter.", "texts": [ " The detailed processes are given as follows. Attitude model for UAH with main rotor flapping dynamics For convenience of analysis, two reference frames are defined before the discussion of the attitude dynamics of UAH, namely, the inertial frame orientation in the three-dimensional space. It means that the method of [100] orientation determination used in this study is feasible by observing the direction of primary dendritic arms in metallography. All samples were machined from the SX test bar by wire cutting after establishing the complete crystal coordinate system, as shown in Fig. 2a. The disc sample (Fig. 2b) was cut perpendicular to the [001] direction, while the cylindrical sample was cut circularly around the [010] direction. Before laser repair, a series of basic process experiments including surface remelting and cladding were conducted on the disc samples Note that the laser beam was perpendicular to the sample surface and moved along the [100] direction, as shown in Fig. 2b. Laser cladding experiments were carried out based on the results of laser remelting. The aim at these tests was to optimize the process window of laser cladding and therefore to produce a large SX deposit conveniently on the flat SX substrate. In order to evaluate the influence of bevel angle on stray grains formation, laser cladding was designed to conduct on the cylindrical sample, as shown in Fig. 2c. In this experiment, the angle (\u03b2) between the [001] direction and laser beam direction was changed by rotating the cylindrical sample along the [010] direction since the laser beam was fixed. The heat flow here also deviated from the [001] direction, which was called as off-axis heat flow. For repair testing, a v-groove was machined on the disc sample, and the laser beam scanning direction was along the [100], as shown in Fig. 4d and 4e. The laser repair processing parameters were optimized with the basic process experiment" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002624_j.compstruct.2019.111561-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002624_j.compstruct.2019.111561-Figure1-1.png", "caption": "Fig. 1. Schematics of the ultra-light release device. (a) Packaged configuration, (b) deployed configuration.", "texts": [ " It weighs only 6 g, and the release device (nonexplosive actuator) weighs less than 1 g. Tensile and fracture toughness tests have been conducted to explore the toughness improvement of SMPCs. The locking force is simulated and tested with consistent results. Also, shape memory recovery tests have been performed to investigate the shape memory effect and deployable properties. Feasibility study on a 3U CubeSat gives the release device a promising engineering application. A combination of HRM and spring hinge is also used for deployment in Fig. 1. The mechanism is comprised a curved release device and a locking member, of which the former is made of SMPC and connected to the main part of the satellite, and the latter is aluminum and linked with the deployable panel. These two components are both designed to be semi-cylindrical shape with interference to produce the locking force. And the non-explosive actuator (SMPC release device) is studied in detail. This device adopts an initial flat and temporary curved shape of 180\u00b0 bending angle. The deployment is achieved when SMPC release device recovers to its original flat shape and the deployable panel thus rotates outward 90\u00b0 under the function of pre-loaded torsion spring" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003063_s11071-020-05666-8-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003063_s11071-020-05666-8-Figure5-1.png", "caption": "Fig. 5 aOrientation of the input spur pinion, ainput, b angle between the reference teeth of the gears mounted on the same shaft, ba, and angle between the vectors directed to the effective mesh points, ua", "texts": [ " The other phase angle Pj represents the phase difference between em j\u00f0 \u00de t\u00f0 \u00de and em 1\u00f0 \u00de t\u00f0 \u00de where P1 \u00bc 0. Pj j \u00bc 2 to Nm\u00f0 \u00de can be defined as Pj \u00bc Xj a\u00bc2 Pa; \u00f025\u00de where Pa is the phase difference between em a\u00f0 \u00de t\u00f0 \u00de and the previous excitation em a 1\u00f0 \u00de t\u00f0 \u00de and it can be calculated as Pa \u00bc Z ua ba\u00f0 \u00de \u00fe p; \u00f026\u00de where Z represents the number of teeth of the driver gear in the ath mesh and ua is the angle between the vectors directed to the effective mesh points of the ath and the a 1\u00f0 \u00deth meshes (Fig. 5). ba represents the angle between the reference teeth of the gears mounted on the same shaft, which is shown in Fig. 5. The mesh stiffness functions of the gear meshes have the same phase relationship with each other. Furthermore, the mesh stiffness and static transmission error of each individual gear mesh are considered to be out-of-phase. Considering a total of V harmonics, the mesh stiffness at the jth mesh in the system is expressed in Fourier series as follows km j\u00f0 \u00de t\u00f0 \u00de \u00bc K0 m j\u00f0 \u00de \u00fe XV v\u00bc1 Kv m j\u00f0 \u00de sin vxjt \u00fe avj \u00fe vPj \u00fe p ; \u00f027\u00de where K0 m j\u00f0 \u00de and Kv m j\u00f0 \u00de are the mean value and the vth harmonic amplitude of the mesh stiffness of the jth mesh, respectively", " It is also noted that the hand of the spiral bevel gears is held as LR in this analysis since the concave flank of the spiral bevel pinion is the drive side in a normal operation; therefore, a change in the gear hand configurations of the spiral bevel gears requires the rotation directions of the gears to be reversed. It is observed that the response of the geared system having RL spiral bevel gears and LR helical gears, whose rotation directions are reversed, is exactly the same as that of the geared system with LR spiral bevel gears and RL helical gears. These results are not shown here for brevity. Figure 17 shows the change in the dynamic bearing force, F rms\u00f0 \u00de by , of bearing 2A as a function of the orientation of the input spur pinion, ainput (Fig. 5). In order not to change the phase angle between the gear meshes as defined by Eq. (25), ainput is taken as L3 = 234 mm L3 = 280 mm L3 = 320 mm L3 = 360 mm 0 2000 4000 6000 8000 10000 12000 0 1000 2000 3000 4000 5000 6000 D yn am ic M es h Fo rc e, F (rm s) m (3 ) [N ] Input Speed, \u03a9input [rpm] 1430 2380Fig. 14 Effect of the length of the third shaft on the dynamic gear mesh force, F rms\u00f0 \u00de m 3\u00f0 \u00de , at the helical gear mesh (3rd stage) forces, F rms\u00f0 \u00de b , of bearing 3B 0 2000 4000 6000 8000 10000 12000 0 10 20 30 40 50 60 Mbx in RL Mby in RL Mbx in LR Mby in LR D yn am ic B ea rin g M om en t, M (rm s) b [N m ] Input Speed, \u03a9input [rpm] Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000957_2013-01-2117-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000957_2013-01-2117-Figure2-1.png", "caption": "Figure 2. Robot's end-effector with SMRs.", "texts": [ " Robot's World and Tool Reference Frames Frame Fworld is determined by using three SMRs, fixed on the robot's base (the magnetic nest for one of them is visible in Fig. 1). The pose of frame F0 is then identified with respect to the Fworld. In order to do so, six parameters are used, xw, yw, zw, \u03b1w, \u03b2w and \u03b3w, which represent the position coordinates and the Euler angles (according to Fanuc's XYZ Euler angle convention) of F0 with respect to Fworld. Frame Ftool is fixed with respect to F6, and is therefore measured directly. In the measurement process, three 0.5\u2033 SMRs are placed on the end-effector (Fig. 2); the position of each of them is measured with respect to F6. The first calibration model uses only the D-H M parameters, and the six parameters identifying F0 with respect to Fworld. As mentioned earlier, the second calibration model also includes five compliance parameters. Robot Kinematic Model The robot's kinematic model is established by using the Modified D-H M notation [22]. Given the vector q of the active-joint variables (\u03b81, \u03b82, \u2026 \u03b86), the end-effector's pose is represented as follows: (8) where (9) and, for i > 2, (10) Finally, is the transformation matrix representing the pose of frame Ftool with respect to frame F6" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003281_j.jmatprotec.2021.117139-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003281_j.jmatprotec.2021.117139-Figure2-1.png", "caption": "Fig. 2. LMD schematic diagram.", "texts": [ " Microstructural studies were conducted in order to observe the grain growth differences between each build strategy and correlate the grain characteristics with the anisotropy from the tensile tests. The DMG MORI LaserTec 65 3D machine was used to fabricate AM built LMD specimens from Stainless Steel 316 L powder feed using three different build strategies: long unidirectional, bidirectional, and short unidirectional raster scan deposition process. The LMD process used in this experiment is illustrated in a schematic diagram as shown in Fig. 2, where a diode laser is used as a laser source, and argon as the shielding gas. A laser power of 1300 W, laser spot diameter of 3 mm, powder deposition rate of 14 g/min, scanning speed of 1000 mm/min and deposition track overlap of 60 % was used. The metal powder was fed coaxially and melted by a diode laser to form a melt pool at the substrate. The deposition head moves with accordance to the defined build strategies\u2019 scan paths and builds the part layer by layer. The powder material used in the LMD process was Stainless Steel 316 L" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002277_978-3-319-27131-6-Figure9.12-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002277_978-3-319-27131-6-Figure9.12-1.png", "caption": "Fig. 9.12 Fourth-order mode of a flexible inner race (k\u00bc+4)", "texts": [], "surrounding_texts": [ "without extensional mode in a cylindrical mode with the forward whirl at the excitation frequency \u03c9. In practice, the inner race is generally flexible in the radial direction. Thus, its vibration mode results from both extensional and cylindrical modes in the forward whirl at the excitation frequency \u03c9, as shown in Fig. 9.10. \u2013 If k\u00bc 2,. . ., N, the flexible inner race has a k-order harmonic mode that vibrates in the radial direction and moves in the forward whirl (k> 0) or backward whirl (k< 0) at the excitation frequency \u03c9 [3]. 194 9 Rotor Balancing and NVH in Rolling Bearings i\u03c9 inner race vibration mode i\u03c9 inner race vibration mode 1 2 3 1 2 3 \u03c9 orbit of race centers Fig. 9.9 Cylindrical mode of a rigid inner race (k\u00bc+1) i\u03c9 inner race vibration mode 1 2 3 1 2 3 \u03c9 orbit of race centers Fig. 9.10 Cylindrical mode of a flexible inner race (k\u00bc +1) Figures 9.11 and 9.12 show the elliptic mode (k\u00bc +2) and fourth-order mode (k\u00bc +4) of the flexible inner race in the forward whirl. In the following section, we discuss how to reduce the emitting noise from the vibrating bearing surface via structure-borne noise through the bearing housing to environment using the emitting airborne wavelength and resulting surface wavelength. The emitting airborne-noise wavelength results as \u03bba \u00bc cT \u00bc c f ) log10\u03bba \u00bc log10f \u00fe log10c \u00f09:18\u00de where c is the noise speed in the environment at 20 C (c 340 m/s) and f is the emitting frequency of the airborne noise. \u03c9 The resulting surface wavelength \u03bbr is function of the vibration integer mode k and surface frequency fs that depends on the surface stiffness: \u03bbr \u00bc F k; f s\u00f0 \u00de Note that the higher the vibration mode and the larger the surface frequency, the smaller the resulting surface wavelength involves. Generally, if the resulting surface wavelength is shorter than the emitting airborne-noise wavelength (\u03bbr< \u03bba), noise emits less to the environment [7]. As a result, the vibrations with high vibration modes emit less airborne noise to the environment than the lower vibration modes at a given airborne-noise frequency f. Furthermore, at increasing the surface frequency fs, the resulting surface wavelengths of high vibration modes reduce to wavelengths that are much smaller than the emitting airborne-noise wavelength at the frequency f. Hence, noise emits much less to the environment. In general, in order to reduce the airborne noise emitting to the environment at the given frequency f, the mode order k and the surface frequency fs must be chosen so that \u03bbr< \u03bba (s. Fig. 9.13). By experience, the extensional mode (k\u00bc 0), flexible cylindrical mode (k\u00bc +1), and elliptic mode (k\u00bc +2) mostly induce much noise than the higher-order modes (k> 2). The calculation of the eigenfrequencies in radial direction (undamped natural frequency [3]) of the bearing races is normally based on the vibration theory of a short circular ring. However, the eigenfrequency is simplified by NSK using the empirical cross-sectional shape constant K for the bearing races as f kHz\u00f0 \u00de \u00bc 941K D d\u00f0 \u00de D K D d\u00f0 \u00de\u00bd 2 k k2 1 ffiffiffiffiffiffiffiffiffiffiffiffiffi k2 \u00fe 1 p \u00f09:19\u00de where D is the outside diameter (mm), d is the bore diameter (mm) of the bearing, and k is the vibration mode. The shape constant of the outer race (OR) is empirically chosen K\u00bc 0.125 for OR with seal grooves and K\u00bc 0.150 for OR without seal grooves. Figure 9.14 displays the eigenfrequencies versus vibration modes for the outer race of the ball bearing type NSK 6305 with D\u00bc 62 mm and d\u00bc 25 mm. To avoid the resonance in the outer race, the excitation frequencies should be far away from the eigenfrequency that depends on the vibration mode of the bearing." ] }, { "image_filename": "designv10_9_0003195_s10846-019-01129-4-Figure13-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003195_s10846-019-01129-4-Figure13-1.png", "caption": "Fig. 13 Test T5. Propeller module assembly. a Propellers; b Motor; c Module final assembly", "texts": [ " The mechanical structure shows itself sufficiently robust even when dealing with a printed device for the next tests. Wires were able to be accessed from all derivation points, observing that one power circuit was able to feed up to two circuits. Fig. 12 presents the connection step by step. The mechanical design was, then, approved; \u2013 T5. Propulsion module test. A propulsion module was built with the actuators and ESC as described in previous sections. The first test evaluated the capacity of the module to connect to other modules, both in mechanical and electrical aspects (Fig. 13). The module passed in all structural tests and was considered suitable for the aircraft prototype. Electrical tests were performed, and the module was able to provide/receive electrical power to/from neighbor modules, even while operating. During trials, the temperature in all critical points has always remained within acceptable ranges. In this way, one concern with the architecture (the possible heating due to the circulation of high currents through long circuits) was discarded. \u2013 T6. Command module test" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000027_icorr.2011.5975445-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000027_icorr.2011.5975445-Figure5-1.png", "caption": "Fig. 5 User posture.", "texts": [ " If the robot detects a bump, the distance from the user\u2019s toe to the bump and the height of the bump are recorded. The scanning time and the angular resolution of the laser range finder are 80 msec and 0.36 deg, respectively. In order to prevent the user from losing his/her balance and falling down by the effect of the additional modification force by the perception-assist which is given regardless of the user\u2019s intention, the robot takes into account ZMP. The user\u2019s body is modeled as shown in Fig. 5. The supporting leg is found by tactile switches located in both soles. Then, the posture of the user\u2019s body region is c calculated using the joint angles of the supporting leg as follows. aspksphspb ,,, (7) where b is the angle of upper body region, sp,h, sp,k and sp,a are the angles of hip, knee and ankle joint of the support leg, respectively. sw,h, sw,k and sw,a are the angles of hip, knee and ankle joint of the swing leg. The positions of each joint are calculated as follows asplksp asplksp Lz Lx ,, ,, cos sin (8) Hspfksph Hspfksph Lzz Lxx ,, ,, cos sin (9) Hswfhksw Hswfhksw Lzz Lxx ,, ,, cos sin (10) )cos( )sin( ,,,, ,,,, kswHswlkswasw kswHswlkswasw Lzz Lxx (11) where Ll and Lf are the lengths of the shank region and the femoral region, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001890_j.triboint.2018.06.005-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001890_j.triboint.2018.06.005-Figure2-1.png", "caption": "Fig. 2. Schematic of the tooth profile.", "texts": [ " Then, the mapping relationship between the friction coefficients and the root stresses is reconstructed via ABRF. The reconstructed method is discussed in detail In Section 3.2. To construct the surrogate model for calculating dynamic root stresses with different friction coefficients, we first establish the geometric model of a spur gear and then perform finite element contact analysis. The basis parameters of the spur gears and lubricant are listed in Table 1. The theoretical tooth profile is derived according to the generation principle. Fig. 2 (a) shows one tooth profile in the coordinate system XfOYf, where O refers to the rotation center of the gear, and axis Yf refers to the symmetry axis of the tooth profile. rb and ra are the radii of the base circle and addendum circle, respectively. \u03b1 and r are the pressure angle and radius of the reference circle, respectively. ri is the distance between point O and arbitrary point i on the profile, and \u03b1i is the corresponding pressure angle. \u03b7i refers to the angle between axis Y and line Oi. In accordance with the generation principle of a tooth profile, the coordinates of arbitrary point i can be expressed as \u23a7 \u23a8\u23a9 = = x r \u03b7 y r \u03b7 sin cos i i i i i i (1) where, = \u2212 \u2212\u03b7 z \u03b1 \u03b1\u03c0 2 (inv inv )i i (2) = = \u2212\u03b1 \u03b8 \u03b1 \u03b1inv tani i i i (3) where, z and \u03b8i refer to the number of teeth and evolving angle at point i, respectively. Fig. 2 (b) shows the relative location of the hob and machined gear tooth. Point O represents the rotation center of the gear. Arc AKB represents the fillet of the hob and point C is the fillet center. rc refers to the fillet radius of the hob. The coordinate system XOY is the global coordinate. X1O1Y1 is the local coordinate system fixed on the hob, in which axis X1 is the pitch line of the hob and axis Y1 is a vertical line through point C. X2OY2 is the local coordinate system fixed on the gear, in which axis Y2 is the symmetry axis of the tooth alveolus" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002037_s11071-017-3461-x-Figure8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002037_s11071-017-3461-x-Figure8-1.png", "caption": "Fig. 8 The schematic diagram and topological graph of RAParM-I", "texts": [ "2 Constraint equations of system It should be mentioned that the dynamic model of system manifested in Eq. (37) is achieved through assembling the dynamic model of arbitrary flexible body j obtained via cutting virtually the joints of mechanism,which contains no constraints. In otherwords, the dynamic model shown in Eq. (37) is open-loop. Consequently, in order to establish the complete dynamic model of system, some constraint equations of system should be introduced into the open-loop dynamic model. The schematic diagramand topological graphof RAParM-I are shown in Fig. 8, fromwhich one can discover that there are three independent closed-loop constraints, i.e., loop I, II and III, respectively. In addition, since the joint position coordinates of flexible body j are introduced in the dynamicmodel, some related joint constraint equations of flexible body j should be constructed to restrain the redundant degrees of freedom caused by the joint position coordinates. Therefore, 8 set of joint constraint equations need to be constructed here. The 8 joints are joints A1, B1, D1, E1, A2, B2, D2 and E2, respectively", " Based upon above analysis, there are totally 22 constraint equations, which can be expressed as follows: (1) Constraint equations for joint A1 rA1 = [\u2212e 0 ] (39) (2) Constraint equations for joint B1 rB1 = [\u2212e 0 ] + R(\u03c61) [ l1 + uend1,x\u0304 uend1,y\u0304 ] (40) (3) Constraint equations for joint D1 rD1 = [\u2212e 0 ] (41) (4) Constraint equations for joint E1 rE1 = [\u2212e 0 ] + R(\u03c62) [ la + uend2,x\u0304 uend2,y\u0304 ] (42) (5) Constraint equations for joint A2 rA2 = [ e 0 ] (43) (6) Constraint equations for joint B2 rB2 = [ e 0 ] + R(\u03c65) [ l1 + uend5,x\u0304 uend5,y\u0304 ] (44) (7) Constraint equations for joint D2 rD2 = [ e 0 ] (45) (8) Constraint equations for joint E2 rE2 = [ e 0 ] + R(\u03c66) [ la + uend6,x\u0304 uend6,y\u0304 ] (46) (9) Constraint equations for closed-loop I rB1 + R(\u03c64) [ la + umid 4,x\u0304 umid 4,y\u0304 ] =rE1 + R(\u03c63) [ l1 + uend3,x\u0304 uend3,y\u0304 ] (47) (10) Constraint equations for closed-loop II rB2 + R(\u03c68) [ la + umid 8,x\u0304 umid 8,y\u0304 ] = rE2 + R(\u03c67) [ l1 + uend7,x\u0304 uend7,y\u0304 ] (48) (11) Constraint equations for closed-loop III rB1 + R(\u03c64) [ l2 + uend4,x\u0304 uend4,y\u0304 ] = rB2 + R(\u03c68) [ l2 + uend8,x\u0304 uend8,y\u0304 ] (49) where rjointi represents the position vector of a certain joint; umid j,x\u0304 and umid j,y\u0304 represent, respectively, the axial and transverse elastic displacements of element node at the position ofmiddle joint (see Fig. 8) for flexible body j ( j = 4, 8); uendj,x\u0304 and uendj,y\u0304 represent, respectively, the axial and transverse elastic displacements of element node at the position of end joint for flexible body j ( j = 1, 2, \u00b7 \u00b7 \u00b7 , 8). These above constraint equations can be uniformly expressed in a compact form as \u03a6 ( q(s), t ) = 0 (50) where \u03a6 ( q(s), t ) \u2208 R 22. Taking first-order differentiation for Eq. (50) with respect to time yields \u03a6c ( q(s), t ) q\u0307(s) + \u03a6 t = 0 (51) where\u03a6c ( q(s), t ) = \u2202\u03a6 ( q(s),t ) \u2202q(s)T represents the constraint Jacobian matrix of system, which is a sparse matrix, \u03a6 t = \u2202\u03a6 ( q(s),t ) \u2202t and q\u0307(s) =[r\u0307TO1 \u03c6\u03071 u\u03071Tf \u00b7 \u00b7 \u00b7 r\u0307TO8 \u03c6\u03078 u\u03078Tf ]T" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002796_j.ast.2019.105437-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002796_j.ast.2019.105437-Figure2-1.png", "caption": "Fig. 2. Illustration of combined spacecraft system and thruster layout.", "texts": [ " Then, the relative position vector can be given in the frame Fp by p = r p i,p \u2212 R p t rt i,t According to the equations of the two-body problem, the relative translational dynamics described in the frame Fp are governed by [27] p\u0307 = v \u2212 S ( \u03c9 p i,p ) p (4) mv\u0307 = \u2212mS ( \u03c9 p i,p ) v \u2212 \u03bcm r3 p ( p + R p t rt i,t )\u2212 mR p t r\u0308t i,t + f (5) where v \u2208R3 is the relative velocity vector; m \u2208R is the mass of the combined spacecraft; \u03bc \u2208 R is the gravity constant; rp \u2208 R is the distance from the center of the Earth to the spacecraft; f =[ fx f y f z ]T \u2208R3 denotes the orbital control force. 2.3. Thruster layout Considering the coupling between rotational and translational motion, a fully actuated actuation system is employed for the service spacecraft. Assume that the service spacecraft is of rectangular shape with dimension Li \u2208 R (i = x, y, z). The thruster configuration is given in Fig. 2 [28], where the total six thrusters Fi \u2208 R (i = 1, \u00b7 \u00b7 \u00b7 ,6) are assumed to be bidirectional with the positive direction shown in this figure. Accordingly, the control input to the combined spacecraft is defined as u = [ f \u03c4 ] = A F , (6) where F = [ F1 F2 F3 F4 F5 F6 ]T \u2208R6 is the control input, and the sign of Fi denotes the direction of the force; the input matrix A \u2208R6\u00d76 is given by A = \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 0 0 1 \u22121 0 0 0 0 0 0 1 \u22121 1 \u22121 0 0 0 0 L y 2 L y 2 0 0 Lz 2 Lz 2 \u2212 Lx 2 \u2212 Lx 2 Lz 2 Lz 2 0 0 0 0 \u2212 L y 2 \u2212 L y 2 Lx 2 Lx 2 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 ", " With the saturation compensator (25), design the control input Fin as Fin = A\u22121 [ N \u03b8\u0302 \u2212 Tx1 \u2212 K3s \u2212 \u03b23sig\u03b1 (s) \u2212 K4\u03be ] (26) with adaptive law \u02d9\u0302 \u03b8 = [\u2212NTs \u2212 P T\u03b24sig\u03b1 (W ) ] , (27) and the conditions \u03bbmin (K3) \u2212 0.5\u03bb2 max (K4) \u2212 0.5\u03b7 > 0, \u03bbmin (K2) \u2212 0.5\u03b7 \u2212 0.5 > 0 (28) hold, where \u03bbmax (\u00b7) denotes the maximum eigenvalue of \u00b7, and \u03b7 is a positive scalar. Then the tracking errors x1, x2 as well as estimation error \u03b8\u0303 converge to a neighborhood of the origin in finite time T , which is given in the proof. Since the actuation system is fully actuated with the thruster configuration shown in Fig. 2, from the expression of input matrix A, it is easy to verify that the input matrix A is full rank. Before giving the proof of the theorem, the following lemmas are introduced to help facilitate the stability analysis of the closed-loop system. In the following pages, let || \u00b7 || stand for the Euclidean norm or its induced norm. Lemma 1. [29] Let d = {x \u2208R12| ||x|| < d } represent an open set that contains the origin, the initial state x (0) and the reference trajectory xr . For ||x (0) || = b, there exists c with b < c < d and T2 > 0 such that the solution x (t) of the initial value problem defined by system (24) satisfies x (t) \u2208 a = {x \u2208R12| ||x|| < a } for all t < T2 , where a = (b + c) /2" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000503_bit.260130504-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000503_bit.260130504-Figure1-1.png", "caption": "Fig. 1. Cell for holding electrodes and solution. Legend: A. Auxiliary platinum electrode; C. Saturated calomel (reference) electrode; E. Enzyme-gelplatinum electrode; F. Fritted disc; G. Gaa dispersion tubes; J. O-ring joints; P. Platinum wires; T. Thermometer; V. Vent.", "texts": [ " An acrylamide gel-enzyme-platinum gauze matrix was prepared after the method of Hicks and Upkide.6 This method was chosen instead of covalent bonding because of its simplicity. The polymerization reagents, enzyme, and platinum gauze were placed to- BIOTECHNOLOGY AND BIOENGINEERING, VOL. XIII, ISSUE 5 GLUCOSE OXIDASE ELECTRODE 633 gether in a deoxygenated chamber. After photopolymerization to form the gel, the matrix was washed several times with distilled water and placed in an H-shape electrolytic cell. The cell is shown in Figure 1. Besides the enzyme electrode, the cell contained a platinum electrode and a saturated calomel electrode. The circuitry for the half-cell potential measurements is shown in Figure 2. In a typical run the cell was filled with a solution initially containing 0.01M D-glucose and 0.01M glucono-d-lactone in one molar phosphate buffer a t pH 7.2 and 37\u00b0C. After several hours nitrogen sweep to deoxygenate the solution, a 6 mA constant dc current was passed between the enzyme electrode and the auxiliary platinum electrode" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002209_s11071-019-05283-0-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002209_s11071-019-05283-0-Figure1-1.png", "caption": "Fig. 1 Schematic of the quadrotor UAV slung-payload system", "texts": [ " In Sect. 4, we detail the stability analysis of the quadrotor aerial transporting system with the proposed controller by using Lyapunov-based analysis. Section 5 shows experimental results and compares the proposed controller with linear quadratic regulator (LQR) controller with regard to the control performance. Finally, some concluding remarks are presented in Sect. 6. 2 Problem formulation This section describes the three-dimensional dynamic model for the quadrotorwith a cable suspended load.As Fig. 1 shows, the payload is attached to a quadrotor via a massless and unstretchable cable. And the payload is hinged by mean of a ball joint at the quadcopter\u2019s center of mass. To describe the kinematics of the quadrotor, let I = {X I , YI , Z I } represent a right hand inertia frame with Z I being the vertical direction to the earth. The body fixed frame is denoted byB = {XB, YB, ZB}. By using the Eulerian\u2013Lagrangian formulation, the threedimensional quadrotor with a slung-payload is given as follows: Mc(q)q\u0308 + C(q, q\u0307)q\u0307 + G(q) = f (t) + fd(t) (1) where q(t) = [x(t), y(t), z(t), \u03b3x (t), \u03b3y(t)]T \u2208 R 5 denotes the system state vector, x(t), y(t), z(t) represent the quadrotor position in the X I , YI , Z I directions, respectively, \u03b3x (t), \u03b3y(t) represent the payload swing angle about X I and YI , respectively, as shown in Fig. 1. The terms Mc(q), C(q, q\u0307) \u2208 R 5\u00d75, G(q), f (t), fd(t) \u2208 R 5 in (1) denote the inertia matrix, the centripetal-Coriolis matrix, the gravity vector, the con- trol input vector, the aerodynamic drag force vector, respectively, which are defined as \u23a7 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 Mc(q)= \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 mc11 0 0 mc14 mc15 0 mc22 0 0 mc25 0 0 mc33 mc34 mc35 mc41 0 mc43 mc44 0 mc51 mc52 mc53 0 mc55 \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 mc11 = mc22 = mc33 = mq + m p mc55 = m pl2 mc44 = m pl2C2 y mc14 = mc41 = m plCx Cy mc15 = mc51 = \u2212m plSx Sy mc25 = mc52 = m plCy mc34 = mc43 = m plSx Cy mc35 = mc53 = m plCx Sy , (2) \u23a7 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 C(q, q\u0307) = \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 0 0 0 c14 c15 0 0 0 0 c25 0 0 0 c34 c35 0 0 0 c44 c45 0 0 0 c54 0 \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 c14 = \u2212 m pl\u03b3\u0307x Sx Cy \u2212 m pl\u03b3\u0307yCx Sy c15 = \u2212 m pl\u03b3\u0307x Cx Sy \u2212 m pl\u03b3\u0307y Sx Cy c25 = \u2212 m pl\u03b3\u0307y Sy c44 = \u2212 m pl2y \u03b3\u0307yCy Sy c45 = \u2212 m pl2x \u03b3\u0307x Cy Sy c54 = m pl2x \u03b3\u0307x Cy Sy c34 = m pl\u03b3\u0307x Cx Cy + m pl\u03b3\u0307y Sx Sy c35 = m pl\u03b3\u0307x Sx Sy + m pl\u03b3\u0307yCx Cy , (3) \u23a7 \u23aa\u23a8 \u23aa\u23a9 G(q) = [ 0 0 g31 g41 g51 x ]T g31 = (mq + m p)g g41 = m pglSx Cy g51 = m pglCx Sy , (4) f = [ fx fy fz 0 0 ]T , (5) fd = [ \u2212 cx x\u0307 \u2212cy y\u0307 \u2212cz z\u0307 \u2212c\u03b3x \u03b3\u0307x \u2212c\u03b3y \u03b3\u0307y ]T " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001880_j.mechmachtheory.2018.04.001-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001880_j.mechmachtheory.2018.04.001-Figure5-1.png", "caption": "Fig. 5. Model for loaded tooth contact analysis.", "texts": [ " M 1 h = \u23a1 \u23a2 \u23a3 1 0 0 P 0 cos \u03d5 1 \u2212 sin \u03d5 1 0 0 sin \u03d5 1 cos \u03d5 1 0 0 0 0 1 \u23a4 \u23a5 \u23a6 (16) M h 2 = \u23a1 \u23a2 \u23a3 cos 1 sin 1 sin \u03d5 2 \u2212 sin 1 cos \u03d5 2 G cos 1 0 \u2212 cos \u03d5 2 \u2212 sin \u03d5 2 E \u2212 sin 1 cos 1 sin \u03d5 2 \u2212 cos 1 cos \u03d5 2 \u2212 G sin 1 0 0 0 1 \u23a4 \u23a5 \u23a6 (17) where 1 = + . { r (1) h = r (2) h n (1) h = n (2) h (18) By solving Eq. (18) , the transmission error and contact path are determined. The loaded tooth contact analysis (LTCA) plays an important part in designing the spiral bevel gear with high performance, and it uses computer technology to simulate the gear meshing process under load to obtain the working performance of gear under the actual working condition [28,29] . The LTCA model is shown in Fig. 5 , and the basic principle is as follows: Firstly, based on TCA, the initial tooth surface clearance is solved. Secondly, the flexibility matrix of tooth surface node is obtained by the finite element method, and flexibility matrix interpolation is carried out. Thirdly, based on the deformation coordination equation and force balance condition, a mathematical programming model for loading issue of spiral bevel gear is established, as shown in Eq. 19 . Finally, the discrete point load and tooth deformation of gear under load are obtained by the nonlinear programming method" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002277_978-3-319-27131-6-Figure8.6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002277_978-3-319-27131-6-Figure8.6-1.png", "caption": "Fig. 8.6 Stress zones on the bearing surfaces", "texts": [ " The tangential force acting upon the asperity results from the viscose shear stress of the oil film as FT \u00bc \u03c4 A \u00bc \u03b7 _\u03b3 ; T\u00f0 \u00de\u2202U \u2202h A \u03b7 _\u03b3 ; T\u00f0 \u00deUA h \u00f08:9\u00de where \u03b7 is the oil dynamic viscosity that depends on the oil shear rate and temperature U is the circumferential velocity of the rolling element h is the oil-film thickness in the contact zone A is the effective area of the contact area 8.2 Failure Mechanisms in Rolling Bearings 177 Equation 8.9 shows that the higher the rolling element velocity U, the larger the tangential force involves. Similarly, the smaller the oil-film thickness h in the EHL, the larger the tangential force acts upon the interface surfaces in the contact area, as shown in Fig. 8.6. At the raceway, the asperity deforms under the tangential force FT. The bending stress on the right-hand side (RHS) of the asperity foot is a tensile stress and on the left-hand side (LHS) of the asperity foot is a compressive stress. On the contrary, at the rolling elements under the tangential force \u2013FT, the bending stress on the RHS of the asperity foot is a compressive stress and on the LHS of the asperity is a tensile stress (s. Fig. 8.6). The initiated microcracks in the bearing surfaces are resulted from the impurity of bearing steels in the production process. If the tensile stress exceeds the ultimate tensile stress of the material, the asperities break up; and it causes additional microcracks in the tension and compressive zones of the ball and raceways. The viscous tangential force in Eq. 8.9 opens the initiated microcracks on the raceway surface in the contact area wider in the rolling direction. The microcracks are closed again when passing the contact zone" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002119_j.apor.2018.07.015-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002119_j.apor.2018.07.015-Figure2-1.png", "caption": "Fig. 2. Earth-fixed frame and body-fixed frame.", "texts": [ " (3) Compared with the FTC schemes in [15\u201317], our proposed scheme integrating fault estimation and FTC can avoid the FDI time delay problem, which improves the reliability of the whole FTC system. The rest of this paper is organized as follows. Section 2 presents the mathematical model to capture the nonlinear motion of a dynamically position vessel. Section 3 proposes the FTC scheme for DP system of vessels under thruster faults. Section 4 provides simulation studies with comparisons on a 1:70 scale model vessel. Section 5 concludes this paper. The reference coordinate frames of vessel motion is illustrated in Fig. 2, the earth-fixed reference frame is denoted as XEOYE and the body-fixed frame is XAY. The coordinate origin O of the earth-fixed reference frame is the original position of the vessel. The axis OXE is directed to the north and the axis OYE is directed to the east. The coordinate origin A of the body-fixed frame is located at the gravity center of the vessel. The axis AX is directed from aft to fore and the axis AY is directed to starboard. The kinematics and kinetics equations of a dynamically positioned surface vessel can be described, respectively, by the following equations: =\u03b7 R \u03c8 \u03c5\u02d9 ( ) (1a) = \u2212 + +M\u03c5 D\u03c5 \u03c4 d t\u02d9 ( ) (1b) where \u03b7=[x, y, \u03c8]T denotes the position vector of the vessel in the earth-fixed frame, consisting of the transverse position x, longitudinal position y, and the yaw angle \u03c8\u2208 [0, 2\u03c0)" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001882_icmimt.2018.8340426-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001882_icmimt.2018.8340426-Figure2-1.png", "caption": "Figure 2. The domain of heat transfer in solids.", "texts": [ " The default thermal conductivity is based on the selected material. Thermal insulation is selected as the default boundary condition for the heat transfer interface. This indicates there is no heat flux across the boundary and thus, the domain is well insulated. For this to be true, the temperature on one side of a boundary must be equal to the other side. Five deposited beam powder nodes are used to model the heat source brought by narrow laser metal deposited beam to a selected boundary shown in Fig. 2. The selected values for deposited beam power, beam origin point, beam orientation and profile is shown in Fig. 3. For the mesh analysis, the different mesh size must be defined for both the laser track and substrate. The maximum element size of 0.1cm and minimum element size of 0.08cm are defined for the laser track section. For the substrate, the maximum element size of 0.4cm and minimum element size of 0.2cm are defined respectively (Fig. 4). The \u201cStudy\u201d section holds all the nodes that define how to solve a model" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001372_s11465-016-0389-7-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001372_s11465-016-0389-7-Figure6-1.png", "caption": "Fig. 6 Motion line graph in the third chain and the corresponding constraint line graph", "texts": [ " 3) The relative direction between the couple in the motion line graph and the couple in the corresponding constraint line graph can be arbitrary. As shown in Fig. 5, \u03c4$v \u00bc 0 is always true in any condition. 2.2.2 Analysis procedures The mobility analysis for the presented mechanism can be generally classified into three steps based on the method and rules discussed in Section 2.2.1. 1) The constraint line graph for each limb or kinematic chain is generated. The four kinematic chains are identical for the PKM illustrated in Figs. 1 and 2. The third kinematic chain is used as an example. As shown in Fig. 6, the motion line graph is composed of four rotations, namely, \u03c91, \u03c92, \u03c93, and \u03c94, and a translation v, which is perpendicular to C3P3 and lies on the plane of the parallelogram mechanism [28]. The motion line graph is five-dimensional, and the corresponding constraint line graph should be one-dimensional. The rules require that no line vector in the constraint line graph should simultaneously intersect with \u03c91, \u03c92, \u03c93, and \u03c94, and should be perpendicular to v. Moreover, only a couple \u03c4 that is simultaneously perpendicular to \u03c91, \u03c92, \u03c93, and \u03c94 can be found. Therefore, the constraint line graph for this chain is a one-dimensional couple constraint, the direction of which is illustrated in Fig. 6. 2) The constraint line graph for the mobile platform is generated by simultaneously considering all the chains of the mechanism. As shown in the arrangement of the four kinematic chains of the PKM in Figs. 1 and 2, the couple constraint provided by the first chain is parallel to that of the third chain and perpendicular to those of the second and fourth chains. Notably, the couple constraint of the second chain is parallel to that of the fourth chain, and all the four couples are parallel to the horizontal plane (i" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001038_1350650116689457-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001038_1350650116689457-Figure3-1.png", "caption": "Figure 3. The tested bearing and its cage: (a) bearing specimen; (b) cage in the tested bearing.", "texts": [ " The geometrical parameters are listed in Table 1. In addition, the cage is made of 45# steel. The bearing cage is guided by the inner ring. Also, there are two guiding lands on either side of the inner ring. In order to measure the motion of the cage mass center in the radial direction and make the eddy transducer probes closer to the cage surface, the outer ring is cut specially to form four grooves, which is located 90 apart in circumference. Each of the cut grooves is of 20mm width and 3.5mm depth, as shown in Figure 3(a). The grooves do not reach the outer raceway. Then, the cage is exposed to larger surface area, which ensures the eddy probes to transduce perfect motion signals of the cage as shown in Figure 3(b). The motions of the cage in radial directions are measured by two probes (yc, zc) installed in the bearing house 90 apart and in the corresponding grooves in the outer ring. The axial motions are also measured by the two probes (xc1, xc2), which are fixed on a panel (shown in Figure 4) and mounted parallel to the bearing axis, focused on the cage side face, 180 apart. The bearing test rig is established as shown in Figure 5, which consists of motor, coupling, rotating shaft, supporting and tested bearings, and load devices" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001014_wcica.2012.6358437-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001014_wcica.2012.6358437-Figure2-1.png", "caption": "Fig. 2. Rotor number and body frame of 4SP quadrotor", "texts": [ " Section III presents the nonlinear dynamic modeling of the 4SP quadrotor, while Section IV illustrates an optimal propellers orientation design. Section V shows the parameters identification results and model verification through computer simulation. Finally, the major conclusions of the paper are drawn in Section VI. 3270 978-1-4673-1398-8/12/$31.00 \u00a92012 IEEE II. 4SP QUADROTOR DESIGN AND WORKING PRINCIPLE A 4SP quadrotor consists of four standard propeller systems in which all four of them spins at counter-clockwise direction, as shown in Fig. 2. Here, the rotor numbers 1, 2, 3 and 4 correspond to the front, left, back, and right rotors. In order to maintain a zero net yaw moment (rotation around z-axis), propeller 2 and 4 are mounted slightly slanted along the x-axis at an angle of \u03b1 (see Fig. 3). Note that the magnitude of the slanting angle, \u03b1, is the same for both propeller 2 and 4, but in the opposite direction. The optimal design value of \u03b1 will be formulated in Section IV. In hovering flight, the sum of rotational moments from each rotor will be completely canceled out by the moment due to the thrust components on x-axis of rotor 2 and rotor 4", " One is the North-East-Down (NED) frame and the other is the body frame. The NED frame is stationary with respect to a static observer on the ground, where axes point towards the North, East and downwards direction. The body frame is placed at the Center of Gravity (CG) of the quadrotor helicopter, where its origin and orientation move together with the helicopter fuselage. It is important to note that the x-axis pointed to the front of the aircraft, the y-axis to the right of the aircraft, and the z-axis pointed downwards in body frame (see Fig. 2). The equations of motion are more conveniently formulated in the body frame for a few reasons [8]: 1) The inertia matrix is time-invariant; 2) Quadrotor body symmetry can greatly simplify the equa- tions; 3) Measurement obtained onboard are mostly given in body frame, or can be easily converted to body frame; 4) Control forces are almost always given in body frame. To obtain the translational and rotational motions between the NED and the body coordinate systems, one has the following well-known navigation equations [9][10]: P\u0307n = Rn/bVb, (1) \u0398\u0307 = S\u22121\u03c9, (2) where the rotational matrix, Rn/b, and the lumped transformation matrix, S\u22121 are given by Rn/b = [ c\u03b8c\u03c8 s\u03c6s\u03b8c\u03c8 \u2212 c\u03c6s\u03c8 c\u03c6s\u03b8c\u03c8 + s\u03c6s\u03c8 c\u03b8s\u03c8 s\u03c6s\u03b8s\u03c8 + c\u03c6c\u03c8 c\u03c6s\u03b8s\u03c8 \u2212 s\u03c6c\u03c8 \u2212s\u03b8 s\u03c6c\u03b8 c\u03c6c\u03b8 ] , (3) S\u22121 = [ 1 s\u03c6t\u03b8 c\u03c6t\u03b8 0 c\u03c6 \u2212s\u03c6 0 s\u03c6/c\u03b8 c\u03c6/c\u03b8 ] , (4) with s\u2217 = sin (\u2217), c\u2217 = cos (\u2217), and t\u2217 = tan (\u2217)" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002970_s00773-020-00746-1-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002970_s00773-020-00746-1-Figure1-1.png", "caption": "Fig. 1 The ship position and motion parameters", "texts": [ " Furthermore, the nonlinear observer is provided to estimate the surge, sway velocity, and the LESO is applied to approximate the high order state in MPC design, namely the yaw rate. This paper is organized as follows: after this introduction, the ship model and control objective are presented in Sect.\u00a02. In Sect.\u00a03, the path following controller that includes LOS, MPC, nonlinear observer and LESO is presented. Then, Sect.\u00a04 provides the compared simulation analysis. Finally, the concluding remarks are given in Sect.\u00a05. The ship position in the horizontal plane and the motion parameters under current disturbance are shown in Fig.\u00a01. The x-axis and y-axis point to the true North and the true East, respectively. \u03c6 is the heading angle from the x-axis. u and v are the surge and sway velocity through the ground, and V = (u2 + v2)1/2 is the ship speed through ground. r is the yaw rate. Vc and \u03c6c are the current speed and direction, respectively. ur and vr are the longitudinal and lateral speed through water, respectively. \u03b2 = arctan(v/u) is the sideslip angle. \u03b4 is the rudder angle, |\u03b4|\u2264 35\u00b0and |\u0394\u03b4|\u2264 3\u20136\u00b0/s are the input constraints including rudder amplitude and rate limit, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000986_j.triboint.2013.02.026-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000986_j.triboint.2013.02.026-Figure2-1.png", "caption": "Fig. 2. Test g", "texts": [ " Prior to the tests with the selected gear oils, several runs (in different days), at the same operating conditions were conducted in order do assess the stability of the test rig and the repeatability of the measurements. The temperature measurements (DTor and DTow) presented a standard deviation of 0:15% of the measured temperatures between tests. The torque measurements presented a standard deviation of 0:2% of the measured value. The speed measurements also presented a standard deviation of 0:2% of the measured speed. Fig. 2 shows a schematic view of the test gearbox. This gearbox has three shafts where five pinions are mounted. The pinions in the middle shaft (pinions 2 and 3) are keyed while the pinions on the first and third shafts are mounted over needle bearings. All of the shafts are supported by ball or roller bearings. The test gearbox allows the selection of two different kinematic relations. Table 1 Performance specifications of the torque transducers. Transducer Capacity (Nm) Nonlinearity (%)a Hysteresis (%)a Repeatability (%)a Temperature rangeb (1C) Input torque 5650 70" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001591_j.mechmachtheory.2016.09.004-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001591_j.mechmachtheory.2016.09.004-Figure1-1.png", "caption": "Fig. 1. Sketch of the 3-RRR PPM.", "texts": [ " Section 3 describes the conditions characterizing the inverse singularities and the forward singularities of the 3-RRR PPM. Section 4 describes the proposed method of the singularity-free path planning with working mode conversion. Section 5 presents the experimental results for verifying the theoretical analyses of the singularities; kinematic uncertainties close the forward singularities and path planning with working mode conversion. Finally, conclusions are drawn in Section 6. The schematic diagram of the 3-RRR PPM with revolute joints is shown in Fig. 1. It consists of a moving equilateral triangular end-effector ( C C C1 2 3) linked to the ground using three legs and a fixed base A A A1 2 3 joined by three serial kinematic chains. Each chain is constituted entirely of three revolute pairs and two links. Each kinematic chain is formed by a proximal link A Bi i and a distal link B Ci i, and the joints are located at Ai, Bi and Ci being of the revolute type (in this paper, i = 1, 2, 3). The length of the proximal links is l1, and l2 is the length of the distal links" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001524_s12206-014-0931-7-Figure14-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001524_s12206-014-0931-7-Figure14-1.png", "caption": "Fig. 14. The 4(rT)2PS with two-two parallel planes.", "texts": [ " Considering two planes are parallel among the four, a special case can be categorized into this section that while two A1 \u22111 A2 n1 n1 A3 n1 A1 A2 \u22111 \u22112 \u22113 n1 n1 A3 \u22114 n4 \u22113 A4 n4 \u22114A4 Fig. 12. The 4(rT)2PS with three parallel planes. A1 \u22111 A2 n1 A3 n1 A1 A2 \u22111 \u22113 n1 A3 \u22114 n4 A4 n4 \u22114A4 n3 \u22112 n3 \u22113 \u22113 A3 A2 \u22112 \u22111 n1 n1 A1 \u22114 n4 A1 \u22111 A2 n1 A3 n1 n1 A1 A2 \u22111 \u22113 n1 A3 \u22114 n4 A4 n4 \u22114A4 A4 n3 \u22112 n3 \u22113 \u22113 n3 (a) General case (b) d1-d2 = l12 Fig. 13. The 4(rT)2PS with two parallel planes. planes are parallel, the other two are also parallel to each other as in Fig. 14(a). The geometric constraint is similar with Eq. (21) but giving k1 = 0, k3 = 1 which shows two translation and two rotation constraints and the mechanism has two DOFs with one rotation and one translation perpendicular to both n1 and n3. Another case with two pairs of parallel constraint planes [39] is shown in Fig. 14(b) with both pairs of parallel planes coincident (d1 = d2 and d3 = d4) and its mobility is one rotation and one translation. When further considering that the two constraint planes are perpendicular to each other in Fig. 14(b), line A1A2 will be perpendicular to A3A4. At the configuration that A1A2 is perpendicular to constraint plane \u22113 (A3A4 is perpendicular to constraint plane \u22111 at the same time), the rotational constraints can be written as: 1 2 1 12 3 1 3 4 3 34 1 3 ( ). . 