[ { "image_filename": "designv10_11_0003284_0094-114x(94)90025-6-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003284_0094-114x(94)90025-6-Figure4-1.png", "caption": "Fig. 4. Multi-module manipulator.", "texts": [ " I), then all the input links are directed counter-clockwise. In this case the platform rotates clockwise. Analogously, when the links are directed clockwise the platform will move counter-clockwise. This fact must he considered while assembling the manipulator, especially during the assembly of the module type of manipulator. Each of the modules consist of an upper platform and a base connected by six links. The base of each subsequent module is connected with the platform of a previous module (Fig. 4). If the input links of all the modules are assembled in the same direction the platform rotation will be the sum of the rotations of the individual platforms. The number of DOF of a module type manipulator is equal to 3n, where n is number of the modules. The platform in each module can rotate 120 \u00b0 and hence the total rotation of the cod platform will he 120 \u00b0. This consideration can he used to efficiently select the type of modules required to perform certain tasks. $. R E V E R S E D I S P L A C E M E N T A N A L Y S I S The formulation of the reverse displacement analysis is as follows" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003284_0094-114x(94)90025-6-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003284_0094-114x(94)90025-6-Figure5-1.png", "caption": "Fig. 5. The manipulator in the ~tion when the .~int ~ l and 7 are ~ l .", "texts": [ " An important consideration of the reverse problem is to determine the workspace so that the platform joint coordinates can be specified. Here the workspace with respect to the platform center O~ will be determined. MMI' 2911--4 132 RASag L ~ et al. It is clearly a section of the sphere. In addition, as the point O~ moves on the surface of the sphere, it is possible to rotate the platform through an angle y about the axis O~ Z~ (O~ Z \u00b0 and O, Z~ r denotes respectively the initial and current axis positions as shown in Fig. 5). Further, y must lie within the range y..,. ~ y ~ Y,m. At any point OD within the workspace the range of rotation of the platform will be governed by the minimum or maximum values of one of the angles (Pl, ~02 and q~3. As ? --, Ym,, (or y - . y~,) the rotation of the platform approaches zero. There are thus two problems, viz., the determination of the work space boundary and the determination of the rotation angle of the platform for each position of the OZ, axis. Consider that the moving pyramid moves about the base pyramid", " Such a motion is produced by a sequence of joint motions 7, 8 and 9 until the three positions of the joint axes !-7, 2-8 and 3-9 are coaxial. It is clear, that when the top pyramid rotates about the edges of the base pyramid, the point Om rotates in planes, which are perpendicular to these edges and generates circles with radii h, which is equal to the perpendicular from the point O~ to the edge. Therefore, the workspace of the point O, on the sphere is limited by lines of intersection of the three planes, which are parallel to the planes OXY, OYZ and OXZ (Fig. 5). The coordinates of the centers of the circles are An i n - l ~ ~beric4d manipulator 133 / \\ l/, \\2 / \\ x,, '~z 134 RA.~M I. AUZADE et al. The edges 09 and 03 are in contact, and Xo: = - h cos 45 \u00b0, Yo, = r cos =3, Zo, = - h cos 45 \u00b0. (ii) For 7 = 7z=,. The sides ! -0-2 and 7-0-8 are in contact (Fig. 6), and Xo= = \u2022 cos=3, Yo, = - - r sin=4, Zo= = \u2022 cos=3. The sides 2-0-3 and 8-0-9 are in contact, and Xo: = - \u2022 sin =,, Yo, = r cos =3, Zol = r cos =3. The sides 3-0-1 and 9-0-7 are in contact, and Xol = \u2022 cos ~'3, Yol = \u2022 cos =3, Zol = - r sin =4" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000818_tie.2019.2939980-Figure15-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000818_tie.2019.2939980-Figure15-1.png", "caption": "Fig. 15. Structure finite element model of the PM motor.", "texts": [ "0 E le c tr o m a g n e ti c T o rq u e ( N \u00b7m ) Frequency (Hz) Common motor Proposed motor 3.59 3.55 1.1 0.09 (b) Fig.14. Electromagnetic torque of two motors. (a) Waveforms. (b) Spectrum B. Modal Analysis It is necessary to perform the modal analysis before calculating the vibration and deformation of the motors. The modal analysis can predict whether the motor will resonate. When the motor is in resonance, the motor will be severely deformed, which produces significant vibration and noise. The structural finite element model of the PM motor, as shown in Fig. 15, is built to perform the modal analysis. In order to accurately simulate the modal parameters of the proposed motor, the housing, the windings, the stator and the cover are Authorized licensed use limited to: Universiteit van Amsterdam. Downloaded on March 14,2020 at 19:20:38 UTC from IEEE Xplore. Restrictions apply. 0278-0046 (c) 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index", " Vibration Generally, the equation of motion for a damped structural system is [ ] [ ] [ ] ( ) M x C x K x F t (9) where [ ]M ,[ ]C , and [ ]K represent the mass, the damping, and the stiffness matrices, respectively. x , x , and x are the vector of acceleration, the velocity, and the displacement of each mesh point, respectively, and ( )F t is the harmonic forces. These electromagnetic forces are calculated in sections A and projected into the structural model in the form of concentrated force [26]. In the simulation, the motor is constrained by elastic support through the former end-cap, shown in Fig. 15. Fig.16 shows the radial acceleration spectra at nN=3000 r/min under no load. It shows that the significant frequency components of the vibration are the integral multiples of the product of the pole number 2p and the rotation frequency fr (fr= nN /60), i.e. 300Hz, 600Hz, 900Hz\u2026 This agrees well with the analytical results. It can be seen from Fig.16 that the vibration of the proposed motor with additional PM interpoles is dramatically lower than that of the common motor. For example, the amplitude of the vibration with the 1st pole-frequency reduces to 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000034_s12206-016-1103-8-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000034_s12206-016-1103-8-Figure1-1.png", "caption": "Fig. 1. Dynamic model of a gear pair.", "texts": [ " (1) and assuming that ( )0p pmq q= , the angular displacement of the pinion can be expressed as: ( ) 1 1( ) cosi p pm pm pp p i ip t t i t i q q J J w j w \u00a5 = = + - +\u00e5 . (2) Similarly, the drag torque ( )gT t can be expressed via Fou- rier series as follow: ( ) 1 ( ) sink g gm gp p k k T t T T k tw f \u00a5 = = + +\u00e5 , (3) where gmT is the mean part of the drag torque, k gpT and kf are the corresponding amplitude of vibratory part and the initial phase of the thk harmonic, respectively. A conventional dynamic model for a spur gear pair is illustrated in Fig. 1. The spur gear teeth are assumed to be without gear backlash and perfectly involute along their meshing region. The angular velocity of the pinion and gear is given by the ,p gq& . ,p gI is the inertia around the rotation axe of the pinion and gear, respectively. ( )gT t is the drag torque acting on the gear. The pinion and the gear are represented by a rigid disk coupled through normal force and friction force. Introducing the modulated speed of the pinion, the torsional vibration equation for the gear, with time-varying meshing stiffness and sliding friction, can be derived as the following differential equation: 1 1 ( ) ( ) ( ) ( ) ( ) ( ) n n j g j g g g w w f f g j j I t F t R t F t R t T tq = = - - = -\u00e5 \u00e5&& , (4) where ( ), j w fF t is the normal and friction force for the thj meshing tooth pair; ( ), g w fR t is the arm of the normal force and friction force, respectively; n is the number of contacted tooth at any given moment, which is established as: ( ) ( )( )floor floorl p act l pn l L Z l L= + - ", " And the friction forces with a periodically varying coefficient of friction in the meshing tooth pairs are derived as follows: ( ) ( ) ( )sign( )j j j f w sF t t F t um= , 1,2j n= L , (16) where ( )j tm is the time-varying coefficient of friction due to varying mesh properties and lubricant film thickness as the gears roll through a full cycle. Theoretically, it is incorporated with the effects of both dry and lubricant friction. However, lubricant friction has very little effect on gear pair torsional behaviors and the predicted motions are not significant though different friction formulations [6, 21, 22]. Therefore, a constant friction coefficient is still used in this paper. su is the relative sliding velocity [23, 24]: p g s p f g fu R Rq q= -& & . (17) With the equations of motion for the gear system of Fig. 1, the motion of the system is simulated using a discrete timestep algorithm. Since the DTE in the gear system is very small, double precision calculation must be performed to ensure accurate simulation. An extremely small integration step is required when the impact take place because the interval between impacts is very small, and the maximum step maxt-D used for the solid contact is given by: ( )max 2f pt t N Np wD = = , (18) where ft is the time of one excited period cycle, N is the initial resolution of the numerical solution" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003134_robot.1991.131621-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003134_robot.1991.131621-Figure3-1.png", "caption": "Figure 3: The null space solution of 81, 82 and 8 3 are represented by the rotational trajectory of B around AC , where B = 360' - 84", "texts": [ " the base frame, OP5 = P8 - d8 ' a8 (19) Note that Op5 is a function of only 81, 8 2 , 83 and 8 4 , since 85 does not affect O p g , such that OP5 = 5 ( 8 1 , 8 2 , 8 3 1 8 4 ) (20) 2) Once Op5 is obtained by (19), then 84 can be determined directly from Op5, independent of 01, 8 2 , and 8 3 . As shown in Fig.2, 2 2 , 2 4 , 2 3 and 2 4 are perpendicular to 23 (zl = 22 x 2 3 , 24 = z 3 x 24) and, therefore, are on the same plane. Thus, the angle between 22 and 2 4 , L ~ 7 , 2 4 , becomes 84 - 180\u00b0, because L2224 = L x 3 1 4 - L 2 3 2 2 - L ~ 4 x 4 and 1 x 3 1 4 = O4 and L x ~ z ~ = LZ424 = goo. Now, if we form a triangle AABC, as shown in Fig.3, then Lm,m = l 8 O o - (84 - 180O) = 360\u00b0 - 8 4 , and the length of three sides are given by - - AB= d 3 , B C = d5 - AC = I I Op5 - dr . a011 dz + dz - 2d3d5cos(360\u00b0 - 84) = E2 (21) Therefore, 6'4 can be obtained by applying the cosine rule to the triangle AABC defined above: (22) 3) Once 84 is obtained, we can compute 81, 82 and 83 from (20) by O p5 = .f(ol I e2 I o3 , e4= ) 2 ~ 5 =O T Y 1 p 5 = f ' ( @ i 7 8 2 ) (23) To solve (23), we first represent Op.5 = [ Opg2.., OpsY, op5z]T, obtained by (19), in terms of the link 2 frame (24) Note that 2p5 defined by (24) is a function of 81 and 8 2 ", " This implies that (26), (27) and (28) embed one degree of freedom of arm redundancy out of total two degrees of freedom of redundancy provided by the arm. It should be observed from the above that arm redundancy is now distributed to a number of reduced sets of equations, individuals of which can be handled independently. In other words, (26), (27) and (28) form a subset of kinematic equations of a redundant arm that allows to resolve arm redundancy in a reduced dimension. The null space solutions of (26), (27) and (28) are on the rotational trajectory of B around with the fixed position of A and C , as shown in Fig.3 With the underdetermined constraint equations, (26), (27) and (28), 81, 82 and 83 can be obtained by using the parameterization method (refer to Sec.3.3). 4) Once 81, 82, 0 3 , and 84 are obtained, then 8 5 , 86 and 87 can be determined by the following procedure: (a) Represent the given approaching vector of the end-effector, ag , in terms of the link 4 frame: A 4 a g = ( R I R Z R ~ R ~ ) - ' ~ S = [ 4 a 8 x , 4 a 8 y , 4 a s Z l T (29) 4 a g is a function of 81, 8 2 , 6 3 , and 8 4 . (b) Since 8s does not affect ag , 4 a 8 is controlled by 8 5 , 86 and 8 7 " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003478_003-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003478_003-Figure7-1.png", "caption": "Figure 7. Measurement set-up for the bending angle. Note that the scales are distorted.", "texts": [ " Various polyimide curing temperatures and different numbers of V-grooves have been used in our investigations of the static bending angle, \u03b1. Figures 4\u20136 show SEM photos of fabricated test structures with three and seven V-grooves per joint. As shown in figure 2, the test structure consists of a 600 \u00b5m \u00d7 500 \u00b5m \u00d7 30 \u00b5m silicon plate bent out of the wafer plane using a polyimide joint consisting of different numbers of 70 \u00b5m wide and 30 \u00b5m deep V-grooves. The number of V-grooves in each joint varies between one and seven. To measure the bending angle, \u03b1, we used a visible laser aligned parallel to the test structure, as shown in figure 7. The angle, \u03b8 , between the incoming laser beam and the beam reflected from the silicon plate was measured to an accuracy better than 1\u25e6. In figure 8, the bending angle, \u03b1, and the relative vertical shrinkage coefficient for the polyimide, \u03b5, are plotted versus the curing temperature. The vertical shrinkage coefficient was calculated by measuring the thickness of a patterned 20 \u00b5m thick polyimide layer on a flat wafer using a profilometer (Dektak). The thickness after 150 \u25e6C softbake is used as a reference" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003608_9783527618811-Figure3.2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003608_9783527618811-Figure3.2-1.png", "caption": "Fig. 3.2 Reference frames for a gyrocompass on a rotating planet.", "texts": [ " In a principal axis frame at the fixed point the equations of motion are therefore I1\u03c9\u0307 + \u03c9\u00d7 I1\u03c9 = mge3 \u00d7 r 66 3 Dynamics The coordinates of e\u03043 in the body frame depend on the parameters used to parameterize the rotation matrix. We need to include the appropriate kinematic equations such as (2.9) or (2.13). The reaction force can be determined from the equation of motion of the reference point which here is fixed 0 = mr\u0308 = \u2212mge\u03043 + fr \u21d2 fr = mge\u03043. \u2666 Example 3.2 A gyrocompass is a device consisting of an axially symmetric rotor mounted in one or more freely moving gimbals (see Fig. 3.2). Gyrocompasses are key components of nautical, air, and space vehicle navigation and control systems. Here we consider a single gimbal gyrocompass with the rotor axis free to move in the horizontal plane of a rotating spherical planet [13]. That is, the axis about which the gimbal rotates is vertical. We wish to write the equations of motion of the gyrocompass in the frame of the gimbal \u2013 not the rotor \u2013 thereby removing the rapid rotation rate of the rotor from the reference frame. The gimbal is assumed to be massless" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003707_0003-2670(93)80050-u-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003707_0003-2670(93)80050-u-Figure1-1.png", "caption": "Fig 1 Set-ups of the flow-injection systems for the chemilummometnc determination of L-glutamme and L-glutamate using peroxidase as catalyst A = 0 1 M phosphate buffer (pH 7 4 for L-glutamate and pH 6 5 for L-glutamme), B = lummol reagent (for composition, see text), C = pumps (for flow-rates, see text), D = injection valve, E = enzyme reactor (filled with co-immobilized glutaminase/glutamate oxidase for the determination of L-glutamine and filled only with glutamate oxidase for the determination of L-glutamate), F = enzyme reactor filled with immobilized peroxidase, G = flow-through cell, H = mixing coil, I = flow-through peroxidase sensor", "texts": [ "lutamate and glutamine were determined by lummol chemilummescence with flow-injection analysis (FIA) based on immobilized L-glutamate oxidase and glutaminase coupled with peroxidase The laboratory-made flowthrough cell of the detector has a measured volume of only 15 jA The hydrogen peroxide produced in the first reaction is detected by lummol chemilummescence catalysed by peroxidase A membrane sensor and enzyme reactor based on immobilized hydrogen peroxidase are used for the determination of hydrogen peroxide It was observed that Arthromyces ramosus peroxidase produced a 100 times stronger luminescence signal than horseradish peroxidase By immobilization of the microbial peroxidase on a membrane inside the flow cell, simplification could be achieved with regard to apparatus, reagents and operation The sensitivity of detection was considerably improved In addition, the concept of a hydrogen peroxide biosensor was realized The membrane sensor shows a detection limit of 1 x 10 -7 M for L-glutamate and 1 x 10 -6 M for L-glutamine The calibration graphs were approximately linear in the range of 1 x 10 -7-6 x 10 -5 M for L-glutamate and 1 x 10-6-2 5 x 10-3 M for L-glutamine The membrane sensor was stable over a period of 10 weeks (> 1000 analyses) Keywords Biosensors, Chemilummescence, Enzymatic methods, Flow injection, Enzyme reactor, Glutamate, Glut amine L-Glutamate is an economically important biotechnological product It is contained in many kinds of foods and contributes to their enhanced flavour The monitoring of L-glutamate is essen- Correspondence to M -R Kula, Institute of Enzyme Technology, Heinnch Heine University Dusseldorf, P 0 Box 20 50, D(W)-5170 Julich (Germany) 0003-2670/93/$06 00 \u00a9 1993 - Elsevier Science Publishers B V All rights reserved tial for food processing and fermentation control In addition, glutamate levels in blood are determined for clinical diagnosis purposes Several methods have been reported for the enzymatic determination of L-glutamate Yao et al [1], Yamauchi et al [2] and Wollenberger et al [3] proposed amperometric enzyme electrodes with immobilized glutamate oxidase Riedel and 232 Scheller [4] developed an amperometric microbial sensor for L-glutamate Puchades et al [5] described a fluorimetric flow-injection analysis (FIA) method for the determination of L-glutamate dehydrogenase Procedures with autoanalysers have been published for the enzymatic spectrophotometric determination of L-glutamate [6] L-Glutamine is applied in medicine and peptide synthesis [7] Further, the L-glutamine concentration is an important process parameter in animal cell culture Romette and Cooney [8] used a Clark-type enzyme electrode for the determination of L-glutamme to control mammalian cell cultures Renneberg et al [9] proposed a glutamme sensor using co-immobilized glutammase and glutamate oxidase with amperometric hydrogen peroxide detection Dullau and Schugerl [10] determined glutamine photometrically in the FIA mode using glutaminase and glutamine dehydrogenase The determination of hydrogen peroxide by chemiluminescence offers numerous advantages [11-14] compared with other methods Light emission can be quantified at levels over a wide linear working range using relatively simple instrumentation Complexed metal ions and peroxidase are used for catalysis The peroxidase-catalysed hydrogen peroxide-lummol chemilummescence has the additional advantage of higher selectivity because pH values less than 9 can be used [15,16] In this work two different kinetic determinations, based on the ultimate generation G Blankenstem et al /Anal Chum Acta 271 (1993) 231 -237 and detection of hydrogen peroxide with lummol and peroxidase are described L-Glutamine and L-glutamate are enzymatically degraded to yield stoichiometric amounts of hydrogen peroxide as follows Glutamate oxidase and glutaminase were coimmobilized on controlled-pore glass (CPG) for the determination of glutamate and glutamme Peroxidase was either immobilized on CPG or on a preactivated membrane according to AssolantVinet and Coulet [17] The CPG-immobilized enzyme was used in an enzyme column and the membrane was placed in the flow cell of the FIA detector Both systems were compared with regard to sensitivity and speed of analysis EXPERIMENTAL Reagents L-Glutamate oxidase was obtained from Yamasa Shoyu (Choshi, Japan) and microbial peroxidase, MP-9 microperoxidase, glutaminase and L-glutamine + H20 ---> L-glutamate + NH 3 L-glutamate + 02 + H 2O (1) 2-oxoglutarate + NH 3 + H 202 lummol + 2H 20 2 --* hv(425 nm) + 3-aminophthalate (2) + 2H 20 + N2 (3) G Blankenstein et al /Anal Chin Acta 271 (1993) 231-237 luminol from Sigma (Neu-Ulm, Germany) All other chemicals were of analytical-reagent grade (Merck, Darmstadt, Germany) Detection of chemtlummescence The channel of the flow cell is directly faced to the rectangular end of a specially designed fibreoptic bundle (Scholly, Denzlingen, Germany) The other end of the fibre-optic bundle (diameter 4 4 mm) is faced to the window of an Oriel Model 77348 photomultiplier tube (PMT) (L 0 T, Darmstadt, Germany) The PMT, housed in a Oriel Model 70680 housing, is connected via a current preamplifier (Oriel Model 70710) to a readout system (Oriel Model 70701) The PMT was powered by a high-voltage power supply (Oriel Model 70705) The voltage for the PMT was maintained at 800 V The output from the readout was recorded on a Synchronic four-channel pen recorder (Metrawatt, Nurnberg, Germany) Data evaluation in FIA was performed manually by peak-height measurements Signal values are given in relative units, corrected for the sensitivity range of the detector Flow-injection system A schematic flow diagram is presented in Fig 1 The FIA system consisted of two piston pumps (Metrohm, Herisau, Switzerland), a low-pressure injection valve (Rheodyne, Cotati, CA), the luminescence detector described above and Teflon tubing (0 8 mm i d) The flow of reagent and carrier was continuously controlled by a flow meter (Promochem, Wesel, Germany) Preparation of the tmmobthzed enzyme reactor The immobilization of the enzyme was carried out by a modified method described by Yao et al [1] The controlled-pore glass (aminopropyl-CPG, pore size 92 8 nm, particle size 130-250 mesh), obtained from Fluka (Neu-Ulm, Germany), was packed into a column (20 mm x 3 mm i d) A 2 5% (v/v) solution of glutaradehyde in potassium phosphate (0 1 M, pH 7 0) was pumped at 1 ml min-1 for 2 h through the column in order to activate the support After the column had been washed with buffer for 2 h, enzymes were loaded on to the column by recirculating 4 ml of enzyme solution through the column at 0 5 ml min -1 for 24 h at 4\u00b0C The amounts of enzyme and buffer used for immobilization were as follows 2 mg of glutamate oxidase (20 U) and 2 mg of glutaminase (15 U) in 4 ml of 0 1 M phosphate buffer (pH 6 5) were used for the glutamane column and 4 mg of glutamate oxidase (40 U) in 4 ml of 0 1 M phosphate buffer (pH 7 4) for the glutamate column The enzyme column was finally washed with glycine buffer (0 1 M, pH 7 0) for 3 h The enzyme reactor was stored at 4\u00b0C when not in use Construction of the flow-through enzyme membrane sensor The hydrogen peroxide sensor consisted of a flow cell into which a membrane with immobilized peroxidase had been integrated [18] 7 mg of microbial peroxidase dissolved in 200 \u00b5l of buffer solution [phosphate-buffered saline (PBS)] (pH 7 0) containing 137 mM sodium chloride, 2 7 mM potassium chloride, 8 mM disodium hydrogenphosphate and 15 mM potassium dihydrogenphosphate, was immobilized on 15 mm 2 of preactivated membrane (Ultrabind, Gelman Sciences, Ann Arbor, MI) following the manufacturer's instructions A 2 6 x 3 2 cm strip of the membrane was cut and placed in the laboratory-made luminometric flow cell The latter was assembled with the enzyme membrane opposite the rectangular end of the fibre-optic bundle as shown in Fig 2 The cell volume was 15 \u00b5l hf 233 234 The hydrogen peroxide formed by the glutamate oxidase reaction was determined by measurmg the light emitted from excited luminol as catalysed by the microbial peroxidase, immobilized on the membrane RESULTS AND DISCUSSION The determination of glutamate and glutamine is based on hydrogen peroxide detection via luminol chemiluminescence Several peroxidases and hexacyanoferrate(III) were used for hydrogen peroxide determination and compared with respect to sensitivity and reliability Different catalysts for the hydrogen peroxide determination via luminol chemiluminescence were tested in relation to sensitivity, reproducibility and stability Subsequently a hydrogen peroxide biosensor was tested with regard to suitability for chemiluminometric glutamate/ glutamine determination Use of hexacyanoferrate(III) as catalyst for lununol chemtluminometrtc determination of Lglutamate The FIA setup is shown in Fig 3 For the determination of L-glutamate, 200 Al of glutamate standard solution were injected into a buffer stream (A), the reagent solution contained 10 mM luminol (B) and 0 1 M hexacyanoferrate(III) (C) as catalyst for the chemilummescence reaction A high sensitivity (0 001 mM) and a wide linear working range from 0 001 to 1 0 MM L- G Blankenstein et al /Anal Chun Acta 271 (1993) 231-237 glutamate were observed The disadvantages are the high background luminescence and the insufficient selectivity with respect to easily oxidizable substances present in real samples caused by hexacyanoferrate(III) in strongly alkaline solution Use of microperoxidase from equine heart as catalyst for the luminol chemiluminescence L-Glutamate The FIA setup is shown in Fig 1 Experiments were first conducted to establish the optimum pH of the enzyme reactors coupled with the optimum pH of the luminol chemilummescence It must be taken into account that Lglutamate oxidase is not stable at pH 7 5 and the intensity of the lummol chemiluminescence is considerably diminished at pH < 8 5 This was the reason why the glutamate oxidase reactor had to be integrated into the carrier channel of the flow-injection set-up The use of 0 1 M phosphate buffer (pH 7 4) as the carrier solution and 2 5 mM luminol in 0 1 M carbonate buffer (pH 10 4) as the reagent solution was selected for FIA The flow-rates of the carrier and reagent were 0 5 ml min -1 Figure 4 shows a typical calibration with the optimized experimental set-up L-Glutamine The FIA set-up is shown in Fig 1 The pH of the carrier solution was chosen as 6 0, allowing both glutaminase and glutamate oxidase catalysis The reagent solution and the G Blankenstem et al /Anal Chun Acta 271 (1993) 231-237 flow-rates were the same as for L-glutamate, hence the maximum hydrogen peroxide generation could be achieved The use of the stoppedflow technique as proposed by Ruzicka and Hansen [19] leads to an improvement in sensitivity for the FIA assay, as shown m Table 1 The sample concentration profile is stopped in the glutamine enzyme column A stop time of 20 s gives sufficient sensitivity and an acceptable sampling rate Figure 4 shows a typical calibration graph for the determination of L-glutamtne A linear relationship between the increase in hydrogen peroxide and the amount of L-glutamme was observed in the range 0 05-5 0 mM Use of immobilized microbial peroxidase from Arthromyces ramosus as catalyst for the detection of hydrogen peroxide The peroxidase of Arthromyces ramosus was tested Akimoto et al [20] found that microbial peroxidase is a potent catalyst for the chemiluminescence reaction of hydrogen peroxide with luminol, the luminescence produced per unit of microbial peroxidase being well over 100 times stronger than that produced by, for example, horseradish peroxidase Therefore, the influence of different flow-rates on the detector peak height was tested The configuration of the set-up was the same as shown in Fig 1 Increasing flow-rates of the carrier and the reagent channel increased the detector signal (Table 2) This can be explained by the fact that the peroxidase reaction is so rapid that the luminescence emission has decreased considerably before reaching the detector cell Therefore, immobilization of the catalyst within the detector cell should cause much higher 235 sensitivity This can be realized by the flowthrough enzyme membrane sensor as described before Determination of L-glutamate and L-glutamme with the hydrogen peroxide biosensor The microbial peroxidase was immobilized on a pretreated membrane and placed in the flowthrough cell of the luminometric detector as shown in Fig 2 The set-up of the whole system is shown in Fig 1 Typical calibration graphs for L-glutamate and L-glutamine are presented in Fig 5 The analytical time for the measurement of one peak was only 30 s for L-glutamate and 40 s for L-glutamme 236 TABLE 3 Comparison between enzyme reactor and biosensor in relation to range of sensitivity Comparison of the chemiluminometric determination of L-glutamate with other detection methods Table 3 shows a comparison between the Lglutamate and L-glutamine determination using the peroxide biosensor and enzyme reactor method with respect to calibration range, sensitivity and reproducibility The biosensor configurations for L-glutamate and L-glutamine are more sensitive and the reproducibility is better The long-term stability of the peroxide biosensor was tested by over 500 injections of a 15 mM hydrogen peroxide standard solution at a flow-rate of 12 ml min - ' (Fig 6) The decrease in the detector signal after 500 injections was not significant Conclusions L-Glutamate and L-glutamine can be rapidly determined via FIA chemiluminescence detection of hydrogen peroxide Immobilized microbial peroxidase is especially suited for the catalytic oxida- G Blankenstein et al /Anal Chun Acta 271 (1993) 231-237 a Microperoxidase from equine heart was used as catalyst for the chemilummescence reaction b 0 1 M hexacyanoferrate(III) was used as catalyst for the chemilummescence reaction ` Microbial peroxidase from Arthromyces ramosus was used as catalyst for the chemiluminescence reaction tion of luminol by hydrogen peroxide resulting in chemilummescence The use of a hydrogen peroxide membrane sensor with immobilized microbial peroxidase results in a very high sensitivity for glutamate/ glutamine determination with the FIA technique The flow-through reactors packed with immobilized glutamate oxidase/glutaminase are operating at their optimum pH values and ensure the highest sensitivity Very wide linear determination ranges can be achieved The long-term stability of the glutamate oxidase reactor and of the hydrogen peroxide sensor are encouraging for application in bioprocess analytical measurements The authors thank Yamasa Shoyu (Japan) for the L-glutamate oxidase F Preuschoff and U Spohn acknowledge financial support from the Federal Ministry of Research and Technology (0319658A) REFERENCES 1 T Yao, N Kobayashi and T Wasa, Anal Chim Acta, 231 (1990) 121 2 H Yamauchi, H Kusakabe, Y Midorikawa, T Fujishima and A Kuninaka, in Third European Congress on Biotechnology, Vol 1, Verlag Chemie, Weinheim, 1984 p 705 3 U Wollenberger, F W Scheller, A " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003855_j.mechmachtheory.2006.01.006-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003855_j.mechmachtheory.2006.01.006-Figure8-1.png", "caption": "Fig. 8. The architecture of a spatial parallel manipulator.", "texts": [ " In fact, these configurations are the traditional singularities and the CDOF of the mechanism is F conf \u00bc 6 d \u00fe Xm 1 j\u00bc1 Rank $ Fnj E \u00bc 6 2\u00fe Xm 1 j\u00bc1 Rank $ Fnj E P 4 \u00f064\u00de All of the above analysis process can be programmed to instantaneously compute the CDOF of a concept mechanism at a computer. The CDOF of the mechanism under any actuation schemes can be searched throughout its whole workspace by a computer. Besides, the CDOF and the forward displacement problems can be simultaneously cracked by embedding the algorithm proposed in this paper into the CAD software directly. 3.3. Analysis on the mobility properties of the end-effector in a 3-UPU spatial parallel mechanism A spatial parallel mechanism shown in Fig. 8 [14] consists of three identical UPU kinematic chains. In order to investigate the terminal constraints of the kinematic chains connecting the mobile end-effector with the fixed base, we establish a fixed Cartesian coordinate system as Fig. 8 shows. The origin of the coordinate system oxyz is superimposed with the center of universal pair B1, and y-axis is along the midline of the base triangle, x-axis passes through one of the two orthogonal axes of universal pair B1 and the z-axis is perpendicular to the base plane. Assume the length of limb B1P1M1 is l1. The screws of kinematic chain B1P1M1 can be obtained: The universal pair B1 can be decomposed as two orthogonal revolute pairs, one of which is about x-axis. From Fig. 8, we can find that the normal line vector of the universal pair plane can be denoted as eB1 \u00bc \u00bd 0 cos b1 sin b1 \u00f065\u00de Therefore, the other revolute pair of B1 can be expressed as x eB1 \u00bc \u00bd 0 sin b1 cos b1 \u00f066\u00de The individual Plu\u0308cker coordinates are $1 \u00bc \u00f0 1 0 0 0 0 0 \u00de $2 \u00bc \u00f0 0 sin b1 cos b1 0 0 0 \u00de The Plu\u0308cker coordinates of slider P1 are $3 \u00bc \u00f0 0 0 0 xM1 yM1 zM1 \u00de The Plu\u0308cker coordinates for the two revolute pairs of M1 can be denoted as $4 \u00bc \u00f0$1 4; $ 0 4\u00de; $5 \u00bc \u00f0$1 5; $ 0 5\u00de where $ 1 4 \u00bc \u00f0 1 0 0 \u00de; $ 1 5 \u00bc \u00f0 0 sin b1 cos b1 \u00de $ 0 4 \u00bc rB1 $ 1 4 \u00bc \u00f0 0 zM1 yM1 \u00de $ 0 5 \u00bc rB1 $ 1 5 \u00bc \u00f0 yM1 cos b1 \u00fe zM1 sin b1 xM1 cos b1 xM1 sin b1 \u00de Therefore $4 \u00bc \u00f0 1 0 0 0 zM1 yM1 \u00de $5 \u00bc \u00f0 0 sin b1 cos b1 yM1 cos b1 \u00fe zM1 sin b1 xM1 cos b1 xM1 sin b1 \u00de Therefore, the kinematic screws of the limb B1P1M1 can be expressed as $B1P 1M1 \u00bc $1 $2 $3 $4 $5 2 6666664 3 7777775 \u00f067\u00de ) The reciprocal screw of the kinematic chain B1P1M1 can be gained: $ r B1P 1M1 \u00bc \u00f0 0 0 0 0 cos b1 sin b1 \u00de \u00f068\u00de Similarly, we can find the terminal constraints of the rest two kinematic chains: $ r B2P 2M2 \u00bc \u00f0 0 0 0 cos a2 cos b2 sin a2 cos b2 sin b2 \u00de \u00f069\u00de $ r B3P 3M3 \u00bc \u00f0 0 0 0 cos a3 cos b3 sin a3 cos b3 sin b3 \u00de \u00f070\u00de In fact, from Fig. 8 we can find that there are the following equations: a2 \u00bc 5p 6 a3 \u00bc p 6 ( \u00f071\u00de Therefore, the terminal constraints exerted to the end-effector are $r E \u00bc $ r B1P 1M1 $ r B2P 2M2 $r B3P 3M3 2 64 3 75 \u00f072\u00de The free motions the end-effector has, denoted by $ F E , can be solved with Eq. (20): $F E $r E \u00bc 0 If d \u00bc Rank\u00f0$r E\u00de 6\u00bc 3, it is corresponding to the singular cases which were discussed thoroughly in [14]. If d \u00bc Rank\u00f0$r E\u00de \u00bc 3, the number of DOFs of the end-effector is M = 6 d = 6 3 = 3. And we can easily solve the free motions of the end-effector: $ F E \u00bc 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 2 64 3 75 \u00f073\u00de Obviously, the DOFs of the end-effector shown in Fig. 8 include three independent translations along the orthogonal coordinate axes. If we introduce three actuations to the prismatic pairs shown in Fig. 8, the three prismatic pairs can be seen as fixed ones. Therefore, the kinematic screws of kinematic chain B1P1M1 can be rewritten as $ actu B1P 1M1 \u00bc $1 $2 $4 $5 2 6664 3 7775 \u00f074\u00de Therefore, the terminal constraints of kinematic chain B1P1M1 under the actuations can be gained: $r1 B1P 1M1 \u00bc \u00f0 0 0 0 0 cos b1 sin b1 \u00de $ r2 B1P 1M1 \u00bc \u00f0 xM1 yM1 zM1 0 0 0 \u00de ( \u00f075\u00de With similar process, we can find the terminal constraints of the rest two kinematic chains of the endeffector when the four sliders are selected as the actuators in the same Cartesian coordinate system: $ r1 B2P 2M2 \u00bc \u00f0 0 0 0 cos a2 cos b2 sin a2 cos b2 sin b2 \u00de $ r2 B2P 2M2 \u00bc \u00f0 xM2 xB2 yM2 yB2 zM2 zB2 0 0 0 \u00de ( \u00f076\u00de $ r1 B3P 3M3 \u00bc \u00f0 0 0 0 cos a3 cos b3 sin a3 cos b3 sin b3 \u00de $r2 B3P 3M3 \u00bc \u00f0 xM3 xB3 yM3 yB3 zM3 zB3 0 0 0 \u00de ( \u00f077\u00de Therefore, the terminal constraints exerted to the end-effector under the given actuations are $ r E \u00bc $r2 B1P 1M1 $ r2 B2P 2M2 $ r2 B3P 3M3 $ r1 B1P 1M1 $ r1 B2P 2M2 $r1 B3P 3M3 2 666666666664 3 777777777775 \u00bc xM1 yM1 zM1 0 0 0 xM2 xB2 yM2 yB2 zM2 zB2 0 0 0 xM3 xB3 yM3 yB3 zM3 zB3 0 0 0 0 0 0 0 cos b1 sin b1 0 0 0 ffiffi 3 p 2 cos b2 1 2 cos b2 sin b2 0 0 0 ffiffi 3 p 2 cos b3 1 2 cos b3 sin b3 2 6666666664 3 7777777775 \u00f078\u00de If we know the configuration of the mechanism (forward displacement) at any time, we can get a $ r E at this configuration" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001280_j.jmapro.2020.02.045-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001280_j.jmapro.2020.02.045-Figure3-1.png", "caption": "Fig. 3. The integrated WR51 waveguide component in the three configurations.", "texts": [ " Specifically, the L-PBF process has been considered, because it allows the development of metal components already assembled with high density (> 99.5 %), good tensile strength and hardness [13\u201316], and a much lower surface roughness than that obtainable by another PBF process, namely the electron beam melting (EBM) [17\u201320]. With the aim of investigating the miniaturization capabilities offered by the L-PBF process, the integrated component of Fig. 2(a) has been designed for three different values of the bending/twisting radius, that is R equal to 50 mm, 40 mm and 30 mm (Fig. 3). It has to be pointed out that R = 30 mm is the minimum length sufficient to allocate the filter, i.e. the bend and twist are fully merged in the filter without any additional mass or envelope. The three components have been electromagnetically designed and simulated by combining the method described in Peverini et al. [21] and CST Microwave Studio. The CAD model has been converted into a STL file in which the deviation control and the angle control [22] have been chosen, so as to reduce the approximation error and to make the discrepancies negligible between the electromagnetics responses of the two models" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001379_tec.2020.3030042-Figure13-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001379_tec.2020.3030042-Figure13-1.png", "caption": "Fig. 13. 3D structures of the windings.", "texts": [ " Considering the coupling deformation in the axial and circumferential directions, the calculation errors of the natural frequencies of the lower-order circumferential modal slightly increase when the axial modal order m=1, but do not exceed 4%. B. Influence of Windings on the Natural Frequencies of Stator Core According to the method of determining the material parameters of the stator core, the mechanical performance parameters of the windings with slot full radio 74.09% are determined: density \u03c12=4568kg/m3, elastic modulus Er=E\u03b8=1.2GPa, Ez=1.6GPa, shear modulus Gr\u03b8=0.46GPa, Grz= G\u03b8z=5GPa, and Poisson\u2019s ratio \u03bcr\u03b8=\u03bcrz=\u03bc\u03b8z==0.3. The 3D finite element model of the windings is shown in Fig. 13(a). The shape of the copper wire in the stator slot is the same as the shape of the stator slot, and the winding end is equivalent to a cylinder with the same volume as the actual end of the prototype, as shown in Fig. 13(b). The modal shapes of stator core with windings under free vibration are shown in Fig. 14. The natural frequencies corresponding to the different modal shapes are calculated and verified by the FEM and the hammering method, the results are shown in Tab. V. The modal identification function of the stator with windings in test software is shown in Fig. 15. In the analytical calculation of the natural frequencies of the stator with windings, the effect of the stiffness of the end windings is ignored, and the mass is equivalent to the windings in the slot" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003710_0957-4158(92)90043-n-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003710_0957-4158(92)90043-n-Figure1-1.png", "caption": "Fig. 1. Walking mechanism. (I) Suction cup. (~) Pivot. (~) Hinge at ankle. (~ Leg. (~) Hinge at crotch.", "texts": [ " MECHANISM OF THE ROBOT T h e r e are m a n y types of walk ing me c ha n i sms on the g round , such as b i p e d l o c o m o t i o n , four - l egged , s ix- legged, etc. S imi lar ly , the re a re a va r ie ty of me c ha n i sms 543 that can be built for the wall-climbing robots. A biped walking robot with a sucker on each foot is a typical example, and has a simple mechanism. As it has a danger of slipping and falling from the wall surface at any time, its control system is very important for safety on the wall. The simple mechanism shown in Fig. 1 was adopted. It has a hinge and a pivot at the ankle and a hinge at the crotch, so it has five degrees of freedom. The walking motion is shown in Fig. 2. The rotation at the ankle of a fixed cup and inclinations of ankle and crotch are combined and a moving path of free leg is controlled to minimize the moment acti.ng on the fixed cup. The sucking force can be produced without any power when the air seal is kept tight at the periphery of the suction cup. However, this is not always attained on a rough wall surface" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001333_tsmc.2020.3018756-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001333_tsmc.2020.3018756-Figure6-1.png", "caption": "Fig. 6. Structure of the actual continuum manipulator. (a) Mechanical model. (b) Cross section of each module.", "texts": [ " To Authorized licensed use limited to: Cornell University Library. Downloaded on September 15,2020 at 06:44:59 UTC from IEEE Xplore. Restrictions apply. further investigate the performance of the control method, we design, fabricate, and assemble a continuum manipulator system consisting of the prototype of the continuum manipulator and the experimental setup, as shown in Figs. 6 and 7. The prototype of the continuum manipulator, made of pneumatic muscle actuators (PMAs), contains two modules [see Fig. 6(a)]. Each module consists of three contractile PMAs, which are identically arranged in parallel and spaced 120\u25e6 apart, and one central extensor PMA [see Fig. 6(b)]. Both the contractile PMAs and the extensor PMA are manufactured with an inner rubber tube surrounded by a braided sleeve, the difference being that the initial angle of the braided sleeves and the initial lengths are different. To ensure the integrality of each module in motion, the central braided sleeve and three outer braided sleeves are connected with plastic connectors spaced 25 mm apart. By inflation and deflation in different contractile PMAs, each module of the continuum manipulator can be bent in different directions", " Simultaneously, the PMA works with a low frequency. Further details regarding the characteristics of the PMA can be found in [47]\u2013[50]. During the following experiments, we assumed that the characteristics of these homemade PMAs were the same. The curvature was assumed to be constant in each module of the continuum manipulator. To avoid damage to the PMAs, each PMA in this article was required to work at a low air pressure range, from 0 bar to 2 bar. Additionally, two control inputs and two degrees of freedom were considered. As shown in Fig. 6(b), the first module of the continuum manipulator was required to bend along the positive direction of the x-axis when actuator 1 was activated. Next, once both actuators 2 and 3 were inflated together, the second module of the continuum manipulator could be bent along the negative direction of the x-axis. Such an operation is sufficient for evaluating the performance of the presented control method. By using the above experimental setup, the performance of the presented control method was experimentally investigated for the following three cases" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001449_j.mechmachtheory.2021.104396-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001449_j.mechmachtheory.2021.104396-Figure6-1.png", "caption": "Fig. 6. Schematic illustration of designed power-skiving tool showing relation between gear profile surface, generating surface and tool cutting-edge. (a) Meshing of internal gear profile surface with generating surface; (b) tool cutting-edge is intersection curve of generating surface and rake surface.", "texts": [ " (37) , u 2 can be obtained as the following function of u 1 and \u03b8gen : u 2 ( u 1 , \u03b8gen ) = \u2212( r g + x ( u 1 ) ) x \u2032 ( u 1 ) \u2212 ( r g \u03b8gr + y ( u 1 ) ) y \u2032 ( u 1 ) + ( r g \u2212 r t ) ( C( \u03b8gr \u2212 \u03b8gt ) x \u2032 ( u 1 ) + S( \u03b8gr \u2212 \u03b8gt ) y \u2032 ( u 1 ) ) ( C( \u03b8gr \u2212 \u03b8gt ) y \u2032 ( u 1 ) \u2212 S( \u03b8gr \u2212 \u03b8gt ) x \u2032 ( u 1 ) ) T an , (38) where \u03b8gr = \u03b8gr ( u 1 ) is shown in Eq. (34) and \u03b8gt = ( z t / z g ) \u03b8gen . Referring to Fig. 5 , the generating surface t r gen of the tool can be obtained by substituting Eqs. (38) and (34) into Eq. (29) , and transforming r r to frame (xyz) t via the relation t r gen ( u 1 , \u03b8gen ) = t A g g A r r r . (39) ii) Determination of cutting-edge During power-skiving (see Fig. 6 ), only the tool cutting-edge meshes with the gear tooth surface. Therefore, the tool cutting-edge can be considered as an arbitrary curve on the generation surface, t r gen . In the present study, the cutting-edge (i is assumed to be constructed by the intersection of a plane rake surface t R rk , which tilts with a specific direction, with t r gen . Referring to Fig. 7 , t R rk can be obtained mathematically as t R rk ( u rx , u ry ) = Tran (0 , 0 , z of f ) Rot (x, \u03b7x ) Tran (0 , u ry , 0) \u23a1 \u23a2 \u23a2 \u23a3 u rx 0 ( u rx \u2212 r out ) T an\u03c4 1 \u23a4 \u23a5 \u23a5 \u23a6 , (40) where z of f (referred to henceforth as the rake-surface-offset) is the offset of the rake surface from the xy -plane of the tool frame (xyz) t , \u03c4 and \u03b7x determine the rake angle relative to the rake surface, u rx and u ry are the arguments of the rake surface, and r out is the tool outer radius" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003775_int.20062-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003775_int.20062-Figure2-1.png", "caption": "Figure 2. The four possible IP states. Observe the orientation of the respective feedback force.", "texts": [ " u 0 (11) Again, it is equivalent to the closed-loop horizontal force case, whose ODE23 is \\u kd Ml u\u0302 kp Ml M m Ml g u 0 (12) the only remarkable effect of the vertical acceleration being on the root locus of the combined forces case. As is well known, both coefficients must be positive to guarantee stability of Equation 11: kd Ml 0r kd 0; kp ~M m ' m~g ]y!! (13) The first condition has a straightforward interpretation; namely, it implies that the feedback control force, Fx , must have a component directly proportional to the pendulum angular speed u. To illustrate this fact, the four possible states of the IP have been represented in Figure 2. Note that in cases b and d the pendulum is returning to its vertical position, whereas in cases a and c it is moving away from it. In all cases, the orientation of the corresponding control force has been indicated. Note that the vertical force-based IP stabilization can be explained in an intuitive way. When the pendulum is falling, the vertical acceleration ]y strengthens IP stabilization. Inversely, when the platform is ascending to recover its original position, the respective positive vertical acceleration detracts from IP stabilization" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001041_j.ijmecsci.2020.106020-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001041_j.ijmecsci.2020.106020-Figure4-1.png", "caption": "Fig. 4. Cutting velocity of the contact surface between the face gear and shaving cutter during shaving.", "texts": [ " The cutting motion of spur face gear shaving is composed of the slip otion of the meshing tooth surface and the feed motion of the shaving utter along the axial direction of the spur face gears. When the shaving utter is rotating, there is only a slip velocity V . The normal velocity o g A g t d c m s n a t t s 3 3 w i o c c a s s i r i \ud835\udc5f b \ud835\udc5b w p o n m s d p S c o t r a f the tooth surfaces of the shaving cutter V sn is equal to the spur face ear\u2019s V fn ; then, the slip velocity is \ud835\udc49 \ud835\udc60\ud835\udc61 = \ud835\udc49 \ud835\udc60 \u2212 \ud835\udc49 \ud835\udc53\ud835\udc5b , as shown in Fig. 4 (a). feed motion is added in the tooth height direction of the spur face ear to achieve full tooth manufacture. When the spur face gears rotate hrough one circle, the shaving cutters feed once in the tooth height irection of the spur face gears. The displacement of the feed motion is alled the feed amount f r , whose units are mm / r . The rate of the feed otion is called the feed rate V feed , whose units are mm / min . Hence, the having velocity at node P is \ud835\udc49 \ud835\udc5d = \ud835\udc49 \ud835\udc60\ud835\udc61 + \ud835\udc49 \ud835\udc53\ud835\udc52\ud835\udc52\ud835\udc51 . When the feed motion is ot activated, \ud835\udc49 \ud835\udc53\ud835\udc52\ud835\udc52\ud835\udc51 = 0 " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000391_s00170-018-1895-z-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000391_s00170-018-1895-z-Figure1-1.png", "caption": "Fig. 1 Deposition strategies for an unequal width track. a Overlapping multi-tracks (traditional method). b A single track with variable width (new method)", "texts": [ " In LMD technology, the cladding track is the basic unit of forming. Under the condition of fixed process parameters, such as fixed laser power, laser spot size, powder feeding rate, and scanning speed, the cladding track will be deposited with a fixed height and width. The track size of LMD is generally larger than the track size in the selective laser melting (SLM) process [8], which can achieve complex shape forming. This would allow the LMD to have relatively high forming efficiency, but with low forming accuracy (Fig. 1a), and this is only suitable for blank forming at present. By adjusting some process parameters, the track can be deposited with a smaller section size to improve forming accuracy, but this reduces forming efficiency. If the height and width of the track can be varied continuously as needed, both forming accuracy and efficiency can be improved at the same time. Some institutions have researched variable height deposition, including experiential model-based methods [9\u201311], and measurement and closed-loop control-basedmethods [12, 13]", " Two parts with variable width structures were deposited with multi-bead overlapping [18, 19]. However, this open-loop prediction model could not guarantee a precise control of the deposition geometry. Furthermore, the surfaces of the deposited parts were uneven. Xiong et al. developed a closed-loop control system and the actual deposition height and width were under control. A thinwalled part with different deposition widths in different layers was deposited [20]. However, a continuously varying width in a single track was not realized. As shown in Fig. 1a, the traditional multi-track overlapping method in LMD will produce the \u201cstaircase effect\u201d with low forming accuracy and efficiency. The repeated heating of these multi-tracks can possibly cause an uneven distribution of internal thermal stress, cracks, and even collapse the molten pool. In order to improve the forming accuracy, efficiency, and property, the present study developed the method of variable width deposition in a single track, as shown in Fig. 1b. Different from the non-uniform slicing method proposed in other studies [9, 10, 12], this method can be called \u201cnon- uniform line\u201d for 3D forming. A laser cladding nozzle for the variable laser spot and a closed-loop control system were developed to maintain shape accuracy during the LMD process. In order to realize a continuous variable laser spot, a hollow laser beam with internal powder feeding nozzle (HLB-IPF nozzle) was applied, which was developed by Shi et al. [21\u201324]. The principle of this nozzle is shown in Fig", " For the deposition of this kind of structure, only when the deposition heights in different width positions are controlled to be equal, the deposition process can continue with good accuracy. Therefore, deposition height control is essential in variable width deposition. The laser spot diameter in Fig. 2 is the major influence factor of the cladding track width. With matched laser powers in different widths, the cladding track width was controlled using the open-loop method. As shown in Fig. 8, the unequal width and equal height track in Fig. 1b was divided into several segments, and each segment had a certain width. The smaller the set segment length, the greater the segment number, and the better the shape of these combined segments to reach the shape of the unequal width track. Let i be the segment number. The laser spot width should match the segment width along the scanning direction. Therefore, each segment has an independent defocus distance di. During the deposition process, if the nozzle moves from a segment to another segment, the Z-axis of the nozzle should move to change the current defocus distance" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003388_978-3-662-04831-3-Figure5.30-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003388_978-3-662-04831-3-Figure5.30-1.png", "caption": "Fig. 5.30: Vector diagram of a cylindrical joint", "texts": [ "48c) (5.48cl) 5.2.2.6 Cylindrical joint (BB2, BB3; constrains two translational and two rotational DOFs). A cylinclrical joint hetween hoclies i ancl j constrains two rotational DOFs ancl two translational DOFs, where the com mon rotation axes of the two hoclies point into the clirection of the common translational motiono The common rotation axis of the two hoclies are chosen in the exLo; -clirection ancl in the exLo; -clirection of frames LQi ancl LQ; fixecl on the hoclies i ancl j, respectively (Figure 5030)0 Two translational DOFs are eliminated - ancl the relative coorclinate x~~Q; is isolated - hy means of the moclel equations of BB3 (straight-line-point follower constraint in the x-clirection)o Two rotational DOFs are eliminated - ancl the relative coorclinate aji is isolated - hy means of the moclel equations of BB2 (parallel-axes constraint in the x-clirection) 0 This provicles the following moclel equations of a cylindrical joint with a relative motion in ancl arouncl a common x-axis:o 232 5" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000601_j.ijrmhm.2018.02.009-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000601_j.ijrmhm.2018.02.009-Figure1-1.png", "caption": "Fig. 1. Schematic of the Sciaky EBAM process [1].", "texts": [ " Wire feed additive manufacturing technology such as the EBAM system developed by Sciaky are of interest for a variety of applications. The EBAM system is capable of depositing relatively large volumes of metal in a short amount of time. High density desposits require suitable materials and parameters. The Sciaky technique essentially utilizes an electron beam welding machine to deposit material in layers. By building up layers of weld beads, vertical walls or other structures can be built. A schematic of the process is shown in Fig. 1 [1]. Low-carbon arc-cast (LCAC) and powder metallurgy (PM) bars were swaged and drawn down to 1.57mm OD wire per ASTM B387 Types 365 and 361, respectively. LCAC and PM plates were rolled to 12.7 mm thickness per ASTM B386 Types 365 and 361, respectively. Chemistry of all materials were tested via GDMS and IGA (LECO) methodology. Arc-cast wire was deposited onto arc-cast substrates; powder metallurgy wire was deposited onto powder metallurgy substrates. Initial trials depositing LCAC with a Sciaky EBAM 300 system were unstable in continuous electron beam operation mode" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003608_9783527618811-Figure2.1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003608_9783527618811-Figure2.1-1.png", "caption": "Fig. 2.1 (a) The geometry of the rigid body transformation (Rn(\u03b8), a) decomposed into a rotation about an axis containing n and a translation along that axis. (b) The two-dimensional case wherein the rigid body transformation is affected by rotation alone.", "texts": [ " Let v1,v2 be two vectors orthogonal to n such that {v1, v2, n} form an orthonormal basis. In this basis let x = \u03b1v1 + \u03b2v2 + \u03b3n, a = a1v1 + a2v2 + a3n. In this basis R = Re3(\u03b8). Thus 1\u2212 cos \u03b8 sin \u03b8 0 \u2212 sin \u03b8 1\u2212 cos \u03b8 0 0 0 0 \u03b1 \u03b2 \u03b3 = a1 a2 0 44 2 Kinematics, Energy, and Momentum We see that \u03b3 is arbitrary and take it to be zero. The remaining components are obtained from ( 1\u2212 cos \u03b8 sin \u03b8 \u2212 sin \u03b8 1\u2212 cos \u03b8 )( \u03b1 \u03b2 ) = ( a1 a2 ) This linear system is nonsingular if \u03b8 = 0. The geometry of Chasles\u2019 theorem is illustrated in Fig. 2.1(a). The two-dimensional version of Chasles\u2019 theorem has particularly transparent algebraic and geometrical derivations. In two dimensions every rigid body transformation has a fixed point and the axis through this point and perpendicular to the plane is the axis of Chasles\u2019 theorem. If we have in mind a motion of an actual rigid body the fixed point need not lie in the body but we can apply the transformation to all points of the plane and thereby discover the fixed point. Algebraically we find the fixed point p from the equation p = Rp + a which is satisfied by p = (I \u2212 R)\u22121a This is the same problem to which the three-dimensional case reduced. In this case the rigid body transformation does not involve translation along the screw axis. The geometry of the two-dimensional case is illustrated in Fig. 2.1(b). 2.2 Angular Velocity 45 Consider rotational motion of a rigid body, i.e., a rigid body motion leaving one point fixed. Let r(0) be the position of a point in the body at t = 0, r(t) its position at time t, and R(t) the rotation operator which carries r(0) to r(t) r(t) = R(t)r(0) R(t) thus traces the orientation of the rigid body in configuration space SO(3). r\u0307 = R\u0307r(0) = R\u0307R\u22121r or r\u0307 = \u2126r \u2126 = R\u0307R\u22121 (2.3) The operator \u2126 is the angular velocity operator. It is skew-symmetric because 0 = d dt (RRt) = R\u0307Rt +RR\u0307t = \u2126 + \u2126t where the fact thatR\u22121 = Rt has been used" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003990_ias.2006.256728-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003990_ias.2006.256728-Figure1-1.png", "caption": "Fig. 1 3-phase PM brushless machines having different stator winding configurations", "texts": [ "ndex Terms \u2014 permanent magnet machines, noise and vibrations. I. INTRODUCTION Recently, a relatively new topology of 3-phase PM brushless machine, often referred to as \u201cmodular\u201d[1][2][3], has emerged which offers a number of significant advantages over conventional PM brushless machines. Its stator winding differs from that of conventional PM brushless machines in that the coils which belong to each phase are concentrated and wound on adjacent teeth, as illustrated in Fig. 1 (a), so that the phase windings do not overlap. This is not only a distinct manufacturing advantage [4], but is also conducive to a high copper packing factor, and, hence, a high efficiency, and to reducing the likelihood of an inter-phase fault. It also results (a) 24-slot/22-pole, 3-phase machine with modular winding in a smaller number of slots for a given number of poles, e.g. 24-slots for a 22-pole machine, as compared to 33-slots for a conventional 3-phase 22-pole brushless machine having concentrated coils, Fig. 1 (b), and a minimum of 66-slots for 22-pole brushless machine having a distributed winding, Fig. 1-4244-0365-0/06/$20.00 (c) 2006 IEEE 1501 1 (c). Further, the modular winding arrangement gives rise to a high winding factor for the fundamental, while the 5th and 7th emf harmonics are significantly reduced. A modular stator winding also yields a fractional number of slots per pole, with the smallest common multiple between the slot number and the pole number being relatively large. Consequently, the cogging torque can be extremely small without the use of skew [5].Hence, a modular PM brushless machine will have a higher torque capability and a lower torque ripple than PM brushless machines equipped with conventional windings" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003284_0094-114x(94)90025-6-FigureI-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003284_0094-114x(94)90025-6-FigureI-1.png", "caption": "Fig. I. The in-parallel spherical manipulator.", "texts": [ " Their functional capabilities have received much attention from many researchers [I-7]. The extension of spherical mechanism capabilities to produce a variety of complicated motions inevitably leads to mechanisms with a more complicated structure and to an increase in the number of DOF. In order to increase the number of DOF of closed mechanisms, in which inputs are connected to ground, it is necessary to use multi-loop parallel mechanisms. In this paper one type of 3 DOF mechanism is presented (Fig. I). This mechanism is formed by pairs of serial links (I-4, 4-?), (2-5, 5-8), (3-6, 6-9)joining two platforms, a \"top platform\" which is the rigid triangle 7-8-9, and rigid triangle I-2-3 which is the \"base platform\". The i (i = I, 2 . . . . . 9) joints are all revolute joints with axes denoted by the vectors S, ( i -- I, 2 . . . . . 9) . The revolute joint axes all intersect at point O which thus form two pyramids with vertices I-2-3-O and 7-8-9-0 . To provide maximum possible pitch roll and yaw of the platform and to have a symmetrical workspace the lengths of all links are made equal. In addition, the angles between successive revolute joint axes, on each of the three series of links are 90 \u00b0 and the link lengths are chosen to be equal to the sides of the base. Hence the bases of the pyramids arc equilateral triangles I-2-3 and 7-8-9. Further, for example, the sum of links I -4 and 4-7 is greater than the distance between the input link joint I and top platform joint 7. This is why the assembled mechanism has folded links ( I -4 and 4-7) as shown in Fig. I. In general, the mechanism can be assembled in two ways which will be discussed below. The simple structure of the platform yields a simple mathematical model. Moving and stationary right handed coordinate systems O, Xt Y~Z~ and O X Y Z are introduced. The origin O of the stationary system is located at the intersection point of the axes the revolute joints along the edges of the pyramids. The directions of the vectors S~, $9 and $7 at the initial position are coincident with the positive directions of the axes OX, O Z and O Y respectively", "978 -0.070 0.192 -0.121 --0.955 0.270 0.165 -0.288 -0.943 0 60 15 6.74 -$7.16 - 13,98 0.983 0.070 0.167 -0.144 -0.250 0.957 0.102 0.%5 -0.236 15 15 30 -36.07 -40.93 -22.97 0.758 -0.651 -0.031 -0.231 -0.313 0.921 -0.609 -0.691 -0.388 30 45 30 -5.73 -52.58 -26.58 0 .004-0.066-0.083 0.044-0.454 0 .889 -0 .096 -0 .888 -0 .448 75 45 30 36.77 -43.01 17.31 0.746 0.434-0.503 0.238 0.532 0.812 0.621-0.726 0.293 130 ~ 1. A,-7~,c~ et a/. joint 2 to joint 3 and the link 3-6 is directed from joint 3 to joint I (Fig. I), then all the input links are directed counter-clockwise. In this case the platform rotates clockwise. Analogously, when the links are directed clockwise the platform will move counter-clockwise. This fact must he considered while assembling the manipulator, especially during the assembly of the module type of manipulator. Each of the modules consist of an upper platform and a base connected by six links. The base of each subsequent module is connected with the platform of a previous module (Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003388_978-3-662-04831-3-Figure6.1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003388_978-3-662-04831-3-Figure6.1-1.png", "caption": "Fig. 6.1: Geometrical representation of a force F and a torque M", "texts": [ " In this chapter constitutive relations of the gravitational force, translational springs and dampers, torsional springs and dampers, and actuators and mo tors will be briefly discussed. In Beetion 6.1 the model equations offorces and torques acting in a plane or in parallel planes will be considered. In Beetion 6.2 the forces and torques acting in a space will be discussed. These constitutive relations will be extensively used in the applications of Volume II. 6.1 Constitutive relations of planar external forces and torques An external force or torque applied to a rigid body is commonly represented (Figure 6.1 and Section 2.1.1.1) geometrically by an arrow (F, M) and for mally by the relations F = F \u00b7 eF and M = M \u00b7 eM (6.1) with the symbols of the amplitudes F of F and M of M possibly changing their signs, and with the unit vectors eF (in the direction of F) and eM (in the direction of M) . A sign convention states that F (or M) is counted positive, F > 0 (or M > 0), if it acts in the direction of the arrow, and negative otherwise. This implies that a force or torque is geometrically represented as an element of a set of geometrical vectors: (1) that are placed on a common line of action (in the 240 6" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003451_robot.2001.933226-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003451_robot.2001.933226-Figure1-1.png", "caption": "Figure 1 : MINIMAN I11 prototype", "texts": [ " 1996 [4] introduced the microrobots\u2019 motion control approach basing on vision sensors similar to Allegro and Jacot, 1997 [ 5 ] . One can distinguish between coarse motion (i.e. navigation of the robot over a long distance) and fine motion (i.e. manipulation of parts under a microscope). The microscope (here: an SEM) can act as the local sensor system monitoring the robots\u2019 fine motion. For being employed inside the vacuum chamber of a conventional SEM, a special prototype, MINIMAN 111, has been implemented (Figure 1). Like all mobile microrobots developed for the FMMS so far, it consists of a mobile positioning unit that can move across a smooth surface in three degrees of freedom (DOF) and a manipulation unit - here, a steel ball carrying the endeffector - that is mounted on the platform. Both the positioning unit and the manipulation unit are each driven by.three tube-shaped piezoelectric \u201clegs\u201d. By bending these legs coordinately, the robot and the manipulator ball respectively can be moved in any direction" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003950_bf00940771-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003950_bf00940771-Figure1-1.png", "caption": "Fig, 1, Manipulator with two degrees of freedom.", "texts": [ " ) e c\u00a2 such that the upper bound on the tracking error in (30) is arbitrarily small, but nonzero. Remark 3.4. variables, the actual control input to the system may be expressed as v( t ) = ~ ' ( t , q(t), q(t)), (31) where e ' ( t , q, dl) a= jo ( t \" q _ z ( t ) ) [u ' ( t , q - z ( t ) , - ~-(q - z ( t ) ) + 4 - ~ ( t ) ) + ~ ( t ) l ~ ( t ) d / (32) For a given u ' ( . , . , \u2022 ) ~ qg, in terms of the original system 4. Example: Manipulator with Two Degrees of Freedom Consider the two-degrees-of-freedom manipulator (for planar tracking) depicted in Fig. 1. The arm can be extended or retracted (translation controlled by vl) and rotated about the vertical axis (rotation controlled by v2). Considering the load as a point mass, the governing equations are (l~ + M)cjl -[tzq~ + M ( q t + a)](q2) 2 = vl, (33a) [J~+J2+txq2+M(q~+a)2]ij2+2[izq~+M(q~+a)]~t~E12=v2; (33b) here, (ql, q2) are the polar coordinates of the mass center C of the arm;/~ is the mass of the arm; M is the load mass; a is the distance from C to the load; Jl is the moment of inertia of the rotation mechanism about vertical axis through 0; -/2 is the moment of inertia of the arm about vertical axis through C" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003388_978-3-662-04831-3-Figure6.3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003388_978-3-662-04831-3-Figure6.3-1.png", "caption": "Fig. 6.3: A body acted upon by a constant force F ; and moment M ;", "texts": [ "1 Gravitational force (weight) In this context the gravitational field will be assumed to act in the negative eyR direction (Figure 6.2). Then the weight Fwi of a body i is Fwi = -mi \u00b7 g \u00b7 eyR or R ( 0 ) Fw = ' -mi \u00b7g = constant, (6.3a) with g as the gravitational constant. Since the line of action of Fwi meets the center of mass Ci of body i , the force Fwi does not generate a moment with respect to C;; i.e. , M L i -o c iwi = \u00b7 6.1.2 Applied force and moment (6.3b) Consider a force represented by an arrow F i of length Fi through the point P; on body i (Figure 6.3). Then 242 6. Constitutive relations of planar and spatial external forces and torques (6.4a) with the unit vector eF, = exF of frame LF and with as the associated algebraic force vector, or FR = A RL F . FL F = ( c~s 'l/J F , - sin 'ljJ F ) . ( Fi ) , \" 2 Sill 'ljJ F , COS 'l/J F \u00dc (6.4b) and finally and with Fi~ := Fi \u00b7 cos'l/JF The torque Mi of Fi with respect to the point OLi , and represented in frame Li is or 6ol Constitutive relations of planar external forces and torques 243 , Y~;oL,) ( cosV;; L, o " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003110_s0093-6413(03)00088-0-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003110_s0093-6413(03)00088-0-Figure9-1.png", "caption": "Fig. 9. Boundary conditions of the FE models.", "texts": [ " 8 is then given as input to the FE model, allowing the code to produce the aij constants by performing a least square analysis between the Cauchy stress values, as a function of the Mooney\u2013Rivling s constants, and the experimental data. The braided cords wound around the rubber tube were modeled by just one tension bar element having a linear behavior. Their elastic moduli Ef s, namely Ef \u00bc 0:4 Gpa for the McKibben strings and Ef \u00bc 18 GPa for the straight fiber sample, were experimentally determined as well. Only a section of the whole muscle was modeled by FEM taking advantage of cylindrical symmetrical boundary conditions. In Fig. 9 the boundary conditions imposed for both models are diagrammatically represented. The upper muscle cap is subjected to a forced displacement according to the contraction ratio resulting from the lab tests. The models were subjected to an internal pressure according to the lab tests as well. Therefore the loading procedure consists of applying the internal pressure and forcing the displacement at the cap nodes. For both models a consistent displacement was assumed for coincident nodes belonging either to the rubber tube or to the approximately rigid cords" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003125_physrevlett.91.018104-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003125_physrevlett.91.018104-Figure1-1.png", "caption": "FIG. 1. Physical picture of cell growth. (a) Schematic of a model cell with radius of curvature R and wall thickness h, whose growth is driven by the inner fluid pressure P. (b) Stressstrain a (solid line) and growth rate G a (dashed line) curves for the cell wall, which is assumed to be a perfectly plastic material yielding only in extension. The wall is elastic (with modulus E) for a strain a smaller then the yield threshold", "texts": [ " Elastic approaches have also been used for bacteria [9], filamentary bacteria [10], and the algae acetabularia [11]. Previous studies obtained only qualitative results and were focused on specific cell types. Here I consider the whole class of walled cells. I demonstrate that a simple model leads to estimations of cell sizes that are in quantitative agreement with biological data and I investigate the possible shapes of these cells. The starting point is a simplified physical description of a cell (Fig. 1). A liquid (the cytoplasm) is contained in a thin elastic shell (the cell wall). The physical parameters involved are the cell radius of curvature R, the wall thickness h, the elastic modulus of the wall material E, 0031-9007=03=91(1)=018104(4)$20.00 wall are mainly regulated by the cell physiology. In the case of plant cells, it has been established [12] that growth is similar to plastic deformations: the wall behaves as an elastic material below a critical strain ay and grows above by yielding to stress. So, the wall is modeled as a perfectly plastic material [13], which yields in extension and not in compression (see Fig. 1). The cell can also regulate the wall plasticity [12], using hormones such as auxin. When a piece of wall is formed, it has a spontaneous radius of curvature R0 that it would hold in the absence of external forcing. As there are no other macroscopic length scales, one expects R0 R. Finally, the growth is slow: the characteristic time for growth is much larger than the time needed to reach mechanical equilibrium; consequently, the cell is assumed to be in mechanical equilibrium. I first estimate the cell mechanical energy. A thin shell has two modes of deformation, stretching and bending [14]. The stretching energy is proportional to the strain 2003 The American Physical Society 018104-1 squared, but if the material undergoes plastic deformations (see Fig. 1), then energy is stored only below the yield strain ay, so the stretching energy (per unit area) scales as Es Eha2y: (1) The elastic energy (per unit area) for bending is proportional to the square of the difference between the mean curvature and the equilibrium curvature 1=R0 1=R, Eb Eh3 1=R 1=R0 2 Eh3=R2: (2) In bending, the outer half of the wall (with respect to the center of curvature) is elongated while the inner half is compressed. When plastic flow occurs, it is restricted to the outer wall, because the material is considered to yield only in extension (Fig. 1). In this case the effective thickness is reduced in the bending energy; however its order of magnitude remains the same. Finally, the potential energy (per unit surface) corresponding to the turgor pressure is proportional to the volume to area ratio, Et PR: (3) The yield strain for most materials is smaller than 10 2, while the aspect ratio h=R for most cells varies between 10 2 and 10 1. So, it is reasonable to consider the limit where ay h=R, so that Es Eb. In this case, a characteristic cell size results from the balance between bending and pressure (Eb Et): R h E P 1=3 : (4) The best fit to the data compiled in Fig", " This value is larger than the values 0:58 and 0:96 computed in the second part of this paper, but it has the same order of magnitude. This agreement is good given the simplicity of the model; however one might notice a departure from this scaling at small radii (Fig. 2). This motivates the study of the opposite limit ay h=R for bacteria and cochlear hair cells. Indeed, experiments by Koch (see Ref. [9]) have shown that the typical yield strain for Bacillus Subtilis is ay 0:45. In this limit, stretching balances the turgor pressure. The tension of the shell scales as the yield stress Ehay (see Fig. 1). The Laplace law requires P =R, so that R h E P : (5) should be proportional to ay. The fit to the experimental data (Fig. 3) gives 1:0, of the same order as the values 1:8 and 0:9 estimated below. It has been implicitly assumed that the yield strain ay varies very little for this class of cells. The forces generated by electric charges have also been neglected, although they could be comparable to the elastic forces [9]. 018104-2 As the scaling laws are in agreement with biological data, I now investigate a more quantitative description of cell shapes", " One would expect c0 to relax towards the actual curvature 2=R [8] and c0 to assume the smallest possible value. Solving Eq. (9) for c0 yields c0 f R whose minimum is reached at a radius R such that PR3= 8. So, the largest radius R0 which a spherical cell would reach corresponds to a prefactor 0:96 (using 0:5) in the first scaling [Eq. (4)]. If the spontaneous curvature c0 is large enough, it is known [38] that spherical vesicles are first unstable to prolate ellipsoid shapes. Recall that the wall growth rate increases with the stress which is proportional to the curvature (see Fig. 1). If the cell adopts the shape of a prolate ellipsoid, then the growth rate is larger at the tips (they have the largest curvature). So the cell will become more and more elongated. This is consistent with the observation that most cells which satisfy the scaling of Eq. (4) grow in tubular forms (capped cylinders). As a limiting case, I now examine the possibility of tubular growth within the present framework. One can seek axisymmetric shapes intersecting the symmetry axis z and matching (possibly for z" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003238_s0022-0728(98)00049-7-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003238_s0022-0728(98)00049-7-Figure3-1.png", "caption": "Fig. 3. Cyclic voltammograms of a poly 2 electrode (G2=1.77 10\u22128 mol cm\u22122) in CH3CN+0.1 M TBAP; the first scan (a) between \u22120.04 and 0.7 V, then two successive scans (b,c) between \u22121.3 and 1.7 V; scan rate, 0.1 V s\u22121.", "texts": [ " It should be noted that both poly 1 and poly 2 films exhibit the same polymeric skeleton. The bilayer GOx electrode was obtained in the following way. The adsorption and electropolymerization of a GOx\u20131 mixture was performed on an underlying poly 2 film (see Section 2). Since GOx catalyzes the aerobic oxidation of glucose with the concomitant production of hydrogen peroxide, the amperometric detection of glucose was assayed in 0.1 M phosphate buffer (pH 7) by potentiostating the electrode surface. Fig. 3 shows the cyclic voltammograms exhibited by the resulting modified electrode upon transfer into a CH3CN+0.1 M TBAP solution free of monomer 2. In the positive region, the poly 2 film exhibits the electrochemical response of the polypyrrole matrix. The apparent surface coverage of electropolymerized 2, G2=1.77 10\u22128 mol cm\u22122, was determined from the charge recorded under the polypyrrole matrix. On the other hand, if the potential scan range is extended to 1.7 V in the positive region, the cyclic voltammogram exhibits an intensive anodic peak at 1.46 V, which may be due to the overoxidation of the polypyrrolic chains (Fig. 3b) [41]. It should be noted that, on the second scan between \u22121.3 and 1.7 V, the electrochemical response of the polypyrrole backbone has vanished totally (Fig. 3c). Owing to its amphiphilic structure, 2 is soluble in aqueous solutions. Consequently the electropolymerization properties of monomer 2 have been examined by cyclic voltammetry in an aqueous 0.1 M LiClO4 solution. In contrast to the CH3CN medium, a more concentrated solution of 2, namely 10 mM, is necessary to observe a polymer formation on the electrode surface. This formation is illustrated by a continuous increase in the size of the typical reversible peak system of the polypyrrole matrix (Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000784_j.jmatprotec.2019.05.008-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000784_j.jmatprotec.2019.05.008-Figure1-1.png", "caption": "Fig. 1. Illustration of the flow pipe principle and the key geometrical parameters: a) flow pipe used in the production line; b) flow pipe assembled on manipulator clamp; c) fine and fractured flow pipe of the traditionally manufactured samples (including collet and pipeline); d) key geometrical parameters and the reference plane.", "texts": [ " The coating is mostly done by the industrial robots during the flow line of automobile production resulting in a uniform coating layer increasing the lifetime and stability which cannot be achieved by applying coatings manually. Schmidt and Burger (2009) reported that during the coating by the robots, the glue on the parts should be sprayed evenly, smoothly, accurately and efficiently. Volkswagen specifies that after assembly, the vehicle should be coated again and then go through regional fine sealing, so that the glue is coated throughout the body with even coloration. The flow pipes for PVC coating are manufactured using laser welding of titanium alloy pipe, as shown in Fig. 1c, but this process has many shortcomings, and among those are:(i) The walls are so thin (< 0.2 mm) that they can be easily perforated, and the bond strength of the pipe cannot be guaranteed. (ii) It involves the use of special and complicated equipment and clamps for pipe welding. In addition to these, the flow pipes are consumable, so the process becomes expensive. Therefore, we propose a direct manufacturing of the flow pipes using the latest metal 3D printing technique which would improve the pipe strength and shorten the fabrication process", " Considering the difficulties in the manufacturing of the flow pipes by the traditional way and the advantages of the SLM, we have designed and fabricated the complex flow pipe using metal Additive manufacturing. CFD simulation was used for performance evaluation and technical issues critical to SLMbased design and fabrication of the flow pipe were analyzed. The results demonstrate that the proposed method to fabricate the flow pipe is more efficient with improvement in the overall strength of the pipe. Fig. 1a illustrates the coating system. \u201cA\u201d denotes the high-pressure pump responsible for transferring PVC glue to the pressure controller at \u201cB\u201d through the high-pressure pipeline \u201cC\u201d. The industrial robot \u201cD\u201d is programmed to spread the PVC glue and \u201cE\u201d denotes the coating controller. The flow pipe is clamped to the industrial mechanical robotic arm (Fig. 1b). By controlling the direction and location of the outlet at the front end of the flow pipe, the mechanical robotic arm spreads the PVC glue uniformly across the back of the door, trunk cover and hood. Thus, the flow pipe needs to be stretched into the gap of the cover. As the gap between the body and the trunk cover is very small, the outer diameter of the flow pipe also needs to be shorter with a complex structure. Fig. 1b and c shows the flow pipe manufactured from titanium alloy in a traditional way, and in this technique, different sections of pipes are cut and then laser-welded together. The size of the pipes is small with thin walls, so the welded parts have weak joints, as indicated by the arrows in Fig. 1c, this two regions are easy to be fractured also due to that they are the collision place during the PVC coating, which often makes the pipes breakable during the coating process increasing the overall cost. The size and coating performance of the traditionally manufactured flow pipes have been studied extensively. In this study, we focus on the size of the flow pipe as shown in Fig. 1d. From the direction, in which the PVC glue flows within the pipe, it is clear that after leaving the outlet, the PVC glue needs to be smoothed by the plane B to spread it evenly. The surface A of the pipe\u2019s bottom must be in parallel with the coating plane B to produce an even thickness of the PVC glue. In addition, the PVC glue must be smooth and free of cuts, so the coating plane B should have a high-quality surface. Flow collision may arise from the mechanical robotic arm\u2019s bias during the coating process and to avoid this, the flow pipe\u2019s strength must be maintained to improve its service life", " 2c) with an average particle size of 32 \u03bcm (Fig. 2d). Our SLM optimized parameters were: 180W laser power, 1200mm/s scanning speed, 25 \u03bcm layer thickness, 80 \u03bcm hatch space, 80 \u03bcm spot diameter as well as using the raster scanning strategy. a) Parameters for optimized flow pipe design The flow pipe for PVC coating consists of a pipeline and a collet. The former is responsible for guiding the PVC glue flow within the pipe and coating the PVC glue via the tail end. By measuring the original size of the flow pipe (Fig. 1d), we determine the assembly dimension of collet for the easy clamping by the mechanical robotic arm, as well as the length and diameter of each part in the pipeline. During the optimization of the flow pipe design, the following problems should be focused. 1) Can the metal supports, which is hard to remove afterward, be avoided or easily removed? 2) How much thin are the walls that can be fabricated? 3) Will the coating uniformity be affected by tough surface at the outlet? The following experimental steps are planned to find the answers to these questions", " Based on the analysis and experimental results presented above, the key points in designing the flow pipe can be summarized as follows. (1) It is critical to improve the hardness and to reduce the stress at the breakpoint of the welded pipeline (the red point in Fig. 5b). In the traditionally fabricated flow pipe, the welding point is weak and prone to fracture. Therefore, the welding point in the new PVC flow pipe was designed to have an arc shape, as shown in Fig. 5d. (2) It is important for the outlet at the tail of the flow pipe and nearby to have good surface quality (Fig. 1c and d). Surface smoothness and processing quality of the outlet have a direct effect on PVC coating quality. Dai and Gu (2015) had investigated that during SLM fabrication, the upper surface quality is usually better than the lower surface. Therefore, the outlet at the tail of the flow pipe should be placed upwards, as shown in Fig. 8a. (3) It is essential to assure the good laser welding quality of the flow pipe and collet. The laser welding process is usually accompanied by the high-energy laser intensity, which is likely to penetrate the thin pipe wall and result in pores" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003083_1.1285943-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003083_1.1285943-Figure6-1.png", "caption": "Fig. 6 Loads on the modified section of the outer ring", "texts": [ " To monitor load and vibration within the bearing structure, a piezoelectric sensor is embedded into a slot cut through the outer ring. The sensor has solid contact with both the top of the slot and the bearing housing. Each time a rolling element passes over the slot, the sensor generates an electrical charge output that is proportional to the load applied to the bearing, Fr . Since the outer ring is structurally supported by the bearing housing, it can be assumed to be rigid. The piezoelectric sensor can be modeled as a spring with a stiffness constant k that is related to its material composition. As shown in Fig. 6, the section of the bearing outer ring where the slot is cut can be modeled as a beam of varying cross-section, with a spring support at the midpoint. To establish the structural model, boundary conditions must first be assigned. Since the ends of the beam are solidly connected to the surrounding bearing structure, which is directly supported by a rigid housing, clamped boundary conditions are considered appropriate. This model is shown in Fig. 7. Furthermore, the segment of the ring encompassed by the slot subtends an angle of 2 sin21(L/D) 52cmax512 deg" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003608_9783527618811-Figure7.5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003608_9783527618811-Figure7.5-1.png", "caption": "Fig. 7.5 A plane chain of two links specified by angles \u03b81, \u03b82 and center of mass coordinates (x1, y1) and (x2, y2).", "texts": [ " Let the length, mass, and inertia tensor relative to the center of mass of link i be Li, mi and Ii, respectively, with i = 1, 2 and let the links and joints be labeled serially from the anchor point. Let the distance from joint i to the center of mass of link i be denoted by ai and let bi = Li \u2212 ai. Clearly, these conventions could also describe a chain of an arbitrary number of links. The general technique we wish to explore involves deriving the Lagrangian in terms of orientation angles \u03b8i and center of mass coordinates (xi, yi) (Fig. 7.5). We will use the center of mass as the reference point for each link. Thus we obtain the Lagrangian L(\u03b81, \u03b82, x\u03071, y\u03071, \u03b8\u03071, x\u03072, y\u03072, \u03b8\u03072) = 1 2 m1(x\u03072 1 + y\u03072 1) + I1\u03b8\u03072 1 + 1 2 m2(x\u03072 2 + y\u03072 2) + I2\u03b8\u03072 2 \u2212m1ga1 sin \u03b81 \u2212m2ga2 sin(\u03b81 + \u03b82) To complete the problem specification we need to impose constraints which produce a chain. These constraints are holonomic and are four in number x1 \u2212 a1 cos \u03b81 = 0 y1 \u2212 a1 sin \u03b81 = 0 x1 + b1 cos \u03b81 \u2212 x2 + a2 cos(\u03b81 + \u03b82) = 0 y1 + b1 sin \u03b81 \u2212 y2 + a2 sin(\u03b81 + \u03b82) = 0 7" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000936_j.mechmachtheory.2019.103607-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000936_j.mechmachtheory.2019.103607-Figure3-1.png", "caption": "Fig. 3. Schematic of the whole helical gear-shaft system: (a) the multibody dynamic model, and its topology of (b) generalized forces and (c) Jacobian matrix. Note that the four body columns in (b) represent the generalized forces of gear, pinion, and shaft-1(2), respectively; five constraint columns represent the fixed joints between gear (pinion) and shaft-1(2), connections between shaft-1(2) and ground, and driving motion; load column is the resistant torque; contact column is the interaction between gear pair.", "texts": [ " The helical gear-shaft system, a typical flexible multibody system, can be readily modeled using multibody dynamics, which has been developed as a powerful tool in the design and analysis of a variety of mechanisms such as automobile vehicles [41] , robots [42] , and precision machines [43] . Multibody dynamics studies the mechanical behaviors of multiple inter-connected bodies that may undergo large deformations and come into contact with each other, and body, constraint (connection), and load are three key components in multibody dynamics modeling. The schematic and topology of the whole gear system, which consists of two main components \u2013 helical gears and shafts \u2013 and the connection (interaction) between them, are shown in Fig. 3 (a\u2013c). (i) The helical gear pair is modeled by the 3D solid elements, which contributes to the majority of system DOFs. To reduce the computational cost while preserving the accuracy, the ALE-like helical gear model is developed. First, the low-frequency approximation technique is adopted, where the contribution of fixed boundary normal modes is ignored while only the constraint modes are considered, as shown in Fig. 2 (a). Then, under the framework of ALE formulation, the DOFs of a helical gear are further minimized to the modal coordinates of three engaging tooth-faces, as illustrated in Fig", " The slight difference might arise from the contact algorithm, as our in-house code uses point-surface contact algorithm while ABAQUS is based on surface-surface contact [44] . Additionally, the results of vertical displacement U y and twist angle \u03b8 along the gear shaft obtained using these two formulations also show a great agreement, as illustrated in Fig. 14 (j\u2013k), and the global NRMSD is shown in Table 5 . Table 6 compares the reaction force and moment at B, where the difference is less than 2.5%. In this example, the influence of tooth-change threshold t c is studied. As illustrated in Fig. 3 (a), the simulation is performed by applying a rotational velocity \u03c9 = \u221210 \u00d7 step (0 , 0 , 0 . 1 , 1) RPM to D of the gear shaft and a resistant torque M = \u2212500 \u00d7 step (0 , 0 , 0 . 1 , 1) Nm to B of the pinion shaft. The acceleration time is 0.1s and total simulation time is t = 3s, which approximately covers the engagement process of 15 teeth. In this example, the nodes of three pairs of tooth-faces are defined as boundary nodes, i.e., tooth-faces 1B, 2B, and 3B of the pinion and tooth-faces 1A, 2A, and 3A of the gear", " This phenomenon is caused by the shapes of contact area between meshing gears, which are actually contact bands [60] , not the theoretical contact lines, as shown in Fig. 15 (a). Theoretically, for the sake of simplicity, the contact line assumption is used to derive the contact ratio of any helical gear pair. However, as a matter of fact, the contact lines are actually a series of bands, whose widths are larger than zero. The width of contact bands is determined by the applied torque and contact stiffness between gear pair, which results in the difference of \u201ctooth-change\u201d thresholds between numerical analysis and theory. As illustrated in Fig. 3 (a), the model is the same as the one studied in Section 3.3 . The only difference lies in the total simulation time, which is changed to t = 10s that approximately covers the engagement process of 50 teeth (about 2 . 5 = 50 / 20 cycles for pinion and 1 . 67 = 50 / 30 cycles for gear). The tooth-change threshold is adopted as t\u0304 c = 0 . 5 , so the toothchange process is implemented at a series of time instants: t\u0304 (i ) c = i + 0 . 5 , i = 0 , 1 , 2 . . . . For clear illustration, we recorded a time-elapse movie for the simulation based on the ALE formulation, see movie S1" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001327_s00170-020-05927-1-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001327_s00170-020-05927-1-Figure1-1.png", "caption": "Fig. 1 Face gear grinding", "texts": [ " Based on the research of the above experts and scholars, in order to further improve the grinding processing efficiency of face gear, this paper proposes a novel method for grinding face gear with disk CBN grinding wheels. The rest of this paper is organized as follow: Section 2 introduces the face gear NC grinding model construction. Section 3 leads to a new face gear NC generating grinding method based on machine tool structure. Section 4 presents the disk CBN wheel grinding face gear along path of contact. The face gear machining test is provided in Section 5, and the conclusions are drawn in Section 6. The principle of disk CBN wheel grinding face gear is shown in Fig. 1. The disk CBN wheel meshes with the face gear by simulating one tooth of the pinion. The rotation parameters of the grinding wheel and the face gear satisfy as: \u03c9 f \u03c9s \u00bc Ns N f \u00f01\u00de where Ns and Nf are the number of teeth of the virtual pinion and the face gear and\u03c9s and\u03c9f are the meshing rotation speeds of the virtual pinion and the face gear, respectively. The principle of rack processing pinion is shown in Fig. 2. \u03bct is the rack profile parameter, \u03b3t is the rack pressure angle, lt = \u03c0m cos \u03b3t/4 is the distance from the rack coordinate origin to the rack profile, st = \u03c0m/2 is the slot width, andm is the rack modulus" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001553_j.matdes.2021.109608-Figure10-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001553_j.matdes.2021.109608-Figure10-1.png", "caption": "Fig. 10. Schematic illustrating the martensite austenite arrangement in the material.", "texts": [ " In Fe-based martensite, there is an anisotropy in the elastic properties and as such also a strong influence of the texture on thermal conductivity. Souissi andNumakura assessed these to be in the order of 160GPa in the [100] direction and 230 GPa in the [110] direction [18]. The thermal conductivity would therefore be lower in the [110] than in the [100] direction. This contradicts the current measurements so that the texture in the martensite is not the direct reason for the anisotropy in thermal conductivity on the printedmaterial resulting in a situation as described in Fig. 10. The anisotropy is significant and requires the influence in dominant phases and cannot be due to a minority effect. This thus implies that there may be an orientation relationship between the austenite and the Laves phase during precipitation that may cause this variation, or it is driven by imperfections in the fuse lines between the layers. In terms of crystallographic orientation relationship between the Laves phase and the austenitic matrix has been reported as (10\u221213) Fe2Nb || (111)\u03b3, [\u221212\u221210]Fe2Mo || [\u221212\u22121] \u03b3 and (0001) Fe2Nb || (111) \u03b3, [10] Fe2Nb || [\u2212110] \u03b3" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003876_978-1-4612-4990-0-Figure16-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003876_978-1-4612-4990-0-Figure16-1.png", "caption": "Figure 16. The limits of motion for the foot as defined by the hip joint and actuators.: The diamond is not actually planar, as shown here, but lies rather on the surface of the sphere defined by motion about the hip.", "texts": [ "........ 13 Figure II. Illustration of the advantage of a rear-to-front strategy over a frontto-rear strategy. ........................... 15 Figure 12. Comparison of the cockroach nervous system with a microcomputer. 16 Figure 13. Three views of a leg from the walking machine. ............... 24 Figure 14. The hydraulic ellipse. .................................... 26 Figure 15. Table showing all of the hip valve settings that are provided by the walking machine. .......................... 28 Figure 16. The limits of motion for the foot as defined by the hip joint and actuators. ................................ 29 Figure 17. The natural motions of the machine. ........................ 30 Figure 18. Single ended cylinder. ................................... 32 Figure 19. Double ended cylinder. .................................. 32 Figure 20. Parts of a spool valve. ................................... 33 Figure 2I. Spool valve with left solenoid activated. ..................... 34 Figure 22. Spool valve with right solenoid activated", " In the Energize setting the direction of pumping set by the operator determines which of the two cylinders lengthens and which shortens. What the Energize and Coast settings really do is ensure that when one cylinder lengthens, the other shortens by the same amount. The settings shown in Figure 15 produce motions of the upper leg about the hip joint that are illustrated in Figure 17. The limits of motion of the hydraulic cylinders define a diamond shaped region on the surface of the sphere defined by the hip joint, as illustrated in Figure 16. The motion illustrated is of the knee joint as viewed from a point to the left of the driver. It is important to note that in the Lift and Place settings both cylinders are being driven in parallel, which results in a nondeterminacy in the motion of the leg, since the cylinder with less friction will move first. 4.2.2 Knee control There are four useful settings for the valves controlling the knee cylinder. There are Right and Left, which move the foot to the driver's right or left powered by the re covery pump" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000734_j.jmapro.2019.10.011-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000734_j.jmapro.2019.10.011-Figure2-1.png", "caption": "Fig. 2. A cross-section of a single-channel cladding layer.", "texts": [ " For better presentation of powder feed rate, another unit (rpm) is provided corresponding to the analysis results described in Section 3. Two responses were evaluated during the fabrication: shape factor ( ) and dilution rate (D). They can be calculated using the following equation: = b H/ (1) Table 3 Design of full factorial experiment and responses of and D. No. P(W) VS(mm/s) Vf (g/min) G(L/min) D 19 350.00 6.00 13.11 15.00 2.7890 0.3562 where b is the width of cladding layer; H is the height of cladding layer; h is the depth of mixed molten area (Fig. 2), measured from the metallographic cross-section of the build after polishing and chemical corrosion using an Olympus laser confocal instrument (light source 405-nm semiconductor laser zoom, optical zoom 1\u20138x, total magnification 108\u201317280x). For each processing condition, each experiment was repeated three times to reduce the random error and follow the experimental principles. All the factors are shown in Table 3. The mean value of three repeated experiments was considered as the measurement result" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000995_1464419320915006-Figure12-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000995_1464419320915006-Figure12-1.png", "caption": "Figure 12. Pre-processing of FE model of housing.", "texts": [ " Bearing nodes of gear transmission system are connected with bearing seats of housing through the bearing stiffness matrix Kb and bearing damping matrix Cb, which can be expressed as Kb \u00bc kxx kxy kxz kx x kx y 0 kyx kyy kyz ky x ky y 0 kzx kzy kz kz x kz y 0 k xx k xy k z k x k y 0 k x k yy k z k , x k y 0 0 0 0 0 0 0 2 666666664 3 777777775 \u00f025\u00de Cb \u00bc cxx cxy cxz cx x cx y 0 cyx cyy cyz cy x cy y 0 czx czy cz cz x cz y 0 c xx c xy c z c x c y 0 c x c yy c z c , x c y 0 0 0 0 0 0 0 2 666666664 3 777777775 \u00f026\u00de The differential equation of motion of bearing element is as follows Mb \u20acqb \u00fe Cb _qb \u00fe Kbqb \u00bc 0 \u00f027\u00de FE model of housing is connected to bearing nodes and grounded at fixed points such as bolt holes. Therefore, condensation nodes are created in all bearing centers in the housing FE model, and these nodes are coupled with corresponding bearing outer ring, as shown in Figure 12. The boundary conditions of housing are set to constrain all DOFs at fixed points such as bolt holes of housing. Based on dynamic substructure theory, finite element model of housing is condensed, and mass matrix Mh and stiffness matrix Kh of condensation nodes are obtained, and damping matrix Ch of housing can be obtained by Rayleigh damping. The differential equation of motion of housing element is Mh \u20acqh \u00fe Ch _q h \u00fe Khqh \u00bc 0 \u00f028\u00de Dynamics model of gear transmission system After establishing the dynamic model of each part, all parts of gear system can be assembled, that is, dynamic equations of gear mesh element, shaft element, and bearing element are connected to obtain the overall system dynamic equation M\u20acq\u00fe C_q\u00fe Kq \u00bc 0 \u00f029\u00de where M, C, and K are mass matrix, damping matrix, and stiffness matrix of gear system, respectively, and q is the displacement vector of node" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000136_tie.2018.2868018-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000136_tie.2018.2868018-Figure3-1.png", "caption": "Fig 3 Flux distribution twisted by armature reaction in MM at starting mode", "texts": [ " assume the shifting angle of \ud835\udc3f and \ud835\udc40 are 2\u03b1 and \u03b2 , respectively. Therefore, the electrical degree \ud835\udf03 of transition matrix does not equal to the electrical degree \ud835\udf03 any more, then the matrix \ud835\udc3f can\u2019t be changed to diagonal matrix \ud835\udc3f under the d-q coordinate transformation, and the mutual inductance \ud835\udc3f and \ud835\udc40 will appear. In loaded operation, the centers of the actual permeance distributions are not easy to show, but the flux distribution twisted by armature reaction can be obviously noticed, for example in Fig.3. According to above-mentioned analysis, when the permeance of stator, rotor and air gap are affected by armature reaction, the \ud835\udf03 in inductance matrix \ud835\udc3f should be replaced by \ud835\udf03 2\u03b1 and \ud835\udf03 \u03b2, and the expressions of matrix \ud835\udc3f\u2217 can be obtained as (6). For this operation mode, \u03b1 and \u03b2 are negative values. With the d-q coordinate transformation, the matrix \ud835\udc3f\u2217 can be derived as (7). \ud835\udc3f\u2217 , \ud835\udc3f\u2217 and the mutual cross-coupling inductance \ud835\udc3f\u2217 are expressed as (8). Differently from the traditional methods [14][18][21], in the proposed method, to get the full information of selfinductance curve, stepping the rotor through 360 degrees is needed" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001319_tec.2020.3007802-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001319_tec.2020.3007802-Figure6-1.png", "caption": "Fig. 6. FEM model of motors of (a) 10p/12s, (b) 6p/36s.", "texts": [ " Stator cylinder yoke 0 Force density on top of teeth 0 2 Force density on yoke fr\uff0cPM2(36\u03b8,t) Teeth Radial direction Circumferential direction 1 2 3 4 5 6 7 8 9 35 36 0 0 0 0 3 2 1 2 1 3 ,r PMf ,ry PMf ,r PMf ,ry PMf HH \u00b7\u00b7\u00b7 \u00b7\u00b7\u00b7 \u00b7\u00b7\u00b7 \u00b7\u00b7\u00b7 \u00b7\u00b7\u00b7 1 Fig.4. Transfer process of force density for integer slot PM motors. 