0 ( ). . 0 l l \u00a2 \u00a2- = =\u00ec\u00ef \u00ed \u00a2 \u00a2- = =\u00ef\u00ee R R a a n n n a a n n n . (22) Thus, the two constraints are dependent and the mechanism at this configuration has one translational and two rotational DOFs about normal n1 and n3. However, when the mechanism rotates about any direction of the two, Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002982_j.ijhydene.2020.07.115-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002982_j.ijhydene.2020.07.115-Figure1-1.png", "caption": "Fig. 1 e (a) Schematic and (b) detailed structure of the direct for electrodes.", "texts": [ " The part of cotton threads that needed to load the catalyst (with a length of 1 cm) was dipped in the prepared catalyst ink and quickly taken out, and then dried at room temperature. The dipping step was repeated until the desired Please cite this article as:Wang S et al., A direct formatemicrofluidic f of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.07.115 catalyst loading was reached. The prepared cotton threadbased electrodes were used as both the anode and cathode. Fuel cell structure Fig. 1 demonstrates the schematic of the direct formate microfluidic fuel cell with cotton thread-based electrodes. The components of the fuel cell were Parafilm sealing film, cotton thread-based electrodes, current collector and support structure made of Polymethyl methacrylate from top to bottom. The function of the sealing film was to reduce evaporation of reaction solutions and isolate from the ambient air. 10 cotton threads taken from hydrophilic medical gauze swab were placed in parallel with a width of 1 mm to form the anolyte or catholyte flow channel" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002116_itec.2018.8450250-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002116_itec.2018.8450250-Figure2-1.png", "caption": "Fig. 2: Schematic representation of the laser beam melting system [8]", "texts": [ " LBM \u2013 also referred as SLM (selective laser melting) \u2013 is a powder bed based additive manufacturing process for the production of metallic components. LBM can be used to manufacture complex components that are currently being used for example in aerospace engineering, medical technology and tool or mold making. The use in drive technology is currently limited, which is why a more detailed investigation of the potentials and application of the LBM in drive technology is necessary [3], [7]. The process flow is described below and shown in Fig. 2. The supply of the powder is carried out in layers by means of a recoater. In the next step, the laser exposures the area of the component layer. For this purpose, the digital component is divided into layers in the pre-process. The generated layer information is used to control the laser. The laser locally melts the areas that need to be solid for the component. Due to this process, components with a material density of over 99% can be manufactured. After these steps, the completion of a layer is completed" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001069_j.snb.2017.12.138-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001069_j.snb.2017.12.138-Figure1-1.png", "caption": "Fig. 1. Schematic representation of cartap recognition of P(S-VP)-AgNPs through electrostatic interactions.", "texts": [ " P(S-VP)-AgNPs and cartap response As mentioned earlier, P(S-VP) block copolymers tend to make icelles in toluene that is good solvent for PS while non-solvent or P2VP. PS block makes the corona while P2VP tend to be away rom toluene making core of the micelles. AgNPs tend to be inside he core since they also don\u2019t prefer a non-polar environment. In he process, when cartap is present in the solution, it tends to be ttracted towards positive charges on the P2VP block inside core of icelles because of its resonating structure (Fig. 1). The mean size and size distribution of P(S-VP)-AgNPs and P(SP)-AgNPs/cartap solution were analyzed using zetasizer. The size istribution profile of P(S-VP)-AgNPs and P(S-VP)-AgNPs/cartap nm, PDI: 0.22; B) P(S-VP)-AgNPs/cartap. avg. size: 89.68 \u00b1 0.57 nm, PDI: 0.08. showed a mean diameter of 104.2 \u00b1 0.68 and 89.68 \u00b1 0.57 nm with PDI of 0.22 and 0.08, respectively (Fig. 2A, B). Interestingly, the mean diameter of P(S-VP)-AgNPs turned out to be more homogeneous after addition of cartap, endorsed by AFM analyses too", " The regularity in the shape and reduction in size of the NPs by addition of cartap can be attributed to the balancing of the surface charges. Zeta potential (surface charge) reveals the interactions of nanoparticle with analyte and surroundings. It can greatly influence particle stability through electrostatic repulsion between particles. The surfaces of P(S-VP)-AgNPs have a positive charge of 20.8 mV, whereas P(S-VP)-AgNPs/cartap exhibit zeta potential of 27.7 mV (Fig. 4A,B). It seems that positive surface charges on P(S-VP)-AgNPs are neutralized by cartap through electrostatic interactions (Fig. 1). FTIR studies of P(S-VP), P(S-VP)-AgNPs, and P(S-VP)AgNPs/cartap were performed to have a deeper understanding of the mechanism of NP formation and recognition of cartap in solution. A comparison between FTIR spectra of P(S-VP), P(S-VP)AgNPs, and P(S-VP)-AgNPs/cartap suggested that nitrogen atoms in the backbone of polymer stabilized AgNPs, since C N stretching vibration peak at 1592 cm\u22121 of P(S-VP) disappeared upon the formation of AgNPs, while the rest of the characteristics peaks for S. Rahim et al" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002277_978-3-319-27131-6-Figure1.7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002277_978-3-319-27131-6-Figure1.7-1.png", "caption": "Fig. 1.7 Curvatures of a plane surface S", "texts": [ " The operating contact angle \u03b1 is calculated using some trigonometric relations of the ball bearing as [1, 3] \u03b1 \u00bc sin 1 \u03c10 sin \u03b10 \u00fe \u03b4affiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u03c120 cos 2\u03b10 \u00fe \u03c10 sin \u03b10 \u00fe \u03b4a\u00f0 \u00de2 q 0 B@ 1 CA \u00bc sin 1 sin \u03b10 \u00fe \u03b4a \u03c10ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi cos 2\u03b10 \u00fe sin \u03b10 \u00fe \u03b4a \u03c10 2 r 2 664 3 775 \u00f01:12\u00de where \u03b4a is the axial displacement of the bearing due to the thrust load. 0 \u03b1 1.3 Bearing Geometry 9 the axial displacement \u03b4a of the bearing vanishes according to Eq. 1.12. The curvature of a plane curve at a given point I is defined as the inversion of the radius of the circle that contacts the curve at this point. In the case of a convex curve at the point I, the curvature has a positive value and a negative value for a concave curve at the point O, as shown in Fig. 1.7. Obviously, the curvature of a line equals zero because the radius at any point on the line is infinite. Note that the larger curvature the plane curve has, the sharper the curve is and vice versa. The curvature of a plane curve at any point is written in its radius r at the contact point as \u03c1 1 r \u00f01:13\u00de where the plus sign is for a convex curve and the minus sign for a concave curve. In fact, the bearing components of balls and inner and outer raceways are not plane surfaces but three-dimensional surfaces" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003369_j.mechmachtheory.2021.104386-Figure9-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003369_j.mechmachtheory.2021.104386-Figure9-1.png", "caption": "Fig. 9. Mesh force of helical gear.", "texts": [ " (22) Here, \u03b1min and \u03b1max denote the minimum and maximum pressure angles of the gear pair, respectively, and T 1 A and AE denote the distances between the two points. To determine the mesh position of a helical gear in each slice over time, the instantaneous roll angle at the first tooth pair in the mesh is defined. Then, the instantaneous pressure angle of each slice is calculated using Eq. (15) . If the value exists between \u03b1min and \u03b1max , \u03b1i , \u03be1 ,n , and \u03be2 ,n are defined because the corresponding slice is in the mesh. Otherwise, the slice is considered not in the mesh. As shown in Fig. 9 , the mesh force of the helical gear pair acts normal to the contact line (blue line). The mesh force is divided into transverse mesh force and the axial mesh force by the helix angle, which are calculated using Eqs. (23) and (24) . F t = F n cos \u03b2 (23) F a = F n sin \u03b2 (24) This study aims to propose a model that rapidly predicts the LSTE of a helical gear pair; therefore, only the transverse mesh stiffness is considered. Using the slice theory [28\u201330] , the helical gear is divided into several spur gear slices, and the transverse mesh stiffness is calculated from the total potential energy of each slice" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001545_j.engstruct.2015.09.008-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001545_j.engstruct.2015.09.008-Figure6-1.png", "caption": "Fig. 6. Diagram of the torsional model of a planetary gearbox used in the tool.", "texts": [ " There are three stages in total and are arranged in the following order: (a) planetary stage with three equally spaced planets supported by two cylindrical roller bearings (CRB) on each planet, and with the carrier supported by two full-component cylindrical roller bearings (fnCRB) in the upwind and downwind locations; (b) a parallel stage with its gear supported by two fnCRB and its pinion supported by two tapered roller bearings (TRB) and (c) a final parallel stage supported in the upwind side by two CRB and two TRB supporting the highspeed shaft (HSS) in the downwind side. The generator is a fixed-speed induction machine with two synchronous speeds: 1200 rpm and 1800 rpm, which correspond to 200 kW and 750 kW power production, respectively. The machine operates at a 5% slip, which translates into operating speeds of 1206 rpm and 1809 rpm. In addition, it is possible to control the generator torque in order to achieve desired power levels. This method is used in the validation example later in the paper. Fig. 6 shows a typical torsional model of a planetary stage in a gearbox. The ring DOF is fixed and only the carrier, planets and sun are allowed to rotate. The planetary stage is connected to the other stages by a flexible shaft. Therefore, the flexibilities considered in the system are the torsional stiffness of the shafts and the linear stiffness of the gear mesh. In reality this stiffness is time variant, but it is kept at its mean value in this work. The tool allows to create a gearbox of different configurations using combinations of planetary and parallel stages" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002107_j.measurement.2018.07.031-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002107_j.measurement.2018.07.031-Figure7-1.png", "caption": "Fig. 7. Photographic view of experimental setup.", "texts": [ " A flowchart for numerical computation is shown in Fig. 6. The time domain data like amplitude of displacement and velocity for 0 to 0.5 s were stored for further analysis. The time step (\u0394t) between two consecutive iterations is fixed to 10\u22126 s. The initial conditions are most important for the convergence of non-linear differential equations. The initial conditions used for the solution of presented equations of motion are: displacement= 10\u221211 mm, and velocity= 10\u22128 mm/s. The photographic view of actual experimental setup is shown in Fig. 7. The shaft is supported on rollers and power was supplied by AC motor through belt and pulley mechanism. The shaft speed variations were controlled by means of variable frequency drive (VFD) of electric motor. The test bearing is mounted on the right side at cantilever portion of shaft and constrained by means of lock nut. The test bearing was fixed in split type housing. The static radial load was applied at the bottom of test bearing housing by means of attached hook and hanger arrangement. A permanent magnet type piezoelectric accelerometer CTC make (Model Number AC-102-1A) having magnetic sensitivity of 100mv/g is mounted on top of test bearing housing for measuring the vibrations signals generated for normal and defective test bearing" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001524_s12206-014-0931-7-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001524_s12206-014-0931-7-Figure1-1.png", "caption": "Fig. 1. Two phases of the rTPS limb.", "texts": [ " Following this, 6rTPS MPMs are discussed in Sec. 7 and non-redundant geometric constraint conditions are proposed. Conclusions are made in Sec. 8. 2. Two phases of the reconfigurable rTPS limb The reconfigurable rTPS limb consists of a reconfigurable Hooke (rT) joint, a prismatic joint and a spherical joint. The reconfiguration of this limb stems from the configuration change of the rT joint which has two rotational degrees of freedom (DOFs) about two perpendicularly intersecting rotational axes (radial axis and bracket axis) as in Fig. 1. A grooved ring is used to house the radial axis and make it have the ability of altering its direction by rotating. The radial axis will be fixed freely along the groove in each phase. This allows the radial axis change with respect to the limb, resulting in two typical phases of the rTPS limb as in Fig. 1. While in Fig. 1(a), the radial axis is perpendicular to the limb (prismatic joint) which is denoted as (rT)1PS, it is collinear with the limb passing through the spherical joint center in Fig. 1(b) and the limb phase is symbolized as (rT)2PS. Set an arbitrary coordinate system oxyz as in Fig. 1(a). Let points A and B denote the spherical joint center and the rT joint center respectively, a and b denote the vectors of points A and B in the oxyz coordinate system. Let the distance between A and B is h, then the geometric constraint of the (rT)1PS limb is given as: ( ) ( ) ( ) ( ) ( ) ( ) 2 2 1 0 2 . cos( / 2) ( ( . ) ). cos ( . ) h h f p f \u00ec - =\u00ef \u00ef - = +\u00ef \u00ed - - -\u00ef =\u00ef - - -\u00ef\u00ee a b a b n a b a b n n n a b a b n n (1) which shows that position of the spherical joint center A is determined by stroke (h) of the prismatic joint and rotational angles (radial axis angle 1f and bracket axis angle 2f ) of the rT joint as in Fig. 1, where 1f is between the limb and its projection on plane \u2211 passing through AB and perpendicular to the bracket axis (n) of the rT joint, n0 is a reference line passing through rT joint center B and perpendicular to n. For the (rT)2PS limb as in Fig. 1(b), radial axis of the rT joint is collinear with the prismatic joint passing through the spherical joint center A. Thus, point A can only lie on the plane \u2211. Geometric constraint of the (rT)2PS limb is given as: ( ) ( ) ( ) 2 2 0 2 . . 0 . cos h d h f \u00ec - =\u00ef\u00ef - = - =\u00ed \u00ef - =\u00ef\u00ee a b a b n a n a b n (2) which shows that position of the spherical joint center A is determined by stroke (h) of the prismatic joint and bracket axis angle ( 2f ) of the rT joint. d is the distance from the coordinate system center o to plane \u2211" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001523_s00170-014-6483-2-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001523_s00170-014-6483-2-Figure7-1.png", "caption": "Fig. 7 Schematic of chip formation in endmilling (Jie Sun and Y.B. Guo, 2008)", "texts": [ " Since end milling is a three-dimensional (3D) cutting process, it involves complex geometry of the milling cutter and interactions with the workpiece. A 3D view of chip formation during a milling process is necessary to identify the specific cutting actions by different cutting edges. By analyzing the end milling process, a 3D view of chip formation has been established by Sun and Guo to highlight the dimensions of a milled chip, specific functions of the side cutting edge and end cutting edge, and the relationship with the process parameters such as axial and radial depth-of-cut (DoC), as shown in Fig. 7 [13]. Four surfaces of the chip, i.e., the top surface, the free surface, the back surface, and the cross-sections, have been defined. The free surface and the back surface are formed by the side cutting edge in sequential cutting, while the machined surface is formed by the tool nose and the end cutting edge. 4.1 Lamella structure of free surface The chip micrographs of LCL on the free surface are shown in Fig. 8. As can be seen from the figure, the free surface of the chip has a loose and lamella structure, which is caused by the shearing mechanism" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002893_tia.2020.3036328-Figure18-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002893_tia.2020.3036328-Figure18-1.png", "caption": "Fig. 18. 3-D FEA thermal models. (a) 6S16P CFRPM. (b) 12S16P CFRPM.", "texts": [ " For small machines under the same copper loss and low speed operation, the one produces the highest torque also produces the highest efficiency. Hence, the global optimization process can be verified. As shown in Table I, the two machines with concentrated winding has higher electrical loading than the two machines with distributed windings. Here, the 6S16P and 12S16P CFRPMs are compared in terms of thermal performance. 1) Thermal Model: The 3-D finite element analysis (FEA) thermal models are shown in Fig. 18, which are totally enclosed under natural convection cooling. It should be noted that the volume of the end winding Vend and the volume of the effective winding Veff satisfy (11). The losses are listed in Table III Vend/Veff = lend/ls. (11) The convection coefficient within the airgap depends on the nature of airflow, and is determined by modified Taylor number in (12) and the Nusselt number Nu in (13) [28] Tam = w2rg\u03b4 3 \u03bcA 2Fg (12) { Nu = 2.0Tam< 1740 Nu = 0.409Tam0.241 \u2212 137Tam\u22120.75Tam> 1740 (13) where w is the angular speed, rg is the average airgap radius, \u03b4 is the airgap length, \u03bcA is the kinematic viscosity of the air, and Fg is set to 1" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003252_tia.2020.3040142-Figure8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003252_tia.2020.3040142-Figure8-1.png", "caption": "Fig. 8. Two CMG topologies for computation. (a) CMG1. (b) CMG2.", "texts": [ " The iteration process is summarized as a flowchart in Fig. 7. As mentioned in Section I, the magnetic field distribution on the airgap of CMGs can also be solve by using SDM, and the analytical model in [10] is used in following comparison. The computation speed and accuracy of SDM, linear HMM, nonlinear HMM, linear FEA, and nonlinear FEA are compared, where nonlinear FEA is set as the benchmark. The FEA model is constructed and calculated in software JMAG-Designer. Two CMGs with different parameters are selected for comparison, as shown in Fig. 8. Their basic parameters are given in Table I. From Fig. 8, the modulator pieces for CMG2 are thinner and the air gap length is shorter, which means the magnetic saturation is severe. It should be noticed that the geometrical parameters of these two CMGs are far from optimal, and they are only used to verify whether analytical methods can consider the magnetic saturation effect. Since some impractical cases could be generated during optimization process, the analytical methods must have accurate performance prediction for them to avoid wrong optimization trend", " As for the limitations of the HMM, it should be noted that the end effect cannot be considered by purely using HMM due to the essence that it uses Fourier series expansion to analyze the harmonic components within CMGs. However, the HMM can be integrated with magnetic equivalent circuit method to form a novel hybrid analytical method, where the end effect can be considered. Some constructive suggestions can be drawn from the topologies of the optimal cases. First, it can be observed that the flux density within the back-yoke part of optimal cases 1 and 2 are higher than that of the initial case, as shown in Fig. 8(b). Thus, the soft-magnetic material is used effectively without increasing redundant weight to the CMGs. Second, the pole arc ratio of PMs is not necessarily required to be one due to the large flux leakage on the modulator. On the contrary, its optimal value should be smaller than one to use PMs efficiently. Besides, the optimal shape of modulator pieces does not always possess a radial side, as can be seen in Figs. 13 and 15 . Hence, it is beneficial to divide the modulator pieces into several layers on the radial direction for further optimization" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001634_humanoids.2017.8246977-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001634_humanoids.2017.8246977-Figure1-1.png", "caption": "Fig. 1. This paper aims to estimate the pose 0Mb and velocity of the floating base with simple estimators to fuse kinematics with IMU data.", "texts": [ " Section II-B quickly reviews how an IMU can provide an estimate of the robot orientation with respect to the gravity field. In Section II-C we present the design of weighting functions, which are used to average the different estimates in Section II-D. Finally, Section II-E discusses how to compensate for potential foot drifts. When the robot is standing on two grounded feet, knowing the pose of the feet in the world: 0ML = [ 0RL 0pL 0 1 ] 0MR = [ 0RR 0pR 0 1 ] , (1) and limb kinematics can provide two estimates of the floating base pose 0\u0302Mb L and 0\u0302Mb R (see Fig. 1). In the case of HRP-2, the kinematic chains for each leg contain flexibilities below the ankles, designed to absorb impacts. We model these flexibilities as 6D linear springs, and use the force-torque sensors for each foot to estimate the associated 6D deformations: wl = Kl [ Lpal rpy(LRal ) ] , wr = Kr [ Rpar rpy(RRar ) ] , where wl/wr are the measured 6D wrenches, Kr/Kl are diagonal positive-definite stiffness matrices, Lpal /Rpar are the translational deformations, LRal /RRar are the angular deformations, and rpy(" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002067_tec.2017.2761787-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002067_tec.2017.2761787-Figure4-1.png", "caption": "Fig. 4. Schematic ETB symbol", "texts": [ " where m+1 represents the additional node whose temperature is Tu. The sum of Qu (e) will be Qu as shown in (10), which makes node m+1 be able to be connected directly with the other nodes in the LPTN. In summary, for representing the convective heat transfer boundary between the FE and the LPTN regions, the ECB element with m+1 nodes should be constructed to represent the convective boundary condition, and [N]hu (e) should be used as its stiffness matrix to be overlapped into the global stiffness matrix. Fig. 4 shows the symbol for the ETB. \u0413Te is assumed to have the same temperature with a node in the LPTN region whose temperature is unknown and represented with Te. The energy conservation can be expressed as: Contrary to ECB with an unknown ambient temperature as its additional degree of freedom, all the nodes on \u0413Te only have one degree of freedom, which means the total number of linear equations is reduced. It is assumed that the temperature in a body element w with more than one node on \u0413Te can be expressed as: \u2211\u2211\u2211 +=== \u22c5+\u22c5=\u22c5= n lj w je l j w j w j n j w j w j w NTNTNTT 1 )( 1 )()( 1 )()()( (19) Nodes from l+1 to n are assumed to have the same temperature of Te" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002890_tia.2020.3033505-Figure11-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002890_tia.2020.3033505-Figure11-1.png", "caption": "Fig. 11. A regular rotor-PM FMPM (i.e. a regular VPM).", "texts": [], "surrounding_texts": [ "Figs. 13 to 15 compares the no-load performances of the proposed FMPM, regular FRPM and VPM. It can be found in Fig. 13 that the absolute value of the cogging torque in the proposed FMPM is the largest. However, due to its high rated torque, its percentage value is only 1.1%, which is lower than the regular FRPM. Then, Fig. 14 indicates that the flux linkage of the proposed FMPM is 80% and 20% higher than that of the regular FRPM and VPM, respectively. Hence, it can be seen in Fig. 15 that the proposed FMPM also has 80% and 20% higher back-EMF than the regular FRPM and VPM. Authorized licensed use limited to: University of Gothenburg. Downloaded on December 19,2020 at 20:34:12 UTC from IEEE Xplore. Restrictions apply. 0093-9994 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information." ] }, { "image_filename": "designv10_9_0000498_tec.2012.2185826-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000498_tec.2012.2185826-Figure1-1.png", "caption": "Fig. 1. SHEFS machines [14]. (a) Cross section of SHEFSM1. (b) Cross section of SHEFSM2. (c) Operation principle of SHEFSM2 (PM only). (d) Operation principle of SHEFSM2 (excitation flux only).", "texts": [ " In Section II, the topologies and operation principles of the series hybrid excitation flux-switching (SHEFS) machines, the SHEFS machines with iron flux bridges and the proposed PHEFS machine are analyzed and compared. The DTC scheme for PHEFS generator dc power system are investigated and discussed in Section III. The proposed DTLC scheme is developed in Section IV. Section V gives the implementation of the DTLC scheme in flux-weakening region. Section VI presents the experimental results and, finally, conclusions are given in Section VII. Two series hybrid excitation flux-switching machines (SHEFSM1 and SHEFSM2) are presented [14], as shown in Fig. 1(a) and (b), respectively. For this group (series hybrid excitation), PMs and excitation windings are in series, the excitation flux pass through PMs, as seen in Fig. 1(d). Due to the magnetic properties of PMs, some drawbacks can be identified [1] as follows. 1) Since the permeability of PMs is close to that of air, the reluctance of the excitation winding\u2019s magnetic circuit is relatively high, which will limit the flux regulation capability. 2) Furthermore, the risk of demagnetization should be considered. In order to overcome the drawbacks of SHEFS machines, [15] has added iron flux bridges as shown in Fig. 2 to the topology of Fig. 1 to enhance the ability of the excitation winding to vary the excitation flux level. As the iron bridge is included and the width is increased the effectiveness of the excitation winding is improved [15]. However, increasing the width of the iron bridges will cause an increase of short-circuit PM flux, as seen in Fig. 2(b). Thus, the utilization ratio of the magnets and machine torque density will be reduced. From the aforementioned analysis, it can be concluded that 1) the series hybrid excitation topologies without iron flux bridge have simple structure, but their excitation current utilization ratio is low, and there is a risk of demagnetization, 2) the series hybrid excitation topologies with iron flux bridge can increase the excitation current utilization ratio to some extent and has no risk of demagnetization; however, high-excitation current utilization ratio and high-PM utilization ratio are contradictory" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002186_j.matlet.2019.126512-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002186_j.matlet.2019.126512-Figure1-1.png", "caption": "Fig. 1. (a) Drawing of the 1 mm-thick tensile test specimen in mm, (b) test stage inside t scanning points of the XCT specimen.", "texts": [ " A sub-size tensile test specimen with 1x1x1 mm gauge volume was cut using wire electrical discharge machining. Using a Bruker MTS1 test stage and Bruker Skyscan1172 X-ray computer tomography (XCT) machine, interrupted tensile tests were carried out, and at each step the gauge volume was scanned at 40 kV using 0.5 mm Al filter at pixel resolution 0.98 lm. Post-processing of the images was carried out using the Bruker commercial software package. A scanning electron microscope FEI Quanta 200 FEG was utilized for fractography at 5 eV. 3. Results and discussion Fig. 1(a) and (b) show the tensile test sample and the test stage inside the XCT machine chamber, respectively. A closer view of the stage and specimen is demonstrated in Fig. 1(c). Fig. 1(d) presents the flow curves of the ASTM and the XCT specimens, which both obtained as described elsewhere [10]. There is a reasonable correlation between the two curves. The specimen was scanned before deformation, at four different strain levels, and after fracture occurred at true strain 0.38. The XCT models of the specimen at each step are presented in Fig. 2. For ease of visualization of the larger pores, only pores with an equivalent spherical diameter (ESD) larger than 8 lm are shown; however, all the pores are considered in the quantitative analysis" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003580_j.mechmachtheory.2020.104238-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003580_j.mechmachtheory.2020.104238-Figure1-1.png", "caption": "Fig. 1. Mesh force diagram of spur gear with tooth tip chipping.", "texts": [ " Then, a more accurate mesh stiffness calculation model of spur gear is established and the potential energy method is adopted to calculate the mesh stiffness. In this model, the friction, manufacturing error and transmission error of gears are neglected because of the little effect on mesh stiffness [ 20 , 21 ]. When applying the potential energy method to calculate the mesh stiffness of gears, the tooth is regarded as a variable section cantilever beam. The mesh force of the gear tooth in the meshing process is shown in Fig. 1 . In the coordinate system XOY, O locates at the center of the gear, X axis is along the tooth symmetry line, and Y axis is perpendicular to the X axis. In the coordinate system UOV, O locates at the center of the gear, V axis passes through the intersection of the base circle and the involute, and U axis is perpendicular to the V axis. In this model, the base circle radius is larger than the root circle radius. As the gears are engaged, the potential energy stored in the gear teeth can be divided into five parts, namely Hertzian contact potential energy U h , axial compressive potential energy U a , bending potential energy U b , shear potential energy U s and fillet foundation energy U f . The total potential energy is the summation of the five parts. And the mesh stiffness can be deduced by the potential energies. The mesh force F can be decomposed into F a and F b , as shown in Fig. 1 . F a = F sin ( \u03b11 ) (1) F b = F cos ( \u03b11 ) (2) where \u03b11 is the pressure angle of action point. The potential energies of U a , U b and U s can be expressed using Eqs. (3) - (5) as follows [19] : U a = F 2 2 k a = \u222b d 0 F 2 a 2 E A x dx (3) U b = F 2 2 k b = \u222b d 0 [ F b ( d \u2212 x ) \u2212 F a h ] 2 2 E I x dx (4) U s = F 2 2 k s = \u222b d 0 1 . 2 F 2 b 2 G A x dx (5) where d describes the distance between the action point and the tooth root circle; h denotes the distance between the action point and the X -axis; x describes the distance of arbitrary point on the involute to the tooth root circle; A x and I x are the area and the moment of inertia of the tooth cross section along the tooth width at arbitrary position of the involute, respectively", " However, when the potential energy method is applied to calculate mesh stiffness, the part above the cross section of the tooth tip has no influence on the calculation of the mesh stiffness, so the cylindrical surface of the tooth tip is approximated to the tooth tip plane, as shown in plane D 1 D 2 D 3 D 4 in the Fig. 2 (a). The intersection line between the fracture surface and the tooth end face is a straight line, as shown AB in Fig. 2 (a). Fig. 2 (b) shows a cross section diagram of a fault location. When the fault occurs, it will affect the position of the neutral surface of the gear tooth, thus affecting the moment of inertia on the cross section. In the Cartesian coordinate system UOV in Fig. 1 , the involute Eq. can be described by Eq. (11) as follows: { u = R b [ sin ( \u03b8x + \u03b1x ) \u2212 ( \u03b8x + \u03b1x ) cos ( \u03b8x + \u03b1x ) ] v = R b [ cos ( \u03b8x + \u03b1x ) + ( \u03b8x + \u03b1x ) sin ( \u03b8x + \u03b1x ) ] (11) Converting it into the XOY coordinate system, the Eq. of the involute L 1 in Fig. 2 (a) becomes: { x = R b { [ sin ( tan ( \u03b1x ) ) \u2212 tan ( \u03b1x ) cos ( tan ( \u03b1x ) ) ] cos ( \u03b12 ) \u2212 [ cos ( tan ( \u03b1x ) ) + tan ( \u03b1x ) sin ( tan ( \u03b1x ) ) ] sin ( \u03b12 ) } y = R b { [ sin ( tan ( \u03b1x ) ) \u2212 tan ( \u03b1x ) cos ( tan ( \u03b1x ) ) ] sin ( \u03b12 ) + [ cos ( tan ( \u03b1x ) ) + tan ( \u03b1x ) sin ( tan ( \u03b1x ) ) ] cos ( \u03b12 ) } (12) herein \u03b8x is the evolving angle of the involute. \u03b1x is the pressure angle at arbitrary point on the involute. The three-dimensional Cartesian coordinate system OXYZ can be established by configuring the Z -axis to perpendicular to the plane XOY in Fig. 1 and point to the outside. Supposing that the point A in Fig. 2 is located on the tooth profile curve whose coordinates are ( x a , y a , 0 ), point B is located on the top line of gear tooth end face (equivalent to to a line) whose coordinates are ( x b , y b , 0 ) and point C is on the top edge of the tooth profile whose coordinates are ( x c , y c , z c ), the Eq. 2 of fracture plane can be determined by Eq. (13) : z = [ ( x \u2212 x a ) ( y a \u2212 y b ) \u2212 ( x a \u2212 x b ) ( y \u2212 y a ) ] ( x a \u2212 x ) ( y a \u2212 y c ) + ( y a \u2212 y ) ( x c \u2212 x a ) z c (13) b b Combining Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002410_j.matlet.2019.126537-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002410_j.matlet.2019.126537-Figure1-1.png", "caption": "Fig. 1. Characterization of the lattice structures: (a) CAD design, and (b) photograph of the SLM lattice sample.", "texts": [ " Optimised scanning parameters by considering the sample density and dimensional accuracy were used in this experiment and are listed as follows: a laser power of 240W, a hatch distance of 50 lm, a laser beam speed of 240 mm/s, a laser spot diameter of 100 lm, and a layer thickness of 30 lm. The laser scanning trajectory follows a zigzag pattern with an angle of 67 between adjacent layers. A regular octahedron unit cell with an overhanging cuboid strut of 45 and length of 750 lm was designed using a CAD software UG NX 10 (Siemens PLM, Germany). The unit cell was then constructed into a cubic lattice structure having a size of 15 15 15 mm3 using a software Magics (Materialise, Belgium). Fig. 1 shows the CAD drawing of the lattice structure and unit cell and photograph of the SLM lattice sample. HIP treatment was carried out at a temper- ature of 900 C and pressure of 120 MPa for 2 h under argon environment. The microstructure of the SLM lattice structures were studied using scanning electron microscope (SEM, Carl Zeiss ULTRA, Germany) and optical microscope (OM, Leica, Germany). In order to study the grain structure, the polished samples were etched with a reagent of 50 ml distilled water, 10 ml HCl and 5 ml HF" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002889_tmag.2020.3032648-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002889_tmag.2020.3032648-Figure2-1.png", "caption": "Fig. 2. (a) Slot-less motor # 1, b) Slot-less motor # 2 with EMCs to consider slotting effect", "texts": [ " Therefore, the slotting effect can be nullified by injecting surface currents (equal and negative to the surface EMCs) to the teeth walls. In this case, the slotted stator can be modeled similar to a slot-less machine. To include the slotting effect, the flux density of the injected current is separately calculated and subtracted from the PM flux of the slot-less machine. Therefore, the air-gap flux density of the original slotted motor (Fig. 1) is calculated by the summation of the air-gap flux of two separate slot-less motors (Fig. 2). In another words, the Poisson\u2019s equation is solved in the uniform air-gap of Fig. 2.a, as opposed to the non-uniform air-gap of Fig. 1, and the slotting effect is considered by a set of EMCs (\ud835\udc3d\ud835\udc60(\ud835\udf11)) in Fig. 2.b. Finally, the overall air-gap magnetic flux density is calculated by using the superposition theorem. The following assumptions are considered. Magnetic saturation is ignored in the analytical model. The machine structure has a 2D symmetry and end effects are ignored. Relative permeability (\ud835\udf07 ) in iron core is assumed infinity The PM\u2019s magnetization direction is in radial direction Authorized licensed use limited to: University College London. Downloaded on November 01,2020 at 22:44:27 UTC from IEEE Xplore", " Assuming a relatively large relative permeability (\ud835\udf07\ud835\udc5f) in iron and inserting relations (2) and (3), into (1), the surface EMC density can take the form: M=B/\u03bc0-H (2) B=\u03bc0\u03bcrH (3) 00 1 n ns aB aBJ r r (4) In cylindrical coordinate system, the normal unity vector on the walls of the stator teeth is along the tangential direction \u03c6, thus only the flux density in the radial direction is relevant in (4), for calculating the surface EMC on the teeth walls. To simplify the problem, the injected currents on the walls of the stator teeth (Fig. 2b) can be transferred to the inner surface of the slot-less stator (at the location of the filled slots) as shown in Fig. 3. The angular length of the equivalent, transferred current is defined by of \u0394\u03b8, and is normally 5 to 10 percent of the slot-opening angle. In Fig. 3, )(arJ and )(' sJ represent the Fourier series function of the armature current and the transferred current. The surface EMCs teeth walls in Fig. 2(b) and its transferred surface current on the stator bore in Fig. 3 must produce equal amount of flux density in the air-gap, in particular in the area below the stator slots. Therefore, according to the Ampere\u2019s law, the relation (5) must hold at any point in the air-gap. ' 0 0( ) ( ) 2 ( ) 2 ( ) / 2 / 2 s slot s R h s i s s R s i i J J R dx x r R r (5) The original surface EMC density )( isJ is calculated based on the relation (4), and is given by: 0 ( , , )1 ( ) s slot i s R h rII r s i slot R B r J dr h (6) where ),( rBrII is the radial flux density in the teeth walls, \u03c5i+ and \u03c5i\u2212 are the angles of the \ud835\udc56\ud835\udc61\u210e stator teeth walls, which are given as the following : s ss i- ss i+ ," ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003069_j.jallcom.2020.155874-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003069_j.jallcom.2020.155874-Figure2-1.png", "caption": "Fig. 2. The cuboid samples used in heating treatment and dog bone shape like samples used in tensile tests, (a) as-built condition, (b) annealed condition.", "texts": [ " Then, the deposit was paused between each layer until the temperature of the previous layer fell below 30 C. The subsequent layer was deposited in a reverse direction. The three steps were conducted repeatedly until the final height of deposited part was 40 mm. The process was conducted under the following parameters: electrical current 100 A, scan speed 200mm/ min, wire feed speed 850 mm/min, tungsten electrode height 3mm. The argon gas flow ratewas 15 L/min through TIG nozzle and 30 L/min through the trailing shield. Fig. 2 depicts sample preparation method. The cuboid samples were used in heat treatment, and dog-bone shape like samples, cut from as-built specimen and annealed cuboid samples, were used in tensile test. It is worth noting that only very small bending of the cuboid specimen will be caused due to the release of residual stress in annealed condition andwill not influence preparation of tensile samples. Fig. 3 displays the dimension of flat, dog-bone shape like tensile samples. m of WAAM setup. Metallographic samples were prepared by polishing with abrasive papers and cleaning by ethanol" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003609_j.mechmachtheory.2021.104342-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003609_j.mechmachtheory.2021.104342-Figure1-1.png", "caption": "Fig. 1. Illustration of the Hertz contact model: (a) Hertz contact model; and (b) Hertz contact stiffness.", "texts": [ " In Section 4 , the linear modal frequencies and shapes of the torsional system are analyzed. In Section 5 , not only the torsional vibro-impact responses, phase plane and vibro-impact forces of the clearance elements are numerically analyzed, but also frequency responses and vibro-impact forces with constant contact stiffness and Hertz contact stiffness are compared respectively. In Section 6 , the vibro-impact results are verified by vehicle tests. Finally, the conclusions are summarized in Section 7 . As shown in Fig. 1 (a), the driving and driven rotors contact elastically with each other when subjected to external force and produce local deformation which increases from point contact to surface contact. Generally, the elastic contact can be regarded as spherical contact [34 , 41] . Based on the Hertz contact theory, when two spheres with radius r i and r j respectively contact with each other subjected to the external force F , the contact displacement \u03bb is [42] \u03bb = 3 \u221a 9 F 2 / 16 R E 2 (1) where R = r i r j / ( r i + r j ) is the equivalent radius of curvature at the contact point, r i is the radius of sphere i , r j is the radius of sphere j", " E = 1 / ( ( 1 \u2212 \u03bc2 i ) / E i + ( 1 \u2212 \u03bc2 j ) / E j ) is the equivalent elastic modulus, E i and \u03bci are the Young\u2019s modulus and the Poisson\u2019s ratio of sphere i , respectively. E j and \u03bc j are the Young\u2019s modulus and the Poisson\u2019s ratio of sphere j, respectively. Based on Eq. (1) , the derivative respect to \u03bb gives the Hertz contact stiffness as follows: k h,i j = d F / d \u03bb = 2 E \u221a R\u03bb (2) According to Eq. (2) , the Hertz contact stiffness k h,i j is nonlinear and increases with the increase of the contact displace- ment \u03bb, as shown in Fig. 1 (b). Clearance, inducing the significant nonlinear features, is widely existed in the components of torsional system, such as gear, spline, universal joint, clutch damper, etc. It is also the main source of the transient vibro-impacts and cannot be eliminated. As shown in Fig. 2 (a), assuming that there is a speed ratio between the driving and driven rotors, the inertia and pitch radius of the driving rotor are J i and R i respectively, and the inertia and pitch radius of driven rotor are J j and R j respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003469_jestpe.2021.3058261-Figure10-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003469_jestpe.2021.3058261-Figure10-1.png", "caption": "Fig. 10. Flux density and flux lines of armature fields at the same electric loading. (a) Yoke structure. (b) Yokeless structure.", "texts": [ " 9(a) and (b) that along the PM radius direction from rb to ra, all the working harmonic amplitudes are decreased. Especially, the variation gradient \u03b2 is constant at the fixed slot/pole combination and rotor structure, as depicted in Fig. 9(c), which is only related with the working harmonic order, that is, the higher order of armature working harmonic, the larger variation gradient along the PM radius direction. Compared to the yoke structure, the variation gradients of yokeless counterparts are larger, which is due to the increase of leakage flux, as shown in Fig. 10. Authorized licensed use limited to: Central Michigan University. Downloaded on May 14,2021 at 16:42:07 UTC from IEEE Xplore. Restrictions apply. 