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 k r 1 (0.22,0.1382) Fig.5. Variation of kr with the slot open coefficient for the 6p/36s motor. V. SIMULATION ANALYSIS In order to verify the analysis above, a 10p/12s fractional slot PM motor and a 6p/36s integer slot PM motor are used as examples and prototyped for experimental tests. Their 2-D FEM models are shown in Fig.6. The electromagnetic radial forces on the stator teeth are loaded onto the stator teeth of the 3-D structural finite element model. The housing and the winding are considered and the motor is constrained by elastic support through the end face. In the simulation, the speed is 600 r/min in the 10p/12s PM motor and 1500 r/min in the 6p/36s PM motor. The damping ratio used in simulation is 0.02 in the 10p/12s motor and 0.03 in the 6p/36s motor. The damping ratio can be extracted from the modal test [5]" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000892_14763141.2019.1586983-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000892_14763141.2019.1586983-Figure2-1.png", "caption": "Figure 2. Key golfer\u2013ground interaction moments: the ground reaction force (GRF) moments in the frontal plane (a) and the pivoting moments about the combined centre of pressure (CP) in the horizontal plane (b). F, FL and FT are the combined, lead-foot and trail-foot GRFs, respectively, and dx , \u03c1L and \u03c1T are the moment arms formed by the combined, lead-foot and trail-foot GRFs, respectively, either against the centre of mass (CM) (a) or the combined CP (b). dL is the moment arm formed by the lead-foot GRF about the CM in the frontal plane. In both planes, a positive (counterclockwise) moment is in the downswing direction, promoting either acceleration of the downswing or deceleration of the backswing. GRF components (Fx; Fy; Fz) and their respective moment arms against the CM and combined CP are also presented.", "texts": [ " The x-axis and the y-axis of the reference frame correspond to the forward/ backward (F/B) axis and the toward/away (T/A) axis, respectively (Figures 1 and 2). Fyz; Fzx; Fxy are the magnitudes of the combined GRF projected to the yz-plane, zx-plane and xy-plane, respectively, Fxyi is the magnitude of the xy-component of a foot GRF, and \u03c4i is the vertical free moment acting on a foot. dx; dy; dz are the moment arms formed by the combined GRF with respect to the systemCM in the yz-, zx- and xy-plane, respectively, while \u03c1i is the moment arm formed by a horizontal GRF with respect to the combined CP on the horizontal plane (Figure 2). The moment arms hold positive values if the resulting moments are counterclockwise, and vice versa. Equation (3) was derived from the definition of the combined CP. Equation (2) can be rewritten as M \u00bc G\u00fe P\u00fe C \u00bc Gx Gy Gz 2 4 3 5\u00fe 0 0 Pz 2 4 3 5\u00fe 0 0 Cz 2 4 3 5 (4) where G is the GRF moment generated by the combined GRF about the golfer-body CM (Figure 2(a)), P is the pivoting moment generated by the horizontal GRFs about the combined CP (Figure 2(b)), and C is the foot contact moment acting directly on the feet. These 3 moment terms in Equation (4) represent different moment generation mechanisms. As shown in Equations (2) and (3), the horizontal moment components (Gx;Gy) can be explained entirely by the GRF moment mechanism, but the vertical moment comes from all 3 mechanisms (Gz \u00fe Pz \u00fe Cz). Sixty-three highly skilled male golfers (handicap \u2264 3), including touring professionals, elite amateur (collegiate) players and teaching professionals, participated in this study: M (\u00b1SD) mass = 83", " With an inclined functional swing plane aligned closely towards the target (Kwon et al., 2012), the F/B axis and the vertical axis become the main axes of rotation. It is clear from the moment profiles that highly skilled male golfers generate the rotations about the F/B axis and the vertical axis by using the GRF moment mechanism and the pivoting moment mechanism, respectively. The majority of the GRF moment about the F/B axis was derived from the lead foot (Figure 6(a)), as the lead-foot GRF vector formed a long moment arm against the body CM near EDA (dL in Figure 2(a)) due to substantial loading on the lead foot. This moment arm must be sensitive to the T/A component of the lead-foot GRF (FyL in Figure 2(a)), as it forms a long moment arm about the CM (i.e., the height of the CM). The line of action of the trailfoot GRF at this position, in contrast, remained close to the body CM. The magnitude of the trail-foot GRF moment about the F/B axis therefore became small and the direction was typically opposite to that of the lead-foot moment (Figure 2(a)). The trail foot, however, was characterised by a greater contribution to the pivoting moment (Figure 6(b)). The pivoting moment was primarily generated by the F/B GRFs of the feet, as the lines of action of the T/A GRFs stayed close to the combined CP (Figure 2(b)). Although the magnitude of the trail-foot forward GRF was smaller than that of the lead-foot backward GRF near EDA (Figure 5(a)), the trail-foot pivoting moment arm must be much longer due to a much larger vertical GRF acting on the lead foot at this point (Figures 2(b) and 5(c)). The trail foot thus generated a larger pivoting moment, utilising a longer moment arm. In summary, it appears that the primary angular role of the lead foot is to generate a large GRF moment about the F/B axis, while that of the trail foot is to generate a large pivoting moment about the vertical axis" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000030_rcs.1786-Figure19-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000030_rcs.1786-Figure19-1.png", "caption": "FIGURE 19 Blocking the fractured limb at the forearm", "texts": [ " We, hereafter, detail the procedures: (i) B_BROS2_reduce_II (A, B, C, D): it performs the reduction of a type II fracture and takes into account the coordinates of the fracture. Figure 18 illustrates a robotized fracture reduction, (ii) B_BROS2_unblock_II (): this procedure unblocks the patient\u2019s limb suffering from a type II fracture once the surgery is completed, (iii) B_BROS2_reduce_III (A, B): it computes the rotation angle of the rotary disorder in the case of a type III fracture and, then, reduces the latter, (iv) B_BROS2_block (): the procedure blocks the limb at the forearm once a manual reduction is performed during SAM or DMB. Figure 19 shows how this is performed. This section describes the behavior of P\u2010BROS, the robotic arm performing fracture reduction according to its type and the triggered operating mode. We point out that the pinning technique used is Judet\u2019s.48 The orientation of the tool \u2018Pinning\u2019 (section 5.3.2), relative to the coordinate system, depends on the type of the fracture. Thus, the Figure 20 shows the orientation of \u2018Pinning\u2019 in the case of a type III fracture. The P\u2010BROS module features several procedures that we hereafter detail: (i) P_BROS_DoublePin (A, B, C, D, HP): it performs parallel pinning using two pins inserted from the external condyle to the lateral humeral column in the case of a type II fracture which requires a double pinning" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003827_tmag.2006.879068-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003827_tmag.2006.879068-Figure1-1.png", "caption": "Fig. 1. Machine cross section.", "texts": [ " However, in the doubly-fed application, the rotor experiences rotating flux waves which can produce lamination eddy currents which could cause excess losses. Shulz et al., [5] suggested that the axially-laminated rotor experiences very high eddy current loss in the laminations and that radially-laminated rotor are more suitable. This paper seeks to investigate this. Digital Object Identifier 10.1109/TMAG.2006.879068 The machine is modeled using Cedrat FLUX 2D. The rotor laminations are axial and modeled individually which produces a very dense mesh (Fig. 1). The laminations are stacked and form a \u201cU\u201d shape. There is spacing between the laminations to produce high axis reluctance. In this machine, the stacking factor is 0.5. The other modeling alternative is to use anisotropic material [5]. In [5], it was found that the optimum stacking factor for this machine is 0.86 (which is different from that found for a synchronous reluctance machine which was 0.5). Details of the test machine are given in Table I; the only difference between the FEA model and the test machine is that the number of axial laminations is halved (with the lamination and insulation layer thickness doubled) to reduce the mesh size and simulation time" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003652_027836499101000502-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003652_027836499101000502-Figure7-1.png", "caption": "Fig. 7. The Lie bracket $[A,SJ of two twists on screw J~A~huJ and ,~B~hb)\u00b7", "texts": [ " Physically [A, B] is a twist that acts on a screw whose axis is the common perpendicular to the axes of both A and B. The pitch of this screw is easily found to be (h,, + hb) + d cot B, where ha is the pitch of the screw on which twist A acts, dcb is the pitch of the screw on which B acts, 0 is the angle between the axes of A and B, and d is the distance between the axes of A and B measured along the common perpendicular. The amplitude of [A, B] equals wcob sin 0, where (\u00d9a and w~ are the amplitudes of A and B respectively. The twist [A, B] is depicted in Figure 7. The Jacobi identity [property (b)] specifies the condition for a body receiving twists about three screws, \u00a31 = [X, [Y, Z]], \u00a32 = [Y, [Z, X]], and \u00a33 = [Z, [X, Y]], to resume the same position after the last twist that it occupied before the first. The order in which the twists are applied is of no consequence; at MARQUETTE UNIV on August 17, 2014ijr.sagepub.comDownloaded from 462 their accumulated effect simply maintains the body in kinematic equilibrium. Hence the screws on which the three twists act are linearly dependent (each of the twists is the negated sum of the other two), so they belong to the same two-system (Ball 1900; Hunt 1978; Gibson and Hunt 1990)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001773_tte.2021.3085367-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001773_tte.2021.3085367-Figure7-1.png", "caption": "Fig. 7. Magnetic flux density distributions under two magnetization operations. (a) Remagnetization. (b) Demagnetization.", "texts": [], "surrounding_texts": [ "The conventional MEC model can predict the no-load AGFD in a computationally efficient way, in which the magnetic reluctance of the stator core is generally ignored. However, it should be noted that a significant magnetic saturation in the stator core will happen when a quite high-level d-axis current is employed to realize different magnetization operations in VFMM. Therefore, the nonlinearity of the stator core should be considered in the MEC solution for a magnetization operation. The magnetic flux density distributions and the relative permeability distributions under two magnetization operations are illustrated in Figs. 7 and 8. Obviously, the stator teeth and yoke show seriously saturated. Based on the nonlinear FE analysis, the stator reluctances Rs1 and Rs2 can be obtained respectively. Furthermore, the MEC models for remagnetization and demagnetization operations are shown in Fig. 9. The magnetomotive force engendered by the d-axis current can be expressed as: m dF NI= (26) where N denotes the number of turns per phase. Authorized licensed use limited to: BOURNEMOUTH UNIVERSITY. Downloaded on July 05,2021 at 00:17:07 UTC from IEEE Xplore. Restrictions apply. 2332-7782 (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. According to the MEC model and piecewise-linear hysteresis model, the remanence predictions of the LCF PMs under different magnetization currents are obtained and compared with FE predictions as indicated in Fig. 10, which exhibits satisfactory agreements. It should be noted that the magnetic reluctances of the stator core under different magnetizing current levels should be changed according to the FE results when the magnetic saturation occurs due to the excessive d-axis current." ] }, { "image_filename": "designv10_11_0001089_tia.2020.3046195-Figure12-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001089_tia.2020.3046195-Figure12-1.png", "caption": "Fig. 12. Predicted peak temperature distributions across the motor components under transient operation for concepts (a) circumferential, (b) axial, and (c) spiral.", "texts": [ " The spiral jacket gives the lowest maximum windings temperature of 156.7 \u00b0C, whereas the axial and circumference jackets have their maximum temperatures of 162.2 \u00b0C and 171.8 \u00b0C, respectively. Fig. 11 shows the predicted temperature distribution of three cooling jackets. The circumference jacket gives the highest temperature because of low convection heat transfer coefficient, comparing to the axial and spiral jackets. Predicted peak temperature distributions across the motor components under the transient operation are displayed in Fig. 12. According to Figs. 9 and 12, the spiral jacket results in lower temperatures across various motor component when compared to other two concepts. Authorized licensed use limited to: Central Michigan University. Downloaded on May 14,2021 at 13:37:14 UTC from IEEE Xplore. Restrictions apply. The optimal 60-slot, 10-pole motor with the spiral cooling jacket concept is prototyped for performance verification. Final motor assembly and setup in the test box is shown in Fig. 13. The rotor is removed from the motor for the static thermal measurement" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001295_j.addma.2020.101234-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001295_j.addma.2020.101234-Figure4-1.png", "caption": "Fig. 4. (a-c) Simulated 3D view of competitive growth and distribution of \u03b2 grains upon solidification of the singletrack Ti6Al4V molten pool as laser scans along the positive X direction. The growth pattern of \u03b2 grains on the horizontal-section of Y=0 is validated with (d) the microstructure result.", "texts": [ " This temperature field was then mapped on to the 3D CA domain using linear interpolation for the CA model mesh since the mesh sizes of the CA model and thermal model are different. Incorporated with this temperature field, Figs. 4(a-c) illustrate the simulated 3D view of the competitive growth and distribution of \u03b2 grains upon solidification of the molten pool with the movement of the laser beam. The simulated \u03b2-grain morphology on the horizontal-section of Y=0 is verified with the microstructure result shown in Fig. 4(d). The Jo ur al Pre -p ro of third Euler angle (gamma, \u03a8) is plotted with different colors to illustrate the grain morphology since a grain has a specific crystallographic orientation and is indicated by a certain gamma value. In this work, the grains predicted by the 3D CA modeling are all marked out by the gamma angles. At the beginning of the simulation, the substrate is occupied by the equiaxial grains that have a uniform grain size and various orientations. After going through a melting and resolidification cycle, the FZ is mainly dominated by the elongated columnar \u03b2 grains, whose normal direction of the growth front is mostly perpendicular to the fusion line that is marked out by the enclosed dashed lines in Fig. 4(c). As the solidification gets close to the central zone of the molten pool, the growth front of the columnar \u03b2 grains on cross-section and longitudinalsection (XY plane) tilts towards the laser scan direction. In the central zone of the molten pool, Jo ur n l P the growth front of \u03b2 grains completely rotates to align with the laser scan direction, as shown on the horizontal-section of Y=0, which is well validated by the microstructure result (Fig. 4(d)). The growth pattern of \u03b2 grains is governed by the thermal history of the DED process. For an AM-deposited track, the shape of its molten pool resembles a \u201cbowl\u201d, and the isotherms are parallel to the \u201cbowl\u201d surface, as illustrated by the inset in Fig. 3. Consequently, the temperature gradient is perpendicular to the isotherms downwards to the unmelted substrate, and \u03b2 grains, in turn, nucleate from the fusion line and epitaxially grow upwards to the center of the molten pool. Since the laser keeps moving instead of interacting with the substrate motionlessly, the back zone of the molten pool becomes another path of heat dissipation other than the vertical conduction downwards to the \u201cbowl\u201d surface. When the solidification gets close to the central zone of the molten pool, the temperature gradient turns rapidly to be almost opposite to the laser scan direction. As a result, the pool tail becomes the fusion line for the central zone of the molten pool, and \u03b2 grains hence rotate their normal direction of the solidification front at the pool tail to be well aligned with the laser scan direction, as illustrated in the region enclosed by the dotted line in Fig. 4(c). Figs. 5(a-c) display the solidification process of \u03b2 grains on the cross-section of X=0 at different time moments. Since only the left half of the temperature field is extracted (inset in Fig. 3), the predicted \u03b2-grain distribution covers the left half of the cross-section and is compared with the right half of the experimental observation (Fig. 5(d)). The growth pattern and morphology of \u03b2 grains are qualitatively captured by the simulation results. However, the average grain size for the simulated results is shorter by approximately 25% than the experimental characterization despite comparable width", " In addition to the elongated columnar grains, some smaller grains of equiaxial shape are also observed while approaching the central zone of the molten pool (Fig. 5(c)). The possible reason is that the normal direction of the growth front, although is aligned with the maximum temperature gradient, may not be perfectly parallel to the extracted cross-section plane. At some points, some elongated grains are intercepted by this cross-section and only their truncated surfaces are displayed, exhibiting a smaller aspect ratio. Particularly for the central zone of FZ, the grains completely rotate by 90\u00b0 to align with the scan direction (Fig. 4). When looking Jo ur al through the cross-section, the short axes of the elongated grains will be captured and exhibit equiaxed morphology. In Fig. 6, the cross-sections of (a) two-track and (b) three-track Ti6Al4V depositions are used to compare the simulation results against the experimental data. The predicted free surface and extracted isotherms for the FZ boundary and HAZ boundary (solid lines) are superimposed on the experimental microstructure, which exhibits a good agreement with the experimental observation (dashed lines)", " Predicted free surface, fusion zone boundary and heat-affected zone boundary (solid lines) vs experimental data (dashed lines) on the cross-section of (a) two-track and (b) three-track Ti6Al4V depositions. Simulated \u03b2-grain distributions within the fusion zone on the (c,d) cross-sections of X=0 and (e,f) horizontal-sections of Y=0 positioning at the solid lines in (c) and (d) for the (c,e) two-track deposition and (d,f) three-track deposition. The predicted \u03b2-grain distribution within the FZ on the horizontal-section of Y=0 (upper surface of the substrate, illustrated in Fig. 3(b)) for two-track and three-track Ti6Al4V depositions are shown in Fig. 6(e) and (f). For the single-track case, Fig. 4(c) depicts the microstructure thoroughly. The region near the fusion line of the first-track is still dominated by the elongated grains of columnar shape; however, the grain morphology is fairly different from each track in the central zone. This difference is associated with the location of the displayed horizontal-section. According to the cross-section views shown in Fig. 6(a) and (b), the molten pool of the second track and third track rotates about 20\u00ba and 40\u00ba in the anticlockwise direction and hence becomes shallower in the substrate due to the overlapping of adjacent tracks" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001560_s00170-021-07375-x-Figure12-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001560_s00170-021-07375-x-Figure12-1.png", "caption": "Fig. 12 The example of (a) the divergent node and (b) the convergent node", "texts": [ " Figure 11 (a) shows the strut fabricated successfully via the proposed adaptive method. While with a constant slicing height as shown in Fig. 11 (b) and (c), the positional errors in the static approach accumulate as the deposition process continues, destroying the final geometric shape of the strut. The intersections of a wire structure occur where two or more struts\u2019 end points merge together, which is defined as a convergent node; when the same end points of struts correspond to the start points of two or more new struts, then, it is called a divergent node, as shown in Fig. 12. As the deposition process for a given strut nears these nodes, some strategies need to be employed to avoid poor weld bead geometry or potential collision between the torch nozzle and the component. For struts emanating from a divergent node, two build options are available. First, the struts could be deposited by alternating the deposition process evenly between them, so in effect, they are built up simultaneously. Alternatively, each strut can be deposited individually in one shot according to their strut number i, as shown in Fig. 12 (a). The first method usually produces poor strut geometry, as shown in Fig. 13 (a). This is mainly due to the slippage of the molten pool during the welding process. The molten pool is prone to be adsorbed towards the adjacent strut whose material has already been deposited so that the deposition process does not proceed in the expected position, resulting in a deformed structure. To avoid this phenomenon, struts at this point need to be continuously deposited and manufactured one-by-one according to their corresponding processing sequence, as shown in Fig", " Since the length of stick out of the torch can be adjusted within a reasonable range, making its path planning more flexible, as stated by Yuan et al. [25], to achieve a collisionfree deposition path, the ctwd may need to be adjusted during the process. As mentioned previously, the struts in the set Scov Pm create a potential collision (between the torch and nearby struts) as the build nears a convergent node. If a strut si is treated as a vector, it has a higher probability of collision in the range \u03bb si ! , as shown in Fig. 12. The max collision area \u03bbmax can be defined as: \u03bbmax \u00bc 1\u2212max \u22c3ni\u00bc1; j\u00bc1 dt si! ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi si! 2 s j! 2\u2212 si! s j! 2 r 0 BB@ 1 CCA \u00f013\u00de Struts must be compared one-by-one at this convergent point to determine the largest collision area. As the torch reaches the range of 1\u2212\u03bbmax\u00f0 \u00de si!, the ctwd should be increased to ascertain the welding torch is outside the collision area, as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000931_j.mechmachtheory.2019.103595-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000931_j.mechmachtheory.2019.103595-Figure1-1.png", "caption": "Fig. 1. 2-PrRS + PR(P)S metamorphic parallel mechanism.", "texts": [ " After an introduction of the mechanism, its inverse kinematic model is analysed and the cloud picture of its workspace is demonstrated in Section 2 . Next, in Section 3 , the stiffness model is formulated with the consideration of the deformation of the main components caused by the actuation and constraints. In Section 4 , the stiffness matrices of the home positions of configurations I and III are obtained and the stiffness distributions in the sub-workspace around the desired trajectory is evaluated. Finally, the conclusions of the above work are summarised in Section 5 . The solid model of the proposed mechanism is illustrated in Fig. 1 . It consists of a mobile platform, a fixed platform, and three supporting limbs. Two of the limbs connect the mobile platform with the fixed platform by a prismatic joint (P) actuated by a linear actuator, an innovative rotatable-axis revolute joint (rR) which axis is rotatable, and a spherical joint (S) in turn. The other limb is composed of an active prismatic joint (P), a revolute joint (R), a lockable prismatic joint ((P)) and a spherical joint (S) successively. Thus, the type of the mechanism is 2-PrRS + PR(P)S" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003846_la0533260-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003846_la0533260-Figure1-1.png", "caption": "Figure 1. Geometry of a cylinder lying horizontally at the interface between a liquid and a gas.", "texts": [ " This can happen if the vertical force that surface tension provides is reduced suddenly, which is most easily achieved by adding surfactant to the water. Contact between two objects can also lead to sinking, however, because a portion of the meniscus is then eliminated.7 To highlight the important aspects of this dynamic process, we study here a simple system that is amenable to both experimental and theoretical investigation and find good agreement between the two approaches. In a typical experiment, a circular cylinder lies horizontally at the interface between a liquid and a gas, as shown in Figure 1. The density, Fs, of the cylinder is chosen such that the interfacial tension, \u03b3, and the weight of displaced fluid (of density F) are too small for the cylinder to remain afloat without some external support. Once this support is removed, the cylinder sinks rapidly taking O(0.1)s to become completely immersed in the bulk fluid. The dynamics of the sinking process are illustrated by the time series in Figure 2. To determine the subsequent motion of the cylinder, we develop a simple hydrodynamic model of the motion allowing us to predict the height, h0, of the cylinder\u2019s center above the undeformed free surface as a function of time t after release", " (9) Acheson, D. J. Elementary Fluid Dynamics; Oxford University Press: Oxford, 1990. 10.1021/la0533260 CCC: $33.50 \u00a9 2006 American Chemical Society Published on Web 03/03/2006 length translating at constant speed in the bulk. If we assume that the form of the flow in the fluid is not changed substantially from this, we may write where the (\u00ea,\u03c8) coordinate system is a two-dimensional polar coordinate system with origin at the cylinder\u2019s center (the angle \u03c8 being measured in the same sense as \u00e2 in Figure 1), R is the (nondimensional) radius of the cylinder, and dots denote time derivatives. In reality, the velocity potential of the flow will be modified by the presence of the interface and so will not take the simple form assumed in (1). However, since the cylinder starts close to half immersed in the fluid, we expect these corrections to be small initially and make use of (1) in what follows. Since the cylinder is accelerating, the reference frame in which (1) was calculated is not an inertial frame" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003136_20.728300-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003136_20.728300-Figure1-1.png", "caption": "Fig. 1. Layout of axial flux machine.", "texts": [ "ndex Terms\u2014 Axial flux, electrical machine, magnetic field, permanent magnet. I. INTRODUCTION AXIAL-flux, permanent-magnet machines with a toroidal slotless winding (Fig. 1) are used as portable generators providing low voltage dc output [1], [2]. They are now being considered for drives of electric and hybrid road vehicles and for generators in wind mills. A set of cylindrical two-dimensional (2-D) models are used in [3] as the basis for a quasi-three-dimensional (3-D) representation of the magnetic field. Although the quasi\u20133D model gives rapid and accurate predications of the main terminal parameters of the machine, it needs some additional parameters (obtained experimentally) such as effective outer and inner radii of the airgap" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003406_2.4191-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003406_2.4191-Figure1-1.png", "caption": "Fig. 1 MAP spacecraft speci cations.", "texts": [ " Because of its distance, 1:5 \u00a3 106 km from Earth, this orbit affords great protection from Earth\u2019s microwave emission, magnetic elds, and other disturbances, with the dominant disturbance torque being solar radiation pressure. It also provides for a very stable thermal environment and near 100% observing efciency, because the sun, Earth, and moon are always behind the instrument\u2019s eld of view. In this orbit MAP sees a sun/Earth angle between 2 and 10 deg. The instrument scans an annulus in the hemisphere away from the sun, so that the universe is scanned twice as Earth revolves once around the sun. The spacecraft orbit and attitude speci cations are shown in Fig. 1. To provide the scan pattern, the spacecraft spins about the z axis at 0.464 rpm, and the z axisconesabout the sun line at 1 rev/h. A 22:5 \u00a7 0:25 deg angle between the z axis and the sun directionmust be maintained to provide a constant power input and to provide constant temperatures for alignment stability and science quality. The instrumentpointingknowledge is 1.8 arcmin (1\u00be ), which is not required for onboard or real-time implementation. The attitudedeterminationhardware consists of a digital sun sensor (DSS), coarse sun sensors, a star tracker, and gyroscopic rate sensors" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001776_00325899.2021.1934634-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001776_00325899.2021.1934634-Figure2-1.png", "caption": "Figure 2. Sample geometry for tensile test (a), impact toughness test (b) and rotation bending test (c) in relation to the building direction (BD). Sample geometries follow the standards ISO 6892 (a), ISO148-1 (b) and DIN 50113 (c).", "texts": [ " Cubes of 10 \u00d7 10 \u00d7 10 mm were manufactured using the different parameter sets for metallographic analyses. The parameter sets and resulting LPBF process times are compared in Table 2. Cylinders with diameters of 12 and 10 mm and heights of 70 and 55 mm were produced for fatigue and tensile testing, respectively. Cuboids with a cross-section of 12 by 12 mm and a height of 60 mm were produced for impact notch testing. The building axis was set parallel to the sample axis. After machining specimens according to Figure 2 were obtained. For comparison, samples of H13 produced by electro-slag remelting (ESR) were also tested. LPBF samples with the maximum density (Q1) were tested without any post-treatment (Q1-AB), in the hardened and tempered condition (Q1-HT), and in the hardened and tempered condition with a prior HIP treatment (Q1-HIP+HT). The samples with lower densities (set Q2 and Q3) were all exposed to a HIP cycle followed by hardening and tempering. With this experimental setup, we can determine whether HIP+HT can compensate for a higher initial defect density with respect to the tensile and fatigue properties", " For tensile testing, cylinders with a test length of 30 mm and a diameter of 5 mm were used. The fatigue test samples were 60 mm long and hourglass-shaped, with the diameter tapered from 10 to 5.25 mm. In the region of diameter tapering, a surface finish by manual longitudinal polishing with abrasive paper (dry polishing with 180/320 grit, followed by short wet polishing with 500 grit) was applied in order to remove all circumferential notches. Standard Charpy-V specimens were used for impact toughness testing. Figure 2 presents schematics of the samples. Not all samples qualities and conditions were fully characterised regarding their microstructure and mechanical properties. Table 3 gives an overview of conducted investigations and the corresponding number of samples. The retained austenite was qualitatively determined by X-ray diffractometry (XRD; Seifert XRD 3003 PTS) with Cr\u2013K\u03b1 X-rays, a step size of 0.1\u00b0, and a counting time of 6 s for each step. The spot diameter was limited to 2.5 mm, and a vanadium filter suppressed K\u03b2 X-rays" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003068_jsvi.1997.1298-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003068_jsvi.1997.1298-Figure3-1.png", "caption": "Figure 3. Modelling schemes used to describe compliant gear bodies; (a) Ring theory, (b) plate theory, and (c) numerically obtained eigensolutions or shape functions.", "texts": [ " Some typical eigenvalues of a compliant gear-like disk are shown in Figure 2, as predicted by FEM. Observe that the in-plane ring modes (in radial direction) are dominant when (ro \u2212 ri )/r\u0304 1\u00b70 where ro , ri and r\u0304 are the outer, inner and mean radii of a disk. Conversely, the out-of-plane plate modes (normal to the disk surface) dominate when (ro \u2212 ri )/r\u0304e 1\u00b70. These two limiting cases are analyzed and integrated in the multi-body dynamics methodology as demonstrated by Figures 3(a) and (b). For a complicated gear blank geometry with arbitrary boundary conditions like Figure 3(c), eigensolutions or shape functions can be obtained a priori, say from FEM. All three cases will be discussed further in section 4. The single gear pair mesh dynamics for systems containing rigid gears was presented in an earlier paper by the authors [9]. This formulation is extended here to include effects of flexibility of the gear blanks themselves as shown in a flowchart form in Figure 4. Like the earlier paper the equations of motion for the gear i in a pair i\u2013j is given in the dual domain (t, ui*) form as follows where t is time, ui*= ft 0 Vi* dt is the mean rotational component and Vi* is the mean rotational velocity of gear i: Mi(ui*)q\u0308i m (t)+Cij\u2212 i m (ui*)q\u0307i m (t)\u2212Cij\u2212 j m (ui*)q\u0307j m (t)+Kij\u2212 i m (ui*)qi m \u2212Kij\u2212 j m (ui*)qj m +Ki sb (ui*)qi m (t)+Ki ff (ui*)qi m (t) =Qi mo (t)+Qi(t)\u2212 (Qij\u2212 i*mg (V*, t)\u2212Qij\u2212 j*mg (V*, t)), (1) where Mi is the inertia matrix, Cij\u2212 i m and Cij\u2212 j m are the generalized damping matrices, Kij\u2212 i m and Kij\u2212 j m are the generalized mesh stiffness matrices, Ki sb is the generalized shaft-bearing stiffness matrix, Ki ff is the generalized structural stiffness matrix for the gear blank i, Qi me is the internal force due to transmission error but it includes parametric effects associated with Kij\u2212 j m (ui*), Qi is the external generalized force on gear i and qi m is the generalized co-ordinate associated with the gear i", " Further hij(ui*) and Gij(ui*) can be decomposed into mean and ui* varying components as hij (ui*)= hij o + hij m (ui*) and Gij(ui*)=Gij o +Gij m (ui*). Now, the ui* varying components can be neglected to give a linear expression for mesh stiffness with position-invariant coefficients. \u02dc \u02dc \u02dc \u02dc \u02dc \u02dc \u02dc Again, this model may not be accurate since the oscillatory components are not usually negligible. Nonetheless, this model yields an eigenvalue problem which can be very easily solved to gain an insight into the dynamic characteristics of the geared system. For a relatively thin compliant gear (thickness/radiusQ 0\u00b71) as shown in Figure 3(a), the plate flexural theory may be used to describe the transverse (normal to the gear body) motions. Also, for most thin gears, (excluding ring and thin rimmed gears which will be studied in section 3.2), the radial motion (towards the mesh) can be neglected since the radial stiffness is relatively high compared to the transverse stiffness. With these assumptions, equations (14a and b) can be reduced as follows, where u\u0304 is ij =[\u2212u\u0304i s ijv u\u0304i s ijx 0] and u\u0304 js ij =[\u2212u\u0304j s ijv u\u0304j s ijx 0] are formed from mesh position vector and qi m =[Ri Gmx Ri Gmy qi mz qi fm ] and qj m =[Rj Gmx Rj Gmy qj mz qj fm ] are the generalized co-ordinates: I*= &100 0 1 0', dri Ps ij (t)= [I* u\u0304 iTs ij Si s ij]qi m , drj Ps ij (t)= [I* u\u0304 jTs ij Sj s ij]qj m ", " (22) Using equation (18), we obtain the following expression for mesh stiffness where offset hij(ui*) and contact length Gij(ui*) and stiffness per unit length Kij can again be obtained from the existing gear contact mechanics programs [31]: Kij\u2212 l m (ui*)=g hij(ui*)+Gij(ui*)/2 hij(u i*)\u2212G ij(u i*)/2 & I* u\u0304i s ij (ui*) SiT s ij 'p\u0302ij o (ui*)Kijp\u0302ijT o (ui*) [I* u\u0304lT s ij (ui*) Sl s ij] ds, l= i, j. (23) The \u2018\u2018pseudo forces\u2019\u2019 acting on gears Qij\u2212 i* mg (V*, t) and Qij\u2212 j* mg (V*, t) vanish due to the orthogonality condition. Therefore the rigid body and the transverse flexural motion equations are uncoupled. The elastic deformation modes of ring gears in epicyclic trains or gears with thin flanks as shown in Figure 3(b) are similar to the radial deformation modes of a ring. Hence the modal functions of a ring [27] can be used in equation (14). The orthogonal shape function matrix S(u) for a ring are given as follows where u is the angular position in the gear co-ordinates Xi G \u2212Yi G \u2212Zi G : S(u)= &cos (u) sin (u) 0 \u2212sin (u) cos (u) 0 0 0 0'S*(u), (24a) S*(u)= [S1 (u) S2 (u) \u00b7 \u00b7 \u00b7 Sr (u) \u00b7 \u00b7 \u00b7 SNs (u)]; (24b) Sr (u)= &C1 (u) C1 (u) 0 C2 (u) C2 (u) 0 ', r=0, 1, 2, . . . , NS . (24c) Here, C1 (u)=g G G F f cos 0r 2 u1, sin 0r+1 2 u1, r is even, r is odd, C2 (u)=g G G F f sin 0r 2 u1, cos 0r+1 2 u1, r is even, r is odd", " Si s ij and Si s ij are the value of the ring shape function S(u) evaluated at sij for gears i and j respectively. Again the \u2018\u2018pseudo forces\u2019\u2019 acting on gears Qij\u2212 i*mg (V*, t) and Qij\u2212 j*mg (V*, t) vanish due to the orthogonality of the rigid body motion and the radial or circumferential flexural motion. It is difficult to obtain theoretical shape functions which may accurately represent the flexural or rigid body motions of the gears which the gear-shaft sub-assemblies deviate considerably from any of the classical structural elements mentioned in the preceding sections such as the one shown in Figure 3(c). For practical systems with complicated geometry, other numerical solutions obtained from say finite element codes [31] can be used to obtain the shape functions S(r, u, z) of unassembled sub-assemblies. These can be assembled in the multi-body dynamics format to model the complete multi-mesh geared system. This modeling scheme reduces equations (14a and b) to the following where qi m = qi fm and qj m = qj fm are flexibility co-ordinates and Si s ij and Sj s ij are shape function S(r, u, z) evaluated at the mesh position sij: drj Ps ij (t)=Si s ij qi m , drj Ps ij (t)=Sj s ij qj m " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001041_j.ijmecsci.2020.106020-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001041_j.ijmecsci.2020.106020-Figure8-1.png", "caption": "Fig. 8. Coupling coordinate systems of the shaving cutte", "texts": [ " \ud835\udc1c\ud835\udfce , \ud835\udc1c = \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 cos \ud835\udf19\ud835\udc50 \u2212 sin \ud835\udf19\ud835\udc50 0 0 sin \ud835\udf19\ud835\udc50 cos \ud835\udf19\ud835\udc50 0 0 0 0 1 0 0 0 0 1 \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 (5) The transformation matrix from the coordinate system S c 0 to S k can e expressed as: \ud835\udc24 , \ud835\udc1c\ud835\udfce = \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 1 0 0 0 0 1 0 \u2212 \ud835\udc38 \ud835\udc60 0 0 1 0 0 0 0 1 \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 (6) The transformation matrix from the coordinate system S k to S s 0 can e expressed as: \ud835\udc2c\ud835\udfce , \ud835\udc24 = \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 cos \ud835\udefd 0 \u2212 sin \ud835\udefd 0 0 1 0 0 sin \ud835\udefd 0 cos \ud835\udefd 0 0 0 0 1 \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 (7) The transformation matrix from the coordinate system S s 0 to S s can e expressed as: \ud835\udc2c , \ud835\udc2c\ud835\udfce = \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 1 0 0 0 0 cos \ud835\udf19\ud835\udc60 \u2212 sin \ud835\udf19\ud835\udc60 0 0 sin \ud835\udf19\ud835\udc60 cos \ud835\udf19\ud835\udc60 0 0 0 0 1 \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 (8) Then, the transformation matrix from the coordinate system S c to S s \ud835\udc2c , \ud835\udc1c = \ud835\udc0c \ud835\udc2c , \ud835\udc2c\ud835\udfce \ud835\udc0c \ud835\udc2c\ud835\udfce , \ud835\udc24 \ud835\udc0c \ud835\udc24 , \ud835\udc1c\ud835\udfce \ud835\udc0c \ud835\udc1c\ud835\udfce , \ud835\udc1c = \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 cos \ud835\udefd cos \ud835\udf19\ud835\udc50 \u2212 cos \ud835\udefd sin \ud835\udf19\ud835\udc50 sin \ud835\udf19\ud835\udc50 cos \ud835\udf19\ud835\udc60 \u2212 cos \ud835\udf19\ud835\udc50 sin \ud835\udefd sin \ud835\udf19\ud835\udc60 cos \ud835\udf19\ud835\udc60 cos \ud835\udf19\ud835\udc50 + sin \ud835\udefd sin \ud835\udf19\ud835\udc50 sin sin \ud835\udf19\ud835\udc50 sin \ud835\udf19\ud835\udc60 + cos \ud835\udf19\ud835\udc50 sin \ud835\udefd cos \ud835\udf19\ud835\udc60 sin \ud835\udf19\ud835\udc60 cos \ud835\udf19\ud835\udc50 \u2212 sin \ud835\udefd sin \ud835\udf19\ud835\udc50 cos 0 0 The radial vector and unit normal vector of the shaving cutter can b \u20d7 \ud835\udc60 ( \ud835\udf07\ud835\udc50 , \ud835\udf03\ud835\udc50 , \ud835\udf19\ud835\udc50 ) = \ud835\udc0c \ud835\udc2c , \ud835\udc1c \u20d7\ud835\udc5f \ud835\udc50 ( \ud835\udf07\ud835\udc50 , \ud835\udf03\ud835\udc50 ) \u20d7 \ud835\udc60 ( \ud835\udf03\ud835\udc50 , \ud835\udf19\ud835\udc50 ) = \ud835\udc0b \ud835\udc2c , \ud835\udc1c \u20d7\ud835\udc5b \ud835\udc50 ( \ud835\udf03\ud835\udc50 ) here L s,c is the upper left 3 \u00d7 3 submatrix of M s,c and \u20d7\ud835\udc5f \ud835\udc60 ( \ud835\udf07\ud835\udc50 , \ud835\udf03\ud835\udc50 , \ud835\udf19\ud835\udc50 ) is t \u20d7 \ud835\udc60 ( \ud835\udf07\ud835\udc50 , \ud835\udf03\ud835\udc50 , \ud835\udf19\ud835\udc50 ) = \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 \ud835\udc5f \ud835\udc4f\ud835\udc50 cos \ud835\udefd cos \ud835\udf19\ud835\udc50 \ud835\udc58 \u2212 \ud835\udf07\ud835\udc50 sin \ud835\udefd + \ud835\udc5f \ud835\udc4f\ud835\udc50 ( sin \ud835\udf19\ud835\udc50 cos \ud835\udf19\ud835\udc60 \u2212 cos \ud835\udf19\ud835\udc50 sin \ud835\udefd sin \ud835\udf19\ud835\udc60 ) \ud835\udc58 \u2212 \ud835\udc5f \ud835\udc4f\ud835\udc50 ( cos \ud835\udf19\ud835\udc50 cos \ud835\udf19\ud835\udc60 + \ud835\udc5f \ud835\udc4f\ud835\udc50 ( sin \ud835\udf19\ud835\udc50 sin \ud835\udf19\ud835\udc60 + cos \ud835\udf19\ud835\udc50 sin \ud835\udefd cos \ud835\udf19\ud835\udc60 ) \ud835\udc59 \u2212 \ud835\udc38 \ud835\udc60 sin \ud835\udf19\ud835\udc60 \u2212 \ud835\udc5f \ud835\udc4f\ud835\udc50 ( cos 1 here k = sin ( \ud835\udf03\ud835\udc500 + \ud835\udf03\ud835\udc50 ) \u2212 \ud835\udf03\ud835\udc50 cos ( \ud835\udf03\ud835\udc500 + \ud835\udf03\ud835\udc50 ) and l = cos ( \ud835\udf03\ud835\udc500 + \ud835\udf03\ud835\udc50 ) + \ud835\udf03\ud835\udc50 sin ( \ud835\udf03\ud835\udc500 + The unit normal vector of the shaving cutter is \u20d7 \ud835\udc60 ( \ud835\udf03\ud835\udc50 , \ud835\udf19\ud835\udc50 ) = \u23a1 \u23a2 \u23a2 \u23a3 cos \ud835\udefd sin \ud835\udf19\ud835\udc50 sin ( \ud835\udf03\ud835\udc500 + \ud835\udf03\ud835\udc50 ) \u2212 cos \ud835\udefd cos \ud835\udf19\ud835\udc50 c \u2212 cos ( \ud835\udf03\ud835\udc500 + \ud835\udf03\ud835\udc50 )( sin \ud835\udf19\ud835\udc50 sin \ud835\udf19\ud835\udc60 + cos \ud835\udf19\ud835\udc50 sin \ud835\udefd cos \ud835\udf19\ud835\udc60 ) \u2212 \ud835\udc60\ud835\udc56\ud835\udc5b ( \ud835\udf03\ud835\udc500 + \ud835\udf03\ud835\udc50 \u2212 cos ( \ud835\udf03\ud835\udc500 + \ud835\udf03\ud835\udc50 )( sin \ud835\udf19\ud835\udc50 cos \ud835\udf19\ud835\udc60 \u2212 cos \ud835\udf19\ud835\udc50 sin \ud835\udefd sin \ud835\udf19\ud835\udc60 ) \u2212 \ud835\udc60\ud835\udc56\ud835\udc5b ( \ud835\udf03\ud835\udc500 + \ud835\udf03\ud835\udc50 .2. Theoretical derivation of the spur face gears The machining coordinate systems of spur face gear shaving are estab re shown in Fig. 8 . The coordinate system S f 0 ( O f 0 , X f 0 , Y f 0 , Z f 0 ) is the oordinate system. S p ( O p , X p , Y p , Z p ) is the occasional coordinate system xis direction. \ud835\udf19f is the rotation angle of the spur face gear, which has t ine with the definition in Fig. 7 . \ud835\udf19\ud835\udc60 \ud835\udf19\ud835\udc53 = \ud835\udc41 \ud835\udc53 \ud835\udc41 \ud835\udc60 = \ud835\udc5a \ud835\udc60\ud835\udc53 r and w e rat can b M \ud835\udc0c \u2212 c \ud835\udc5f . (17 A \ud835\udc63 w ) , \ud835\udc50 = \ud835\udc53 he re o f the m toot T havin \ud835\udc5f w n [18 T . here N f is the number of teeth of the spur face gear and m sf is the driv Then, the transformation matrix from the coordinate system S s to S f k,s0 , M s0,s are given in the Appendix" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003388_978-3-662-04831-3-Figure1.9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003388_978-3-662-04831-3-Figure1.9-1.png", "caption": "Fig. 1.9: Roller rig of the German railway company (DB AG)", "texts": [], "surrounding_texts": [ "1.4 Prototype applications of rigid-body mechanisms 13", "14 1. Introduction", "1.4 Prototype applications of rigid-body mechanisms 15" ] }, { "image_filename": "designv10_11_0001410_j.mechmachtheory.2021.104291-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001410_j.mechmachtheory.2021.104291-Figure3-1.png", "caption": "Fig. 3. Schematic illustration of one discrete rolling position in the form of a simplified system of springs.", "texts": [ " The validity of the algorithm is tested against existing research and commercial software tools resulting in a discussion about the various gear meshing effects during power transmission. The basic idea of determining the current gear mesh stiffness is to compute the actual tooth contact deformation for a discrete rolling position. At this explicit meshing state, the ratio of the applied force F and the calculated deformation x delivers the desired stiffness value c. In accordance to Weber and Banaschek [1] , this total tooth contact deformation consists of three independent components, see Fig. 2 and Fig. 3 : Hertzian contact deformation \u03b4H , tooth bending deformation \u03b4B,k and deformation \u03b4C,k due to the flexibility of the area between gear tooth and wheel body. The index k means 1 for the pinion and 2 for the wheel, respectively. While the determination of the local deformation \u03b4H caused by the Hertzian pressure stays equal to the findings of Weber and Banaschek [1] , the present approach computes directly the sum of the two global latter ones - bending deformation \u03b4B,k and clamping deformation \u03b4C,k - by means of the Isogeometric Analysis [22] in three-dimensional space", " A parameter i defines a theoretical distance in meshing direction between pinion and wheel at the corresponding contact point i . So, the influence of manufacturing errors, profile modifications, mesh interference and/or deformations due to the operating conditions can be considered here by suitable geometry operations. The resulting load distribution f i along the involved contact lines is also used in the calculation of the Hertzian pressure deformation \u03b4H and hence makes Eq. (1) nonlinear. The simplified system of springs in Fig. 3 is a schematic illustration of Eq. (1) . In detail, it shows a snapshot of the tooth engagement where the driving pinion presses against a constrained wheel. It also clearly indicates that the number of tooth pairs being in mesh and their corresponding contact conditions vary on their way from the beginning of the gear meshing at point A to the end at point E. However, as all gear teeth on the respective wheel body have the same underlying geometry and hence the same stiffness characteristics, only a single pair of teeth is used for the determination of all compliance factors \u03b1i, j in Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000513_1.g004803-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000513_1.g004803-Figure1-1.png", "caption": "Fig. 1 Illustration of combined spacecraft system and thruster layout.", "texts": [ " Then, by using backstepping (which is a recursive design technique by considering some state variables as \u201cvirtual controls\u201d), a relative translational and rotational controller for the combined spacecraft is designed without a priori information about the mass and inertia matrix. To address the problem of input saturation, an auxiliary systemmodified fromRef. [14] is introduced. The finite-time convergence of reference tracking and inertia parameter identification is finally guaranteed, and numerical simulations demonstrate the effectiveness of the proposed controller. Consider the combined spacecraft operating in a disturbance-free environment. As shown in Fig. 1, the combined system is composed of a service spacecraft, a manipulator, and a noncooperative target without control capability. It is assumed that the three components are rigid and no relative motion exists between them. Due to the coupling between the translational and rotational motion, even between control force and control torque [15], six-degree-of-freedom (6-DOF) relative coupled dynamics are adopted for the combined spacecraft. Let F i (O-xiyizi) be the Earth-centered inertial frame. Define Fp (Op-xpypzp) as the body frame of the combined spacecraft, where Fp is fixed on the center of massOp of the combined spacecraft; and Opxp, Opyp, and Opzp are three mutually perpendicular axes, as shown in Fig", " According to the fundamental equation of the two-body problem with an assumption of small spacecraftmass relative to theEarth [18], the relative translational dynamics described in Fp can be represented as [19] p\u0307 v \u2212 S \u03c9p i;p p (3) mv\u0307 \u2212mS \u03c9p i;p v \u2212 \u03bcm r3p p Rp t r t i;t \u2212mRp t r t i;t f (4) where p rpi;p \u2212 Rp t r t i;t is the relative position from the desired position to the current position, v is the relative velocity, \u03bc is the Earth\u2019s gravitational parameter,m is themass of the combined spacecraft, rp is the distance from the center of the Earth to the combined spacecraft, and f is the orbital control force. A fully actuated system is employed for both the position and attitude control [20]. As illustrated in Fig. 1, there are six thrusters, and each thruster generates a force of Fi i 1; : : : ; 6 parallel with the axes of Fp. It is assumed that the thrusters are bidirectional with the positive direction shown in the figure. The control input to the combined spacecraft can be written as u f \u03c4 AF (5) where F F1 F2 F3 F4 F5 F6 T is the thrust input, and A is the input matrix. Assume that the center of mass of the noncooperative target has been estimated in the precapture phase [21,22]. The center of mass of the combined spacecraft can then be obtained by combining with the known inertia properties of the service spacecraft" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003989_0278364906065826-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003989_0278364906065826-Figure4-1.png", "caption": "Fig. 4. Experimental system.", "texts": [ " From the viewpoint of medical applications, this is a major advantage compared with a contact based approach. Figure 3 illustrates the difference between a conventional approach (Figure 2 I) and the proposed one (Figure 2 II). The proposed approach can cover a large sensing area as shown in Figure 3(b) while a number of scanning motions is needed to cover the same area when using a conventional approach. As can be seen from these examples, the proposed approach completes the sensing in an efficient manner, since it can obtain global information instead of local information. Figure 4 shows the developed sensor system and an overview of the main part of the line laser sensor unit. The sensor system is composed of a force applying part and a displacement capturing part. The force applying part includes an air compressor for supplying compressed air, a high speed solenoid valve, and at James Cook University on March 16, 2015ijr.sagepub.comDownloaded from at James Cook University on March 16, 2015ijr.sagepub.comDownloaded from an air hose sending the compressed air from the compressor to the valve. The high speed solenoid valve is the key element of the sensor for achieving a quick response. The valve can operate with the maximum switching frequency of 500 Hz under the supply pressure ranging from 0.05 MPa to 0.25 MPa. The displacement capturing part is composed of a line laser sensor (KEYENCE Co., Ltd.: LJ-080) for obtaining the distance between the environment and the sensor within the designated line segment and an actuator for moving the sensor around the rotating axis as shown in Figure 4(b). This mechanical configuration allows us to capture the shape of the environment. We define two coordinate systems: the absolute system o(O \u2212 XYZ) whose origin is fixed to the earth and the sensor coordinate system s(Os \u2212XsYsZs) whose origin is fixed to the sensor frame being at \u03b8o=0. The sensing area of the displacement sensor is given by [Xmin s , Y min s ] = [\u221220, \u221220] mm and [Xmax s , Y max s ] = [20, 20] mm in the plane of Zs = \u2212H in s as shown in Figure 4(b). We are particularly interested in the distribution of deformation of the object. Let us now define d(Xs, Ys) as follows: d(Xs, Ys) = da(Xs, Ys) \u2212 db(Xs, Ys) (1) where the subscript a and b denote after and before force impartment respectively and d(Xs, Ys) expresses the net displacement of the object. For example, d(0, 0) is shown in Figure 4(b). Using the line laser sensor under the locked actuator, we can obtain the distribution of deformation along the Xs line where the laser can scan. By applying a rotational motion for the line laser sensor, we can obtain the distribution of deformation along the Ys line. Let us now define the at James Cook University on March 16, 2015ijr.sagepub.comDownloaded from deformation matrix M \u2208 Rn\u00d7m as follows: M(p) = d(p)(Xs1, Ys1) \u00b7 \u00b7 \u00b7 d(p)(Xsm, Ys1) ... ... d(p)(Xs1, Ysn) \u00b7 \u00b7 \u00b7 d(p)(Xsm, Ysn) (2) where m, n and the superscript (p) denote the number of sampling data along the Xs axis, the number of sampling data along the Ys axis, and the p-th trial, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000624_1.5040635-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000624_1.5040635-Figure3-1.png", "caption": "FIG. 3. Powder feeding nozzle in the center of the multiple blue DDLs.", "texts": [ " In contrast, the coaxial nozzle is arranged coaxially regarding the laser beam axis (i.e., Z axis in Fig. 1), as shown in Fig. 2(b). While the lateral powder feeding is dependent on cladding direction because of one directional powder flow toward the melt pool,14 coaxial powder feeding is independent of cladding direction, thus this nozzle allowing three-dimensional cladding. In order to maintain the cladding with 3D motion, powder must be fed coaxially to the laser beam axis. We arranged a powder feeding nozzle in the center of the multiple blue DDLs, as shown in Fig. 3. A hole is bored so that the powder feeding nozzle positions in the center of the focusing lens. Thanks to the nozzle being in the center, powder is uniformly irradiated by laser beams around the powder flow. Thus, it enables us to achieve 3D motion cladding. We developed the system for the laser cladding process using the multiple-laser-beam overlapping with the center nozzle powder feeding, as shown in Fig. 4. Six blue DDLs are guided through the optical fibers connected on the processing head" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003737_cdc.2003.1272286-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003737_cdc.2003.1272286-Figure5-1.png", "caption": "Fig. 5: Performance of the standard 3-sliding controller [SI", "texts": [ "2 which corresponds to the asymptotics stated by Theorem 4. The performance of the controller with the measurement error magnitude O.1m is shown in Fig. 4. It is seen from Fig. 4c that the control U is continuous function off. The steering angle vibrations have magnitude of about 12 degrees and frequency 1 which is also quite feasible. The performance does not change when the frequency of the noise varies in the range 100 - 100000. The performance of the standard 3-sliding controller [8- 101 in the absence of noises is demonstrated in Fig. 5 . The advantages of the new controller are obvious (compare Figs. 2d, 5h). Simulation shows that the standard controller is also much more sensitive to the parameter choice. A new arbitraq-order sliding mode controller is proposed. It is actually only the second know family of such controllers. It is also a sliding-mode controller of a new type, because it provides for sliding motion on a manifold of codimension higher than 1 by means of control continuous everywhere except this manifold. As a result the chattering effect of such a controller is significantly reduced" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000706_0954406219854112-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000706_0954406219854112-Figure1-1.png", "caption": "Figure 1. Three degree-of-freedom nonlinear dynamic model of a gear pair.", "texts": [ " Three degree of freedom nonlinear dynamic model of a gear transmission system Three degree of freedom motion differential equations of a gear transmission system Under the complicated working conditions of coal mining, the transmission system, having high speed and large torque, is the part with the most frequent failures in a shearer.29 Especially, the input end of the transmission system has the highest failure rate. Therefore, the gear pair at the input end is taken as the research object, and a three degree-of-freedom nonlinear dynamic model of a single-stage spur gear pair is established. The model is shown in Figure 1. And the geometric parameters of the gears in the model are shown in Table 1. To fully demonstrate the dynamic characteristics of the system, the model considers many nonlinear factors. First, since the coal seam is uneven, the torque fluctuates considerably while mining. Therefore, the related wave force of the external input torque is considered to fit the load characteristics of coal mining. Excluding the torque, the cutting drum is also subjected to a large three-way force that indirectly acts on the bearings of the transmission system" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001455_s10489-021-02459-3-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001455_s10489-021-02459-3-Figure2-1.png", "caption": "Fig. 2 Leader-follower formation configuration", "texts": [ " So (10) can be rewritten as: w\u0307 = M\u22121 n \u03c4 \u2212 M\u22121 n Hnw + fdis, (11) where fdis = M\u22121 n (ddis \u2212 M q\u0308 \u2212 H q\u0307) \u2208 R 4\u00d71 denotes the external disturbances and model uncertainties of robot, which can be regarded as the total disturbances of the system. The vector w = [w1, w2, w3, w4]T and wi = q\u0307i , i = 1, 2, 3, 4. Assumption 1 The uncertain terms M , H and the unknown disturbances ddis are all bounded. In addition, the total disturbances fdis is also bounded. The positional relationship between the follower robot RF and the leader robot RL in the inertial coordinate system is shown in Fig. 2. The position and direction angle of RL and RF are represented by [xl, yl, \u03b8l] and [xf , yf , \u03b8f ], respectively. It is assumed that the parameters of the leader robot and the follower robot are the same. According to (4), in the inertial coordinate system, the kinematics model of RL can be expressed as: \u23a1 \u23a3 x\u0307l y\u0307l \u03b8\u0307l \u23a4 \u23a6 = R 4 \u23a1 \u23a3 cos \u03b8l \u2212 sin \u03b8l 0 sin \u03b8l cos \u03b8l 0 0 0 1 \u23a4 \u23a6 \u23a1 \u23a3 1 1 1 1 \u22121 1 1 \u22121 \u22121 L+l 1 L+l \u22121 L+l 1 L+l \u23a4 \u23a6 \u23a1 \u23a2\u23a2\u23a3 w1l w2l w3l w4l \u23a4 \u23a5\u23a5\u23a6 , (12) where [w1l , w2l , w3l , w4l]T are the angular velocities of four wheels of RL" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003358_20.312735-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003358_20.312735-Figure3-1.png", "caption": "Fig. 3 Flux distribution at 6 = 37\"", "texts": [ " Practical application shows that this scheme not only simplifies the computation, but also offers a satisfying result as long as the selected displacement point from the curves is not unreasonably too far from the chosen operating point. Fig. 2 shows the calculated results of Eo, X d and X, for a 4-pole interior-magnet type PM motor. Note that at the at the torque angle around 37\", there is a dip on the Eo curve and a crest on the x d curve. This is due to the fact that, at the magnetic bridge region between the rotor bar and the corners of magnet, the direction of the flux produced by the magnetizing armature reaction is opposite to the direction of the end leakage flux of the magnets. This is shown in Fig. 3 in which we have introduced programming technique to isolate the magnet component and the d-axis armature reaction component from the resultant loading fields. Thus, under certain load condition, the bridge which is the main path of the magnet leakage flux becomes least saturated. As a result, the end leakage flux of the magnets increases rapidly. This leads to a dip on the EO curve. At the same time, due to the significant reduction of the magnet component of air-gap flux, the magnetic path for the d-axis component of armature reaction turns out to be much less saturated; consequently, Xd increases notably" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000970_j.mechmachtheory.2019.103747-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000970_j.mechmachtheory.2019.103747-Figure2-1.png", "caption": "Fig. 2. Coordinate assignments and link and joint parameters for the proposed non-symmetric 5R-SPM (a) the first kinematic chain (b) the second link, (c) the third link and the end-effector.", "texts": [ " The proposed non-symmetric 5R-SPM for this application ( Fig. 1 (b)) consists of orthogonal links in one kinematic chain and arbitrary links in the other. The Y-shaped design of the first link yields high link stiffness and joint rigidity in the first kine- matic chain [9] . Besides, the arbitrary links of the second kinematic chain allow for minimizing the size of the mechanism, avoiding collisions, and maximizing the stiffness of the second kinematic chain. The kinematic chains of the non-symmetric 2DOF 5R-SPM is illustrated in Fig. 2 . The end-effector is connected to the base via two kinematic chains. The first kinematic chain contains active joint 1 and passive joint 5, and the second kinematic chain includes active joint 2 and passive joints 3 and 4. The axes of all joints intersect at the center of the mechanism. To describe the kinematics, we set up five coordinate systems. We attached the reference coordinate system, denoted by X 0 Y 0 Z 0 , to the base in a way that Y 0 aligns with the axis of active joint 1 and Z 0 is perpendicular to the axes of active joints 1 and 2. The X 0 axis is determined by the right-hand rule. We also assigned coordinate systems 1\u20133 to links 1\u20133 and the end-effector coordinate system, denoted by X EE Y EE Z EE , to the end-effector, respectively. Z 1 , Y 2 , and X 3 are perpendicular to the planes of links 1, 2 and 3, respectively. X EE is aligned with the axis of joint 5 and Y EE is aligned with the axis of joint 4. The first chain is orthogonal, meaning that the angle between axes of joints 1 and 5, and joints 4 and 5 is \u03c0 /2 ( Fig. 2 (a)). \u03bb denotes the angle between the two active joints ( Fig. 2 (a)) and \u03b3 and \u03be denote the length of links 2 and 3, i.e. the angle between axes of joints 2 and 3 and joints 3 and 4, respectively ( Fig. 2 (b) and (c)). The link length parameters \u03bb, \u03b3 and \u03be are ranged between zero and \u03c0 /2. The upper limit is sufficient since it leads to orthogonal 5R-SPM which would cover the whole S 2 workspace. Parameters \u03b8 i , i = 1 , 2 , 3 , 4 , 5 denote the joint variables of joints 1\u20135 and are defined as rotation angle of link 1 relative to the base, link 2 relative to the base, link 3 relative to link 2, the end-effector relative to link 3, and the end-effector relative to link 1, respectively. The axes of joints 1\u20135 are along Y 0 , X 2 , Z 3 , Y EE and X EE , respectively ( Fig. 2 ). In the home configuration, the reference and the end-effector coordinate systems coincide ( \u03b81 = \u03b85 = 0 ). For \u03b3 = \u03be = \u03c0/ 2 the described mechanism turns into a special symmetric 5R-SPM with link length of \u03c0 /2 for all the moving links. Also, for \u03bb = \u03b3 = \u03be = \u03c0/ 2 it becomes an orthogonal 5R-SPM. A new geometrical methodology was developed to specify the configurations and singularities of the designed non- symmetric 5R-SPM with one orthogonal chain. This methodology is inspired by the basic approach proposed by Danaei et al", " Since both links of the first kinematic chain are orthogonal, only configurations 1 and 3 from Table 1 may occur, meaning that, with respect to the first chain, any arbitrary end-effector position is either regular or in finite singularity. Referring to Fig. 4 , finite singularity occurs when Z EE becomes aligned with Y 0 ( Z EE = [0 \u00b1 1 0] T , \u03bc = 0 or \u03c0 ), corresponding to geometrical configurations (i) and (j) in Fig. 3 . In this situation, as shown in Fig. 5 , while Z EE is fixed, X EE can rotate around Y 0 . In other words, for the given end-effector vector Z , there are infinite number of solutions for \u03b8 and \u03b8 . Since \u03bc = \u03b8 + \u03c0/ 2 (see EE 1 2 5 Fig. 2 ), the denominator of Eq. (3) , S \u03bc, becomes zero at C 5 = 0 . Therefore, the finite inverse singularity of the first chain (refereed to as FI-1 in the rest of this paper) occurs at C 5 = 0 . Then, by rewriting Eq. (1) and substituting equivalent parameters for the second chain (see Table 2 , row 2), we obtain Z 3 = 1 S 2 \u03c3 { (Y EE \u00d7 X 2 ) \u00d7 (C \u03b3 Y EE \u2212 C \u03be X 2 ) \u00b1 \u221a (C \u03b3 + \u03be \u2212 C \u03c3 )(C \u03c3 \u2212 C \u03be\u2212\u03b3 ) (Y EE \u00d7 X 2 ) } (4) where \u03c3 is the angle between the axis of second joint X 2 and Y EE . The axis X 2 = [ S \u03bb C \u03bb 0] T is fixed and Y EE can be obtained from Z EE \u00d7 X EE , where Z EE is the given end-effector position and X EE can be calculated form Eq", " In this case, the kinematics of the second chain cannot be obtained; therefore, it would not be further investigated. Otherwise, based on the end-effector\u2019s position and the values of \u03b3 and \u03be , all four types of configurations in Table 1 may occur for the second chain. For | \u03b3 \u2212 \u03be | < \u03c3 < \u03b3 + \u03be , the configuration is regular (geometrical configurations (a) to (c) in Fig. 3 ) and four solutions for the inverse kinematics problem exists. \u03c3 = | \u03b3 \u00b1 \u03be | yields inverse singularity of the second chain, in which the axes X 2 , Z 3 , Y EE are coplanar. In this situation, according to Fig. 2 , link 3 is completely folded or unfolded with respect to link 2, corresponding to C 3 = 0 . \u03b3 = \u03be yields instantaneous inverse singularity of the second chain (corresponding to geometrical configurations (d) to (g) in Fig. 3 and refereed to as II-2 in the rest of this paper) and \u03b3 = \u03be results in finite inverse singularity (refereed to as FI-2 in the rest of this paper). As shown in Fig. 6 , for \u03b3 = \u03be = \u03c0/ 2 geometrical configuration (h) and for \u03b3 = \u03be = \u03c0/ 2 geometrical configurations (i) and (j) occur", " Finite forward singularity for \u03be = \u03c0/ 2 corresponding to geometrical configurations (i) and (j) from Fig. 3 at (a) X EE = Z 3 and (b) X EE = \u2212Z 3 . infinite number of solutions (geometrical configurations (i) and (j) in Fig. 3 ). The former corresponds to the instantaneous forward singularity (refereed to as IF in the rest of this paper) and the latter is related to the finite forward singularity or self-motion (refereed to as FF in the rest of this paper). The forward singularity occurs when joint axes X EE , Y EE , and Z 3 become coplanar. In this condition, according to Fig. 2 , end-effector is completely folded or unfolded with respect to link 3, corresponding to C 4 = 0 . In other words, as depicted in Fig. 8 , the two assembly modes of the forward kinematics are determined by the sign of C 4 . Finally, | \u03b7 \u2212 \u03c0/ 2 | > \u03be yields a negative radicand which indicates that the given input variables are impossible or out-of-workspace. C As depicted in Fig. 9 , while in finite forward singularity, the end-effector and link 3 can freely move around axis X EE even if both active joints (and links 1 and 2) are locked", " (A.14) , we have \u23a7 \u23a8 \u23a9 \u03c9 y = \u02d9 \u03b81 , B\u03c9 y = E \u02d9 \u03b82 , S 1 \u03c9 x + C 1 \u03c9 z = 0 . (6) Eq. (6) shows that, in forward singularity, actuator velocities \u02d9 \u03b81 and \u02d9 \u03b82 only affect \u03c9 y . It also indicates that, for a given \u02d9 \u03b81 and \u02d9 \u03b82 , there exist infinite number of solutions for \u03c9 EE ( \u03c9 x and \u03c9 z can take different values as long as they satisfy the third row of Eq. (6) ). Now that the instantaneous forward singularity of the mechanism is analyzed, it can be shown to occur at C 4 = 0 . Ac- cording to Fig. 2 (c) and Eq. (A.1) , we may express X 3 and X EE in coordinate system 3 as 3 X 3 = [1 0 0] T and 3 X EE = 3 R EE [1 0 0] T = [ C 4 C \u03be S 4 \u2212 S \u03be S 4 ] T . Now, using Eq. (A.13) , one obtains detJ DA = \u2212X T 3 X EE = \u2212C 4 . Therefore C 4 = 0 results in forward singularity. Nevertheless, the Jacobian analysis could not specify the type of singularity (either instantaneous or finite), whereas from the proposed geometrical analysis, it is known that for \u03be = \u03c0 /2, C 4 = 0 yields instantaneous forward and for \u03be = \u03c0/ 2 it results in finite forward singularity", " For instance, one can use this approach to analyze the singularities of general 5R-SPM, 3-RRR SPMs [1,26,27] , 1RR-2RRR SPM [2] , or Asymmetrical SPM [3] . We also suggest further study on singularity curves, as in [20] , and kinematic calibration, as in [28] , for the non-symmetric structure of 5R-SPM. In future, one may also investigate the feasibility of using the value of the radicand in Eq. (1) as an index for closeness to singularity. Declaration of Competing interest None. Based on the coordinate assignment of the proposed non-symmetric 5R-SPM in Fig. 2 , we obtained the orientation of the end-effector related to the reference coordinate system for the first kinematic chains as 0 R EE = 0 R 1 1 R EE where (A.1) 0 R 1 = R Y 0 (\u03b81 ) and 1 R EE = R X 1 (\u03b85 ) , and for the second kinematic chain as 0 R EE = 0 R 2 2 R 3 3 R EE where (A.2) 0 R 2 = R Z 0 (90 \u2212 \u03bb) R X 2 (\u03b82 ) , 2 R 3 = R Y 2 (90 \u2212 \u03b3 ) R Z 3 (\u03b83 ) , and 3 R EE = R X 3 (90 \u2212 \u03be ) R Y EE (\u03b84 ) . A1. Instantaneous kinematics From the first kinematic chain, we obtained the angular velocity of the end-effector in terms of \u02d9 \u03b81 and \u02d9 \u03b85 : \u03c9 EE = \u02d9 \u03b81 Y 0 + \u02d9 \u03b85 X EE . (A.3) From Fig. 2 (a) we can see that Y 0 is perpendicular to X EE ; so by left-multiplying Eq. (A.3) by Y T 0 , the second term in the right-hand-side of Eq. (A.3) vanishes. Thus we obtained the instantaneous kinematic equation for the first chain: Y T 0 \u03c9 EE = \u02d9 \u03b81 . (A.4) For the second kinematic chain, we have \u03c9 EE = \u02d9 \u03b82 X 2 + \u02d9 \u03b83 Z 3 + \u02d9 \u03b84 Y EE . (A.5) Since X 3 is perpendicular to both Z 3 and Y EE ( Fig. 2 (c)), left-multiplying Eq. (A.5) by X T 3 results in X T 3 \u03c9 EE = \u02d9 \u03b82 X T 3 X 2 . (A.6) Combining Eqs. (A.4) and (A.6) and rewriting it in matrix form yields J I [ \u02d9 \u03b81 \u02d9 \u03b82 ] = J D [ \u03c9 x \u03c9 y \u03c9 z ] , (A.7) where [ \u03c9 x \u03c9 y \u03c9 z ] T is the vector of the end-effector\u2019s angular velocity, \u02d9 \u03b81 and \u02d9 \u03b82 are the actuators velocities, and J I = [ 1 0 0 X T 3 X 2 ] and J D = [ Y T 0 X T 3 ] are the inverse and forward Jacobian matrices, respectively. J D is a 2 \u00d7 3 matrix and therefore non-invertible; thus we cannot derive the Jacobian matrix from Eq", "16) where M = [ M x M y M z ] T is the negative of the external moments exerted on the end-effector, and \u03c4 1 and \u03c4 2 are the actuators\u2019 torque. In the forward kinematics problem, we seek a solution for the orientation of the end-effector ( Z EE ) in terms of the given active joint variables \u03b81 and \u03b82 . To find the solution for Z EE , we first obtained rotation matrices 0 R 1 and 0 R 2 and joint axes X EE and Z 3 for the given \u03b81 and \u03b82 ; then we used the geometric approach to determine Y EE based on axes X EE and Z 3 and the respective angles between them and Y EE , which are \u03be and \u03c0 /2 (refer to Fig. 2 (c)); finally we obtained Z EE = X EE \u00d7 Y EE . From Eq. (5) , we derived Z EE by calculating X EE \u00d7 Y EE and simplifying it using triple product expansion a \u00d7 (b \u00d7 c ) = (a . c ) b \u2212 (a . b ) c as Z EE = 1 S 2 \u03b7 { C \u03be (Z 3 \u00d7 X EE ) \u00b1 \u221a S 2 \u03be \u2212 C 2 \u03b7 X EE \u00d7 (Z 3 \u00d7 X EE ) } . Then, by substituting Z 3 = 0 R 2 2 R 3 [0 0 1] T , X EE = 0 R 1 [1 0 0] T , S \u03b7 = \u2016 Z 3 \u00d7 X EE \u2016 , and C \u03b7 = Z T 3 X EE we obtained Z EE = 1 G 2 + H 2 { \u2212C \u03be [ GS 1 H GC 1 ] \u00b1 \u221a G 2 + H 2 \u2212 C 2 \u03be [ HS 1 \u2212G HC 1 ] } , (A.17) where G = S \u03bbS \u03b3 S 2 \u2212 C \u03bbC \u03b3 and H = S 1 (C \u03bbS \u03b3 S 2 + S \u03bbC \u03b3 ) + C 1 C 2 S \u03b3 " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000726_2.0571913jes-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000726_2.0571913jes-Figure1-1.png", "caption": "Figure 1. Experimental setup of (a) the specially designed microdroplet cell and (b) the diameter of the capillary tip.", "texts": [ " The potentiodynamic polarization tests were performed from a potential of 200 mV, which is lower than the open circuit potential (OCP), to 9.0 V or the pitting potential at a scan rate of 1 mV/s. The EIS measurements at the OCP were potentiostatically run with an AC amplitude of 10 mV, measured in the frequency range from 10\u22122 to 105 Hz. The results of the EIS test were analyzed using the Gamry Echem Analyst program. In the case of the DED-produced AM Ti-6Al4V sample, micro-electrochemical experiments were performed using a microdroplet cell, as shown in Fig. 1a. The microdroplet cell technique enables the microelectrode to be aligned to the desired spot of the working electrode; it also enables the direct measurement of local currents during the electrochemical polarization. For the microdroplet cell tests, a capillary tip with a diameter of 330 \u03bcm was fabricated (Fig. 1b), and silicon paste was used for sealing to prevent the leaking of the solution from the capillary. The electrochemical measurements such as polarization and EIS were performed at least three times for reproducibility. CPT tests.\u2014The CPT tests for AM Ti-6Al-4V and conventional SM Ti-6Al-4V were performed in 3.5 wt% NaCl aqueous solution by using a flushed port cell. The SCE was used as the reference electrode, whereas a carbon rod was utilized as the counter electrode. A potential of 4.5 V was applied using a potentiostat (Gamry PCIB-4750), and the temperature was increased at a ramp rate of 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003855_j.mechmachtheory.2006.01.006-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003855_j.mechmachtheory.2006.01.006-Figure2-1.png", "caption": "Fig. 2. A spatial four-bar mechanism.", "texts": [ " Consequently, the term Pm 1 j\u00bc1 Rank\u00f0$Fnj E \u00de will be five and be two more than Pm 1 j\u00bc1 F j M in [6] which equals the result of Eq. (24). So the CDOF proposed in [6] can also be denoted as F conf \u00bc M \u00fe Xm 1 j\u00bc1 Rank $ Fnj E \u00bc Rank $ F E \u00fe Xm 1 j\u00bc1 Rank $ Fnj E \u00bc 6 d \u00fe Xm 1 j\u00bc1 Rank $ Fnj E \u00f030\u00de Eq. (30) has the same form as that in [6] but is much simpler. 3. Applications and discussions 3.1. Analysis on the mobility properties of a spatial four-bar mechanism A spatial four-bar mechanism, shown in Fig. 2 [6], consists of 2-RR (two revolute pairs) kinematic chains. To analyze the free motion of the end-effector BC, we first decompose the spatial parallel mechanism to form two kinematic chains connecting link BC with the base and then study the reciprocal screws of each kinematic chain. Now, we first analyze the terminal constraints of kinematic chain AB exerted to link BC. The coordinate system oxyz is established as Figs. 2 and 3 show, the origin of the coordinate system is superimposed with pair A, z-axis is along the axis of revolute pair A, and y-axis is perpendicular to the base plane, and therefore, x-axis is naturally parallel to the base plane", " (7), we can find the pitch of the screw (twist): h \u00bc s \u00f0s0 \u00fe hs\u00de ksk2 \u00bc LP \u00feMQ\u00fe NR L2 \u00feM2 \u00fe N 2 \u00bc 0 \u00f036\u00de With Eq. (11), we can find the projecting point of the origin on the axis is rOP \u00bc s \u00f0rOP s\u00de ksk2 \u00bc 1 L2 \u00feM2 \u00fe N 2 M\u00f0R Nh\u00de N\u00f0Q Mh\u00de N\u00f0P Lh\u00de L\u00f0R Nh\u00de L\u00f0Q Mh\u00de M\u00f0P Lh\u00de 2 64 3 75 \u00bc xB yB 0 2 64 3 75 \u00f037\u00de Therefore, Eq. (35) indicates that the end-effector BC can make a free rotation about a line passing through point \u00f0 xB yB 0 \u00de with a direction \u00bd 0 0 1 , which is just its self-rotation axis\u2014z 0-axis shown in Fig. 2. So, the end-effector only has one rotational DOF about z 0-axis; and as a result, we can only either select pair B or select C as the actuation. In application, this mechanism can be utilized as an adjustable bearing. 3.2. Analysis on the mobility properties of the end-effector in a 4-PUU spatial parallel mechanism A spatial parallel mechanism, shown in Fig. 4 [6], is made up of 4-PUU (one prismatic pair and two universal pairs) kinematic chains. To investigate the mobility properties of the end-effector, we first decompose the spatial parallel mechanism to be four kinematic chains connecting the end-effector with the fixed guides and then analyze the reciprocal screws (terminal constraints) of each kinematic chain according to the above analysis steps" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003388_978-3-662-04831-3-Figure6.8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003388_978-3-662-04831-3-Figure6.8-1.png", "caption": "Fig. 6.8: Torsional spring and damper", "texts": [ " Then Fi acts in ( -eji) direction and Fj acts in the direction of eji\u00b7 6.1.3.3 Actuator. Forces between two bodies generated by hydraulic, pneu matic, or magnetic actuators are defined by complete analogy to the above sign conventions. They may be written in the form (6.18) 6.1.3.4 Torsional spring and damper. Torsional (rotational) springs and dampers between two bodies are always assumed to act around the axis of a revolute joint that connects these bodies. Consider two rigid bodies i and j connected at a point P by a revolute joint (Figure 6.8). Assurne that a torsional spring and a torsional damper act around the rotation axis of the joint, and that they are attached to the arrow Tj fixed on body j and arrow ri fixed on body i. This spring damper element exerts torques of equal magnitude but opposite orientation on the bodies i and j (action = reaction}. Let '1/Jji be the difference between the rotation angles of the bodies j and i (measured as the angle from r i to r j), and let '1/JjiO be the angle of the undeformed spring. As a torque Mi is positive if it acts (for a compressed spring ('1/Jji > '1/JjiO)) counter-clockwise on the body i, and clockwise on the body j, it is formally described by the relation Mi:= [er\u00b7 ('1/Jji- '1/JjiO) + dr \u00b7 ~ji] \u00b7 ezR, (6" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003795_iros.2004.1389922-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003795_iros.2004.1389922-Figure2-1.png", "caption": "Fig. 2. Circular soh mho1", "texts": [ " FEASIBILITY INVESTIGATION THROUGH PHYSICAL SIMULATlON In this section, in a physical simulation, we assess the feasibility of a deformable robot t o crawl and jump. As mentioned in the previous section, crawling and jumping can he performed using the elastic potential energy associated with deformation. Let us verify this approach through a physical simulation before we go on to a prototype of a deformable robot. A. Modeling of circular sofr mbor Let us simulate the behavior of the circular soft robot illustrated in Figure 2. The circular soft robot consists of a circular elastic shell with a set of soft actuators inside, as shown in Figure 2-(a). The robot has eight SMA coils labelled as A through H. Extending or shrinking actuators deforms the robot body, i.e., the circular shell, as shown in Figure 2-(b). We apply open-loop PWM control to the coils. A periodic voltage panem is applied to the set of SMA coils during crawling. As illustrated in Figure 3, periodic voltage patlems are denoted by the set of coils active during the first time step. The elastic shell of the robot is modeled as an elastic object while actuators are modeled as rheological objects [7], so as to be able to describe the inelastic nature of the SMA coils and polymer gel actuators. We can specify the contraction rate; maximum contraction, and maximum generated force of an SMA coil using a three-element model with a slider" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001735_j.msea.2021.140990-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001735_j.msea.2021.140990-Figure1-1.png", "caption": "Fig. 1. The image of LPBF-AM Ti6Al4V block with assigned direction and dimensions.", "texts": [ " Each layer fabrication involved bi-directional laser scanning, where consecutive linear laser tracks were inversely directed and separated by 120 \u03bcm between their centers. Scanning orientation in each layer was rotated by 90\u25e6 after an interlayer delay of 16s. The activity of oxygen in the processing chamber was kept below 50 ppm. The input energy density as per the involved laser and process parameters was 52.08 J/mm3. The image of LPBF-AM block of Ti6Al4V depicting build direction (Z) and the laser scanning strategy is provided in Fig. 1. The printed components were analyzed for their microstructure using nano scanning electron microscope (SEM) by FEI. Accurate measurement of density of wrought and LPBF-AM Ti6Al4V was carried out using pycnometer with nitrogen gas. The test was repeated multiple times on different regions of the wrought and LPBF-AM Ti6Al4V. In addition to the LPBF-AM Ti6Al4V and wrought Ti6Al4V, the tests were also performed on the conventionally heat-treated 1 mm3 block of wrought Ti6Al4V, which involved solutionizing at 1323 K for 15 min followed by quenching in water", " The given regions of the LPBF-AM and wrought Ti6Al4V block were scanned using Olympus Panametrics V211 0.125-inch diameter (shear wave) and V312 0.125-inch diameter (longitudinal wave) unfocused immersion transducers at 10 MHz and 20 MHz. The unfocussed immersion transducers with a low (10 MHz) and a high (20 MHz) frequency were used in order to identify their effect on the spatial resolution due to change in the frequency. The former transducer recorded the shear wave velocity at several spots on the sample at different rotations along the axis perpendicular to scanned surface (Fig. 1). The latter transducer was used to generate pulses for the raster scans of samples, and record signals reflected by the sample (Fig. 1). A JSR Ultrasonic DPR 300Pulse/Receiver internally operated the pulse source and time trigger and the data was collected by a Tektronix MDO 3024b. The scanning rate was maintained at 512 signals per 20s. Here, it should also be noted that 0.125-inch (3.175 mm) diameter of both Olympus Panametrics V211 (shear wave) and V312 (longitudinal wave) immersion transducers employed for EBME measurements in the present study restricted EBME scanning measurements to not less than the length scale of 0.125-inch (3", " This indicates that in spite of the complex fluid dynamics and thermokinetics associated with LBPF-AM process that generally leads to a higher probability of generating three-dimensional physical (morphological) defects (pores and cracks), under the set of LBPF-AM processing parameters employed in the present work and mentioned earlier, no such detectable defects existed in the sample which was also later confirmed by optical and SEM microscopy observations. Based on the EBME technique described earlier, LPBF-AM and wrought Ti6Al4V were scanned at 10 MHz and 20 MHz to compute effective dynamic bulk modulus (Kd) and density (\u03c1). The planar contour plots of the scans in 3D volume from the top face (XY; Fig. 1b) of LPBFAM block, were generated to reveal an average distinct spatial distribution of Kd and \u03c1 (Fig. 3a\u2013d). The average spatial resolution of both Kd and \u03c1 clearly and significantly increased in the planar contour plots of 20 MHz compared to that of 10 MHz (Fig. 3a\u2013d). This is attributed to lower ultrasound wavelength at higher frequency (20 MHz) which may be influenced by the microstructural aspects such as crystallographic defects present in the material. Furthermore, although overall values of Kd and \u03c1 for 10 MHz were slightly higher than those for 20 MHz, the variation of these values for 10 MHz (Kd:105" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000346_j.mechmachtheory.2017.09.013-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000346_j.mechmachtheory.2017.09.013-Figure1-1.png", "caption": "Fig. 1. Bennett linkage.", "texts": [], "surrounding_texts": [ "is, the Bricard-related linkages, which were proposed by Bricard [10] in his study on a mobile octahedron. Moreover, Baker summarized the Bennett-based SLOLs systematically and obtained their loop equations [11-13] . Chen described the existing SLOLs in her thesis [14] .\nAs the two major categories of SLOLs, Bennett-based linkages and Bricard-related linkages both have restrictions on the geometric parameters. The research on the relevance between these two categories is limited. Song et al. [15] proposed a reconfigurable linkage between the line-symmetric Bricard linkage and the Bennett linkage. He also constructed a reconfigurable mechanism that can be reconfigured among five types of SLOLs [16] . However, these studies focused on specific linkages, the relevance of the two categories for general linkages was not examined.\nAn SLOL can move only when it follows specific geometric requirements, but it features excellent deployability compared with planar linkages. SLOLs have been the focus of studies on deployable mechanisms, and many researchers have paid considerable attention to this field. Gan and Pellegrino [17,18] first proposed the SLOLs that can be folded to a tight bundle and deployed to a plane polygon. Chen et al. [19,20] studied the deployability of plane-symmetric and three-fold symmetric Bricard linkages. Viquerat et al. [21] studied the deployability of a plane-symmetric Bricard linkage. These studies showed that the three-fold Bricard linkage can be folded completely and deployed to a plane triangle or plane hexagon and the plane-symmetric Bricard can be deployed to a rectangle given specific geometric parameters.\nHowever, the existing studies on the synthesis of SLOLs focus on new geometric configurations, and the verification of the synthesis methods is conducted through prototyping. Furthermore, the theories to analyze the mobility of new configurations are limited. Deployable mechanisms are one industrial application of SLOLs. The deployability analysis of SLOLs created through type synthesis remains inadequate. Screw theory can be used to analyze the mobility of overconstrained mechanisms. Huang et al. proposed [22,23] a modified Kutzbach\u2013Gr\u00fcbler criterion and analyzed numerous overconstrained linkages, they also analyzed the order of Bennett-based SLOLs [24] and proposed two theorems to analyze the mobility of SLOSs [25] . In this study, we proposed a series of Bennett-based SLOLs using the second synthesis method. The screw motion equations of these SLOLs are obtained, the singular states of the SLOL are also analyzed based on the screw motion equation. Then, the mobility of the obtained SLOLs is analyzed by screw theory. Subsequently, the relationship between the symmetric 6R linkages and Bricard-related linkages is studied, and the deployability of the symmetric 6R linkages is analyzed. Finally, the symmetry of the obtained linkages is analyzed, and the appropriate configurations for deployable mechanisms are selected.\nThis paper is organized as follows: In Section 2 , the Bennett linkage is introduced briefly. In Section 3 , a series of 5R, 6R SLOLs are synthesized using Bennett linkage as the basic units. In Section 4 , the deployability of symmetric linkages is analyzed, and the obtained linkages are selected based on their symmetry. In Section 5 , a conclusion is given.\n2. Bennett linkage\nThe geometry of the Bennett linkage is shown as below: As a SLOL, Bennett linkage should follow the below geometric constraints: \u23a7 \u23aa \u23a8\n\u23aa \u23a9 a 1 = a 3 = a, a 2 = a 4 = b \u03b11 = \u03b13 = \u03b1, \u03b12 = \u03b14 = \u03b2 R i = 0(i = 1 , 2 , 3 , 4) \u2223\u2223 a\nsin \u03b1\n\u2223\u2223 = \u2223\u2223 b sin \u03b2 \u2223\u2223 (1)\nwhere \u03b1i (i = 1 , 2 , 3 , 4) denotes the twist of link i, a i denotes the length of link i, R i denotes the joint offset.\nFor the revolute variables, they follow the following condition: {\n\u03b81 + \u03b83 = 2 \u03c0, \u03b82 + \u03b84 = 2 \u03c0\ntan\n\u03b81 2 tan \u03b82 2 =\nsin \u03b2+ \u03b1 2 sin \u03b2\u2212\u03b1 2\n(2)\nIn Bennett linkage, define \u03b81 as \u03b8 , \u03b82 as \u03d5, we have AC =\n\u221a\na 2 + b 2 + 2 ab cos \u03d5 , BD =\n\u221a\na 2 + b 2 + 2 ab cos \u03b8 . Define AC = 2 l,\nBD = 2 m , then Bennett linkage satisfies the following screw motion equation [26] ,\nm ( $ A \u2212 $ C ) = l( $ B \u2212 $ D ) (3)\n3. Type synthesis of SLOLs based on Bennett linkages\nAs a 4R SLOL, Bennett linkage can be used to constructed 5R, 6R SLOLs. In this section, we combine multi Bennett linkages, overlap the links with same parameters, then eliminate the overlapped links, fix part of the coincident joints, and translate the rest coincident joints to the single joints, then a new 5R or 6R kinematic chain is obtained. Using screw theory to analyze the mobility of the kinematic chain, the chain with one DOF is the SLOL, which we want to construct. The detailed process is shown as blow.", "3.1. Type synthesis of 5R SLOL\nTake two Bennett linkages ABCF and C \u2032 F \u2032 ED, which have the following relationship, { a I = a II \u03b1I = \u03b1II\n(4)\nwhere I and II indicate the linkages ABCF and C \u2032 F \u2032 ED.\nCombine the two Bennett linkages and overlap the link CF and C \u2032 F \u2032 as shown in Fig. 2 , then eliminate the overlapped\nlink CF and C \u2032 F \u2032 , fix the coincident joints F and F \u2032 , translate the coincident joints C and C \u2032 to a single joint, thus the link AF and F \u2032 E become to one rigid link AE, link BC and C \u2032 D are connected by the joint C, we get a single loop kinematic chain ABCDE.\nIn Fig. 2 , solid line indicates the link, cylinder indicates the joint, dashed line indicates the overlapped link. In order to define the DH parameters of the linkages and denote the motion screw of the joint, we use the arrow to indicate the positive direction of the revolute joint.\nNow we analyze the mobility of the kinematic chain ABCDE by screw theory. As kinematic chain ABCDE is constructed\nby two Bennett linkages I and II, so we have,\n$ C = $ C \u2032 , $ F = $ F \u2032 (5)", "In the two Bennett linkages, we have, { m I ( $ A \u2212 $ C ) = l I ( $ B \u2212 $ F ) m II ( $ C \u2032 \u2212 $ E ) = l II ( $ F \u2032 \u2212 $ D )\n(6)\nwhere m I , l I , m II , l II denote the length of the diagonal line of linkages I and II.\nAs the screw motion equation is independent with reference coordinate system, we substitute Eq. (5) into Eq. (6) , elimi-\nnate $ C \u2032 , $ F and $ F \u2032 , then we have,\nm I\nl I $ A \u2212 $ B +\n( m II\nl II \u2212 m I l I\n) $ C + $ D \u2212 m II\nl II $ E = 0 (7)\nWhen the coincident joint F is fixed, we have,\n\u03b8F \u2212 \u03b8F \u2032 = K (8)\nwhere K is a constant value.\nWhen the linkage I or II is moving, as K is a constant value, the revolute variables of linkage I and II are ganged. The\nkinematic chain ABCDE in motion is shown as Fig. 3 .\nIn Fig. 3 , K is a constant value, so the geometric parameters of link AE keeps constant. The geometric parameters of other links keep constant, too. When the linkages I and II move, only the lengths of m I , l I , m II , l II change, Eq. (6) always exists. For the new kinematic chain ABCDE, Eq. (7) always exists, only the coefficients changes in motion.\nEq. (7) is the motion screw equation of kinematic chain ABCDE. We analyze the case when the coefficients of Eq. (7) equal zero firstly, in which case the kinematic chain ABCDE is in singular configuration, then we analyze the general case with none of coefficients equals zero. We analyze this case in two categories:\n(a) One of the lengths m I , l I , m II , l II equals zero. According to Section 2 , we conclude that this case happens only when\na = b and \u03b1 + \u03b2 = \u03c0 . In this case, the linkage I or II folds to a line, it is in singular state. Then, Eq. (7) does not exist, the chain ABCDE is in singular state.\n(b) None of the lengths m I , l I , m II , l II equals zero, but m II l II \u2212 m I l I = 0 . According to Section 2 , we have \u221a\na 2 I + b 2 I + 2 a I b I cos \u03b8I a 2 I + b 2 I + 2 a I b I cos \u03d5 I =\n\u221a\na 2 II + b 2 II + 2 a II b II cos \u03b8II a 2 II + b 2 II + 2 a II b II cos \u03d5 II\n(9)\nFrom Eqs. (4) and (9) , we have\n(a 2 I b I + b I b 2 II + 2 a I b I b II cos \u03d5 II ) cos \u03b8I + (a 2 I b II + b 2 I b II ) cos \u03d5 II = (a 2 I b II + b 2 I b II + 2 a I b I b II cos \u03d5 I ) cos \u03b8II + (a 2 I b I + b I b 2 II ) cos \u03d5 I\n(10)\nDefine A = a 2 I b I + b I b 2 II , B = 2 a I b I b II , C = a 2 I b II + b 2 I b II , then Eq. (10) can be expressed as:\n(A + B cos \u03d5 II ) cos \u03b8I + C cos \u03d5 II = (C + B cos \u03d5 I ) cos \u03b8II + A cos \u03d5 I (11)\nDefine k I =\nsin \u03b2I + \u03b1I\n2\nsin \u03b2I \u2212\u03b1I\n2\n, k II =\nsin \u03b2II + \u03b1II\n2\nsin \u03b2II \u2212\u03b1II\n2 , then we have the followings according to Eq. (2) : \u23a7 \u23a8 \u23a9 cos \u03b8I = 1 \u2212k 2 I \u2212(1+ k 2 I ) cos \u03d5 I 1+ k 2 I +(k 2 I \u22121) cos \u03d5 I\ncos \u03b8II = 1 \u2212k 2 II \u2212(1+ k 2 II ) cos \u03d5 II 1+ k 2 +(k 2 \u22121) cos \u03d5 II\n(12)\nII II" ] }, { "image_filename": "designv10_11_0000460_tim.2019.2893011-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000460_tim.2019.2893011-Figure9-1.png", "caption": "Fig. 9. Planet gear with a tooth root crack. (a) Planet gear and (b) tooth root crack processed by wire cutting.", "texts": [], "surrounding_texts": [ "The data are collected in the normal condition of the planetary gearbox for comparison with that in faulty conditions. The observed original data series and the tacho-pulse train are shown in Fig. 11(a) and (b), respectively. The speed profile of the center shaft of the sun gear is shown in Fig. 11(c). The observed original data series in a planet gear tooth root crack condition is shown in Fig. 12. Conventionally, the fault feature of the planet gear tooth root crack is identified by the related sideband cluster with a space, e.g., 3.55\u00d7 in this paper, around the mesh frequency (order) and its harmonics. Thus, the spectra of synchronous averaged synthetic vibration provided by the conventional vibration separation scheme are shown in Fig. 13 for comparison. In Fig. 13(a), the sideband around the sixth harmonic of the mesh frequency 71\u00d7 is more than others. In the magnified plot shown in Fig. 13(b), the fault feature can be barely measured by the marked order lines: 442.45\u00d7, 426\u00d7, and 429.55\u00d7. However, the sideband is too low to determine the fault. To address this issue, the proposed scheme is applied. The kurtogram of the observed vibration is shown in Fig. 14. The frequency band of the determined optimal filtering parameters is marked by an ellipse with dashed line, where the center frequency is foc = 6933.33 Hz and the bandwidth is Bo = 1066.67 Hz. Then, the optimal complex envelope is demodulated from the optimal filter band. Subsequently, the equi-angle sampling with a constant angular increment, \u03b8 = 2\u03c0/(71 \u00d7 64), is implemented to convert the imaginary and real parts of the envelope data series by choosing the center shaft of the carrier as the reference shaft. Then, the vibration separation technique is perform on the envelope with the Tukey window function (window length: 5 \u00d7 64 points, which is corresponding to the angle of five teeth) and synthetic gear envelopes of the planet gear are constructed according to the teeth mesh sequence of the planet gear, Pp,n , which is listed in Table II. Next, the RDA is applied on these synthetic planet gear envelopes with averaging eight times in this paper, where each data block points for the SA corresponds to ten complete revolutions of planet gear. Moreover, the kurtosis values of synthetic planet gear envelopes are calculated. These synthetic planet gear envelopes after RDA and their kurtosis values are shown in Fig. 15. It is noted that the synthetic planet gear envelope shown in Fig. 15(c) has the maximum kurtosis (kurtosis = 5.73); thus, it is the optimal one suitable for the spectral analysis. For comparison, the optimal synthetic planet gear envelopes obtained in the abnormal and normal conditions of the test rig are shown in Fig. 16(a) and (b), respectively. In Fig. 16(a), a prominent peak can be observed in the synthetic planet gear envelope in almost every cycle of the carrier, it is corresponding to the tooth root crack. On the contrary, the periodicity can hardly be noted in the normal condition shown in Fig. 16(b). Finally, the order spectra of the synthetic envelope related to the planet gear tooth root crack and normal condition are obtained by spectral analysis, and the corresponding results (0\u223c70\u00d7) are shown in Fig. 17. The characteristic order lines related to the planet gear tooth root crack, 3.55\u00d7 and its harmonics, are exposed clearly in the order envelope spectrum obtained by spectral analysis on the synthetic planet gear envelope (see Fig. 17). In contrast, only order lines with insignificant amplitude in the normal condition can be observed. It can be concluded that the plot of order envelope spectrum obtained by the proposed scheme can be utilized to expose the localized planet gear crack clearly. By combining the envelope extraction, vibration separation and the RDA, the interferences beyond the demodulation band are almost removed, the SNR is increased in the resonance zone, the random noise and other nonsynchronous order components are reduced dramatically, which make the fault pertained characteristic order lines prominent. From these results, we can find that the proposed scheme is effective for the localized tooth root crack detection of planet gear." ] }, { "image_filename": "designv10_11_0000576_1.4960094-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000576_1.4960094-Figure1-1.png", "caption": "FIG. 1. Details of the instrument.", "texts": [ " The instrument is developed based on an instrument for analyzing the dynamics of a rolling element bearing which was developed by the authors.21 That instrument is used to analyze the rotational accuracy of high-precision bearings. The error motion of the driver system of the instrument is less than 0.15 \u00b5m. This instrument applied the same driver system to control the system errors. A high-speed camera is used to capture images of cage motion which is working at different speeds, and the imaging processing software Motion is used to obtain the trajectory of the cage. Finally, a program is used to evaluate cage behavior. Fig. 1 shows the structural details of the instrument. The driver system consisted of a servo motor, flexible coupling, and an aerostatic spindle. The high-precision mandrel was mounted on the top of the aerostatic spindle. The replaceable mandrel is used to support the test bearing and avoid damage in the accuracy of aerostatic spindle while changing the test bearing. Each mandrel can be used to adapt one series of bearings. The error motion of the aerostatic spindle is less than 0.15 \u00b5m when it works up to 3450 rpm without loading" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003083_1.1285943-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003083_1.1285943-Figure7-1.png", "caption": "Fig. 7 Model of the modified bearing outer ring", "texts": [ " The piezoelectric sensor can be modeled as a spring with a stiffness constant k that is related to its material composition. As shown in Fig. 6, the section of the bearing outer ring where the slot is cut can be modeled as a beam of varying cross-section, with a spring support at the midpoint. To establish the structural model, boundary conditions must first be assigned. Since the ends of the beam are solidly connected to the surrounding bearing structure, which is directly supported by a rigid housing, clamped boundary conditions are considered appropriate. This model is shown in Fig. 7. Furthermore, the segment of the ring encompassed by the slot subtends an angle of 2 sin21(L/D) 52cmax512 deg. The difference in ring thickness between the center and the end of the slot is determined by: D5 1 2 ~dm1db2A~dm1db!22L2! (7) Using the parameters given in Fig. 2, the difference in ring thickness was calculated to be D50.55 mm. Since cmax56 deg is the maximum angle at which the bearing load q(c) is applied, and the thickness difference D is less than 18 percent of the thinnest section of the ring ~calculated as (D22h2dm2db)/2 53", ", respectively. The centroid of the cross-section is located at: yc5 3wh2 22wg~h22h1!@~3p24 !h214h1# 6wh223pwg~h22h1! . (17) and the area of the cross-section is: CTOBER 2000 coustics.asmedigitalcollection.asme.org/ on 01/28/2 Ac5wh22 1 2 pwg~h22h1!, (18) The moment of inertia about the centroid is then: l05 1 3 wh2 322wg~h22h1!F S 5p 16 2 2 3 D h2 21S 2 3 2 p 8 D h1h21 p 16 h1 2G 2Fwh22 1 2 pwg~h22h1!Gyc 2 (19) where yc is given by Eq. ~17!. Assuming that the curvature of the nonprismatic beam shown in Fig. 7 is determined by the moment of inertia and bending moment at a, then d2y da2 5 1 E \u2022 M ~a ! Io~a ! (20) where a is a function of c as given in Eq. ~8!. The slope and deflection are then given by: u~a ![ dy da 5 1 E E 0 a M ~a ! Io~a ! da1C1 (21) y~a !5E 0 a u~a !da1C2 (22) where C1 and C2 are constants of integration determined by the boundary conditions. With the moment of inertia Io given by Eq. ~19! and h1 , h2 and yc given by Eqs. ~14!, ~15! and ~17!, respectively, the outer ring structural model becomes mathematically quite complex ~the problem is statically indeterminate" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000520_tte.2019.2959400-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000520_tte.2019.2959400-Figure1-1.png", "caption": "Fig. 1. Different geometries of rotor flux barriers for a SynRel motor including: (a) circular shaped [20] and (b) Zhokovski [11] flux barriers", "texts": [ " Thus, these motors are named PM-Assisted SynRel (PMASynRel) motors [7]. The torque density in SynRel and PMASynRel motors can be improved by increasing the saliency ratio, which is defined by different reluctances that the rotor exhibits along the orthogonal d and q axes [8]. This ratio is highly influenced by the geometry of rotor flux barriers. The most common one is the C-shaped which is associated with straight lines to define the flux barriers. The circular flux barriers are also employed in some cases to make the flux passing the rotor, more smoothly [1], (Fig. 1. a). In other cases, the barrier is composed of the conic-shaped segments [9] including: hyperbolic, parabolic, or semi-elliptical shape or segments, which are expressed by Zhokovski's function [10], [11], (Fig. 1. b). Recently, the Conformal Mapping (CM)-based methods are applied for the modelling and magnetic field analysis of the electrical machines; some of which are based on the wellknown Schwarz\u2013Christoffel (SC) transformation techniques, that allows them to transform field analysis from a complex geometry into an equivalent problem, defined on a simpler domain with an easier analytical solution [12]-[15]. In addition, analytical models, based on Magnetic Equivalent Circuit (MEC) methods, are presented in [16], [17] for fast and accurate analysis of the SynRel and the PMASynRel motors to be applied in the design and optimization procedures" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001726_j.jmapro.2021.02.024-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001726_j.jmapro.2021.02.024-Figure1-1.png", "caption": "Fig. 1. A printed part with the front view (X-Z), top view (X-Y) and side view (Y-Z) demonstration, and a schematic representation of the 67\u030a counter-clockwise rotation, island-based scanning strategy.", "texts": [ " A FEI Tecnai Osiris (Scanning) Transmission Electron Microscopy (S/TEM) at 200 kV working conditions was used. High angle annular dark-field (HAADF)-Energy Dispersive X-Ray (EDX) images were acquired and analyzed in a Bruker Esprit 1.9 software. Within this S/TEM system, four Super-X Windowless Energy Dispersion X-ray (EDX) detectors enable a fast acquisition, high low-energy counts (oxygen detection) and nano-scale elemental mapping using the ChemiSTEM EDX technology. Rectilinear samples (shown in Fig. 1) were printed in a Renishaw AM400 machine using the AlSi10Mg default parameters for both CP and SP batches (i.e., producing the Conventional Default, CD, and the Specialty Default, SD, samples, respectively) and two optimized sets of parameters for the SP batch (i.e., producing the Specialty Optimized, SO, samples), as listed in Table 2. All samples were printed on a build plate initially at room temperature. The build plate temperature rises to some extent during printing, i.e., depending on the process", ", through porosity minimization in the as-built state, a method commonly practiced for LPBF processing [38\u201341]). It is noteworthy that SO1 and SO4 parameter sets represent comparable VED values while differing largely in the individual values of laser power and scanning velocity. While they both yield similar porosity contents (0.22% for both), the SO1 sample exhibits a higher UTS and%El. The detailed procedure for parameter optimization will be presented in a separate publication. All samples were printed in an argon environment. Fig. 1 shows the schematic representation of the scanning strategy and the demonstration of the printed part with a support structure. An island-based scanning strategy with a hatch angle of 67\u25e6 counter-clockwise rotation was applied for all printed samples, which is shown to enhance the densification of the printed part [42]. Referring to the coordinate system shown in Fig. 1, there are three viewing sections: front view (XZ plane), side view (YZ plane) and top view (XY plane). Side view sections have been used in this study for the metallographic analysis. Samples for metallographic analysis of the printed microstructure were prepared using the same metallographic process used for the powder samples. In the as-polished state, optical microscopy was carried out to capture the image of a sample surface for porosity analysis. For each sample, at least three cross-sections were made" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003882_s10458-006-9004-3-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003882_s10458-006-9004-3-Figure9-1.png", "caption": "Fig. 9 Chemical source (gray area) located near a vessel branch. Distances are in microns", "texts": [ " In this case, using acoustic signals to avoid measuring gradients is effective in allowing robots to respond before they pass the target, but does not enable robots to locate the target\u2019s position around the vessel wall. This issue also arises in the control using guides to reduce acoustic signal power. The behaviors discussed above, as well as simulations in previous studies [13], consider a target on the wall of a long pipe of uniform thickness. Targets near a branch of the circulation raise further issues because the branches restrict the volume through which the chemical can move and alter the fluid flow from the parabolic form of Eq. 1. As a specific example, Fig. 9 shows the geometry of two vessels of radius R = 5\u00b5m of Table 1 connecting to a slightly larger vessel. For the circulatory system, flow is generally faster in larger vessels, implying the total cross section of the smaller branches exceeds that of the larger vessel. Quantitatively, branching vessels roughly conserve the sum of the cubes of their diameters [57]. For a split into two branches of equal diameters shown in Fig. 9, the corresponding radius of the larger vessel is 3\u221a2 R, with modestly faster fluid flow. In the figure, the branches have angles \u00b120\u25e6 with respect to the larger vessel. The target area is the same length as in Fig. 1 and wraps around the upper vessel. The gradient following and communication controls respond differently depending on the direction of flow. When the flow is from the smaller vessels into the larger one (\u201cmerging\u201d) the communication protocols have little effect on the number of robots reaching the target: those protocols rely on robots moving to the wall upstream of the target and then moving passively until they reach the target" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003807_j.euromechsol.2005.11.001-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003807_j.euromechsol.2005.11.001-Figure3-1.png", "caption": "Fig. 3. Member of the first one-rotational and two-translational DOFs asymmetrical PKM family.", "texts": [ " As a matter of fact, if the fixed joints are locked, then a 1-DOF motion can always happen because we have a planar 4R sub-chain explained by R(O,y) \u2229 G(y) = R(O,y). See Fig. 2(b) for a better view of that limb. This problem can be overcome by using another generator of X(y) without an unactuated planar subchain. Alternatively, one can exchange the location/order of the P and R joints or use a cylindrical joint. The other members of the family are obtained by replacing the generator RRR of G(x) by equivalent chains producing also G(x) and by replacing the generator PRRR of X(y) by other generators of the same Schoenflies motion. Fig. 3(a) shows a representative of a family of PKMs that can provide the platform with one-translational-tworotational DOFs. That mechanism uses one planar-spherical limb and two other limbs, each of which generates the 5-DOF product of G(x) and R(N,y) motions. Another example of planar-spherical limb is shown in Fig. 3(b). The equivalent generators of planar-spherical kinematic bonds are described online (Herv\u00e9, 2003). In this family of mechanisms, two limbs produce G(x)RN,y) and a third limb produces G(y)S(N). One can readily show G(x)R(N,y) \u2229 G(y)S(N) = T (z)R(N,x)R(N,y). The last proposed family is represented here by the mechanism of Fig. 4. It uses two limbs that are similar to the ones used in Fig. 3(a) and the third limb generates T (z)S(O). Notice, however, that this mechanism cannot be actuated using the three P joints. Remarks. \u2022 Among the three limbs, two limbs have the same architecture and produce the same motion type. Only two limbs with distinct architectures are sufficient to realise the kinematic constraint of the platform motion in each of the PKMs proposed. However, three limbs are used to ensure that there is one actuator per limb. \u2022 The shape of links to be used can be further optimised for better space utilisation" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003625_robot.2000.846403-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003625_robot.2000.846403-Figure1-1.png", "caption": "Figure 1. Kinematic scheme of the ASEA IRb-6 industrial manipulator.", "texts": [ " ) , z) will be called the instantaneous dexterity ellipsoid of the mobile manipulator. This ellipsoid is described by the following equation E q o , T ( U ( * ) , = { 7 E R' I 7TD&tT(U(') , 2)7 = l} ' (17) 3 Examples 3.1 IRb-6 manipulator mounted on a holo- nomic platform First we shall consider the industrial manipulator ASEA IRb-6 mounted on a holonomic, one dimensional mobile platform (a track). Table 1 collects Denavit-Hartenberg parameters of this manipulator, whereas its kinematic scheme is shown in figure 1. The kinematics of this manipulator, expressed in the Carte- arm I I I I I I Oi di ui with a substitubion a23 = a2c2 + u3c3 + d5s4. Since the dimension of the manipulator taskspace is larger then of its jointspace, the manipulator remains always singular, and for any configuration x E R5 its manip- ulability m(z) = zero. Now let us suppose that the ASEA IRb-6 manipulator has been mounted on a holonomic one dimensional mobile platform (a track), enabling the motion along the base frame axis Yo. The kinematics of the platform alone are represented in the form of a simple 1-dimensional control system In accordanace with [7], the platform squared instantaneous mobility mi,,T(u(" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000374_tie.2018.2795525-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000374_tie.2018.2795525-Figure2-1.png", "caption": "Fig. 2. The distribution of the eddy current in the secondary:(a) laterally asymmetric secondary on the curve rails (b) the flat-solid secondary (c) the ladder-slit secondary", "texts": [ " The primary consists of the iron core and the three-phase windings. The secondary consists of the aluminum and back-iron plate. The width of the secondary is larger than that of the primary