2168-6777 (c) 2021 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. As shown in Fig. 11, the corresponding torque components have been analyzed and compared, where the variation trends of torque versus slot opening are accordance to the variation of armature working flux density", " INFLUENCE OF ARMATURE FIELDS ON POWER FACTOR In this section, the power factor of various PM machines have been analyzed and compared. According to analysis mentioned above, the power factor is determined by the leakage flux and the armature flux linkage. First, the leakage flux of various topologies have been compared in Fig. 14. It can be seen that with the increase of slot opening, the leakage fluxes are decreased. And the leakage flux is more serious for the yokeless structure as drawn in Fig. 10. Meanwhile, the proportion of leakage flux is inverse to the pole ratio, where the leakage flux of PMSM is maximum. However, the power factor of PMSMs is significantly higher than the high pole ratio PMVMs, that is, the higher leakage flux is not the main cause of low power factor of PMVMs. Further, neglecting the influence of leakage flux and high order harmonics of armature fields, the power factor of high pole ratio yoke PMVMs can be further simplified as: _ _ _ 1 1 0 0 0 1 0 + 2 2 1 2 r r aa p a p a p w w w r r a PF B B B k k kPR PR p p p PR + + + (25) where only the main harmonics with order of path and prth are taken into consideration" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002956_tte.2020.2997607-Figure13-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002956_tte.2020.2997607-Figure13-1.png", "caption": "Fig. 13. Temperature distribution within the DRMWM on hybrid mode with different current density: (a) 5A/mm2; (b) 7A/mm2.", "texts": [ " Since both the PMs on the inner rotor and outer rotor improve the magnetic flux density in the air gap, the maximum flux density can be even larger than conventional single-rotor PM machines. The flux density distribution of the DRMWM are given in Fig. 12 at the moment when the air-gap flux density distribution in Fig.7 and Fig.8 are calculated, respectively. It can be seen that the maximum flux density in rotor in DRMWMs, they might be demagnetized when the working temperature is too high. Since the power of DRMWM on hybrid mode reach maximum, a thermal analysis has been carried out for this condition. From Fig.13, it can be seen that the highest temperature occurs on the inner rotor PMs, 83 \u00b0C for current density 5A/mm2 and 134 \u00b0C for current density 7A/mm2, respectively. If the rated power needs to be improved, water-cooling method must be adopted to prevent further temperature increase. TABLE III SUMMARY OF MESH AND MATERIAL PROPERTIES OF FEA MODEL. Mesh property Air-gap mesh property 168940 elements 88811 nodes Radial direction division: 3 Circumferential direction division: 1440 PM material Iron core material N35EH 50JN700 Authorized licensed use limited to: Murdoch University" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003584_tte.2021.3054510-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003584_tte.2021.3054510-Figure6-1.png", "caption": "Fig. 6 Experimental test platform", "texts": [ " The experimental platform is composed of the BCU (braking control Unit), EMAC (electromechanical actuator controller, in which the proposed NDO-based FTSM control strategy is integrated), EMA, the wheel test bench, and the host computer. An aircraft simulation model is established in the computer, and the aircraft speed and wheel load signals are updated in real-time according to the braking torque and wheel speed detected by related sensors. The wheel test bench has two main functions: one is to load the wheel to simulate the aircraft load, another one is to adjust the drum speed to simulate the aircraft speed. The experimental test platform is shown in Fig. 6. During the braking test, the drag motor drags the drum to the aircraft speed calculated by computer, and the initial speed is the landing speed of the aircraft. The loading system on the wheel test bench will load the wheel with the target load calculated by the computer, and the initial load is the landing load of the aircraft. Then the computer will transmit the preset braking signal to the BCU. After receiving the braking signal, the BCU calculates the braking control signal according to the amplitude of the braking signal, and the anti-skid signal according to the sliding state of the wheel" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002258_physreve.93.032402-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002258_physreve.93.032402-Figure1-1.png", "caption": "FIG. 1. Problem settings: (a) Schematic illustration of a sperm cell in shear flow. (b) Orientation vector d and angle \u03b8 . A material point X0, located at the head-tail junction, is the origin of the orthonormal body frame \u03bei . (c) The tilt angle \u03c8 is defined as \u03c8 = tan\u22121(d3/|d1|), where di is the Cartesian component of d.", "texts": [ " II, we describe 2470-0045/2016/93(3)/032402(9) 032402-1 \u00a92016 American Physical Society a numerical method, and in the following Sec. III, we show upward swimming of the sperm cell and discuss torque balance of the cell. We also discuss stability of the rheotaxis by using a discrete-time stability analysis, and conclude this study in Sec. IV. For the numerical analysis, a sperm cell is considered to be immersed in an incompressible Newtonian liquid, with viscosity \u03bc, adjacent to a two-dimensional (2D) plane of infinite dimensions. The Cartesian coordinates are defined as x = (x1,x2,x3), with base vector ei , as shown in Fig. 1(a). The subjected shear flow is given by v\u221e(x) = (\u03b3\u0307 x3,0,0), where \u03b3\u0307 is the shear rate. Due to the small scale of a sperm cell, the flow field can be assumed as the Stokesian regime, and is described by the boundary integral equation: v(x) = v\u221e(x) \u2212 1 8\u03c0\u03bc \u222b J(x,y) \u00b7 q(y) dS(y) + 1 8\u03c0 \u222b v(y) \u00b7 T(x,y) \u00b7 n(y) dS(y), (1) where x is an observation point, q is the surface traction acting on the cell surface y, and n is the outward unit vector. J(x,y) and T(x,y) are the single- and double-layer potentials of Green\u2019s function, bounded by an infinite nonslip surface at x3 = 0 [23]", " Full expression of J and T are shown in Appendix A. Due to the slender morphology of the flagellum, the contribution of this double-layer integral becomes negligibly small. The double-layer term is then not included in this study, similar to previous work [9], and Eq. (1) is simplified to: v(x) v\u221e(x) \u2212 1 8\u03c0\u03bc \u222b J(x,y) \u00b7 q(y) dS(y). (2) We also assume that the cell swims so as to satisfy the following force-free and torque-free conditions:\u222b q(y) dS(y) = 0, \u222b q(y) \u2227 (y \u2212 X0) dS(y) = 0, (3) where X0 is the head-tail junction point as shown in Fig. 1(b). The geometry of human and bull sperm is likened to an asymmetric ellipsoid [4]. To mimic the elliptical sperm head, the following mapping function is used, X sp 1 = X1, X sp 2 = aX2 a + b \u2212 X1/ , X sp 3 = X3 c + X1/ , (4) where Xsp is a material point of the sperm head, X is the material point of a sphere with radius , and a, b, and c are nondimensional shape parameters. The parameters are set as, /L = 4.17 \u00d7 10\u22122, a = 3.0, b = 2.0, and c = 4.0, to ensure that the morphology is similar to that of human sperm cells", " The cell surface, including both head and flagellum, is then discretized by 908 triangular elements with 457 material points. To accurately describe the motions of the flagellum, an orthonormal body frame is defined as \u03bei , with basis vector gi , as follows. The body frame origin, equivalent to the headtail junction, is described by a material point, X0. The cell orientation vector d is set as, d = (Xh g \u2212 X0)/|Xh g \u2212 X0|, where Xh g is the center of mass of the head. The basis vector, g1, is defined as g1 = \u2212d. The \u03be2 and \u03be3 axes are then set as mutually orthogonal directions, as shown in Fig. 1(b). It is assumed that there is a rigid connection between the head and flagellum, with the flagellum waveform specified a priori for a given transformation. The flagella beat for a human and bull sperm show a left-handed helicoid [24]. To express timedependent flagellum beat, Smith et al. [11] has shown the following formula of the centerline of the flagellum, which is parametrized by \u03be1: \u03be2 = A cos(k\u03be1/L \u2212 2\u03c0f t), (5) \u03be3 = \u2212\u03b1A sin(k\u03be1/L \u2212 2\u03c0f t), where L is the flagellum length, f is the beat frequency, k is the wave number, A is the amplitude parameter, and \u03b1 is the chirality parameter", "1L and the height is high enough so that the repulsive force magnitude becomes negligibly small. We numerically confirmed the result does not change so much by setting the repulsive force (data not shown). For further details of the numerical methodology, please refer to Appendix A. III. RESULTS AND DISCUSSION Typical results of the sperm cell in shear flow (\u03b1 = 0.4, \u03b3\u0307 /f = 0.1) are shown in Fig. 2 and in the Supplemental Material [25]. The cell is initially located at X0 = (0,0,L), and is aligned parallel to the direction of flow, e1 [see Fig. 1(a)]. In the Stokes flow regime, the fluid viscosity simply functions as a multiplier of the force and traction. \u03bc is then taken to be at unity, without the loss of generality. When f t is small, the sperm cell swims toward the direction of flow. When the cell is swimming downstream, it gradually approaches the surface and gradually moves towards the wall, as shown in Fig. 2(a). Then, the background vorticity causes the cell to change direction and move against the flow, which is called the weather vane effect [17,19]. After turning, the sperm cell remains near the wall and continuously swims upward against the shear flow. For a more quantitative analysis, the angle relative to the flow direction has been defined as \u03b8 = cos\u22121(d \u00b7 e1), shown in Fig. 1(b). The change in \u03b8 over time is plotted in Fig. 2(c). It can be seen that \u03b8 rapidly increases, at approximately f t = 150, when the sperm cell turns upstream. After f t = 200, \u03b8 remains close to \u03c0 for a long duration, which indicates stable upward swimming of the sperm cell. B. Orientation of a sperm cell Next, we investigate the effect of the shear rate \u03b3\u0307 on the orientation of the sperm cell. The maximum orientation angle, \u03b8max, was observed under simulated conditions, with the same initial position and the wave form, \u03b1 = 0", " Negative torque appearing in Fig. 5 yields escape motions from the wall. To see the escape motion in detail, the time sequence of the cell motion with \u03b1 = 0.2 and \u03b3\u0307 /f = 0.1 is shown in Fig. 6(a) and the Supplemental Material [25]. We see that the sperm cell gradually rotates in a clockwise direction and the swimming direction is changed from upward 032402-4 to downward. For more detailed analysis, we investigate the attitude of the sperm cell by using the tilt angle \u03c8 , which is defined as \u03c8 = tan\u22121(d3/|d1|) [cf. Fig. 1(c)]. A positive value of \u03c8 indicates the cell heading to the positive x3 direction, whereas its negative value indicates heading to the wall. The time change of \u03b8 and \u03c8 with \u03b1 = 0.2 and \u03b1 = 0.4 are shown in Figs. 6(b) and 6(c), respectively. Shear rate is set as \u03b3\u0307 /f = 0.1 for both cases. At the beginning of the simulation (f t 200), the angle \u03b8 gradually increases and it reaches almost \u03c0 at f t 200 for both \u03b1 cases. The angle \u03c8 also changes from 0 to \u22120.5\u03c0 at f t = 200 and it rapidly recovers to zero", " Since the flagellum changes its shape in time, we need to consider dynamic stability. Or [27] investigated dynamic stability of a Purcell\u2019s three-link swimmer near a boundary wall. Using similar manner to Or [27], we will investigate the dynamic stability of the sperm cell. Let u = (x1,x2,x3, ,\u03c8,\u03c6)T denote the three-dimensional position and orientation of the sperm cell. is the orientation angle, which is defined as = \u00b1 cos\u22121(d \u00b7 e1). The sign of is determined by the sign of d2. \u03c8 is the tilt angle, as shown in Fig. 1. \u03c6 is the rolling angle around the \u03be1 axis, whose quaternion expression can be written as (\u03c6,g1). Then, we have following dynamical system of the sperm cell: u\u0307(t) = F (u,t), (9) where F is a time-periodic function. When the flagellar shape changes periodically in time, the system can be written as the following discrete-time dynamical system: uk+1 = F (uk), (10) where k is the discrete time and uk is the solution of the continuous-time equation of (9) at time t = kT and T is the period of flagellum beat" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000039_978-1-84996-220-9-Figure7.12-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000039_978-1-84996-220-9-Figure7.12-1.png", "caption": "Figure 7.12 Modification of the ZMP position: (a) humanoid robot without manipulation; (b) humanoid robot pushing wall; (c) humanoid robot carrying an object; (d) definition of heel and toe", "texts": [ "2, the change of the ZMP position due to the hand reaction force in the sagittal plane is given by 7 Motion Planning for a Humanoid Robot Based on a Biped Walking Pattern Generator 199 xzmp \u2212 x\u0304zmp = 2 \u2211 j=1 (zH j \u2212 zzmp) f (x) H j +(xzmp \u2212 xH j) f (z) H j M(z\u0308G + g) , (7.15) where pH j = [xH j yH j zH j] and f H j = [ f (x) H j f (y) H j f (z) H j ] ( j = 1,2) denote the position of the hand and the hand reaction force, respectively. Let us explain the physical interpretation of Equation 7.15. Figure 7.12 shows the effect of the hand reaction forces onto the position of the ZMP. As shown in Figure 7.12(a), when the hand does not contact the environment, pZ = p\u0304Z is satisfied. On the other hand, when pushing the wall as shown in Figure 7.12(b), the position of the ZMP will shift to the back of the robot. Also, when carrying an object as shown in Figure 7.12(c), the position of the ZMP will shift to the front of the robot. Figure 7.13 shows the result of the pushing manipulation where the humanoid robot walks while pushing a large object placed on the floor [10]. In this case, by using the weight of the object and the friction coefficient between the floor and the object, the hand reaction force in the horizontal direction can be predicted. By substituting the predicted hand reaction force into Equation 7.15, the modification of the ZMP position can be calculated" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003369_j.mechmachtheory.2021.104386-Figure12-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003369_j.mechmachtheory.2021.104386-Figure12-1.png", "caption": "Fig. 12. FE model for helical gears.", "texts": [ " Some studies [ 37 , 38 ] also used the partial gear FE models to validate their analytical models. In this study, the FE models of the pinion and gear consist of five and eight teeth, respectively. The number of nodes and elements of the pinion FE model is 63,308 and 13,640, respectively. On the other hand, the total number of nodes and elements of each gear FE model is slightly different, but it is around 152,0 0 0 nodes and 33,500 elements. From the FEA results, the mesh quality of FE models is considered to provide high enough resolution for the analysis. As shown in Fig. 12 , two master nodes are developed in the geometric centers of the pinion and gear. The nodes on the inner surface of pinion are coupled with the master node of the pinion and the master node is restrained for all degrees of freedom except rotation direction. The nodes on the inner surface of the gear are coupled with the master node. All degree of freedom of the master node and all nodes on the cutting plane is restrained. An external torque 314 Nm is applied to the master node of pinion. A static analysis is run at several meshing positions along the path of contact and the FE models are rotated through one base pitch rotation" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002666_s42243-020-00396-y-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002666_s42243-020-00396-y-Figure1-1.png", "caption": "Fig. 1 Schematic illustration of HAM. a DED process; b LR process", "texts": [ " In this paper, the surface morphology, microstructure evolution and properties of HAM 316L stainless steel are investigated with the discussion of mechanisms. HAM system consists of a Fronius TPS 5000 arc power source, an IPG YLS-10000 laser device, a six-axis KUKA robot and an argon-purged deposition chamber. A thick plate with a geometric size of 160\u00a0mm \u00d7 50\u00a0mm \u00d7 30\u00a0mm was deposited by this system. The process parameters of HAM are given in Table\u00a01. Schematic illustration of HAM is shown in Fig.\u00a01. The adjacent scanning tracks were opposite with the spacing of 8\u00a0mm (Fig.\u00a01a). Twenty-five layers were deposited with the height of 2.5\u00a0mm and the time interval of 1\u00a0min. The surface of the component is smooth when using laser remelting technology with the scanning direction parallel to deposition direction (Fig.\u00a01b). The spacing between two adjacent laser tracks was 5\u00a0mm. 316L wire with the diameter of 1.2\u00a0mm was employed as the starting material, and the chemical composition (wt.%) is given in Table\u00a02. HAM process was executed in a specifically designed processing chamber with the contents of oxygen less than 0.008%. The specimens of HAM 316L component were prepared by standard mechanical polishing for metallographic microstructure analysis. A mixture solution (4\u00a0g CuSO4, 20\u00a0mL HCl and 20\u00a0mL H2O) was used as the etching agent" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001586_b978-0-12-803137-7.00003-3-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001586_b978-0-12-803137-7.00003-3-Figure7-1.png", "caption": "Fig. 7 (A) Parallel articulated-cable exercise robot (PACER): home-based cable-driven mechanism for upper extremities rehabilitative exercises [104,105], (B) robotic physical exercise and system (ROPES): a cable- driven robotic rehabilitation system for lower extremity [102,106] which is driven by seven motors installed on the frame labeled 1\u20137.", "texts": [ " The state of the art for lower-limb exoskeletons presented by Dollar and Herr [14] showed that having knowledge of the biomechanics of walking is important to build an exoskeleton that can interact with the user with minimal chances of harm. Alamdari et al. [103] comprehensively surveyed the clinic- and home-based rehabilitation devices for upper and lower limbs therapy to recognize the situations which need human-robot interaction to be considered. For training patients under rehabilitation with an exoskeleton, physical human-robot interaction is a major concern for a safe and comfortable usage. For example, in Refs. [104,105] as shown in Fig. 7A, a cable-driven end-effector-based exoskeleton named PACER is directly coordinated with a human arm, and in Refs. [102,106] as shown in Fig. 7B, a cable-driven exoskeleton named ROPES is in intimate contact with human lower limbs. For modeling, analyzing and deep understanding of human-robot interaction, the musculoskeletal model of the human body as well as multibody dynamics of the exoskeleton need to be integrated and modeled [15,125] Therefore, the model is able to estimate the muscle activities in cooperative motions and enables the design analysis and optimization of robotic exoskeletons. Safety is one of the top priorities when designing any kind of exoskeleton [107], as they interact closely with humans" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003469_jestpe.2021.3058261-Figure25-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003469_jestpe.2021.3058261-Figure25-1.png", "caption": "Fig. 25. The model with 10-pole-pair PM rotor. (a) Halbach PM rotor with PM pole-arc of 0.5. (b) Equivalent magnetizing current model with PM pole-arc of 0.5. (c) Surface-mounted PM rotor with PM pole-arc of 1. (d) Equivalent magnetizing current model with PM pole-arc of 1.", "texts": [ " It is found that the high leakage flux is not the main cause of low power factor, and the low power factor of PMVMs is mainly due to the low proportion of armature working flux density. While the higher armature working harmonic amplitudes, the lower proportion of which. What\u2019s more, there is the tradeoff in stator slot opening design. APPENDIX A In order to verify the accuracy of equivalent magnetizing currents of PMs, the 10-pole-pair halbach PM rotors with pole-arc ratio of 0.5 and 1 have been taken as the examples, as presented in Fig. 25, where the stators are slotless. Especially, the model with pole-arc ratio of 1 is actually the regular surface-mounted PM, and the equivalent surface current density of which is zero. The air-gap flux density produced by PMs and equivalent magnetizing currents are compared in Fig. 26. It can be observed that the good agreement can be achieved, where the slight errors are due to only the harmonic order within 200 has been considered. Authorized licensed use limited to: Central Michigan University" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002930_j.mechmachtheory.2020.103824-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002930_j.mechmachtheory.2020.103824-Figure2-1.png", "caption": "Fig. 2. Schematic of piston, connecting rod and crank.", "texts": [ " These dynamic equations are unique in that, the lateral motion at the piston pin and the angular motion around the piston pin can be directly used to determine the interaction variables between the piston pin and the small end bearing, such as eccentricity ratio \u025b , average angular velocity \u03c9\u0304 and coordinate angle \u03b2 . Moreover, using this formulation, the motions at the four corners of piston skirt are accurately defined using the lateral motion at piston pin and the angular motion around piston pin. This allows considering the effects of unsymmetrical skirt geometry due to piston pin offset. A schematic of crank train mechanism is shown in Fig. 2 . O, A, B are the centers of crank journal, crank pin and piston pin, respectively. \u03b8 c is the angular position of crank. x r and y r are the displacements at the center of gravity of connecting rod in the horizontal and vertical directions. \u03c6r is the angular position of connecting rod according to the central line of cylinder liner. x pin and y pin are the displacements of piston pin in the horizontal and vertical directions. l 1 is the distance between the center of big end bearing and the center of gravity of connecting rod", " Secondly, the effects of piston secondary motion on reciprocating motion of piston and planar motion of connecting rod are evaluated. Thirdly, the effects of the clearance between piston skirt and cylinder liner and the clearance between piston pin and small end bearing, are studied respectively. Fig. 6 shows the simulated results of the piston secondary motion during an engine cycle of 720 \u00b0 of crankshaft. Fig. 6 (a) gives piston pin lateral displacement and lateral velocity, and Fig. 6 (b) shows the piston tilting angle and tilting speed. The positive values in Fig. 6 are in accordance with the indications shown in Fig. 2 . It can be seen that the piston travels from one side of the liner to another repeatedly during an engine cycle. Impacts or bounces can be produced when the piston contacts with the liner, since the fluctuations of curves of the lateral motion and the tilting motion can easily be seen at these moments. The results show that the maximum lateral displacement of piston pin is 15 \u03bcm, which is just the input clearance between piston skirt and cylinder liner in the simulation. And the maximum tilting angle is 0", " Of course, the engine type in the reference [5] is not same to that in this paper, so the maximum lateral displacements of the piston are different. The lateral motion of piston in Fig. 6 (a) can be explained using the small end bearing force F xpr of connecting rod, since this force is the driving inputs of piston secondary motion. The small end bearing force F xpr and the combustion force F gas in one engine cycle are shown in Fig. 7 . The positive values of the curves indicate forces toward the thrust side, namely the right-hand side of cylinder liner in Fig. 2 . Comparing the curves in Figs. 6 and 7 , it can be concluded that the directions of piston lateral motion are always determined by that of the small end bearing force F xpr . It can also be seen that the large fluctuations of the small end bearing force F xpr , are perfectly synchronized with contact occurrence between piston skirt and cylinder liner. This confirms that the small end bearing forces can be significantly influenced by piston secondary motion, which is just the response result excited by the small end bearing force at the same time" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001833_j.engfailanal.2017.04.017-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001833_j.engfailanal.2017.04.017-Figure3-1.png", "caption": "Fig. 3. Tooth model of helical gear.", "texts": [ " According to meshing characteristic of helical gear, the theoretical time-varying length lt(t) of contact line can be calculated by: \u23a7 \u23a8\u23aa \u23a9\u23aa l t v t \u03b2 v t \u03b5 p b \u03b2 \u03b5 p v t \u03b5 p \u03b5p v t \u03b2 \u03b5 p v t \u03b5p ( ) = \u22c5 sin \u22c5 \u2264 cos < \u22c5 \u2264 ( \u2212 \u22c5 ) sin < \u22c5 \u2264 t t b t \u03b2 bt b \u03b2 bt t \u03b1 bt bt t b \u03b1 bt t bt (10) where vt = \u03c9rb denotes the translating velocity along transverse section. \u03c9 and rb represent angular velocity and radius of basis circle respectively. Obviously, the above mentioned calculating method can't be used to calculate TVMS of helical gears directly. However, if helical gears are divided into some independent thin pieces whose thickness is dy (shown in Fig. 3), then the helical gears can be considered as a series of staggered spur gears with no elastic coupling since they are usually negligible for narrow-faced gears with low helix angles. Then the stiffness of the whole tooth can be obtained by doing integration along face width [14]. Referring to [19], the final expressions for bending mesh stiffness kb, shearing mesh stiffness ks and axial compressive stiffness ka are obtained by: \u2211 \u222b k d\u03b1 y= 1 \u0394b i N \u03b1 \u03b1 \u03b1 \u03b1 \u03b1 \u03b1 \u03b1 \u03b1 \u03b1 \u03b1 E \u03b1 \u03b1 \u03b1 \u03b1 =1 \u2212 \u2032 3[1 + cos \u2032 (( \u2212 \u2032) sin \u2212 cos )] ( \u2212 ) cos 2 [sin + ( \u2212 ) cos ]1 2 1 2 1 2 2 2 3 (11) \u2211 \u222b k d\u03b1 y= 1 \u0394s i N \u03b1 \u03b1 \u03bd \u03b1 \u03b1 \u03b1 \u03b1 E \u03b1 \u03b1 \u03b1 \u03b1 =1 \u2212 \u2032 1" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001790_j.mechmachtheory.2016.04.010-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001790_j.mechmachtheory.2016.04.010-Figure4-1.png", "caption": "Fig. 4. Contact model between the jth roller and cage.", "texts": [ "(5), A, B, C, D are functions of normal load, lubrication temperature of inlet and velocity of contact surface, see Ref. [15] for detailed expressions; sj is slide-roll ratio of the jth roller. The additional moments caused by Tj i and Tj o are depicted in Eq.(6). Mi Tj \u00bc XNP i\u00bc1 qijm \u03bc j l 2 \u2212 m\u2212 1 2 W lc Mo Tj \u00bc XNP i\u00bc1 qojm \u03bc j l 2 \u2212 m\u2212 1 2 W lc 8>>< >>: \u00f06\u00de In this section, the classic slice method is applied to save computing time of contact force between roller and cage's cross beam, as compared with that of improved slice method. The contact model is shown in Fig. 4, where {op;xp,zp} is coordinate system of cage pocket center which coincides with {orc;xrc,yrc,zrc}. The deformation \u03b4cmj between the mth slice of the jth roller and cross beam of cage is expressed as following. \u03b4cmj \u00bc jrc jj\u2212Xm tan \u03b2 j \u2212C jm rc j\u2264CP \u03b4cmj \u00bc 0 rc jNCP ( \u00f07\u00de In Eq.(7), Xm \u00bc l 2\u2212\u00f0m\u22120:5\u00deW lc; rcj is tangential distance between the jth roller and cage pocket center; \u03b2j is skewing angle of the jth roller; CP is circumferential clearance of cage pocket. The contact force Qcj between the jth roller and cage's cross beam is shown in Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000931_9781118703274.ch2-Figure2.63-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000931_9781118703274.ch2-Figure2.63-1.png", "caption": "Figure 2.63 Flow conditions and forces at the rotor blade with (a) high and (b) low blade peripheral speed or rotor speed", "texts": [ "62(a) and (b) illustrates the change in the torque-producing tangential force Ft given the same wind conditions and only slightly changed blade pitch angle or angle of attack (\ud835\udefd or \ud835\udefc). On the other hand, stall-controlled machines with a synchronous generator and frequency controller or double-fed asynchronous generator permit variable-speed turbine operation. Such configurations mean that the peripheral speed of the blades and thus the angle of attack can be altered by adjusting the turbine speed (see Figure 2.63). Regulatory interventions similar to those of blade pitch-adjustable (active-stall or pitch-controlled) turbines are possible, such that the machine output can be matched to grid or consumer requirements by the adjustment of the generator speed. As a result, optimal output ranges can be approached and, as described in what follows, only a proportion of the available power drawn for the protection of machine components and energy consumers. In spite of the constant frequency of the grid, the speed of a wind turbine can be influenced \u2022 mechanically by varying the transmission ratio if the generator speed is constant (cf" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002084_j.ymssp.2018.03.033-Figure9-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002084_j.ymssp.2018.03.033-Figure9-1.png", "caption": "Fig. 9. Finite element model of driving gear: (a) whole gear, (b) single tooth, (c) detail of the initial crack in the tooth root.", "texts": [ " The initial crack length is assumed as 0.2 mm. The crack increment size at each crack propagation step is set to 0.2 mm. To ensure the accuracy of the propagation path, the mesh of the cracked tooth is encrypted. In addition, the mesh of the crack tip region is further refined, and each crack increment introduced during crack propagation is divided into four equal parts to reconstruct the mesh of gear. The FE model of the driving gear and the details of the cracked tooth with an initial crack are shown in Fig. 9. Based on the dynamic motion equations, the dynamic load at every contact point can be calculated. The external torque of 48 N m is applied to the driven gear. The pinion speed of 3000 rpm is selected. Fig. 10 shows the dynamic load and the static load with the crack length of 1 mm under the initial angle of 45 . The maximum dynamic load is significantly greater than the maximum static load. The maximum dynamic load appears at the moment that the teeth begin to enter the single-tooth engagement" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001202_978-3-319-32552-1_49-Figure49.13-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001202_978-3-319-32552-1_49-Figure49.13-1.png", "caption": "Fig. 49.13 Car-like vehicle in the presence of sliding", "texts": [ " In these cases, the control laws presented in the previous sections may not give full satisfaction. We show in this section that these control laws can still be used successfully, provided that sliding is taken into account at the modelling level and estimated online via a dedicated observer. For simplicity, only the path following problem is addressed, but the techniques here presented can be extended to other control problems. Extended Kinematic Model Consider the two-wheels schematic representation of a car-like vehicle on Fig. 49.13. The angles \u02c7R and \u02c7F are introduced in order to represent the sliding of the rear and front wheels respectively. More precisely, denoting the centres of the rear and front wheels as PR and PF respectively, \u02c7R is the angle between the vector PRPF and the velocity vector vR of PR, whereas \u02c7F represents the angle between the steering direction and the velocity vector vF of PF. The kinematic modeling of Sect. 49.2 is easily extended to the present case [49.14], resulting in the following model 8\u0302 \u02c6\u0302\u0302< \u02c6\u0302\u0302\u0302 : PxD u1 cos" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002805_tte.2019.2956867-Figure15-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002805_tte.2019.2956867-Figure15-1.png", "caption": "Fig. 15. Experiment platform.", "texts": [ "html for more information. in which the black part is ferrite. As shown in Fig. 14(c) and (d), the slots of rotor and stator are embedded with ferrite and NdFeB PMs. During the machine design and analysis process, the optimal simulation results are selected. However, considering the actual manufacture and installation level, the shapes of NdFeB PMs on the stator and ferrite PMs on the rotor of the prototype machine are modified slightly to simplify the manufacture and installation process. As shown in Fig. 15, the experiment platform of the three phase DPMEV prototype machine is built. The experimental equipment mainly consists of oscilloscope, DC power supply and prototype machine. The DC power supply is used to supply power to the DC motor. Then, the DC motor rotates and drives the DPMEV prototype machine to rotate via the coupling. The oscilloscope is connected to the wire drawn from the phase winding of the DPMEV prototype. Hence, the no-load back-EMF waveform can be tested and recorded by the oscilloscope" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000806_j.mechmachtheory.2012.08.011-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000806_j.mechmachtheory.2012.08.011-Figure2-1.png", "caption": "Fig. 2. Thin-rimmed spur gears with inclined webs and the mating gear. (a) Left web gear. (b) Center web gear. (c) Right web gear. (d) Mating gear.", "texts": [ " 1 are known through the LTCA, a so-called \u201cUnit Force\u201dmethod is used to calculate the contact stresses on tooth surfaces of the contact teeth, it means to calculate the tooth load distributed onunit contact area of the tooth surface [9\u201312]. Tooth root bending stresses of the deformed thin-rimmed gears can be calculated by three dimensional FEMusing themodels shown in Fig. 3when the tooth loads on the reference points are known. Three types of the inclined web gears and a solid mating gear as shown in Fig. 2 are used as research objects in this paper. Fig. 2(a), (b) and (c) are the thin-rimmed spur gears with the inclined webs on the left side of the tooth, the center of the tooth and the right side of the tooth separately. They are simply called left web gear, center web gear and right web gear respectively. Sometimes, they are also called left inclined web gear, center inclined web gear and right inclined web gear respectively in order to make a distinction with the thin-rimmed gears with straight webs (simply called straight web gears). Web inclination angles are 45\u00b0 for all the three types of the gears as shown in Fig. 2(a), (b) and (c). Fig. 2(d) is the solid gear used as the mating gear of these thin-rimmed gears when they are engaged together. Tooth numbers, modules, the pressure angles and the profile shift coefficients of all the gears in Fig. 2 are z1=z2=z3=z4=50, m=4, \u03b1=20\u00b0 and x1=x2=x3=x4=0. Structural dimensions of these gears are also shown in Fig. 2. Torque load is 294 Nm and this condition is used for all the calculations in this paper. Fig. 3 is the FEM models used for deformation and stress analyses of the thin-rimmed inclined web gears under the centrifugal load conditions. Fig. 3(a), (b) and (c) are used for the left, the center and the right inclined web gears respectively. Joint circles of the webs with the bosses are fixed as FEM boundary conditions as shown in Fig. 3. Fig. 4 is the FEMmodels used for the deformation and stress analyses of the thin-rimmed straight web gears under the centrifugal load conditions. Fig. 4(a), (b) and (c) are used for the left, the center and the right straight web gears respectively. Also, the joint circles of the webs with the bosses are fixed as the FEM boundary conditions. Fig. 5 is the FEMmodel used for LTCA of the thin-rimmed gears deformed by the centrifugal loads when these deformed gears are engagedwith the solid mating gear shown in Fig. 2(d). The joint circles of thewebs with the bosses of the thin-rimmed gears are also fixed as the FEM boundary conditions in LTCA (used to calculate the deformation influence coefficients with the FEM). For the solid mating gear, boundary nodes on the three surfaces as indicated with \u201cFixed\u201d in Fig. 5 are fixed as the FEM boundary conditions. Though only the FEMmodel of the thin-rimmed center inclinedweb gear is given in Fig. 5, the FEMmodels for the other thin-rimmed gears can bemade automaticallywith the developed softwarewhen gearing parameters, engagement position parameters, structural dimension parameters and web angle are given. (a) Left straight web & 0min-1 (b) Left inclined web & 0min-1 Deformation and stress analyses are conducted for all the three types of the thin-rimmed inclined web gears shown in Fig. 2(a), (b) and (c) when the centrifugal loads are applied. In order to understand the centrifugal deformation of these gears, the calculated centrifugal deformation of all the gears is increased by 2000 times and images of the gears deformed by the centrifugal loads are illustrated in Fig. 6. Fig. 6(a), (b) and (c) are the images of the left, the center and the right inclined web gears deformed by the centrifugal loads. Fig. 6(d) is the image of the thin-rimmed right straightweb gear deformed by the centrifugal load", " 8(a), (b) and (c), the horizontal axes are the radial deformation of thewebs and the vertical axes are the radial positions of the points on the webs. Fig. 8(d) is a comparison of the web deformation for the three types of the inclined gears. FromFig. 8, it is found that the rightwebgear has the greatestweb radial deformation and the leftweb gear has the smallest web radial deformation. Axial deformation of the webs is also given in Fig. 9. In Fig. 9(a), (b) and (c), the horizontal axes are the axial deformation (in the direction of Z-axis as shown in Fig. 2(b)) of thewebs and the vertical axes are the radial positions of the points on thewebs. Fig. 9(d) is a comparison of the web axial deformation among the three types of the gears. From Fig. 9, it is found that the right web gear has the greatest axial deformation and the left web gear has the smallest axial deformation. Tooth root stresses resulting from the centrifugal load are calculatedwith FEM software [5,10\u201312]. Longitudinal distribution of the maximumroot bending stress point at the filet is given in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003082_lra.2020.3010218-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003082_lra.2020.3010218-Figure1-1.png", "caption": "Fig. 1. Kinematic model representation of the mobile manipulator.", "texts": [ " The kinematic modelling contains two parts: the first is the forward kinematics, which given the joint positions calculates the robots end-effector pose (position and orientation) and the second is the inverse kinematics that given the end-effector pose leads to the joint positions. For a redundant robot, the latter is usually an optimization process in which the redundancy of the robot is utilized in different ways to realize different sub-tasks in parallel to the main task [21]. The forward kinematics for a mobile manipulator can be derived from the kinematic models of the two subsystems, i.e., the mobile base and the manipulator. Fig. 1 shows a standard WMM with reference coordinates defined. We denote \u03a3w, \u03a3b, \u03a3m, and \u03a3ee as the world reference frame, mobile base frame, manipulator reference frame, and end-effector frame, respectively. The forward kinematics of the manipulator with respect to \u03a3m can be expressed as xm = hm(qm), (1) where xm \u2208 Rr is the pose of the end-effector in \u03a3m, hm(qm) denotes the forward kinematics for the manipulator, and qm \u2208 Rm is the generalized manipulator coordinate. Then, the forward kinematics for the entire WMM can be expressed as x(q) = xw(q) = h(qb, qm) = Tqb + Tw b (qb)T b mhm(qm), (2) where x \u2208 Rr is the pose of the end-effector in \u03a3w; q = [qTb , q T m]T \u2208 Rn, qb \u2208 Rnb are the generalized coordinates for the WMM and the mobile base, respectively; T \u2208 Rr\u00d7nb is a constant transformation matrix, which expresses the relationship between the coordinates of the mobile base and the pose of the Authorized licensed use limited to: Cornell University Library" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000262_j.triboint.2011.03.012-Figure10-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000262_j.triboint.2011.03.012-Figure10-1.png", "caption": "Fig. 10. Plot of the asperity contact pressure calculated at a pressure of 55 MPa.", "texts": [ " (For interpretation of the references to color in this figure legend, the reader is middle and decreases at the corners, the hydrodynamic pressure distribution leads to the maximum deflection in the bearing center. Therefore, the bearing shell becomes a concave shape. The elastic shaft is bent due to the load in the antipodal direction. As a consequence of both elastic deformations, asperity contact is established on the edges of the bearing, as marked with red circles in Fig. 9. As this mechanism yield asperity contact and wear, significant friction occurs at the ends of the bearings. This effect can also be seen in the calculated asperity contact pressure as shown in Fig. 10, where the maximum pressure between asperities is reached at the ends of the bearings. Simulation predicts the mean torque to be 4.9 Nm which agrees well with the mean torque of 5.170.7 Nm experimentally found on the LP06 bearing test rig. While 55 MPa is a common specific load for slider bearings in big engines, 75 MPa is clearly beyond normal working conditions. For this load asperity friction becomes dominant as the lubricating oil film thickness further decreases significantly. A load of 75 MPa causes significantly increased asperity contact and simulation showed therefore a strong dependence on the used wear profile" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002003_iccar.2016.7486697-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002003_iccar.2016.7486697-Figure3-1.png", "caption": "Figure 3. A: The abstraction ofthe kinematic model. B: Projection into the x-y-plane: The wrist center has to be placed in the x-z-plane ofthe BCS.", "texts": [ " Following the decoupling principle, as classically used for common six-DoF manipulators, we define the two sub-problems as the inverse position and the inverse orientation problem [6]. To achieve this, the joints 81 ..4 are used to solve the inverse position problem up to the wrist point, while 85 .. 7 are used to realize the orientation of the endeffector. The deterministic elbow motion on a circular path allows the definition of an intuitive self-motion manifold angle O. The angle describes the rotation of the elbow around the axis from shoulder to wrist (Fig. 3A). However, to correctly determine the joint angles, it is necessary to view this circular path as a projection into the x-y -plane, there forming an ellipse. Based on this projection, we can choose 83 in the correct quadrant with respect to the underlying ambiguities. At this point, an elliptical tangent equation is used to resolve the ambiguities for 83 , To simplify the calculation, the algorithm starts with an initial rotation of the scene. Assuming that the base coordinate system (BCS) is centered at the base of the robot, we rotate the desired target pose about the z-axis of the BCS, with the result that the center ofthe wrist now comes to lie in the x-z-plane (Fig. 3B). This is possible because only 81 depends on the real target position, while all other joint angles are independently solvable. Starting with this scenario, the position of the elbow in zero position (0 = 0\u00b0) is easy to determine and is further used to calculate the target elbow position for a desired angle O. Based on this elbow position, all joint angles can be determined geometrically to solve the inverse position problem. Finally, the last three joints can be calculated analytically for the inverse orientation problem. In summary, we will take five steps as shown in Fig. 2. C. Inverse Kinematics Solution Considering the kinematics abstraction in Fig. 3A, let M be the target pose matrix with respect to the BCS. The inverse position is solved to the wrist center position w, calculated by \u00b0M6 = M\u00b7 6M7 -1=: W = [~~] (1) As mentioned before, it is necessary to place the wrist center in the x-z-plane of the BCS in an initial step. To achieve this, we can extract the rotation angle ep out of a projection into the x-y-plane and rotate w around the z-axis (BCS) with (2) and w' = Rz.-ip . w (3) where Rz.-ip is an elemental rotation by the angle -ep around the z-axis" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002107_j.measurement.2018.07.031-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002107_j.measurement.2018.07.031-Figure3-1.png", "caption": "Fig. 3. Mesh model of test bearing housing.", "texts": [ " The stiffness\u2019s of cantilever portion of the shaft and bearing housing has been computed through finite element analysis. The computed value of shaft stiffness is 2.638\u00d7104N/mm with consideration of actual loading condition. The test bearing housing is mounted on shaft to support the test bearing. The stiffness of this asymmetric bearing housing in radial X direction has been computed through ANSYS software. The computed value for stiffness of test bearing housing is 2.42\u00d7107N/mm. The mesh model of test bearing housing is shown in Fig. 3. 2.3. Stiffness coefficient of elastohydrodynamic lubricant film It is essential to find the minimum film thickness to confirm the amount of lubrication at contact surfaces. The damping due to presence of lubricant film at contact surfaces between rolling elements and bearing races also depends on additives and based oil. The lubricant can be analysed by liquid chromatography [33], lubricant adsorption capacity [34,35] and lubricant additives. The minimum lubricant film thickness is found at outlet zone of rolling contact" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002946_soro.2019.0076-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002946_soro.2019.0076-Figure5-1.png", "caption": "FIG. 5. An exploded view of the SLAK showing how all its parts fit together (A). Note that the anti-kink cords (18) cannot be seen as they are contained in the sealed tubes (6). The SLAK is worn as shown in (B). Color images are available online.", "texts": [ " The design of the PPIA is closely coupled to the design of the flexible fabric sleeve and webbing that connect it to the thigh and calf. Figure 4 shows how the SLAK consists of three PPIAs that are positioned behind the leg. The side PPIAs add extra bulk and mass compared with Veale et al.\u2019s21 single PPIA orthosis (the SLAK\u2019s volume is 5 L and its mass is 1.95 kg). However, they potentially have the benefit of increasing the SLAK\u2019s ROM and torque output, because they eliminate the torque counteracting lateral support cords of the single PPIA orthosis. An exploded view of the SLAK is shown in Figure 5A with accompanying component descriptions in Table 4. Simply explained, the SLAK is made of three fabric layers connected FIG. 2. The PIA (A) and PPIA (B) are made of a flexible tube, diameter D, that produces a torque s when inflated to a pressure P at an angle h. When the actuator is attached to a limb or other articulated body, the distance between the body\u2019s joint center and the line projected parallel from the PPIA\u2019s mountain fold is the pleat misalignment pa (C). In this work, an anti-kink cord running through the PPIA\u2019s tube prevents choking of air flow in the PPIA", " The constraint layer introduces the folds in the sleeve layer and, hence, tubes, thus forming PPIAs. The outer constraints also hold the PPIAs away from the base layer so that when they are inflated they do not squeeze the wearer\u2019s leg. Last, the base layer enables the PPIAs to be coupled to the leg with velcro (hook-and-loop fastener) and buckles. A more detailed explanation of how the SLAK was constructed, along with scale drawings of all the custom components, can be found in the Supplementary Data. In addition, as seen in Figure 5B, the SLAK was stitched to jeans that were internally padded (Neoprene rubber sheet, RS-stocknr. 