core, and the overhang of the winding oversteps the width of the secondary. The parameters of primary are shown in the Table I. In Fig.1, only the aluminum plate is slit, the back-iron plate remains unchanged. Therefore, the ladder-slit secondary is also simple. When the vehicle is running in the turning of the rail shown in the Fig.2 (a), the primary installed under the bogie will be at a displaced position, the paths of the eddy current in different secondaries with the lateral displacements will be shown in the Fig.2 (b)-(c). In the Fig.2 (b)-(c), the regions I and III are the overhangs of the secondary and the region II is the active zone between the primary and secondary. In addition, in the Fig.2 (c), the region I ' is the coupled zone of the secondary conductor and the overhang of the windings, the region I '' is the coupled zone of the secondary side bar and the overhang of the windings, as well as the region III ' and III '' .It can be seen that the current in ladder-slit secondary is more inerratic than it in flat-solid secondary, and the x-component of the eddy current in the region I is much smaller, the edge effect is much smaller consequently. In order to stabilize the vehicle in the curve rails, the ladder-slit type secondary shown in the Fig", " The current induced in the secondary is produced by the variable magnetic field and the relative motion of the primary and secondary, the two ways are all related to the frequency and the eddy current increase with increase with the frequency when the slip is same. When the frequency is relatively small, the path of eddy currents is relatively short, and then the proportion of x-component is relatively large in the active zone. Therefore, in the Fig.6, the value of Jy increases with the increase of frequency; the value of Jx decreases with the increase of frequency in the active zone (II) and increases in the overhangs of the secondary. In the Fig.6, the flat-solid secondary is divided into three regions I, II and III as shown in Fig.2 (b). Due to the edge effect, the eddy current of the region II includes Jy and a certain proportion of Jx. The value of Jy decreases with the increase of y 0278-0046 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. coordinate values, and the value of Jx increases with the increase of y coordinate values in Fig.6 (b). Moreover, the value of Jy increases with the increase of frequency. In the Fig.6, the ladder-slit secondary is divided into five regions I', I'', II, III', and III'' as shown in Fig.2(c). In the region of the secondary conductor (I'', II, III'), the value of Jy has no obvious change and the x-component of eddy current is very small. In the region of the side-bar (I', III'') which is used to provide the return path of the eddy current, the value of Jx is very high and Jy is very small. The distribution of the current induced in the secondary is shown in the Fig.7 and the arrow shows the flow direction of eddy current at one pole pitch. In the Fig.7, the active zone (region II) is coupled area of primary and secondary, namely the width of the primary core and the overhang (region I, III) is the region out of stack of the primary" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003385_b97376_5-Figure5.8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003385_b97376_5-Figure5.8-1.png", "caption": "FIGURE 5.8.1. The geometry of the snakeboard.", "texts": [ " Spinning the momentum wheel causes a countertorque to be exerted on the board. The configuration of the board is given by the position and orientation of the board in the plane, the angle of the momentum wheel, and the angles of the back and front wheels. Let (x, y, B) represent the position and orientation of the center of the board, 1/J the angle of the momentum wheel relative to the board, and (h and (h the angles of the back and front wheels, also relative to the board. Take the distance between the center of the board and the wheels to be r. See Figure 5.8.1. Following Bloch, Krishnaprasad, Marsden, and Murray [1996], a simpli fication is made that we shall also assume here, namely that (h = -\u00a22 , J1 = h. The parameters are also chosen such that J + Jo + J1 + h = mr2, where m is the total mass of the board, J is the inertia of the board, J0 is the inertia of the rotor, and J1 , J2 are the inertias of the wheels. This simplification eliminates some terms in the derivation but does not affect the essential geometry of the problem. Setting \u00a2> = \u00a21 = - \u00a22 , then the configuration space becomes Q = SE(2) x S 1 x S 1 , and the Lagrangian L : TQ ---+ IR is the total kinetic energy of the system and is given by 1 2 2 1 2 '2 1 " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001320_j.jmapro.2020.06.041-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001320_j.jmapro.2020.06.041-Figure1-1.png", "caption": "Fig. 1. Model set up: (a) schematic of SLM process, (b) gauss heat source and (c) FE meshed model.", "texts": [ " LED=P/(vht) (1) where P denotes the laser power, v is the scan speed, h is the hatch space and t is the layer thickness. Vickers hardness tests at the cross section of the molten pool were carried out based on a DHV-1000ZTEST microhardness tester with a load of 100 g and an indentation time of 15 s. Samples for metallographic observations were polished, and etched with a 4% nitric acid alcohol solution. The microstructure in the bottom layer of the samples was characterized using the back-scattered scanning electron microscope (Quanta 250). Fig. 1 shown the schematic diagram of the SLM process for metal powder. When the laser beam irradiates the surface of a powder bed, the laser energy is absorbed by the metal particles. The absorbed energy melts the powder, and the melted metal penetrates into the adjacent powder layer form a small molten pool. A three-dimensional finite element thermo-model was established to analyze the thermal performance using the commercial ABAQUS software. For heat transfer problems, the laser beam was modeled as a gauss heat flux, via a usersubroutine DFLUX (Fig. 1(b)). During the SLM process, heat losses due to convection and radiation were also taken into account for proper description of the thermal behavior. The FE model developed for powder bed fusion process simulation was presented in Fig. 1. The powder layer had the size of 2\u00d71\u00d70.04 mm3 and it was meshed with the fine size of 0.02\u00d7 0.02\u00d7 0.013 mm3 (Fig. 1(c)). The H13 tool steel block with the dimensions of 3\u00d7 2\u00d70.5 mm3 was taken as the substrate and it was mashed with the coarse size of hexahedron element structure. The three-dimensional simulation model was meshed into 59,310 elements. A non-linear transient thermal analysis was performed to obtain the temperature evolution during the laser melting process. The transient spatial distributions of the temperature field satisfy the differential equation of 3D heat conduction in the component, which can be expressed as [24,25]: \u239c \u239f \u2202 \u2202 = \u2202 \u2202 \u239b \u239d \u2202 \u2202 \u239e \u23a0 + \u2202 \u2202 \u239b \u239d \u2202 \u2202 \u239e \u23a0 + \u2202 \u2202 \u239b \u239d \u2202 \u2202 \u239e \u23a0 +\u03c1c T t x k T x y k T y z k T z Q (2) where T is the temperature of the powder part, \u03c1 is the material density, c is the specific heat capacity, t is the interaction time, k is the thermal conductivity of the material, and Q is heat generated per volume within the component", " In addition, once the accumulative internal thermal stress exceeds the fracture strength, the unmelted defect will tend to crack [30]. As the applied laser power increased or scan speed decreased (and thus at higher LED), the molten pool dimensions increase gradually. A higher laser energy produces sufficient liquid-phase diffusion, heat transfer and metal flow within the melt pool, which enhance the metallurgical bonding of between the adjacent tracks and promote densification. The effects of laser power and scan speed on the temperature variation with time at the center point (P1 in Fig. 1) of the first layer are shown in Fig. 4. The temperature of the monitoring point rises up rapidly to a maximum, and then decreases sharply as the laser beam moves away. As the laser power increases, the maximum temperature increases considerably from 2085 to 2851 \u00b0C. Meanwhile, the liquid lifetime of molten pool increases from 0.39 to 0.60ms (Fig. 5(a)). On the contrary, as the utilized scan speed increases from 300 to 800mm/ s, the maximum temperature reduces clearly from 3644 to 1827 \u00b0C. Accordingly, the liquid lifetime of the molten pool reduces markedly from 1" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000620_s11071-018-4338-3-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000620_s11071-018-4338-3-Figure1-1.png", "caption": "Fig. 1 Leaf spring mounting", "texts": [ " Additionally, the profile of the modern leaf spring is not a circular arc, despite the fact that leaf springs are usually designed based on a circular arc profile following the ideal uniform strength beam model. It should be noted that most modern leaf springs are not close to either the elliptic or the circular arc profile curves.Accurate description of the geometry of the leaf spring profile curve, however, is necessary in order to develop credible virtual prototyping mod- els that capture accurately the spring deformations and forces. Because the profile curve of the leaf spring, as shown in Fig. 1, can be complex, it is advantageous to use three-dimensional geometric data acquisition techniques to extract the spring geometric information. To this end, automatic geometric data acquisition (AGDA) techniques are discussed in this paper. The three-dimensional scanning technology has been of particular interest due to its potential for rapid and accurate measurement of complex three-dimensional geometry. The technology has been applied in various engineering fields for uses such as surveying buildings [2], road surface condition evaluation [3], evaluation of production samples after manufacturing for quality control, as well as for reverse engineering applications [4]", " Based on the geometric features of the leaf spring, the relaxed uniform cubic B-spline is proposed to represent the spring profile curve using the scanning point cloud. A discussion on the conventional piecewise-tapered modeling approach used for parabolic leaf springs is also provided in this section. It is shown that, by using ANCFelements, the tapered geometry of the leaf spring can be systematically and accurately described. 5.1 Leaf spring configuration The general leaf spring configuration is shown in Fig. 1. The leaves are clamped together by the center bolt, and the leaf spring assembly is fixed to the spring seat by a set of U-bolts, while the spring seat is rigidly attached to the axle. The leaf spring is connected to the chassis using the shackle at one end and a pin joint at the other end. The shackle can have a small rotation to allow for small longitudinal translation of the spring with respect to the chassis. Leaf springs are designed to have pre-stress in order to reduce the stress of the master leaf when the spring is mounted on the vehicle", " In order to account for the pre-stress caused by the assembly process, the configuration before assembly shown in Fig. 8a should be used as the initial stress-free configuration, the mapping relation is shown as the solid line arrows in Fig. 11, and thus Ji = Ju . Therefore, there exists initial stress in the configuration of the leaf spring assembly since J = JeJ\u22121 u = J0J\u22121 u and the initial strain \u03b50 = ( J\u22121T u ( JT0 J0 ) J\u22121 u \u2212 I ) /2. The difference between the assembly configuration and the un-deformed configuration ed0 = e0 \u2212 eu is used to determine the desired pre-stress value. As shown in Fig. 1, the leaf spring is connected to the chassis at one end using the shackle and at the other end using a pin joint. It is also rigidly connected to the axle at the spring seat by a set of U-bolts at the center section. In this investigation, it is assumed that the chassis, shackle, and leaf spring eye can be modeled as rigid bodies since they are relatively stiff compared to the flexible leaf spring. The chassis, axles, and leaf springs can all be considered as one ANCF/FE mesh in which the constraint equations and connectivity conditions, including the pin joint constraints, can be formulated using linear algebraic equations" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003523_robot.1988.12156-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003523_robot.1988.12156-Figure1-1.png", "caption": "Figure 1: Notation Used in the Discussion.", "texts": [ " Joints 0 and n + I, located in the world and end effector, respectively, are imaginary joints for convenimce of notation. One coordinate system is associated with each angular and linear velocity vector so that its motion relative to the preceding system is defined by its associated velocity vector. The expressions 3; and 3 are the relative angular and linear velocities of the coordinate system after the ith angular velocity vector between joints j - l and j with respect to the previous system. Refer to figure 1. Since 3; and 3 are represmtations of the error in the unknown parameters, they are constant with respect to joint configuration. The expression Pf is the point of application of the i\u2019th angular velocity vector between joints J - 1 and 3 . The extended angular and linear velocities of the tool can be written as: For a Hartenberg-Denavit [6] model, the quantity d, equals A92 + Aa; and equals A12 + Ar2, where 2 is a unit vector along the motion axis between bodies z and z - 1 and 2 points along the z axis" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003349_1464419001544124-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003349_1464419001544124-Figure9-1.png", "caption": "Fig. 9 (Left) Scheme of the high-speed air test spindle and (right) three-dimensional computer model of the bearing mounted on the test spindle (dynamic deformation shape including bearing waviness)", "texts": [ " Owing to the more advanced mathematical bearing model, identification of both the normal and tangential damping (Fig. 8) of the rolling contact is possible. A disadvantage of the new test set-up might be the sensitivity of the measurement results to the influence of the preloading tool acting on the outer ring. However, the tests showed good repeatability of the identification method. The new test rig developed has an even simpler design than the one presented in Section 3. A standard highspeed spindle for vibration testing of rolling bearings was adapted for the measurements (see Fig. 9). The spindle is carried by aerostatic bearings and acts, at the same time, as the rotor of an electric motor. A single test bearing is mounted on the spindle and the bearing outer ring is axially preloaded by a soft spring mounted on a pneumatic loading tool. A soft preloading spring is used for dynamic decoupling of the bearing from the preloading tool. It is assumed that the bearing is mechanically decoupled from the spindle and the loading device. As mentioned above, vibrations of the bearing outer ring are not excited by external forces but by the \u2018internal\u2019 excitation due to the waviness of the bearing raceways and rolling elements (see also Section 4.3). The radial and axial vibrations of the bearing outer ring and K01699 \u00a9 IMechE 2000 Proc Instn Mech Engrs Vol 214 Part K at Eindhoven Univ of Technology on January 5, 2015pik.sagepub.comDownloaded from the axial vibrations of the motor casing are measured with accelerometers. Together with the test rig described above, an advanced mathematical model of the bearing mounted on the test spindle was developed in reference [2] (see right-hand part of Fig. 9). This model can be used to translate the identified modal damping ratios into physical damping coefficients representing the rolling contact properties. The three-dimensional bearing model accounts for the following features influencing the bearing dynamics: (a) EHL contact stiffness and damping (both in the normal and tangential directions), modelled by nonlinear Hertzian springs and viscous dampers respectively (see Fig. 8). (b) full flexibility of the bearing outer ring; (c) waviness of the raceways and rolling elements (note that surface topography is described in an efficient way by a small number of statistical parameters using the features of \u2018self-affine\u2019 fractals); (d) diameter variations of the rolling elements; (e) cage run-out (leading to non-uniform ball spacing)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000828_j.mechmachtheory.2019.103658-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000828_j.mechmachtheory.2019.103658-Figure8-1.png", "caption": "Fig. 8. Illustration of the tooth contact pattern under different conditions: (a) uniform distribution and (b) contact concentrated on one side of the tooth surface.", "texts": [ " 7 , OA represents the theoretical gear position, denoted \u03b8 in Fig. 7 (a). OB represents the position when it is affected by tooth form deviations, denoted \u03b8 f in Fig. 7 (b). OC represents the position when it is further affected by contact deformation under a given load, denoted \u03b8d in Fig. 7 (c). For the contact status, it may significantly affect the contact pressure distribution of the tooth surfaces. The desired contact status can distribute the load uniformly on the tooth surface, as illustrated in Fig. 8 (a). The tooth contact may be concentrated on one side of the tooth surface when affected by machining and assembly errors, as illustrated in Fig. 8 (b). Thus, it is important to analyze the contact behavior between mating tooth surfaces when evaluating the transmission performance. As the contact position varies continuously during the transmission process, the skin model shapes generated in Section 3 must be segmented to solve the contact problem. As shown in Fig. 9 , each pair of mating tooth surfaces is segmented according to the angle of rotation, and then the contact problem is solved at each position. For example, position 5 shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003013_s0921-8890(99)00058-5-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003013_s0921-8890(99)00058-5-Figure1-1.png", "caption": "Fig. 1. Concept of on-line trajectory generation.", "texts": [ " A manipulator working in hazardous environment (in nuclear plants or reactors, for example) may require a new optimized trajectory to be generated on-line if an obstacle is found in the path of the manipulator on which it is actually moving. Thus, on-line trajectory generation may be considered as the computation of \u2217 Corresponding author. E-mail addresses: sab@it.dtu.dk (S.A. Bazaz), tondu@dge.insatlse.fr (B. Tondu) the next trajectory at the same time the manipulator is executing the present one. Fig. 1 depicts such motion. Here, the manipulator is moving between points P2 and P3 while the trajectory generator calculates the trajectory between points P3 and P4. This requires the knowledge of only one point (P4 in this case) lying after the existing segment for calculating the trajectory between points P3 and P4. Economical utilization of manipulator needs the fast execution of a given task with a smooth motion having at least the continuity of position, velocity and acceleration (jerk, if required) between two adjacent segments" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003813_1.2098890-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003813_1.2098890-Figure2-1.png", "caption": "Fig. 2 3-DOF Planar parallel manipulator", "texts": [ " 7 in the above equation we obtain ti = BiB\u0303i\u22121ti\u22121 + Bip\u0303i\u0307i 12 We introduce the notation ti = Bi,i\u22121ti\u22121 + pi\u0307i 13 where Bi,i\u22121 = 1 O \u2212 Ai 1 14 pi = ei Diei for revolute joint 15 pi = 0 ei for prismatic joint 16 where Ai is the cross product matrix of ri\u22121+di . Matrix Bi,i\u22121 may be called the twist propagation matrix while pi, the twist generator. The twist ti is thus the sum of twist ti\u22121 and the twist generated at the joint i, both evaluated at Ci. Equation 13 is recursive in nature and is in fact the forward recursion part of the recursive Newton-Euler algorithm proposed by Luh et al. 12 . Modeling of the 3R-Planar Platform Manipulator Figure 2 shows the 3R planar platform manipulators with three degrees of freedom 20 . For the sake of simplicity we restrict ourselves to system that has: 1 only revolute joints, 2 identical legs; and 3 a moving platform in the shape of an equilateral triangle. The three-degrees-of-freedom three-dof planar manipulator consists of three identical dyads, numbered I, II, and III coupling the platform P with the base, such that their fixed pivots lie on the vertices of an equilateral triangle, as well. The proximal and the distal links of each dyad are numbered 1 and 2, respectively", " Velocity Analysis. Since the manipulator is planar, we use twodimensional position vectors, three-dimensional twist vector t = ,v T, and three-dimensional wrench vectors w= n , f T, where is the angular velocity, v is the two-dimensional velocity vector, n is the angular moment, and f is the two-dimensional force vector. For each chain, we define position vectors di from the ith joint axis to the mass center of link i ,ri from mass center of link i to the i+1 st joint axis, and ai=di+ri as shown in Fig. 2. The twist of the end effector of any chain is given by Saha and Schiehlen 17 as tP = BP3t3 17 where BP3 = 1 0T Er3 1 ; E = 0 \u2212 1 1 0 t3, the twist of the third link with respect to its mass center, is computed recursively for each serial chain from its preceding link as t3 = B32t2 + p3\u03073 18 B32 = 1 0T E r2 + d3 1 ; p3 = 1 Ed3 where the 3 3 matrix B32 is the twist-propagation matrix and p3 is the twist generator, t2 is the twist of link 2 with respect to its mass center; \u03073 is the relative rate of the third joint, while 0 is the two-dimensional zero vector and 1 is the 2 2 identity matrix" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000650_tia.2018.2880143-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000650_tia.2018.2880143-Figure7-1.png", "caption": "Fig. 7. Winding configuration of the test motor. (a) Without modified winding, (b) With modified winding.", "texts": [ " RESULTS In order to validate the characteristics of the modified winding shape and the cylindrical copper shield, the experimental setup is composed including oscilloscope, test motor, SVPWM inverter, and dynamo set, as shown in Fig. 5. Fig. 6 (a) shows the appearance of the six-pole nine-slot test motor (IPMSM) used in experiment and Fig. 6 (b) shows the plastic end plate, which is used to electrically separate the bearing and the stator. Moreover, the brush is contacted to measure the shaft-to-frame voltage. Fig. 7 shows the test models with and without modified winding shape. Moreover, Fig. 8 shows the cylindrical copper shield construction. Due to the end plated is the plastic material, separate wire is used to connect the copper shield with the ground (housing). 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. methods The simulation is performed using the equivalent circuit model, as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000064_s12206-017-0239-5-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000064_s12206-017-0239-5-Figure2-1.png", "caption": "Fig. 2. Single track deposition and dimensional characteristics.", "texts": [ ", median laser power of 900 W, powder feed rate of 5.0 g/min, scanning speed of 850 mm/min, coaxial gas flow rate of 8.0 L/min, and powder gas flow rate of 2.5 L/min) were defined in Table 2 to analyze the effect of each process parameter on the deposited single-track geometry. A 35 mm long single track was deposited repetitively onto a substrate three times according to each corresponding process parame- E. M. Lee et al. / Journal of Mechanical Science and Technology 31 (7) (2017) 3411~3418 3413 ter, as shown in Fig. 2(a). In order to observe the deposited track geometry, the specimen was cut 10 mm away from the single-track starting point using a diamond wheel. For observing the cross-sectional profile using stereoscopic microscope images, the surface of the cut specimen\u2019s cross section was polished to prevent scratches and etched with hydrochloric and nitric acid in a 3:1 ratio. Fig. 2(b) shows the bead cross section observed using a stereoscopic microscope (50 \u00d7 magnification). In this figure, H is the deposited bead height; W is the bead width; and D is the dilution depth representing the thickness of the melted substrate mixed with the deposited materials. In addition, two combined parameters, specific energy density, E (J/mm2), and powder feeding density, G (g/mm2), were defined as in Eqs. (1) and (2) to investigate their influence on the resulting deposited single-track geometry" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000998_j.jsv.2020.115374-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000998_j.jsv.2020.115374-Figure3-1.png", "caption": "Fig. 3. Position of the field points.", "texts": [ " Table 2 lists the characteristic frequencies of the bearing when it is applied to a motorized spindle. Assume that the bearing operates under an excellent lubrication condition. The bearing axial preload is maintained at 500 N. The bearing rotational speed range is set as 10,000e45000 r$min 1 and the step size is 1000 r$min 1 to analyze the relationship between the bearing noise and the rotational speed. The damping coefficients [44e46] are presented in Fig. 4. Two points are selected to analyze the radiation noise of the ACCBB. As shown in Fig. 3, the analysis points are both located in the bearing plane, 100 mm away from the bearing axis. The noise at the analysis points are characterized by SPL. To analyze the bearing noise in a steady state, the nonlinear dynamic differential equations are solved by Gear stiff integration algorithm with variable steps [47], and then the obtained vibrational velocities are transformed from the time domain to the frequency domain by fast Fourier transform (FFT). The vibrational velocities in the frequency domain are imported into the FE model of the bearing to obtain the normal velocities on the surface of each bearing component" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003066_s0003-2670(98)00083-x-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003066_s0003-2670(98)00083-x-Figure1-1.png", "caption": "Fig. 1. Cyclic voltammograms at a bare gold electrode (1 mm diameter) of (a) 0.5 mM hydrogen peroxide. (b) 1 mM ascorbic acid; (c) 0.5 mM potassium hexacyanoferrate(III) 0.5 mM potassium hexacyanoferrate(II). (d) 1 mM ferrocene carboxylic acid in 0.2 M phosphate buffer (pH 7.1); Scan speed 25 mV s\u00ff1.", "texts": [ " The GOD \u00aelm was cross-linked by holding the electrode over an atmosphere of glutaraldehyde for ca. 1 h at 48C. While it may be speculated that the pyridyl nitrogens of PySSPy may play a part by linking themselves to the NH 3 residues of GOD through weak hydrogen bond formation, it is more likely that GOD is present simply as a crosslinked layer on the SAM. The cyclic voltammograms (CVs) of hydrogen peroxide, ascorbic acid, hexacyanoferrate(II) and ferrocene carboxylic acid (FCA) in a buffer solution (pH 7.1) are shown at bare Au (Fig. 1) and SAM modi\u00aeed Au (Fig. 2(A) and (B)) electrodes. It can be seen that these compounds show their characteristic electrochemistry at a bare Au electrode (Fig. 1). The Faradaic response, however, is suppressed to some extent on an electrode modi\u00aeed for 1 h (Fig. 2(A)). The suppression is more evident at the electrode modi\u00aeed for a longer time (Fig. 2(B)). This is obviously due to the barrier properties of the monolayer which bring about the decrease in background current. Creager and Olsen [9] observed that at a 6-mercaptohexanolcoated gold electrode, the oxidation of FCA is more strongly suppressed than hexamethylferrocene oxidation. We found that a PySSPy-modi\u00aeed electrode does not present a signi\u00aecant barrier to the transport of FCA (or FCA )", " The peak current is related to the surface coverage by the relation ip n2F2A\u00ff 4RT where n represents the number of electrons involved in the reaction, A (cm2) is the area of the electrode, \u00ff (mol cm\u00ff2) is the surface coverage and other symbols have their usual meaning. The surface coverage was found to be 1.7 10\u00ff12 mol cm\u00ff2. We attempted to determine the approximate rate of the reaction (k) [Eq. (1)] from an analysis of the CVs assuming k to be large. Andrieux and Saveant [17] have analysed the CVs in the framework of a model of a chemically modi\u00aeed redox electrode. Based on extensive computation, a working curve showing the relationship between numerical values of ip/nFA (DnFv/RT)1/2C and log[k\u00ff /(DnFv/RT)1/2] (Fig. 1 in [17]) is given. Here n represents the number of electrons involved in the reaction, A (cm2) is the area of the electrode, C is the bulk concentration, D is the diffusion coef\u00aecient and the other parameters have their usual signi\u00aecance. The value of k can thus be calculated from such a working curve. For the SAM-modi\u00aeed electrode, an analysis of the CVs gave an average value for the ratio ip/nFA(DnFv/RT)1/2C of 0.410. Using this value and Fig. 1 in [17] the rate constant, k, for reaction {eq. Eq. (2)} was calculated to be 2.8 106 M\u00ff1 s\u00ff1. The results have shown that the PySSPy layer suppresses Faradaic responses due to dioxygen, hydrogen peroxide and to a limited extent ascorbic acid. It still allows transport, although somewhat limited, of FCA, a redox mediator. GOD can successfully be incorporated into the SAM monolayer with no serious loss of bioactivity. Large catalytic currents are observed with a linear response over a fairly wide range of glucose concentrations" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003894_mcs.2005.1499390-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003894_mcs.2005.1499390-Figure2-1.png", "caption": "Figure 2. Pumping strategy with instantaneous transitions from standing to squatting and vice versa. The 6 o\u2019clock figure shows the rider at the lowest point of the swing\u2019s trajectory transitioning from a squatting position (dotted red) to a standing position (solid black). (Figure modified from [4].)", "texts": [ " The child then travels toward the highest point while standing, and returns to the squatting position in the vicinity of the highest point. On the return journey, the child is again squatting while approaching the midpoint, and stands up near the midpoint, thus repeating the process. A look around the neighborhood playground reveals that children playing on swings generally follow the same strategy. In this article, we show that if the transitions to standing and squatting occur instantaneously, then this pumping strategy is time optimal (Figure 2). The rider-and-swing system is modeled as a pendulum with a bob of mass m attached to a fixed support by a rope of variable length l(t). The rope is taken to be massless, and the angle of the rope with respect to the vertical is denoted by \u03b8(t) (Figure 3). Let l+ and l\u2212, satisfying 0 < l\u2212 < l+, denote the maximum and minimum lengths of the pendulum corresponding to squatting and standing, respectively. Let L (1/2)(l+ + l\u2212) be the mean length of the pendulum. Dissipative forces such as bearing friction and wind drag are ignored", " By standing and squatting at appropriate times during the motion, it follows from (4) that the rider increases the amplitude of oscillation of the swing. When the process is carried out in reverse, by standing at the highest point and squatting at the lowest point of the swing\u2019s trajectory, the amplitude of oscillation of the pendulum is decreased. The amplitude of oscillation can thus be increased or decreased by suitably altering the length of the pendulum. The pumping strategy described previously and shown in Figure 2 leads to a geometric increase in the mechanical energy of the system [8]. In this strategy, the rider does the most work on the swing per oscillation, since the rider stands up at the lowest point, in the presence of the maximal gravitational and centrifugal forces, and squats at the highest point, where the centrifugal force vanishes and the component of the gravitational force along the length of the swing reaches its minimum. Since the work done on the swing is converted into stored energy, an increase in the mechanical energy of the system results in a corresponding increase in the amplitude of oscillation", " When the swing must be pumped to increase its amplitude of motion, substituting \u03c6 = (2n + 1)\u03c0 in (22) and using (17) and (19) we have u\u2217(t) = sgn[2p1(t)x2(t) + p2(t)x1(t)] = sgn [ 2 1 \u2212 2\u03b5u\u2217 sin \u03c9t cos \u03c9t + 1 1 + \u03b5u\u2217 sin \u03c9t cos \u03c9t ] = \u2212 sgn[x\u2217 1(t)x\u2217 2(t)]. (24) When the amplitude of oscillation of the swing must be decreased, substituting \u03c6 = 2n\u03c0 in (22) yields u\u2217(t) = sgn[x\u2217 1(t)x\u2217 2(t)]. (25) Optimal trajectories for the two cases are shown in Figure 6. The optimal control strategies (24) and (25) are in feed- back form, and (24) corresponds to the pumping strategy shown in Figure 2, where the rider stands up at the lowest point and squats at the highest point. To solve the time-optimal control problem for the nonlinear system (8), we use techniques from geometric optimal control [24]. Replacing l by u as the control input in (8), we have x\u0307 = h(x,u) x2 u2 \u2212g u sin x1 , (26) problem for the nonlinear system (26) by considering an auxiliary system with velocities in the segment joining h\u2212(x) and h+(x). To illustrate this idea, we introduce the auxiliary system x\u0307 = F (x) + G(x)v, |v| \u2264 1, (27) where F (x) c 2a x2 \u2212 g 2 b sin x1 , G(x) \u2212b l 2a x2 \u2212 g 2 l sin x1 , August 200554 IEEE Control Systems Magazine x1 (a) x2 Target Circle xini Standing Squatting x1 x2 Standing Squatting Target Circle xini (b) and a (l+l\u2212)2, b l+ + l\u2212, and c l2+ + l2\u2212" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000088_j.jsv.2017.12.022-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000088_j.jsv.2017.12.022-Figure5-1.png", "caption": "Fig. 5. Clearance type non-linear function [25].", "texts": [ " It consists of normal vector and rotational radii of effective mesh point which can be expressed as: hl \u00bc n Nlx;Nly;Nlz; llx; lly; llz o (23) The mesh force Fm along LOA is calculated from translational dynamic transmission error (d) and unloaded transmission error (eu): Fm \u00bc km,f \u00f0d eu\u00de cm, _d _eu (24) in which km denotes the mesh stiffness derived from loaded and unloaded TE expressed in Equation (15) and cm is the empirical mesh damping ratio. Dynamic transmission error d describes the difference between ideal and real position at certain rotation speed which can be written as: d \u00bc hTp, n xp; yp; zp; qpx; qpy; qpz o hTg, n xg; yg; zg; qgx; qgy; qgz o : (25) The clearance type nonlinear function f \u00f0d eU\u00de has three stages depending on the relationship between (d eu) and backlash bc as shown in Fig. 5: f \u00f0d e\u00de \u00bc 8< : d eu bc; d eu bc; 0; bc < d eu 0 \u2208 R are specific rotor coefficients and l > 0 \u2208 R is the arm length", " The actuator dynamics are taken into account using the following actuator model \u02d9\u0302u = T\u22121r (ucmd \u2212 u\u0302) , (16) where Tr > 0 \u2208 R is the time constant for the approximated behavior of the squared rotor speeds. Note that through the computation of the incremental moments \u2206 ~M and using the control allocation (15), the input commands ucmd are continuously being reallocated. In this section, the performance of the controller presented in Sections III-IV is shown in an outdoor flight test. The testbed is the AscTec Firefly [27] which can be seen in Figure 1. For flight tests, the controller runs at a rate of 1kHz on a Gumstix Overo FireSTORM Computer-OnModule (CoM) which communicates with the AscTec Autopilot. The controller is designed in Simulink R\u00a9 and ported to C using the Simulink R\u00a9 CoderTM. For the flight test the parameters in Table I have been used. The subscripts Base and Inc indicate the gains that correspond to the baseline or incremental controllers respectively. The time constants used for the filter (14) and the actuator model (16) can be obtained from the last row" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003744_6.2004-875-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003744_6.2004-875-Figure2-1.png", "caption": "Figure 2. Definition of the Launch Plumb-line Euler Attitude Angles", "texts": [ "1 Kinematics coordinate correction The initial X-33 ascent controller design incorrectly1 assumed an airplane Euler angle coordinate frame instead of a launch plumb-line coordinate frame as used by the X-33 guidance command. The order of rotations for the airplane Euler angles is defined by yaw-pitchroll ( - - , or 3-2-1), whereas the order of rotations for< ) 9 the launch plumb-line system that is used for X-33 and most other launch vehicles is defined by pitch-yaw-roll ( - - , or 2-3-1). The different rotation ordering) < 9 causes a difference in the kinematics equations of motion, and the controller gains. The launch plumb-line kinematics equations of motion can be derived from the following Figure 2. The launch plumb-line kinematics equations of motion are given by (in contrast to the airplane kinematics equations of motion ):1 ) 9 < 9 < < 9 9 9 < 9 < 9 \u00de \u0153 ; \u00d0 \u00d1 \u00d0 \u00d1 < \u00d0 \u00d1 \u00d0 \u00d1 \u00de \u0153 ; \u00d0 \u00d1 < \u00d0 \u00d1 \u00de \u0153 : ; \u00d0 \u00d1 \u00d0 \u00d1 < \u00d0 \u00d1 \u00d0 \u00d1 cos sec sin sec sin cos tan cos tan sin (5) The corresponding nominal body rate control functions, which are obtained by inverting (5), are given by: : \u0153 \u00d0 \u00d1 \u00de \u00de ; \u0153 \u00d0 \u00d1 \u00d0 \u00d1 \u00d0 \u00d1 \u00de \u00de < \u0153 \u00d0 \u00d1 \u00d0 \u00d1 \u00d0 \u00d1 \u00de \u00de 9 ) < ) 9 < < 9 < 9 ) 9 < sin cos cos sin cos sin cos (6) where the over-bar denotes a nominal trajectory variable" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003629_bf00188926-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003629_bf00188926-Figure8-1.png", "caption": "Fig. 8A-D. Stick figures of the mesothoracic (anterior pair) and metathoracic (posterior pair) legs were plotted from digitized records of escape movements in tethered animals videotaped from the ventral surface. Since they were tethered, the leg movements did not actually turn the animal's body. A is an example of a type I turn. The wind stimulus was placed 45 ~ from the rear of the animal. In this and all other stick figures the curved arrow indicates direction of leg movement. T 1 legs are not indicated. Note all four of the T 2 (Top) and T 3 (Bottom) legs move backward, while the T2 legs move toward the source of the wind stimulus. B is another type I turn, this time from a 60 ~ stimulus. C is an example of a type II turn from a 90 ~ stimulus. In this case the contralateral T 3 leg moves forward rather than backward. Side views confirmed that the tarsus was contacting the ground. D is an example of a type III turn from a 120 ~ stimulus. Here both T 3 legs move forward due to CF flexions. This would move the animal backward in a free ranging situation. The opposing movements of the ipsilateral T 2 and T 3 legs could only occur in a tethered situation since both legs had tarsi contacting the substrate making them power strokes. Were the animal's body actually moving, some compromise movement would have to have occurred", "texts": [ " In most trials, we were not able to visualize the leg movements well enough to permit the same kind of quantitative t reatment as we made with the tethered preparation. However, we were able to recognize the basic leg movements of the tethered preparat ion in enough free ranging preparat ions to understand how these leg movements drive the body through the escape turn. In tethered animals, the FT joints of the T2 segment did not vary with wind angle. The FT joint of the leg ipsilateral to the wind source extended while the FT joint on the contralateral leg flexed (Fig. 8). In free ranging animals this pushed the front of the animal away f rom the wind source (Fig. 9). This then provides the basic turning force for all turns regardless of wind angle. With regard to the CF joints, the tethered records revealed three different types of leg movements. In the simplest type of movement , all o f the CF joints extend driving the legs backward. We refer to this as a type I turn. All responses to winds f rom 45 ~ , and 95% of responses to winds f rom 60 ~ are type I turns (Fig. 8A and B and Table 1). In the freely moving animals, such leg movements push the animal forward as the FT joints turn the animal away f rom the wind source (Fig. 9A). When the wind tube was placed at 90 ~ (directly to the side of the animal) 61% of the responses were type I, but 35 % of the responses included flexion of the T3 CF joint contralateral to the wind (Fig. 8C and Table 1). In tethered animals this caused the contralateral T3 leg to be turn described by Camhi and Levy (1988). With the wind tube situated in front of the animal (120~ 39% of the turns included flexion of both T3 CF joints, which pulls both of these legs forward (Fig. 8D and Table 1). We refer to this as a type III turn. In freely moving animals, flexion of both CF joints pulls the animal's body backward over the legs (Fig. 9C). The animal then thrusts forward in a movement similar to a type I turn. These movements can turn the animal in excess of 90*. Effect of initial joint angle on rate of movement pulled forward. The ipsilateral T3 CF joint still extended driving that leg backward. We refer to this as a type II turn. In freely moving animals, the opposing CF movements of a type II turn result in a larger turn with little or no forward movement (Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001253_tmag.2019.2952446-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001253_tmag.2019.2952446-Figure6-1.png", "caption": "Fig. 6. Simulation model under a pole pitch with stator slots.", "texts": [ " Considering that the MMF varies with time and space, it can also be expressed as \u03bc 1,3,5 ( , ) cos( )F t F t p (4) where \u03c9 is the angular rotation speed corresponding to electrical frequency f of rotor, p is the pole pairs number, and F\u03bc is the amplitude of the \u03bc-th harmonic of the MMF F(\u03b8,t), it can be obtained by performing Fourier decomposition on F(\u03b8), the calculation result as shown in Fig. 5(b). B. Calculation of the air-gap permeance The air-gap length corresponding to the tooth is uniform and the magnetic flux density is basically the same. Thus, the magnetic potential can be calculated by \u03b4t N m \u03b4t 0 ( )B H F (5) where B\u03b4tN is the magnetic flux density at point N in the air gap corresponding to the stator tooth, as shown in Fig. 6. In 0018-9464 (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. range of the entire tooth pitch, the outer surface of the stator can be regarded as the equal magnetic potential surface, so the air-gap MMF at each position is Ft. And the effective air-gap length at one pitch can be calculated by 0 \u03b4t m \u03b4t ( , )= ( , ) F H B (6) where Bt(\u03b8,) is the distribution of the air-gap flux density" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001005_tasc.2020.2990774-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001005_tasc.2020.2990774-Figure7-1.png", "caption": "Fig. 7. Magnetic flux tube division of air gap between stator and mover at unaligned position. (a) Part I. (b) Part II.", "texts": [ " Referring to the loop current analysis method in the circuit theorem, this paper lists five loop equations for the equivalent magnetic circuit: R11\u03c61 +R12\u03c62 +R13\u03c63 +R14\u03c64 +R15\u03c65 = 4 (F1 + F2 + F3) (1) R21\u03c61 +R22\u03c62 +R23\u03c63 +R24\u03c64 +R25\u03c65 = 4F1 (2) R31\u03c61 +R32\u03c62 +R33\u03c63 +R34\u03c64 +R35\u03c65 = 4F1 (3) R41\u03c61 +R42\u03c62 +R43\u03c63 +R44\u03c64 +R45\u03c65 = 4F2 (4) R51\u03c61 +R52\u03c62 +R53\u03c63 +R54\u03c64 +R55\u03c65 = 4F2 (5) And they are simplified as following: \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 R11 4Rsp1 4Rsp1 4Rsp2 4Rsp2 4Rsp1 R22 4Rsp1 4Rsp2 0 4Rsp1 4Rsp1 R33 0 \u22124Rg1 4Rsp2 4Rsp2 0 R44 4Rsp2 4Rsp2 0 \u22124Rg1 4Rsp2 R55 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 \u00b7 \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 \u03c61 \u03c62 \u03c63 \u03c64 \u03c65 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 = \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 4(F1 + F2 + F3) 4F1 4F1 4F2 4F2 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 (6) In this formula: R11 = 4 ( Rsp1 +Rsp2 +Rsp3 + 1 2 Rg3 + 1 4 Rmp + 1 2 Rsy2 +Rsy1 ) (7) R22 = 4(Rsp1 +Rg1) (8) R33 = 4(Rsp1 +Rg1) (9) R44 = 4(Rg1 +Rsp2 +Rg2) (10) R55 = 4(Rg1 +Rsp2 +Rg2) (11) Next, the reluctance of each part of the air gap is specifically determined. In the division of the flux tube, the stator tooth containing the windings is divided into three segments, and the lengths are h1, h2, Lp-h1-h2 respectively. The magnetic permeability of the air gap is \u03bc0 = 4\u03c0 \u00d7 10\u22127. The air gap reluctance component Rg1 and Rg2 are [9] Rg1 = \u03c0 \u00b7 Cs 2 \u00b7 \u03bc0 \u00b7 Ls \u00b7 h1 (12) Rg2 = Cs \u03bc0 \u00b7 Ls \u00b7 h2 (13) In the Fig. 6, h1 = Lp/5, h2 = 3Lp/5. In order to calculate Rg3, the air gap flux tube is divided into four parts as shown in Fig. 7. In the Fig. 7(a), h3 = Cm/2\u2212Bs/2, h4 = Cm/2\u2212 Authorized licensed use limited to: Auckland University of Technology. Downloaded on June 02,2020 at 09:20:54 UTC from IEEE Xplore. Restrictions apply. Bs/2 +Bm/3, and the calculation expression can be expressed as Rg3a = \u03c0/2 \u03bc0 \u00b7 Ls \u00b7 ln (h4/h3) (14) Rg3b = \u03c0 (h3 \u2212 \u03b4) + 2\u03b4 2\u03bc0 \u00b7 (h3 \u2212 \u03b4) \u00b7 (Ls + Lm)/2 (15) Rg3c = \u03c0/2 \u03bc0 \u00b7 Ls \u00b7 ln(h3/(h3 +Bs/2)) (16) The flux tube of the air gap between the ends of the stator and the mover is shown in Fig. 7(b). The flux tube Rg3d can be seen as a sector rotated by 180\u00b0. The size of this sector is determined by 3D FEM. The sphere center is the center of stator and mover tip connection. The expressions are r1 = 1 2 \u00b7 \u221a \u03b42 + h4 2 (17) r2 = r1 + \u221a 2 2 \u00b7 Bs/2 + h3 +Bm/3 + h3 4 (18) Rg3d = 1 \u03bc0 \u00b7 (r1 + r2) \u00b7 ln(r2/r1) (19) Rg3 = 1 1/Rg3a + 1/Rg3b + 1/Rg3c + 1/Rg3d (20) The reluctance of each segment of the stator tooth is represented by Rsp1, Rsp2, Rsp3 and the reluctance of each segment of the stator yoke is represented byRsy1,Rsy2 and the reluctance of the mover tooth is represented by Rmp" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003855_j.mechmachtheory.2006.01.006-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003855_j.mechmachtheory.2006.01.006-Figure3-1.png", "caption": "Fig. 3. The fixed coordinate system.", "texts": [], "surrounding_texts": [ "The rank of the kinematic screws of the chain can be gained with algebra method:\nR\u00f0$ABCDE\u00de \u00bc 3\nThe rank deficiency of the chain is\nrABCDE \u00bc nABCDE R\u00f0$ABCDE\u00de \u00bc 5 3 \u00bc 2 \u00f024\u00de\nwhere nABCDE denotes the total number of the simplified screws [6] of the kinematic chain ABCDE.\nThe reciprocal screws (terminal constraints) of the kinematic chain can be obtained:\n$r ABCDE \u00bc\n$r 1 $ r 2 $ r 3\n2 64 3 75 \u00f025\u00de\nwhere\n$ r 1 \u00bc \u00f0 0 0 1 0 0 0 \u00de $r 2 \u00bc \u00f0 0 0 0 1 0 0 \u00de $ r 3 \u00bc \u00f0 0 0 0 0 1 0 \u00de\nThe free motions the end effector can execute will be gained according to Eq. (20):\n$ F E \u00bc\n$ f 1 $ f 2 $f 3\n2 64 3 75 \u00f026\u00de\nwhere $ f 1 \u00bc \u00f0 0 0 1 0 0 0 \u00de, and $ f 1 denotes one rotational constraint moment about z-axis; $ f 2 \u00bc \u00f0 0 0 0 1 0 0 \u00de, and $ f 2 denotes one translational constraint force along x-axis; $ f 3 \u00bc \u00f0 0 0 0 0 1 0 \u00de, and $ f 3 denotes one translational constraint force along y-axis.\nAs a matter of fact, $F E is a subspace spanned by $ABCDE. If we add M \u00bc Rank\u00f0$F E\u00de \u00bc 3 actuations to any three revolute pairs, revolute pairs A, B, and C for example, the kinematic screws of the chain become:\n$DE \u00bc $D\n$E\n\u00f027\u00de\nThe reciprocal screws of (27) will be\n$ r DE \u00bc\n0 0 1 0 0 0\n0 0 0 1 0 0\n0 0 0 0 1 0 xD xEffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0xD xE\u00de2 \u00fe \u00f0yD yE\u00de 2 q yD yEffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0xD xE\u00de2 \u00fe \u00f0yD yE\u00de 2 q 0 0 0 xEyD xDyEffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0xD xE\u00de2 \u00fe \u00f0yD yE\u00de 2 q\n2 6666664\n3 7777775 \u00f028\u00de\nTherefore, the free motions the end effector can execute under these actuations will be gained according to Eq. (20) again\n$Fn1 E \u00bc 0 0 1 yD xD 0 0 0 0 yD yEffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi\n\u00f0xD xE\u00de2 \u00fe \u00f0yD yE\u00de 2 q \u00f0xD xE\u00deffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0xD xE\u00de2 \u00fe \u00f0yD yE\u00de 2 q 0\n2 664\n3 775 \u00f029\u00de\nSo, M1 \u00bc Rank\u00f0$Fn1 E \u00de \u00bc 2. As a matter of fact, in this case, Eq. (29) is a subspace spanned by Eq. (27). Similarly, we can go on adding actuations to the chain to analyze the effects on the free motions of the end-effector. We can find that the number of free motions of the end-effector will not reduce to zero until five actuations\nare applied to the chain. Consequently, the term Pm 1\nj\u00bc1 Rank\u00f0$Fnj E \u00de will be five and be two more than Pm 1 j\u00bc1 F j M\nin [6] which equals the result of Eq. (24).", "So the CDOF proposed in [6] can also be denoted as\nF conf \u00bc M \u00fe Xm 1\nj\u00bc1\nRank $ Fnj\nE\n\u00bc Rank $ F E\n\u00fe Xm 1\nj\u00bc1\nRank $ Fnj\nE\n\u00bc 6 d \u00fe\nXm 1\nj\u00bc1\nRank $ Fnj\nE\n\u00f030\u00de\nEq. (30) has the same form as that in [6] but is much simpler.\n3. Applications and discussions\n3.1. Analysis on the mobility properties of a spatial four-bar mechanism\nA spatial four-bar mechanism, shown in Fig. 2 [6], consists of 2-RR (two revolute pairs) kinematic chains. To analyze the free motion of the end-effector BC, we first decompose the spatial parallel mechanism to form two kinematic chains connecting link BC with the base and then study the reciprocal screws of each kinematic chain.\nNow, we first analyze the terminal constraints of kinematic chain AB exerted to link BC. The coordinate system oxyz is established as Figs. 2 and 3 show, the origin of the coordinate system is superimposed with pair A, z-axis is along the axis of revolute pair A, and y-axis is perpendicular to the base plane, and therefore, x-axis is naturally parallel to the base plane. If we presume the coordinates of pair B are \u00f0 xB yB 0 \u00de, the Plu\u0308cker coordinates of pairs A and B can be denoted as", "$A \u00bc \u00f0 0 0 1 0 0 0 \u00de $B \u00bc \u00f0 0 0 1 yB xB 0 \u00de\nTherefore, the kinematic screws of kinematic chain AB can be denoted as\n$AB \u00bc $A\n$B\n\u00f031\u00de\nThe reciprocal screws of $AB are\n$r AB \u00bc\n$ r1 AB $r2 AB $ r3 AB $r4 AB\n2 66664\n3 77775 \u00f032\u00de\nwhere\n$r1 AB \u00bc\nxBffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2\nB \u00fe y2 B\np yBffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2\nB \u00fe y2 B\np 0 0 0 0\n!\n$ r2 AB \u00bc \u00f0 0 0 1 0 0 0 \u00de $ r3 AB \u00bc \u00f0 0 0 0 1 0 0 \u00de $ r4 AB \u00bc \u00f0 0 0 0 0 1 0 \u00de\nSimilarly, the terminal constraints of kinematic chain DC in the same Cartesian coordinate system can be solved:\n$r DC \u00bc\n$ r1 DC $r2 DC $ r3 DC $ r4 DC\n2 66664\n3 77775 \u00f033\u00de\nwhere\n$ r1 DC \u00bc\nxB xDffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0xB xD\u00de2 \u00fe \u00f0yB yD\u00de 2 q yB yDffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0xB xD\u00de2 \u00fe \u00f0yB yD\u00de 2 q 0 0 0 xDyB xByDffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0xB xD\u00de2 \u00fe \u00f0yB yD\u00de 2\nq !\n$r2 DC \u00bc \u00f0 0 0 1 0 0 0 \u00de $ r3 DC \u00bc \u00f0 0 0 0 1 0 0 \u00de $ r4 DC \u00bc \u00f0 0 0 0 0 1 0 \u00de\nTherefore, the terminal constraints exerted to link BC are\n$ C BC \u00bc\nxBffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2\nB \u00fe y2 B\np yBffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2\nB \u00fe y2 B\np 0 0 0 0\nxB xDffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0xB xD\u00de2 \u00fe \u00f0yB yD\u00de 2 q yB yDffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0xB xD\u00de2 \u00fe \u00f0yB yD\u00de 2 q 0 0 0 xDyB xByDffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0xB xD\u00de2 \u00fe \u00f0yB yD\u00de 2 q 0 0 1 0 0 0\n0 0 0 1 0 0\n0 0 0 0 1 0\n2 66666666664\n3 77777777775 \u00f034\u00de" ] }, { "image_filename": "designv10_11_0000998_j.jsv.2020.115374-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000998_j.jsv.2020.115374-Figure2-1.png", "caption": "Fig. 2. Massespringedamping model of an ACCBB.", "texts": [ " This study has a high calculation accuracy. The total RN of an ACCBB and its frequency spectrum are studied by the analysis of the vibrational response of the bearing components. Then the distribution characteristics and directivity of the sound field of an ACCBB are discussed. Fig. 1 illustrates the schematic of an ACCBB. In this study, the external forces acting on the ceramic bearing are analyzed only in the axial directionwith the preload. A bearing system is simplified as a massespringedamping model, as presented in Fig. 2. In Figs. 1 and 2, the generalized coordinate system {O; X, Y, Z} is fixed in the bearing plane. Subscript i, o and b mean inner ring, outer ring and ceramic ball, respectively. The j denotes the order number of the ceramic ball. Oi is the geometric center of the inner ring. The geometric center of the outer ring, Oo, coincides with the coordinate origin, O. Di and Do are the raceway diameters of the inner and outer rings. ri is the distance from the coordinate origin to the geometric center of the inner ring", " The Lagrange theorem is used in a group of independent generalized coordinates to characterize the dynamic relationship of a bearing system [34]. Thus, the equations of motion of ceramic bearing were obtained. d vt vT v _ql vT vql \u00fe vV vql \u00fe vR v _ql \u00bc Ql (1) where ql denotes the lth generalized coordinate; Ql denotes the lth generalized force; T represents the kinetic energy of ceramic bearing; V represents the potential energy of ceramic bearing; R represents the dissipation function of ceramic bearing. As shown in Fig. 2, in general, the outer ring is fixed, i.e. its kinetic energy is considered to be zero. Apart from the local contact deformation, each component of the bearing will be considered a rigid body. The location vector of the geometric center of the inner ring, r!i, can be written as r!i \u00bc xi i !\u00fe yi j !\u00fe zi k ! (2) The derivative, _r!i of r!i is the velocity vector of the geometric center of the inner ring and can be calculated by _r!i \u00bc _xi i !\u00fe _yi j !\u00fe _zi k ! (3) The position of the jth ceramic ball can be represented by the polar coordinate, r", " Therefore, _fj can be derived as _4j \u00bc _qj Di 2rb _4i _qj (8) In summary, the kinetic energy of the jth ceramic ball can be rewritten as Tj \u00bc 1 2 mj _rj 2 \u00fe rj _fj 2 \u00fe rj _qj cos fj 2 \u00fe \u00f0 _xi\u00de2 \u00fe \u00f0 _yi\u00de2 \u00fe \u00f0 _zi\u00de2 \u00fe2 _rj cos fj cos qj rj _qj cos fj sin qj rj _fj sin fj cos qj _xi \u00fe2 rj _qj cos fj cos qj \u00fe _rj cos fj sin qj rj _fj sin fj sin qj _yi \u00fe2 _rj sin fj \u00fe rj _fj cos fj _zi # \u00fe 1 2 Jj _qj Di 2rb _4i _qj 2 (9) The total kinetic energy of all ceramic balls can be calculated by Tb \u00bc XN j\u00bc1 Tj (10) where Tb represents the total kinetic energy of all ceramic balls and N is the number of the ceramic balls. The position of the inner ring is the coordinate of the geometric center, (xi, yi, zi), relative to the fixed coordinate system, {O; X, Y, Z}, in Fig. 2; the vibrational velocity of the inner ring relative to the absolute coordinate system is ( _xi _yi _zi). Therefore, the kinetic energy of inner ring can be calculated by Ti \u00bc 1 2 mi _x2i \u00fe _y2i \u00fe _z2i \u00fe 1 2 Ji _4 2 i (11) where Ti represents the kinetic energy of the inner ring,mi is themass of the inner ring, Ji denotes themoment of inertia of the inner ring, _fi denotes the rotational angular velocity of the inner ring. The kinetic energy of cage is the combination of the vibrational kinetic energy and rotational kinetic energy" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001572_tmech.2021.3067335-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001572_tmech.2021.3067335-Figure7-1.png", "caption": "Fig. 7. Joint moments produced by external load and cables: (a) \ud835\udc41\ud835\udc41th, (b) (\ud835\udc41\ud835\udc41 \u2212 1)th, and (c) \ud835\udc56\ud835\udc56th joint. The group surrounded by the orange dotted line was considered to be one body to analyze the force and moment of the CMRJ.", "texts": [ " To calculate the friction caused by contact between the cable and segment path, we assumed the cable and CMRJ to follow the Coulomb model according to a previous study [26]. The cable tensions at the joint in the CMRJ were calculated using the friction coefficient and joint angle of the CMRJ: \ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50\ud835\udc4e\ud835\udc4e\ud835\udc4f\ud835\udc4f\ud835\udc59\ud835\udc59\ud835\udc52\ud835\udc52,\ud835\udc51\ud835\udc51 = \ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50\ud835\udc4e\ud835\udc4e\ud835\udc4f\ud835\udc4f\ud835\udc59\ud835\udc59\ud835\udc52\ud835\udc52,\ud835\udc51\ud835\udc51\u22121\ud835\udc52\ud835\udc52 \u2212\ud835\udf07\ud835\udf07( \ud835\udf03\ud835\udf03\ud835\udc56\ud835\udc56\u22121+\ud835\udf03\ud835\udf03\ud835\udc56\ud835\udc56 2 ). (15) The external load \ud835\udc39\ud835\udc39\ud835\udc52\ud835\udc52\ud835\udc52\ud835\udc52\ud835\udc61\ud835\udc61 acts on the distal segment of the CMRJ; the cable tensions and external load determine the moment of the \ud835\udc41\ud835\udc41th joint (see Fig. 7(a)). The \ud835\udc41\ud835\udc41th joint moment is calculated as the cross-product of the forces and distances between the force working points and center of rotation. Next, we constructed a system consisting of the \ud835\udc41\ud835\udc41 th and (\ud835\udc41\ud835\udc41 \u2212 1)th segments to consider the forces acting on the (\ud835\udc41\ud835\udc41 \u2212 1)th joint, as shown in Fig. 7(b). If there are no springs or Authorized licensed use limited to: Carleton University. Downloaded on May 27,2021 at 11:52:50 UTC from IEEE Xplore. Restrictions apply. 1083-4435 (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. > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 6 actuators in the system, the sum of the forces in the system is zero as all of the forces in the system cancel each other. Thus, the system moves due to external forces. This system can be applied to all joints, as shown in Fig. 7(c). The joint moment \ud835\udc40\ud835\udc40\ud835\udc51\ud835\udc51 \ud835\udc57\ud835\udc57\ud835\udc50\ud835\udc50\ud835\udc51\ud835\udc51\ud835\udc50\ud835\udc50\ud835\udc61\ud835\udc61 can be expressed as follows: \ud835\udc40\ud835\udc40\ud835\udc51\ud835\udc51 \ud835\udc57\ud835\udc57\ud835\udc50\ud835\udc50\ud835\udc51\ud835\udc51\ud835\udc50\ud835\udc50\ud835\udc61\ud835\udc61 = \ufffd\ud835\udc43\ud835\udc43\ud835\udc50\ud835\udc50\ud835\udc4e\ud835\udc4e\ud835\udc4f\ud835\udc4f\ud835\udc59\ud835\udc59\ud835\udc52\ud835\udc52 \ud835\udc57\ud835\udc57 4 \ud835\udc57\ud835\udc57=1 \u00d7 \ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50\ud835\udc4e\ud835\udc4e\ud835\udc4f\ud835\udc4f\ud835\udc59\ud835\udc59\ud835\udc52\ud835\udc52,\ud835\udc51\ud835\udc51 \ud835\udc57\ud835\udc57 + \ud835\udc43\ud835\udc43\ud835\udc52\ud835\udc52\ud835\udc52\ud835\udc52\ud835\udc61\ud835\udc61 \u00d7 \ud835\udc39\ud835\udc39\ud835\udc52\ud835\udc52\ud835\udc52\ud835\udc52\ud835\udc61\ud835\udc61 , (16) where \ud835\udc43\ud835\udc43\ud835\udc50\ud835\udc50\ud835\udc4e\ud835\udc4e\ud835\udc4f\ud835\udc4f\ud835\udc59\ud835\udc59\ud835\udc52\ud835\udc52 \u2208 3 \u00d7 1 is the position of the contact point between the cable and \ud835\udc56\ud835\udc56th segment based on the center of the contact line. \ud835\udc43\ud835\udc43\ud835\udc52\ud835\udc52\ud835\udc52\ud835\udc52\ud835\udc61\ud835\udc61 \u2208 3 \u00d7 1 is the tip position applied by an external load based on the center of the contact line. As each joint can only rotate in one direction, the joint moments calculated from (16) are removed except from the joint rotation direction" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003388_978-3-662-04831-3-FigureA.2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003388_978-3-662-04831-3-FigureA.2-1.png", "caption": "Fig. A.2.1: Vector diagram used in the definition of the kinetic energy of a rigid body", "texts": [], "surrounding_texts": [ "Ao2 Lagrange formalism of a rigid body under spatial motion 291\nA.2.1 Kinetic energy of an unconstrained rigid body\nConsider a \"point mass\" with the mass m located at the point Q of an inertial frame R (Figure Ao2ola)o The kinetic energy of the point mass with respect to R is\nTk = ~ ( R~t (r~0)) T 0 ( R~t (r~0)) 0 m (Ao2o2)\n1 (R o R ) T (R o R ) lllll = 2 r QO 0 r QO 0 m E .Ii\\\\. 0\nConsider an unconstrained rigid body of mass m, with center of mass C and volume V, with a reference point P fixed on the body, and a vector r PO from the origin 0 of R to the point P (Figure Ao2olb)o\nConsider a mass element of mass dm of the body at an arbitrary point Q on the body, specified by the vector\nT := TQOo (Ao2o3)\nThe kinetic energy of the body is\n(Ao2.4)\nwhere the velocity vector R,;.R := Rr~0 is measured and represented in Ro Consider a second frame L with origin 0 L = P fixed on the bodyo Then the vector r = TQO can be written as (Figure Ao2olb)\nr R o- rR _ rR + vR _ rR + ARL 0 vL o- QO- PO A - PO A o\nThe velocity vector Rj-R is\nRoR RoR +RoR r = rpo X\nor\nDue to the rigid-body property\nLXL := 0\nand to the relation\nAo RL- ARL -L - OWLR\nthe resulting velocity vector is\n(Ao2o5a)\n(Ao2o5b)\n(Ao2o5c)\n(Ao2o6)\n(Ao2o7a)\n(Ao2o7b)", "292 A. Appendix\nInserting (A.2.7b) into (A.2.4) yields the following expressions for the kinetic energy of the rigid body, written with respect to the reference point P:", "A.2 Lagrange formalism of a rigid body under spatial motion 293\nTkP =~I (RrR) T. (RrR) dm (A.2.8)\n11(R\u00b7R RL -L L)T (R R RL L L) = 2 r PO + A \u00b7 w LR \u00b7 X \u00b7 r PO + A \u00b7 w LR \u00b7 X dm = ~ . ( Rr-~0 ) T . ( Rr-~0) . I dm\n11(( L)T (-L )T ALR ARL -L L)d + 2 X . W LR \u00b7-.._:,._... \u00b7 W LR \u00b7 X m\n= 13\n+ ( RT~o) T 0 A RL 0 wi;R 0 I XL dm.\nTogether with\nT~p :=!I xLdm (A.2.9a)\nas the vector from the origin P of L to the center of mass C of the body, with\nand\nI dm=m\nthis yields\n1 II R 0 R 11 2 (R 0 R ) T RL - L L Tkp= 2 \u00b7m\u00b7 Tpo +m\u00b7 Tpo \u00b7A \u00b7wLR\u00b7Tcp\n+~I xLr \u00b7(wiR) T \u00b7 (wiR)\u00b7 xL dm\nor\n1 II R 0 R 11 2 (R 0 R ) T - R RL L Tkp= 2 \u00b7m\u00b7 Tpo +m\u00b7 Tpo \u00b7wLR\u00b7A \u00b7Top\n+~I llwiR \u00b7 xLII 2 dm.\nU sing the vector relation\nI Iw \u00b7 xll 2 = (w x x)T \u00b7 (w x x) = (w x x)T \u00b7 d = wT \u00b7 (x x d) ..._\"_,__..,\n=:d\n(A.2.9b)\n(A.2.9c)\n(A.2.10)\n=wT\u00b7 [xx(wxx)]=wT\u00b7 [(xT\u00b7x)\u00b7w-(x\u00b7xT)\u00b7w]\n=wT\u00b7 [(xT\u00b7x)\u00b7I3-x\u00b7xT]\u00b7w\nyields" ] }, { "image_filename": "designv10_11_0003068_jsvi.1997.1298-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003068_jsvi.1997.1298-Figure5-1.png", "caption": "Figure 5. Schematic of the gear mesh with associated co-ordinate systems.", "texts": [ " The \u2018\u2018pseudo forces\u2019\u2019 Qij\u2212 i*mg (V*, t) and Qij\u2212 j* mg (V*, t) arise due to the coupling between the finite mean rotation of the gear with respect to the mesh ij and the flexible deformation of the gear blank itself (see the Appendix for identification of symbols). The co-ordinate systems for a typical gear pair are given in detail in an earlier paper by the authors [9]. For the sake of clarity, a brief discussion together with the modifications necessary to represent the flexibility of the gear blanks is presented here. Figure 5 shows a few co-ordinate systems for a typical external gear body where X\u2013Y\u2013Z is an inertial reference frame and Xi G \u2212Yi G \u2212Zi G and Xi Gm \u2212Yi Gm \u2212Zi Gm are non-inertial frames necessary to completely define the motion of the gear body. Body co-ordinate system Xi G \u2212Yi G \u2212Zi G is fixed to the gear blank i and hence it represents the true motion of the gear. The generalized co-ordinates of each gear are given as qi =[RiT G qiTqiT f ]T, where Ri G is the rigid body translational, ui is the rigid body rotational and qi f is the gear blank flexibility co-ordinates as defined in an earlier paper by Vinayak et al", " The dynamic component Qij m (t)=Qij me (t)+Qij md (t) consists of an elastic force Qij me (t) and a dissipative force Qij md (t). The elastic mesh force Qij me (t)=Qij mg (t)+Qij me (ui*) consists of Qij mg (t)=Kij m (t) [di q \u2212 dj q ], where di q \u2212 dj q is the gross motion of the blanks and an internal, parametric excitation force Qij me (t)=Kij m (t) [di e \u2212 dj e ] due to the static transmission error STE= dij e = di e \u2212 dj e . Here, Kij m is the generalized mesh stiffness matrix. The analytical model of reference [9] is modified to include the effects of flexible gear blanks. Consider an external helical gear of Figure 5 as described in the mesh co-ordinates xij \u2212 sij \u2212 hij. The mesh is modelled by a linear array of springs distributed over the length of contact Gij, as proposed in references [8, 9], which depends on the tooth surface modifications, gear shaft misalignments and other mounting errors. The net contact zone may be off-center on the tooth facewidth say by a length hij. The elastic mesh force Fij s ij at a point Ps i in the direction p\u0302ij, is >Fij s j (t)>=Kij(t)>[dri Ps ij \u2212 drj Ps ij]>ds, (2) where Kij(t) is a scalar value for mesh stiffness per unit length of contact", " Since ui, j m \u2019s are infinitesimally small, vi 1 qi m and Gi 1 I, where I is an identity matrix. Further, u\u0304i, j s j is an asymmetrical matrix formed from u\u0304i, j s ij =[u\u0304i, j s ijx u\u0304i, j s ijy u\u0304i, j s ijz ]T and is given by u\u0304i, j s ij (t)= & 0 u\u0304i, j s ijz \u2212u\u0304i, j s ijy \u2212u\u0304i, j s ijz 0 u\u0304i, j s ijx u\u0304i, j s ijy \u2212u\u0304i, j s ijx 0 ' = & 0 u\u0304i, j s ijzr \u2212u\u0304i, j s ijyr \u2212u\u0304i, j s ijzr 0 u\u0304i, j s ijxr u\u0304i, j s ijyr \u2212u\u0304i, j s ijxr 0 '+ & 0 u\u0304i, j s ijzf \u2212u\u0304i, j s ijyf \u2212u\u0304i, j s ijzf 0 u\u0304i, j s ijxf u\u0304i, j s ijyf \u2212u\u0304i, j s ijxf 0 '. (7) With reference to Figure 5, u\u0304i, j s ijr can be given by the sum of u\u0304i, j mr , position vector of the pitch point in geometric co-ordinates and the unit mesh vector q\u0302ij as u\u0304i, j s ijr = u\u0304i, j m + sijq\u0302ij. The pitch position vectors are u\u0304i m =AiTj[Rj G \u2212Ri G ] and u\u0304j m =AjTj[Ri G \u2212Rj G ], where j=fi/ (fi +fj). These can now be used to obtain an expression for du\u0304i s ij du\u0304j s ij as du\u0304i s ij (t)= jd[AiT(t) (Rj G (t, ui*)\u2212Ri G (t, ui*))]+ sijdq\u0302ij + du\u0304i s ijf (t), (8a) du\u0304j s ij (t)= jd[AjT(t) (Ri G (t, ui*)\u2212Rj G (t, ui*))]+ sijdq\u0302ij + du\u0304i s ijf (t)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003131_robot.1999.770008-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003131_robot.1999.770008-Figure4-1.png", "caption": "Figure 4. Geometric constraint to calculate hlimir during upslope walking.", "texts": [ " Therefore, the desired hip height of the biped is computed based on geometric considerations (considering the global slope, transition location from double to single support and the desired step length). This results in a desired body height which varies with the slope gradient. For upslope walking, the height limit of the biped is computed based on the desired step length, the distance from the front ankle at which the double support phase transits to the single support phase, and the singularity consideration of the back supporting leg during the double support phase (see Figure 4). We denote hlimir to be the hip height limit measured along the direction of the gravitational field from a global slope. By geometric consideration, the hip height limit hlimi, is computed by Equation (4): hbm,, = ,/- - r tan p (4) where 1, +1, is the total length of the leg (excluding the foot); ,b is the slope gradient; and r = s1 cos p + 1, . A factor kheighr is multiplied to the height limit hlimir to give the desired height of the hip from a global slope, h& kherghr is typical chosen to be around 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000621_j.matpr.2018.03.039-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000621_j.matpr.2018.03.039-Figure3-1.png", "caption": "Figure 3 Remote Displacement Fixed End Figure 4 Remote Displacement Shackle End", "texts": [], "surrounding_texts": [ "14514 Jenarthanan M.P et al/ Materials Today: Proceedings 5 (2018) 14512\u201314519\n2.2 Material Properties Material originally used for this leaf spring[6] is spring steel EN45 [2], Mechanical properties of steel EN45 are\nlisted in Table 2.", "Jenarthanan M.P et al / Materials Today: Proceedings 5 (2018) 14512\u201314519 14515\nfixed end, all translations are constrained as well as rotations except z-axis. In Shackle end, translation along x-axis and rotation along z-axis are released while all other DOFs are arrested.\nAssume Leaf Spring is in static loading condition shown in Figure 5 (without speed factor) and analyze Total Deformation and Von-Mises Stress values of both Steel and Hybrid Composite Leaf Spring. [7] Load Calculation: Weight of Vehicle, W1= 2150 Kg,Additional Weight (Passengers and Luggage), W2= 750 Kg. Total Weight, W= 2900 Kg. Load Acting on Leaf Spring, F= m\u00d7a F= 2900\u00d79.81 F= 28449 N (For all four-Leaf Springs): F= 7112.25 N (For one Leaf Spring)\nThen the assembly is meshed to for finite elements (Figure 6). Then the setup is solved for Total Deformation and Von-Mises Stress for both Steel Spring and Hybrid Composite [10].The results obtained for static structural analysis are listed in Table 4and the results are shown in Figures 7-10.", "14516 Jenarthanan M.P et al/ Materials Today: Proceedings 5 (2018) 14512\u201314519" ] }, { "image_filename": "designv10_11_0003626_iros.1999.811675-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003626_iros.1999.811675-Figure1-1.png", "caption": "Fig. 1 Nomenclature of gliding configuration in regular creeping motion", "texts": [ " However, when the snake makes creeping motion, the abdomen flank of the body becomes an edge like that of a ski in order to prevent the slippage in the normal direction of the body. So the snake has friction characteristics such that slip is easy along the body but difficult in the normal direction. These characteristics transform the contraction/relaxation motion of the muscle into propulsive creeping motion like the flowing of a river. The direction along the body axis is determined as the tangential direction and the orthogonal direction of body axis is determined as the normal direction. The nomenclature is shown in Fig. 1. For simplicity of the analysis, the conventional gliding theory assumed that: (1) The body is expressed by a continuum. (2) Distribution of torque is independent of the gliding configuration. (3) Analysis by 0-7803-5 1 84-3/99/$10.00 0 1999 IEEE 1399 static kinematics. (4) No slippage in the normal direction. However, these assumptions are not strictly valid, so recently Ma has proposed another analysis, which includes dynamics and normal direction slippage [2] and considers the relationship between the gliding configuration and torque distribution in terms of the muscular power consumption 131", "a E H ere, Serp (a) is con st ant (0.40 5 < Serp (a) 1 at the beginning and \u03bc \u2248 0 when the temperature reaches the melting point at the interface. For simplicity, the coefficient of friction was set to be constant throughout the modelling, and the value of the friction coefficient was chosen \u03bc = 0.5 since the duration of the welding process was short. The mesh used in this simulation is divided into two regions for each rod. Near the weld interface, smaller elements were generated to increase the accuracy of simulation (see Fig. 3). The two rods used in the simulation are the same material with a length of 17 mm, and radius of 12.5 mm. The rods are in contact initially at the intended weld interface and the initial temperature is set at room temperature. The Arbitrary Lagrangian Eulerian (ALE) technique was used for the simulation of friction welding process. The ALE formulation is an intermediate method between the Lagrangian, and Eulerian methods which allows the arbitrary and independent movement of mesh inside the domains with respect to the material" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003068_jsvi.1997.1298-Figure21-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003068_jsvi.1997.1298-Figure21-1.png", "caption": "Figure 21. Different orientations of a gear assembly (III).", "texts": [ " Since there is a strong coupling between the rigid body mesh dynamics and the gear body flexural dynamics, this relative rotation should give rise to \u2018\u2018pseudo\u2019\u2019 forces Qi j\u2212 j*mg (V*, t) and Qi j\u2212 i*mg (V*, t) as discussed earlier in section 3. This effect may be easily observed by comparing the forced responses for an LTI geared assembly but evaluated at selected spatial operating points given by the rotational position u*= ft 0 V* dt. Assembly IV is chosen as an example to illustrate this phenomenon since the rotational position of the gears are uniquely identified with respect to the holes in the first gear as shown in Figure 21. Due to the symmetry of the holes only three intermediate anti-clockwise rotational positions, u*=0, 30 and 60\u00b0, are adequate to represent the various orientations of the gears. Figure 22 shows the cross-point accelerance A12 P/Qzz spectra at three different spatial positions. The first few modes which are predominantly rigid body modes are virtually unchanged but the higher modes, corresponding to the flexible gear body modes, are strongly affected by a change in the gear orientation. Figure 22(b) shows an expanded view of the resonance peaks corresponding to the (0, 2) flexible body modes of the two gears. The first peak is due to the flexible body mode of the driver gear which has three holes within its body. As the gears rotate through 60\u00b0, there is a considerable shift in the frequency of this resonance (050 Hz). This is because the local stiffness of the gear increases as the hole moves away from the meshing zone (refer to Figure 21), thereby resulting in a corresponding increase in the frequency associated with this resonance. The second peak however is due to the driven gear which resembles an annular disk. Since there is no change in the \u2018\u2018local\u2019\u2019 stiffness of the driven disk with respect to the mesh as both gears rotate, no appreciable deviation in the resonant frequency is observed. This parametric coupling phenomenon can be very easily studied by the proposed multi-body dynamics methodology, unlike other numerical techniques such as finite elements" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003710_0957-4158(92)90043-n-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003710_0957-4158(92)90043-n-Figure8-1.png", "caption": "Fig. 8. Analysed motion on a vertical wall.", "texts": [], "surrounding_texts": [ "To build up a control program, the walking motion was simulated by a computer . Two cases are presented as an example. One is walking on a vertical wall, and the other is a transition motion f rom the vertical wall to the ceiling. In Fig, 8 the analysed motion on a vertical wall is presented and for each station the force acting on the fixed sucker is shown in Fig. 9 by using the corresponding letters. The abscissa is the distance h and / is given in Fig. 4. The transition motion from a vertical wall to ceiling is shown in Fig. 10. It can be seen that the most severe condition is given by point i or j in this figure and this is verified from Fig. 9, i.e. the largest value of F/W is assumed for a point of i or j. The required negative pressure in the cup is given in Fig. 11 on the curves of blower performance. Assumed curves of A and B correspond to lesser and larger leakages, respectively. The amount of leaked air depends on the wall surface roughness and the shape and material of the peripheral lip. If the surface is fiat and smooth, the leaked air is small and higher pressure can be obtained for the same motor input voltage. As the air flow through the fan is used for motor cooling in this case, the small amount of leaked air is significant with regard to motor cooling. On the other hand, a higher input voltage produces a larger negative pressure margin, therefore the safer situation is attained. To compromise these opposite conditions, the input voltage is controlled to give a large enough pressure margin, which is taken as 150 mmH20. On the curve of B in Fig. 11, points i and j do not have large enough margins for a maximum input voltage of V = 84 V, and these situations are avoided in practical experiments by adjusting the fixed position on the ceiling. 6. W A L K I N G E X P E R I M E N T S" ] }, { "image_filename": "designv10_11_0000998_j.jsv.2020.115374-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000998_j.jsv.2020.115374-Figure5-1.png", "caption": "Fig. 5. Be model of the ACCBB.", "texts": [ " To analyze the bearing noise in a steady state, the nonlinear dynamic differential equations are solved by Gear stiff integration algorithm with variable steps [47], and then the obtained vibrational velocities are transformed from the time domain to the frequency domain by fast Fourier transform (FFT). The vibrational velocities in the frequency domain are imported into the FE model of the bearing to obtain the normal velocities on the surface of each bearing component. The velocities as the boundary condition are imported into the boundary element (BE) model. Finally, the radiation noise of the bearing is calculated by the acoustic BEM. The BE model is shown in Fig. 5. Table 1 Major technical parameters of the ACCBB. Bearing specification Value Internal diameter of bearing (mm) 17 External diameter of bearing (mm) 35 Pitch diameter (mm) 26 Width of bearing (mm) 10 Diameter of ball (mm) 4.5 Number of balls 12 Contact angle ( ) 15 Width of cage (mm) 9.1 Internal diameter of cage (mm) 23.4 External diameter of cage (mm) 27.6 Pocket diameter of cage (mm) 4.6 Groove curvature radius coefficient of inner ring 0.515 Groove curvature radius coefficient of outer ring 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000686_0954406219832333-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000686_0954406219832333-Figure4-1.png", "caption": "Figure 4. Geometry of the adopted samples.", "texts": [ " Experimental\u2013numerical study of plastic collapse of Additive Manufacturing (AM) reticular structures The plastic behavior of Additive Manufacturing (AM) structures was investigated by testing several reticular samples. Numerical simulations of the performed tests were employed to assess the capability of FEA to reproduce the behavior of such structures and predict their collapse. Some samples of A357 aluminum alloy, characterized by an internal reticular structure with Kagome cells, were manufactured using a Renishaw AM250 available at the Department of Mechanical Engineering of the Politecnico di Milano. Two geometries were printed, schematically presented in Figure 4, differing in the diameter of the trusses (0.5\u20131.5mm). All the specimens were subjected to compression under quasi-static loading conditions using the aforementioned testing machine available at the Free University of Bozen-Bolzano. During the tests, the samples were placed in the middle of the compression plates (Figure 5) and a ramp of displacement was imposed to the upper plate, while the reaction force was measured and recorded up to total collapse. No extensometer were mounted on the structure but it was reasonable to assume that the displacement of the upper plate is representative of the compression of the samples, being their stiffness much lower than the stiffness of the testing machine itself" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000225_amm.762.219-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000225_amm.762.219-Figure6-1.png", "caption": "Fig. 6 Kinematics schema of the motor mechanism c2", "texts": [], "surrounding_texts": [ " \n \n\n\u22c5=\u21d2\n \n \n\n\u2212++\u22c5\u2212\u22c5 =\n\u2212++\u22c5\u2212\u22c5 =\n\u22c5=\u21d2\n \n \n\n\u22c5\u2212\u2212\u22c5 =\n\u22c5\u2212\u2212\u22c5 =\n=\n+++\u2212++++=\n+\u2212==\u21d2 +\n\u2212+\u22c5\u22c5 =\n)arccos(cos)(sin )sin(sin\nsin\n)cos(cos cos\n)arccos(cos)(sin sinsin2\nsin\ncoscos2 cos\n];sin)sin(cos)cos[(4)sin()cos(4\n);arccos(coscos\n101010\n3\n6 10\n3\n6 10\n111\n3\n6 1\n3\n6 1\n03\n66\n222\n0\n22\n442662 3 2 2\n2 1 2 3 2 2321\n6\n\u03d5\u03d5\u03d5 \u03b8\u03d5\u03d5\n\u03d5\n\u03b8\u03d5\u03d5 \u03d5\n\u03d5\u03d5\u03d5 \u03d5\u03d5\n\u03d5\n\u03d5\u03d5 \u03d5\n\u03d5\u03d5\u03d5\u03d5\u03d5\u03d5\n\u03d5\u03d5\u03d5\nsign\nl\nyyfa\nl\nxxfa\nsign\nl\nbya\nl\nbxa\nAl\nbybxabybxaA\neAAl AA\nAAAAAA\nAM\nAM\nK\nK\nKKKK\n\u2213 \u2213\n(3)\n \n \n\n\u2212+\u22c5\u22c5+\u2212+\u22c5\u22c5=\n+\u22c5\u2212\u2212\u22c5+\u22c5+\u22c5=\n+\u22c5\u2212\u2212\u22c5+\u22c5+\u22c5=\n+\u22c5\u2212\u2212\u2212+\u22c5\u2212\u2212\u2212\u22c5++\u22c5++=\n\u22c5=\u21d2\n \n \n\n+\u22c5+\u2212 =\n+\u22c5+\u2212 =\n++\u2212+++\u2212=\n\u22c5=\u21d2\n \n \n\n\u22c5+\u22c5+\u2212 =\n\u22c5+\u22c5+\u2212 =\n)sin(sin)cos(cos\n)]sin([2)sin(4\n)]cos([2)cos(4\n)]sin([)]cos([)sin()cos(3\n)arccos(cos)(sin )sin(\nsin\n)cos( cos\n)]sin([)]cos([\n)arccos(cos)(sin sinsin\nsin\ncoscos cos\n6106104\n3\n2\n22222\n1\n888\n1\n3 8\n1\n3 8\n2\n3\n2\n31\n333\n6102 3\n6102 3\nKAKA\nAMK\nAMK\nAMAMKK\nFK\nFK\nFKFK\nKA\nKA\nyyaxxaA\nfyyabyaA\nfxxabxaA\nfyyfxxbybxaA\nsign\nl\ngyy\nl\ngxx\ngyygxxl\nsign\ne\nalyy\ne\nalxx\n\u03d5\u03d5\u03d5\u03d5\n\u03b8\u03d5\u03d5\n\u03b8\u03d5\u03d5 \u03b8\u03d5\u03b8\u03d5\u03d5\u03d5\n\u03d5\u03d5\u03d5 \u03b2\u03d5\n\u03d5\n\u03b2\u03d5 \u03d5\n\u03b2\u03d5\u03b2\u03d5\n\u03d5\u03d5\u03d5 \u03d5\u03d5\n\u03d5\n\u03d5\u03d5 \u03d5\n(4)\nDetermining driving forces of the main mechanism\nRELATIONSHIPS COMPUTING\nIn step 1 (starting from system 5) it calculated the all external forces from the mechanism (The\ninertia forces, gravitational forces and the force of the weight of the cast part).\n \n \n\n \n \n\n\u22c5\u2212=\n\u22c5\u2212\u22c5\u2212=\n\u22c5\u2212=\n \n \n\n\u22c5\u2212=\n\u22c5\u2212\u22c5\u2212=\n\u22c5\u2212=\n \n \n\n\u22c5\u2212=\n\u22c5\u2212\u22c5\u2212=\n\u22c5\u2212=\n \n \n\n\u22c5\u2212=\n\u22c5\u2212\u22c5\u2212=\n\u22c5\u2212=\n \n \n\n\u22c5\u2212=\n\u22c5\u2212\u22c5\u2212=\n\u22c5\u2212=\n \n \n\n=\u22c5\u2212=\n\u22c5\u2212\u22c5\u2212=\n\u22c5\u2212=\n \n \n\n\u22c5\u2212=\n\u22c5\u2212\u22c5\u2212=\n\u22c5\u2212=\u22c5\u2212=\n \n \n\n\u22c5\u2212=\n\u22c5\u2212\u22c5\u2212=\n\u22c5\u2212=\n \n \n\n\u22c5\u2212=\n\u22c5\u2212\u22c5\u2212=\n\u22c5\u2212=\n1010\n11,1011,10\n11,10\n88\n8989\n89\n7\n77\n7\n35\n55\n5\n44\n44\n4\n66\n66\n66\n33\n33\n3\n11\n1212\n12\n11,10\n1010\n1010\n8\n88\n88\n7\n77\n77\n5\n55\n55\n4\n44\n44\n6\n66\n3\n33\n33\n1\n11\n11\n0\n\u03d5\u03d5\u03d5\n\u03d5\u03d5\u03d5\n\u03d5\u03d5\u03d5\nG\ni\nG\niy\nG\nG\nix\nG\nG\ni\nG\niy\nG\nG\nix\nG\nM\ni M\nM\niy M\nM\nix\nG\ni\nG\niy\nG\nG\nix\nG\nG\ni\nG\niy\nG\nG\nix\nG\nG\ni\nG\niy\nG\nG\nix\nG\nH\ni\nH\niy\nG\nHG\nix\nG\nG\ni\nG\niy\nG\nG\nix\nG\nG\ni\nG\niy\nG\nG\nix\nG\nJM\ngmymF\nxmF\nJM\ngmymF\nxmF\nJM\ngMyMF\nxMF\nJM\ngmymF\nxmF\nJM\ngmymF\nxmF\nJM\ngmymF\nxmF\nJM\ngmymF\nxmxmF\nJM\ngmymF\nxmF\nJM\ngmymF\nxmF\nM\n(5)\nIs then calculated all the forces from couplers. In the end we can determine and (three) driving forces [1-5]. In figure 5 can be monitored engine element c1 composed of kinematic elements 8-9.", "Determine motive power Fm1 with relations of the system 6; being two relations of calculation may be carried out a check.\n \n \n\n\u2212\u2212 =\u21d2=++\u22c5\u21d2=\n\u2212\u2212 =\u21d2=++\u22c5\u21d2=\n\u2211\n\u2211\n10\n10\n)10(\n10\n10\n)10(\nsin 0sin0\ncos 0cos0\n10\n2102\n10\n2102\n\u03d5 \u03d5\n\u03d5 \u03d5\ny H iy G\nm\ny H iy Gmy\nx H ix G\nm\nx H ix Gmx\nRF FRFFF\nRF FRFFF\n(7)\nIn figure 7 can be monitored engine element c3 composed of kinematic elements 1-2, and\ndetermine motive power Fm3 with relations of the system 8 [1-5].", " \n \n\n+ =\u21d2=++\u22c5\u2212\u21d2=\n+ =\u21d2=++\u22c5\u2212\u21d2=\n\u2211\n\u2211\n1\n1\n)1(\n1\n1\n)1(\nsin 0sin0\ncos 0cos0\n1\n313\n1\n313\n\u03d5 \u03d5\n\u03d5 \u03d5\ny E iy G\nm\ny E iy Gmy\nx E ix G\nm\nx E ix Gmx\nRF FRFFF\nRF FRFFF\n(8)\nConclusions\nForging manipulators themselves have become more prevalent in the industry today. An idea of establishing the incidence relationship between output characteristics and actuator\ninputs is proposed (see the relations from systems 3 and 4).\nThe main problems are solving positions, speeds and motor forces of the main mechanism. In\nthe end we can determine and (three) driving forces (the relations from systems 6-8).\nReferences [1] F. Gao, W. Z. Guo, Q. Y. Song, F. S. Du, Current Development of Heavy-duty Manufacturing\nEquipment, Journal of Mechanical Engineering, Vol. 46, No. 19, 2010, p. 92-107.\n[2] H. Ge, F. Gao, Type Design for Heavy-payload Forging Manipulators, Chinese Journal of\nMechanical Engineering, Vol. 25, No. 2, 2012, p. 197-205.\n[3] G. Li, D.S. Liu, Dynamic Behavior of the Forging Manipulator under Large Amplitude\nCompliance Motion, Journal of Mechanical Engineering, Vol. 46, No. 11, 2010, p. 21-28.\n[4] C. Yan, F. Gao, W. Guo, Coordinated kinematic modeling for motion planning of heavy-duty\nmanipulators in an integrated open-die forging center, Journal of Engineering Manufacture, Vol. 223, No. 10, 2009, p. 1299-1313. [5] K. Zhao, H. Wang, G. L. Chen, Z. Q. Lin, Y. B. He, Compliance Process Analysis for Forging\nManipulator, Journal of Mechanical Engineering, Vol. 46, No. 4, 2010, p. 27-34." ] }, { "image_filename": "designv10_11_0001253_tmag.2019.2952446-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001253_tmag.2019.2952446-Figure2-1.png", "caption": "Fig. 2. Simulation model of the SPMSM.", "texts": [ " The air-gap flux density along the circumference could be described as 0 m ( , ) ( , )= ( , ) ( , )= ( ) ( , ) F t B t F t H (1) where \u03bc0 represents the vacuum permeability, F(\u03b8,t), Hm(\u03b8) and \u03b4(\u03b8,\u03b1) are the distribution of the MMF, PM thickness and the effective air-gap length, respectively. According to Maxwell's tensor method, the no-load radial electromagnetic force density can be expressed as 2 2 0 r 0 m ( , ) ( , ) 2 2 ( ) ( , ) B t F t p H (2) The fast and accurate calculation method is introduced based on a 6-pole/36-slot SPMSM, the main parameters and simulation model of the motor are shown in Table I and Fig. 2, respectively. A. Calculation of the MMF The machine model without slots under a pole pitch, as shown in Fig. 3, is analyzed by magnetostatic solver of Maxwell. The magnetic potential drop on the air-gap can be calculated by 0 m 0 ( ) ( ) ( ) B H F (3) where B0(\u03b8) is the air-gap flux density neglecting the stator slots, and Hm are respectively the length of the air-gap and the magnet thickness, and [\u03b4(\u03b8,\u03b1)+ Hm(\u03b8)] is always constant in SPMSM, regardless of the magnetization direction and the shape of the PM" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000108_tec.2018.2820083-Figure19-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000108_tec.2018.2820083-Figure19-1.png", "caption": "Fig. 19. Deformation when applying 2500Hz radial force and bending moment together", "texts": [ " The value of F is set to 1.25N, which is half of 2.5N. For the frequency of force, two typical frequencies are used, 1200Hz and 2500Hz, which are close to the two modal natural frequencies of pulsating modal and bending modal shape obtained from modal test in the section V. Fig. 16, 17 and 18 show the deformation response of the stator caused by radial force and bending moment together, radial force only, and bending moment only, respectively, where the frequencies of radial force and bending moment are 1200Hz. Fig. 19, 20 and 21 show the corresponding results when the frequencies of radial force and bending moment are 2500Hz. In these figures, the situation is 1=9 , and only the two instants are shown when the deformation are maximum. From Fig. 17 and Fig. 18, it can be seen that the maximum deformation of the bending mode is nearly 10 times higher than that of the pulsating mode. While in Fig. 20 and Fig. 21, the maximum deformation of the pulsating mode is nearly 10 times higher than that of the bending mode" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000977_j.triboint.2020.106258-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000977_j.triboint.2020.106258-Figure1-1.png", "caption": "Fig. 1. Schematic diagram of a main reducer: (a) isometric view; (b) top view.", "texts": [ " A greater amount of heat generated also means a large amount of required lubricant or means of cooling, and, in conclusion, more weight and more fuel consumption. Sources of power losses in a gearing system can be categorized into two main groups: (a) Load-dependent (friction induced) losses are related to friction losses at the tooth contact and bearing, (b) Loadindependent (viscous) losses are due to fluid dynamic behavior caused by a host of factors, namely gear windage and churning that are due to the drag and pumping of oil/air on the gear face and sides, fluid pocketing/squeezing during tooth engagement, etc [2]. In areo-engine applications (Fig. 1) where tip tangential speeds are higher than 90\u2013120 m/s, the windage power losses greatly contributes to the power losses [3]. Windage power losses are referred to as the power losses due to the fluid drag (pressure and viscous) acting on the gear surfaces when it is rotating in free air or air-oil mist [4]. Various published experimental studies on windage behavior of high-speed gears are available. At the earliest Anderson and Loewenthal [5,6] set up an algebraic to estimate windage of a spur gear, which takes into account gear structure, working condition, and fluid properties, meanwhile, the gear radius and rotational speed were identified as the crucial parameters to rule the windage losses" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000679_b978-0-12-814062-8.00018-2-Figure16.14-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000679_b978-0-12-814062-8.00018-2-Figure16.14-1.png", "caption": "Figure 16.14 AddAero Mfg. Ti 6Al 4V Rocket Nozzle (EBM-ARCAM A2X) surfacefinished by the Extreme ISF Process (A) and the stereolithography (STL) showing the cooling internal channels (B), AddAero Mfg. Ti 6Al 4V Injector Assembly (EBMARCAM Q201 ) (C) and computer-aided design (CAD) Model of the full Rocket Assembly [D(a)] Injector Assembly [D(b)] Rocket Nozzle. EBM, Electron beam melting.", "texts": [ " This best practice will ensure the capture of as many surface features as possible, even after the surface finishing process of the AM-built component.) The total processing time was under 24 hours, and this technique is capable of processing as many parts as necessary (more than 10,000 if necessary), since the process takes places in a vibratory bowl that comes in many different sizes and configurations. Another good example is the surface finishing by Extreme ISF of an EBM Ti 6Al 4V Rocket Nozzle (ARCAM A2X) in collaboration with AddAero Mfg. (Fig. 16.14) [54,57,58]. This project demonstrates the capabilities of the Extreme ISF Process applied to the aerospace field. The as-built component is c. 28 cm height, 11 mm diameter across the combustion chamber, 4 cm diameter across the throat, and 9.6 cm diameter at the exit. The surface roughness of the component was reduced from an Ra of 25 \u03bcm to an Ra of 0.08 \u03bcm in the exterior and an Ra of 2.2 \u03bcm in the interior, for a 99.6% improvement of surface roughness in the exterior and a 91% in the interior" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000779_j.aca.2019.05.003-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000779_j.aca.2019.05.003-Figure5-1.png", "caption": "Fig. 5. The urea and creatinine contents and the ratio of the urea to creatinine concentrations of spot urine samples.", "texts": [ " 1c) and the reference methods (bromothymol blue and batch method for urea and creatinine, respectively). Fig. 4 shows good Pearson's correlation between the reference method (abscissa) and our proposed method (ordinate) for urea (Fig. 4a, r2\u00bc 0.980) and creatinine (Fig. 4b, r2\u00bc 0.955). In addition, the statistical paired t-test suggests that the proposed method and the reference method are not significantly different at 95% confidence level: for urea, tstat\u00bc 1.83 and tcrit\u00bc 2.10; for creatinine, tstat\u00bc 2.09 and tcrit\u00bc 2.10) [65]. Fig. 5 presents the urea and creatinine content and their ratio in spot urine samples as determined by our method. These results are useful for the association of DPI with kidney function in humans. In this work, the FIA-GD-C4D/PEDD system was successfully applied to the simultaneous determination of the two biomarkers of renal function, viz. urea and creatinine in human urine, without any special sample preparation. Using the optimized condition, this system showed good linearity (r2> 0.99) in ranges of 30e240mg L 1 and 10e500mg L 1, and detection limits of 9" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003270_s0043-1648(00)00493-2-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003270_s0043-1648(00)00493-2-Figure1-1.png", "caption": "Fig. 1. Scheme of the twin-disc machine.", "texts": [ " The twin-disc machine is frequently used to determine some material properties, namely surface contact fatigue and wear resistance. Being a simple device, it was chosen to evaluate the relative contact fatigue resistance of the tested ADI, when submitted to different operating conditions. The used machine allows maximum Hertzian contact pressure to reach 4 GPa and the maximum slide-to-roll ratio can attain more than 40% (2|U1 \u2212 U2|/(U1 + U2)), where U1 and U2 represent the linear tangential velocity of each disc surface. Surface lubrication is assured by permanent oil injection into the contact zone (see Fig. 1). This machine is equipped with magnetic sensors that detect occurrences like spalls or other significant surface damage. It also provides a close control of the normal force applied to the contact and of the lubricant temperature. In order to avoid the re-circulation of debris through the contact zone a small tank provided with magnets was used at the lubricant outlet to capture small metallic particles. After circulation through the main tank, filtering and pumping, the probability of re-entry of debris at the contact between the test discs was very low" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001059_j.mechmachtheory.2020.104101-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001059_j.mechmachtheory.2020.104101-Figure9-1.png", "caption": "Fig. 9. Rotationally adjustable 4-bar mechanism with 2 additional DOFs (rotational motors).", "texts": [ " However, in this case it is further enhanced by introducing additional DOFs. The exploration process and the whole variety of achieved solutions were presented in previous work [32] . The chosen solution (that relates to Fig. 7 ) was first modified by adding prismatic joints to bars (2, 3) in order to introduce the two additional DOFs ( Fig. 8 ). However, the same motion can be achieved by applying 2-link modules that are driven by rotational motors, thus obtaining the new solution that is presented in ( Fig. 9 ). This paper is focused on the rotationally adjustable 4-bar mechanism from Fig. 9 . It has two additional DOFs (total of 3 DOFs calculated using the Kutzbach-Gr\u00fcbler equation) with rotational motors (R 1 , R 2 ) instead of cylinders (S 1 , S 2 ), which were previously used in paper [33] . Each 2-link module is composed of 2 rotationally connected elements, which can be seen in Fig. 9 at joints E and F. These elements are the upper elements (BE and CF) that are rotationally connected with the femur (joints B, C), and also the lower elements (AE and DF) that are rotationally connected with the tibia (joints A, D). The rotational motors (R 1 , R 2 ) are used in the revolute joints (B, C) between the femur and the upper elements of 2-link modules. In the next step, the dimensional optimisation, illustrated with a 4-bar mechanism for simplification purposes, was per- formed mainly to obtain the distances between joints A, B, and C, D", " (1) ) is searched for by changing the parameters\u2019 values. An optimal mechanism is obtained with the following parameters: l 1 = 38.8, l 2 = 48.6, l 3 = 43, l 4 = 37.3, Z A = 13.9, Y A = 49.7 [mm], \u03b1o = 120 \u00b0, \u03b2 = 162 \u00b0. A model was built in ADAMS using its basic rigid elements such as links and cylinders, as shown in Fig. 11 . In order to connect elements into a movable mechanism, rotational and translational joints are applied. The optimized 4-bar mechanism is improved in accordance to the selected kinematic scheme in Fig. 9 by incorporating 2 additional DOFs with 2-link modules. Their dimensions have to be chosen in order to achieve suitable distances between joints A and B, as well as C and D. At first, revolute eccentric pins are applied as the upper elements BE and CF of the 2-link modules (navy blue elements in Fig. 11 ). These are rotationally connected with bushings at the ends of lower elements AE and DF, which are presented in Figs. 9 and 11 .The data obtained from the optimization process, and the results of simulations for the linearly adjustable 4-bar mechanism, are used as a basis for selecting the dimensions of the 2-link modules. The optimal lengths of the anterior and posterior elements are 43 mm (l 2 between C and D) and 48.6 mm (l 3 between A and B), respectively, whereas the global minimum / maximum required anterior and posterior lengths obtained during the simulations of the linearly adjustable 4-bar mechanism are equal to 42.69 mm / 45.89 mm and 46.58 mm / 51.27 mm [33] . The final dimensions of the 2-link modules are equal to 4 mm (eccentricity r e1 is equal to BE in Fig. 9 ) and 44 mm (length |AE|) for the upper and lower elements of the anterior 2-link module, and 5 mm (eccentricity r e2 is equal to CF in Fig. 9 ) and 49 mm (length |DF|) for the upper and lower posterior elements. These values are chosen while keeping in mind the possible small dimensions of eccentricities, the option of covering a large space with different trajectories, and also the motors\u2019 angular range of rotation for the expected length changes (resolution of control). After the optimisation process, assumptions and equations are introduced in order to design a model with imposed movement for carrying out simulations. In the simulations, the angular velocity of femur movement is no longer considered constant", " For these reasons, by applying 2 additional DOFs, as the prismatic joints in the crossing bars, a linearly adjustable 4-bar mechanism is obtained in Fig. 8 . It is a compromise solution with structure simplified to planar motion, but it has the ability to reproduce the knee movement with a satisfying accuracy. Nevertheless, the prosthesis solution in Fig. 8 cannot be considered feasible from biomechanical viewpoint both for the sliders and the overall size. Thus, the solution is converted in the linkage design to the rotationally adjustable 4-bar mechanism in Fig. 9 made of revolute joints only (except for the main linear motor). Therefore its mechanical design with reduced sizes can be more convenient for rehabilitation or orthopaedic implementation. Moreover, the new mechanism\u2019s main advantage is the possibility of real-time control, as well as being able to alter the dimensions of a 4-bar mechanism during motion. This feature is not even present in other mechanisms that imitate the knee joint\u2019s movement in 3D [29] . The assumed reference ICR trajectory (Walker et al" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000494_icphm.2019.8819423-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000494_icphm.2019.8819423-Figure2-1.png", "caption": "Fig. 2. Assumed crack propagation path to determine the total mesh stiffness.", "texts": [ " The equations of motion for the system considering the linear displacement, velocity, and acceleration in the y-direction and the rotary displacements, velocities, and accelerations of the pinion, gear, motor, and load are given by [9], [10], [23]: m1y1=Fk+Fc-k1y1-c1y1, (1) m2y2=Fk+Fc-k2y2-c2y2, (2) I1\u03b81=kp \u03b8m-\u03b81 +cp \u03b8m- \u03b81 -Rb1 Fk+Fc , (3) I2\u03b82=Rb2 Fk+Fc -kg \u03b82-\u03b8b -cg \u03b82- \u03b8b , (4) Im\u03b8m=M1-kp \u03b8m-\u03b81 -cp \u03b8m- \u03b81 , (5) Ib\u03b8b=-M2+kg \u03b82-\u03b8b -cg \u03b82- \u03b8b , (6) Fk=kt Rb1\u03b81-Rb2\u03b82-y1+y2 , (7) Fc=ct Rb1 \u03b81-Rb2 \u03b82-y1+y2 , (8) Equations (1)-(8) were solved simultaneously to obtain the vibration signals, i.e. displacement, velocity, and acceleration of the pinion and gear. The solution of this set of differential equations depends on the calculation of the total effective mesh stiffness for different fault conditions of the pinion and gear. To determine the total effective mesh stiffness, a simplified model based on the potential energy method was adopted [24], as illustrated in Fig. 2. This model assumes that the crack is initiated at the root of the 15th tooth of the pinion and propagates through a straight line with size a and constant inclination angle \u03b2 = 45o with respect to the centerline of the tooth. Fig. 2 also shows the angle between centerline and radius intersecting the tangent line drawn from the addendum of the root, \u03b1g, the half height of the top land of the tooth, hr and the half tooth angle, \u03b12. In order to have a more realistic representation of the signal, the effects of TPE were included in the dynamic response of the system. The schematic representation of the TPE model is presented in Fig. 3. In this figure, the TPE, Er, is interpreted as the relative difference between the design profile, PD, and the actual profile, PA, caused by the lack of precision of machinery employed in the manufacturing process, LA, is an infinitesimal section of the tooth profile that is amplified to show the effect of the tooth profile error" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000716_j.mechmachtheory.2019.07.013-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000716_j.mechmachtheory.2019.07.013-Figure7-1.png", "caption": "Fig. 7. Coordinate systems for obtaining the generating lines of the grinding disk wheel.", "texts": [ " 6 , a discretization grid of tooth surface of the face gear is displayed on radial projection. The contact lines of the gear tooth surface constitute the grid lines in the profile direction. The grid lines in the longitudinal direction are comprised of a set of equally spaced parallel lines. Each intersection node belonging to the numerical grid on the tooth surface of the face gear will be ground by the disk wheel. The generating profiles of the grinding disk wheel are consistent with the section geometry at the toe end of the reference conical spur involute shaper ( Fig. 7 ). However, the thickness t g of top land of the grinding disk needs to be designed less than or equal to the width t l of the top land at the heel end of the reference conical spur involute shaper, which can be obtained through the aforementioned method. Otherwise, excessive cutting will occur at the heel end of the tooth surfaces of the being-generated face gear. The derivations for the unit normal and the position vector of the generating surfaces of the grinding disk wheel are explained in this subsection. Fig. 7 shows the installation relationship between the disk wheel and the reference conical spur involute shaper. A coordinate system S t with origin O t in the center of the disk is established. The generating profiles can be obtained by transforming the section geometries of the reference conical spur involute shaper (taking the thickness modification of the disk into consideration) from coordinate system S s to coordinate system S t , in which the profile of the grinding disk is defined.