506-3157; RS Components, Corby, United Kingdom). The jeans located the SLAK in the correct position behind the knee, and the padding increased the grip between the jeans and the smooth artificial leg that the SLAK was tested on. This reduced the amount the SLAK shifted downward during actuation. However, the padding also made the SLAK difficult for a human to don and doff, hence a zipper allowed the front of the jeans leg to open" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000239_iros.2011.6094415-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000239_iros.2011.6094415-Figure3-1.png", "caption": "Fig. 3. Target specifications of new hand based on average of young Japanese female [19, 22, 23] (Note: Draw line doesn't show the strict outline of Japanese female hand shape.)", "texts": [ " and two servomotors are located inside of the hand. Towards design concept E), planetary gears are used in the new hand for the final reduction gear. Although miter gears and bevel gears were adopted inside of the previous hand, they are not used in the new hand. To realize design concept F), we referred to the anthropometry database of Japanese [19, 22, 23]. Although there are several measured items concerning human hands in the database, the principal dimensions were selected from the database for designing the new hand. Fig. 3 shows the selected dimensions and the average for young Japanese females. Based on the design concepts D), E) and F), the new hand was developed. During the mechanical design stage, the link length and thickness of the new hand were deformed to be from 90% to 110% of the average dimension of a young Japanese female. Fig. 4 shows the new developed hand and its principal dimensions. As shown in Figs. 3 and 4, the dimensions of the new hand are almost that of a young Japanese female. Fig. 5 shows an illustration of the new hand mechanism" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003252_tia.2020.3040142-Figure13-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003252_tia.2020.3040142-Figure13-1.png", "caption": "Fig. 13. Flux density distribution of optimal case 1. (a) Nonlinear HMM. (b) FEA.", "texts": [], "surrounding_texts": [ "For a specific application scenario, the gear ratio, stack length, air-gap length, and outer diameter of a CMG is fixed, and the other geometrical parameters can be optimized. Besides, the material of PMs and silicon steel are settled before optimization, and they are selected as N35H and 50JN270, respectively. The eddy current loss of PMs and iron loss of silicon steel within CMGs is small compared to the power it transmits when it works at rated condition. Additionally, the efficiency of CMGs can be maintained at a high level if the silicon steel within CMGs are not highly saturated, and the output torque of CMGs will decrease if its silicon steel part is highly saturated. Therefore, individuals with low efficiency can be tossed out automatically by optimization algorithm as long as the output torque is set as an optimization objective. Besides, the torque ripples of CMGs are very low if the pole-pair combinations of CMGs are well selected [17]. This can also be observed in Fig. 9, the torque ripple of CMG1 is about 8%, while the torque ripple of CMG2 is below 1%, which is almost ignorable. Thus, the efficiency and torque ripple are not set as the optimization objectives. The weaknesses of CMGs are its low torsional stiffness and high manufacture cost compared to mechanical gearboxes [29]. The torsional stiffness is directly determined by the peak transmitted torque of CMGs, which is represented by Tp. The high cost of CMGs is caused by the usage of PMs since the price of NdFeB is almost one hundred times of that of steel. Thus, the torque versus PM volume ratio should be maximized, which is represented by Tp/VPM. Additionally, the rotational inertia of CMGs is an important index, since a smaller rotational inertia means a better dynamic response characteristic. Since the lowspeed rotor is connected to the output shaft, its rotational inertia J is set as an optimization objective, which can be expressed as J = 1 4 \u03c1La [ \u03b21 ( R4 mid,1 \u2212R4 4 ) + \u03b22 ( R4 mid,2 \u2212R4 mid,1 ) +\u03b23 ( R4 5 \u2212R4 mid,2 )] (38) where \u03c1 is the density of the silicon steel. Furthermore, we should avoid the irreversible demagnetization of PMs on the CMGs during rated operation. Since the rated operating temperature of gearboxes varies from scenarios to scenarios, we choose the gearbox in wind turbine for instance, where the rated operating temperature is about 60 to 70 \u00b0C [30]. In this article, Trated is set as 60 \u00b0C. As can be observed in Fig. 11, the irreversible demagnetization occurs when the magnetic flux density within the PMs drops below the knee point [31], and the knee point decreases with the increase of temperature. Hence, the absolute magnetic flux density on the outer surface of the PMs on the low-speed rotor and high-speed rotor should be above the magnetic flux density on the knee point at rated operating The individual number in one generation is set as 20; the maximum number of generations is set as 100. Besides, a CMG with 4 pole-pair PMs on the high-speed rotor and 11 pole-pair PMs on the stator is selected for the optimization study, and the value range of design variables are given in Table III. The airgap, the inner radius, the outer radius, and the axial length of the studied CMG are set as constants during optimization, whose values are 0.5 mm, 30 mm, 100 mm, and 60 mm, respectively. Additionally, the remanence and knee point magnetic flux density of N35H at rated operating temperature are 1.15 T and 0.22 T, respectively." ] }, { "image_filename": "designv10_9_0003016_j.oceaneng.2020.108257-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003016_j.oceaneng.2020.108257-Figure2-1.png", "caption": "Fig. 2. AUV2000 body-fixed and earth-fixed coordinate systems.", "texts": [ " 1 is a hybrid AUV designed to integrate the outstanding characteristics of conventional AUV and underwater glider (a type of AUV that employs variable-buoyancy propulsion instead of traditional propellers or thrusters). Therefore AUV2000 can operate in two separate modes, specifically without using the thruster (Glider mode) and using the H.N. Tran et al. Ocean Engineering 220 (2021) 108257 thruster (AUV mode). However, in this paper, we only focus on designing the depth controller for AUV2000 in AUV mode. In accordance with SNAME (SNAME, 1950), the 6-DOF nonlinear kinematic and dynamic equations of motion of AUV are described in the earth-fixed frame {e} and the body-fixed frame {b} as shown in Fig. 2. According to Fossen, we have coordinate transform relating the translational velocities and the rotational velocities between {b} and {e} for various underwater vehicles in general and AUV in particular as follows: \u23a7 \u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 \u23a1 \u23a3 x\u0307 y\u0307 z\u0307 \u23a4 \u23a6 = J1(\u03b72) \u23a1 \u23a3 u v w \u23a4 \u23a6 \u23a1 \u23a3 \u03c6\u0307 \u03b8\u0307 \u03c8\u0307 \u23a4 \u23a6 = J2(\u03b72) \u23a1 \u23a3 p q r \u23a4 \u23a6 (1) where \u03b71 = [ x y z ]T : the position of the vehicle with respect to {e} \u03b72 = [\u03c6 \u03b8 \u03c8 ] T : the orientation (roll, pitch, yaw) of the vehicle with respect to {e} \u03c51 = [ u v w ] T : the translational velocities of the vehicle with respect to {b} \u03c52 = [ p q r ]T: the rotational velocities of the vehicle with respect to {b} Following to (Prestero, 2001), the 6-DOF nonlinear dynamic equations of motion of AUV2000 can be expressed as m [ u\u0307 \u2212 vr +wq \u2212 xG ( q2 + r2)+ yG(pq \u2212 r\u0307)+ zG(pr + q\u0307) ] = \u2211 Xext (2a) m [ v\u0307 \u2212 wp+ ur \u2212 yG ( r2 + p2)+ zG(qr \u2212 p\u0307)+ xG(qp+ r\u0307) ] = \u2211 Yext (2b) m [ w\u0307 \u2212 uq+ vp \u2212 zG ( p2 + q2)+ xG(rp \u2212 q\u0307)+ yG(rq+ p\u0307) ] = \u2211 Zext (2c) Ixxp\u0307+ ( Izz \u2212 Iyy ) qr+m[yG(w\u0307 \u2212 uq+ vp) \u2212 zG(v\u0307 \u2212 wp+ ur)] = \u2211 Kext (2d) Iyyq\u0307+(Ixx \u2212 Izz)rp+m[zG(u\u0307 \u2212 vr +wq) \u2212 xG(w\u0307 \u2212 uq+ vp)] = \u2211 Mext (2e) Izzr\u0307+ ( Iyy \u2212 Ixx ) pq+m[xG(v\u0307 \u2212 wp+ ur) \u2212 yG(u\u0307 \u2212 vr+wq)]= \u2211 Next (2f) where m is the AUV\u2019s mass, (xG, yG, zG) is the center of gravity, and Ixx, Iyy, Izz respectively are inertial moments about the x, y, and z axes" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002696_j.addma.2020.101401-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002696_j.addma.2020.101401-Figure1-1.png", "caption": "Fig. 1. (a) Print schematic for a series melt pools using constant laser parameters, to ease sectioning. Depositions were made on a printed substrate 3 mm thick. (b) Top view of a single deposition SEM image. Outline of the required sectioning range to measure accurate penetration of laser during deposition.", "texts": [ " The single deposition technique was used to investigate the shape, morphology and amount of material deposited without having to account for point distance and hatch spacing. To calculate the absorbed energy density during 316L steel deposition, Eq. (1) was applied [8]: =E \u03b7P\u03c4 \u03c0\u03c3 D \u03c4 absorbed 2 (1) where P is the effective laser power, \u03b7 is the absorptivity, set at 0.4, D is the thermal diffusivity equal to 5.38\u00d710\u22126 m2 s\u22121, \u03c3 is the laser spot diameter of 65 \u03bcm and \u03c4 is the exposure time of the laser [8,3,41]. The samples were printed on the head of removable bolts screwed on to the build plate, to minimise damage when separating them from the build plate (Fig. 1a). The depositions analysed were printed on a 3mm additively manufactured substrate using standard processing parameters of 200W laser power and 80 \u03bcs exposure time, using a hatch spacing of 110 \u03bcm and a point distance of 65 \u03bcm. The substrate layer was used to ensure the uniformity of the final surface height before printing single depositions. Low magnification SEM was used to collect information about the circularity and size of the material deposited, and then the samples were sectioned in 2mm thick lamellas, to investigate the cross-section of the melt pool" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002051_j.jmatprotec.2017.05.043-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002051_j.jmatprotec.2017.05.043-Figure5-1.png", "caption": "Fig. 5. Schematic of four-layer deposition of powdered titanium alloy Ti-6Al-4V on substrate of the same material by \u00b5-PTA process showing deposition direction and location of three Ktype thermocouples.", "texts": [ " Figure 4 presents the algorithm used for analyzing the temperature distribution obtained by FES. Fig. 3. Geometry of 3D model used for finite element simulation of multi-layer metallic deposition by \u00b5-PTA process with upper inset showing its enlarged view and lower inset depicting photograph of the actual multi-layer deposition obtained experimentally. Fig. 4. Algorithm used in analysis of temperature distribution in multi-layer metallic deposition by \u00b5-PTA process. 3. Experimental validation Figure 5 depicts the schematic of deposition of 8 mm high and 50 mm long straight wall using powdered titanium alloy Ti-6Al-4V on substrate of the same material and having dimensions 80 mm x 80 mm x 20 mm in four layers of equal thickness 2 mm by \u00b5-PTA process. The process parameters used in the experimental validation were same as used in the finite End of all time-steps Define element type, material properties and other parameters Building model and meshing Apply thermal boundary condition and heat source for first time step Activate layer elements for first time step Compute and store nodal temperature Increment time step End Yes No Activate new elements, move heat source and update boundary conditions Start element simulation that were selected considering the quality of the deposition. Their values are: micro-plasma arc power: 400 W; travel speed of the worktable: 190 mm/min.; and powder mass flow rate: 3.5 g/min. The thermal cycles generated during \u00b5-PTA arc heating were measured with three K-type thermocouples placed in the location as shown in Fig. 5. Schematic representation of experimental apparatus used for multi-layer deposition of metallic material by \u00b5-PTA process is depicted in Fig. 6. Figures 7a to Fig. 7c compares the finite element simulated and experimentally obtained thermal cycles in four-layer deposition of powdered titanium alloy Ti-6Al-4V in the back and forth direction on substrate of the same material. The experimental data were acquired by three K-type thermocouples located in the substrate material as shown in Fig. 5. Figure 8 depicts the maximum temperature of each deposition layer recorded by the three thermocouples. It can be seen from Figs. 7 and 8 that FE simulated thermal cycles agrees with slight under prediction of thermal cycles as compared to experimental results for all the layers of deposition. Similar trends of thermal cycles were observed by Ding et al. (2011) from temperature field simulation of wire and arc additive layer manufacturing process. While depositing the 1st layer, the temperature recorded by the thermocouple located near to the starting point of deposition (i", " Variation of properties of the substrate material (i.e. titanium alloy Ti-6Al-4V) with temperature: (a) thermal conductivity; (b) density; and (c) specific heat (Mills, 2002). Fig. 3. Geometry of 3D model used for finite element simulation of multi-layer metallic deposition by \u00b5-PTA process with upper inset showing its enlarged view and lower inset depicting photograph of the actual multi-layer deposition obtained experimentally. Fig. 4. Algorithm used in analysis of temperature distribution in multi-layer metallic deposition by \u00b5-PTA process. Fig. 5. Schematic of four-layer deposition of powdered titanium alloy Ti-6Al-4V on substrate of the same material by \u00b5-PTA process showing deposition direction and location of three Ktype thermocouples. Fig. 6. Schematic of experimental apparatus used for multi-layer deposition of metallic materials by \u00b5-PTA powder deposition process. Fig. 7. Comparison of simulated and experimental thermal cycles recorded by the three thermocouples located at (a) TC1; (b) TC2; and (c) TC3; in multi-layer metallic deposition", " Geometry of 3D model used for finite element simulation of multi-layer metallic deposition by \u00b5-PTA process with upper inset showing its enlarged view and lower inset depicting photograph of the actual multi-layer deposition obtained experimentally. End of all time-steps Define element type, material properties and other parameters Building model and meshing Apply thermal boundary condition and heat source for first time step Activate layer elements for first time step Compute and store nodal temperature Increment time step End Yes No Activate new elements, move heat source and update boundary conditions Start Fig. 4. Algorithm used in analysis of temperature distribution in multi-layer metallic deposition by \u00b5-PTA process. Fig. 5. Schematic of four-layer deposition of powdered titanium alloy Ti-6Al-4V on substrate of the same material by \u00b5-PTA process showing deposition direction and location of three Ktype thermocouples. Fig. 6. Schematic of experimental apparatus used for multi-layer deposition of metallic materials by \u00b5-PTA powder deposition process. (a) (b) (c) Fig.7. Comparison of simulated and experimental thermal cycles recorded by the three thermocouples located at (a) TC1; (b) TC2; and (c) TC3; in multi-layer metallic deposition" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002629_s00170-019-04558-5-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002629_s00170-019-04558-5-Figure3-1.png", "caption": "Fig. 3 Propeller simulator 3D model Fig. 4 Schematic diagram of cylindrical slicing surface", "texts": [ " To begin with, create a DAT format point cloud file with 3D coordinates provided by the feature points table; import the file to Unigraphics NX software and fit points of the same height with B-spline curve as well as smooth curves chain. Then, geometry transformation is performed. These transformations include rotation shift where the helix angles \u03b1 are calculated by screw pitch, translation shift based on the trim amount YR and distance from maximum thickness to the trailing edge, andwinding shift that winds the section curve to the respective heights of the cylinder. The last step is to form a \u201cblade sheet\u201d and eventually the blade entity via \u201csewing\u201d the blade sheet, as in Fig. 3. It is saved as a propeller slice model in the STL file format in the Unigraphics NX software. It is well known that errors may occur in the STL file, which may result in inaccurate slicing paths and reduce the precision of the WAAMpropeller parts. Therefore, the exported propeller STL model must be checked and repaired. In this paper, theMagics software developed by Materialise is used to inspect and repair the propeller STL model, and the normal direction, holes, and gaps in the model are repaired", "5 s. In the process of producing propeller simulator with WAAM, 8\u201310 photos of point cloud file are taken along the predetermined trajectory. These files are auto-stitched; then, high-precision point cloud files of propeller simulator are prepared. Post-processing is a necessary step to obtain the actual 3D model of the propeller. Point cloud files are imported into Geomagic qualify. 3D model after packaging, patching, and smoothing is shown in Fig. 8. Target propeller model created by UG is in Fig. 3. A comparative analysis is performed after point cloud file fitting. The specific steps are listed as follows: (1) Import the scanned model into Geomagic qualify software as the testing object and import the target model as the reference object. The target model is defined as point cloud M1, and the scanned model is defined as point cloud N1. (2) Use the \u201cfour-point method\u201d to roughly align the two cloud files. Select four feature points on N1, which form a feature point pair with four feature points at the corresponding position on M1, as is shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001890_j.triboint.2018.06.005-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001890_j.triboint.2018.06.005-Figure3-1.png", "caption": "Fig. 3. The finite element model for gear contact analysis.", "texts": [ " (14) is rewritten as \u23a7 \u23a8 \u23aa \u23aa \u23a9 \u23aa \u23aa = \u2212 + \u2212 + \u2212 + + + + = \u2212 + + + \u2212 + + \u2212 + \u2212 \u2212 X r h \u03b8 \u03be r\u03b8 \u03b8 \u03be r h r \u03b8 h \u03b8 \u03be r\u03b8 \u03b8 \u03be Y r h \u03b8 \u03be r\u03b8 \u03b8 \u03be r h r \u03b8 h \u03b8 \u03be r\u03b8 \u03b8 \u03be ( )sin( ) cos( ) ( ) [ sin( ) cos( )] ( )cos( ) sin( ) ( ) [ cos( ) sin( )] f c c c c f c c c c 2 2 2 0.5 2 2 2 0.5 (15) where, \u2264 \u2264 \u00b0\u03b80 h r tan 20 c . When =\u03b8 0, the transition curve remains tangent to the dedendum circle. The transition curve is tangent to the involute profile given that =\u03b8 h r tan 20 c 0 . The tooth profile is obtained according to the equations of the involute and transition curves. Then, the geometric and finite element models of the gear are established in ABAQUS (Fig. 3). The pinion and gear are meshed by hexahedral elements (C3D8R). We generate a dense mesh distribution on the gear teeth and a sparse mesh distribution on the gear felly by simultaneously considering the computing accuracy and efficiency of finite element contact analysis. A total of 19 nodes are observed along the profile direction, whereas 31 nodes along the lead direction, thereby providing the finite element model with 91,200 elements for the pinion and gear. The degrees of freedom of the pinion or gear center are restricted, except for the rotational freedom around the z-axis", " To control the damping ratio within 0.1, the coefficients =\u03b1 400 and = \u00d7 \u2212\u03b2 3 10 6 are applied. The counterclockwise rotation speed and torque are loaded at the pinion and gear center around the z-axis, respectively. To verify the finite element model, we compare the maximum root stress of the gear contact analysis with Charbert's [39] and Filize's [40] results. The maximum root stress at the high point of single tooth contact (applied torque 100 Nm and rotation speed 200 rpm) is 35.88MPa, according to the model in Fig. 3 (\u03bc=0). The root stresses of Charbert's and Filize's models are 29.20MPa and 39.12MPa, respectively. The deviations in the prediction results can be explained as follows: 1) Charbert's result was achieved based on the static finite element analysis of one tooth under plane-strain conditions, in which the effects of the root fillet, contact ratio and dynamic load were neglected; 2) In the root stress prediction model by Filize, the root fillet and pressure angle were included, but the contact ratio, dynamic load and tooth width were not considered" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001890_j.triboint.2018.06.005-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001890_j.triboint.2018.06.005-Figure6-1.png", "caption": "Fig. 6. Test rig for measuring the root stress of a gear box.", "texts": [ " Electromotor 1 is used to drive the input shaft of the gear box, and electromotor 2 is an electric generator used to apply load on the gear box. The energy generated by electromotor 2 is transmitted to electromotor 1 as feedback driving. The input rotation speed and torque are collected by sensor 1, and the output rotation speed and torque are collected by sensor 2. These signals are transferred to the virtual instrument by the data acquisition card. The rotation speed of the electromotor is controlled by the frequency converter. The test rig for measuring root stress is shown in Fig. 6 (a). The root strain signals are acquired using strain gauges, which are mounted on the risky section of the dedendum along the lead direction, seen in Fig. 6 (b). The risky section on the dedendum are determined via using 30\u00b0 tangent method. The gears was run-in before the test under the lubrication condition, and the parameters of the lubricant are given in Table 1. Furthermore, the root stresses under various working conditions (different rotation speeds n or torques T, with and without lubrication) are measured with strain gauges. Without loss of generality, the root stresses measured by the strain gauges of row #3 are considered. Electrical noise and the vibration of the gear box interfere with strain signals; hence, the time domain average method is utilized to eliminate interference signals", " The measured and calculated root stresses always generate saltation at the highest and lowest point of single tooth contact (i.e. point C and D in Fig. 7). The saltation is a key characteristic to find the corresponding stress value at each meshing position, because the time coming in mesh cannot be tracked in the measurement. According to the saltation of root stress curves, the meshing position at C & D can be determined, thereby inferring the meshing positions corresponding to other measured stress values in Fig. 7. The three measured stresses \u03c3i m are acquired from the strain gauges in row #3 (Fig. 6 b). Correspondingly, the calculated stress is equal to the average node stress in the region covered by each strain gauge. Hence, the number of strain gauges \u03bb is 3 in the flowchart of the tooth friction coefficient (seen in Fig. 1). Error threshold \u03b5=0.001 is sufficient for the following case. Fig. 9 (a) illustrates the comparative results of the gear friction coefficients without lubrication at a rotation speed of 500 rpm and an applied torque of 100 Nm. The friction coefficient calculated by the proposed method decreases from the engaging-in point to the pitch point first and then increases from the pitch point to the engaging-out point" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002890_tia.2020.3033505-Figure24-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002890_tia.2020.3033505-Figure24-1.png", "caption": "Fig. 24. Temperature verification of the proposed FMPM prototype at rated load. (a) Stator. (b) Rotor.", "texts": [ " In order to validate the feasibility of the proposed FMPM, a proposed 18-stator-slot/13-rotor-slot FMPM prototype is built and tested. Its key parameters are listed in Table III. As it has an odd rotor slot number, attentions should be paid on the unbalanced magnetic force beforehand. Fig. 23 compares the unbalanced magnetic force with the tangential force, which drives the rotor. It can be seen that the unbalanced magnetic force is 34.6N, which is only 9% of the tangential force 374.1N. Thus, the unbalanced magnetic force of the prototype is small and can be neglected. Besides, Fig. 24 shows the temperature distribution of the prototype at rated load condition. It can be seen that the maximum temperature is 109.7\u2103. The insulation grade is designed as F, and the ambient temperature is set as 40\u2103. Thus, the maximum temperature is lower than the limitation of F grade, i.e. 155\u2103. The stator and rotor structures are shown in Fig. 25, and the test bed is illustrated in Fig. 26. Authorized licensed use limited to: University of Gothenburg. Downloaded on December 19,2020 at 20:34:12 UTC from IEEE Xplore" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000039_978-1-84996-220-9-Figure4.5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000039_978-1-84996-220-9-Figure4.5-1.png", "caption": "Figure 4.5 Top view of the simulation and experiment environment with two poles and a table. The initial and final configurations of the robot are also shown", "texts": [ " Next, anticipation and regaining motions are computed to smoothly connect the reshaped portion with the collision-free part of the original trajectory. Finally, inverse kinematics (IK) is applied to satisfy the constraints of the hands at each sample of the reshaped trajectory that synchronizes the upper body task with the lower body motion. As a result, this reshaping eliminates the collision locally as shown in Figure 4.4. We have applied the proposed method to plan a motion to carry a bulky object in an environment with several obstacles as shown in Figure 4.5. The proposed method is implemented as an off-line planner on the assumption that the environment is completely known. In this case, what matters is not the weight of the object but its geometric complexity. Figure 4.6 shows the experimental results of the planned motion. Since the distance between the two lamps is shorter than the bar length, the bar should pass through at an angle. At the beginning of the motion, the computed trajectory for the bar makes the robot move to the left, then walk forward with a certain angle to the path through the gap (Figure 4" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000161_tmag.2010.2044043-Figure12-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000161_tmag.2010.2044043-Figure12-1.png", "caption": "Fig. 12. Dynamic deformation caused by , , and . (a) View from the -direction. (b) View from the -direction.", "texts": [ " The distribution of rotates in the same direction as the magnetic field. Though the current of phase A reaches the maximum in Fig. 11, relatively large dynamic force density does not appear in the phase belt of phase A. Like the static forces, in the coil ends except the portion close to the core, the involute and the knuckle portion experience larger dynamic forces than the nose portion, as marked by the ellipse. The corresponding deformation based on the computation of operating deflection shapes is illustrated in Fig. 12. Though is larger in the involute and the knuckle portion, stronger deformation appears at the nose portion, as marked in Fig. 12(a) by the ellipse with a solid line. The maximum displacement in the forced vibrations is . In addition, the deformation of the nose portion of the coil ends in two successive phase belts is in the opposite direction at a certain instant, as shown by the ellipse with a dash line. In a phase belt, e.g., the one indicated in Fig. 11, the dynamic deformation at the nose portion of coil ends 1\u20136 is also different. Fig. 13 shows the magnitude of displacement of each coil end as a function of solution angle, and it can be seen that the nose portion of the outermost coil ends 1 and 6 experiences larger displacement than that of the other four coil ends" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001584_j.jsv.2016.08.014-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001584_j.jsv.2016.08.014-Figure2-1.png", "caption": "Fig. 2. Coupling between two consecutive links inside a kinematic chain.", "texts": [ " In order to find the dynamic stiffness matrix of a kinematic chain, composed of both rigid and flexible bodies connected by joints, it is necessary to start from the concepts outlined in the previous section. The dynamic stiffness matrix K of an arch maps the small deformations of the end-nodes into a wrench containing the dynamic forces and torques at the extremities of the element. Now, let us consider a quadratic function Vn defined in terms of matrix K : V \u00bc 1 2 qTK q; q\u00bc u1 1 u2 1 \" # (17) where q is the 12-dimensional array of deformations of the extremity nodes. Function Vn has the form and units of a potential energy. Fig. 2 describes a flexible body, labelled with number 1, coupled to a second body, either flexible or rigid, labelled with number 2, by means of a joint. Recalling Eq. (11), displacement array u2 1 can be expressed in terms of u1 2, belonging to the second body, and \u03b8, i.e. u2 1 \u00bc Gu1 2\u00feH\u03b8 (18) in which matrix G, derived from vector d, is used to consider a rigid-body displacement. Notice that without rigid displacement matrix G becomes the identity matrix 16. For the flexible body 1 function Vn can be written as V 1 \u00bc 1 2 u1 1 u2 1 \" #T K 1;1 1 K 1;2 1 K 2;1 1 K 2;2 1 2 4 3 5 u1 1 u2 1 \" # (19) with K 1 being the dynamic stiffness matrix of the flexible body" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001326_1.3640593-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001326_1.3640593-Figure3-1.png", "caption": "Fig. 3 S w i v e l e d rocket e n g i n e", "texts": [ " An interesting observation is found in the coefficient of the damping term. The implication is that there is positive damping whenever rjri > 0, but an instability tendency whenever 7777 < 0. Equation (12) is valid irrespective of the physical mechanism whereby TO executes the motion qi. The action-reaction forces between M and m can be of any type; e.g., elastic, electrostatic, or magnetic. For this reason no specific mechanism has been indicated in Fig. 2. A S w i v e l e d Rocket Engine on a Veh ic le M o v i n g in T w o D imens ions . Fig. 3 shows the schematic. Again we make an identification of terms between equation (11) and Fig. 3. As noted earlier, the assumption is made that the variations in mass and inertia associated with thrust production are negligible. NH = TO, / . . ( i ) = 1 a 4 8 8 / S E P T E M B E R 1 9 6 2 0 Jy 0 As in the previous example, since the motion is assumed to be two dimensional, the inertias I x , I v and J x , J u are immaterial. Linear and Angular Motions co<\u00b0> = kco &>'<\u00bb = k5, qi = -(I L + & Note that qi is not an independent motion but follows from the 5-motion; i.e., the engine has only the 5 degree of freedom relative to the vehicle", " = m/M Again, for a prescribed 5(0 , equation (13) represents a linear equation for co with time-varying coefficients. An interesting effect, the well-known \"tai l -wags-dog\" phenomenon, can be seen from (13) for simple-harmonic, small-amplitude engine motion. Take sin 8 = 8 cos 5 = 1 5 = \u2014 J225 ( f l = frequency of 5-motion) and neglect all nonlinear terms in (13). T h e result is (7, + 2/i)co = { - T L { 1 + M)\"1 + [J + / i ( l + Z /L ) ] f i 2 l 5 (14) For sufficiently low frequencies, the 0 2 - term in (14) is negligible and the sense of vehicle acceleration co is as expected according to Fig. 3. But, as the swiveling frequency increases, the 122-term becomes increasingly important to the point where it finally nullifies the thrust moment. The critical frequency is a 2 = TL (1 + m)[7 + 7 . (1 + l / L ) ] Beyond this frequency the tail wags the dog, i.e., the sense of vehicle acceleration is controlled b y the engine inertia moment rather than the thrust moment. Transactions of the AS M E Downloaded From: http://appliedmechanics.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000193_j.cma.2011.04.006-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000193_j.cma.2011.04.006-Figure4-1.png", "caption": "Fig. 4. Reference blade profile definition.", "texts": [ " When whole crowning of the gear tooth surface is applied, only four areas exist provided with crowning in longitudinal and profile directions (Fig. 3(b)). Those zones correspond to zones 1, 3, 7 and 9 in Fig. 3(a), because areas 2, 4, 5, 6, and 8 (Fig. 3(a)) do not exist when whole crowning is applied. In order to achieve the surface modifications described above, a modified imaginary generating crown-gear will be applied for computerized generation of the geometry of the bevel gear. The geometry of the imaginary generating crown-gear is based on the geometry of a reference blade profile (Fig. 4). Both sides of the blade profile will be defined in coordinate system Sc, fixed to the blade, with its origin Oc placed on the middle of the segment OaOb, with axis xc directed along the pitch line and the axis yc directed towards the addendum height of the reference blade. Auxiliary coordinate systems Sa and Sb (see Fig. 4), with origins in Oa and Ob, are rigidly connected to the blade profiles that will define the driving and coast sides of the theoretical crown gear, respectively, and having their origins on the intersection of the pitch line with the respective blade profiles. The axes ya and yb of coordinate systems Sa and Sb are directed along the reference straight profile of the blade towards the addendum height of the blade. The profile of the blade is represented in coordinate systems Sa and Sb (see Fig. 4) for left and right sides as ra;b\u00f0u\u00de \u00bc apf \u00f0u u0\u00de2 u 0 1 2 66664 3 77775: \u00f09\u00de Here, u is the blade profile parameter, apf is the parabola coefficient for profile crowning, and u0 is the value of parameter u at the tangency point of the parabolic profile with the corresponding ya or yb axis. The upper and lower signs of apf correspond to representation of profile geometry in coordinate systems Sa and Sb for the left and right sides, respectively. The following conditions are established in order to apply profile crowning by considering three parts for the active part of the reference blade profile: If u > u0t , then apf \u00bc apft and u0 \u00bc u0t (area A of zones 1, 2, and 3 in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000990_j.mechmachtheory.2013.05.006-Figure14-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000990_j.mechmachtheory.2013.05.006-Figure14-1.png", "caption": "Fig. 14. Roller positions in two limit states of relative displacement between inner and outer rings. a) Limit state I of relative displacement. b) Limit state II of relative displacement.", "texts": [ " \u03b4jk \u00bc 3:81 2 1\u2212\u03c52 \u03c0E 2 4 3 5 0:9 Qjk 0:9 w0:8 \u00f08\u00de According to displacement\u2013deformation compatibility condition of bearings, with the same deflection angle between inner and outer rings, the variation of maximum local deformation \u03b4jk of Roller 1 is equal to the variation of relative displacement between inner and outer rings shown in Fig. 12. The discontinuous distribution of rollers in bearings will generate fluctuation of both the relative displacement of inner and outer rings and the maximum roller load. Fig. 14 shows two limit states of the relative displacement between inner and outer rings during running process of bearings. In Fig. 14a, Rollers 1 and 2 are symmetrically distributed in relation to the direction of radial load. In Fig. 14b, Roller 1 is placed in the location of external radial load action. When Roller 1 in Fig. 14a rotates from its position to the position of Roller 2, a cycle with the period of 2\u03c0/n was passed both in relative displacement between inner and outer rings and the maximum roller load. Fig. 15 shows the fluctuation of relative ring displacements and maximum loads in a running period of 2\u03c0/n. When two rollers are symmetrically distributed in relation to the direction of radial load, the maximum load and maximum contact pressure reach to minimal values. When a roller is placed in the location of external radial load action, the maximum load and maximum contact stress reach to maximal values" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003340_j.addma.2021.101881-Figure18-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003340_j.addma.2021.101881-Figure18-1.png", "caption": "Fig. 18. Vertical residual deformation after support removal (ASR) using 2- layer LLM without tuned MPM.", "texts": [ " The obtained residual deformation before and after separating the teeth support from the cantilever beam is shown in Fig. 17. Compared to those results in the benchmark no-lumping case (see Fig. 14), the prediction error is very small, thus demonstrating good accuracy of the 2-layer ELLM employing a tuned MPM to avoid stress and deformation overestimation. As a supplemental study, the computed residual deformation in vertical build direction after support removal using 2-layer LLM without the tuned MPM is shown in Fig. 18 as a comparison. It is seen that the prediction error for the maximum vertical deformation becomes larger compared to Fig. 17(b) with reference to the benchmark results in Fig. 14. This phenomenon strongly proves that material property tuning X. Liang et al. Additive Manufacturing 39 (2021) 101881 is necessary to improve the accuracy of the layer lumping method. As a further step, the 3-layer ELLM is studied in this example. Correspondingly, two more adjusted MPMs (#2 and #3) are needed in addition to the real MPM (#1) for IN718" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001723_s00170-015-7481-8-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001723_s00170-015-7481-8-Figure3-1.png", "caption": "Fig. 3 Schematic of the first method for the observation of the powder flow [18]", "texts": [ "2 mm thickness (the light sheet was obtained as a diode laser passed through a cylindrical glass), and a powder feeder system including a coaxial nozzle with four symmetrical nozzle tips. In this research, the spherical pure titanium particles were chosen as the feeding material, and the particle diameter was limited by the separation of the molecular sieve to simplify the analysis, and the equivalent diameter of the particles can be considered as 0.07 mm in this study. Two photography methods were proposed to obtain the powder flow images referring to literature [18]. The first method is shown in Fig. 3. The high-power magnesium light lamp irradiates the powder flow, and the angle between the lamp light and the high speed camera is less than 90\u00b0. By using this method, the moving powder particle will be imaged by the camera with appropriate exposure time te1 due to the scattered light from the powder particles. Figure 4 shows the schematic of the second observation method. The zone irradiated by the light sheet can be imaged in the camera with the exposure time te2. In Fig. 4a and b (top view), the light sheet irradiates the powder flow along the two symmetrical planes, respectively, so the images of the powder flow through two symmetrical planes can be obtained" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002228_tcst.2019.2958015-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002228_tcst.2019.2958015-Figure2-1.png", "caption": "Fig. 2. System structure of hybrid vision/force control.", "texts": [ " Therefore, when the interaction control with the environment is performed at the end of the soft robot, the motion trajectory of the end can be visually controlled and the deformation and motion deviation due to the external contact force can be compensated by the force sense feedback. This article proposes a hybrid vision/force control method for position control and force control of a soft robot in contact with the environment. Since the two kinds of feedback are, respectively, defined in different frames, the control tasks are also in the corresponding frame. Specifically, the visual servo control task is defined in the image frame, while the force control task is defined in the sensor frame. Fig. 2 shows the system structure of hybrid vision/force control. Therefore, the main problem of hybrid control is how to decompose the control task and make two controllers complementary to each other. The normal vector n of the contact plane is supposed to be a priori or obtained by force sensing. The force control task is defined in the space formed by n S f x = n nT x. (30) The motion control space is defined orthogonal to the force control space {(I \u2212 n nT )x}. A compliance controller is used to implement force control in the constraint space {S f }" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002022_978-3-319-40036-5-Figure2.36-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002022_978-3-319-40036-5-Figure2.36-1.png", "caption": "Fig. 2.36 (a) Schematic of fibers connected to SU8 droplet (b) Optical micrograph of the SU8 droplet (c) Image of light shining in the droplet (c) Image of light shining in the droplet (Reproduced from Yardi et al. [126], manuscipt accepted and under publising in Springer)", "texts": [ " Due to its advantages like high sensitivity, low-weight, high capacity to transfer information, invulnerability to electromagnetic interference and low-cost, varied applications are integrating these sensors [124]. The sensing mechanism works on the basis of changes in optical properties such as UV\u2013Vis absorption, bio or chemiluminescence, reflectance and fluorescence brought by the interaction of the biocatalyst with the target analyte [125]. A SU8 based optical biosensor has been reported by Yardi et al. A novel technique has been developed to tag standalone optical fibres to a substrate using laser exposed SU8 micro-droplet (Fig. 2.36). The stitched optical fibres show high transmissibility for both aligned and misaligned configurations of the fibres [126]. 2 Microfluidics Overview 75 Mass based sensors rely on transduction of mechanical energy. Cantilever based mass sensors are the most commonly used mechanical sensors that measure changes in mass through its oscillating frequency shift. Cantilevers came to use as highly sensitive biosensors after the advent of atomic force microscopy (AFM) [127]. They were used as a tip in AFM to measure the force between the tip and the sample through tip deflection or changes in resonant frequency of a vibrating cantilever" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000262_j.triboint.2011.03.012-Figure12-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000262_j.triboint.2011.03.012-Figure12-1.png", "caption": "Fig. 12. Plot of the hydrodynamic pressure calculated for a load of 75 MPa.", "texts": [ " The problem in using the direct input from measurement is that the interpolation is currently not able to define the complex wear profile with the use of a cubic surface, therefore linear interpolated areas arise. At the crossing point from cubic to linear interpolated zones discontinuities occur at which the partial derivative of the gap height cannot be evaluated numerically with the result that there is no hydrodynamic pressure in this area. This in turn causes severe asperity contact. Therefore, an axially symmetrical and in every grid point continuous wear profile is defined based on the measured values, see Fig. 11. Fig. 12 depicts the three-dimensional hydrodynamic pressure distribution of the test-bearing (middle) and the support-bearings (left and right) for the specific load of 75 MPa. One can see that due to the higher load and consequently different characteristic wear profile, the hydrodynamic pressure distribution clearly differs from the corresponding results for 55 MPa. For 75 MPa the large amount of worn shell material at the corners result in a pressure concentration at the axial center of the bearing. Also in circumferential direction a significant influence of the used wear profile can be seen" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001131_j.mechmachtheory.2013.01.004-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001131_j.mechmachtheory.2013.01.004-Figure3-1.png", "caption": "Fig. 3. Kinematic description of Hoberman's angulated element.", "texts": [ " However, the present work using the screw theory only focuses on the scissor like elements with straight rods. The Hoberman's units with angulated rods using the screw theory are not considered in the literatures. Prior to probing the mechanism theory of the Hoberman's angulated element, this paper will first present the kinematic description of the element. Asmentioned earlier, themain character of theHoberman's Linkage is that everyHoberman's angulated element subtends a constant angle during the motion. The simplest angulated scissor element is shown in Fig. 3. The revolute joint in the middle connect the two angulated links of equal configuration. Therefore, points A, B, C and D can be seen as being constrained tomove along either of the dash lines P1 and P2. Then we can interpret an angulated link as a PRRP linkage shown in Fig. 3(b), which has two prismatic joints and two revolute joints. Thus the two PRRP linkages of the Hoberman's angulated element are individually movable with a single degree of freedom. Therefore, the angulated element will be movable only when the two linkages share the same coupler curve at point E [16]. The Hoberman's angulated element can be considered as a parallel mechanism. It consists of the linkage ABE and linkage CDE, which are connected by a common joint E. Its mobility can be analyzed by the method, which is based on the screw theory, as proposed in Ref" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001319_j.jsv.2014.12.018-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001319_j.jsv.2014.12.018-Figure3-1.png", "caption": "Fig. 3. Schematic and 3D CAD model of single-stage gear transmission. (1) Fixed gear; (2) idler gear with toothed impulse wheel; (3) input shaft; (4) output shaft; (5) synchronizer.", "texts": [ " A sinusoidal excitation with varying amplitude and a frequency according to second rotation order (30 Hz) is superimposed on the constant input shaft rotation of 900 rev/min in all measurements to simulate conditions arising in a 4-cylinder 4-stroke engine. The main engine order of fluctuations for such an engine is the second engine order [2]. The single-stage gear transmission consists of one gear pair with a synchronizer for the idler gear on the output shaft. A schematic and CAD model of the gear transmission are shown in Fig. 3. The input shaft includes the fixed gear, which is mounted on the shaft by a spline shaft connection. The idler gear and the single-cone synchronizer are mounted on the output shaft. The idler gear can rotate relative to the output shaft by a needle\u2010roller bearing. The synchronizer body with the gearshift sleeve is fixed to the output shaft and guides the synchronizer ring. Two different states of the gearshift mechanism are possible. First of all, a non-shifted condition is possible when the gearshift sleeve is not connected to the idler gear" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002439_j.ejcon.2019.12.003-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002439_j.ejcon.2019.12.003-Figure3-1.png", "caption": "Fig. 3. Schematic diagram of trajectory planning.", "texts": [ " The reference linear velocity of the tractor s v r = \u221a \u02d9 x2 r + \u02d9 y2 r and the tractor reference angular can be obtained y r = arctan 2( \u0307 yr , \u02d9 xr ) (10) lso, the reference angular velocity of tractor can be formulated as 1 r = \u02d9 \u03d5 r = y\u0308 r \u0307 xr \u2212 x\u0308 r \u02d9 yr \u02d9 x2 r + \u02d9 y2 r (11) he simple geometry of the connection between tractor and trailer an be governed by [ x 2 r y 2 r ] = [ x r y r ] \u2212 d [ cos \u03b8r sin \u03b8r ] (12) here ( x 2 r , y 2 r ) is the reference coordinate of the trailer point K . Schematic diagram of trajectory planning is shown in Fig. 3 , here the turning center of tractor and trailer is the point O , R 0 epresents the turning radius of the tractor. Assuming that d is mall compared with R 0 , the turning radius of the tractor is aproximately equal to the turning radius of the trailer. Draw a circle ith point O as the center and R 0 as the radius, then the diagram an be obtained. Since APK is a right triangle, it is easy to get os ( \u03c0 2 \u2212 (\u03d5 r \u2212 \u03b8r ) ) = d 2 R 0 (13) rom (13) , it can be deduced that r = \u03d5 r \u2212 arcsin d 2 R (14) M R g \u03b8 w ( e e b t w l 4 p c f r 4 s t u q b m r R b t s d b\u23a7\u23aa\u23a8 \u23aa\u23a9 4 I t l A p q w t c q w v T a{ w n eanwhile, it can be concluded that 0 = v r w 1 r (15) Taking the derivative of both sides of (14) with respect to time ives \u02d9 r = w 1 r \u2212 d( \u02d9 w 1 r v r \u2212 \u02d9 v r w 1 r ) 2 v 2 r \u221a 1 \u2212 ( dw 1 r 2 v r )2 (16) here \u02d9 w 1 r = " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002415_s40964-019-00094-6-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002415_s40964-019-00094-6-Figure1-1.png", "caption": "Fig. 1 Common LPBF layout", "texts": [ " The unobstructed view of the exposed top surface during the layerwise PBF fabrication allows for the monitoring in an unprecedented manner including both the melt pool and the associated ejecta. A qualify-as-you-go in\u00a0situ methodology will be required to ensure the reliability. Within the family of PBF processes, metal laser powder bed fusion (M-LPBF) has been optimized to fabricate complex structures with a diversity of metal powders. This process operates by focusing a laser onto a uniform layer of powder, which selectively melts (welds) the powder to a baseplate or previous layers of melted powder (Fig.