{ r ( g ) t ( u sg , l sg ) = M ts ( r s ( u s , l s ) \u2213 [ ( t s \u2212 t l ) / 2 0 0 1 ]T ) z s = b a = L 0 \u2212 L 1 (20) where, M ts = \u23a1 \u23a2 \u23a3 0 \u22121 0 E gs 0 0 \u22121 b a 1 0 0 0 0 0 0 1 \u23a4 \u23a5 \u23a6 (21) Here, E gs represents the distance between axis z s of the reference shaper and axis z t of coordinate system S t , and is predefined" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000327_j.mechmachtheory.2017.05.014-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000327_j.mechmachtheory.2017.05.014-Figure1-1.png", "caption": "Fig. 1. The derivation of non-circular gear.", "texts": [ " Generating processing is based on the meshing trajectory of gear pair and it is the most widely used method for the theoretical analysis of gear pair. According to the method of gear meshing with point contact on the surface [9] , the tooth numbers of helical shaper cutter N S should be more than the tooth numbers of helical non-circular gear N 1 and the difference between N S and N 1 is 2 or 3 to getting good contact situation. According to the generating method, the tooth surface of non-circular gear is generated by the tooth surface of shaper cutter. As shown in Fig. 1 (a), the meshing process of non-circular gear with shaper cutter can be considered as shaper cutter meshing with rack-cutter o and the non-circular gear meshing with the same rack-cutter simultaneously, Fig. 1 (b) shows the relationship of the three pitch surfaces. In Fig. 1 (a), S o ( X o Y o Z o ) is the fixed coordinate system of rack-cutter, S s ( X s Y s Z s ) is the fixed coordinate system of shaper cutter and S 1 ( X 1 Y 1 Z 1 ) is the fixed coordinate system of non-circular gear. S o \u2032 ( X o \u2032 Y o \u2032 Z o \u2032 ) is the movable coordinate system of rack-cutter, S s \u2032 ( X s \u2032 Y s \u2032 Z s \u2032 ) is the movable coordinate system of shaper cutter and S 1 \u2032 ( X 1 \u2032 Y 1 \u2032 Z 1 \u2032 ) is the movable coordinate system of non-circular gear. Any one of the three pitch surfaces, which were shown in Fig. 1 (b), is doing pure rolling with the other two surfaces at the same time. So, the displacement L oo \u2032 can be replaced as r s \u00b7 \u03d5s and r 1 \u00b7 \u03d51 . The mathematical equation of \u03d51 , r 1 and L oo \u2032 can be defined as: \u23a7 \u23a8 \u23a9 L oo \u2032 = r s \u00b7 \u03d5 s \u03d5 1 = L oo \u2032 r 1 = r s \u222b \u03d5 s 0 1 r 1 d\u03d5 r 1 = a (1 \u2212k 2 ) 1 \u2212k cos ( n 1 \u03d5 1 ) (1) Where, r 1 is the pitch radius of non-circular gear; r s is the pitch radius of shaper cutter; \u03d51 is the rotation angle of noncircular gear; \u03d5s is the rotation angle of shaper cutter; a is the semi-major axis of non-circular gear; k is the eccentricity ratio of non-circular gear; n 1 is the order of non-circular gear. With the method of coordinate transformation, the coordinate transformation matrix M 1 \u2032 s \u2032 are presented as follows: M 1 \u2032 s = M 1 \u2032 1 \u00b7 M 1s \u2032 \u00b7 M s \u2032 s = \u23a1 \u23a2 \u23a3 cos \u03d5 1 cos \u03d5 s \u2212 sin \u03d5 1 sin \u03d5 s \u2212 cos \u03d5 1 sin \u03d5 s \u2212 sin \u03d5 1 cos \u03d5 s 0 \u2212 sin \u03d5 1 ( r 1 + r s ) cos \u03d5 1 sin \u03d5 s + sin \u03d5 1 cos \u03d5 s cos \u03d5 1 cos \u03d5 s \u2212 sin \u03d5 1 sin \u03d5 s 0 cos \u03d5 1 ( r 1 + r s ) 0 0 1 0 0 0 0 1 \u23a4 \u23a5 \u23a6 (2) The shaper cutter, which is shown in Fig. 1 , can be deemed as cylindrical gear and the mathematical equation of shaper cutter can be shown as follows: \u2212\u2192 r s (s ) ( \u03d5 s , \u03bes ) = \u23a1 \u23a2 \u23a3 r bs [ cos ( \u03d5 os + \u03d5 s \u2212 \u03bes ) \u2212 \u03d5 s sin ( \u03d5 os + \u03d5 s \u2212 \u03bes )] \u2212r bs [ sin ( \u03d5 os + \u03d5 s \u2212 \u03bes ) + \u03d5 s cos ( \u03d5 os + \u03d5 s \u2212 \u03bes )] p \u03bes 1 \u23a4 \u23a5 \u23a6 (3) Where, p is spiral parameter; r bs is the pitch radius of shaper cutter; \u03d5os is the helix angle of base circle in shaper cutter; \u03d5s is the rotational angle and \u03be s is torsion angle. And the unit normal of shaper cutter: \u2212\u2192 n s (s ) ( \u03b2s , \u03d5 s ) = [ \u2212 cos \u03b2s sin ( \u03d5 os + \u03d5 s \u2212 \u03bes ) \u2212 cos \u03b2s cos ( \u03d5 os + \u03d5 s \u2212 \u03bes ) \u2212 sin \u03b2s ] (4) Where, \u03b2s is the base spiral angle of shaper cutter" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000970_j.mechmachtheory.2019.103747-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000970_j.mechmachtheory.2019.103747-Figure5-1.png", "caption": "Fig. 5. Finite inverse singularity of the first kinematic chain corresponding to geometrical configurations (i) and (j) from Fig. 3 at (a) Z EE = Y 0 = [0 1 0] T and (b) Z EE = \u2212Y 0 = [0 \u2212 1 0] T .", "texts": [ " (1) and substituting equivalent parameters for the first chain (see Table 2 , row 1), one obtains X EE = 1 S 2 \u03bc { (Z EE \u00d7 Y 0 ) \u00d7 (C \u03c0/ 2 Z EE \u2212 C \u03c0/ 2 Y 0 ) \u00b1 \u221a (C \u03c0 \u2212 C \u03bc)(C \u03bc \u2212 C 0 ) (Z EE \u00d7 Y 0 ) } (3) = 1 S 2 \u03bc { \u00b1 \u221a 1 \u2212 C 2 \u03bc(Z EE \u00d7 Y 0 ) } = \u00b1Z EE \u00d7 Y 0 S \u03bc where \u03bc is the angle between the axis of first joint, Y 0 = [0 1 0] T , and the given end-effector position Z EE . Since both links of the first kinematic chain are orthogonal, only configurations 1 and 3 from Table 1 may occur, meaning that, with respect to the first chain, any arbitrary end-effector position is either regular or in finite singularity. Referring to Fig. 4 , finite singularity occurs when Z EE becomes aligned with Y 0 ( Z EE = [0 \u00b1 1 0] T , \u03bc = 0 or \u03c0 ), corresponding to geometrical configurations (i) and (j) in Fig. 3 . In this situation, as shown in Fig. 5 , while Z EE is fixed, X EE can rotate around Y 0 . In other words, for the given end-effector vector Z , there are infinite number of solutions for \u03b8 and \u03b8 . Since \u03bc = \u03b8 + \u03c0/ 2 (see EE 1 2 5 Fig. 2 ), the denominator of Eq. (3) , S \u03bc, becomes zero at C 5 = 0 . Therefore, the finite inverse singularity of the first chain (refereed to as FI-1 in the rest of this paper) occurs at C 5 = 0 . Then, by rewriting Eq. (1) and substituting equivalent parameters for the second chain (see Table 2 , row 2), we obtain Z 3 = 1 S 2 \u03c3 { (Y EE \u00d7 X 2 ) \u00d7 (C \u03b3 Y EE \u2212 C \u03be X 2 ) \u00b1 \u221a (C \u03b3 + \u03be \u2212 C \u03c3 )(C \u03c3 \u2212 C \u03be\u2212\u03b3 ) (Y EE \u00d7 X 2 ) } (4) where \u03c3 is the angle between the axis of second joint X 2 and Y EE " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003815_taes.1987.310835-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003815_taes.1987.310835-Figure1-1.png", "caption": "Fig. 1. Reference frame and spacecraft model.", "texts": [ " However, unlike [7-9] the attitude motion is defined only on a subset of the Euclidean space and therefore, some of the arguments in the proof of stability of the closed-loop system differ from those of [7, 8]. Section II presents the mathematical model and the attitude control problem. An adaptive control law is derived in Section III, and simulation results are presented in Section IV. 11. SPACECRAFT MODEL AND CONTROL PROBLEM Consider a spacecraft in a circular orbit in an inverse square gravitational field, and assume that the attitude of the space vehicle has no effect on the orbit. With reference to Fig. 1, let xl, x2,X3 be the frame of principal axes of inertia. Let I,, 12, 13 be the principal axis moments of inertia of the spacecraft. The reference axes {gi} are defined as follows: (3 is along the local radius vector from the gravitational center E, through the spacecraft center of mass E; 92 is normal to the plane of orbit; and (l, i2, 93 is a dextral righthanded system. The spacecraft angular velocity w = (W1 , c2, co3)T with respect to inertial space is given by [10] Wo [E204 2]= (coo + 0,) sin02 + 03 (Wo0 + 1) COS02 COS03 + 02 sin03 (Wo + 6,) cos02 sin03 + 02 COS03J 02, 03 are the pitch, yaw, and roll angles, respectively; and we define 0 = (01, 02, 03)T E R3 R(0) - [ W, (0) = [ sin02 COS 02 COS 03 COS 02 sin 03 0 sin 03 COS 03 1 0 ; O0 wo sin02 WO CoS 02 COS 03 -0O COS 02 sin 03 Here T denotes transposition, and Rk denotes the Euclidean space of dimension k" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001379_tec.2020.3030042-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001379_tec.2020.3030042-Figure6-1.png", "caption": "Fig. 6. Schematic diagram before and after elastic deformation of cylindrical shell.", "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) < 4 A. Energy Equations of Stator Yoke For the stator yoke, it is assumed that the linear element originally perpendicular to the mid-surface will remain linear after the shell undergoes small elastic deformation, but not perpendicular to the reference surface, as shown in Fig. 6. Based on the above assumptions, the displacement of any point inside the cylindrical shell can be expressed as y y y ( )u u r R r r R v v R R w w (13) where \u03c6 and \u03c8/R represent the axial and circumferential rotation angles of the linear element perpendicular to the mid-surface of the cylindrical shell, respectively. According to the three-dimensional elastic theory, the potential energy and the kinetic energy of the cylindrical shell can be expressed as 2 1 /2 2 y \u03b8 \u03b8 z z /2 0 r\u03b8 r\u03b8 rz rz \u03b8z \u03b8z 1 ( 2 ) L r L r PE rdrd dz (14) 2 1 2 2 2 /2 2y y y y y /2 0 /2 2y 2 2 2 /2 0 2 /2 2 2 2 2 2 /2 0 2 2 { [( ) ( ) ( ) ] 2 [2 ( ) 3( ) 12 4 ( ) ]} L r L r L L L L u v w KE rdrd dz t t t Rh u v w t t t h u v R R t t t tR v d dz t t t (15) where \u03c1y is the shell density, r2 and r1 are the outer and inner radius of the cylindrical shell" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003566_0094-114x(94)90031-0-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003566_0094-114x(94)90031-0-Figure2-1.png", "caption": "Fig. 2. Screw triangle associated with the displacement of two points.", "texts": [ " (2) By defining the pitch p of the screw as p = ( ~ ) / ( t a n -~), (3) we have the coordinates for the unit screw ~i/: ~i/= (q; qo + pq) = (g~; a,/x g,/+ pl,/). (4) We seek to rewrite the screw ~j in the following form: gi, =f , So, +ASo, + ' . . + / . s o . , m ~< 6. (5) wherefk, k = I, 2 . . . . . m, are scalar functions of the free parameters, and So,, k ffi 1, 2 . . . . . m, are 6-vectors, the components of which are functions of known constants (specified parameters). Ideally m would equal ( 7 - b), but unfortunately this seems to be true for only odd values of b (i.e. b = 5, 3, I). 3. !. Two points As shown in Fig. 2, R~ and S~ are two specified points on a rigid body. We want to find all the possible screws for displacing R, and S~ to Rj and Sj, respectively. The position vectors of R~, S~, Rj, and Sj are specified; they are r , s , rj and sj, respectively. The free parameter is chosen to be ~bu, which is the rotation parameter of the incompletely determined screw, N e. According to Tsai and Roth [3], the analytic expressions for the resultant screw are '~ = ke(ne tan ~ + le tan ~ + le x ne tan ~ tan ~) , 1 tan ~ = k e [ l _ (no" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000879_j.apor.2019.01.030-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000879_j.apor.2019.01.030-Figure2-1.png", "caption": "Fig. 2. The Body-fixed Coordinate and Earth-fixed Coordinate of the surface vessel.", "texts": [ " The measured data were utilised in the closed-loop control process and logged in the USB drive for the following analysis. \u2022 Host computer: Host computer installing the software LabVIEW was used to control the model and deploy the control and operation program remotely. The mathematical model of Hoorn includes hydrodynamic and manoeuvring characteristics. As the reverse motion dynamics are quite different, the forward motions of the vessel are considered. The motions of the Hoorn are defined in two interrelated coordinates, named Earthfixed coordinate and Body-fixed coordinate [34] shown in Fig. 2. The mathematical model of Hoorn was developed based on experimental approaches [35]. The conservation of linear and angular momentum, as well as the models of rudder and propeller, can be expressed as the following equations [36]: M C D g( ) ( ) ( )s s s s s s E+ + + = + (1) c= (2) n T n n1 ( ) n c= (3) where s denotes the velocity items of the ship\u2019s translated and rotation motion, including surge, sway, heave velocity, and roll, pitch, yaw speed; M the inertia matrix; C ( )s the matrix of Coriolis and centripetal terms containing the added mass; D ( )s the matrix of damping terms; g ( )s the vector of restoring forces and moments arisen from gravity and buoyancy; s ship\u2019s position and orientation; the vector of control inputs; E the vector of environment forces and moments; c the commanded rudder angle; the actual rudder angle; T n,n c and n are the time constants, commanded shaft speed and current shaft speed, respectively", " After remotely deploying the developed program into the myRIO, the neural network based controller would work in the Time Loop with interval time at 0.1 s and use the processed data with the sampling rate at Hz10 . Considering the accuracy limitation of the employed low-cost GPS, only the course keeping experimental tests were reported in this study. The aim of the experiments is to maintain the ship sailing forward with fixed yaw angle. Thus, the direction of the ship will be stabilised on the corresponding yaw angle, which is explained as the rotation around Z axis in Fig. 2. In order to validate the control performance of the proposed autopilot, two experiment scenarios with different courses at and225 255\u00b0 \u00b0 were conducted (see Fig. 6). It is worth noting that the remote control range was limited due to the practical WIFI range at 100m, thus experiment results in 100 s were reported. In order to highlight the performance of the proposed control system, the experiments of BP RBFNN based controller and PD based controller developed in [43] were also performed for comparison" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001745_j.matchar.2021.111047-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001745_j.matchar.2021.111047-Figure1-1.png", "caption": "Fig. 1. Schematics of process parameters and scanning strategy for the fabrication of L-PBF AISI 316 L parts.", "texts": [ " On the other hand, there is a set of process parameters in L-PBF process that can be modified such as laser power (P), hatch distance (HD), scan velocity (vs), and layer thickness (LT) with proper selection of scanning strategy. The laser scanning strategy has been an important factor in determining better surface quality and reducing residual stress effects in L-PBF parts. \u2018Quad Islands\u2019 was chosen as a divisional scanning strategy. The schematics and the scanning strategy are illustrated in Fig. 1. The geometry of the parts was 5 mm \u00d7 15 mm (height \u00d7 diameter) and the parts were manufactured using a Laser Powder Bed Fusion system from Aconity 3D (AconityMIDI), with a maximum building volume of 170 mm of diameter and 400 mm of vertical displacement. The radiation source was single mode fiber laser with a maximum power of P = 1 KW, a wavelength of \u03bb = 1070 nm, and a spot size (diameter) in the range of 80\u2013500 \u03bcm. The volumetric energy density (VED) has been the most representative process parameters in additive manufacturing industries and VED has relationship with Power, P (watts), scanning speed, vs (mm/s), layer thickness, LT (\u03bcm), hatch distance, HD (\u03bcm), and according to the equation below: VED = P vs \u00d7 LT \u00d7 HD An experimental design was made by taking into consideration the parameters previously mentioned along with some constraints for the determination of processing parameters" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000775_tro.2019.2906475-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000775_tro.2019.2906475-Figure2-1.png", "caption": "Fig. 2. Generic planar CDPR with two attached pendulums.", "texts": [ " The basic concept is to add an additional inertial load to the mobile platform. Any forces applied to such a load will also generate an equal and opposite reaction force on the platform. This concept has been employed widely in the form of reaction wheels, an inertial disk used for attitude control of satellites, and as well as with tuned mass dampers, which are employed in skyscrapers for eliminating structural vibrations induced by disturbances, such as wind. Consider a rigid pendulum coupled to the shaft of a motor mounted at some location on the mobile platform (see Fig. 2). Due to the unbalanced nature of the pendulum-shaped load mass, an applied torque along the motor shaft will produce a corresponding reaction torque as well as a reaction force tangential to the position of the pendulum along its arc of motion. Depending on where the actuator is mounted on the platform, the reaction force from the pendulum will also produce a secondary set of reaction moments due to the displacement of the force from the various rotational axes. If two identical pendulum actuators are added to the platform and mounted such that they are mirrored about the zy plane and with their axes of rotation inline with the platform x-axis, it becomes possible to produce a pure moment about the y-axis while maintaining the ability to produce the coupled force moment pair of a single pendulum", " The reason for using a two-pendulum design is due to its mechanical simplicity and the fact that it requires only two additional actuators to fully regulate the CDPR out-of-plane dynamics. The proceeding sections provide an updated dynamic model for a generic CDPR with two added pendulum actuators and a detailed analysis on the ability of the proposed reaction system to regulate out-of-plane platform dynamics. In order to define the kinetic and potential energy terms for the pendulum actuators, it is first necessary to obtain an expression of their rotational and translation velocities. Consider the platform mounted pendulums of Fig. 2. The location of the center of mass of the ith pendulum, with respect to the ground frame, is found to be pa,i = p+Rg pra,i +Rg a,i la,i (9) where ra,i is the offset from the platform center to the pendulum mount point and la,i is the displacement from the pendulum axis of rotation to its center of mass. Taking the time derivative of (9), the pendulum velocity is found as p\u0307a,i = p\u0307+Rg p(\u03c9p \u00d7 ra,i) +Rg a,i(\u03c9a,i \u00d7 la,i). (10) The angular velocity is simply the sum of the angular velocity of the pendulum about its revolute joint \u03b8\u0307a,i with the angular velocity of the platform", " Let A = Df(x0) be the linearized Jacobian matrix of f where Aij = \u2202fi/\u2202xj denotes the entry of row i and column j of matrix A. Then, f is asymptotically stable at x0 if the linearized system x\u0307 = Ax is stable at x0. Proof: The proof of Theorem 1 has been provided in [22]. To avoid the repetition, the proof is not presented in this paper. Definition 1: The vibrations of the CDPR in the qi and qj directions are said to be coupled if vibration of the CDPR in the qi-direction excites the CDPR\u2019s vibrations in the qj-direction and vice versa. Consider the generic planar CDPR presented in Fig. 2 with two added pendulum actuators. Suppose the tension in each cable is controlled by a proportional-derivative (PD) controller. The tension in each cable can then be represented as \u03c4i = \u2212kcp\u03b4li \u2212 kcd\u03b4\u0307li, where \u03b4li = li \u2212 l0,i denotes the difference between the total length of the cable li and the nominal length of cable in the static equilibrium condition l0,i and kcp andkcd are the proportional and derivative controller gains, respectively. Similarly, suppose that the torque of each pendulum is controlled by a PD controller such that \u03c4a,i = \u2212kp\u03b8p,i \u2212 kd\u03b8\u0307p,i where kp and kd denote the pendulum controller gains", " Regarding consideration of the most severe case for the coupling conditions between the system planar and nonplanar vibrations in the provided analysis and also having the equivalent damping effects in all planar directions, we can conclude that for any vibration in any direction of the system, the energy of the whole linearized system, as illustrated in Fig. 4, will be dissipated to reach the static conditions, which, based on Theorem 1, means the asymptotic stability conditions for the whole nonlinear system, as illustrated in Fig. 2, are satisfied. It is worth mentioning that (33) shows a specific condition of the systems parameters where an uncoupled vibrational mode shape can happen in out-of-plane directions of z and \u03b8x without stimulating the pendulum mechanism to suppress the system energy. However, the condition of (33) can be easily violated in the CDPR design for all points of the workspace. In order to validate the proposed reaction system, a prototype (see Fig. 5) was built and tested using the test setup shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003608_9783527618811-Figure4.2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003608_9783527618811-Figure4.2-1.png", "caption": "Fig. 4.2 Two-wheeled robot.", "texts": [ "32) (A3 + ma2) d dt (\u03c8\u0307 + \u03c6\u0307 cos \u03b8) = 0 (4.33) From (4.31) we conclude that \u03c6 = \u03bdt + \u03c60 for constants \u03bd and \u03c60. From (4.33) we conclude \u03c8\u0307 + \u03c6\u0307 cos \u03b8 = \u03c8\u0307 + \u03bd cos \u03b8 = h and \u03c8 = (h\u2212 \u03bd cos \u03b8)t + \u03c80 for constants h and \u03c80. Using these results the translation equations become x\u0307 = \u2212a(h + \u03bd cos \u03b8) cos(\u03bdt) y\u0307 = \u2212a(h + \u03bd cos \u03b8) sin(\u03bdt) This system of ordinary differential equations describes motion on a circle. Therefore the rolling disc of constant inclination angle rolls on a circle. 4.3.3 Consider the idealized robot shown in Fig. 4.2. The robot consists of a body and two wheels and it is driven by torques \u03c41 and \u03c42 applied to the wheels. Let B0 be the body, Bi the ith wheel, B = B0 \u222a B1 \u222a B2 and mi, ri are the mass and the center of mass of Bi, respectively. The inertia tensor for the collection of rigid bodies is I(B, r0) = I(B0, r0) + I(B1, r1) + I(B2, r2) + 1 2 a2m1(I \u2212 i\u2297 i) + 1 2 a2m2(I \u2212 i\u2297 i) = I(B0, r0) + 2I(B1, r1) + a2m1(I \u2212 i\u2297 i) = I0 + 2I1 + m1a2(j\u2297 j + k\u2297 k) L = 1 2 m(x\u03072 + y\u03072) + 1 2 I \u03b8\u03072 + 1 2 I1(\u03c6\u03072 1 + \u03c6\u03072 2) where m = m0 + 2m1, I = I0 + 2I1 + m1a2" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003879_j.wear.2004.11.018-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003879_j.wear.2004.11.018-Figure1-1.png", "caption": "Fig. 1. Elastic sphere rolling over an elastic plane (a) and between two Vgrooves (b). In (b) the deformation of the ball and grove at the contact is not shown.", "texts": [ " Microslip, in rolling contacts, depends on the \u2018creep\u2019 moion, or relative velocity, and on the elasticity, of the points n the opposite surfaces, as they pass through the contact atch. In the case of pure rolling of identical bodies, the reep motion is null, and no microslip takes place. Theoetical quantification of friction losses in rolling contacts is chieved by applying elastic contact theory together with an ssumed friction law (usually Amontons\u2019 law, i.e. a constant oefficient of friction) at each contact point [13]. Fig. 1 could ive us an idea about the creep motion likely to take place in rolling ball contact. In Fig. 1a a ball rolls without spin on a lane elastic surface. Because of the different relative surface peeds across the contact patch, the well-known Heathcote lip case occurs. In Fig. 1b, the case of a ball rolling between wo V-grooved rails is depicted. The main rolling motion of he ball can be resolved into a rolling and a spinning motion at ach contact with the groove surfaces. Consequently, if there rom dry to lubricant friction and the hysteretic behavior are easured and global tendencies of these phenomena as a unction of the preload and viscosity of the lubricant are emirically derived. These experiments are extended to different all materials or coatings in [17]. In all these experiments the ysteretic behavior is quantified by the steady-state friction orque and rest slope as defined by the Dahl curve [20]" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000417_s00170-018-2799-7-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000417_s00170-018-2799-7-Figure1-1.png", "caption": "Fig. 1 Skiving model: a configuration of skiving, b cutter definition", "texts": [ " Therefore, in order to universally identify the cutting edge curve of the skiving cutter and analyze the relationship between geometric factors of skiving and the motions, firstly, this work analyzed the working principle of skiving and established the kinematic model of skiving. Next, a discrete cutting edge curve identifies method which was proposed based on the surface conjugate theory, and the spatial contact motion that corresponds to the cutting edge was analyzed in follow. At last, the cutting edge curve identification and the skiving motion analysis were performed for an involute machining to proof the effectiveness of proposed method. The working configuration of skiving is illustrated as in Fig. 1a, wherein the dynamic workpiece coordinate frame O\u2032w-X\u2032wY\u2032wZ\u2032w is affixed in the workpiece, rotating around the Zw-axis with a rotation angle \u03c6w relative to the static workpiece coordinate frame Ow-XwYwZw. Meanwhile, the dynamic cutter coordinate frame O\u2032c-X\u2032cY\u2032cZ\u2032c is affixed on the cutter, rotating aroundZc-axis with a rotation angle \u03c6c relative to static cutter coordinate frame Oc-XcYcZc, and moving along the Zwaxis with displacement \u0394F. In initial, the Xw-axis is coincided with the Xc-axis and taken the same direction", " In order to adjust the cutting condition between the cutting edge and workpiece, the cutter might be shifted along the Zcaxis. Thus, the eccentricity Ec is defined as the distance from the center point P of the rake flank SR to pointOc. Besides, all types of rake flanks like plane, cone, and sphere are unified denoted as SR; thus, its mathematical expression can be identified by point P. Accurate movement relationship is significantly to guarantee the correct profile manufacturing during skiving, in which the main generating motion performed profile is improving along the desired helical slot. As shown in Fig. 1a, on the one hand, the rotation speed of cutter nc and rotation speed of workpiece nw keep a constant ratio i to maintain the primary generating relationship between the rotation angles \u03c6c and \u03c6w. On the other hand, an additional differential rotation ncf is applied on the cutter, and a synchronized linear motion F that parallel to the Zw-axis is also implemented. Then, both the ncf and F compose the feed motion. In order to manufacture the correct surface, the rotation angles of both workpiece and cutter need are according to the following relationship: \u03c6c \u00bc i\u03c6w \u00fe\u0394\u03c6 \u00f03\u00de where \u0394\u03c6 = 2\u03c0ncft; it denotes the differential rotation angle of cutter" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001357_j.addma.2020.101670-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001357_j.addma.2020.101670-Figure1-1.png", "caption": "Fig. 1. a) CAD drawing, b) EB-PBF-manufactured specimens, c) location of the as-manufactured and post-treated specimens on the build plate, d) unidirectional scanning strategy and the coordination system, e) drawing of the LCF test specimen and f) a real test specimen used in the LCF test.", "texts": [ " A layer thickness of 70 \u00b5m was used throughout the build. The beam current, beam velocity, and line offset (refers to the distance between two hatch lines) were 28 mA, 4.8 m/s, and 200 \u00b5m, respectively, during the hatch melting. The hatch melting followed a unidirectional pattern (snake false), and the hatch direction was altered 67\u25e6 after each layer. In total, forty-nine vertical bars were manufactured, in which only eleven bars with a similar location were used for thermal post-treatments, and LCF testing. Fig. 1 (a\u2212 d) shows the CAD drawing and location of the samples on the build plate, as well as the unidirectional scanning pattern used to manufacture the specimens The build time for manufacturing the forty-nine bars was approximately 58 h. The condition used for the heat treatment (HT), and hot isostatic pressing (HIP) and coupled HIP-HT cycles are given in Table 1. Argon was used as the media in all the cycles. A forced convection cooling with high-pressure argon gas was used for rapid cooling. The post-treatment conditions were designed to homogenize the distribution of Ti, Nb, and Al helping the formation of the \u03b3\u2032, and \u03b3\u2032\u2032 E. Sadeghi et al. Additive Manufacturing xxx (xxxx) xxx precipitates, and avoiding the formation of the \u03b4 and Laves phases for the overall improvement in the mechanical properties. Due to a high number of rather large specimens manufactured on the build plate, the effect of location on the microstructure of the specimens was negligible (not presented here), which is in agreement with the literature [25]. Out of the eleven specimens randomly selected in this study (see Fig. 1c), one specimen was used in the as-manufactured condition, one specimen was subjected to HIP, six specimens were exposed to HIP-HT, and three specimens were only subjected to HT. One sample per each condition was used for the microstructural characterization, and the rest was used for the LCF testing. The selected specimens were then machined to produce cylindrical button-head type specimens for the LCF testing, having gage section length and diameter of 19.05 \u00b1 0.25 and 6.35 \u00b1 0.01 mm, respectively (see Fig. 1(e\u2212 f)). The tensile strain-control LCF testing was conducted in an Instron (8802, Massachusetts, the US) servo-hydraulic test frame using a \u00b1 250 kN load cell at room temperature (24 \u00b1 0.5 \u2103) in accordance with ASTM E606 [29]. The strain was measured using an Instron dynamic extensometer (2620\u2013826, Massachusetts, the US). The HIP-HT specimens were subjected to zero-to-tension cyclic loading (R-ratio of 0) at a frequency of 0.5 Hz, and strain ranges of 0.5%, 0.75%, and 1%. The HT specimens were subjected to a similar condition but only at one strain range of 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003876_978-1-4612-4990-0-Figure14-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003876_978-1-4612-4990-0-Figure14-1.png", "caption": "Figure 14. The hydraulic ellipse.: This illustrates the connection of the cylinders in the Energize valve setting. A quantity a of oil entering at the left moves the left shaft up by a distance d, transferring a quantity f3 of oil to the top of the right cylinder. This forces the right shaft down by the same distance d and expels the original quantity a of oil from the lower right. Since the two cylinders are anchored to the frame of the machine at the tops, the total length of actuator between the two anchoring points remains constant. Hence the intersection of the two shafts at the bottom traces out an ellipse.", "texts": [ " It is getting more difficult to identify the waves of recoveries in this gait. .................................... 13 Figure 9. The well known alternating tripods gait. ..................... 13 Figure 10. A further reduction of drive time. .......................... 13 Figure II. Illustration of the advantage of a rear-to-front strategy over a frontto-rear strategy. ........................... 15 Figure 12. Comparison of the cockroach nervous system with a microcomputer. 16 Figure 13. Three views of a leg from the walking machine. ............... 24 Figure 14. The hydraulic ellipse. .................................... 26 Figure 15. Table showing all of the hip valve settings that are provided by the walking machine. .......................... 28 Figure 16. The limits of motion for the foot as defined by the hip joint and actuators. ................................ 29 Figure 17. The natural motions of the machine. ........................ 30 Figure 18. Single ended cylinder. ................................... 32 Figure 19. Double ended cylinder. ..", " Each upper cylinder is single ended, that is, the shaft emerges from one end of the cylinder and the other end is closed. The lower cylinder is double ended, with the shaft emerging from both ends of the cylinder. The most important natural motion for walking is the drive stroke, in which a loaded leg is moved rearward. The natural motion here is a straight line stroke of the leg parallel to the desired motion of the center of gravity of the machine. By a particular connection of the cylinders of the upper leg, illustrated in Figure 14, it is possible to provide this natural motion. In this connection, the upper ports of the two cylinders are connected together and the lower ports are connected to a drive pump. When quantity of oil a is driven into the lower port of one cylinder, the shaft is pushed up some distance d. An amount of oil f3 is driven out of the upper port of the cylinder and into the upper port of the other cylinder, driving the shaft of that cylinder down the same distance d, forcing a oil out of the lower port of the other cylinder" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003813_1.2098890-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003813_1.2098890-Figure1-1.png", "caption": "Fig. 1 Two bodies connected by a kinematic pair", "texts": [ " In this work, Saha and Schiehlen 17 showed that the NOC of a parallel manipulator may be split into three parts\u2014one full, one block diagonal, and one lower triangular, and proposed a recursive minimal-order forward dynamics algorithm for parallel manipulators. Examples of up to two degrees-of-freedom planar manipulators were included and various physical interpretations were reported. Background Twists, Wrenches, and Equations of Motion. In this section, some definitions and concepts associated with the formulation of the kinematics and dynamics of articulated rigid body systems coupled by lower kinematic pairs will be briefly reviewed. See 18,19 for further details. Figure 1 shows two rigid links connected by a kinematic pair. The mass center of the ith link is at Ci while that of link i\u22121 is at Ci\u22121. The axis of the ith pair is represented by a unit vector ei. We attach a frame Fi with origin Oi and axes xi, yi, and zi, to link i\u22121 such that zi is along ei. The global inertial reference frame F0 with axes x, y, and z is attached to the base of the manipulator, and unless otherwise specified, all quantities will be represented in this global frame in the balance of the paper" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003201_027836402320556430-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003201_027836402320556430-Figure4-1.png", "caption": "Fig. 4. The relationship between phase, phase velocity and the orbits of the (a) juggling and (b) hopping systems. Shown with black lines are typical one-cycle orbits, corresponding to a certain phase velocity, and with dashed lines, the curves \u03c6 = \u03c0/2 and \u03c6 = 3\u03c0/2.", "texts": [ " By integrating the dynamics x\u0308 = \u2212\u03b3 and noting that collisions occur when x = 0, we obtain the time since the last impact and the time between impacts, a computationally effective instance of eqs. (12) and (13), as t\u2212 = x\u03070 \u2212 x\u0307 \u03b3 and s = t\u2212 + t+ = 2x\u03070 \u03b3 , (17) respectively. The change of coordinates h : (R+ \u00d7 R) \u2212 (0, 0) \u2192 S1 \u00d7 R + from ball coordinates to phase coordinates is given by h(x, x\u0307) = (\u03c6, \u03c6\u0307) where, following the recipe (eq. (14)), we take \u03c6 = \u03c0(x\u03070 \u2212 x\u0307) x\u03070 and \u03c6\u0307 = \u03c0\u03b3 x\u03070 . (18) In Figure 4(a) we illustrate the relationship between phase, phase velocity and the orbits of the juggling model. We model a single, vertical hopping leg, a mass m = 1 attached to a massless spring leg, by a dynamical system with three discrete modes: flight, compression and decompression. The latter two modes each have the dynamics of a linear, damped spring. Flight mode is entered again once the leg has reached its full extension. The equations of motion are x\u0308 = \u2212g \u2212\u03c92(1+ \u03b22)x \u2212 2\u03c9\u03b2x\u0307 \u2212\u03c92 2(1+ \u03b22 2 )x \u2212 2\u03c92\u03b22x\u0307 if x > 0 flight if x < 0 \u2227 x\u0307 < 0 compression if x < 0 \u2227 x\u0307 > 0 decompression, (19) where \u03c9 and \u03b2 are parameters which determine the spring stiffness \u03c92(1 + \u03b22) and damping 2\u03c9\u03b2 during compression", " (20) To determine the phase of this system, it suffices to derive the period, s(xb), of a cycle starting at (xb, 0). The value of s is obtained by summing the decompression time td , the flight time tf , and the compression time tc. It is shown in the appendix that s(xb) = td + tf + tc = (\u03c0 \u2212 \u03b8l)e \u03b2\u03c0(1\u2212 xb) 1\u2212 kb (21) \u2212 2 \u03b3 \u03c9(1\u2212 kb) \u221a 1+ \u03b22e\u03b2\u03b8l ( xb 1\u2212 xb ) + \u03b8l \u03c9 , where \u03b8l tan\u22121( 1 \u03b2 ). Given the period corresponding to a particular xb, we define the phase of a point (x, x\u0307) to be \u03c6(x, x\u0307) = 2\u03c0t\u2212(x, x\u0307)/s(xb). In Figure 4(b) we illustrate the relationship between phase, phase velocity and the orbits of the hopping model. It can be shown that s is a diffeomorphism on (\u2212\u221e, 0). We may, therefore, work equally well with the conjugate map, g(T ) s \u25e6 f \u25e6 s\u22121(T ), (22) representing each orbit of the system (eq. (19)) uniquely by its period. Knowing how to juggle one ball, or control one leg, should somehow lead us to a way of juggling two balls or synchronizing the controllers of two legs. We now show how to use the reference field (eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000238_1.4033045-Figure11-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000238_1.4033045-Figure11-1.png", "caption": "Fig. 11 Top-view of machine coordinates", "texts": [ " Since the rotation of the cradle is implemented by the resultant motion of the vertical slider and the horizontal slider, the position of vertical and horizontal sliders defined in coordinate system Sp can be represented as Dx1 \u00bc re cos\u00f0/i \u00fe hG\u00de Dy1 \u00bc re sin\u00f0/i \u00fe hG\u00de (36) where Dx1 and Dy1 are the relative positions of the vertical and horizontal sliders in coordinate system Sp, respectively. Machine top-view plane is defined by xPzP -plane of the machine frame coordinate system Sp, as shown in Fig. 11. On this plane, the projection of machine plane becomes a line and passes the pitch apex of the generated gear Op. The angle made between the axis of the generated gear and axis xP is the machine rootangle RB (angular position of B axis). The rotating axis of rootangle base is defined as point Or with a distance of Eb from the origin point Op along the axis of the generated gear (axial displacement of the generated gear). Coordinate system Sb\u00f0Or xbybzb\u00de is attached to the sliding base. The coordinate transformation from Sb to Sp can thus be obtained Mbp\u00f0RB\u00de \u00bc 1 0 0 Eb cos\u00f0RB\u00de 0 1 0 0 0 0 1 Eb sin\u00f0RB\u00de 0 0 0 1 2 664 3 775 (37) The pitch apex Op moves along with the rotation of the machine root base as Eb 6\u00bc 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000620_s11071-018-4338-3-Figure22-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000620_s11071-018-4338-3-Figure22-1.png", "caption": "Fig. 22 Simplified suspension system with two double-leaf springs and one axle", "texts": [ " This comparison clearly shows that the SSM solution agrees well with the HOBE42 solution for the tip vertical displacement. By contrast, the GCM solution gives smaller values because of the locking phenomenon. Accordingly, it can be concluded that the SSM locking alleviation works well even for the dynamic analysis of the initially curved and tapered structure, which is consistent with the conclusion drawn from the static analysis. 10.5 Unilateral bump negotiation Using the ANCF-RN concept, a simplified suspension assembly is built as shown in Fig. 22. The central ele- Fig. 23 Simplified spring-damper quarter vehicle model ments of the leaf spring are rigidly clamped to the axle reference node. The mounting shackle reference nodes and the other mounting end of the leaf spring are fixed. To clearly show the orientation of the reference nodes, the gradient vectors at the reference nodes rx , ry and rz are plotted as red, green, and blue arrows, respectively. Since the road in general is not perfectly flat, a bump on the road surface usually incurs larger impact load Fd than the steady load Fst during stable driving" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0002457_gsecongeo.18.6.575-Figure84-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0002457_gsecongeo.18.6.575-Figure84-1.png", "caption": "FIG. 84. A neutral surface fold showing the distribution of stresses.", "texts": [ " At the upper and lower limits of a bed folded according to the neutral surface law we have r\u2022: X/ro 2 + 2rot for the boundary of the tension side and r: = X/ro :m 2rot for the boundary of the compression side. Hence the apparent thickness t is expressed as t \u2022 r\u2022 mrs. = V'ro\u2022'-Jr - 2roTm V'ro\u2022'--2roT. Expanding the radicals by the binominal theorem and reducing we get --+ ... (4) t= T 2--[- ro 2 In general the dips of the beds at r\u2022, ro and r2 are not the same in neutral surface folding, as can be seen from Fig. 84. To work out the relations of dip, strata length and shape of ends for the general neutral surface fold appears to be mathematically difficult, and in this paper we will limit the discussion to the case where the folding has the same features as parallel folding. In order for this relation to exist the term T\u2022'/ro \u2022' in Equation (4) must drop out, when we have t -- 2T and our fundamental conditions reduce to those of Equation (I) under parallel folds, since the apparent thickness then becomes the true thickness and is a constant", " As just mentioned, neutral surface conditions can exist in thin beds even if closely folded, or in thick beds if very gently folded if the physical conditions of the rock are suitable, but the case of a thick bed fairly well lvent \u2022without rupture of some sort is difficult to visualize. It is posssible that this might be brought about by intermittent and cumulative movements during the interval between which the bending stresses became dissipated through the work of setting the rock, like a piece of steel being annealed or set by heat. After each set, if the forces and bending were repeated in the correct fashion, a fold of considerable magnitude might finally result. Fig. 84 has been drawn on the assumption that a neutral surface fold of this sort could be formed. For this figure the neutral surface was first drawn as a series of circles of varying radii, and then by the above formulae the position of various beds calculated and plotted. As dra'wn the figure is an anticline, but by reversing it the conditions .become synclinal. The typical conditions in a neutral surface fold for a given horizon are as follows: I. Above the neutral surface there would 'be tension in the anticlines and compression in the synclines, with a place of no, stress at the point of inflection somewhere on the limb" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003388_978-3-662-04831-3-Figure1.13-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003388_978-3-662-04831-3-Figure1.13-1.png", "caption": "Fig. 1.13: Drawings and photographs of serial and parallel robots", "texts": [ " Such a tailor-made program for a specific single application can be made computationally quite efficient. The major drawback of such a special-purpose program is its lack of flexibility for handling other types of applications. Practicing engineers must usually be capable of theoretically modeling and simulating complex mechanisms of quite different types in a short time: 1. Like serial robots with various degrees offreedom that include many rigid bodies subject to large spatial motion, various joints and actuators (e.g. Figure 1.13a, [20], [21], [22], [23], [24]). 2. Like parallel robots 2.1 constructed as multi-axis test facilities including up to 17 rigid bodies subject to large spatial motion together with 8 universal, 8 spherical, and 8 prismatic joints ( e.g. Figure 1.13b, [25], [26], [27], [28], [29], [30], [31]); or 2.2 constructed as hexapods including from 1 to 13 rigid bodies subject to large spatial motion, with 6 universal, 6 spherical, and 6 prismatic joints ( e.g. Figure 1.13c, [32], [33], [34]). 3. Like off-road vehicles including various rigid bodies subject to large spa tial motion and a large number of dissipative and elastic connection el ements as well as revolute and universal joints. Compare the following two examples: 3.1 The truck of Figure 1.14 that has been modeled by the general pur pose rigid-body analysis program NUSTAR. The model includes 17 rigid bodies subject to large spatial motion, 8 universal joints, 5 rev olute joints, 4 tire models, an engine model and more than 32 spa tial spring and damper elements" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000970_j.mechmachtheory.2019.103747-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000970_j.mechmachtheory.2019.103747-Figure7-1.png", "caption": "Fig. 7. Working modes of the proposed 5R-SPM (a) C 5 > 0 and C 3 > 0, (b) C 5 > 0 and C 3 < 0, (c) C 5 < 0 and C 3 > 0, and (d) C 5 < 0 and C 3 < 0.", "texts": [ " 3 and refereed to as II-2 in the rest of this paper) and \u03b3 = \u03be results in finite inverse singularity (refereed to as FI-2 in the rest of this paper). As shown in Fig. 6 , for \u03b3 = \u03be = \u03c0/ 2 geometrical configuration (h) and for \u03b3 = \u03be = \u03c0/ 2 geometrical configurations (i) and (j) occur. Finally, for \u03c3 < | \u03b3 \u2212 \u03be | or \u03c3 > \u03b3 + \u03be , there is no solution for the inverse kinematics problem and the given end-effector position is out of workspace. Since the inverse singularities occur at C 3 = 0 and C 5 = 0 , the proposed 5R-SPM has four solutions for inverse kinematic in regular configuration (four working modes), based on the sign of C 5 and C 3 ( Fig. 7 ). The former indicates the solution of the first chain and the latter corresponds to the solution of the second chain. By rewriting Eq. (1) for the forward kinematics, we have Y EE = 1 S 2 \u03b7 { (Z 3 \u00d7 X EE ) \u00d7 (C \u03c0/ 2 Z 3 \u2212 C \u03be X EE ) \u00b1 \u221a (C \u03be+ \u03c0/ 2 \u2212 C \u03b7)(C \u03b7 \u2212 C \u03be\u2212\u03c0/ 2 ) (Z 3 \u00d7 X EE ) } (5) = 1 S 2 \u03b7 { C \u03be X EE \u00d7 (Z 3 \u00d7 X EE ) \u00b1 \u221a S 2 \u03be \u2212 C 2 \u03b7(Z 3 \u00d7 X EE ) } where \u03b7 is the angle between axes Z 3 and X EE . Eq. (5) shows that, in a regular configuration, the forward kinematics has two solutions which corresponds to two assembly modes of the mechanism" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003710_0957-4158(92)90043-n-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003710_0957-4158(92)90043-n-Figure5-1.png", "caption": "Fig. 5. Coordination on the wall.", "texts": [ " (a) Pure slipping on a vertical wall; (b) Pure falling on a vertical wall; (c) Rotational slipping on a vertical wall; (d) Falling off on the floor; (e) Falling off from the ceiling; l~F/W > 1 (1) F/W > h/r (2) ItF/W> 1 f o r / / r < 1 (3) ItF/W > 1/r f o r / / r > 2 F/W > l/r - 1 (4) F/W > 1/r + i. (5) most severe condition is falling off from the ceiling, so the pace of walking on the ceiling should be taken as being lower. Rotational slipping on a vertical wall is the next most severe condition. When the model is moving on a vertical wall or is in transition to another wall, the coordinates of the center of gravity must be known to examine the safety conditions at any time. This can be done by using the coordinates on the wall and model geometry as shown in Fig. 5. The angles of or, /3, 7 and 6 are measured by the sensors and h and ! are calculated from these angles. If the frictional coefficient /~ is assumed, the required negative pressure in the sucker can be estimated by combining Figs 4 and 5, i.e. F/W or I~F/W in Fig. 4 can be determined by h and ! in Fig. 5, which gives the minimum required sucking force. The minimum required pressure Po(Po = F/S, where S is the base area of the sucker) can be given on the blower performance map, shown in Fig. 6 as an example. On the other hand, just after a cup is fixed on the wall, the negative pressure is measured, which is P in Fig. 6 for example. It gives a little larger value than P0. The input voltage of the blower, V, must be increased to V = V1 to get a certain pressure margin. But in this case it is important to know whether P is on curve A or B" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003014_s0003-2670(98)00806-x-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003014_s0003-2670(98)00806-x-Figure1-1.png", "caption": "Fig. 1. Biosensor scheme.", "texts": [ " The following apparatus was used: a Metrohm G41 VA-Detector potentiostat, a model 868 Amel recorder connected to a Mitek-MK 5001 digital multimeter, an electrode for oxygen determination supplied by Universal Sensor (US), New Orleans, USA. The electrode used was of the gaseous diffusion amperometric type (Clark electrode). Since the original cap of the commercial electrode used was unsuitable for operation in organic solvents, it was replaced with a similar cap of the same size made of PTFE. Also the original rubber O-ring used to \u00aex the gas-permeable membrane was replaced with a small PTFE ring. The O2 determination electrode and the modi\u00aeed cap are shown in Fig. 1. The gas-permeable membranes were supplied by Radelkis (Budapest). The dialysis membrane used was of the D-9777 type and supplied by Sigma (St. Louis, Mo, USA). The tests were run in a 25 ml thermostated glass cell provided with a forced circulation water jacket (supplied by Marbaglass, Rome) connected to a Julabo model VC 20B thermostat (Germany). The solvents used in the tests were kept under constant stirring using a magnetic microstirrer from Velp Scienti\u00aeca (Italy). Butyrylcholinesterase from horse serum (500 U per mg of solid), choline oxidase from Alcaligenes Species (500 U per mg of solid) and butyrylcholine chloride were supplied by Sigma (Milan), kappa- carrageenan and glycine were from Fluka (Switzerland), n-hexane for RPE analysis, potassium monobasic phosphate and potassium dihydrogen phosphate were from Carlo Erba (Milan), chloroform (stabilised with amylene) RS for liquid chromatography was supplied by Merck (Germany), organophosphorus pesticides and carbamates were supplied by Riedel de-Hae\u00c8n (Seelze, Germany). The water content of the organic solvents (anhydrous or saturated with water) used in the present work and expressed as a percentage by weight was determined using a model DL18 Karl Fischer titrator supplied by Mettler (Switzerland). The results obtained are set out in Table 1. The proposed biosensor (Fig. 1) was obtained using a gas diffusion amperometric electrode for oxygen as electrochemical transducer and two enzymes, butyrylcholinesterase and choline oxidase, both immobilised as described in the following. Using this biosensor on the basis of two enzymatic reactions in series: Butyrylcholine !butyrylcholinesterase choline butyric acid (1) Choline 2O2 H2O !choline oxidase Betaine 2H2O2 (2) a correlation may be found between the substrate (butyrylcholine) concentration and the oxygen consumed in the enzymatic reaction catalysed by the choline oxidase, and consequently, with the decrease of the current intensity circulating in the measurement apparatus", " The inhibition biosensor described in this paper differs from the one described by the above-mentioned authors insofar as our OPEE uses a bienzymatic system operating in series that has already been tested in previous investigations carried out in an aqueous environment [8,9], or in aqueous solution containing very small percentages of organic solvent [6,31]. Furthermore, in our case, measurements were carried out in a truly non-aqueous environment. Indeed, as shown in Table 1, water percentage both in hexane and chloroform, even when water saturated, are always lower than 0.1% (w/w), and using a gaseous diffusion amperometric sensor as indicator electrode. Some parts of the latter were made out of PTFE (see Fig. 1) so as to stand up to prolonged immersion in organic solvents. The resulting biosensor was completely original and capable of operating in organic solvents such as chloroform, and even more satisfactorily in mixtures such as chloroform\u00b1hexane. In practice, the bienzymatic biosensor proposed is similar in its geometry to other monoenzymatic OPEEs recently developed by us [26\u00b128]. Kappacarrageenan gel immobilisation is both simple to achieve and effective as regards enzyme entrapment, which can thus be achieved without undue loss of enzymatic activity (preliminary measurement indicates a speci\u00aec activity of the immobilised enzyme of the order of 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003242_s0094-114x(00)00003-3-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003242_s0094-114x(00)00003-3-Figure3-1.png", "caption": "Fig. 3. 