\u00a01). Process feedback is generally limited from most commercial grade systems and will be an inevitable requirement for the full qualification of AM-fabricated structures due to a general lack of confidence in the existing open-loop systems [1]. Metal ejecta (spatter) during the lasing process is a common occurrence and has been examined previously to determine or predict the quality of the melt and resulting fabricated structure [2\u20135]. The final destination of the spatter after ejection can fall within the boundaries of the structure under fabrication thereby introducing contamination of unintended material in subsequent layers" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001723_s00170-015-7481-8-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001723_s00170-015-7481-8-Figure6-1.png", "caption": "Fig. 6 The single powder stream obtained by the method in Fig. 4b", "texts": [ " One of the important parameters introducing to the model is the average velocity vp of the powder particles in the powder flow. By using the first photography method, the average velocity vp can be calculated by a method which has been developed and validated in previous studies [18], i.e., the average length of white line segments in the image divided by the exposure time. To obtain the parameters a and l, the single powder stream image obtained by the method in Fig. 4b was analyzed (as shown in Fig. 6). Because the gray level is proportional to the mass concentration, the characteristic radius b of the powder stream at distances L1 and L2 from the nozzle exit were measured by the image analysis and substituted into Eq. (6), respectively, and then the parameters a and l can be calculated out by solving the equations. In this case, the average velocity vp of the powder particles was calculated out to be 4500 mm s\u22121 with an exposure time of 2\u00d710\u22124 s, and the parameters a and l were calculated out as about 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003492_j.jmapro.2021.04.020-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003492_j.jmapro.2021.04.020-Figure3-1.png", "caption": "Fig. 3. Residual stress measurement scheme adopted for HPNGV component during CPP flow.", "texts": [ " Thicker components are accompanied by higher stiffness, which helps to constraints deformation to withstand the curl-up effect via stress relaxation and/or redistribution much comfortably compared to thinner components [32]. Furthermore, upon grit blasting performed on HPNGV components removed from baseplate induces a significant magnitude of compressive residual stresses varying from 750 MPa to 650 MPa, which agrees with the work done Manojakumar et al. [33] where the residual stress shows a compressive behaviour in the grit-blasted condition of SLM processed CoCrMo alloy. Interestingly, the deviations in the measured stress values, as shown in Fig. 3, may be due to the surface roughness of the HPNGV component in the as-built condition caused by the sintering of adjacent powders while printing the part [34]. However, during grit blasting, the sintered powders loosely bonded are removed by imparting with high-pressure glass beads, which provides a much smoother surface, resulting in a decrease in the measured stress deviations values. Fig. 6 shows the variation of residual stresses on the Inconel 718 HPNGV component at standard post-processing techniques (Figs" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000753_j.engfailanal.2011.11.004-Figure16-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000753_j.engfailanal.2011.11.004-Figure16-1.png", "caption": "Fig. 16. Distribution of the uniaxial stress of the shaft for load case II.", "texts": [ " In compliance with the norms defined in [23], the analysis of the drive shaft of the BWE was carried out for two load cases: the BWE moves forward, the drives of both pairs of caterpillar tracks are involved, shaft loads due to the torque and the corresponding vertical forces on the arm L = 600 mm from the center of mass of the gearbox: T1z,max = 282 kNm and H1max = 31.2 kN \u2013 load case I, the BWE turns right backward, the drive of one pair of caterpillar track is excluded \u2013 the other drive is maximally loaded, the shaft load: T2z,max = 592 kNm and H2max = 65.5 kN \u2013 load case II. The uniaxial stress field, according to the Huber\u2013Hencky\u2013von Mises hypothesis [1,4,8,9], for case I of the load, is presented in Fig. 15 while Fig. 16 presents the maximum values of uniaxial stresses obtained for case II. The characteristic values of the working stress obtained by the finite element method are presented in Table 5. Fatigue analysis at the point of fracture can be carried out by using the Goodman endurance diagram. The minimum recommended value of the amplitude stress is ra = 380 MPa [24], whereas the minimum value of tensile strength is [25]: rm = 1100 MPa. These values are presented by points A and B (Fig. 17) and they define the fatigue boundary line", " However, for real exploitation conditions, this line must be corrected. In compliance with the recommendations [26\u201329], the corrected minimum value of the amplitude stress (ra,m = 210 MPa) was defined, whereas the minimum value of tensile strength was established experimentally (Table 3) and it is rm,m = 940 MPa. These values are denoted with points C and D (Fig. 17) and they define the modified boundary of the Goodman diagram. The charateristic points for testing the shaft for fatigue are denoted with numbers from 1 to 7 in Fig. 16. All values of the corresponding component stresses (presented in Table 5) were obtained by the finite element method and they are below the line A\u2013B, which represents the fatigue boundary. However, as the line C\u2013D was chosen to be the relevant line of fatigue, the values of the corresponding component stresses at the point of fracture (item 1) are above this line, which leads to the conclusion that fatigue safety is not provided. The same results were also reached by fatigue analysis with the application of the finite element method" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003535_j.mechmachtheory.2021.104436-Figure16-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003535_j.mechmachtheory.2021.104436-Figure16-1.png", "caption": "Fig. 16. Schematic of OES-limbs.", "texts": [ " They are 6 OB-limbs and 12 OE-limbs, which are shown in Table 7. In this table, [RR] represents that axes of 2 R-joints intersect at a point (O2). [RRR] represents that axes of 3 R-joint intersect at a point (O1). [PRRR] represents that axes of 2 R-joints intersect at the center (O1) of PR-joint. [TPRR] and [TRRR] represent that axes of 2 R-joints intersect at the remote motion center (O1)of TR and TP-joint. The OE-limbs constructed in Table 7 have 4 types of OS-limbs, which are limbs SR [RR], SP [RR], SRR and SPR. The structures of OESlimbs are shown in Fig. 16. The OES-limb is equivalent to the OB-limb from the kinematic perspective, so it has the same motion and constraint screws. All of them contain a constraint force $F1 along the O1O2 direction. The equivalent replacement method is applied to 41 OB-groups, and a total of 535 different orientation groups are synthesized, of J. Zhang et al. Mechanism and Machine Theory 166 (2021) 104436 which 14 types are the OES-groups. There are 6 representative and research significance OES-groups, which are groups SR [RR]&SRR, SR [RR]&SPR, 2-SR [RR]&Sp [RR], SR [RR]&2-Sp [RR], 2-SR [RR] and SR [RR]&Sp [RR]. These 6 OES-groups are composed of the OES-limb SR [RR] and the other OES-limbs in Fig. 16. They have the same motion and constraint performances with OB-groups. Based on Tables 5 and 6, it can be analyzed that the moving platforms of OES-groups SR [RR]&SRR and SR [RR]&SPR have 2 rotational DOFs around O2, which are controlled by 2 inputs of group; the moving platforms of OES-groups 2-SR [RR]&Sp [RR] and SR [RR]&2-Sp [RR] have 3 rotational DOFs around O2, which are controlled by 3 inputs of group. In summary, inputs of 4 OES-groups SR [RR]&SRR, SR [RR]&SPR, 2-SR [RR]&Sp [RR] and SR [RR]&2-Sp [RR] can completely determine the orientation of moving platform, but do not affect the position of O2 on the spherical surface, so these groups are defined as \u2019pure OES-groups\u2019" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001510_j.mechmachtheory.2014.01.014-Figure13-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001510_j.mechmachtheory.2014.01.014-Figure13-1.png", "caption": "Fig. 13. Three-dimension model and investigated parameters of the FS.", "texts": [ " (28) for a tooth rim of radius rm of 81 mm, a cross-sectional height h of 2.37 mm, a maximum radial displacement u0 of 1.072 mm, a roller angle \u03b2 of 30\u00b0, and a FS tooth number of FS of 204; the variation in the distribution is similar to the distribution of the tooth rim circumferential strain in Fig. 11. In this section, an FEA-based simulation is used to verify the method developed here, and three groups of experiments are conducted. An FS with the following parameters is used to illustrate the entire approach, as shown in Fig. 13. The cylinder length L is 160 mm, the diameter of the middle surface d1 is 160.8 mm, the thickness of the cylinder th1 is 1.6 mm, and the thickness at the tooth rim th2 is 2.373 mm. The width of the tooth rim b is 25 mm, and the distance of the tooth rim from the top side of the FS f is 8 mm. The diameter of the fixed hole at the bottom df l is 80 mm. A taper tooth with an engaging angle of 20\u00b0 is used, for a height from the middle surface of the FS ch of 2.08 mm and a tooth number z1 of 204. To verify the method developed here, three FEA models using different parameters are built in the ANSYS environment" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003492_j.jmapro.2021.04.020-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003492_j.jmapro.2021.04.020-Figure4-1.png", "caption": "Fig. 4. Residual stress measurement scheme adopted for HPNGV component during SPP flow.", "texts": [], "surrounding_texts": [ "Figs. 7 and 8 show the influence of heat treatment on the magnitude of residual stresses of the HPNGV component with and without baseplate. It is evident from the results that the heat treatment helps in stress-relieving. It is observed that the residual stress in the as-built HPNGV component is found to be tensile, varying from 150 MPa (at location 1) to 650 MPa (at location 4) at the surface. When heat-treated, the residual stress values changes from tensile to compressive of almost uniform value ~200 MPa at all location of the HPNGV component (refer Fig. 7). Fig. 8 shows the comparison of as-built and heat-treated HPNGV component after removal of the baseplate. With the removal of the baseplate in the as-built HPNGV component, the stresses redistribute almost uniformly at all locations in tensile nature of around 650 MPa (similar values with the baseplate condition in Fig. 7). However, in the heat-treated HPNGV component, the stress changes from compressive nature to almost zero across all the location on the component. Fig. 9 compares the magnitude of residual stress values among asbuilt and heat-treated HPNGV components after grit blasting. In both N. B. K et al. Journal of Manufacturing Processes 66 (2021) 189\u2013197 as-built and heat-treated conditions, the stress is compressive and almost uniform throughout all locations on the surface. However, the heattreated HPNGV component is marginally compressive, i.e. 100 MPa more than the as-built component. What is interesting to note here is that the, although as-built HPNGV component had a high magnitude of tensile residual stress value of around 650 MPa after removal of the baseplate, after grit blasting complete reversal on the nature of stress along with significant enhancement in the magnitude of compressive residual stress values (~700 MPa), developed due to the efficient manner via redistribution of stresses across all locations of the as-built HPNGV component in an almost uniform manner (i.e. from +650 MPa to - 700 MPa). On the other hand, the heat-treated component responded to the grit blasting process more sluggishly (i.e. from ~0 MPa to 800 MPa). Because of the above, it is evident that the as-built HPNGV component was more sensitive to the grit blasting process compared to the heat-treated component. The percentage of the difference in residual stress between as-built and heattreated HPNGV component after the grit-blasting process was found to N. B. K et al. Journal of Manufacturing Processes 66 (2021) 189\u2013197 varying from 10 % to 25 % with a standard deviation of 5 %, indicating that marginal difference among the two post-processing techniques compared. Therefore, it is a more economical approach to adopt the proposed CPP technique on a case by case basis." ] }, { "image_filename": "designv10_9_0002116_itec.2018.8450250-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002116_itec.2018.8450250-Figure6-1.png", "caption": "Fig. 6: Schematic partial view of a PM rotor. Shown is the parameter variation of the two degrees of freedom defined in this context: a) wire cross-section and b) coil position", "texts": [ " The impact of skewing and different relative positions between stator and rotor on the anisotropy was considered as well. The tool chain was validated by comparison of measurement results with simulation results of the conventionally laminated reference motor (see Fig. 8a and Fig. 11a). After adapting the model regarding geometry and material data, the best possible rotor active part design was identified by varying the following two degrees of freedom: \u2022 Copper wire cross-section to gain the best possible damping while minimizing the ohmic losses (see Fig. 6a) \u2022 Radial position and therewith the flux which is enclosed by the particular coils considering mechanical and manufacturing process boundary conditions (Fig. 6b) Referring to Fig. 6, four possible coil positions I to IV and three different cross-sections A3,i were defined. A coil side located at the pole gaps (position I) represents the concept described in [19], a serially connected meandering rotor coil. Considering that one coil segment always consists of two components, an axially aligned part and a peripherally aligned connection part, the short-circuited coils underneath the magnets can approximately be described as two parallel-connected meandering coils with half the cross-section each", " Though three-dimensional effects could hardly be taken into account, using the tool chain was suitable for dimensioning the rotor active part. The worst operating point regarding magnetic anisotropy in surface-mounted PMSM is usually the operating point of maximum q-current (due to saturation) and negative maximum d-current (due to permanent magnet field weakening). Thus, the anisotropy of this operating point is the most crucial design parameter to ensure a stable self-sensing operation of the machine. The anisotropy depending on the positioning of the axial parts referring to Fig. 6 in peripheral direction is shown in Fig. 7. A coil located at q-axis (position I) encloses the whole permanent magnet flux, whereas a coil side position towards the d-axis (positions II to IV) leads to decreased enclosed flux. Fig. 7 shows two different wire cross-sections with A3,2 > A3,1. In the present case, a wire with the crosssection A3,1 will only fulfill the anisotropy requirements if it is directly positioned in q-axis, whereas in case of A3,2, position III would be adequate. This is why the coil sides should be located close to the q-axis and should be as large as feasible to obtain the best possible damping effect" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002700_tmech.2020.3015133-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002700_tmech.2020.3015133-Figure5-1.png", "caption": "Fig. 5. Force analysis of the continuum manipulator : (a) Diagram and force analysis of distal end unit coupled with the wire. (b) Diagram and force analysis of the intermediate unit coupled with the wire.", "texts": [ " Kbending = Mz \u2206\u03b3z = E \u00b7 w \u00b7 ay3 12 \u00b7 ax \u00b7 f1 (6) f1 = 12\u00b7s4\u00b7(2\u00b7s+1) (4\u00b7s+1)5/2 arctan \u221a 4 \u00b7 s+ 1+ 2\u00b7s3(16\u00b7s2+4\u00b7s+1) (4\u00b7s+1)2\u00b7(2\u00b7s+1) (7) where s = ay/t. Based on the mechanical model, the deformation of the flexible unit is analyzed. The overall deformation of the continuum manipulator is obtained by superimposing multiple flexible units. The continuum manipulator can traverse the space through different proximal input forces. Based on the assumption 1),2),3), the force-transmitting contact of the wire is analyzed to established real-time boundary conditions, as shown in Fig.5. There is no relative sliding of the wire on the upper part of the distal end bending unit of the continuum manipulator, and there is relative sliding of the wire at the intermediate unit. Therefore, the force of the distal end and intermediate units are different. The force analysis of the distal end unit is shown in Fig. 5(a). The force balance equation of the wire is defined as O2n+1 : FT2n+1+FN2n+FT2n= 0 O2n : FT2n+Ff2n\u22121+FN2n\u22121+FT2n\u22121= 0 (8) where FN2n and FN2n\u22121 is the normal pressure, FT2n , FT2n+1 and FT2n\u22121 is the tension of the wire, Ff2n\u22121 is friction, n is the number of the distal end bending unit. Based on the assumption 2) and Fig.5(a), the magnitude of the deformation force required for the distal end bending unit [36] is obtained as FT2n+1 = FT2n\u22121(cos( \u03b8n4 )\u2212 \u00b5 \u00b7 sin( \u03b8n4 )) cos( \u03b8n4 ) + \u00b5 \u00b7 sin( \u03b8n4 ) (9) where \u00b5 is the coefficient of friction, \u03b8n is the bending angle of the distal end bending unit. The force analysis of the intermediate unit i is shown in Fig. 5(b). The force balance equation of the wire is obtained as O2i+1 : FT2i+1 +Ff2i +FN2i +FT2i = 0 O2i : FT2i +Ff2i\u22121 +FN2i\u22121 +FT2i\u22121 = 0 (10) where FN2i and FN2i\u22121 is the normal pressure, FT2i , FT2i+1 and FT2i\u22121 is the tension of the wire, Ff2i\u22121 and Ff2i is friction. Based on the assumption 2) and Fig.5(b), the magnitude of the deformation force of the intermediate units i can be obtained as FT2i = FT2i\u22121 (cos( \u03b8i4 )\u2212 \u00b5 \u00b7 sin( \u03b8i4 )) (cos( \u03b8i4 ) + \u00b5 \u00b7 sin( \u03b8i4 )) (11) where \u03b8i is the bending angle of the intermediate unit i. The magnitude of the input force for the next unit i+1 can be obtained as FT2i+1 = FT2i\u22121 (cos( \u03b8i4 )\u2212 \u00b5 \u00b7 sin( \u03b8i4 )) 2 (cos( \u03b8i4 ) + \u00b5 \u00b7 sin( \u03b8i4 )) 2 (12) Based on the assumption 4), Equation(1), (2) and the inherent structure of the flexible unit that contains two elliptical flexible hinges, the force on the flexible unit and corresponding deformation can be simplified as F = [0, 0, 0, 0, 0,Mzi] (13) Authorized licensed use limited to: Cornell University Library" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001141_iros.2014.6943257-Figure10-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001141_iros.2014.6943257-Figure10-1.png", "caption": "Fig. 10: Advantage of new delta joint on slopes: resulting PSI angle control enables LAURON to orientate its feet relatively to the gravitational vector (principle drawing - body pitch adaption to inclination not shown).", "texts": [ " The inclino behavior considers the ground contact values (GCi), the Xi, Yi, Zi values, the IMU roll and pitch angles and orientation offsets (offset rollr, offset pitchr). PscaleoffsetX and PscaleoffsetY are scaling parameters to influence the speed of the adjustment. LAURON\u2019s inclino behavior fulfills three functions: the body orientation is controlled by individual leg motions in Z-direction, the CoM position is shifted to maximize the static stability and finally the delta joint angles (see Fig. 10) are used to minimize the joint torques. These three functions are presented in detail in the following pseudo-code section. Algorithm 3 inclino behavior Require: Xi,Yi,Zi \u2013 foot tip X,Y,Z-position of legi GCi \u2013 Ground Contact value of legi [0, 1] IMUroll, IMUpitch \u2013 IMU sensor values of body orientation offset rollr , offset pitchr \u2013 user-defined roll and pitch offsets \\\\ Calculate foot point plane inclination 1: FPplane(roll, pitch) = CalculateFPPlane(ALL Xi,Yi,Zi) 2: rolldesired = 0.5 \u00b7 (IMUroll + FPplane(roll)) 3: pitchdesired = 0", " This value will result in a more favorable load distribution while still keeping the legs within their kinematic ranges. Finally the inclino behavior controls the newly added delta joint of LAURON V to minimize the torques acting on each joint and in return the overall energy consumption of the robot. It controls the PSI angle, which is the component in X-direction of the angle between the gamma leg segment and the Z-axis of the robot base frame. By setting the PSI angle to the inclination of the slope the legs stand parallel to the gravity vector. Figure 10 illustrates the PSI angle and the advantage of adapting the PSI angle. On the left side of this Figure LAURON does not make use of its improved kinematic (PSI = 0). This standing pose results in very large torques, especially in the alpha joints. The right side shows the same position with activated PSI angle control resulting in much smaller loads, less energy consumption and better overall stability. The desired PSI angle is transformed into the corresponding \u03b4-joint angles by the inverse kinematic" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003145_s0022-3913(52)80045-9-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003145_s0022-3913(52)80045-9-Figure1-1.png", "caption": "Fig. 1 4 . - - I n f l a m m a t i o n a n d necros is u n d e r den t ina l t ubu l ae of deep ly p r e p a r e d cavi ty . This occurs w h e t h e r cav i ty was filled w i th s i l icate o r zinc p h o s p h a t e cement . ( P h o t o g r a p h c o u r t e s y Dr. H. A: Zander ; t r o m J.A.D.A. 44:193, 1952.)", "texts": [ " If the weight is powerfid enough to overcome the cohesive force of these molecules they will \"give up\" or slip past each other, and the specimen will divide in two. This is shear, and a value can he assigned to the force necessary to produce shear in a given specimen. Now, if the weight is applied at some point removed from the support, the term applied to the test is diagonal tension, and the force necessary to produce a failure of the specimen is, as the above figures show, considerably less than the value for pure shear. Dental cements act as bond by a keying action (Fig. 1). What we really have to consider is the combined strength of these keys to shear or diagonal tension. It is not clear whether the keys are in pure shear or whether, due to the shrinkage which occurs in the setting of all dental cements, they are in diagonal tension? When a cemented inlay is.placed in axial traction, the strength of the cement bond will be determined by the following factors: (1) Strength of the cement in shear. (2) Roughness of the interface between the inlay and the tooth. (3) Areas involved in the bond" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000039_978-1-84996-220-9-Figure5.4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000039_978-1-84996-220-9-Figure5.4-1.png", "caption": "Figure 5.4 (a) An object (wok) with predefined grasping positions for two arms of ARMAR-III (b) The 3D projection of the reachability spaces for both arms of ARMAR-III", "texts": [ " For each object to be grasped or manipulated by the robot, a collection of feasible grasps is stored in a database. This collection of feasible grasps holds information about the transformations between the end effector and the final grasping position, the type of grasp, the preposition of the end effector and some grasp quality descriptions. These database entries can be generated automatically (e.g., with GraspIt! [22] or GraspStudio [29]) or, like in the following examples, by hand. A wok with 15 feasible grasps for each hand of the humanoid robot ARMAR-III can be seen in Figure 5.4(a). To grasp an object o (located at position Po) with the end effector e by applying the grasp gk of the feasible grasp collection gce o, the IK problem for the pose Po k has to be solved: Po k = T\u22121 k \u2217Po. (5.4) To grasp a fixed object with one hand, the IK-problem for one arm has to be solved. In case of the humanoid robot ARMAR-III, the operational workspace can be increased by additionally considering the three hip joints of the robot. This leads to a 10 DoF IK problem. Typically, an arm of a humanoid robot consists of six to eight DoF and is part of a more complex kinematic structure", " Since this IK-solver is used within a probabilistic planning algorithm, this approach fits well in the planning concept. The use of a reachability space can speed up the randomized IK-solver. The reachability space represents the voxelized 6D-pose space where each voxel holds information about the probability that an IK query can be answered successfully [4, 11]. It can be used to quickly decide if a target pose is too far away from the reachable configurations and therefor if a (costly) IK-solver call makes sense. The reachability space of the two arms of ARMAR-III is shown in Figure 5.4(b). Here the size of the 3D projections of the 6D voxels is proportional to the probability that an IK query within the extent of the voxel can be answered successfully. The reachability space is computed for each arm and the base system is linked to the corresponding shoulder. 5 Efficient Motion and Grasp Planning for Humanoid Robots 137 The reachability spaces can be computed by solving a large number of IK requests and counting the number of successful queries for each voxel. Another way of generating the reachability space is to randomly sample the joint values while using the forward kinematics to determine the pose of the end effector and thus the corresponding 6D voxel [4]" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000220_j.asoc.2012.05.031-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000220_j.asoc.2012.05.031-Figure7-1.png", "caption": "Fig. 7. Cross section of the clad and substrate.", "texts": [ " This parameter shows the amount of powder material dilution as a result of mixing with the substrate material. Since in most conditions the powder material has a better quality than the substrate material, dilution phenomena decreases the clad quality. To obtain a good quality layer, the clad dilution should be kept as low as possible. From another aspect, low dilution will result in a poor bond between the clad and the substrate. The relation between the laser energy, scanning speed and the mass flow rate is very complicated and has a multi modal behavior [23]. Fig. 7 shows a schematic illustration of the clad cross section and its related areas. According to this figure, h is the clad height and d is melt pool depth. In this study, these two parameters are modeled as a function of laser power, powder mass flow rate and scanning speed as following: h = f1(P, m\u0307, V) (8) d = f2(P, m\u0307, V) (9) where P is laser energy, m\u0307 is powder flow rate and V is the scanning speed. Assumption an ideal mixing inside the melt pool, dilution is defined as: dilution = d (10) h + d The optimal design of LSFF process requires functions f1 and f2 that represent the amount of clad height and melt pool depth" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002705_j.mechmachtheory.2020.104006-Figure15-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002705_j.mechmachtheory.2020.104006-Figure15-1.png", "caption": "Fig. 15. Measurement results of laser tracker.", "texts": [ " The inverse kinematics solution of redundant circular-sliding manipulator during the motion planning process can be calculated in real time by using the analytical inverse kinematic parameterized method proposed in this paper. According to the actual size of the redundant circular-sliding manipulator, the start and end positions, i.e., ( \u2212365, \u2212214, 244) mm , (365, \u2212152, 448) mm , and multiple intermediate point positions are input to the upper computer to plan a given path in the task space. The movement of the redundant circular-sliding manipulator is as shown in Fig. 14 . During the movement of the redundant circular-sliding manipulator in Fig. 15 , we randomly selected 30 sets of the poses of the end-effectors. The corresponding inverse kinematics solution is obtained for each group through the analytical inverse kinematic parameterized method proposed in this paper, and the three target ball center coordinates at the end of the manipulator can be successfully measured under each configuration. The redundant circular-sliding manipulator is controlled according to these 30 sets of joint angles. Each time the manipulator reaches a configuration, the laser tracker is used to sequentially measure the coordinates of the center at target tee 1, target tee 2 and target tee 3. By measuring the center coordinates of the three target tees at the end of the manipulator under 30 configurations, the measurement results are shown in Fig. 15 . Comparing 30 sets of actual poses of redundant sliding manipulators measured in the tool coordinate system with the nominal poses, the error distribution of these 30 sets of poses is calculated as shown in Fig. 16 . We can see that the position errors and attitude errors of the measuring points are very small, and the effectiveness and high accuracy of the analytical inverse kinematic parameterized method proposed in this paper can be proved. Therefore, the physical experiment proves that the analytical inverse kinematic parameterized method proposed in this paper is very successful in calculating the inverse kinematics analytical solution of the redundant circular-sliding manipulator with high precision" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000931_9781118703274.ch2-Figure2.29-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000931_9781118703274.ch2-Figure2.29-1.png", "caption": "Figure 2.29 Centre of gravity of rotating blade", "texts": [ " The centripetal acceleration of the head b0 = \ud835\udf14A \u00d7 ( \ud835\udf14A \u00d7 r0 ) and d\ud835\udeda dt = \ud835\udedaA \u00d7 \ud835\udeda = \ud835\udedaA \u00d7 ( \ud835\udedaA + \ud835\udedaR ) = \ud835\udedaA \u00d7 \ud835\udedaR gives the acceleration of the centre of gravity b = \ud835\udedaA \u00d7 ( \ud835\udedaA \u00d7 r0 ) + ( \ud835\udedaA \u00d7 \ud835\udedaR ) \u00d7 r\u2032 + ( \ud835\udedaA + \ud835\udedaR ) \u00d7 (( \ud835\udedaA + \ud835\udedaR ) \u00d7 r\u2032 ) or with components b = \ud835\udedaA \u00d7 ( \ud835\udedaA \u00d7 ( r0 + r\u2032 )) \u23df\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23df\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23df centripetal acceleration from \ud835\udf14A + 2\ud835\udedaA \u00d7 ( \ud835\udedaA \u00d7 r\u2032 ) \u23df\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23df\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23df Coriolis acceleration + \ud835\udedaR \u00d7 ( \ud835\udedaR \u00d7 r\u2032 ) \u23df\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23df\u23de\u23de\u23de\u23de\u23de\u23de\u23de\u23df centripetal acceleration from \ud835\udf14R (2.51) which we will now examine in detail, so as to be able to interpret the individual accelerations clearly. Centripetal acceleration due to yawing When the offset of the rotor head is r0 = ||r0|| ex = r0ex or that of the rotor blade centre of mass from the tower axis is r\u2032 = y\u2032ey + z\u2032ez then from Figure 2.29 the resultant is r0 + r\u2032 = r0ex + y\u2032ey + z\u2032ez. Allowing for a yaw control angular velocity of \ud835\udedaA = \ud835\udedaAez yields the determinant for yaw speed \ud835\udedaA \u00d7 ( r0 + r\u2032 ) = |||||| ex ey ez 0 0 \ud835\udf14A r0 y\u2032 z\u2032 |||||| = \u2212\ud835\udf14Ay \u2032ex + \ud835\udf14Ar0ey and thus the centripetal acceleration from \ud835\udf14A b\ud835\udf14A = \ud835\udedaA \u00d7 ( \ud835\udedaA \u00d7 ( r0 + r\u2032 )) = |||||| ex ey ez 0 0 \ud835\udf14A \u2212\ud835\udf14Ay \u2032 \ud835\udf14Ar0 0 |||||| or b\ud835\udf14A = \u2212\ud835\udf142 A r0ex \u2212 \ud835\udf142 A y\u2032ey. (2.52) For rotors with two symmetrical blades, the component becomes \ud835\udf142 A y\u2032ey = 0 and thus engenders an intrinsic moment that loads the blade structure and, in pitch-regulated machines, the blade bearings. The residual acceleration b\ud835\udf14A = \u2212\ud835\udf142 A r0ex (2.53) only results in a moment along the x axis. Yaw control can generally attain only low angular velocities \ud835\udf14A, so that b\ud835\udf14A and the resulting stresses play only a secondary role. Centripetal acceleration due to blade rotation From Figure 2.29, the radius of rotation of the centre of gravity is r\u2032 = y\u2032ey + z\u2032ez and its angular velocity is \ud835\udedaR = \u2212\ud835\udf14Rex. Therefore the velocity at Sp is \ud835\udedaR \u00d7 r\u2032 = |||||| ex ey ez \u2212\ud835\udf14R 0 0 0 y\u2032 z\u2032 |||||| = \ud835\udf14Rz \u2032ey \u2212 \ud835\udf14Ry \u2032ez and the centripetal acceleration is bR = \ud835\udedaR \u00d7 ( \ud835\udedaR \u00d7 r\u2032 ) = |||||| ex ey ez \u2212\ud835\udf14R 0 0 0 \ud835\udf14Rz \u2032 \u2212\ud835\udf14Ry \u2032 |||||| Therefore bR = \u2212\ud835\udf142 Ry \u2032ey \u2212 \ud835\udf142 Rz \u2032ez. (2.54) Although the forces or moments resulting from centripetal acceleration place loads on both blades and bearings, these components have no effect on yaw control in symmetrically arranged rotors" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001170_we.1656-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001170_we.1656-Figure7-1.png", "caption": "Figure 7. Preloaded configuration of the adapted model (fine lines: undeformed; coarse lines: deformed).", "texts": [ " The deformation of each of the two nonlinear spring elements is half the value predicted by (15), being theirQ-\u03b4 curve, the one illustrated in Figure 6b (for dw=20 mm and s=0.943). The function of the COMBIN14 linear spring element is to simulate the preload of the ball by reducing its initial length L/3 to a new value L/3-x. This shortening causes an elongation in the COMBIN39 nonlinear spring elements, being their new length L/3 + \u03b4P/2, where \u03b4P< x because the rings get closer to each other; as a consequence, a preload (QP) is developed in the ball, as pointed out in Figure 7. The rest of the FE model is the same as the one presented in detail in previous work.8 Figure 8 shows a detail, where the following features can be outlined (see8 for a more extensive description): the inner ring is attached to the fixed element (simulated by a rigid surface) by pretensioned bolts (M12/10.9 preloaded to the 70% of their yield stress), and the external loads are applied in the center of the bearing and transmitted to the outer ring via MPC elements. The present work analyzes two commercial bearings with the geometric parameters shown in Table I" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002508_j.triboint.2019.03.048-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002508_j.triboint.2019.03.048-Figure5-1.png", "caption": "Fig. 5. Cross-sectional drawing of intermediate gearbox according to Hu et al. [16].", "texts": [ " 4 presents the flow rate evolution with rotational speed: up to 1000 rpm, the oil flow rate decreases as speed increases then an increase of the flow rate can be noticed for higher values of the rotational speed. Leprince et al. [33] had already underlined the existence of different flow regimes according to speed, but the results are slightly different: firstly the oil flow rate decreases as speed increases, but above 1000\u20131500 rpm the flow rate is nearly constant with speed. The difference can be explained as follows: there is a specific maximum flow rate at different structures or locations, and when that maximum value is reached, it will no longer increase with the increase in speed. Fig. 5 shows the three-dimensional (3D) model of the intermediate gearbox. To save calculation time and keep calculation precision, the real intermediate gearbox is changed as follows: the first change is to simplify the internal structure of the gearbox which mainly includes gears, the oil guide device, and casing wall while excludes other complex or less important parts, such as chamfers, fillets et al. The second change is to remove the rims of the gear pair, because when validation of the numerical approach was performed, it was found that the rims only had a small effect on the oil flow rate, while removing rims can greatly reduce the amount of calculation" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001300_1350650115577402-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001300_1350650115577402-Figure3-1.png", "caption": "Figure 3. Hydrodynamic effect between ball and cage pocket. (a) Rotating by axis xb, (b) rotating by axis zb.", "texts": [ " According to the amplitude of the clearance between the cage pocket and the ball dbp (Figure 2 shows the displacement of cage pocket and ball), taking into consideration both the roughness of the ball eb and the cage ep, two interaction models are used bp4 ffiffiffiffiffiffiffiffiffiffiffiffiffiffi \"2b \u00fe \" 2 p q \u00f02:a\u00de bp 4 ffiffiffiffiffiffiffiffiffiffiffiffiffiffi \"2b \u00fe \" 2 p q \u00f02:b\u00de If equation (2.a) is tenable, the interaction is assumed to be Hertz contact. The normal load between the cage pocket and ball was calculated using the Hertz point contact theory,21 and the tangential load between cage pocket and ball is equal to the normal load multiply friction coefficient. Otherwise, if equation (2.b) is tenable, the interaction is assumed to be hydrodynamic lubrication. A Reynolds equation22 is then used to calculate the interaction force. The interactions in two directions, shown as Figure 3, are assumed to be independent of each other. Fl and Ml are the interaction force and moment between cage and ring. The fluid dynamic problem occurring in the interaction between ring and cage is at NANYANG TECH UNIV LIBRARY on May 30, 2015pij.sagepub.comDownloaded from solved using the \u2018\u2018short journal bearing\u2019\u2019 hydrodynamic solution23 as equation (3) WM \u00bc RgB 3 g C2 g \"2 \u00f01 \"2\u00de 2 \u00f0!1,2 \u00fe !c\u00de \u00f03:a\u00de W \u00bc RgB 3 g 4C2 g \" \u00f01 \"2\u00de 3=2 \u00f0!1,2 \u00fe !c\u00de \u00f03:b\u00de W \u00bc 2 Rg 3Bg Cg 1ffiffiffiffiffiffiffiffiffiffiffiffi 1 \"2 p \u00f0" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001710_j.cja.2015.03.003-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001710_j.cja.2015.03.003-Figure5-1.png", "caption": "Fig. 5 Method to get the point on ZX-plane of the robot coordinate system.", "texts": [ " The direction of the normal line of this circle is the Z-direction of the robot coordinate system. The intersection point between the normal line and the base plane is the origin of the robot coordinate system. Step 4: The ZX-plane of the robot coordinate system is determined. When the robot is at the mechanical zero position, the SMR (B38.1 mm) is placed on the 6 holes (B10 mm) on the flange for measurement. The 6 points obtained from the measurement are used to fit a circle. The center of this circle is the point on the ZX-plane of the robot coordinate system (see Fig. 5). Step 5: The robot coordinate system is established. The robot coordinate system is established through the origin of the coordinate system, the Z-direction, and the point on the ZX-plane. Analysis of the position errors in Section 2 shows that the error surface of the robot is spatially variable. It may lead the error ns of the robot TCP. compensations in different regions to respond differently to the same change in different grids. Therefore, several representative areas in the region to be calibrated are selected to analyze the variation of the compensation effect", " Determination of optimal samples dx.doi.org/10.1016/j.cja.2015.03.003 grid step and its absolute position error meets the accuracy requirements, then it is selected as the optimum grid step of the given region. According to industrial robots performance criteria and related test methods up to China\u2019s national standard and professional standard (GB/T 12642\u2013\u20132001), 8 suitable positions must be determined within the cube of the working region to examine the pose accuracy of an industrial robot. As shown in Fig. 5, Ci\u00f0i \u00bc 1; 2; . . . ; 8\u00de are selected as the cubic vertices (see Fig. 8). There are 4 planes to be selected for a pose experiment based on the standard requirement. In this case, the planes are C1\u2013C2\u2013C7\u2013C8, C2\u2013C3\u2013C8\u2013C5, C3\u2013C4\u2013C5\u2013C6, and C4\u2013C1\u2013C6\u2013C7. 5 points (P1, P2, P3, P4, and P5) that must be measured are on the diagonals of the measuring planes in the standard requirement. P1 is the center of the cube. The positions of other point P2 to P5 are shown in Fig. 9. To describe the errors within the entire grid space as much as possible, the points on the other two diagonals are added" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001106_0278364914552112-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001106_0278364914552112-Figure2-1.png", "caption": "Fig. 2. Schematic of the active SLIP model.", "texts": [ " The classic SLIP is a completely passive model, meaning that it is not possible to add or remove energy to/from the system. While this does not necessarily pose a disadvantage, there are situations when it would be beneficial to be able to modify the amount of energy in the system, for example when hopping up and down a stair-step-like terrain. This lack of actuation limits the reachable system states. One approach to overcome these limitations is to add a piston-like linear actuator to the passive SLIP model, \u2018act, placed in series with the spring, as shown in Figure 2. We will then refer to this model as the active SLIP; \u2018act,0 defines the initial/equilibrium value of the actuator. During flight, any movement of the actuator does not have an effect on the system\u2019s dynamics, while during the stance phase, the actuator can either compress (\u2018act . \u2018act,0) or extend (\u2018act \\ \u2018act,0) the spring, thus respectively adding or removing energy to/from the system. The dynamics of the leg length during stance phase, (1), becomes \u20ac\u2018= g(\u2018k \u2018k, 0 \u2018act) sin u + \u2018 _u2 Displacing the actuator during the stance phase affects all three dimensions of the next apex state reached" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002801_asjc.2249-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002801_asjc.2249-Figure1-1.png", "caption": "FIGURE 1 Referential frames of MAV", "texts": [ " Section 4 presents the simulation results. Finally, the conclusions are given. By considering the Newton-Euler formulation, the full 6 degree of freedom DOF of the quad-rotor MAV is expressed as [22]: . d = R1(\ud835\udf4b)v (1) . \ud835\udf4b = R\u22121 2 (\ud835\udf4b)\ud835\udf4e (2) F = m( .v + \ud835\udf4e \u00d7 v) (3) \ud835\uded5 = I . \ud835\udf4e + \ud835\udf4e \u00d7 I\ud835\udf4e, (4) where, the inertial position is d = [x, \ud835\udc66, z]T \u2208 R3, the attitude described by \ud835\udf4b = [\ud835\udf19, \ud835\udf03, \ud835\udf13]T \u2208 {\u2212\ud835\udf0b, \ud835\udf0b}, the non-inertial expression of the linear velocity is v = [u, v,w]T \u2208 R3 and the non-ine \ud835\udf4e = [p, q, r]T \u2208 R3 (see Figure 1). Moreover, m is the MAV mass, rotation matrices R1(\ud835\udf4b) \u2208 SO(3) and R2(\ud835\udf4b) \u2208 R3\u00d73 transform linear and agular velocities from body to inertial frame. These matrices are written as: R1(\ud835\udf4b) =[ c\ud835\udf13c\ud835\udf03 \u2212s\ud835\udf13 s\ud835\udf19 + c\ud835\udf13 s\ud835\udf03s\ud835\udf19 s\ud835\udf13 s\ud835\udf19 + c\ud835\udf13 s\ud835\udf03c\ud835\udf19 s\ud835\udf13c\ud835\udf03 c\ud835\udf13c\ud835\udf19 + s\ud835\udf13 s\ud835\udf03s\ud835\udf19 \u2212c\ud835\udf13 s\ud835\udf19 + s\ud835\udf13 s\ud835\udf03c\ud835\udf19 \u2212s\ud835\udf03 c\ud835\udf03s\ud835\udf19 c\ud835\udf03c\ud835\udf19 ] (5) and R2(\ud835\udf4b) = [ 1 0 \u2212s\ud835\udf03 0 c\ud835\udf19 c\ud835\udf03s\ud835\udf19 0 \u2212s\ud835\udf19 c\ud835\udf19c\ud835\udf03 ] (6) where, s\u2217 = sin(\u2217) and c\u2217 = cos(\u2217) are chosen to simplify the notation. The inertia tensor I = diag[Ix, I\ud835\udc66, Iz] \u2208 R3\u00d73 assume that the vehicle is symmetric and constant when expressed in the body frame", " For the first step, small angles (see for more details[13]) are assumed, where full model (1)\u2013(4) can be expressed as follows: ?\u0308? = (I\ud835\udc66 \u2212 Iz) Ix . \ud835\udf03 . \ud835\udf13 \u2212 \ud835\udc57r Ix \u03a9a . \ud835\udf03 + \ud835\udf0f\ud835\udf19 Ix + \u0394\ud835\udf19 (16) ?\u0308? = (Iz \u2212 Ix) I\ud835\udc66 . \ud835\udf19 . \ud835\udf13 + \ud835\udc57r I\ud835\udc66 \u03a9a . \ud835\udf19 + \ud835\udf0f\ud835\udf03 I\ud835\udc66 + \u0394\ud835\udf03 (17) ?\u0308? = (Ix \u2212 I\ud835\udc66) Iz . \ud835\udf03 . \ud835\udf19 + \ud835\udf0f\ud835\udf13 Iz + \u0394\ud835\udf13 (18) x\u0308 = Tt m (C\ud835\udf13S\ud835\udf03C\ud835\udf13 + S\ud835\udf19S\ud835\udf13 ) + \u0394x (19) ?\u0308? = Tt m (C\ud835\udf13S\ud835\udf03S\ud835\udf13 + S\ud835\udf19C\ud835\udf13 ) + \u0394\ud835\udc66 (20) z\u0308 = Tt m (C\ud835\udf19C\ud835\udf03) + g + \u0394z (21) Due to time scale dynamics for rotational and translational motion, the following strategy shown in Figure 1 is adopted. Consider the disturbed attitude dynamics as: . \ud835\udf09 = \ud835\udc53 (\ud835\udf09, t) + g(\ud835\udf09)u + \u0394(t) (22) Y = h(\ud835\udf09)\ud835\udf09 + n(t) (23) where \ud835\udf09 = [\ud835\udf19, . \ud835\udf19, \ud835\udf03, . \ud835\udf03, \ud835\udf13, . \ud835\udf13]T , \ud835\udc53 (\ud835\udf09, t) = \u23a1\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 . \ud835\udf19 a1. \ud835\udf03 a2. \ud835\udf13 a3 \u23a4\u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 , g(\ud835\udf09) = \u23a1\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 0 0 0 b1 0 0 0 0 0 0 b2 0 0 0 0 0 0 b3 \u23a4\u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 , (24) u = [\ud835\udf0f\ud835\udf19, \ud835\udf0f\ud835\udf03, \ud835\udf0f\ud835\udf13 ]T with a1 = (I\ud835\udc66\u2212Iz) Ix . \ud835\udf03 . \ud835\udf13 \u2212 \ud835\udc57r Ix . \ud835\udf03\u03a9a, a2 = (Iz\u2212Ix) I\ud835\udc66 . \ud835\udf19 . \ud835\udf13 + \ud835\udc57r I\ud835\udc66 . \ud835\udf19\u03a9a, a3 = (Ix\u2212I\ud835\udc66) Iz . \ud835\udf03 . \ud835\udf19, b1 = 1 Ix , b2 = 1 I\ud835\udc66 , b3 = 1 Iz , \u0394(t) = [0,\u0394\ud835\udf19, 0,\u0394\ud835\udf03, 0,\u0394\ud835\udf13 ]T includes uncertainties and perturbations satisfying |\u0394(t)| \u2264 L, where L > 0 is an upper bound of the perturbation, \u03a9a = \u03a91 \u2212 \u03a92 + \u03a93 \u2212 \u03a94 is the residual rotor angular velocities, Y is the available state, where h(\ud835\udf09)describes which state is measured, and n(t) is an additive bounded noise" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000931_9781118703274.ch2-Figure2.4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000931_9781118703274.ch2-Figure2.4-1.png", "caption": "Figure 2.4 Airflow and forces on a rotor blade segment", "texts": [ " For the sake of clarity, the physical processes will be shown for a single rotor blade. Multiblade arrangements for fast-running turbines (e.g. with z = 2, 3 or 4 lift-type blades) can be handled by extension of this system, considering conditions at a single blade of z-fold depth. Depending on blade radius, Figure 2.2 shows that there is different flow behavior at the profile for different blade angles (Figure 2.3). The combined effect of velocity components and the resultant forces are shown for a single blade element in Figure 2.4. Total values (forces, moments, power) are obtained by the integration of the corresponding values over the blade radius, or by summation of the components of individual blade sections. A segment at radius r of a blade rotating with angular velocity \ud835\udf14R experiences two airflows: that due to the wind deceleration across the swept area, v2 = v2ax + v2t (2.18) and that due to the speed of the rotating element at the given radius, v = \u2212\ud835\udf14R \u00d7 r. (2.19) If we disregard the cone angle then, in the direction of the resultant velocity component, \ud835\udc63r = \u221a \ud835\udc632 2ax ( \ud835\udf14Rr + \ud835\udc632t )2 , (2", " The largely rigid grid connection means that the generator (within the relatively narrow slip range of asynchronous machines) keeps the turbine at a near-constant speed; i.e. the peripheral speed \ud835\udc63p is approximately constant. Wind speeds exceeding nominal levels cause higher angles of attack and thus (in the appropriate design) stalling (Figure 2.60(b)), when the airflow \u2018unsticks\u2019 from all or part of the blade profile. Depending upon the angle of attack, therefore, as shown in Figure 2.5, the lift coefficient ca = f (\ud835\udefc) and the lift forces dFA (see Figure 2.4) are reduced in certain ranges and the drag coefficients cw = f (ca, \ud835\udefc) or the drag forces increase. As a result, the torque-creating tangential force Ft (the sum of all partial forces dFt) does not significantly exceed its nominal values (Figure 2.60(d)). When the turbine is under full load and the wind speed climbs beyond the nominal range, this results \u2013 in spite of the greater levels of energy available \u2013 in lower rotor torque and lower performance coefficients. The performance characteristics (Figure 2" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001790_j.mechmachtheory.2016.04.010-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001790_j.mechmachtheory.2016.04.010-Figure2-1.png", "caption": "Fig. 2. Schematic diagram of roller forces.", "texts": [ " Assuming that the surfaces of bearing components are absolutely smooth, the crowned shape of roller has some deviation from the roller mid-length point due to the machining factors of crowned profile, causing roller's mass center to deviate from the axial center. In Fig. 1, \u03b4r is the radial displacement of inner ring; Pd is bearing radial clearance;oi ,oi' are the center of inner ring of unloaded bearing and loaded bearing, respectively; \u03c6j is azimuth angle of the jth roller. When cylindrical roller bearing is working at high-speed, roller is simultaneously acted by combined forces of inner, outer raceways and cage, as shown in Fig. 2. Due to machining factors of roller crowned profile, roller's mass center Om always doesn't coincide with its axial center Orc. Consequently, roller convexity excursion leads to an asymmetrical distribution of contact stress between roller and raceway due to roller's centrifugal force, which exacerbates tilting and skewing of roller. Where {O;X,Y,Z} is inertial coordinate system of bearing; {om;xm,ym,zm} is coordinate system of roller's mass center; {orc;xrc,yrc,zrc} is coordinate system of roller's axial center; Subscript {i,o} represent inner raceway and outer raceway, respectively; \u03b8j is tilting angle of the jth roller; Nj i, Nj o are normal force between the jth roller and raceways; Tji, Tjo are oil drag force between the jth roller and raceways; MNj i , MNj o are additional moment due to Nj i and Nj o; MTj i , MTj o are additional moment due to Tj i and Tj o; Qcj, Fcj are normal force and tangential friction force between the jth roller and cage's cross beam, respectively; Mcj is additional moment due to Fcj; Fmj is centrifugal force of the jth roller" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000160_acc.2009.5160136-Figure9-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000160_acc.2009.5160136-Figure9-1.png", "caption": "Fig. 9. Coordinate systems for flywheel and spring model. ~. denotes constants while tp. are variable angles. Note that only one spring is modeled\", although both springs are used for notational purposes here.", "texts": [ " (6) The outerlnost positions of the spring <;,s,o and 'PS,6 (which have no mass points in the model) follow from the equations: 'Ps,o == nlax( ps, ~MF - 1r + 4>ss, 'PS,l - c.t>nom,l ) (7) FR,i = Fcentrifugal,i + Fredirection,i + Fbias,i. (9) With an effective DMF radius r~ the centrifugal force is simply found as (i == 1... 5): ( . .)? \u00b72Fcentrifugal, i == m i r 'Ppri + 'PS, i - ~ mi r 'Ppri \u2022 'PDMF - cl>ss, 'PS,5 +cl>nom,6)' (8) where ~PS is the half width of the primary slopper and ss is the half width of the secondary stopper~ analogously (see Fig. 9). If the outennost spring elelnents are not compressed by a stopper, this choice of 'Ps,o and 'PS,6 will render the outennost spring elelnents idle. Depending on the DlinlDlax functions in the equations (7) and (8), the switching functions af, u~, u~ and a~ can be calculated (see section IV-A). 1.J Radialforees on the spring: For calculating the friction of the spring mass elements in the spring channel. it is required to calculate the radial forces FR,i that act on these mass elelnents. Three different influences are considered for each of the Inass elelnents (i = 1" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000348_bf02322339-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000348_bf02322339-Figure1-1.png", "caption": "Fig. 1--Schematic view of the half-plane submitted to a concentrated load, the reference plane and the light source", "texts": [ " In terferometr ic measurements on PMMA, combined with simultaneous measurements of the elastic constants E and v of the material , al lowed the evaluat ion of ct and c,. The values for the constants of the material were: 9 ct = --1.01 X 10-Scm2/Kp; cr = --3.24 \u2022 10 -5 cm2/Kp (3) The emerging l ight front S (z , y, z) after t ravers - ing the plate or reflected f rom the rear face is deviated and vector w, which expresses the displacement (RR') of a generic point R on the plate, as it is projected on a reference plane at distance zr from the mid-p lane of the plate (Fig. 1), is given by: wt.r = Zr grad As~.r (x, y) (4) The reference plane is placed either in front of the specimen for the reflected rays or behind the specimen for the t ransmit ted rays. Introducing either relation (I) or (2) for the transmitted or the refleeted l ight rays we obtain: - .> w = C grad (~'1 -t- ~ ) (5) where constant C takes the values: C = Ct ---- zrdct (for t ransmit ted light) (6) and C = Or ~- zrdcr (for reflected l ight from the rear face) (7) Similarly, it can be shown that the deviat ion w on the reflected l ight - rays f rom the front face a r e given by: ud wt -- z r - - ~ grad (~1 -k Ce) which may be also expressed by relat ion (6) if one puts: ~d C -- Ct = zr - - (8) E Concentrated Normal Load at the Straight Boundary Consider a thin plate of a homogeneous, isotropic and elastic mater ia l in a state of general ized plane stress occupying the negative half-plane, and a re fe r - ence frame Oxg associated with it, as in Fig", " The sum of principal stresses at point R is defined by the function ~(z) of the complex variable z = x + iy given by: iP 9 (z) = (9) 2nz where the load P is considered as posit ive if it is compressive. The sum of principal stresses at any point of the plate is expressed in complex form by: 4Re~(z) = (r + ~2) (10) where the function ~(z) -- [ u ( x , y ) \u00a7 i v (x , y ) ] is expressed by eq (9). Introducing relat ion (10) and taking into consideration the Cauchy-Riemann relationships, we obtain for w in complex form: w = 4 C ( au i Ou ) + (11) ax 0y where w is referred to a reference f rame with origin the projection R' of a generic point R of the plate on the reference screen Sc (Fig. 1). If w is referred to a fixed reference f rame O'x'y', it becomes: W = (x' + iy') (12) with X ~ . ~ ( ' ' ) 0x = Y + 4 C - - (13) 0Y Quanti ty W expresses the deviations of the reflected or t ransmit ted light rays on screens Sc placed ei ther in front or behind the specimen. These rays at the constrained zone, surrounding the singulari ty of the stress field, due to a significant lateral contraction there, as well as a considerable variat ion of the ref ract ive index, are deviated by different amounts, depending on the slope of lateral faces and the var ia - t ion of the refract ive index", "60%, one sees that the error in accepting the diameter BD as the max imum diameter of the epicycloid is of the order of 2.3 percent. This facilitates the evaluation of the external ly applied load by measuring the diameter BD of the epicycloid and applying relation (19), where the global constant C* is already known from the geometry of the exper imental setup and the properties of the material. Oblique Loads in Half-planes Consider now the case of an oblique concentrated load at the straight boundary of the half-plane. If the angle subtended between the direction of application of load and the posit ive x-axis (Fig. 1) is equal to ~, the stress function r expressing the sum of principal stresses, is given by: P = 9 (cos ~ + i sin ~) (z) 2~z which for ~ ---- x/2 becomes relat ion (9). Int roducing the values of the derivatives of r into eqs (19) and (20) we obtain for the initial curve: C*P 1 I tc*r = 1 Z 3 and (23) t o = [zj = [ ~C*P[ 1/3 Relation (23,2) shows that the ini t ia l curve for the oblique load is again a circle of the same radius as in the case of normal load. The equations for the epicycloid are: C*P I 1/~ t r 0 ~ (24) iC* P W : ro e-iS -- - - e - i ( 2 ~ + r 2nro 2 Equation (24,2) may be wri t ten in parametric form a s : X=ro{cosO~[cos(20+r t (25) Y = -- ro{sint} ~ [sin (20 + r Again, for , ---- =/2 we obtain the parametr ic equations for the normal load [eqs (22)]" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000284_0022-2569(67)90005-5-Figure8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000284_0022-2569(67)90005-5-Figure8-1.png", "caption": "Figure 8. Locating a pair of conjugate lines in a modified R - G - G - R linkage.", "texts": [ "2 above) and from Eq. (2) the pitch h o\u00a3 $23 determined. 3.2. If, in the configuration shown in Fig. 7, members 2 and 3 were joined not by a profile pair but by a baH-ended coupler AB of any len~h aligned along q, the construction for $.,3 would be precisely the same for the instant in question. But a fourth member, the coupler, is now introduced, free to spin about its axis AB, and thus possesses two degrees of freedom relative to 1 unless provided with one additional constraint. Such a constraint is shown in Fig. 8. Here the members have been re-numbered, and it is required to find $1 a. The velocity vector va is perpendicular to a plane shown as = containing A and the shaft axis 12, and v B is likewise perpendicular to plane ft. From 2.2 above it follows that planes and fl are polar planes with their poles at A and B. Therefore a pair of conjugate lines w t and w 2 can be found (2.12.1 and 2.19), one where ~ and fl intersect, and the other along AB. Using q, w t and w2 the determination of $13 proceeds as in 2", " A 1-R-2-G-3-G 4R-1 linkage (in which the coupler 3 has two degrees of freedom relative to l) can be modified so that its mobility is uniformly equal to 1 by suppressing one of the three degrees of rotational freedom in one of the G-pairs. Instantaneous first-order kinematic equivalence to such a modification is obtained by replacing one of the G-pairs by two revolute pairs intersecting at its centre B and joined by an intermediate connecting member. Such a linkage then becomes l-RI2-2-G23-3-Ra4-4-R4s-5-R51-1, and is used as an example in [8]. $13 may be determined by adapting the method of 3.2, shown in Fig. 8. Two polar planes ~ and fl can be found in a similar way, ~ containing the centre of G23(A ) and axis 12, fl containing B and axis 51. q must be a line not in the polar plane fl that intersects all three of 34, 45 and 51, i.e. q is any convenient line passing the point where 51 passes through the plane defined by 34 and 45. From now on the method of 2.19 (and 2.17) can be pursued. 3.9. In a more general instance of this same linkage with no intersecting axes for the revolute pairs, any three lines from the oo ~ lines intersecting all three of 34, 45 and 51 may be chosen" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001655_j.mechmachtheory.2018.01.012-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001655_j.mechmachtheory.2018.01.012-Figure2-1.png", "caption": "Fig. 2. Generating conical surface of grinding wheel in \u03c3 a .", "texts": [ " A technique based on the elimination method and the geometric construction is suggested to detect the solution existence and to get the initial value for solving the systems of nonlinear equations met during computing the conjugate zone and the contact line. The numerical example investigation is implemented. 2. Geometry of generating surface of grinding wheel A coordinate system \u03c3a { O a ; i a , j a , k a } is associated with a disk-shaped conical grinding wheel and the unit vector k a is along its axial line as shown in Fig. 2 . By means of the sphere vector function [21] , the equation of the generating conical surface, g , can be represented in \u03c3 a as ( ra ) a = u m a ( \u03b8, \u03b4g ) = u sin \u03b4g cos \u03b8 i a + u sin \u03b4g sin \u03b8 j a + u cos \u03b4g k a , (1) where u and \u03b8 are the two curvilinear coordinates of g . Here the symbol \u03b4g denotes the half taper angle of the conical grinding wheel. According to differential geometry, the unit normal vector of g can be worked out from Eq. (1) as ( n) a = \u2202 ( ra ) a \u2202\u03b8 \u00d7 \u2202 ( ra ) a \u2202u \u2223\u2223\u2223 \u2202 ( ra ) a \u2202\u03b8 \u00d7 \u2202 ( ra ) a \u2202u \u2223\u2223\u2223 = na ( \u03b8, \u03b4g ) = cos \u03b4g cos \u03b8 i a + cos \u03b4g sin \u03b8 j a \u2212 sin \u03b4g k a . (2) The direction of ( n) a in Eq. (2) is from the entity of the emery cutter to the space as shown in Fig. 2 . Furthermore, by means of the methodology proposed in Ref. [22] , the two principal directions of g can be determined as follows: ( g1 ) a = \u2202 ( ra ) a \u2202u \u2223\u2223\u2223 \u2202 ( ra ) a \u2202u \u2223\u2223\u2223 = m a ( \u03b8, \u03b4g ) = sin \u03b4g cos \u03b8 i a + sin \u03b4g sin \u03b8 j a + cos \u03b4g k a , (3) ( g2 ) a = ( n) a \u00d7 ( g1 ) a = na ( \u03b8, \u03b4g ) \u00d7 m a ( \u03b8, \u03b4g ) = \u2212 ga ( \u03b8 ) = sin \u03b8 i a \u2212 cos \u03b8 j a . (4) Accordingly, a right-handed principal frame, \u03c3P { P ; g1 , g2 , n} , can be established at an arbitrary point P on the generating conical surface g ", " When S = 2 , the generating conical surface, (2) g , is adopted to grind the helicoid facing to the big end (the heel), and i a = i , j a = j , and k a = k . d d d 3.2. Equation of generating surface and its characteristic parameters According to the coordinate system setting mentioned above, from Eq. (1) , the equation of the generating conical surface, (S) g , ( S = 1 , 2 ) can be attained in \u03c3 d as ( rd ) d = u sin \u03b4gS sin ( \u03c0 S \u2212 \u03b8 ) i d + ( \u22121 ) S u sin \u03b4gS cos ( \u03c0 S \u2212 \u03b8 ) j d + ( \u22121 ) S ( u cos \u03b4gS \u2212 r g tan \u03b4gS ) k d , (6) where the notation r g indicates the radius of the grinding wheel as illustrated in Fig. 2 . From Eq. (2) , the unit normal vector of (S) g can be represented in \u03c3 d as ( n) d = cos \u03b4gS sin ( \u03c0 S \u2212 \u03b8 ) i d + ( \u22121 ) S cos \u03b4gS cos ( \u03c0 S \u2212 \u03b8 ) j d + ( \u22121 ) S+1 sin \u03b4gS k d . (7) From Eqs. (3 ) and (4) , the two base vectors g1 and g2 of the principal frame \u03c3 P on (S) g can be expressed in \u03c3 d as ( g1 ) d = sin \u03b4gS sin ( \u03c0 S \u2212 \u03b8 ) i d + ( \u22121 ) S sin \u03b4gS cos ( \u03c0 S \u2212 \u03b8 ) j d + ( \u22121 ) S cos \u03b4gS k d , (8) ( g2 ) d = cos ( \u03c0 S \u2212 \u03b8 ) i d + ( \u22121 ) S+1 sin ( \u03c0 S \u2212 \u03b8 ) j d . (9) Via the coordinate transformation, the vectors rd and n can be represented in \u03c3 o1 as ( rd ) o1 = R [ j o1 , \u03b3m ] R [ i od , \u03b5 S ] ( rd ) d = x o1 i o1 + y o1 j o1 + z o1 k o1 , (10) ( n) o1 = R [ j o1 , \u03b3m ] R [ i od , \u03b5 S ] ( n) d = n x i o1 + n y j o1 + n z k o1 , (11) where x o1 = A x u + B x , y o1 = A y u + B y , and z o1 = A z u + B z " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003000_tmrb.2020.3034258-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003000_tmrb.2020.3034258-Figure1-1.png", "caption": "Fig. 1. A schematic of a three-tube CTCR with its configuration parameters.", "texts": [ " It is well known in robotics that the particular representation of data, for instance of rotations and postures for such learning problems, can have crucial influence on the approximation quality of such learning, which was recently shown in [16]. Therefore, we also investigate empirically which representations of C and Q are suited for our problem. A CTCR consists of n \u2265 2 concentric superelastic NiTitubes nested in each other. These tubes can be thermally set to arbitrary shapes considering the recoverable strain limit of 5-8%. Each tube can be defined by several parameters such as length, diameter, and section curvature. For this work, we use a CTCR consisting of three tubes (see Fig. 1). Each tube i \u2208 {1, 2, 3} (1 being the innermost tube), consists of a straight and a curved section with respective lengths denoted by Ls,i and Lc,i. The curved section is described by a constant curvature \u03bai. Each tube has inner and outer diameters denoted by din,i and dout,i. The tube parameters for the robot used in this work are stated in Tab. I. A CTCR is actuated by individually rotating and translating each tube. Rotation of each tube is denoted using the angle Authorized licensed use limited to: University of Gothenburg" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002438_j.ijmecsci.2019.105397-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002438_j.ijmecsci.2019.105397-Figure2-1.png", "caption": "Fig. 2. Universal numerical simulation modeling for aviation spiral bevel gear tooth flank.", "texts": [], "surrounding_texts": [ "2\ne t\nn\n\ud835\udc3a\na\nn\n\ud835\udc3f\nc c\nC\na\n\ud835\udc3e\n3\no t t l e t t t l\n3\nf t f c\nf t n w i ( t t g 1\n\ud835\udc53\nm(\nl p n g t [ o T\nf t t fl t\n3\nt c\no\n\ud835\udc39\nl\n.2. Tooth flank curvature analysis\nIn the Euclidean space, \u03a3i (i = 1,2) is represented by p i ( \ud835\udf19, \ud835\udf03), there xists ( \ud835\udf19, \ud835\udf03) \u2208A representing the basic design variable domain. With the ooth flank definition, n i is presented as \ud835\udc56 ( \ud835\udf19, \ud835\udf03) = n \ud835\udc56,\ud835\udf19 \u00d7 n \ud835\udc56,\ud835\udf03 \ud835\udc64\ud835\udc56\ud835\udc61\u210e n \ud835\udc56 \u2260 \ud835\udfce (8)\nConsidering the assumed regularity of modeling the \u03a3i , it can yield\n\ud835\udc38 \ud835\udc56 =\nd [ p \ud835\udc56 ( \ud835\udf19, \ud835\udf03) ] d \ud835\udf19 \u22c5 d [ p \ud835\udc56 ( \ud835\udf19, \ud835\udf03) ] d \ud835\udf19 , \ud835\udc39 \ud835\udc56 = d [ p \ud835\udc56 ( \ud835\udf19, \ud835\udf03) ] d \ud835\udf19 \u22c5 d [ p \ud835\udc56 ( \ud835\udf19, \ud835\udf03) ] d \ud835\udf03 ,\n\ud835\udc56 =\nd [ p \ud835\udc56 ( \ud835\udf19, \ud835\udf03) ] d \ud835\udf03 \u22c5 d [ p \ud835\udc56 ( \ud835\udf19, \ud835\udf03) ] d \ud835\udf03\n(9)\nre introduced to represent their unit normal vector as\n[ \ud835\udc48 ] \ud835\udc56 ( \ud835\udf19, \ud835\udf03) = n \ud835\udc56 ( \ud835\udf19, \ud835\udf03) \u2215 ||n \ud835\udc56 ( \ud835\udf19, \ud835\udf03) || = n \ud835\udc56 ( \ud835\udf19, \ud835\udf03) \u2215 \u221a \ud835\udc38 \ud835\udc56 \ud835\udc3a \ud835\udc56 \u2212 \ud835\udc39 \ud835\udc56 2 (10)\nThen, the following relations are provided as\n\ud835\udc56 = \u2212\nd [ n [ \ud835\udc48 ] \ud835\udc56 ( \ud835\udf19, \ud835\udf03) ] d \ud835\udf19 \u22c5 d [ p \ud835\udc56 ( \ud835\udf19, \ud835\udf03) ] d \ud835\udf19 , \ud835\udc40 \ud835\udc56 = \u2212 d [ n [ \ud835\udc48 ] \ud835\udc56 ( \ud835\udf19, \ud835\udf03) ] d \ud835\udf19 \u22c5 d [ p \ud835\udc56 ( \ud835\udf19, \ud835\udf03) ] d \ud835\udf19\n= \u2212\nd [ n [ \ud835\udc48 ] \ud835\udc56 ( \ud835\udf19, \ud835\udf03) ] d \ud835\udf03 \u22c5 d [ p \ud835\udc56 ( \ud835\udf19, \ud835\udf03) ] d \ud835\udf19 , \ud835\udc41 \ud835\udc56 = \u2212 d [ n [ \ud835\udc48 ] \ud835\udc56 ( \ud835\udf19, \ud835\udf03) ] d \ud835\udf03 \u22c5 d [ p \ud835\udc56 ( \ud835\udf19, \ud835\udf03) ] d \ud835\udf03 (11)\nIn the tooth flank discretization and NURBS fitting, the tooth flank an be expressed as an arbitrary \u03a3i ( i = 1,2). Thus, C i on the \u03a3i ( i = 1,2) an be defined by the position vectors\n\ud835\udc56 ( \ud835\udc60 ) = p [ \ud835\udc36 ] [ \ud835\udf03[ \ud835\udc36 ] ( \ud835\udc60 ) , \ud835\udf19[ \ud835\udc36 ] ( \ud835\udc60 ) ] (12)\nWhere, as for C i , its unit tangent vector is represented by\nd C \ud835\udc56 ( \ud835\udc60 ) d \ud835\udc60 =\nd { p [ \ud835\udc36 ] [ \ud835\udf03[ \ud835\udc36 ] ( \ud835\udc60 ) , \ud835\udf19[ \ud835\udc36 ] ( \ud835\udc60 ) } d \ud835\udf03 \u22c5 d [ \ud835\udf03[ \ud835\udc36 ] ( \ud835\udc60 ) ] d \ud835\udc60\n+\nd { p [ \ud835\udc36 ] [ \ud835\udf03[ \ud835\udc36 ] ( \ud835\udc60 ) , \ud835\udf19[ \ud835\udc36 ] ( \ud835\udc60 ) } d \ud835\udf19 \u22c5 d [ \ud835\udf03[ \ud835\udc36 ] ( \ud835\udc60 ) ] d \ud835\udc60\n(13)\nnd the derivative along C i of the unit normal vector is\nd n [ \ud835\udc48 ] \ud835\udc56\nd \ud835\udc60 =\nd [ n [ \ud835\udc48 ] \ud835\udc56 ( \ud835\udf19, \ud835\udf03) ] d \ud835\udf03 d [ \ud835\udf03[ \ud835\udc36 ] ( \ud835\udc60 ) ] d \ud835\udc60 + d [ n [ \ud835\udc48 ] \ud835\udc56 ( \ud835\udf19, \ud835\udf03) ] d \ud835\udf19 d [ \ud835\udf19[ \ud835\udc36 ] ( \ud835\udc60 ) ] d \ud835\udc60\n(14)\nTo this end, K N [i] of \u03a3i ( i = 1,2) is yielded as\n[ \ud835\udc56 ] \ud835\udc41 = \u2212 d \ud835\udc02 \ud835\udc56 ( \ud835\udc60 ) d \ud835\udc60\n\u22c5 d \ud835\udc27 [ \ud835\udc48 ] \ud835\udc56\nd \ud835\udc60 (15)\n. Determination of loaded contact pattern\nHere, at the initial moment, the elastic contact deformation has not ccurred yet because there is no load applied on the tooth flank. Here, he tooth contact points solved from the improved TCA is the initial ooth flank contact position in NLTCA. Then, with change of the applied oad, at each tooth flank contact position, there exists the corresponding lastic contact deformation. The instantaneous loaded contact deformaion pattern becomes an ellipse where its center is the contact point at he initial position. Finally, the instantaneous contact ellipses which are ime-varying at all the center point positions can constitute the whole oaded tooth contact pattern for NLCTA.\n.1. Instantaneous contact ellipse center\nThe tooth point is very critical to determination of the contact perormance evaluations [44] , such as the tooth contact strength including he contact pattern, contact pressure and contact stress, and the noise actors including the transmission error [1,2] . To get the instantaneous ontact ellipse center, Fig. 3 shows an improved kinematic arrangement\nor the tooth contact points in TCA solution. It is notation that the esablishments of the Cartesian three-dimensional coordinate systems are eeded to satisfying the right-hand rule. Generally, for gear tooth flank ith P i ( \ud835\udf19i , \ud835\udf03i ) (i = 1,2) which can be calculated by tooth flank modeling n O i ( X i , Y i , Z i ) (i = 1,2). Here, tooth flank point is represented by r i i = 1,2) and n i (i = 1,2). \u03a3i (i = 1,2) are needed to be rotated to reach the ooth contact position and this motion can be represented by M i-f . At he same position P\n\u2217 ( \ud835\udf191 , \ud835\udf031 , \ud835\udf191 , \ud835\udf032 ), it is needed to satisfy the theory of earing [1] . Therefore, TCA equation set can be yielded as ( Figs. 2 and 3 ) \ud835\udc47\ud835\udc36\ud835\udc34 ( \ud835\udf192 , \ud835\udf032 , \ud835\udf191 , \ud835\udf031 ) = 0 \u21d2 { \ud835\udc2b f \u2236 ( \ud835\udc2b f ) 1 ( \ud835\udf191 , \ud835\udf031 ) = ( \ud835\udc2b f ) 2 ( \ud835\udf192 , \ud835\udf032 )\n\ud835\udc0d f \u2236 \ud835\udc0d 1 ( \ud835\udf191 , \ud835\udf031 ) = \ud835\udf12\ud835\udc0d 2 ( \ud835\udf192 , \ud835\udf032 )\n\u21d2 ( M 2\u2212 f \ud835\udc2b 2 ( \ud835\udf192 , \ud835\udf032 ) = M 1\u2212 f \ud835\udc2b 1 ( \ud835\udf191 , \ud835\udf031 ) M 2\u2212 f \ud835\udc27 2 ( \ud835\udf192 , \ud835\udf032 ) = \ud835\udf12M 1\u2212 f \ud835\udc27 ( \ud835\udf191 , \ud835\udf031 ) 1\n(16)\nThen, the basic transformation matrix representing tooth contact eshing kinematics is yielded as\nM \ud835\udc61 \u2212 \ud835\udc53 ) \ud835\udc56 = ( M \ud835\udc61 \u2212 \ud835\udc54 ) \ud835\udc56 \u22c5 ( M \ud835\udc54\u2212 \ud835\udc4e ) \ud835\udc56 \u22c5 ( M \ud835\udc4e \u2212 \ud835\udc4f ) \ud835\udc56 \u22c5 ( M \ud835\udc4f \u2212 \ud835\udc50 ) \ud835\udc56 \u22c5M \ud835\udc50\u2212 \ud835\udc53\n= \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 1 0 0 \u2212\n( \u0394\ud835\udcc1 \ud835\udc4b ) \ud835\udc56\n0 1 0 \u2212 ( \u0394\ud835\udcc1 \ud835\udc4c ) \ud835\udc56 0 0 1 \u2212 ( \u0394\ud835\udcc1 \ud835\udc4d ) \ud835\udc56 0 0 0 1 \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 cos ( \u0394\u2118 \ud835\udc4d ) \ud835\udc56 \u2212 \ud835\udc60\ud835\udc56\ud835\udc5b ( \u0394\u2118 \ud835\udc4d ) \ud835\udc56 0 0 \ud835\udc60\ud835\udc56\ud835\udc5b ( \u0394\u2118 \ud835\udc4d ) \ud835\udc56 cos ( \u0394\u2118 \ud835\udc4d ) \ud835\udc56 0 0 0 0 1 0 0 0 0 1 \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 \u00d7\n\u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 cos ( \u0394\u2118 \ud835\udc4c ) \ud835\udc56 0 \ud835\udc60\ud835\udc56\ud835\udc5b ( \u0394\u2118 \ud835\udc4c ) \ud835\udc56 0 0 1 0 0 \u2212 \ud835\udc60\ud835\udc56\ud835\udc5b ( \u0394\u2118 \ud835\udc4c ) \ud835\udc56 0 cos ( \u0394\u2118 \ud835\udc4c ) \ud835\udc56 0 0 0 0 1 \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 \u00d7\n\u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 1 0 0 0 0 cos ( \u0394\u2118 \ud835\udc4b ) \ud835\udc56 \u2212 \ud835\udc60\ud835\udc56\ud835\udc5b ( \u0394\u2118 \ud835\udc4b ) \ud835\udc56 0 0 \ud835\udc60\ud835\udc56\ud835\udc5b ( \u0394\u2118 \ud835\udc4b ) \ud835\udc56 cos ( \u0394\u2118 \ud835\udc4b ) \ud835\udc56 0 0 0 0 1 \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 0 0 \u22121 0 0 1 0 0 1 0 0 0 0 0 0 1 \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 (17)\nWhere, in order to establish the TCA equation set, in the estabished meshing coordinate system, it needs to satisfy the two following oints: i) gear and pinion tooth flank points need to get the same vector, amely ( r f ) 1 = ( r f ) 2 and ii) gear and pinion tooth flank points need to et a collinear normal vector, namely N 1 = \ud835\udf12N 12 . In accurate solution o Eq. (16) , a key is accurate determination of the initial contact point 9] . It means that M i-f (i = 1,2) is needed to be firstly determined. Morever, as mentioned in Ref. [9] , the accurate initial value problem for CA solution was also taken into account [9] .\nIn applications of TCA arrangements, the matching target points rom the gear and pinion flank can be determined as the initial elasic deformation position and center points of the instantaneous loaded ooth contact ellipse. Then, loaded elastic deformation appears, and the ank geometric shape changes in every time, as well as the loaded conact pattern.\n.2. loaded contact pattern boundary\nFig. 4 represents the basic determination of the loaded contact patern of tooth flank which is comprised of all the instantaneous loaded ontact ellipses at each the initial contact point position.\nHere, at this loaded contact position, if T INP is known, the total force f a tooth interaction as\n= T \ud835\udc3c \ud835\udc41 \ud835\udc43 r f ( \ud835\udf19, \ud835\udf03) \u00d7 N f ( \ud835\udf19, \ud835\udf03) or T \ud835\udc3c \ud835\udc41 \ud835\udc43 \u2212 1 r f \u2212 1 ( \ud835\udf19, \ud835\udf03) \u00d7 N f \u2212 1 ( \ud835\udf19, \ud835\udf03) + T \ud835\udc3c \ud835\udc41 \ud835\udc43 \u2212 2 r f \u2212 2 ( \ud835\udf19, \ud835\udf03) \u00d7 N f \u2212 2 ( \ud835\udf19, \ud835\udf03)\n(18)\nThe sign 1 and 2 present the gear and pinion tooth flank. Where, the oad distribution of the single or two pairs of gear tooth flank contact is", "Fig. 3. Kinematic arrangement for determining instantaneous contact ellipse center.\nt t e\n\ud835\udc36\nc\n\ud835\udc3d\nw s\n\ud835\udeff\nl [\n\ud835\udf06\naken into account and its detailed can refer to Ref. [45] . In consideraion of main material properties, such as E [1] , E [2] , v [1] and v [2] , there xists the comprehensive coefficient as\n= 2\n[ 1 \u2212 ( \ud835\udc63 [ 1 ] )2\n\ud835\udc38 [ 1 ] +\n1 \u2212 ( \ud835\udc63 [ 2 ] )2\n\ud835\udc38 [ 2 ]\n] \u22121 (19)\nMoreover, there exists a following integration regarding to Hertz ontact solution as\n= \u222b \ud835\udf0b\u22152\n0\n1 \u221a\nsin 2 \ud835\udf03\ud835\udc36\ud835\udc43 + \u03a62 \ud835\udc50\ud835\udc5c \ud835\udc60 2 \ud835\udf03\ud835\udc36\ud835\udc43\nd \ud835\udf03\ud835\udc36\ud835\udc43 (20)\nhere, determination of \u03a6 can refer to Ref. [45] . To this end, in NLTCA olution, the loaded elastic contact deformation can be represented as\n= 3 \ud835\udc39 \ud835\udc3f\ud835\udc47\ud835\udc36\ud835\udc34 \ud835\udc3d \ud835\udc36\ud835\udf0b\ud835\udc4e \ud835\udc36\ud835\udc43\n(21)\nConsidering the loaded contact deformation, in determination of the oaded contact pattern of tooth flank, there is \u0394s = | MP\n\u2217 | = \ud835\udf0c, it yields 1]\n\ud835\udc56 = \ud835\udc3e [ \ud835\udc56 ] \ud835\udc41\n\u0394\ud835\udc60 2 = 1 \ud835\udc3e\n[ \ud835\udc56 ] \ud835\udc41 \ud835\udf0c2 (22)\n2 2", "Fig. 4. The loaded tooth contact pattern of tooth flank for spiral bevel gears.\nc\n\ud835\udf06\nw . d (\n\ud835\udf06\nt\n\ud835\udc5e\n\ud835\udf0f\n\ud835\udefc f\nc m\n\ud835\udc35\n\ud835\udc4e\nw\n\ud835\udc34\n\ud835\udc35\n\ud835\udc3e\nt o\n4\no r t t t [ c t\n4\nt d t s i F t d\nZ\ng t t t d a(\nAs for spiral bevel gear flank \u03a3i (i = 1, 2), K N [i] , K I [i] and K II [i] exist a\nertain relation satisfying the Euler equation. The \ud835\udf06i (i = 1, 2) is finally\n\ud835\udc56 =\n\ud835\udf0c2 2 ( \ud835\udc3e [ \ud835\udc56 ] \ud835\udc3c \ud835\udc50 \ud835\udc5c \ud835\udc60 2 \ud835\udc5e \ud835\udc56 + \ud835\udc3e [ \ud835\udc56 ] \ud835\udc3c\ud835\udc3c \ud835\udc50 \ud835\udc5c \ud835\udc60 2 \ud835\udc5e \ud835\udc56 )( \ud835\udc56 = 1 , 2) (23)\nhere, q i (i = 1, 2) represents the angle between | MP \u2217 | and e I [i] (i = 1, 2) The coordinate system ( P\n\u2217 ; \ud835\udf0f, \ud835\udf02) in tangent plane \u03a0 is established to efine the instantaneous ellipse. The direction of vector | MP\n\u2217 | in plane \ud835\udf0f, \ud835\udf02) is \ud835\udf03CP .\nIn the loaded tooth contact pattern boundary, there exists\n1 \u2212 \ud835\udf062 = \u00b1 \ud835\udeff (24)\nTo determine the instantaneous ellipse, there are the following relaions are\n1 = \ud835\udefc[ 1 ] + \ud835\udf03CP , \ud835\udc5e 2 = \ud835\udefc[ 2 ] + \ud835\udf03CP , \ud835\udf0c 2 = \ud835\udf0f2 + \ud835\udf022 , \ud835\udc50\ud835\udc5c\ud835\udc60 \ud835\udf03CP =\n\ud835\udf0f \ud835\udf0c , \ud835\udc60\ud835\udc56\ud835\udc5b \ud835\udf03CP = \ud835\udf02 \ud835\udf0c\n(25a\u2013e)\nWith the geometric transformations, it can be yielded as [1]\n2 ( \ud835\udc3e [ 1 ] I cos 2 \ud835\udefc[ 1 ] + \ud835\udc3e [ 1 ] I I sin 2 \ud835\udefc[ 1 ] \u2212 \ud835\udc3e [ 2 ] I cos 2 \ud835\udefc[ 2 ] \u2212 \ud835\udc3e [ 2 ] I I sin 2 \ud835\udefc[ 12 ] ) + \ud835\udf022 ( \ud835\udc3e\n[ 1 ] I \ud835\udc60\ud835\udc56 \ud835\udc5b 2 \ud835\udefc[ 1 ] + \ud835\udc3e [ 1 ] I I cos 2 \ud835\udefc[ 1 ]\n\u2212 \ud835\udc3e [ 2 ] I sin 2 \ud835\udefc[ 2 ] \u2212 \ud835\udc3e [ 2 ] I I cos 2 \ud835\udefc[ 12 ] )\n\u2212 \ud835\udf0f\ud835\udf02 [ ( \ud835\udc3e\n[ 1 ] I \u2212 \ud835\udc3e [ 1 ] I I ) \ud835\udc60\ud835\udc56\ud835\udc5b (2 \ud835\udefc [ 1 ] ) \u2212 ( \ud835\udc3e [ 2 ] I \u2212 \ud835\udc3e [ 2 ] I I ) \ud835\udc60\ud835\udc56\ud835\udc5b (2 \ud835\udefc\n[ 2 ] ) ] = \u00b12 \ud835\udeff (26)\n[ 1 ] can be selected randomly. For instance, it can select \ud835\udefc[ 1 ] by satisying the following relation\n( \ud835\udc3e [ 1 ] I \u2212 \ud835\udc3e [ 1 ] I I ) \ud835\udc60\ud835\udc56\ud835\udc5b (2 \ud835\udefc [ 1 ] ) \u2212 ( \ud835\udc3e [ 2 ] I \u2212 \ud835\udc3e [ 2 ] I I )\n\ud835\udefc[ 2 ] = \ud835\udefc[ 1 ] + \ud835\udf0e[ \u0398]\n}\n\u21a6 tan 2 \ud835\udefc[ 1 ]\n=\n( \ud835\udc3e [ 2 ] I \u2212 \ud835\udc3e [ 2 ] I I ) sin \ud835\udf0e [ \u0398]\n( \ud835\udc3e [ 1 ] I \u2212 \ud835\udc3e [ 1 ] I I ) \u2212 ( \ud835\udc3e [ 2 ] I \u2212 \ud835\udc3e [ 2 ] I I ) \ud835\udc50 \ud835\udc5c\ud835\udc60 \ud835\udf0e[ \u0398]\n(27)\nThe Eqs. (26) and (27) can show that the projection of the loaded ontact pattern in tangent plane \u03a0 is a ellipse and its equation is deterined as\n\ud835\udf0f2 + \ud835\udc34 \ud835\udf022 = \u00b1 \ud835\udeff (28)\na CP and b CP are represented as [1]\n\ud835\udc36\ud835\udc43 = \u221a |||| \ud835\udeff\ud835\udc34 ||||, \ud835\udc4f \ud835\udc36\ud835\udc43 = \u221a |||| \ud835\udeff\ud835\udc35 |||| (29)\nhere,\n= 1 4\n( \ud835\udc3e\n[ 1 ] \u03a3 \u2212 \ud835\udc3e [ 2 ] \u03a3 \u2212\n\u221a\n\ud835\udc54 2 1 \u2212 2 \ud835\udc54 1 \ud835\udc54 2 cos 2 \ud835\udf0e + \ud835\udc54 2 2\n) (30a)\n= 1 4\n( \ud835\udc3e\n[ 1 ] \u03a3 \u2212 \ud835\udc3e [ 2 ] \u03a3 +\n\u221a\n\ud835\udc54 2 1 \u2212 2 \ud835\udc54 1 \ud835\udc54 2 cos 2 \ud835\udf0e + \ud835\udc54 2 2\n) (30b)\n[ i ] \u03a3 = \ud835\udc3e [ i ] I + \ud835\udc3e [ i ] II , \ud835\udc54 \ud835\udc56 = \ud835\udc3e [ i ] I \u2212 \ud835\udc3e [ i ] II (30c,d)\nWith the data-driven determination for the loaded tooth contact patern boundary, it can get a basic constraint to the high-order topology ptimization of grinding tooth flank.\n. High-order topology optimization\nThe higher the density of the tooth flank grid points, the more obvius the high-order characteristics. In this end, in consideration of mateial removal scale in accurate NC grinding of aviation spiral bevel gears, he microscopic topography is time-varying by referring to the optimizaion of the loaded tooth contact pattern. It is worth notation that though he loaded tooth contact pattern does not exist directly on tooth flank 46,47] , it can be prescribed as an important constraint on the loaded ontact performance evaluation in the proposed high-order topology opimization.\n.1. High-order topology\nWith the application of high-order universal machine-tool settings, hey can be applied to get a high order tooth flank topology which is istinguished with the conventional first or second-order tooth flank opology [46] . Due to the geometric accuracy control in the microscopic cale of the ground surface, the accurate tooth flank topology expression s of great significance to the actual NC grinding of spiral bevel gears. ig. 5 shows the basic high-order topology expression in coordinate sysem O P ( x, y, z ) which is consistent with the one in the tooth surface iscretization. This topology is represented as a polynomial\n\ud835\udc3a = \u2118 0 + \u2118 1 \ud835\udc4b \ud835\udc3a + \u2118 2 \ud835\udc4c \ud835\udc3a + \u2118 3 \ud835\udc4b \ud835\udc3a 2 + \u2118 4 \ud835\udc4b \ud835\udc3a \ud835\udc4c \ud835\udc3a + \u2118 5 \ud835\udc4c \ud835\udc3a 2 + \u2118 6 \ud835\udc4b \ud835\udc3a 3\n+ \u2118 7 \ud835\udc4b \ud835\udc3a 2 \ud835\udc4c \ud835\udc3a + \u2118 8 \ud835\udc4b \ud835\udc3a \ud835\udc4c \ud835\udc3a 2 + \u2118 9 \ud835\udc4c \ud835\udc3a 3 \u22ef (31)\nActually, this expression is an accurate polynomial fitting of the rinding tooth flank points at each grinding process. Meanwhile, the ooth flank points are determined by applying modeling and discretizaion when the universal machine-tool settings having high-order characeristics are given. Thence, the current tooth flank topology represents ata-driven expression with respect to universal machine-tool settings s\np [ \ud835\udc3c\u2212 \ud835\udc3d ] )[ \u0398] ( \ud835\udf19\ud835\udc3b , \ud835\udf03 ) \u2192 Z \ud835\udc3a ( \ud835\udf19\ud835\udc3b , \ud835\udf03 ) \u2245\u2236 Z \ud835\udc3a ( \ud835\udc4b \ud835\udc3a , \ud835\udc4c \ud835\udc3a ) (32)" ] }, { "image_filename": "designv10_9_0003340_j.addma.2021.101881-Figure25-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003340_j.addma.2021.101881-Figure25-1.png", "caption": "Fig. 25. Mesh generation and symmetrical plane constraint for the quarter canonical part.", "texts": [ " Moreover, for the purpose of preventing detaching, a thin reinforcement strip is added to the lower end of the part to enhance connection to the large build plate (see Fig. 24 (a) and also Ref. [18]). Note this base reinforcement was not included in the Ti6Al4V canonical part reported in Ref. [28]. Regardless of the small triangle opening, at least bi-plane geometrical symmetry can be observed for the canonical part. In order to save computational time, the small triangle opening and the cone belt are neglected in the simulation. Thus, only a quarter of the canonical part as shown in Fig. 25 is modeled in the layer-wise simulation. Considering the overhang feature, the canonical part is divided into two sections in the build direction for mesh generation. To mostly keep a uniform thickness for equivalent layers, the element thickness is set around 0.53 mm. As a result, there are 121 equivalent layers in the build direction while 97 layers are contained from the bottom to the overhang position (0\u201351.8 mm). Hexahedral elements are preferred to mesh the quarter part except in a transitional layer using mixed tetrahedral mesh (see Fig. 25) degraded from hexahedral elements with respect to the drastically increase in cross sectional area in the build direction. In this way, computational cost can be saved by employing fewer elements. Otherwise, when the full size canonical part is meshed using single element type, there can be nearly 360,000 hexahedral elements [18] or 340,000 tetrahedral elements [28] for the 60-layer model. In the meshing scheme employed in this work, there are 72,636 mixed elements and 83,033 nodes in the 121-layer quarter part" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001510_j.mechmachtheory.2014.01.014-Figure22-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001510_j.mechmachtheory.2014.01.014-Figure22-1.png", "caption": "Fig. 22. Circumferential strain distribution under a transmission load.", "texts": [ " Using the analysis above, the maximum circumferential strain in the assembly state occurs along the minor axis of the FS, and the distribution of the circumferential strain for the three models (the narrow tooth rim, the wide tooth rim and the full FS model) is consistent with the corresponding theoretical result. 6.3.3.2. Experiment for the complete FS model in the transmission state. The model developed here is further verified by simulating the complete FS model in the transmission state. For a transmission torque T of 800 N\u00b7m and the experimentally obtained distribution of the engaged forces [2], the transmission forces are exerted on the tips of the engaged teeth. Fig. 22 shows the calculated circumferential strain of the FS in the transmission state. The maximum circumferential strain of 21.1 \u00d7 10\u22125 and the minimum circumferential strain of \u221215.7 \u00d7 10\u22125 occur at the back plane and the front plane near the contact point of the inner FS surface and the roller, respectively. Seven paths are defined in the same manner as before. The effect of the load breaks the symmetry of the distribution of the circumferential strain in the tooth rim with respect to the major axial direction" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000975_j.proeng.2014.03.099-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000975_j.proeng.2014.03.099-Figure2-1.png", "caption": "Fig. 2. Monitored parameters on the cutting edge.", "texts": [ " In the first step the edge radius \u03c1r, K factor and edge roughness were monitored. For measuring these parameters the Infinite Focus System G4 from the Alicona Company was used. The measuring principle of this device and measuring methods are described in the article \u2018Evaluation of the cutting tool when Inconel 718 is machined\u2019 [9] by my colleague. A very important fact is that based on the recorded deviances it is possible to measure the roughness in the area where the tool wear will be increased [5,6,8], see Fig. 2. For the test these values of edge radius \u03c1r and tool geometry were used, see Table 1. During the manufacturing process from grinding to deposition of thin layer the parameters on the cutting edge were monitored. The first case, see Fig. 3a, shows how the edge radius increases during the time of the rectification process. From Fig. 3b it is evident that with the increasing of the rectification time, the value of the cutting edge increases and the quality of the faces is better, which means that the value of the roughness decreases, see Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003169_j.mechmachtheory.2020.103844-Figure9-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003169_j.mechmachtheory.2020.103844-Figure9-1.png", "caption": "Fig. 9. The Delta PM: (a) architecture; (b) wrench space; (c) definitions of the proximal wrench.", "texts": [ " For a PM, if it is at a proximal interaction singular configuration, at least one of the reciprocal products of proximal wrenches and their corresponding actual proximal twists is equal to zero . Lemma 2. For a PM, if \u03bd = 0 , the PM is free of proximal interaction singularity. The proximal motion-force interactability is worst or proximal interaction singularity occurs when \u03bd = 0 . To illustrate the proximal wrench identification of the proposed approach, four examples are presented. As shown in Fig. 9 , once again, the Delta PM based on the 3- R ( S S )( S S ) mechanism is used as an analytical case. The 2nd limb is selected for analysis. As identified in Section 2.1.1, there are two physically available wrenches, namely, 3 S DW = (B 2,1 C 2,1 ; c 2,1 \u00d7 B 2,1 C 2,1 ) and 4 S DW = (B 2,2 C 2,2 ; c 2,2 \u00d7 B 2,2 C 2,2 ). These two physically available wrenches together form a wrench space 2 WS = span { 3 S DW , 4 S DW }, as shown in Fig. 9 (b), which coincides with the plane : B 2,1 B 2,2 C 2,1 C 2,2 . The proximal wrench 2 S PW , which belongs to the wrench space 2 WS and transmits the input twist from the actuated joint most effectively, is the identification target. In this case, the actual proximal twist of the actuated revolute joint is 2 S APT = (B 2,1 B 2,2 ; a 2 \u00d7 B 2,1 B 2,2 ). It generates a velocity 2 v VDT = A 2 B 2 \u00d7 B 2,1 B 2,2 on the proximal application point p A 2 (i.e., point B 2 ) as shown in Fig. 9 (c). To transmit 2 v VDT most effectively, 2 S PW = (B 2,2 C 2,2 ; b 2 \u00d7 B 2,2 C 2,2 ) on the plane : B 2,1 B 2,2 C 2,1 C 2,2 is identified. In this condition, the angle \u03b8 reaches the minimum value. Similarly, the proximal wrenches in the 1st and 3rd limbs are identified as 1 S PW = (B 1,2 C 1,2 ; b 1 \u00d7 B 1,2 C 1,2 ) and 3 S PW = (B 3,2 C 3,2 ; b 3 \u00d7 B 3,2 C 3,2 ). The second case can be seen in Fig. 10 . The 3- P ( S S ) S PM is composed of three P ( S S ) S limbs. The 3rd limb is selected to illustrate the analysis, in which there are two physically available wrenches, namely, 5 S DW = (B 3,1 C 3 ; c 3 \u00d7 B 3,1 C 3 ) and 6 S DW = (B 3,2 C 3 ; c 3 \u00d7 B 3,2 C 3 )" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002089_j.jsv.2018.01.018-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002089_j.jsv.2018.01.018-Figure1-1.png", "caption": "Fig. 1. Rolling element bearing schematic.", "texts": [ " The goal of this work is to validate the accuracy of the proposed technique and treatment of the bearing nonlinearity, which has not been carried out in any of the previous work. Values of the system parameters are sought that generate nonlinear phenomena such as jump resonance, and the results are confirmed with numerical integration. A secondary objective is to provide a better understanding of healthy bearing behavior by studying the frequency response for key system parameters. A schematic diagram of a rolling element bearing is shown in Fig. 1. The bearing has clearance c, inner raceway radius Ri, outer raceway radius Ro, and rolling element radius R. The outer raceway is rigidly fixed and the shaft is rigidly fixed with the inner raceway. The shaft is given two degrees of freedom in the y and z direction. The deformation of each rolling element depends on the position of the inner raceway, bearing geometry, and clearance. The deformation of the jth rolling element can be described with respect to the yz coordinate system \ud835\udeffj = v cos\ud835\udefcj + w sin \ud835\udefcj \u2212 c (1) where v and w are the translational displacements of the shaft and \ud835\udefcj is the angle between the y-axis and the line connecting the origin of the reference frame and the center of the jth roller" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000684_20131218-3-in-2045.00128-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000684_20131218-3-in-2045.00128-Figure4-1.png", "caption": "Fig. 4 Schematic representation of the plant", "texts": [ " 3 consists of two links: a horizontal link called the rotating arm and a vertical link called the pendulum. The DC motor rotates the stiff arm at one end of the horizontal plane. The opposite end of the arm is instrumented with a joint whose axis is along the radial direction of the motor. The pendulum is attached to the joint. The flat arm is instrumented with an encoder at one end such that the encoder shaft is aligned with the longitudinal axis of the arm. This encoder measures the pendulum angle. The schematic representation of the system is shown in Fig. 4. The Lagrangian method is used to obtain the equations of motion of the rotary inverted pendulum system. The generalized co-ordinates for the system are the angular displacements of the rotating arm (\u03b8) and the pendulum angle (\u03b1). The general form of Lagrange function L of the system is given as L = Total Kinetic Energy (T) \u2013 Potential Energy (V) Taking the horizontal plane where the arm lies as the datum plane, the only potential energy in the mechanical system is gravity, i.e. cos( )V mgl= \u03b1 (1) The kinetic energies in the system arise from the moving hub, the velocity of the point mass in the x- direction, the velocity of the point mass in the y-direction and the rotating pendulum about its centre of mass 2 21 1 1 [( cos( ) ( sin( ) ] 2 2 2eq BT J m r L L J2 2= \u03b8 + \u03b8 \u2212 \u03b1 \u03b1) + \u2212 \u03b1 \u03b1) + \u03b1\u027a \u027a \u027a \u027a \u027a 2 2 2 21 2 ( ) cos( ) 2 3eqJ mr mL mLr= + \u03b8 + \u03b1 \u2212 \u03b1 \u03b8\u03b1\u027a \u027a\u027a \u027a (2) The Lagrangian can be formulated as L T V= \u2212 2 2 2 21 2 ( ) cos( ) cos( ) 2 3eqL J mr mL mLr mgL= + \u03b8 + \u03b1 \u2212 \u03b1 \u03b8\u03b1 \u2212 \u03b1\u027a \u027a\u027a \u027a (3) Once the Lagrange function of the system is known, the mathematical model of the system is found in the form ( ) output eq d L L T B dt \u03b4 \u03b4 \u03b4\u03b8\u03b4 \u2212 = \u2212 \u03b8 \u03b8 \u027a \u027a ( ) 0 d L L dt \u03b4 \u03b4 \u03b4 \u03b4 \u2212 = \u03b1 \u03b1\u027a (4) 2 2 2 2 4 3 eq g g m m g t g m eq m m g t g m a J mr K J b mLr c mL d mgL K K K e B R K K f R = + + \u03b7 = = = \u03b7 \u03b7 = + \u03b7 \u03b7 = Substituting (3) into (4), we obtain the equations of motion of the system as 24 cos( ) sin( ) 0 3 mLr mL mgL\u2212 \u03b1 \u03b8 + \u03b1 \u2212 \u03b1 =\u027a\u027a \u027a\u027a 2 2( ) sin ( ) cos ( )eq output eqJ mr mLr mLr T B+ \u03b8 + \u03b1 \u03b1 \u2212 \u03b1 \u03b1 = \u2212 \u03b8\u027a\u027a \u027a\u027a \u027a\u027a (5) The output torque (Toutput ) of the driving unit on the load shaft is ( )m m g output m g t g m V K K T K K R \u2212 \u03b8 = \u03b7 \u03b7 (6) Substituting (6) into (5), we obtain the nonlinear model of the system as follows cos( ) sin( ) cos( ) sin( ) 0 ma b b e fV b c d 2\u03b8 \u2212 \u03b1 \u03b1 + \u03b1 \u03b1 + \u03b8 = \u2212 \u03b1 \u03b8 + \u03b1 \u2212 \u03b1 = \u027a\u027a \u027a\u027a\u027a \u027a \u027a\u027a \u027a\u027a (7) Where Equation (7) represents the nonlinear model of the system" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002171_j.optlastec.2019.105593-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002171_j.optlastec.2019.105593-Figure6-1.png", "caption": "Fig. 6. Distribution of grain structure of IN718 coating.", "texts": [ " According to the material properties of IN718 and the elemental segregation phenomena obtained by EDS, it can be judged that the precipitated phase between dendrites is laves phase. Near the surface layer of the coating (Fig. 3(a4-e4)), heat can be dissipated by both the coating below and the surface layer at the same time, so the cooling rate is higher, and most equiaxed and cellular crystals are obtained. When the laser power is 1500W, refined equiaxed crystals can be obtained. With the increase of laser power, the temperature of molten pool rises and the cooling rate decreases, thus larger structure can be obtained. As shown in Fig. 6, the grains at both ends of IN718 coating are mainly coarse columnar grains and grow perpendicular to the melting boundary to the top of the coating. This is because the direction perpendicular to the melting boundary has the largest temperature gradient and the fastest heat dissipation, and these grains almost perpendicular to the melting pool boundary are easier to grow up. From the Fig. 7 there are no macro-cracks and pore defects in the cross-section, but micro-cracks appear in the middle of the coating under the observation of SEM" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001442_j.actamat.2018.02.025-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001442_j.actamat.2018.02.025-Figure2-1.png", "caption": "Figure 2. Drawings of (a) central hole (CH), (b) in-plane shear (SH), (c) uniaxial tension (UT) samples; all units are in [mm]; blue dots indicate the start and end points of the DIC extensometer.", "texts": [ " The surface displacement and strain fields are determined using Digital Image Correlation (VIC2D, Correlated Solutions). The cross-head speed for all experiments on CH- specimens is min/5.0 mm . To ensure a comparable strain rate of 0.01/s, a cross-head speed of min/05.0 mm is chosen for the SH-specimens. For all cases, the axial M ANUSCRIP T ACCEPTE D ACCEPTED MANUSCRIPT Gorji, Tancogne-Dejean and Mohr (revised version, Dec 3, 2017) 6 displacements is obtained from a mm25 long virtual extensometer (see blue dots in Fig. 2). Thirteen Uniaxial Tension (UT) specimens with a 10mm wide and 30mm long gage section are extracted from the Ti-6Al-4V box structures (see Fig. 2c). Different from the CH- and SH-specimens where the gage sections comprised only one prior-beta grain, multiple prior-beta grains are loaded simultaneously in the UT-specimens. The same acquisition setup (1 Hz using an AVT-Pike F-505B camera with a mm90 macro lens) and DIC software (VIC2D, Correlated Solutions) are also employed to carrying out the UTexperiments. All UT-experiments are performed with min/5.0 mm cross-head speed to provide approximately the same strain rate as in the gage sections of CH- and SHspecimens" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000817_tac.2012.2191180-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000817_tac.2012.2191180-Figure1-1.png", "caption": "Fig. 1. The -link inverted pendulum. Figure adapted from [11].", "texts": [ " This is easily seen: if (a3) holds then there exists a node such that the number of edges going from the node to some nodes in is one. Since , node and so property (a2) in Theorem 3 is satisfied. Remark 4 will be useful later when applying Theorem 3 to the linearized dynamics of the multilink inverted pendulum, which are derived next. It is of interest to study the strong structural controllability properties of the multilink inverted pendulum. In this section the dynamics of an -link inverted pendulum will be derived. The system (see Fig. 1) consists of rigid mass-less rods (or links) of length , with a point mass located at the end of link . The angle made with the vertical by link is denoted , where . The base of is attached to a stationary surface via a smooth frictionless hinge. The joints between links are also assumed to be smooth and frictionless. The dynamics of the -link inverted pendulum can be derived via Lagrange\u2019s equations (see [12]). Define the position of mass in Cartesian coordinates as , then The kinetic energy of link , , is " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003281_j.jmatprotec.2021.117139-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003281_j.jmatprotec.2021.117139-Figure6-1.png", "caption": "Fig. 6. Section location on tensile specimen for micrograph and microindentation measurements.", "texts": [ " 294 (2021) 117139 measurement. After the tensile tests, the specimens\u2019 fracture surface topologies were scanned using the Zeiss Smart Zoom 5, via a 3D depthof-focus reconstruction method using 34 times magnification with a 30 \u03bcm resolution. The specimens were sectioned at the grip length area, 30 mm away from the edge, and the sectioned surface was etched in a solution of 5% vol. nitric acid, 5% vol. hydrochloric acid, and 90 % vol. ethanol. The section location and measurement surface are illustrated in Fig. 6. Micrographs of the microstructure were captured using a Zeiss Light Microscope and characterised using Fiji software. To measure the grain size, the ASTM E112\u2212 13\u2019s Abrams Three-Circle procedure was used due to its suitability for measuring non-equiaxed grain structures, typically observed for LMD-built materials (ASTM, 2014). The results were then plotted against the yield strength from the tensile tests and correlated via the Hall-Petch relationship. The Hall-Petch relationship describes the correlation between microstructural grain size and yield stresses via the following equation (Kashyap and Tangri, 1995; Hansen, 2004): \u03c3y = \u03c30 + k \u0305\u0305\u0305 d \u221a (1) where \u03c3y is yield strength, \u03c30 is a material constant that governs the stresses for grain dislocation movement, k is the Hall-Petch slope coefficient, and d is the grain size", " The long unidirectional raster scan build strategy exhibited the highest UTS, yield strength, and fracture strain among the LMD specimens, followed by the bidirectional and short unidirectional raster scan build strategies respectively, and the reverse trend is true for the Young\u2019s modulus result. The tensile test results indicate that there is an anisotropic tensile effect between the different build strategies. Microstructure images for the long unidirectional, bidirectional, short unidirectional raster scan build strategies and stock bar specimens are shown in Fig. 13. The section surface subjected to the microscope measurement for each sample is illustrated in Fig. 6. The mean grain size for each build strategy specimen type condition were taken from the micrograph images as seen in Fig. 13 and compiled in Table 2. To measure these grain characteristics, the Abrams threecircle procedure was used to derive the mean grain size. The mean grain size for each condition were subsequently plotted against the experimental yield strength results in a Hall-Petch plot as shown in Fig. 14. From the Hall-Petch plot, a best fit linear trendline was applied to derive the \u03c30 constant and k coefficients and were found to be 212 MPa and 722 MPa respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000560_j.mechmachtheory.2013.06.001-Figure12-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000560_j.mechmachtheory.2013.06.001-Figure12-1.png", "caption": "Fig. 12. An example of spatial mechanism.", "texts": [ " The deviations of outer and inner paths from nominal path are plotted in Fig. 11(b). A suitable portion of the traced path can be selected depending on a given application. The proposed framework can be applied to spatial mechanisms also. As a closed chain manipulator has been analyzed in the previous section, an example of open chain manipulator is chosen here to illustrate the application of screw theory to spatial mechanisms with errors considered. The mechanism consists of three links with revolute joints as shown in Fig. 12. Table 7 gives specifications of the chosen mechanism. Taking initial position of a point CP on the output link as and th the po p0 \u00bc r3 r2 r1 0 @ 1 A \u00f021\u00de e transformation matrices as, A1 \u00bc c\u03b81 \u2212s\u03b81 0 0 s\u03b81 c\u03b81 0 0 0 0 1 0 0 0 0 1 0 BB@ 1 CCA; A2 \u00bc 1 0 0 0 0 c\u03b82 \u2212s\u03b82 r1s\u03b82 0 s\u03b82 c\u03b82 r1 1\u2212c\u03b82\u00f0 \u00de 0 0 0 1 0 BB@ 1 CCA; A3 \u00bc c\u03b83 0 s\u03b83 \u2212r1s\u03b83 0 1 0 0 \u2212s\u03b83 0 c\u03b83 r1 1\u2212c\u03b83\u00f0 \u00de 0 0 0 1 0 BB@ 1 CCA \u00f022\u00de sition of CP is obtained in the following steps. p \u00bc A1A2A3p0 \u00bc c\u03b81 \u2212s\u03b81 0 0 s\u03b81 c\u03b81 0 0 0 0 1 0 0 0 0 1 0 BB@ 1 CCA 1 0 0 0 0 c\u03b82 \u2212s\u03b82 r1s\u03b82 0 s\u03b82 c\u03b82 r1 1\u2212c\u03b82\u00f0 \u00de 0 0 0 1 0 BB@ 1 CCA c\u03b83 0 s\u03b83 \u2212r1s\u03b83 0 1 0 0 \u2212s\u03b83 0 c\u03b83 r1 1\u2212c\u03b83\u00f0 \u00de 0 0 0 1 0 BB@ 1 CCA r3 r2 r1 1 0 BB@ 1 CCA \u00bc r3 c\u03b81c\u03b83\u2212s\u03b81s\u03b82s\u03b83\u00f0 \u00de\u2212r2s\u03b81c\u03b82 r3 s\u03b81c\u03b83 \u00fe c\u03b81s\u03b82s\u03b83\u00f0 \u00de \u00fe r2c\u03b81c\u03b82 r1 \u00fe r2s\u03b82\u2212r3c\u03b82s\u03b83 1 0 BB@ 1 CCA: \u00f023\u00de Transformation matrices A1, A2 and A3 are obtained from the Rodrigues parameters given in Table 8" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001876_j.mechmachtheory.2018.04.002-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001876_j.mechmachtheory.2018.04.002-Figure1-1.png", "caption": "Fig. 1. Coordinate systems applied to the meshing simulation.", "texts": [ " Constructing an instantaneous conjugate contact curve derived from the fully conjugated mating gear set and a modified curve derived from the real meshing gear set, the transmission error can be effectively separated, and the contact point and contact pattern easily determined. The approach presented herein requires significantly less computational effort than the generalized approach, by reducing the number of nonlinear equations from 5 to 2. Furthermore, a numerical example and experimental tests are presented in this paper to validate the proposed approach for TCA. The coordinate systems associated with the contact model are shown in Fig. 1 . The geometry of the tooth surfaces of a pair, comprised of a mating pinion and gear, can be represented by position vectors in the coordinate system S 1 and S 2 , rigidly connected to the pinion and the gear, respectively, as r i = r i ( u i , v i ) i = 1 , 2 (1) where, u i and v i are the surface generating parameters, and subscripts 1 and 2 represent the pinion and gear, respectively. The generalized algorithm is based on two contact conditions: coincidence of the two surface position vectors and align- ment of the unit normal vectors at the contact point" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001510_j.mechmachtheory.2014.01.014-Figure19-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001510_j.mechmachtheory.2014.01.014-Figure19-1.png", "caption": "Fig. 19. Circumferential strain distribution in the assembly state.", "texts": [ " The average without the edge value corresponds to the practical case, and the variation of distribution is similar to the theoretical result. However, the amplitude of the variation is doubled because the contact force is increased in the wide tooth rim for the same maximum radial displacement. 6.3.3.1. Experiment for the complete FS model in the assembly state. The complete FS model with teeth is constructed under zero transmission loads to simulate the assembly state. The circumferential strain of the FS with teeth in the assembly state is shown in Fig. 19. The maximum circumferential strain of 5.53 \u00d7 10\u22125 and the minimum circumferential strain of \u22127.61 \u00d7 10\u22125 occur at the front edge of the FS near the short axis section and the roller contact zone, respectively. The same seven paths are defined as for the wide tooth rim. These paths are not symmetrical along the middle plane of the tooth rim because the radial displacement of the FS is not symmetrical, which shows as a coning deformation. The circumferential strains along these paths are shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003016_j.oceaneng.2020.108257-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003016_j.oceaneng.2020.108257-Figure1-1.png", "caption": "Fig. 1. AUV2000 prototype.", "texts": [ " Section 3 proposes the design of nonlinear disturbance observer (NDO) and backstepping controller for the depth-plane motion of the AUV and also analyzes the robust stability of the proposed controller under propeller torque\u2019s effect and model uncertainties. In Section 4, the numerical simulations and discussions are carried out to validates the previous analysis and design. Finally, the conclusions of this work are presented in Section 5. The model will be considered in this paper is the AUV2000 mentioned in (Tran et al., 2019), AUV2000 shown in Fig. 1 is a hybrid AUV designed to integrate the outstanding characteristics of conventional AUV and underwater glider (a type of AUV that employs variable-buoyancy propulsion instead of traditional propellers or thrusters). Therefore AUV2000 can operate in two separate modes, specifically without using the thruster (Glider mode) and using the H.N. Tran et al. Ocean Engineering 220 (2021) 108257 thruster (AUV mode). However, in this paper, we only focus on designing the depth controller for AUV2000 in AUV mode" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001241_j.jclepro.2017.02.167-Figure9-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001241_j.jclepro.2017.02.167-Figure9-1.png", "caption": "Fig. 9. (a) Surface preparation by laser cladding, and (b) macro geometry of the as-received laser cladded part.", "texts": [ " With this, the plastic deformation within subsurface or in substrate could be modeled based on the vonMises yield criterion by using Eqs. (9) and (11). Eq. (10) described the depth of plastic deformation beneath machined surface. Finally, a dimensionless ratio between the uncut chip thickness and critical cladded thickness was presented when the critical cladded thickness was calculated by Eq. (12). This algorithm had been realized with the Matlab tool software programming. Surface preparation was realized by a semi-conductor laser cladding equipment, as shown in Fig. 9(a). Medium carbon steel AISI 1045 with F120 mm in diameter and 200 mm in length was selected as the substrate material, while Cr-Ni-based stainless steel powder was used as the raw cladding material. The powder had the nominal compositions of 0.23 wt% C, 1.79 wt% Si, 14.28 wt% Cr, 3.29 wt% Ni and Fe in balance. Prior to laser cladding process, the substrate had to be descaled by sanding, degreasedwith gasoline or acetone and dried in air. The substrate material bar was mounted on a three-jaw chuck rotating around a horizontal axis and was set in front of a lateral synchronous feed devicewhich, in turn, could be traversed horizontally. The laser cladding parameters were summarized as follows: laser power 3 kW, scanning velocity 5.1 mm/s, footstep 7 mm, carrier/shielding gas (N2) pressure 0.5 MPa, and powder feed rate 450 g/min. As shown in Fig. 9(b), the profile of the final cladding is irregularity with a maximum thickness of 2.5 mm. Orthogonal machining experiments were carried out on a computer numerical control (CNC) turning center (PUMA200MA, Daewoo). This CNC turning center is equippedwith a spindle power of 28 kW and the maximum spindle speed of 6000 rpm. The original cladding material was firstly peeled off in order to eliminate the irregularity and defects. Orthogonal cutting is a type of metal cutting in which the cutting edge of the cutting tool is perpendicular to the direction of cutting speed" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001524_s12206-014-0931-7-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001524_s12206-014-0931-7-Figure3-1.png", "caption": "Fig. 3. The 2(rT)2PS with parallel constraint planes.", "texts": [ " A special topology exists when the two planes are coincident as in Fig. 2(b) in which the platform can be simplified by a line segment A1A2, from Eq. (3) there is: 1 2 1( ). 0\u00a2 \u00a2- =R a a n . (5) Thus, line A1A2 is perpendicular to normal n1 and located in the constraint plane \u22111 as in Fig. 2(b). The platform has a plane motion and a local rotation about A1A2. Another special topology of the mechanism is with angle \u03b1 = \u03c0/2 in which the two limbs work in two perpendicular planes. When two constraint planes are parallel to each other, there is n1 = n2 as in Fig. 3(a). Set the unit vector of line A1A2 as 12\u00a2m expressed in the moving coordinate system and locate the moving coordinate center Q on the line between A1 and A2. There is: 1 1 12 1 1 1 2 1 12 2 1 2 ( ). ( ). ( ). ( ). q q l d l d \u00a2 \u00a2+ = + =\u00ec\u00ef \u00ed \u00a2 \u00a2+ = + =\u00ef\u00ee R R R R a q n m q n a q n m q n (6) where l1q and l2q are the distances from points A1 and A2 to the moving coordinate center Q. Respectively, subtracting the second equation from the first one in Eq. (6) and subtracting the second equation multiplied by l1q from the first one multiplied by l2q in Eq. (6), there is 1 2 12 1 12 1 2 1 2 1 1 2 12 ( ) . cos . ( ) / ( ) q q q q l l l d d l d l d l b\u00a2- = = -\u00ec\u00ef \u00ed = - -\u00ef\u00ee Rm n q n (7) where \u03b2 is the angle between line A1A2 and n1. l12 is the distance between points A1 and A2. It can be seen that line A1A2 has fixed angle with normal n1 and the coordinate center Q of the platform is constrained on plane \u2211q parallel to the two limb constraint planes and between them as in Fig. 3(a). Furthermore, from the first equation in Eq. (7), there is 1 2 12 12cosd d l lb- = \u00a3 . (8) This gives a physical constraint that distance between the two parallel constraint planes should be shorter than the distance between the two spherical joints in the platform. Distance between the two parallel planes determines the motion behavior of the moving platform (A1A2) and its workspace. Generally, when ||d1-d2|| 0\u00de because a finite double support period is not possible due to the lack of knee. The simplest walking model [9,23,39] represents a particular version of the compass-gait biped, assuming that the mass of the leg is negligible compared to the mass of the hip \u00f0m=mH \u00bc 0\u00de and the centres of mass of the legs are placed at the feet \u00f0a \u00bc 0\u00de", " This phenomenon, which is inevitable for a walker with straight legs and only 2- dimensional motion, is commonly ignored in the literature since it can be avoided by means of lateral motion [8,28], or using a mechanism to retract the swing foot without changing the mass distribution of the leg [10,11,40]. After this, the next time that the swing foot reaches the ground level is at heel strike impact. At this impact time, the constrained kinetic energy of the walker is lost, and the velocity of the centre of the hip revolute joint is redirected from one inverted pendulum arc to the next. To study the general motion of the compass biped, four generalized coordinates are used (Fig. 3). These variables define the vector of generalized coordinates q \u00bc q1 q2 q3 q4\u00bd T which describes the configuration of the biped. Coordinates q1 and q2 give the \u00f0x; z\u00de-position of PR with respect to the absolute inertial frame. Coordinate q3 indicates the absolute orientation of the right leg, and q4 denotes the relative angle of the left leg with respect to the right one, i.e., the inter-leg angle.1 For the system at hand, the elements of the dynamic model are outlined in Appendix B. Based on Section 3, we can see that the kinetic energy decomposition at the pre-impact time depends on the impact configuration and the dynamic parameters", " According to [24], a compass-gait biped with actuation at the ankle (which is represented by the stance foot joint) and at the hip can walk following asymptotically stable limit cycles if the following two conditions are satisfied: (1) the restored mechanical energy (Wapp in our paper) is kept constant in every step and equals the energy lost at heel strike, and (2) the desired inter-leg angle q4 is achieved before the heel strike. The latter implies that just before the impact, _q 4 \u00bc 0. 1 Note that angles q3 and q4 are defined positive with the sense indicated in Fig. 3. That is, q3 is defined positive in the clockwise direction, and q4 is defined positive in the counterclockwise direction. To define the state of the system at pre-impact time, the following considerations are taken into account: The right foot PR is assumed to be the pre-impact stance foot \u00f0S R\u00de, i.e., q2 \u00bc 0, and point PL is the swing foot which is colliding the ground \u00f0I L\u00de. This also implies that _q 1 \u00bc _q 2 \u00bc 0 since PR is in contact with the ground without slipping before impact. The configuration at impact is fully defined by the stance leg angle q3, which equals q4=2 when the collision takes place", " The kinetic and potential energies of the compass-gait biped can be obtained as 2 Poin T \u00bc 1 2 _qT M _q \u00bc 1 2 mv2 CR \u00femv2 CL \u00femHv2 CH ; \u00f0B:1\u00de U \u00bc mg rCR \u00femg rCL \u00femHg rCH ; \u00f0B:2\u00de where _q \u00bc _q1 _q2 _q3 _q4\u00bd T is the vector of generalized velocities; M is the 4 4 dimensional mass matrix of the walker; vCR ;vCL ;vCH and rCR ; rCL ; rCH denote, respectively, the absolute velocity and position of the centres of mass2; and g is the gravitational acceleration vector. To consider a general case, this vector has an inclination / with respect to the vertical (Fig. 3) which represents the slope angle in the case of pure passive walking. The mass matrix M can be derived by expanding (B.1). Its expression has the following symmetric form M\u00f0q\u00de \u00bc M11 M12 M13 M14 M22 M23 M24 M33 M34 Sym: M44 2 6664 3 7775; \u00f0B:3\u00de where the 10 independent elements have the expressions M11 \u00bc 2m\u00femH; M12 \u00bc 0; M13 \u00bc \u00f0m\u00f0a\u00fe l\u00de \u00femHl\u00de cos q3 mb cos\u00f0q4 q3\u00de; M14 \u00bc mb cos\u00f0q4 q3\u00de; M22 \u00bc 2m\u00femH; M23 \u00bc \u00f0m\u00f0a\u00fe l\u00de \u00femHl\u00de sin q3 mb sin\u00f0q4 q3\u00de; M24 \u00bc mb sin\u00f0q4 q3\u00de; M33 \u00bc m\u00f0a2 \u00fe b2 \u00fe l2\u00de \u00femHl2 2mbl cos q4; M34 \u00bc mb2 \u00fembl cos q4; M44 \u00bc mb2 : \u00f0B:4\u00de Expanding Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000108_j.ijmecsci.2011.02.005-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000108_j.ijmecsci.2011.02.005-Figure5-1.png", "caption": "Fig. 5. Ring shapes corresponding to (a) s", "texts": [], "surrounding_texts": [ "Apparently, for rings of finite thickness self-intersecting shapes are not possible because they are not planar, nevertheless for a very thin ring such a shape may be considered as a good approximation of its equilibrium state. A tube evidently cannot take a self-intersecting shape, but there is a good reason to expect that tubes subject to sufficiently high pressure posses equilibrium shapes with areas of contact (lines of contact of their cross sections). Flaherty et al. [4] suggest similarity transformations to be used for the determination of such shapes, but realise this idea in a very complicated way. Moreover, the construction developed in [4] for the said purpose makes use of the curves G0n corresponding to the pressures s0n, which are wrongly regarded as curves with isolated points of contact as it was noted and discussed above. Below, an alternative approach is presented for constructing equilibrium ring (tube) shapes with lines (areas) of contact based on the same \u2018\u2018similarity\u2019\u2019 idea that actually arises out of the following property of Eqs. (22) and (23). Under the transformation \u00f0s,k\u00de/\u00f0s=l,lk\u00de, where l is a nonzero real number, each equation of form (22) corresponding to certain constants m and s transforms into an equation of the same form but with new coefficients: m/l2m, s/l3s. The same holds true for Eq. (23) if e/l4e in addition. In other words, Eqs. (22) and (23) are invariant with respect to the similarity transformation L : \u00f0s,k;m,s,e\u00de/\u00f0s=l,lk; l2m,l3s,l4e\u00de. Consequently, the parametric equations (25) imply that the shapes whose parameters are related by such a transformation L are similar, the respective scaling factor being 1=l. Accordingly, if a closed curve G is scaled in this way, then its length L and area A change to L=l and A=l2, respectively. Thus, given nZ2, let the curve Gcn of length Lcn \u00bc 2p be the equilibrium shape with points of contact corresponding to the contact pressure scn and let G\u0302 be the shape (of the same length) with lines of contact corresponding to a pressure s\u03024scn. The curve G\u0302 is constructed in two steps. First, scaling the curve Gcn with a factor \u00f0s\u0302=scn\u00de 1=3 one obtains another curve G\u0302cn which has the same number of contact points because it is similar to the curve Gcn but corresponds to the pressure s\u0302 and its length is L\u0302cn \u00bc 2p\u00f0scn=s\u0302\u00de1=3oLcn. Then, the curve G\u0302 is obtained by substituting each point of contact of the curve G\u0302cn by a line segment of length 2p\u00f01 \u00f0scn=s\u0302\u00de1=3 \u00de=n along the respective symmetry axis of the curve G\u0302cn so as its total length to become 2p. Examples of shapes with lines of contact are presented in Figs. 7 and 8. It is clear that the tangent, normal and position vectors of a shape G\u0302 with lines of contact constructed in the foregoing way are continuous at each point of the curve G\u0302. However, its curvature suffers jumps at the end points of the line segments used to substitute the contact points of the respective auxiliary curve G\u0302cn because the limit values of the curvature from the bent parts of the curve and from the line segments are ffiffiffiffiffiffi 2m p a0 and zero, respectively. Consequently, the moment and force also suffer jumps at the aforementioned points since their limit values from the bent parts of the curve are Mb \u00bc D\u00f0 ffiffiffiffiffiffi 2m p \u00fek3\u00de, Nb \u00bc 0, Qb \u00bc 7D ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P\u00f0 ffiffiffiffiffiffi 2m pq \u00de, \u00f065\u00de while along each line of contact the resultant pressure is zero and Ml \u00bc Dk3, Nl \u00bc 0, Ql \u00bc 0: \u00f066\u00de \u00bc 28:56; (b) s\u00bc 56:09; (c) s\u00bc 81:81. s\u00bc 70:7; (b) s\u00bc 140; (c) s\u00bc 207:2. Eqs. (65) and (66) follow by the constitutive equation (20), the general solution (21) of Eqs. (7)\u2013(9) and (23). Thus, the local balances (4) and (5) of the force and moment are violated for the shapes with lines of contact. Fortunately, however, the total balancesI G\u0302 F0\u00f0s\u00de ds\u00bc I G\u0302 pn\u00f0s\u00de ds, \u00f067\u00de I G\u0302 M0\u00f0s\u00de ds\u00bc I G\u0302 F\u00f0s\u00de n\u00f0s\u00de ds, \u00f068\u00de of these quantities are satisfied. Indeed, Eqs. (67) and (68) hold on the curve G\u0302cn since it corresponds to an equilibrium shape without jump discontinuities of the force and moment. On the other hand, G\u0302 \u00bc G\u0302cn [ fLine segmentsg and the integrals in Eqs. (67) and (68) taken along the line segments are equal to zero because here p\u00bc0, M0\u00f0s\u00de \u00bc 0 and F\u00f0s\u00de \u00bc 0. In our opinion, this property of the constructed curves G\u0302 allows this shapes to be regarded as equilibrium ring (tube) shapes with lines (areas) of contact at least in the week sense discussed above. In the light of the results presented in this section, it should be remarked that the similarity law (5.4) obtained in [4, Section 5], which concerns the conductivity of a buckled tube conveying an incompressible viscous fluid, has to be revised. Actually, this law, which expresses the conductivity of a tube with areas of contact through that of a tube whose cross sections have just points of contact, should be replaced by the following one C\u00f0s\u00de \u00bc scn s 4=3 C\u00f0scn\u00de, s4scn, \u00f069\u00de where C\u00f0s\u00de denotes the conductivity of a tube subject to pressure s. It is necessary to do so because scn is the unique pressure for which there exists an equilibrium tube shape of n-fold symmetry whose cross sections have only isolated points of contact." ] }, { "image_filename": "designv10_9_0001468_j.mechmachtheory.2018.09.005-Figure9-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001468_j.mechmachtheory.2018.09.005-Figure9-1.png", "caption": "Fig. 9. (a)\u2013(c) Motion sequences of a model of motion type AI-BI-DII.", "texts": [ "1a) and \u03b3 D = \u03b1D , \u03b3 A = \u03b1B , \u03b1K = \u03b2K + \u03b3 K , u B + v D = w A , u K + v K = w K . (A.1b) Their corresponding models are the parts with linkages A, B and D of case I and case II assemblies in Fig. 8 . For the motion type AI-BI-DII, we have one solution, \u03b1B = \u03b2D + \u03b3 A , \u03b1K = \u03b2K + \u03b3 K , u B + v D = w A , u K + v K = w K , (A.2) \u03bbD = w D u D = s \u03b3 D s \u03b1D \u00b7 c \u03b3 A c \u03b1B . When we choose the following parameters in Eq. (A.3) , where the unit of the link lengths is millimeter, a model of motion type AI-BI-DII is constructed, as shown in Fig. 9 . \u03b1A = \u221230 \u25e6, \u03b2A = \u221275 \u25e6, \u03b3 A = 45 \u25e6, u A = 4 , w A = 11 . 464 , \u03b1B = 75 \u25e6, \u03b2B = 45 \u25e6, \u03b3 B = 30 \u25e6, u B = 4 , w B = 8 , (A.3) \u03b1D = \u221230 \u25e6, \u03b2D = 30 \u25e6, \u03b3 D = \u221260 \u25e6, u D = 2 , \u03bbD = 4 . 732 . For the motion type AI-BII-DI, we have two special solutions, \u03b1D = \u2212\u03b3 A , \u03b3 D = \u2212 \u03b1B , \u03b1K = \u03b2K + \u03b3 K , u B + v D = w A , u K + v K = w K , (A.4a) \u03bbB = w B u B = t \u03b3 B t \u03b1B , and \u03b3 D = \u03b1D , \u03b3 A = \u03b1B , \u03b1K = \u03b2K + \u03b3 K , u B + v D = w A , u K + v K = w K , (A.4b) \u03bbB = w B u B = t \u03b3 B t \u03b1B . The Eq. (A.4a) and Eq. (A.4b) are special cases of AI-BI-DI in Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002147_j.ymssp.2019.02.033-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002147_j.ymssp.2019.02.033-Figure1-1.png", "caption": "Fig. 1. Iwan model and hysteresis loop of Jenkins element.", "texts": [ " Next, a detailed description of Iwan beam element is provided. Then, the experiment of a cantilever beam with a bolted joint is presented. The section 4 deals with the model simulation and updating based on instantaneous frequencies and amplitudes of the principal dynamic response components. Finally, this paper ends up with some conclusions and lists some recommendations for future work. Based on the bilinear model, Iwan proposed a new model, namely Iwan model, to characterize the hysteresis phenomenon of nonlinear structural system. As shown in Fig. 1(a), the discrete Iwan model is made up of a series of Jenkins elements. Each Jenkins element is an ideal elastic-plastic element consisting of a spring element and a Coulomb friction element. Fig. 1(b) shows its hysteresis loop of force-displacement. Since the yield displacement of each Jenkins element is different, the Iwan model can be used to simulate the local slip and global slip phenomenon of bolted joints. It can represent local slip behaviors of bolted joints when some Jenkins elements in the Iwan model yield and it can be used to describe global slip phenomenon when all the Jenkins elements yield. As for the discrete Iwan model, its restoring force can be expressed as: f \u00bc XN i\u00bc1 kix xj j 6 x i f i sgn\u00f0 _x\u00de xj j > x i \u00f01\u00de where f is the restoring force, ki \u00bc k=N is the stiffness of ith spring element, f i is the yield force of ith Coulomb friction element, and x i is the yield displacement of ith Jenkins element" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001957_s00170-015-7137-8-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001957_s00170-015-7137-8-Figure1-1.png", "caption": "Fig. 1 a 3D finite element model and b laser scanning pattern", "texts": [ " The effects of the line energy (LE) on the temperature distribution, melt pool dimensions, and resultant cooling rates across the melt pool were presented in detail with the purpose to obtain reasonable LEs for AA8009 alloy. The phase transformations and their effects on the properties of the part were also discussed based on the thermal analysis at the optimized LEs. Furthermore, in order to validate the reliability of the model, corresponding experiments were performed to study the surface morphologies of single deposited tracks, the microstructures, and phase composition of the SLM-built parts under the optimized LEs. Finite element analysis is carried out using the ANSYS code. As shown in Fig. 1a, the finite element model investigated consists of two different parts: (1) a AA8009 alloy substrate; (2) a single powder layer, with respective dimensions of 3\u00d7 1.5\u00d71 and 3\u00d71.5\u00d70.03 mm. In order to obtain sufficient calculation accuracy and reduce computational time, the layer part which irradiated by the laser beam is finely meshed with the solid 70 hexahedral element sizes equal to 50 \u03bcm (onethird of the laser beam diameter), and coarser mesh is used for the substrate. In this simulation, the laser power varies from 160 to 400 W while the scanning speed is fixed to 200 mm/s. The solid layer is scanned in a unidirectional pattern by five straight tracks. The length of each track is 2 mm, as illustrated in Fig. 1b. For the simulation process, the nodal temperatures are monitored in subtime steps. If the powder state elements reach the melting point, their material properties are then updated for the solid state elements. When the laser exposure time is reached, the laser beam moves to the next load step, and the previous load step is deleted. Simulations of the moving laser beam and the material state transition from powder to solid are accomplished by a user written subroutine implemented in ANSYS parametric design language (APDL)" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002679_jmr.2020.126-Figure8-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002679_jmr.2020.126-Figure8-1.png", "caption": "Figure. 8. The 3D model of the 18Ni-300 MS block and the location of the specimens cut from the denoted blocks (a) vertical built sample (Z-built) and horizontal built sample (XY-built). Note: Z-plane (beam scanning surface) specimens: #1, #3, #5, and #7. X-plane (side surface) specimens: #2, #4, #6, and #8.", "texts": [ " Along the built height direction, the bottom part has a higher value in hardness than those in the middle and top parts. This may be contributed to the finer cellular structure in the bottom part due to the high cooling rate during the solidification process. The pre-alloyed 18Ni-300 MS powder from EOS, named as MS1, was adopted to fabricate the 18Ni-300 MS sample by an EOS M290 machine at Jacksonville State University (Jacksonville, AL). The particle size is in the range of 15\u201362 \u03bcm and the chemical composition of the raw powder in weight percent is available in the material sheet [53]. As shown in Fig. 8, to study the effects of built orientation and built height on the microstructure and property anisotropy of MS alloy, two sets of tensile testing coupons with different orientations were picked. They have a gauge section of 25 mm in length, 6 mm in width, and 4 mm in thickness, respectively, which were chosen by following the requirements of the ASTM-E8M standard [54]. The coupons were built by following the process parameters in the machine defined by EOS GmbH, namely a layer thickness of 40 \u03bcm, a scan speed of 960 mm/s, a hatch distance of 0", "o rg /c or e/ te rm s. h tt ps :// do i.o rg /1 0. 15 57 /jm r. 20 20 .1 26 hatch strategy, and 380 W of laser power, as listed in Table II. During the manufacturing process, the stripes hatch pattern was rotated 67\u00b0 with respect to the former layer. Two sets of tensile specimens were cut by a precision lowspeed saw from the as-built block part to investigate the evolution of the microstructure in the X-plane (side surface, or YZ-plane) and the Z-plane (beam scanning surface, or XY-plane), as shown in Fig. 8. The sample surfaces were prepared with the standard metallographic procedures (grinding followed by fine polishing down to 0.05 \u03bcm colloidal alumina) for microstructure analysis and the microhardness tests. Microstructural examinations were performed by OM (Nikon Model Epiphot 200, Tokyo, Japan), XRD (X\u2019Pert MPD, Philips, Amsterdam, Netherlands), Apreo field emission SEM (Thermo Scientific\u2122, Waltham, Massachusetts), and EBSD (Helios 600 FIB machine equipped with an EBSD detector from EDAX, Waltham, Massachusetts)" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003484_j.triboint.2021.107022-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003484_j.triboint.2021.107022-Figure3-1.png", "caption": "Fig. 3. Torsional dynamic model of SBG.", "texts": [ " Regard the contact as a massless spring and adopted the linear force model [31], thus, the transient mixed lubrication contact stiffness as a function of time can be given as k(t) = \u0394F(t) \u0394h0(t) = F(t) \u2212 F(t \u2212 dt) h0(t) \u2212 h0(t \u2212 dt) (7) The time-variant contact damping of transient mixed lubricant is closely related to contact stiffness based on Ref. [22,32] and given as c(t) = 2\u03be \u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305 k(t)Ie \u221a (8) where Ie = IgIp/(Igrpm 2 +Iprgm 2) indicates the equivalent mass representing gear inertia Ig and pinion inertia Ip, rbg and rbp represent the mean contact radii of gear and pinion, respectively. \u03be is damping ratio, in the present study, \u03be = 0.15 was adopted [2]. In SBG driving system, the rotation axes of pinion and gear intersect perpendicularly at a point as described in Fig. 3. Assuming that the pinion and gear are rigid bodies, besides, ignore the effect of supporting bearings and shafts. Moreover, the transient mixed lubrication contact along line of action can be accurately simulated by the nonlinear timevariant stiffness and damping that were calculated through the method introduced in Section 2. In this research, the rotational displacement of pinion and gear were focused to investigate the vibration behaviors of SBG. Also, the nonlinear backlash, actual time-variant Z. Wang et al. Tribology International 160 (2021) 107022 contact radii of gear and pinion, and static transmission error obtained by LTCA method were all counted. Utilizing the lumped parameter method [23], a two-degree-of-freedom torsional dynamic model of SBG as shown in Fig. 3 can be derived as Ig\u03b8g \u22c5\u22c5 + rgkcf ( \u03b4 \u2212 e ) + rgcc ( \u03b4 \u22c5 \u2212 e\u22c5 ) = \u2212 Tg (9a) Ip\u03b8p \u22c5\u22c5 + rpkcf ( \u03b4 \u2212 e ) + rpcc ( \u03b4 \u22c5 \u2212 e\u22c5 ) = Tp (9b) where Ig and Ip indicate the mass moments of inertia of gear and pinion, rg and rp represent the time-variant rotating contact radii of gear and pinion, kc and cc are the time-vary comprehensive contact stiffness and damping of transient mixed lubrication, Tg and Tp are the applied torques of gear and pinion, e and \u03b4 is the time-vary static transmission error and ideal dynamic transmission error, f(\u03b4-e) is nonlinear backlash function, and the ideal dynamic transmission error \u03b4 was deduced as \u03b4 = rp\u03b8p \u2212 rg\u03b8g (10) While the nonlinear backlash function with gear pair clearance 2b can be defined as f \u239b \u239d\u03b4 \u2212 e \u239e \u23a0 = \u23a7 \u23a8 \u23a9 \u03b4 \u2212 e \u2212 b \u03b4 \u2212 e \u2265 b 0 \u2212 b < \u03b4 \u2212 e < b \u03b4 \u2212 e + b \u03b4 \u2212 e \u2264 \u2212 b (11) The actual dynamic transmission error v defined as" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002339_s10846-018-0884-7-Figure6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002339_s10846-018-0884-7-Figure6-1.png", "caption": "Fig. 6 A sequence of snapshots during the unfolding of the robotic arm: (1) joint angles at {0, 0, 0, 0} radians; (2)-(3) intermediate state; (4) joint angles at {0, \u2212\u03c0 , \u03c0 , 0} radians", "texts": [ " Such arm motion results in the displacement of the center of gravity (CoG) and the change of the moments of inertia of the overall system, which, in its turn, creates additional torques and forces on UAV body causing the displacement of the UAV and losing the hover state. Hence, in our scenario, SMC theory based intelligent T2FNN controller is used to maintain a constant hover (at x = 0 m, y = 0 m, z = 1.5 m) and stabilize UAV platform when the motion of the robotic arm is commanded in the xzplane. The two motions that are considered for our scenario are unfolding and folding of the robotic arm. The former is commanded starting from initial joint angles {0, 0, 0, 0} radians to final joint angles {0, \u2212\u03c0 , \u03c0 , 0} radians, as shown in Fig. 6, while the latter is the motion of the arm in opposite direction. The simulation scenario can be summarized as follows: \u2013 UAV hovers with the folded arm for the first 10 s; \u2013 The robotic arm is unfolded in the next 10 s followed by the folding of the arm for another 10 s; \u2013 The above two steps are repeated one more time; \u2013 Finally, UAV hovers with the folded arm for the final 10 s. Two different cases are considered for the aforementioned scenario. In the first case, the performance of the proposed T2FNN controller is investigated when there are no external disturbances in the control system", " In this case, the efficacy of the proposed control strategy is evaluated not only in the presence of internal uncertainties caused by arm motion, but also in the presence of external disturbances such as wind gust. Throughout the simulation, the maximum operating speed of the end-effector is restricted to 100.0 mm/s. The mean value of the wind speed is selected as \u03bcv = 2.5 m/s. In addition, in order to create different noise levels, five different standard deviation of the wind speed are chosen as \u03c3v = {0, 0.1, 0.3, 0.5, 1.0} [m/s]. For the dynamical simulations, the coaxial tricopter equipped with the 4-DOF manipulator with all revolute joints is implemented in ROS and Gazebo simulator as shown in Fig. 6. The coaxial tricopter intrinsic parameters are listed in Table 1. For the link masses (including the mass of motors) the following values have been considered ml1 = 155 g, ml2 = 255 g, ml3 = 76 g and ml4 = 64 g, while the inertia moments, which are measured at the center of gravity of their corresponding rigid bodies, are given in Table 2. While parameters such as mass (m, ml1, ml2, ml3, ml4) and the UAV arm length (l) are directly measured, the moment of inertia values are obtained from their SolidWorks CAD model" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002291_j.optlastec.2016.09.019-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002291_j.optlastec.2016.09.019-Figure5-1.png", "caption": "Fig. 5. Deposition of overhanging structure with different strategies, (a) Deposition by horizontal slices and displacement between adjacent layers; (b) Deposition by normal direction slices.", "texts": [ " The drag force of coaxial surrounding alignment gas curtain on powders reduces the effect of gravity and dominates the motion direction of the powders. The powder beam spraying is kept thin and straight into the molten pool [13,15]. Meanwhile, the alignment gas can suppress the molten pool on an inclined soleplate to prevent the molten pool from flowing down. In depositing an overhanging structure, some research use the strategy of horizontal slicing and shifting between layers [6\u20138], as shown in Fig. 5(a). The cladding head keeps vertical spraying. Every upper layer shifts an overhanging part by means of surface tension of the molten pool to build an inclined wall with an inclined angle \u03b1. Too long overhanging part leads to flow down and collapse of the molten pool, thus the inclined angle \u03b1 should be limited. Assuming \u0394x is the overhanging length, and h is the deposition height, the inclined angle \u03b1 is calculated as: \u03b1 arctan x h= (\u0394 / ) As shown in Fig. 5(a), \u03b1 increases gradually from the bottom up. If \u03b1 exceeds the maximal inclined angle \u03b1max, the molten pool will flow down and the cladding layers can no more be formed. In Fig. 5(b), the cladding head varies its orientation continuously and changes its spatial angle in order to keep the irradiation/spray direction of laser, powder and gas always along the tangential direction of the curved surface. There is no shifting between layers above and below, and the molten pool has always adequate area for supporting. The maximal inclined angle is no longer limited. As is seen from Fig. 5(a), there is distinctly zigzag as well as \u201cstep effect\u201d on the surface of the formed part, and the width of the wall decreases with the changing of the inclined angle. While in Fig. 5(b), the \u201cstep effect\u201d can be completely eliminated and the width of the wall can be kept constant. The experimental setup includes HLB-IPF head with series number of JGRF-102-2 (as shown in Fig. 4), IPG fiber laser with model of YLS2000-TR 2kw and with laser wavelength of 1064 nm, KUKA robot KR 60-3F with programming language of KRL, an external rotation platform and GTV PF2/2 powder feeding system. On the basis of previous trials, the processing parameters are chosen as Table 1 In Table 1, the defocusing distance of \u22123 mm is inside \u201cself-healing effect\u201d interval between \u22122" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002961_j.jallcom.2020.156020-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002961_j.jallcom.2020.156020-Figure1-1.png", "caption": "Fig. 1. Schematic drawing of the twin-wire WAAM system for in-situ alloying of NiTi binary alloy.", "texts": [ " Also, the high intensity of the neutron source generates good resolution at high acquisition rates, which allows for in-situ thermal investigations [62] as performed in the present study. With those complementarities in mind, it is valuable to provide more in-situ neutron diffraction analysis on the phase transformation of NiTi during heat treatment as currently most of the corresponding information is acquired by X-ray analysis. Schematic drawing of the WAAM system for binary Ni53Ti47 insitu alloying fabrication is shown in Fig. 1. Since the chemical composition of the Ni-rich NiTi sample was designed at Ni53Ti47 (at%), during the in-situ WAAM process, according to the chemical composition calculation considering wire diameter, element density, and element atomic weight, the wire feed speeds of the two 0.9 mm independent pure Ni and Ti wires were set at 560 mm/ min and 800 mm/min, respectively. The deposition current was set at 140 A and the torch travel speed was set at 95 mm/min, thus the specific deposition energy during the dual-wire WAAM process was controlled at 19" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001031_physreve.90.043002-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001031_physreve.90.043002-Figure1-1.png", "caption": "FIG. 1. (Color online) Schematic of the geometry of the system. The red circle indicates the orientation of the squirmer\u2019s thrust, which is defined by the polar angle \u03b8 = \u03c6 relative to the positive x\u0302 axis. The swimmer\u2019s translational and rotational locomotion velocity vectors are denoted by U and , respectively.", "texts": [ " We then present the perturbation analysis and the viscoelastic constitutive model used to solve for the time-averaged kinematics of locomotion in a viscoelastic fluid. Finally, we present and discuss the results of the perturbation analysis. II. MATHEMATICAL MODEL The system geometry consists of a two-dimensional (2D) cylindrical swimmer of radius R with its central axis positioned a distance d from an infinite planar no-slip boundary. The swimmer moves with translational velocity U oriented at an angle \u03c6 to the positive x\u0302 axis, and rotates with angular velocity . A schematic of the system geometry is shown in Fig. 1. A. Swimmer model Here, we study a swimmer that propels itself via an imposed tangential surface motion with no surface deformation. This so-called \u201csquirmer\u201d model is widely used to describe the self-propulsion of a microorganism with metachronal beating of cilia on its surface. In this model, the small radial displacements of cilia are neglected so that the shape of the swimmer remains unchanged, with x\u0302 = x\u0302s 0 describing the undeformed (cylindrical) surface of the swimmer, S0, in a moving reference frame at the center of the swimmer", " The instantaneous position of a material point, x\u0302s , on the surface of a squirmer is then given by x\u0302s = x\u0302s 0 + \u03b5 x\u0302s 1 ( x\u0302s 0,t\u0302 ) , (1) where \u03b5 1 is a small dimensionless parameter describing the amplitude of tangential oscillations of the surface [27] and all symbols with carets over them represent dimensional quantities. As is common practice [31\u201333], truncating Blake\u2019s original boundary condition [27]\u2014which is an infinite sum\u2014 to include only the first two modes then yields x\u0302s 1 ( x\u0302s 0,t\u0302 ) = [\u03b2\u03021(t\u0302) sin(\u03b8 \u2212 \u03c6) + \u03b2\u03022(t\u0302) sin (2(\u03b8 \u2212 \u03c6))] e\u03b8 , (2) where \u03b2\u0302n(t\u0302) (n = 1,2) are periodic functions of time with frequency \u03c9 [both taken to be \u221d R sin(\u03c9t\u0302) here for simplicity], \u03b8 is the cylindrical polar angle measured from the positive x\u0302 axis (Fig. 1), and \u03c6 is the polar angle characterizing the orientation of the swimmer\u2019s thrust. 043002-2 The Lagrangian body motion described by Eqs. (1) and (2) leads to a tangential surface velocity u\u0302s which, in the swimmerfixed frame, can be expressed as u\u0302s = [B\u03021 sin(\u03b8 \u2212 \u03c6) + B\u03022 sin (2(\u03b8 \u2212 \u03c6))] e\u03b8 , (3) where B\u0302n = \u03b5 d\u03b2\u0302n/dt\u0302 (n = 1,2). In an unbounded domain, the first coefficient, B\u03021, sets the swimming speed while the second coefficient, B\u03022, does not affect the swimming speed in the Stokes regime and merely sets the mixing generated by the swimmer as a result of the motion of its cilia", " It is worth noting that the existence of an attraction layer in the 2D problem does not necessarily extend to the 3D case since there may be substantial differences between the near-field fluid dynamics of cylindrical and spherical swimmers near a no-slip boundary. This work was partially supported by the NSF under Grant No. DMR-0820404 through the Penn State Center for Nanoscale Science. A.M.A. acknowledges support from NSF Grant No. CBET-526 1150348. APPENDIX: STOKES FLOW AROUND A SQUIRMER NEAR A NO-SLIP BOUNDARY Here, we present the Stokes flow field for a self-propelled two-dimensional squirmer of radius R whose center is a distance d from a no-slip surface. The schematic of the problem 043002-9 is shown in Fig. 1. We start with the general solution of the biharmonic equation \u22074\u03c8 = 0 for the stream function \u03c8 . For simplicity, we use bipolar coordinates (\u03be,\u03b7), defined in terms of Cartesian coordinates (x\u0302,y\u0302) as \u03b7 + i \u03be = ln x\u0302 + i(y\u0302 + \u03baR) x\u0302 + i(y\u0302 \u2212 \u03baR) , (A1) or equivalently x\u0302 = h\u0302\u22121 sin \u03be, y\u0302 = h\u0302\u22121 sinh \u03b7, (A2) where h = (cosh \u03b7 \u2212 cos \u03be )/\u03baR is the scale factor and \u03ba2 = (d/R)2 \u2212 1. The surface of the cylindrical swimmer can be described by \u03b7 = \u03b71 = sinh\u22121 \u03ba in bipolar coordinates. Therefore, the stream function satisfying the no-flow condition at infinity can be written as h\u0302\u03c8\u0302 = [ \u221e\u2211 n=0 \u03c7\u0302n(\u03b7)e\u2212in\u03be ] , (A3) where all constants are complex, extracts the real part, and \u03c7\u0302n are defined as \u03c7\u03020 = G\u03020 cosh \u03b7 + H\u03020\u03b7 cosh \u03b7 + K\u03020 sinh \u03b7 + M\u03020\u03b7 sinh \u03b7, \u03c7\u03021 = G\u03021 cosh 2\u03b7 + H\u03021 + K\u03021 sinh 2\u03b7 + M\u03021\u03b7, \u03c7\u0302n = G\u0302n cosh(n + 1)\u03b7 + H\u0302n cosh(n \u2212 1)\u03b7 + K\u0302n sinh(n + 1)\u03b7 + M\u0302n sinh(n \u2212 1)\u03b7" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001791_j.mechmachtheory.2016.05.001-Figure3.2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001791_j.mechmachtheory.2016.05.001-Figure3.2-1.png", "caption": "Fig. 3.2. The force decomposition situation of UPR leg.", "texts": [ " Thus, Fri for the SPR leg can be expressed as following Fri \u00bc Fai Fpi;1 \u00bc Wi Fei ;Wi \u00bc 1 0 0 \u22121 : \u00f013\u00de For the UPR type leg, there are four possible decomposed force components which produce four possible deformations. The active force Fai produces longitudinal deformation along ri. The constrained forces Fpi at U joint can be equivalent to one force Fpi,1 at ai, which produces a flexibility deformation. Fpi,1 is parallel with Fpi and active in the opposite direction. The constrained torque Tpi in the UPR leg can be decomposed into two elements Tpi,1 and Tpi,2 which produce a torsional deformation and a bending deformation, respectively. Tpi,1 is along with ri, and Tpi, 2 is perpendicular to ri (see Fig. 3.2). Let \u03c4pi,1 and \u03c4pi,2 be the unit vector of Tpi,1 and Tpi,2, respectively. From the geometrical constraints of the UPR leg, it leads to \u03c4pi;1 \u00bc \u03b4i;\u03c4pi;2\u22a5\u03b4i;\u03c4i\u22a5Ri2;\u03c4pi;1\u22a5Ri2 \u00f014a\u00de \u03c4i, \u03c4pi,1 and \u03c4pi,2 are in the same plane. Thus, it leads to \u03c4pi;2\u22a5Ri2;\u03c4pi;2 \u00bc \u03b4i Ri2: \u00f014b\u00de From Eq. (14a), Tp1,1 can be expressed as following: Tpi;1 \u00bc spi;1Tpi; spi;1 \u00bc \u03c4i \u03b4i \u00bc Ri1 Ri2\u00f0 \u00de \u03b4i \u00f015a\u00de From Eq. (14b), Tp1,2 can be expressed as following: Tpi;2 \u00bc spi;2Tpi; spi;2 \u00bc \u03c4i \u03b4i Ri2\u00f0 \u00de \u00bc Ri1 Ri2\u00f0 \u00de \u03b4i Ri2\u00f0 \u00de: \u00f015b\u00de Thus, Fri for the UPR type leg can be expressed as following: Fri \u00bc Fai Fpi;1 Tpi;1 Tpi;2 2 664 3 775 \u00bc Wi Fei ;Wi \u00bc 1 0 0 0 \u22121 0 0 0 spi ;1 0 0 spi ;2 2 664 3 775: \u00f016\u00de For the UPU-type leg, the constrained force Fpi at ci can be equivalent to a force Fpi,1 at ai and a torque Tpi" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001495_1.4031366-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001495_1.4031366-Figure2-1.png", "caption": "Fig. 2 Schematic diagram of transmissivity measure", "texts": [ " The transmissivity of laser through the powder layer analysis is the first focus in this study. In order to accomplish this purpose, the laser beam was focused on the powder layer which was placed on a high transmission ratio glass. A calorimeter was placed under the glass with powder. Thus, when the laser irradiates on the powder layer, the calorimeter can record the maximal laser powder, which can be considered as the original transmitted laser power. When the powder began to melt under the laser irradiation, the laser beam would be cut off by the molten pool (Fig. 2). Six curves are presented in Fig. 3, which presents the power evolution with original laser beam; with glass; with powder A; with powder B, and powder A with thickness 75 lm and 100 lm, respectively. From the diagram, first, the effect of glass can be ignored. It can be found that the major laser power was absorbed by the powder layer, the transmissivity of laser can be obtained less than 15% with small particle size powder (powder A), about 18% with large particle size powder (powder B). When the thickness of powder layer increases to 75 and 100 lm, the laser power can be reduced from 4" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001584_j.jsv.2016.08.014-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001584_j.jsv.2016.08.014-Figure3-1.png", "caption": "Fig. 3. Render model of the Agile Eye.", "texts": [ " To the best author's knowledge, although the dynamic stiffness matrix of the non-classical damped system can theoretically be obtained the corresponding complex eigenproperties cannot be easily obtained. The Wittrick\u2013Williams algorithm works only with conservative systems and its extension to complex solutions of continuous dissipative system is still an important open issue in structural dynamics. In this section, the dynamic stiffness model developed in the previous section is applied to study the Agile Eye, a pure rotational 3-dof SPM developed by Gosselin [44,45]. The Agile Eye, shown in Fig. 3, has three limbs each made of two curved links, here named proximal and distal links, coupled by means of passive revolute joints. The proximal links are coupled to the BP by means of actuated revolute joints, while three further passive revolute joints connect the distal links to the MP. All the joints have axes intersecting at a common point, i.e. the centre of the spherical motion. Geometric, structural and inertial parameters are reported in Tables 1 and 2. To obtain the GDSM of the Agile Eye the generalized dynamic stiffness matrices of each leg must be assembled" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000039_978-1-84996-220-9-Figure3.3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000039_978-1-84996-220-9-Figure3.3-1.png", "caption": "Figure 3.3 Relative hand\u2013object task description: (a) with respect to the cylinder; and (b) with respect to the hand", "texts": [ " This allows, for instance, one to describe the position 3 Whole-body Motion Planning \u2013 Building Blocks for Intelligent Systems 71 of one hand with respect to the other, the orientation of the head to the body, etc. It is also possible to describe robot link transformations with respect to objects in the environment, such as the position of the hand with respect to an object, or the direction of the gaze axis with respect to an object. The choice of the order of the relative coordinates yields some interesting aspects. This is illustrated in Figure 3.3 for a simple planar example. Representing the movement of the hand with respect to the cylinder results in Figure 3.3 (a). A coordinated hand\u2013object movement has to consider three task variables (x y \u03d5). Switching the frame of reference and representing the object movement with respect to the hand, such as depicted in Figure 3.3 (b), leads to a description of the movement in hand coordinates. In this example, this might be advantageous, since the object is symmetric and can be approached from any side. While in the first case the task variables are dependent, in the second case \u03d5 and y are invariant and can be set to zero. There are many other examples, such as representing a gazing controller as an object in headcentered coordinates which is \u201cpointed\u201d to by the focal axis, or a pointing controller in a similar way. 72 M" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000329_1.4003180-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000329_1.4003180-Figure3-1.png", "caption": "Fig. 3 Maximally regular T2R1-type parallel manipulator with bifurcated spatial motion of the moving platform: \u201ea\u2026 constraint singularity and \u201e\u201eb\u2026 and \u201ec\u2026\u2026 branches with spatial motion; limb topology P P \u00b8R R-P \u00b8R \u00b8R \u00b8R R-Pa R \u00b8RS", "texts": [], "surrounding_texts": [ "a s t l l\nF f s t\n0\nDownloaded Fr\nnd two rotations and the PM has instantaneously the following tructural parameters: iMF=4, iNF=1, and iTF=0, given by Eqs. 1 \u2013 3 . This bifurcation occurs when q3=0. In this configuration, he rotation axes of the two last revolute joints of limbs G1 and G2 ie in the same plane. The axes of the last revolute joint of the G2\nig. 1 T2R1-type parallel manipulator with uncoupled and biurcated spatial motion of the moving platform: \u201ea\u2026 constraint ingularity and \u201e\u201eb\u2026 and \u201ec\u2026\u2026 branches with spatial motion; limb opology P P \u00b8R R-P \u00b8R \u00b8R \u00b8R R-P \u00b8R \u00b8RS\nimb and the last but one revolute joint of the G1 limb coincide.\n11010-4 / Vol. 3, FEBRUARY 2011\nom: http://mechanismsrobotics.asmedigitalcollection.asme.org/ on 06/13/2\nThe PMs can escape from this constraint singularity by bifurcating in one of the two branches presented in diagrams b and c see Figs. 1 and 2 . The bifurcation in constraint singularity can be used to change the motion type of moving platform 6. To achieve this change, one of the last revolute joints of the G1- or G2-limb has to be instantaneously locked up when the moving platform\npasses through constraint singularity. By locking up the last revo-\nTransactions of the ASME\n014 Terms of Use: http://asme.org/terms", "l b G s a\nf v g m =\nf v g m =\nc t z d\nw f\n5 t\nu p g o a p w a m e r\n4 S l f t i t f b t o s o i\nJ\nDownloaded Fr\nute joint of the G1-limb, the parallel mechanism goes in the ranch with spatial motion of the moving platform in diagram b Figs. 1 and 2 . By locking up the last revolute joint of the\n2-limb, the parallel mechanism works in the branch with the patial motion of the moving platform in diagram c see Figs. 1 nd 2 .\nThe branch in diagram b Figs. 1 and 2 is characterized by the ollowing parameters: RG1 = v1 ,v2 , , , RG2 = v1 ,v2 , 3 , , , and RG3 = v1 ,v2 ,v3 , , , . Equation 4 ives SF=3 and RF = v1 ,v2 , . In this branch, the parallel echanism has the following structural parameters: MF=3, NF 0, and TF=0, given by Eqs. 1 \u2013 3 . The solutions in diagram b Figs. 1 and 2 are not overconstrained NF=0 . The branch in diagram c Figs. 1 and 2 is characterized by the ollowing parameters: RG1 = v1 ,v2 , , , RG2 = v1 ,v2 , 3 , , , and RG3 = v1 ,v2 ,v3 , , , . Equation 4 ives SF=3 and RF = v1 ,v2 , . In this branch, the parallel echanism has the following structural parameters: MF=3, NF 0, and TF=0, given by Eqs. 1 \u2013 3 . The solutions in diagram c Figs. 1 and 2 are not overconstrained NF=0 . We note that independent linear velocities v1, v2, and v3 of haracteristic point H and angular velocities , , and of he moving platform have directions parallel to the x0-, y0-, and 0-axes of the reference frame. For the parallel manipulator in iagrams b and c Figs. 1 and 2 , Eq. 8 becomes\nv1\nv2\n= 1 0 0 0 1 0\n0 0 1 r1 cos q\u03071 q\u03072 q\u03073 9\nhere r1=HG=HK defines the dimensions of the moving platorm and = for the solution in diagram b Figs. 1 and 2 and = for the solution in diagram c Figs. 1 and 2 .\nMaximally Regular Solutions With Bifurcated Spaial Motion\nMaximally regular solutions can be derived from the PM with ncoupled motions in Figs. 1 and 2 by replacing the actuated rismatic joint with translational motion q3 by a planar paralleloram loop Pa of type R R R R Figs. 3 and 4 . A revolute joint f the parallelogram loop is actuated and q3 represents its rotation ngle. If r1=HG=HK=MN, the Jacobian matrix of linear maping Eq. 8 of the parallel manipulators in diagrams b and c Figs. 3 and 4 is the 3 3 identity matrix throughout the entire orkspace. A one-to-one correspondence exists between the actuted joint velocity space and the operational velocity space of the oving platform v1= q\u03071, v2= q\u03072, and = q\u03073 . Three joint paramters lose their independence in the planar parallelogram loop l G3=3 and Eq. 6 gives rl=3.\nThe limbs isolated from the parallel mechanisms in Figs. 3 and have the following degrees of connectivity: SG1=4, SG2=5, and\nG3=6. In the configuration associated with the constraint singuarity in diagram a Figs. 3 and 4 , the vector spaces iRGj have the ollowing bases: iRG1 = v1 ,v2 , , , iRG2 = v1 ,v2 ,v3 ,\n, , and iRG3 = v1 ,v2 ,v3 , , , . In this configuraion, Eq. 4 gives iSF=4 with iRF = v1 ,v2 , , . The movng platform has instantaneously four independent motions two ranslations and two rotations and the PM has instantaneously the ollowing structural parameters: iMF=4, iNF=4, and iTF=0, given y Eqs. 1 \u2013 3 . This constraint singularity occurs when q3=0. In his configuration, the rotation axes of the two last revolute joints f limbs G1 and G2 lie in the same plane as in the counterpart olutions in Figs. 1 and 2. One of the last revolute joints of the G1r G2-limb has to be instantaneously locked up, as in the solutions n Figs. 1 and 2, when the moving platform passes through the\nournal of Mechanisms and Robotics\nom: http://mechanismsrobotics.asmedigitalcollection.asme.org/ on 06/13/2\nconstraint singularity diagram a Figs. 3 and 4 for bifurcating into one of the two branches in diagrams b and c Figs. 3 and 4 .\nThe branch in diagram b Figs. 3 and 4 is characterized by the following parameters: RG1 = v1 ,v2 , , , RG2 = v1 ,v2 ,\nv3 , , , and RG3 = v1 ,v2 ,v3 , , , . Equation 4\nFEBRUARY 2011, Vol. 3 / 011010-5\n014 Terms of Use: http://asme.org/terms", "g m =\nf v\n0\nDownloaded Fr\nives SF=3 and RF = v1 ,v2 , . In this branch, the parallel echanism has the following structural parameters: MF=3, NF 3, and TF=0, given by Eqs. 1 \u2013 3 . The branch in diagram c Figs. 3 and 4 is characterized by the ollowing parameters: RG1 = v1 ,v2 , , , RG2 = v1 ,v2 ,\n3 , , , and RG3 = v1 ,v2 ,v3 , , , . Equation 4\n11010-6 / Vol. 3, FEBRUARY 2011\nom: http://mechanismsrobotics.asmedigitalcollection.asme.org/ on 06/13/2\ngives SF=3 and RF = v1 ,v2 , . In this branch, the parallel mechanism has the following structural parameters: MF=3, NF =3, and TF=0, given by Eqs. 1 \u2013 3 .\nThe solutions in diagrams b and c Figs. 3 and 4 have three overconstraints NF=3 . Nonoverconstrained solutions can be ob-\nss\ntained from these solutions by using a G3-leg of type Pa RS\nTransactions of the ASME\n014 Terms of Use: http://asme.org/terms" ] }, { "image_filename": "designv10_9_0000155_tie.2011.2157294-Figure9-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000155_tie.2011.2157294-Figure9-1.png", "caption": "Fig. 9. (a) Current paths from one short-circuit end arc to the other. (b) Their lumped-parameter representation.", "texts": [ " The leakage inductance values La and Lc found in this way, however, are so small that they can be reasonably approximated by zero, as well as their resistances. In other terms, damper end connections can be modeled as actual short circuits between the bars. It is important to observe, however, that the aforementioned approximation holds only for those damper cage design solutions where a complete short-circuit end ring is used [Fig. 2(c)], while in the case of partial short-circuit arcs [Fig. 2(b)], parameters Lc and Rc will be shown to require experimental model tuning. The reason is shown in Fig. 9, where the damper cage portions in two generic adjacent poles (\u201ci\u201d and \u201ci + 1\u201d) are considered. If interpole connections are present, damper currents can flow from one pole to the other through two paths in parallel, indicated as \u201cpath A\u201d and \u201cpath B\u201d: The former is practically a short circuit, while the latter (passing through rotor pole and yoke laminations) has an equivalent impedance whose value is practically impossible to predict by calculation. As a consequence, parameters Ra and La can be set to zero in the case of continuous end ring, while in the case of removed interpole connections, these parameters can be determined based on tests, as discussed in Section V-B", " 2(b)], a first-attempt simulation is performed by setting the resistive parameter Rc equal to a very large value (10 M\u03a9) in the external circuit linked to damper bars [Fig. 5(c)]. This corresponds to imposing that no current can flow between dampers of different poles. The results obtained with this assumption are shown in Fig. 14(a). The comparison shows a good accuracy for X \u2032\u2032 d but a large error for X \u2032\u2032 q . This suggests that, even if interpole connections are removed, some damper cage current can flow from one pole to the others through rotor laminations [path B of Fig. 9(a)]. The phenomenon is made possible because damper bars and rings are not insulated, so an external current flow via pole body and rim can reasonably occur [11], [15]. A parameter calibration is thereby performed on the FE model of the generator without interpole connections based on stationary unbalanced test results. The calibration is done by adjusting parameters Rc and Lc so that the machine complex impedance viewed from the supply terminals (Figs. 11 and 12) is the same (in magnitude and phase) in both test and simulation" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000060_13506501jet578-Figure12-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000060_13506501jet578-Figure12-1.png", "caption": "Fig. 12 Dent location on outer race", "texts": [ " In this investigation, the bearing dynamic simulation starts with having the inner race at rest and exponentially increasing the inner race speed such that after a period of 5 ms the inner race achieves the desired steady-state speed. The effect of a surface defect (e.g. dent) in the DBM is demonstrated by simulating a ball bearing containing ten balls with a dent located on the outer race. The dent is at 30\u25e6 from the Y -axis on the Y \u2212Z-plane, and along the Z-axis on the Z\u2212X -plane, as shown in Fig. 12. To clearly demonstrate the effect of dent on bearing operation, a simple case of a bearing with 5 \u00b5m interference was considered (i.e. the radius of the inner race plus the ball diameter is 5 \u00b5m larger than the outer race radius). In this configuration the balls experience the same contact loading condition, as shown in Fig. 13(a). However, in the presence of a dent on the outer race, the contact force exhibits fluctuations indicating vibrations excited due to the dent (Fig. 13(b)). Note that Figs 13(a) and (b) are tracking the forces acting on only a single ball, as other balls will have a similar response" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001170_we.1656-Figure13-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001170_we.1656-Figure13-1.png", "caption": "Figure 13. Acceptance surfaces for p=0.0, p=0.1, and p=0.2.", "texts": [ "2 are adopted for the preload; and three, the overall load capacity of the bearings (axial, radial, and moment) remains almost constant from preloads ranging from p= 0 to p= 0.5 and then decreases almost linearly to zero. With the theoretical model, not only pure axial, radial, and moment static load capacities can be estimated but also the load combinations that will lead to the static failure of the bearing. For such purpose, a \u2018three-dimensional acceptance surface\u2019 is defined, in such a way that the validity of any FA-FR-M load combination is assured by an inside-surface checking.3 Figure 13 shows the acceptance surfaces for preload values of p= 0, p= 0.1, and p= 0.2. As pointed out in the introduction section, a preload of approximately 7\u201310% of the maximum admissible deflection of the balls is usually adopted for yaw and Wind Energ. (2013) \u00a9 2013 John Wiley & Sons, Ltd. DOI: 10.1002/we pitch bearings (p=0.07 and p=0.1). Figures 14\u201316 show the corresponding curve fits in the FA-FR, FA-M, and FR-M coordinate planes. The surfaces and the resulting coordinate planes have been normalized with respect to the axial capacity of the bearing with no preload (p=0" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001723_s00170-015-7481-8-Figure2-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001723_s00170-015-7481-8-Figure2-1.png", "caption": "Fig. 2 Schematic of the interaction of two symmetric powder streams", "texts": [ " (8), the mass concentration of the single powder stream in the plane x1-O1-y at the distance S below the nozzle exit plane can be calculated by c x1; y; S\u00f0 \u00de \u00bc mp 4\u03c0vp l \u00fe Scsc\u03c6\u2212x1cos\u03c6\u00f0 \u00de2a2 exp \u2212 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x1sin\u03c6\u00f0 \u00de2 \u00fe y2 q l \u00fe Scsc\u03c6\u2212x1cos\u03c6\u00f0 \u00dea 0 @ 1 A 22 64 3 75 \u00f013\u00de Further, the mass concentration of the symmetric double powder streams can be investigated based on the analysis of the single powder stream, and the interaction of two powder streams can be considered as a simple superposition in the same coordinate system. The schematic of the interaction of two symmetric powder streams is shown in Fig. 2. A unified coordinate system XYZ must be built to realize the superposition, and then the mass concentration of the single powder stream in the plane x1-O1-y can be transformed into the coordinate system XYZ. From the geometric relationship in Fig. 2, the following relationship can be obtained: O1O ! \u00bc S f \u2212S cot\u03c6 \u00f014\u00de where Sf is the distance between the intersection point of the center line of the single powder stream (the theoretical focus position) and the nozzle exit plane. So the coordinate transform can be given by x1 \u00bc X \u00fe O1O ! \u00f015\u00de y \u00bc Y \u00f016\u00de With substitution of Eqs. (14), (15), and (16) into Eq. (13), the mass concentration caused by the first powder stream at a distance S below the nozzle exit plane in coordinate system XYZ can be calculated by c1 X ; Y ; S\u00f0 \u00de \u00bc mp 4a2\u03c0vp l \u00fe Scsc\u03c6\u2212 X \u00fe S f \u2212S cot\u03c6 cos\u03c6 2 exp \u2212 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X \u00fe S f \u2212S cot\u03c6 sin\u03c6 2 \u00fe Y 2 q a l \u00fe Scsc\u03c6\u2212 X \u00fe S f \u2212S cot\u03c6 cos\u03c6 0 @ 1 A 22 64 3 75 \u00f017\u00de Due to the symmetry, the mass concentration caused by the second powder stream can be written as c2 X ; Y ; S\u00f0 \u00de \u00bc mp 4a2\u03c0vp l \u00fe Scsc\u03c6\u2212 \u2212X \u00fe S f \u2212S cot\u03c6 cos\u03c6 2 exp \u2212 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u2212X \u00fe S f \u2212S cot\u03c6 sin\u03c6 2 \u00fe Y 2 q a l \u00fe Scsc\u03c6\u2212 \u2212X \u00fe S f \u2212S cot\u03c6 cos\u03c6 0 @ 1 A 22 64 3 75 \u00f018\u00de Therefore, the mass concentration caused by the symmetrical double powder streams at a distance S below the nozzle exit plane in the unified coordinate system can be obtained by c 0 X ; Y ; S\u00f0 \u00de \u00bc c1 X ; Y ; S\u00f0 \u00de \u00fe c2 X ; Y ; S\u00f0 \u00de \u00f019\u00de Because the other double powder streams are symmetrical to the symmetric double powder streams formed by the first powder stream and the second powder stream at Y=X, the function of the mass concentration caused by the other double powder streams is the inverse function of Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002277_978-3-319-27131-6-Figure4.6-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002277_978-3-319-27131-6-Figure4.6-1.png", "caption": "Fig. 4.6 Interference rings (interferogram) of the oil-film thickness", "texts": [ " 4.5, the EHD pressure spike is additionally proportional to oil velocity squared at the minimum oil-film thickness. Moreover, the outflow velocity 4.3 Oil-Film Pressures in the Hertzian Contact Area 69 wmin depends on the oil-film thickness hmin and the ball rolling velocity U in the rolling direction x. Furthermore, the EHD pressure spike depends on two parameters of the minimum oil-film thickness and the air- and oil-bubble fraction due to air releasing and cavitation at the oil outflow (cf. Fig. 4.6). The induced gas bubbles reduce the sectional area of the oil outflow. Therefore, the higher the gas bubble fraction at the oil outflow area, the higher the EHD pressure spike encounters. In this case, the oil outflow velocity at the minimum oil-film thickness increases; hence, the EHD pressure spike grows respectively according to Eq. 4.5. Figure 4.6 schematically displays the oil-film thickness in the Hertzian contact zone. The central oil-film thickness hc is nearly constant in the Hertzian region. Just in front of the contact-area outflow, the oil-film thickness reduces to the minimum thickness hmin due to the elastic deformation of the balls and flow separation. The minimum oil-film thickness also occurs at the left and right outflow sides of the Hertzian region due to the same reasons. Furthermore, the outflow oil wakes take place behind the Hertzian contact area due to flow separation" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001520_j.jsv.2014.09.004-Figure10-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001520_j.jsv.2014.09.004-Figure10-1.png", "caption": "Fig. 10. Vibration modes with significant values of b\u00f0\u03d5i ;\u03c8 j\u00de. (a) mode (A), (b) mode (B), (c) mode (C), (d) mode (D), (e) mode (E), (f) mode (F).", "texts": [ " However, as seen in Fig. 9(b), (c), and (d), there are large peaks in high frequency range for the modes withm\u00bc8, 16, and 24, respectively. This indicates that the vibration modes with high mode orders have a tendency to have strong correlations with the tangential modes. These trends can be understood by examining the corresponding vibration modes. The significant vibration modes with large values of jb\u00f0\u03d5i;\u03c8 j\u00dej are designated as (A) through (F) in Figs. 8 and 9. The corresponding mode shapes are shown in Fig. 10. The modes (A) and (B) are the bending modes of the core with the bolted regions being undeformed. The motion of the mode is almost 2D in the X Y plane. The values of b\u00f0\u03d5i;\u03c8 j\u00de for these modes are high, because their shapes on \u0393N are similar to the shape of cos \u00f00\u00deer . The mode (C) is also a bending mode of the core toward the center of the core showing octagonal shape. It means that it is similar in shape with cos \u00f08\u03b8\u00deer on \u0393N . The mode (D) is a bending mode of the teeth, toward circumferential direction" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002555_j.jsv.2019.115117-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002555_j.jsv.2019.115117-Figure1-1.png", "caption": "Fig. 1. Six DOF multi-body dynamic model of bearing.", "texts": [ " The paper is organized in the following manner; section 2 describes the MBD and AE models of REB, section 3 details experimental procedure of determining surface topography properties, section 4 is for discussion of results and finally, the paper is concluded in section 5. In this study, for modelling the dynamic behavior of REB, a modified version of the model developed by Sawalhi and Randall [7] is used. The modification in the existing model is done by including the effect of high-frequency resonator in both x and y directions. Fig. 1 shows the diagram of the multi-body dynamic model for simulating the vibration response of a rolling element bearing. . The model shown in Fig. 1 is for healthy bearing and has six degrees of freedom. It includes the masses of the outer raceway plus the pedestal(mp) inner raceways plus the shaft(ms) and resonator (mr). The static load Fr acts at the shaft center. The high-frequency resonator employed here consists of a spring-mass-damper system (kr , mr and cr) and is excited by virtue of high frequency resonant mode of bearing. The equations governing the dynamics of REB are given as [7]. ms \u20acxs \u00fe cs _xs \u00fe ksxs \u00fe fx \u00bc 0 (1) ms \u20acys \u00fe cs _ys \u00fe ksys \u00fe fy \u00bc Fr (2) mp\u20acxp \u00fe cp \u00fe cr _xp \u00fe kp \u00fe kr xp krxr cr _xr fx \u00bc0 (3) mp \u20acyp \u00fe cp \u00fe cr _yp \u00fe kp \u00fe kr yp kryr cr _yr fy \u00bc0 (4) m \u20acy \u00fe c _y _y \u00fe k y y \u00bc0 (5) r r r r p r r p mr \u20acxr \u00fe cr _xr _xp \u00fe kr xr xp \u00bc0 (6) where xs,ys and xp, ypare x and y coordinates of shaft(inner race) and pedestal(outer race) respectively, xrand yrare x and y coordinates of resonator, cpand cs are equivalent damping for pedestal(with outer race) and shaft(with inner race) material respectively, and Fris total radial force acting on bearing" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0001379_978-3-319-22056-7-Figure3.4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0001379_978-3-319-22056-7-Figure3.4-1.png", "caption": "Fig. 3.4 Model of the symmetrical rotor before body separation", "texts": [ " Main part of many working machines, centrifuges, fans, pumps, turbines, electromotors, generators etc. are rotors which can be modelled as a shaft disc-system. Due to external impact force an accidence in rotors may occur. In Fig. 3.3 a damaged fan is shown. Due to impact between rotor and stator a shovel of a fan is broken and remained part of the rotor changes its steady-state motion. In this section motion of the remained rotor is studied. Physical model of the rotor is a symmetrically supported shaft-disc system (Fig. 3.4) usually called Jeffcot rotor. In middle of an elastic shaft whose rigidity is k1, a disc with mass M is settled. Mass of the shaft is neglected. Motion of the disc is in-plane. Mass centre of the disc S, which is also the geometric centre, moves in the x Oy. Rotor rotates with constant angular velocity . Moment of inertia of the disc is IS for axis z in mass centre S. It is assumed that a part of the body with mass m is separated. It causes change in motion of the remainder body. Aim of this example is to determine motion of the remainder body after mass separation", "224) It is assumed that motion of the rotor centre S is in the Oxy plane and corresponding differential equations of motion are due to (5.224) m dx\u0308 dt + Fex = Fr x + \u03b5 dm d\u03c4 (ux \u2212 x\u0307), (5.225) m d y\u0308 dt + Fey = Fr y + \u03b5 dm d\u03c4 (uy \u2212 y\u0307). (5.226) Substituting projections of the elastic force (5.222) on x and y axis into (5.225) and (5.226), we have m dx\u0308 dt + Fe(\u03c1) cos\u03d5 = Fr x + \u03b5 dm d\u03c4 (ux \u2212 x\u0307), (5.227) m d y\u0308 dt + Fe(\u03c1) sin\u03d5 = Fr y + \u03b5 dm d\u03c4 (uy \u2212 y\u0307). (5.228) Let us introduce connection between Cartesian and polar coordinates (see Fig. 3.4) x = \u03c1 cos\u03d5, y = \u03c1 sin\u03d5, (5.229) i.e., \u03c1 = \u221a x2 + y2, \u03d5 = tan\u22121 ( y x ) . (5.230) Substituting (5.230) into (5.227), (5.228) we have m dx\u0308 dt + x F \u2032 e (\u221a x2 + y2 ) = Fr x + \u03b5 dm d\u03c4 (ux \u2212 x\u0307), (5.231) m d y\u0308 dt + yF \u2032 e (\u221a x2 + y2 ) = Fr y + \u03b5 dm d\u03c4 (uy \u2212 y\u0307), (5.232) 5.7 Vibration of Jeffcott Rotor 171 where F \u2032 e( \u221a x2 + y2) = F \u2032 e(\u03c1) = Fe(\u03c1)/\u03c1. Introducing the complex deflection function z = x+iy and the complex conjugate function z\u0304 = x \u2212 iy, equation of vibration of the rotor is mz\u0308 + zF \u2032 e( \u221a zz\u0304) = Fz + \u03b5 dm d\u03c4 (uz \u2212 z\u0307), (5" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000027_icorr.2011.5975445-Figure7-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000027_icorr.2011.5975445-Figure7-1.png", "caption": "Fig. 7 Virtual wall area.", "texts": [ " 6, max is the amount of the maximum hip joint torque which is defined to protect the user from the injury. The perceptionassist torque for walking-assist is calculated using eq. (13). )(, )( ,)( )(,0 max max crisafezmp crisafezmpsafe safezmp cri safezmp walk ddxSgn ddxd dSgnx d dx (13) )sgn( , zmp zmpZMPczmp xSgn xxx where xc,ZMP is the center position of the support polygon, dsafe and dcri are shown in Fig. 6. max, dsafe and dcri are experimentally defined. When the robot detects a bump, a virtual wall area is generated in front of the bump as shown in Fig. 7(a). It assumes that the first point which is judged as a bump by the environmental sensing is the origin. The virtual wall area is shown by the trapezoid represented by l, h and H in Fig. 7 (a). Here, H means the height of the bump, l, h are the experimentally defined parameters as shown in Fig. 7(a). In the experiments to define l and h, some subjects walk at normal speed (about 1.4m/sec) [23]. Then, we defined l and h as minimum values in which the subjects could overcome the bump. The location of the toe of the user\u2019s swing leg is calculated using eq. (11). If the user\u2019s foot enters the virtual wall area as shown in Fig. 7(a), the robot judges the user might stumble on the bump and generates the additional motion modification force along the virtual wall in addition to the power-assist force to avoid the collision with the bump. The additional motor torque generated by the effect of the additional motion modification force (i.e., the perception-assist torque) is written as follows. add addk addh fJ T , , (14) where h,add is the additional hip joint torque, k,add is the additional knee joint torque, J is Jacobian matrix and fadd is the additional motion modification force generated along the virtual wall", " After the user\u2019s foot is lifted over the bump, the robot estimates whether the top surface of the bump has enough space to place the user\u2019s foot on it. If the top surface of the bump has enough space to place the user\u2019s foot on it, the robot takes the additional perception-assist torque away from the user and performs the normal power-assist. In the case that the top surface of the bump is too narrow, if the robot recognizes the ground ahead on the bump, the robot performs another perception-assist to overcome the bump as shown in Fig. 7(b). Meanwhile, if the robot cannot recognize the ground ahead on the bump, the robot tries to turn back the user\u2019s foot because the robot cannot find the space to place the user\u2019s foot on it safety. Thus, the robot takes into account ZMP to prevent the user from losing his/her balance and falling down in any case. The flowchart of the perception-assist is shown in Fig. 8. The robot performs the perception-assist in accordance with the flowchart shown in Fig. 8 in addition to the power-assist represented in eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0003046_j.simpat.2020.102080-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0003046_j.simpat.2020.102080-Figure1-1.png", "caption": "Fig. 1. Schematic diagram of the main reducer: (a) Isometric view; (b) top view [35].", "texts": [ " This paper provides prerequisites towards pursuing the researches on the windage loss of meshing spiral bevel gears under oil-jet lubrication. In some gear units with the highest rated power exceeded 100 MW level, at least 1 MW power losses would produce even if it is a best-designed gear transmission model [1]. Specially, the power losses in gearboxes can be identified as gear losses, bearing losses, seal losses. etc. The gear losses can be further subdivided into meshing losses, windage losses, and churning losses [2\u20136]. In the main reducer of aero-engines (see Fig. 1), especially for the spiral bevel gears, which at present can be manufactured with a flank milling method [7\u20139] through a flexible free-form milling machining process for each gear type [10\u201313], and not only that, a new double contact milling [14\u201315] emerged. jet lubrication is the uniquely feasible and effective method to provide the lubrication and cooling. It cannot be neglected that the windage power loss experienced by the high-speed gear pumping the surrounding air or air-oil mist may account for a few percent of the total power losses, which leads to the degradation of the lubrication oil, the excessive wear of the turbomachinery and the additional heating of oil, resulting in more maintenance, cooling cost and ongoing expense of an internal gearbox" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002893_tia.2020.3036328-Figure1-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002893_tia.2020.3036328-Figure1-1.png", "caption": "Fig. 1. Topologies of CFRPM machines. (a) 12S16P. (b) Proposed 6S16P.", "texts": [ " It has been shown that fractional-slot windings can help to reduce the cogging torque. Then, the authors in [20] and [21] have investigated the effect of PM arrangement and optimum number of magnet pieces on torque performance considering their influence on working airgap flux density harmonics. Additionally, a small gap between two adjacent magnets under one stator tooth can help to reduce the cogging torque [22]. To increase the torque density, the consequent pole permanent magnet is first employed in the FRPM machine [23], as shown in Fig. 1(a). The torque density and PM utilization are found to be improved because of the strengthened modulation effect and halved PM consumption. Subsequently, several different consequent pole FRPM machines are investigated in [24]. Although torque density can be improved by using some flux focusing structures, e.g., Halbach PM array [9], the PM structure becomes complex, which will increase the PM manufacturing cost significantly. To further increase the torque density while employing a simple structure, multitooth structure is employed in FRPM machines [25]", " Due to that the proposed 6S16P CFRPM machine shows much higher torque ripple than the 12S16P FRPM and its consequent pole type, for a fair comparison, several techniques are employed to reduce the torque ripple of the proposed 6S16P CFRPM to a level comparable to the 12S16P FRPM and its consequent pole type. The prototypes are made to validate the analyses in Section V, and some conclusions are drawn in Section VI. 0093-9994 \u00a9 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See https://www.ieee.org/publications/rights/index.html for more information. Authorized licensed use limited to: California State University Fresno. Downloaded on June 26,2021 at 14:21:53 UTC from IEEE Xplore. Restrictions apply. As shown in Fig. 1(b), the proposed CFRPM machine with 6S16P can be viewed as a CFRPM machine with stator split tooth. All PMs are surrounded by irons on three sides while conventional CFRPM machines have some PMs surrounded by irons on two sides. Therefore, this topology features more iron poles than PM poles providing more support and more contacting area for PMs. The airgap permeance is influenced as well. The proposed CFRPM machine has a doubly salient structure, and its stator permeance \u039bs(\u03b8s), rotor permeance \u039br(\u03b8s, t), and resultant airgap permeance \u039bg(\u03b8s, t) can be described as (1), (2), and (3), respectively [26] \u039bs(\u03b8s) = \u039bs0 + \u039bs1 cos(iNs\u03b8s) (1) \u039br(\u03b8s, t) = \u039br0 + \u039br1 cos(Nr\u03b8s \u2212Nr\u03a9rt) (2) \u039bg(\u03b8s, t) \u2248 \u039bs(\u03b8s)\u039br(\u03b8s, \u03b8)/(\u03bc0/g) \u2248 \u039bs0\u039br0 + \u039bs1\u039br0 cos(iNs\u03b8s) + \u039br1\u039bs0 cos(Nr\u03b8s \u2212Nr\u03a9rt) + 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000193_j.cma.2011.04.006-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000193_j.cma.2011.04.006-Figure3-1.png", "caption": "Fig. 3. Areas of profile and longitudinal crowning to be applied to straight and skew bevel gears; (a) partial crowning and (b) whole crowning.", "texts": [ " Rotations of the being-generated bevel gear (straight or skew) and the imaginary crown-gear are related by wi \u00bc wcg Ncg Ni ; \u00f0i \u00bc 1;2\u00de; \u00f08\u00de where wi and Ni are the angle of rotation and number of teeth of the pinion (i = 1) or the gear (i = 2), respectively, during their theoretical generation, and wcg is the corresponding angle of rotation of the generating crown-gear. Two types of surface modifications, whole and partial crowning, will be investigated in order to get the more effective way to modify a forged bevel gear. Fig. 3 shows a bevel gear tooth surface divided in nine zones wherein partial crowning (Fig. 3(a)) is applied, or in four zones wherein conventional or whole parabolic crowning (Fig. 3(b)) is applied. With respect to Fig. 3(a), representing the application of partial crowning: (i) Zone 5 is an area of the bevel gear tooth surface where profile and longitudinal crowning are not applied. (ii) Zones 1, 3, 7, and 9 are areas of crowning in profile and longitudinal directions. (iii) Zones 2 and 8 are areas of crowning only in profile direction. (iv) Zones 4 and 6 are areas of crowning only in longitudinal direction. When whole crowning of the gear tooth surface is applied, only four areas exist provided with crowning in longitudinal and profile directions (Fig. 3(b)). Those zones correspond to zones 1, 3, 7 and 9 in Fig. 3(a), because areas 2, 4, 5, 6, and 8 (Fig. 3(a)) do not exist when whole crowning is applied. In order to achieve the surface modifications described above, a modified imaginary generating crown-gear will be applied for computerized generation of the geometry of the bevel gear. The geometry of the imaginary generating crown-gear is based on the geometry of a reference blade profile (Fig. 4). Both sides of the blade profile will be defined in coordinate system Sc, fixed to the blade, with its origin Oc placed on the middle of the segment OaOb, with axis xc directed along the pitch line and the axis yc directed towards the addendum height of the reference blade", " 4) for left and right sides as ra;b\u00f0u\u00de \u00bc apf \u00f0u u0\u00de2 u 0 1 2 66664 3 77775: \u00f09\u00de Here, u is the blade profile parameter, apf is the parabola coefficient for profile crowning, and u0 is the value of parameter u at the tangency point of the parabolic profile with the corresponding ya or yb axis. The upper and lower signs of apf correspond to representation of profile geometry in coordinate systems Sa and Sb for the left and right sides, respectively. The following conditions are established in order to apply profile crowning by considering three parts for the active part of the reference blade profile: If u > u0t , then apf \u00bc apft and u0 \u00bc u0t (area A of zones 1, 2, and 3 in Fig. 3(a)). If u 6 u0t and u P u0b , then apf = 0 and u0 = 0 (area B of zones 4, 5, and 6 in Fig. 3(a)). If u < u0b , then apf \u00bc apfb and u0 \u00bc u0b (area C of zones 7, 8, and 9 in Fig. 3(a)). Parameters \u00f0apft ; u0t \u00de, and \u00f0apfb ;u0b \u00de control the crowning and position of areas A and C, respectively, for profile crowning. By considering u0t \u00bc u0b \u00bc 0 and apft \u00bc apfb we can take into account a conventional parabolic profile for the reference blade profile. Similarly, by considering apft \u00bc apfb \u00bc 0 we can take into account a conventional straight profile for the reference blade profile. Blade profiles corresponding to the left and right sides, are represented in coordinate system Sc as rc\u00f0u\u00de \u00bc Mca;bra;b\u00f0u\u00de; \u00f010\u00de where Mca;b \u00bc cos ad sin ad 0 pm 4 sin ad cos ad 0 0 0 0 1 0 0 0 0 1 2 6664 3 7775: \u00f011\u00de Here, ad represents the pressure angle of the reference blade profile, and the upper and lower signs correspond to the left and right blade profiles", " (16) is applied for generation of the driving side of the bevel gear (left side) and the lower sign is applied for generation of the coast side of the bevel gear (right side). The modified angle aa will be denoted as a a and is given by a a\u00f0u; h\u00de \u00bc aa\u00f0u\u00de \u00fe Daa\u00f0h\u00de \u00bc xc\u00f0u\u00de Ro ald\u00f0h h0\u00de2 h : \u00f017\u00de The following conditions have to be observed in Eq. (17) in order to provide longitudinal partial crowning to the surfaces of the imaginary generating crown-gear (Fig. 7). Three areas will be considered: If h < h0t , then ald \u00bc aldt and h0 \u00bc h0t (area D of zones 1, 4, and 7 in Fig. 3(a)). If h P h0t and h 6 h0h , then ald = 0 (area E of zones 2, 5, and 8 in Fig. 3(a)). If h > h0h , then ald \u00bc aldh and h0 \u00bc h0h (area F of zones 3, 6, and 9 in Fig. 3(a)). Parameters \u00f0aldt ; h0t \u00de and \u00f0aldh ; h0h \u00de control the crowning and position of areas D and F, respectively, for longitudinal crowning. By considering h0t \u00bc h0h \u00bc Ro Fw=2 and aldt \u00bc aldh we can take into account a conventional longitudinal parabolic crowned surface for the imaginary crown-gear. Similarly, by considering aldt \u00bc aldh \u00bc 0 we can take into account a non-modified surface in longitudinal direction for the imaginary generating crown-gear. According to the ideas described above, a point P(u,h) is given in coordinate system Sh by (see Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002698_tnnls.2020.3007509-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002698_tnnls.2020.3007509-Figure5-1.png", "caption": "Fig. 5. Geometry of six-link planar serial robot manipulator.", "texts": [ " scaled by \u03c4 , and the first two models\u2019 MSSREs converge with order O(\u03c4 2), while the third model\u2019s MSSREs converge with order O(\u03c4 3). That is, the three models are consistent with ZeaD formulas for computing the FMP of the Zhang matrix. As a consequence, the convergence and effectiveness of the DZNN-1 model and two new proposed models for computing the FMP of the Zhang matrix are substantiated, and only the new proposed models are inverse-free. In this section, we apply the IFDZNN-1 model (9) to a path-tracking task on a six-link planar serial robot manipulator. The geometry of the robot manipulator is presented in Fig. 5. For the simplicity of numerical experiment, the length of each link is set to 1 m, and the nonlinear forward kinematics mapping ra k = g(\u03b8k) \u2208 R2 is obtained, where \u03b8k = [\u03b81 k , \u03b8 2 k , \u03b8 3 k , \u03b8 4 k , \u03b8 5 k , \u03b8 6 k ]T \u2208 R6 denotes the joint angle vector at instant tk , and ra k is the end-effector\u2019s actual position at instant tk . Then, we have the following pointwise linear relation between the end-effector Cartesian velocity r\u0307 a k and the joint velocity \u03b8\u0307k : r\u0307 a k = J (\u03b8k)\u03b8\u0307k where J (\u03b8k) \u2208 R2\u00d76 is the Jacobian matrix" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000753_j.engfailanal.2011.11.004-Figure13-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000753_j.engfailanal.2011.11.004-Figure13-1.png", "caption": "Fig. 13. Model of the drive shaft with the zones of support (A and B) and load transmission (C).", "texts": [ " According to the project documentation, the shaft support was realized through plain bearings A and B, while at the point C there is transmission of the torque to the caterpillar tracks of the undercarriage (Figs. 4 and 13). At the point of support C, the torque is transmitted from the shaft through the sprocket to the caterpillar track chain. The contact between the sprocket and the shaft is accomplished with a press fit. At points A and B, there is a contact between the drive shaft and the carrying structure of the BWE through the plain bearings transmitting radial and axial forces. The support types, A, B and C, are presented in Fig. 13. A 3D model of the drive shaft was built by assembling all structural parts (Fig. 14). The model represents a continuum discretized by 10-node tetrahedral elements [1,4], for the purpose of creating an FEM model (92,817 nodes and 56,624 elements). Table 4 Microchemical analysis of the material at the point of fracture. Percentage of chromium (Cr) and nickel (Ni) in the zone of fracture Points of taking samples S1 S2 S3 Weld material Transition zone Base material \u2013 below transition zone Base material \u2013 without weld Base material \u2013 without weld Cr Ni Cr Ni Cr Ni Cr Ni Cr Sample 1 22" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000281_tmech.2012.2182777-Figure3-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000281_tmech.2012.2182777-Figure3-1.png", "caption": "Fig. 3. Walking configuration in steady state. The rectangles represent the foot boundaries, and the thick and thin lines represent the COM trajectories in the single and double support phases, respectively. The small circles represent the initial/final COM positions in left/right support phase.", "texts": [ " Note that the WS is represented as a 2-D vector in each plane and the velocity terms are multiplied by Tc . The walking of the bipedal robot can be described by identifying the WSs at particular points because of its repetition. Since the WSs at the end of each single support phase are identical, they are considered as a desired WS under the assumptions that the WSs are in steady state and the ZMP variation does not occur when converting the CS into the desired WS. To convert the CS into the desired WS, only one period of the walking configuration is sufficient in steady state, as shown in Fig. 3. The walking configuration can be fully described by initial or final WS for both left and right support phases since the WS is in steady state with no ZMP variation. Notation 1: In the derivation, the following notations are used: xli initial sagittal WS in left support phase; xlf final sagittal WS in left support phase; xri initial sagittal WS in right support phase; xrf final sagittal WS in right support phase. Note that the lateral WSs yli , ylf , yri , and yrf are similarly defined. In the single support phase, the following two state equations are obtained from (1) and (2) with p(t) = 0 and q(t) = 0: Zlf = AT s s l Zli , Zrf = AT s s r Zri (5) with Z = [x y ], At = [ Ct St St Ct ] where t is a variable to denote T ss l or T ss r " ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0002414_j.carbon.2019.08.039-Figure5-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0002414_j.carbon.2019.08.039-Figure5-1.png", "caption": "Fig. 5. Schematic representation of the propulsion mechanism of visible-light-powered CNC figure can be viewed online.)", "texts": [ " E \u00bc hc l ; (1) where h, c, l represent the Planck constant, speed of light, cutoff wavelength, respectively. According to Eq. (1), the band gap energy of TiO2 and CNC/TiO2 nanomotors could be determined as 3.1 eV and 2.48 eV, respectively. The decrease of the band gap energy of CNC/ TiO2 nanomotors indicates that CNCs could act as an electrontransfer channel and thus the photogenerated electrons may transfer to CNCs, which narrowed the band gap of CNC/TiO2 nanomotors and enhanced the photocatalytic activity of TiO2 [32e34]. Fig. 5 shows a schematic of the CNCs/TiO2 nanomotor and the corresponding \u201con-the-fly\u201d water decontamination. Under visiblelight irradiation, the electrons in the CM-TiO2 are activated and enter the conduction band across the forbidden band, leaving holes in the valence band. As the carbon phase of the CNCs accepts photogenerated electrons [35], the photogenerated electrons will transfer to the CNCs and react with hydrogen ions, as described by Reaction 2, and the remaining photogenerated holes will engage in the water oxidation (Reactions 3 and/or 4) [36,37]" ], "surrounding_texts": [] }, { "image_filename": "designv10_9_0000560_j.mechmachtheory.2013.06.001-Figure4-1.png", "original_path": "designv10-9/openalex_figure/designv10_9_0000560_j.mechmachtheory.2013.06.001-Figure4-1.png", "caption": "Fig. 4. Joint error and concept of virtual link. a) Joint error, Dmax \u2212 dmin. b) Virtual rotational link, rv.", "texts": [ " Clearance between the hole and pin at a joint introduces an error in the functioning of mechanism and this error is termed as \u2018joint-error\u2019 in the present work. Though maximum material conditions for hole and pin are critical for assembly purpose, clearance is the maximumwhen hole and pin are at their least material conditions. In other words, maximum hole and minimum pin sizes lead to larger clearance. As the pin can contact the hole at any one point, maximum error of rv will occur at the joint (Fig. 4(a)). In the present work, it is represented by a virtual link of dimension rv and its angular position is taken to vary from 0 to 360\u00b0, as the contact between the pin and hole can occur anywhere along the circumference. In terms of screw theory, a joint-error can be treated as a virtual link connected to an adjacent link by a virtual screw $v (see Fig. 4(b)). In this section, variation in coupler point position is investigated with error in one joint. Four bar mechanism with one virtual link is shown in Fig. 5. Screw $1\u2032 associated with joint-1\u2032 is also shown. Input is given to link-2 and angle \u03b82 is varied. The virtual link ra is very small in comparison with active links and angle \u03b8a is varied from 0 to 360\u00b0, as the contact can occur along any point on the circumference of the hole/pin for every \u03b82. able 2 odrigues parameters for the four-bar mechanism-without manufacturing errors" ], "surrounding_texts": [] } ]