3-PRPS spatial manipulator.", "texts": [ " From the expression of g it is clear that the rank de\u00aeciency of Hs will lead to linear dependency of the column vectors gi and in turn the matrix C will be rank de\u00aecient. Hence, if Hs is rank de\u00aecient, the system will not be STLC. To see the e ect of rank de\u00aeciency of Hk, we rewrite Eq. (1) as l H k X M X \u00c8X Z \u00ff X, \u00c7X \u00ffHs X t \u00ffI\u00ffH k Hk n 9 where H k is the pseudo-inverse of the matrix Hk given by HT k HkHT k \u00ff1 and n is any generalized vector such that I\u00ffH k Hk n lies in the null space of Hk: From this equation we can see that if Hk loses rank, then it's pseudo-inverse H k does not exist or in other words the Lagrange 4 The 3-DOF spatial manipulator (see Fig. 3) falls under this category. In this case three Cartesian coordinates and three orientation variables are required to describe the motion of the top platform. However, since the mechanism has three degrees of freedom, the six coordinates are related to each other by three complex non-linear equations (see also Section 4). P. Choudhury, A. Ghosal /Mechanism and Machine Theory 35 (2000) 1455\u00b11479 1461 multipliers l becomes in\u00aenite. Hence, if matrix Hk, of dimension 6 3, has rank less than 3, the constraint forces become in\u00aenite", " The singular curves along with the workspace boundary for this manipulator are shown in the left column of Fig. 2. The controllability matrix for this manipulator has dimension 6 6. The regions where the STLC condition is violated are shown on the right-hand side of Fig. 2 along with the workspace boundary. It can be seen that the nature of the singular and non-STLC regions are the same, i.e., STLC condition is not satis\u00aeied around a singularity curve. P. Choudhury, A. Ghosal /Mechanism and Machine Theory 35 (2000) 1455\u00b114791464 The 6-DOF 3-PRPS hybrid manipulator shown in Fig. 3 has two prismatic actuations in each leg [2]. The equations of motion are given by: M \u00c8t a Z HF 12 where M 2666664 MpE3 X3 i 1 Qi \u00ff Mp \u00c4R X3 i 1 Qi \u00c4qi ! Mp \u00c4R X3 i 1 \u00c4qiQi Ip Mp \u00ff R2E3 \u00ff RRT X3 i 1 \u00c4qiQi \u00c4qi 3777775 P. Choudhury, A. Ghosal /Mechanism and Machine Theory 35 (2000) 1455\u00b11479 1465 Z 2666664 Mp o o R \u00ff g X3 i 1 Ui o \u00ffIpo MpR o R o \u00ff g X3 i 1 qi Ui 3777775 H k1 k2 k3 s1 s2 s3 q1 k1 q2 k2 q3 k3 q1 s1 q2 s2 q3 s3 F fk1 fk2 fk3 fs1 fs2 fs3 T As described earlier, M is the mass matrix, Z contains all the centripetal and Coriolis terms, matrix H is the force transformation matrix, F denote the vector of input actuations" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000931_j.mechmachtheory.2019.103595-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000931_j.mechmachtheory.2019.103595-Figure7-1.png", "caption": "Fig. 7. Motion modes of a wheel-tracked robot with metamorphic parallel leg.", "texts": [ " 6 b, there are significant differences between the workspace shape of a metamorphic parallel mechanism and that of a general parallel mechanism without any metamorphic characteristics. The workspace of the metamorphic parallel mechanism can be regarded as the integration of that of two parallel mechanisms. Although the workspace shape is irregular, it can meet two different demands at different times, as long as the design of its motion trajectory is reasonable. If the metamorphic parallel mechanism is applied to the design of mechanical legs, the advantages would be brought fully into play. Fig. 7 shows a wheel-tracked robot using the abovementioned mechanism as its mechanical leg, which can realise walking on the flat ground, steering or maintaining stability using the rotational DOF around the Y -axis and translational DOF along the Z -axis of configuration I, as shown in Fig. 7 a. In addition, the robot can use the rotational DOF around the X -axis and translational DOF along the Z -axis of configuration \u2162 to assist itself to overcome obstacles, as shown in Fig. 7 b. It should be noted that the mechanical leg shown in Fig. 7 changes the end link into a wheel to improve the robot\u2019s trafficability. As mentioned above, the basic functions required of the mechanical leg are to be able to walk and steer on a flat ground, and to assist the robot to overcome obstacles. Therefore, the mobile platform needs to realize a wide range of rotation, and can still move after rotating to a certain configuration, for accomplishing some fine adjustment of the posture. In the following research, the stiffness model is formulated with the consideration of the deformation of the main components caused by the actuation and constraints, then the sub-workspaces are determined after the motion trajectories of the endpoint of the mechanism are given according to the requirements" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001207_052002-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001207_052002-Figure7-1.png", "caption": "Figure 7. Gap between shaft and bearing pads Figure 8. Deformation of bearing under load", "texts": [ " The plot to the right in Figure 6 which displays the hydrodynamic pressures from a side view shows that for this design just the segments of the rear cone are loaded. The pads of the front cone are all unloaded. This phenomenon is known from double-row spherical roller bearings where the bearing row on the gearbox side carries more load than the one on the rotor side. The reason for this pattern is the axial displacement of the shaft with the consequence that the gap between the front pads and the shaft increases so there is almost no hydrodynamic pressure build-up. Figure 7 shows the three-dimensional gap for the simulated bearing. The gap of the front cone is larger than 5 mm which is much too high for a hydrodynamic pressure build-up. The Science of Making Torque from Wind (TORQUE 2020) Journal of Physics: Conference Series 1618 (2020) 052002 IOP Publishing doi:10.1088/1742-6596/1618/5/052002 The axial displacement of the shaft is facilitated by the geometry of the bearing housing. Figure 8 reveals that the bearing housing deforms due to the axial load. A stiffer design of the housing would counteract this behavior" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000594_tia.2018.2799178-Figure15-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000594_tia.2018.2799178-Figure15-1.png", "caption": "Fig. 15. Prototype machines with 12S/10P combination. (a) All ETW S3p. (b) Alternate ETW S3p.", "texts": [ " For other two electrical machines, the heavier asymmetric saturation of adjacent teeth can be seen for of the Alternate ETW S3p machine. That is to say, the larger torque ripple will be generated. It can be seen that the conclusion drawn based on 12S/10P machine analysis can be employed to complementary 12S/14P combination. Therefore, the conclusion should be also valid for electrical machines with other slot/pole number combinations. For the FCS PM machines analyzed in this paper, two prototypes have been built. They are the All ETW S3p and Alternate ETW S3p machines, as shown in Fig. 15. The open-circuit back-EMF waveforms of two electrical machines are measured, as shown in Fig. 16. It can be seen that the measured back-EMFs are a bit lower than the 2D finite element (FE) predicted one due to the end-effect and practically the same as the 3D FE result. There are still some slight differences, since the 3D FE modelling of the end region is pretty hard and the measurement errors are unavoidable in reality. Besides, the Alternate ETW S3p machine has a larger open-circuit back-EMF than the All ETW S3p machine for both predicted and measured results since the winding factor for the Alternate ETW S3p machine is larger" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001374_j.optlastec.2020.106825-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001374_j.optlastec.2020.106825-Figure1-1.png", "caption": "Fig. 1. (a) 3-D Physical model and (b) 2-D representation of the physical model for SLM process.", "texts": [ " The laser energy absorption coefficient of the powder bed (\u03b5) can be expressed including area fraction of voids (\u03b1h) and solid (\u03b5s) as follows, \u03b5 = \u03b1h\u03b5h +(1 \u2212 \u03b1h)\u03b5s (6) The value of solid emissivity was taken as 0.19 for the powder material, Ti6Al4V [7]. The formulation for the determination of area fraction of voids,\u03b1h \u03b1h = 0.908\u03c62 1.908\u03c62 \u2212 2\u03c6 + 1 (7) and laser energy absorption coefficient of voids, \u03b5h were taken from the study of Mishra et al. [7] \u03b5h = \u03b5s [ 2 + 3.082 ( 1\u2212 \u03c6 \u03c6 )2 ] \u03b5s [ 1 + 3.082 ( 1\u2212 \u03c6 \u03c6 )2 ] + 1 (8) The physical representations of a real 3-D SLM process and corresponding 2-D model are depicted in Fig. 1 in Cartesian coordinate frame. A representative elementary volume is selected for the problem definition as shown in Fig. 1(a) and the 2-D region in Fig. 1 (b) is used for the analytical model. In the actual SLM process, the laser source moves over the powder layer following a specified path. There are successive laser scanning processes to form the intended shape by moving the laser source forward and backward. However, the model developed is designed for a single scan only. The scan time may change depending on the length scanned and the material characteristics. The melting region forms over the powder layer during the application of laser power and then it solidifies", " There are successive melting and solidification processes during the production of intended shape. Therefore, it is assumed that there are three sub-regions in the representative elementary volume; melting pool, powder layer and solid layer. It is assumed that the laser beam is stationary, and the effect of laser power is reflected inside the region as though there were a volumetric heat generation. An instantaneous view of the cross section on x-y plane K. O\u0308kten and A. Biyikog\u0306lu is depicted for the representative elementary volume in Fig. 1(b). In the analytical formulation of the problem, the solution domain is taken as half of the 2-D area around the symmetry axis at x = 0. The evaporation and shrinkage of the melting region due to instantaneous evaporation is neglected during the SLM process. The porous material is assumed to be isotropic and homogeneous. The laser power absorptivity is assumed not to vary with the angle of incidence of laser beam relative to the melt pool surface. Melting and solidification temperatures are used to determine the region of melt pool" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001069_j.isatra.2020.10.026-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001069_j.isatra.2020.10.026-Figure1-1.png", "caption": "Fig. 1. Quad-rotor reference frame.", "texts": [ " (24) The estimation error of e = (e1, e2, e3)T converges to zero in finite-time. Then, once the estimation error e tends to zero in finite-time, the resulting closed-loop system \u03a3cl2 is given by \u03a3cl2 : \u23a7\u23aa\u23aa\u23a8\u23aa\u23aa\u23a9 \u03b5\u03071 = s\u0302 \u2212 \u03b3 \u03b51, \u02d9\u0302s = \u22122L|s\u0302| 1 2 sign(s\u0302) + \u03bd, \u03bd\u0307 = \u2212 L2 2 sign(s\u0302), (25) here the two last equations denotes a Super Twisting Algorithm. y selecting a suitable gain L, then s\u0302 = \u02d9\u0302s = 0 in finite-time and a OSM is achieved. w o E a t \u03a3 w s i t u a b w a o r s o p w c t r T v \u03a3 3. Quadrotor model Let us consider a quadrotor aircraft as shown in Fig. 1, where the set (oE , xE , yE , zE) represents the Earth-fixed coordinate frame, which is chosen as the inertial reference; the set (oB, xB, yB, zB) denotes the Body-fixed coordinate frame, which is attached to the body. The variables \u03c6, \u03b8 and \u03c8 represent the Euler angles, hile the vector \u0393 is determined by the coordinates between the rigin of the Body-fixed coordinate frame and the origin of the arth-fixed coordinate frame. According to [18], the dynamical model of a quadrotor aircraft, nd its motion is described in a body-fixed coordinate frame with he origin at the center mass, is given as: : \u23a7\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 x\u0308 = 1 m [ (c\u03c8 s\u03c6 + c\u03c8c\u03c6s\u03b8 )U1 + \u03b4x ] y\u0308 = 1 m [ (\u2212c\u03c8 s\u03c6 + s\u03c8c\u03c6s\u03b8 )U1 + \u03b4y ] z\u0308 = 1 m [ (c\u03c6c\u03b8 )U1 \u2212 mg + \u03b4z ] \u03c6\u0308 = 1 Ixx [ U3 \u2212 (Izz \u2212 Iyy)\u03b8\u0307 \u03c8\u0307 + \u03b4\u03c6 ] \u03b8\u0308 = 1 Iyy [ U5 \u2212 (Ixx \u2212 Izz)\u03c6\u0307\u03c8\u0307 + \u03b4\u03b8 ] \u03c8\u0308 = 1 Izz [ U7 \u2212 (Iyy \u2212 Ixx)\u03c6\u0307\u03b8\u0307 + \u03b4\u03c8 ] (26) here m represents the vehicle mass, g is the gravity force, (\u00b7) = sin(\u00b7) and c(\u00b7) = cos(\u00b7)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001449_j.mechmachtheory.2021.104396-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001449_j.mechmachtheory.2021.104396-Figure5-1.png", "caption": "Fig. 5. Schematic illustration of barrel-shaped generating surface meshing with internal gear with shaft angle .", "texts": [ " In such a case, the shape of curve R c1 R 0 R c2 changes depending on the particular geometry of the reference concentric cylindrical surface of the gear. This section introduces the four-step method proposed in the present study for the design of power-skiving tools, namely: (i) Construction of internal gear based on kinematic relationship between internal gear and spur rack (see Fig. 4 ); (ii) Construction of generating surface of power-skiving tool based on internal gear profile surface (see Fig. 5 ); (iii) Determination of cutting-edge of tool based on generating surface and rake surface; and (iv) Construction of clearance surface. (i) Construction of internal gear For an involute tooth profile, the geometric characteristics of the internal gear profile can be completely defined by the meshing spur rack profile parameters, including the helix angle \u03b2g , the normal pressure angle \u03b1n , the gear tooth normal module m n , the addendum d am , the dedendum d dm , and the shift coefficient \u03beg (see Fig", " t n and t r are obtained from the coordinate transformations t n = t A g g n and t r = t A g g r , respectively. If \u03c9 gen = 0 , then \u2202 t r \u2202 \u03b8gen \u00b7 t n = 0 . (37) Solving Eq. (37) , u 2 can be obtained as the following function of u 1 and \u03b8gen : u 2 ( u 1 , \u03b8gen ) = \u2212( r g + x ( u 1 ) ) x \u2032 ( u 1 ) \u2212 ( r g \u03b8gr + y ( u 1 ) ) y \u2032 ( u 1 ) + ( r g \u2212 r t ) ( C( \u03b8gr \u2212 \u03b8gt ) x \u2032 ( u 1 ) + S( \u03b8gr \u2212 \u03b8gt ) y \u2032 ( u 1 ) ) ( C( \u03b8gr \u2212 \u03b8gt ) y \u2032 ( u 1 ) \u2212 S( \u03b8gr \u2212 \u03b8gt ) x \u2032 ( u 1 ) ) T an , (38) where \u03b8gr = \u03b8gr ( u 1 ) is shown in Eq. (34) and \u03b8gt = ( z t / z g ) \u03b8gen . Referring to Fig. 5 , the generating surface t r gen of the tool can be obtained by substituting Eqs. (38) and (34) into Eq. (29) , and transforming r r to frame (xyz) t via the relation t r gen ( u 1 , \u03b8gen ) = t A g g A r r r . (39) ii) Determination of cutting-edge During power-skiving (see Fig. 6 ), only the tool cutting-edge meshes with the gear tooth surface. Therefore, the tool cutting-edge can be considered as an arbitrary curve on the generation surface, t r gen . In the present study, the cutting-edge (i is assumed to be constructed by the intersection of a plane rake surface t R rk , which tilts with a specific direction, with t r gen ", " Thus, even if the tool is re-sharpened, the profile of the cutting-edge remains the same. In other words, the shape of the re-sharpened tool is basically the same as that of a brand-new tool (albeit, the length of the tool is shorter). Consequently, the cutting situation between the tool and the gear workpiece also remains unchanged after the tool is resharpened. Recalling the discussions in the previous section, the generating surface produced by the internal gear no longer has a constant cross-sectional profile along its axis (see Fig. 5 ). Rather, the profile changes like a negative-shifted gear tooth profile. Consequently, referring to Fig. 8 (a), if no rake-surface-offset is provided along the tool axis (i.e., z of f = 0 ), the generating surface and clearance surface will interfere. In other words, the clearance surface interferes with the internal gear profile. Accordingly, referring to Fig. 8 (b), an appropriate rake-surface-offset, z of f , must be assigned. The cutting-edge of a skiving tool is the intersection curve between the generating surface and the rake surface" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000767_s12206-019-0203-7-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000767_s12206-019-0203-7-Figure2-1.png", "caption": "Fig. 2. Determinations of (a) initial angle; (b) separate angle.", "texts": [ " According to the sine theorem, the rotational angle of the geometric center G1 noted by GJ can be calculated as follows: sinarcsin 0, 2 sin 3arcsin , 2 2 sin 32 arcsin ,2 2 G G G G a a a a a a J pJ J p pJ p J J pp J p \u00ec \u00e6 \u00f6 \u00e6 \u00f9\u00ce\u00ef \u00e7 \u00f7 \u00e7 \u00fa\u00e7 \u00f7 \u00e8 \u00fb\u00ef \u00e8 \u00f8 \u00ef \u00e6 \u00f6 \u00e6 \u00f9\u00ef= - \u00ce\u00e7 \u00f7\u00ed \u00e7 \u00fa\u00e7 \u00f7 \u00e8 \u00fb\u00e8 \u00f8\u00ef \u00ef \u00e6 \u00f6 \u00e6 \u00f9\u00ef + \u00ce\u00e7 \u00f7 \u00e7 \u00fa\u00e7 \u00f7\u00ef \u00e8 \u00fb\u00e8 \u00f8\u00ee . (2) Given a gear pair with eccentricity, the pitch circle and reference circle are not coincident, and the action line direction is back and forth. Therefore, the tooth contact states with eccentricity of the gear system is determined by the proposed initial angle and separate angle. As shown in Fig. 2, a pair of mesh teeth starts from contact point 11A and separates from contact point 11A\u00a2 . The action line 1 2B B is tangent to the base circles of the pinion and gear at points 1B and 2B . 11C and 21 ,C respectively denote the middle points of the tooth tip of the pinion and gear at the starting contact state, whereas 11C\u00a2 and 21C\u00a2 represent the similar points at the separating contact state. 11F and 11F \u00a2 are the intersection points between the tooth involute curve and the basis circle of the pinion at the starting and separating contact states, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001001_j.jestch.2020.03.011-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001001_j.jestch.2020.03.011-Figure1-1.png", "caption": "Fig. 1. 2D sectional view of squirrel cage induc", "texts": [ " Because of these properties, IMs are easy to manufacture, durable, cost-effective, and require little maintenance [14]. The lack of a brush mechanism in IMs eliminates both the electrical losses in the brush and the mechanical losses between the commutator and the brush. Due to all these advantages, IMs are often preferred in electric vehicles [15], household appliances [16], and many industrial applications [17,18]. Squirrel cage IMs are divided into two groups as singlecage and double-cage according to rotor structure. Single-cage and double-cage structures are given in Fig. 1. Motor manufacturers generally offer standard values such as efficiency, rated voltage, rated current, rated torque, and rated power of the machine as label values. IM equivalent circuit must Please cite this article as: O. \u00c7etin, A. Dalcal\u0131 and F. Temurtas , A comparative stu networks with unmemorized training, Engineering Science and Technology, an be known for speed-position control and performance at different loads. The parameters such as power factor, current, input power, and efficiency of the motor can be calculated for different load values by using the equivalent circuit parameters" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003131_robot.1999.770008-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003131_robot.1999.770008-Figure6-1.png", "caption": "Figure 6. (a) A global slope whose gradient is different from that of the actual slope; and (b) a global slope whose gradient is the same as that of the actual slope.", "texts": [ " However, instead of using the force feedback approach, we set the ankle torque of the swing leg to zero when the swing foot touches the upslope surface. This allows the swing foot to orient itself and adapt to the slope passively (see [ 13 for details). When both the heel and the toe of the swing foot are on the slope, they trigger the transition from the single support phase to the double support phase. The biped then computes the gradient of the global slope based on the joint angles. Note that the global slope gradient is not the same as the real slope gradient since both feet are not on the same slope yet (see Figure 6(a)). The global slope is an imaginary intermediate slope whose gradient is between the level ground gradient (equal to zero) and the actual upslope gradient. However, the biped considers the global slope to be the actual terrain slope during the double support phase. It computes the desired walking height based on the global slope. When the biped switches to the single support phase, it continues to compute the desired walking height based on the global slope. The swing leg trajectory of the single support phase is also planned using the global slope. However, when the biped is in the double support phase again, both its legs are on the actual slope and the global slope will have the same gradient as the actual slope (see Figure 6(b)). Note that the during transition walking, the actual step length of the biped may vary significantly from the desired step length. For the level-to-upslope transition, the variation in the step length is due to the premature landing of the swing foot. The biped will reach a steady walking gait as it continues to walk on the same slope. The usage of the global slope instead of the local slope to compute the desired height of the biped is analogous to the usage of a low-pass filter to get rid of high frequency noise" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003299_ias.1995.530283-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003299_ias.1995.530283-Figure1-1.png", "caption": "Fig. 1 . Model of salient pole PM motor", "texts": [ " At first stage of the proposed method, 3-phase balanced ac sine wave voltage of high frequency is applied to the PM motor at rest by a PWM inverter. Since the motor at rest is in the condition of step out, no synchronous driving torque is developed and then the rotor does not turn. For applying the voltage, the armature current data are measured and recorded. The locus of the armature current-vector becomes an civall because of the saliency of the PM motor. The orientation of the current-vector ellipse gives an information on the rotor position. A. Modeling o,f PMMotor Fig. 1 shows: an analytical model of a salient pole PM motor without damper windings Since the rcitor has permanent magnets of which permeability nearly equals to that of air, the motor has salient pole characteristic. As shown in the figure, two kinds of coordinate system are defined as folllows. One is the a-P coordinates of which a-axis is defined in the direction of the U-phase armature winding. The other is the d-q coordinates of which d-axis is defined in the direction of the rotor magnet IV-pole" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000108_tec.2018.2820083-Figure20-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000108_tec.2018.2820083-Figure20-1.png", "caption": "Fig. 20. Deformation when applying 2500Hz radial force only", "texts": [ " 16, 17 and 18 show the deformation response of the stator caused by radial force and bending moment together, radial force only, and bending moment only, respectively, where the frequencies of radial force and bending moment are 1200Hz. Fig. 19, 20 and 21 show the corresponding results when the frequencies of radial force and bending moment are 2500Hz. In these figures, the situation is 1=9 , and only the two instants are shown when the deformation are maximum. From Fig. 17 and Fig. 18, it can be seen that the maximum deformation of the bending mode is nearly 10 times higher than that of the pulsating mode. While in Fig. 20 and Fig. 21, the maximum deformation of the pulsating mode is nearly 10 times higher than that of the bending mode. The reason of this phenomenon is that when 1200Hz is close to the modal frequency 1496 Hz of bending modal obtained from modal test in section V, the bending modal dominates the vibration deformation. When 2500Hz is close to the modal frequency 2498 Hz of pulsating modal obtained from modal test in section V, the pulsating modal dominates the deformation. It is important to complete the modal analysis or modal test of the structure of the motor" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003951_tia.2005.863907-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003951_tia.2005.863907-Figure6-1.png", "caption": "Fig. 6. Locus of the stator flux vector during a positive torque command with (a) classic DTC and (b) DTC EMC.", "texts": [ " In this case, instead of a simple commutation of the common-mode voltage, at least three commutations occur with the consequent common-mode current spikes, as it will be shown both in the simulation and experimental results. However, the benefits of a significant reduction of the common-mode emissions of the drive are paid back with a poorer exploitation of the dc link capability of the inverter (no zero voltages are employed), with higher ripples both in the flux and torque waveforms and finally with higher harmonic contents of the stator voltages and current. The obtained increase of the stator flux and torque ripples can be easily deduced also from Fig. 6 which shows the locus of the stator flux vector during a positive torque command with the classic DTC and the DTC EMC. It highlights that the flux locus with the DTC EMC is sharper than that obtained with the classic DTC, given the sampling time of the control system and the amplitude of the hysteresis bands of the flux controller. It should be also remarked that the use of this new DTC strategy is quite straightforward to apply, since the proper voltage space vector is created at every sampling time" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001395_s12206-020-1240-y-Figure10-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001395_s12206-020-1240-y-Figure10-1.png", "caption": "Fig. 10. Circumferential temperature distribution of coil and stator: (a) crown part (x = -53 mm); (b) cross-section (x = 0 mm); (c) welded part (x = 53 mm).", "texts": [ " The stator is cooled by oil flowing in the stator flow paths, and the coil is cooled by oil sprayed on the coil at both ends; there is no oil flow in the coil inside the stator, indicating that heat transfer by conduction is dominant. Conductive heat transfer includes conduction in the circumferential and longitudinal directions. The conduction in the circumferential direction is affected by the insulation paper, and that in the longitudinal direction is affected by the insulator of the welded part. Fig. 10 depicts the temperature distribution in the circumferential direction of the stator and coil. While cooling of the upper motor is efficient, the temperature increases toward the lower part. In the case of the lower part, the temperatures at the 4:30 and 7:30 positions are higher than that at the 6:00 position due to the oil flowing to the outlet between the housing and the stator. The middle section of the coil has no oil flow, and heat transfer is dominated by conduction. However, conduction in the circumferential direction is inefficient because of the insulation paper" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003608_9783527618811-Figure7.3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003608_9783527618811-Figure7.3-1.png", "caption": "Fig. 7.3 Reference frames used to analyze gravity gradient stabilization of a satellite.", "texts": [ " The method is called the gravity gradient stabilization because it exploits the radial variation of the Earth\u2019s gravity. This application involves the yaw-pitch-roll angles and a linear stability analysis. For an alternative treatment which emphasizes the technology of the problem see [79]. 198 7 Applications 7.2.1 We assume the satellite orbit to be circular of radius a. There is a local reference frame f\u0304 such that f\u03043 points vertically downward to the center of the Earth, f\u03041 is tangent to the orbit and f\u03042 is normal to the orbit plane (see Fig. 7.3). Following Section 1.1.6, rotations of the satellite can be specified by composing rotations about f\u03043 by angle \u03c8, about f\u20322 by angle \u03b8 and about f\u2032\u20321 by angle \u03c6. The angles \u03c8, \u03b8, \u03c6 are the yaw, pitch, and roll angles, respectively. Thus the rotation matrix f = f\u0304Re3(\u03c8)Re2(\u03b8)Re1(\u03c6) = f\u0304R (7.1) and we find R(\u03c8, \u03b8, \u03c6) = (7.2) cos \u03c8 cos \u03b8 \u2212 cos \u03c6 sin \u03c8 + sin \u03c6 sin \u03b8 cos \u03c8 sin \u03c6 sin \u03c8 + cos \u03c6 sin \u03b8 cos \u03c8 sin \u03c8 cos \u03b8 cos \u03c6 cos \u03c8 + sin \u03c6 sin \u03b8 sin \u03c8 \u2212 sin \u03c6 cos \u03c8 + cos \u03c6 sin \u03b8 sin \u03c8 \u2212 sin \u03b8 cos \u03b8 sin \u03c6 cos \u03b8 cos \u03c6 The angular velocity relative \u03c9 f to f is obtained in terms of yaw-pitch-roll from the derivative of (7" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003925_tmag.2005.846262-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003925_tmag.2005.846262-Figure4-1.png", "caption": "Fig. 4. Space variation of force and flux distribution at S = 0.", "texts": [ " The leakage inductance of the stator end windings becomes large by considering magnetic saturation. Then, if we use larger leakage inductance of the stator end windings, its voltage drop becomes large, resulting in a smaller torque. Moreover, if we consider core loss under the stronger degree of saturation, we obtain a large core-loss current that means a large voltage drop of the stator leakage impedance, resulting in a smaller torque. The space variation of the radial electromagnetic force is presented in Fig. 4. It is shown that the radial force is big at the position where sthe flux density is big as shown in Fig. 4, and is approximately flat in the teeth and becomes a small value at the positions where the rotor slot exists. Fig. 5 shows the time variation of the force at the different teeth. It is shown that the force at tooth 1 is the same as that at tooth 4 and is bigger than those at teeth 2 and 3, because the stator winding is distributed in three slots as shown in Fig. 1(a). Figs. 6 and 7 show the radial force and its spectrum at a tooth for different slips. It is shown that the force at the teeth is bigger than that at the slots and have a fundamental frequency of two times the line frequency 50 Hz" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000476_j.msea.2019.05.097-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000476_j.msea.2019.05.097-Figure1-1.png", "caption": "Figure 1. Schematic of the butterfly sample used for pure shear and combined loading stress states (dimensions in mm). Geometry from [39].", "texts": [ " Six different sample geometries were machined, from the additively manufactured walls, and used to evaluate the fracture behavior in seven different stress states and in two primary orientations: one in which the properties parallel to the vertical build direction (BD) were probed and one in which the properties perpendicular to the vertical build direction (\u27c2BD) were probed. The equibiaxial tension punch samples, as detailed in reference [38], were machined from the plane orthogonal to the other samples. Butterfly specimens with geometry optimized by Dunand and Mohr [39], as shown in Figure 1, were used to evaluate pure shear and combined tension/shear loading under plane stress. Wire EDM was used to machine the outer profile of the butterfly samples and CNC milling was used to machine the reduced thickness gauge region of these samples. Central hole tension (CH) and notched tension (NT) samples, also designed to maintain a plane stress state at fracture with the geometries as shown in Figure 2, were machined using wire EDM. The central hole tension sample is designed such that it maintains a uniaxial tension stress state up to fracture at the perimeter of the circle in the center of the gauge region" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003864_s00419-006-0027-7-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003864_s00419-006-0027-7-Figure9-1.png", "caption": "Fig. 9 Musculoskeletal model of the lower limb: a eight muscles and b generalized coordinates", "texts": [ " The kinematical data used is the one obtained for the normal experiment as explained in Sect. 3. The model of the lower limb skeletal system adopted, is composed by three rigid bodies, the thigh, the shank and the foot. The movement is performed in the sagittal plane and is described by five generalized coordinates, the angle \u03b1, describing the rotation of the thigh, the angle \u03b2, describing the knee flexion, the angle \u03b3 for the ankle plantar flexion, the horizontal position of the hip joint, xhip, and the vertical position of the hip joint, zhip, as schematically shown in Fig. 9b. The pelvis and trunk are assumed to remain in the vertical position during the movement, what is reasonable for normal walking. The masses, center of mass locations, and the mass moment of inertia in the sagittal plane are obtained using the regression equations presented in Winter [53], as functions of the subject\u2019s body mass, height, thigh length and shank length. The eight muscle units considered in this analysis are shown in Fig. 9a. The muscles were modelled by Hill-type muscle models composed by a contractile element CE and a series elastic element SE, while the force of the parallel elastic element PE is neglected, Fig. 7. In this model all the structures in parallel to the CE and the SE are represented by a total passive moment around the joints, which includes additionally the passive moments generated by all other passive structures around the joints, like ligaments, too. The formula for the passive moments around the hip, knee and ankle are functions of \u03b1, \u03b2 and \u03b3 as proposed by Riener and Edrich [38]" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001311_j.mechmachtheory.2020.103978-Figure13-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001311_j.mechmachtheory.2020.103978-Figure13-1.png", "caption": "Fig. 13. An anthropomorphic 11-DOF manipulator.", "texts": [ " A circular path centred at [ 0 700 500 ]T mm with a radius of R = 450 mm and oriented of \u03c0 2 relative to X -axis is also tracked. Fig. 9 shows a rectangular path followed by an anthropomorphic manipulator of 9-DOFs with lazy configuration vectors, while Fig. 10 represents the same path followed with complex configuration vectors. A circular path is also tracked by the same robot. A tracking with lazy configuration vectors is shown in Fig. 11 while Fig. 12 illustrates a tracking with complex configuration vectors. An anthropomorphic 11-DOF manipulator is shown in Fig. 13 . The dimension of the workspace and the configuration space are R 6 and R 11 , respectively. In this example, five joints have to be fixed to reduce the redundant manipulator to nonredundant ones. Thus, by following the same procedure as previously, in addition to the joint \u03b82 , the following elbow joints \u03b85 , \u03b86 , \u03b87 , and \u03b88 are also maintained fixed. The rest of the joints are calculated via Paul\u2019s method. By moving the center of the final frame from 0 11 to 0 9 and multiplying each term of U w [ 0 0 0 1 ] T = 0 P 9 by 1 H 0 , we obtain a system of equations defined in (A" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001228_tvt.2020.3041336-Figure26-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001228_tvt.2020.3041336-Figure26-1.png", "caption": "Fig. 26. Prototype of FSCW-IPM motor with an uneven airgap rotor and vibration test platform. (a) 3-D model. (b) Prototype structure. (c) Test platform. (d) Sensor position.", "texts": [ " To observe the main vibration mode of Authorized licensed use limited to: Cape Peninsula University of Technology. Downloaded on December 18,2020 at 15:42:30 UTC from IEEE Xplore. Restrictions apply. 0018-9545 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. FSCW-IPM motor through experiment, three IEPE acceleration sensors are used to test vibration acceleration and displacement. The sensors are mounted at the motor shell, as is shown in Fig. 26(d). The mounting positions of sensor1 and sensor2 are 90 degrees apart in space, while the mounting position of sensor3 varies as needed. Acceleration waveforms tested by sensor1 and sensor2 are shown in Fig. 31. Amplitudes of acceleration waveforms are closed, and phases of waveforms are in opposite. These indicate acceleration phase angle is twice of mechanical angle. According to vibration theory and FEA results, the main vibration mode order of the FSCW-IPM motor becomes 2 [26]. To observe vibration mode more clearly, vibration displacements of the motor shell are further measured by quadratic integration of acceleration waveforms [13], [26]. To present half of the 2nd vibration mode, sensor1 and sensor2 are fixed as shown in Fig. 26(d). The positions of sensor2 and sensor1 are considered as 0 deg and 90 deg, respectively. Sensor3 is shifted by 180 degrees from the position of sensor1, and all the measured displacement signals are recorded. Taking the vibration signals measured by sensor1 and sensor2 as the references and comparing phase shifts of all the measured signals, approximated spatial vibration displacement waveform at a certain time can be obtained. Fig. 32 shows the approximated displacement waveform, which clearly shows one periodic sinusoidal wave is within 180 degrees mechanical angle" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001203_j.jallcom.2020.156886-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001203_j.jallcom.2020.156886-Figure8-1.png", "caption": "Fig. 8. Schematics of slip length along three different loading directions, (a) VD, (b) 45 direction, (c) HD.", "texts": [ " Regarding to the columnar grains, previous results showed that the prior grain boundaries, as well as possible grain boundary a phase could effectively prevent dislocation from transferring across [26]. In order to easily understand the effect of the columnar grains on the anisotropic tensile behaviors, the influence of several factors inside the columnar grains was ignored, and supposed that inside the columnar grain was uniform medium, so that a simplified effective slip path schematic for the three orientation samples, including the VD, HD and 45 direction, is presented in Fig. 8. During the tensile loading process, the shear stress generally played a more important role in determining alloy deformation and small cracks initiation with respect to the normal stress. Thus, the effective slip path (the direction with greater shear stress) for sample loaded along the VD was approximately equal to that in the HD, as shown in Fig. 8a, c. By comparison, the effective slip path for the sample loaded along 45 direction was obvious longer than that along the VD and the HD (Fig. 8b). Based on Hall-Petch relation, it could be reasoned out a minimum tensile strength of the sample loaded along the 45 direction than the sample in the VD or HD. Obviously, the inferred conclusion was inconsistent with the experimental test results, indicating that the columnar b grains could not induce the anisotropic loading force. Apart from the columnar morphology, crystallographic texture was another factor to be considered. The XRD result revealed that a typical a texture in the alloy was formed from the b<100>//VD fiber texture" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001267_j.jclepro.2020.120491-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001267_j.jclepro.2020.120491-Figure7-1.png", "caption": "Fig. 7. Exoskeleton high compliance ankle joint coordinate system distribution.", "texts": [ " 6, the structure body is connected by three dynamic and static platforms through three identical branches. Each branch contains two rotating pairs (R) and one spherical pair (S). The static platform end is connected with the rotating pair, and the dynamic platform end connects with the spherical side. The mechanical diagram could be obtained by simplifying each structure, and the dynamic and static platforms are equivalent to two congruent equilateral triangles, and the branch is equivalent to a chain structure composed of a rod member, a spherical pair and a rotating pair. As shown in Fig. 7, in order to analyze the spatial position changes of the mechanical components, corresponding dynamic and static coordinate systems are established on the dynamic and static platforms. Invert the ankle joint simplifies the mechanism so that the moving platform at the upper-end position and the static platform at the lower-end position. Taking the equivalent triangle structure center of the static platform as the origin o, the x-axis passes through a triangle point C1 and the positive direction point to the triangle outside, the z-axis is perpendicular to the triangle structure and the positive direction is vertical upward, and the y-axis follows the three-dimensional coordinates", " could be expressed as \u00bdr\u2019 cosqi; r\u2019 sinqi; 0 T , among them r\u2019 is equivalent regular triangle circum circle radius in dynamic platform, through the Euler transform matrix T, its pose could be consistent with the corresponding vector pose in the static coordinate system, that is, in the static coordinate system: o\u2019Ai ! \u00bcT,\u00bdr\u2019 cosqi; r\u2019 sinqi; 0 T (11) Put it into the vector equation and sort it out, you could get it in the static coordinate system.o xyz The lower vector equation is: \u00bdX; Y ; Z T \u00feT , \u00bdr\u2019 cosqi; r\u2019 sinqi; 0 T , vi !\u00bc0 (12) After finishing the above formula, you could get X, Y versus a, b, g numerical relationship as follows: 8>>< >>: a \u00bc g X \u00bc 1 2 r\u2019 cos b 1 2 r\u2019\u00f0cos a\u00de2 \u00fe 1 2 r\u2019\u00f0sin a\u00de2 cos b Y \u00bc r\u2019 sin a sin b (13) As shown in Fig. 7, the connection A1C1 could divide the active rod B1C1 and static platform :OC1B1 into angle f11 and angle f12 two parts, that is, for the entire mechanism, :OCiBi could be divided into angle fi1 and angle fi2. In DAiBiCi, the cosine theorem could be used inDAiBiCi to obtain the angle fi1, its specific values as follows: fi1 \u00bc arccos CiB 2 i \u00fe CiA 2 i BiA 2 i 2,CiBi,CiAi (14) where CiBi, BiAi is known as connecting rod lengths, CiAi is the distance between the Ai Point and Ci under the stationary coordinate system O-XYZ: CiAi \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi XAi XCi 2 \u00fe YAi YCi 2 \u00fe ZAi ZCi 2q (15) At the same time, under the static coordinate system O-XYZ, OAi " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000610_pedstc.2018.8343802-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000610_pedstc.2018.8343802-Figure1-1.png", "caption": "Fig. 1. (a) Cross section view of the proposed 12/14/12 MVRM and (b) arrangement of eight coils in one phase.", "texts": [ " Then, in section III, the static and dynamic performances of the novel machine and two other topologies are obtained and compared through a finite-element analysis to better clarify the superior operation of the proposed machine. The normal dynamic performance of the novel machine with single pulse control (SPC) is given in section IV. Also, section IV investigates the faulty performance of the proposed MVRM, followed by the conclusions in section V. II. MACHINE STRUCTURE The cross section view of the proposed structure is presented in Fig. 1(a). This MVRM consists of two stators: an inner 12-pole stator in the form of a common rotor, an outer stator with six diametrically-placed C-shaped modules, and a segmented 14-pole rotor, indicating that this machine has higher number of rotor poles than the stator poles. There are three phases, each one consists of eight windings wound on the teeth of the inner and outer stators and connected in series which is shown in Fig. 1(b). In addition, six permanent magnets are placed in the pole-to-pole area, connecting the outer modules teeth to form six closed C-core modules. The operating principle of the proposed topology is elucidated in Fig. 2. When only the coil is excited (Fig. 2(a)), the flux path is closed through the air-gaps. When, there is no excitation in the coil, the flux path of the PM is closed through the back-iron of the module (Fig. 2(b)). However, when the coil is excited, the flux path of the PM is added to that of the module generated by the coil, and hence the attraction force is enhanced which yields a noticeable enhancement in the output torque of the motor" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000035_1350650116684275-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000035_1350650116684275-Figure1-1.png", "caption": "Figure 1. Boundary condition type of different tooth surfaces.", "texts": [ " For the bulk temperature field in the gear meshing process, the heat source only comes from the friction heat between the tooth surfaces. Thus, the term qv is equal to zero. Furthermore, the bulk temperature field is in steady state, which means the temperature is constant over time. Therefore, equation (1) can be simplified as l @2 @2x \u00fe @2 @2y \u00fe @2 @2z \u00bc 0 \u00f02\u00de To solve the above differential equation, it is necessary to determine the boundary conditions. For the transmission gear, various surfaces belong to different types of boundary conditions, as shown in Figure 1. Nonmesh surface, addendum surface and the dedendum surface, belong to the third kind of boundary conditions (T), which require known temperature of lubricant and the convective heat transfer coefficient. As the mesh surface is subjected to a mixed boundary of second and third kinds (S&T), the temperature of lubricant and the convective heat transfer coefficient should be given. In addition, the frictional heat flux should also be identified. Between the two contact surfaces, there is no heat conduction due to symmetry" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001452_tro.2021.3076563-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001452_tro.2021.3076563-Figure4-1.png", "caption": "Fig. 4. Stiffness testing rig, with the corresponding section of the torque curve \u03c4 being measured. Samples were secured to a fixture with the base segment set at an angle \u03b81. F is the tensile force provided by a load cell, \u03d5 is the displacement between the segments, and L is the distance between the vertex and the point where the force is applied.", "texts": [ " We then calculated the change in gravitational energy Vg between the stable and threshold states and modeled the transformation energy as the sum of these two components. 1) Stiffness Measurements: To characterize the nonlinear stiffness of individual vertices, we measured the stiffness torque \u03c4 as a function of displacement\u03d5. We tested two sets of samples: one group had a smaller backlash\u03d5b = 5.75\u25e6, and the other had a larger backlash\u03d5b = 11.25\u25e6. The lower segment of each sample was folded to an angle \u03b81 and fixed at its base (see Fig. 4). For the smaller backlash, \u03b81 was fixed at 5\u25e6, 7.5\u25e6, 10\u25e6, and 12.5\u25e6; for the larger backlash, \u03b81 was fixed at 10\u25e6, 12.5\u25e6, 15\u25e6, and 17.5\u25e6. We applied a point force F to the tip of the upper spinal crease at a distance L from the vertex with a Mecmesin MultiTest 2.5i and calculated \u03c4 = F \u00b7 L. We measured the displacement of the probe to calculate the deflection of\u03d5 between the spinal creases. The probe displaced linearly 50 mm, resulting in a total angular displacement of 40\u25e6. The displacement was measured in four sections, alternating the direction of the applied force to avoid snap-through behavior" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001443_s00521-021-05922-x-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001443_s00521-021-05922-x-Figure1-1.png", "caption": "Fig. 1 Earth-fixed frame and Body-fixed frame", "texts": [ " Numerical simulations and comparative experiments are provided in Sect. 6. Finally, Sect. 7 summarizes the full text and introduces the future research content. The motion state of USV in actual navigation is very complex, which mainly includes six degrees of freedom: surge velocity u, sway velocity v, yaw rate r, heave velocity w, rolling rate p and pitching rate q [25, 26]. Earthfixed frame and Body-fixed frame are usually used to describe the relationship between them, which can be referred to in Fig. 1. (x, y) is used to describe the position coordinates of USV, w stands for the course of USV. The kinematics and dynamics equations of unmanned aerial vehicles are described as (1) and (2). _x \u00bc u cos\u00f0w\u00de vsin\u00f0w\u00de _y \u00bc usin\u00f0w\u00de \u00fe vcos\u00f0w\u00de _w \u00bc r 8 >< >: \u00f01\u00de m11 _u m11fu \u00feru \u00bc su \u00fe bu m22 _v m22fv \u00ferv \u00bc bv m33 _r m33f \u00ferr \u00bc sr \u00fe br 8 >< >: \u00f02\u00de where fu \u00bc m22 m11 vr d11 m11 u, fv \u00bc m11 m22 ur d22 m22 v and fr \u00bc m11 m22 m33 uv d33 m33 r, ru \u00bc Dufu, rv \u00bc Dvfv and rr \u00bc Drfr represent the uncertain dynamics of each item, respectively, Du, Dv and Dr stand for uncertain parameters, su and sr are used to describe the force and moment that cause the USV to forward and turn, respectively, bu, bv and br represent the unmeasurable time-varying external disturbances in all directions" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003037_mssp.1996.0082-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003037_mssp.1996.0082-Figure2-1.png", "caption": "Figure 2. A gear train, with excitation and load link.", "texts": [ " Thus the above system, although simple, captures the essential elements of a real gear transmission mechanism. Each component of the system is modeled as a linear second-order lumped-parameter system. The only source of non-linearity comes from the modeling of contact interaction between the gear teeth. This contact interaction couples the driver and the driven side of the gear train. The result is a set of coupled non-linear second-order differential equations which cannot be solved in closed form, but which can be numerically simulated. A schematic of such a system is given in Fig. 2. The nomenclature for the dynamic model is given in Table 1. Using this nomenclature, the motor/gear/link system can be treated as a pair of multibody systems, which are coupled by the non-linear tooth interaction force as described in Section 4. The equations of motion of the motor/input-coupling/pinion system are M1&u Mu Iu 1'= &bMu M + tM(t) bIu I + kIuI \u2212Rb1[F+G]' where M1 is the inertia matrix, computed in the usual manner. Similarly, the load/output-coupling/link system is described as M2&u 2u O u L'= & +Rb2[F+G] bOu O + kOuO MLCL sin (uL)g ' where, again, M2 is an inertia matrix" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003210_tsmcc.2002.807284-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003210_tsmcc.2002.807284-Figure4-1.png", "caption": "Fig. 4. Boundary layer and intermediate region.", "texts": [ " In this study, the control structure using an auto-tuning neuron with the SMC can be schematically shown in Fig. 3, where u1 is the sliding control defined in (6); u2 is the neural control defined in (10); and u = d(u1; u2) is a function of u1 and u2 defined by u = d(u1; u2) = u1; if js(e)j > + (e)u1 + (1 (e))u2; if < js(e)j + u2; if js(e)j : (11) In (11), s(e) is a scalar function described in (5); > 0 is the boundary layer thickness; is a small positive value to form an intermediate region as illustrated in Fig. 4; and (e) = js(e)j (12) is a function of error e used as a weighting factor of u1 and u2. From (11) and (12), we know that (e) 2 (0; 1]. The overall control procedure can be summarized as follows. First, if the initial state of system is outside the boundary layer, then it is subject to the sliding control u1 forcing the state trajectory toward the boundary layer. Second, if it goes near the boundary layer, i.e., entering in the intermediate region, let the control input u be a convex combination of u1 and u2 such that the control switching between u1 and u2 can be smooth and continuous" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003710_0957-4158(92)90043-n-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003710_0957-4158(92)90043-n-Figure2-1.png", "caption": "Fig. 2. Walking path.", "texts": [ " S imi lar ly , the re a re a va r ie ty of me c ha n i sms 543 that can be built for the wall-climbing robots. A biped walking robot with a sucker on each foot is a typical example, and has a simple mechanism. As it has a danger of slipping and falling from the wall surface at any time, its control system is very important for safety on the wall. The simple mechanism shown in Fig. 1 was adopted. It has a hinge and a pivot at the ankle and a hinge at the crotch, so it has five degrees of freedom. The walking motion is shown in Fig. 2. The rotation at the ankle of a fixed cup and inclinations of ankle and crotch are combined and a moving path of free leg is controlled to minimize the moment acti.ng on the fixed cup. The sucking force can be produced without any power when the air seal is kept tight at the periphery of the suction cup. However, this is not always attained on a rough wall surface. Therefore an active method of keeping the cup in negative pressure is required in order to use it as a robot component. Suckers can be divided into two categories, i" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001732_j.autcon.2021.103609-Figure15-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001732_j.autcon.2021.103609-Figure15-1.png", "caption": "Fig. 15. Examples of different configurations for PPEF with reference to the cross joint.", "texts": [ " The PID controller maintained the gripping force well against Vset throughout the task amid disturbances. Apart from this control algorithm, we also demonstrated the force feedback with the same gripper hardware using the Q-learning algorithm [26]. By controlling the rotation of eight servo motors, the PPEF can change into different configuration to assume the painting or polishing state. Six combinations are possible with reference to the cross joint: main upper, main lower, left branch upper, left branch lower, right branch upper, and right branch lower. Representative examples are shown in Fig. 15 for graphical clarity. The wrist and knuckle servos collectively determine which portion of the cross joint the PPEF shall K.H. Koh et al. Automation in Construction 125 (2021) 103609 work on. In the GUI, the operator can select the configuration corresponding to the pipe section requiring the service task. The robot will immediately let the PPEF module assume the selected configuration. The state of the PPEF configuration is displayed in the GUI and can be seen from the RVIZ panel. By selecting the correct configuration, the high-level control program prepares the pre-defined path pattern to be generated, resulting in a polish or paint trajectory for the PPEF" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001070_j.mechmachtheory.2020.104127-Figure15-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001070_j.mechmachtheory.2020.104127-Figure15-1.png", "caption": "Fig. 15. BVS general arrangement.", "texts": [ " Two cameras are parallel arranged to obtain the image of external objects. Basic parameters of the BVS fulfill the requirements, i.e., on the range and the precision of K&C test. The optical targets traced are in the binocular vision coordinate system (BVCS) and need to be transferred to the vehicle coordinate system (VCS). The BVCS is referred to O c \u2212 XY Z and the VCS is referred to O \u2212 xyz. Four optical targets ( A, B, C, D ) are placed on the wheel jig. Point E is the center of the wheel jig and point W is the center of wheel shown in Fig. 15 . The wheel rotation axis vector r c EW in the BVCS is expressed by r c EW = r c AC r c BD \u2223\u2223r c EW \u2223\u2223/ \u2223\u2223r c AC r c BD \u2223\u2223 (26) The wheel rotation axis vector r EW in the VCS is obtained by using the rotation transformation. r EW = M r c EW (27) where M is the direction cosines from the BVCS to the VCS and is expressed as M = [ cos \u03b1x cos \u03b2x cos \u03b3x cos \u03b1y cos \u03b2y cos \u03b3y cos \u03b1z cos \u03b2z cos \u03b3z ] (28) where \u03b1 , \u03b2 and \u03b3 are the angles between X -axis in O c \u2212 XY Z to x -axis, y -axis, z -axis in O \u2212 xyz" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001780_tro.2021.3082020-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001780_tro.2021.3082020-Figure9-1.png", "caption": "Fig. 9. Results of closed loop position control using ionic liquid stretch sensors as proprioceptive feedback, with circular trajectory input (dashed black line) for two-segment, dual bend direction continuum manipulator. Plot shows relative density of distal vertebra x-y position data for 40 consecutive revolutions.", "texts": [ " 8 shows the experimental setup for the initial trials and normal-view scatter plots of the resulting end vertebra center position error following 50 cycles through the three target points. A more complex target trajectory in task space involving simultaneous tracking with all sensors (in this case, a 100-mm diameter circle with \u03b8Dx = \u2212\u03b8Px and \u03b8Dy = \u2212\u03b8Py maintained throughout, at a rate of 5.24mm/s) was converted into four sensor trajectories using constant curvature kinematics as described in [1] and [8]. Fig. 9 presents the density of x\u2013y position data after 40 revolutions. Errors in z (not shown), which were observed to be small, form a conical spread consistent with the position of the continuum robot fulcrum. The maximum error observed during closed-loop control trials was 4.9% TCL. Deviation maxima occur at the intersection of the x and y bending axes leading to an imperfect circular trajectory. This can be largely attributed to overestimation of the required input at axis intersections resulting from the oversimplified constant curvature model" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003218_robot.1991.131559-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003218_robot.1991.131559-Figure1-1.png", "caption": "Figure 1: A spatial displacement of a rigid body.", "texts": [ " Haug, 1989, and Nikravesh, 198S, use rotational quaternions to develop dynamics models for mechanical systems. None of these worlis uses dual quaternions to formulate the dynamics problem. This paper gives the first CH2969-4/91/0000/0090$01 .OO 0 1991 IEEE formulation of a general dynamics problem using dual quaternion components. 1 Spatial Displacements A spatial displacement can be described by a sixdimensional rigid transforination from a moving reference frame, M ' , to a fixed reference frame, F. (See Figure 1.) The transformatioii can be described by a. rotation matrix, [A], and a translation vector, d = (d,, d,, &). 1.1 The Iinage Space Transformation ltavani and Roth showed that a spatial displacement can be represented by a geornetric trarisforniation i l l to an eight diiziensiorial Image Space, 4 = (%.lo) = (Qii + Q z j + Q3X: + Q4) + \u20ac(&si + Qd + Q7k + Q s ) . where the syinbols i , j , and X: are quaternion units, and t is the dual unit and has the property E' = 0. The first four terms in the dual quaternion are the Eulw parameters for the rotation matrix [A] and are tl(:nolecl by: (1) Q1 = s , sin $, Q" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001176_j.mechmachtheory.2020.103969-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001176_j.mechmachtheory.2020.103969-Figure7-1.png", "caption": "Fig. 7. Virtual prototype of a four-segment CDCM.", "texts": [ " The indirect realization of multi-point contact impedance control in configuration space is important for uniformly realizing the multi-point impedance control based on the convex combination of the target dynamics of all contacting points. On the other hand, it is also necessary to determine the location of the contacting points by the estimator presented in the Proposition 2 or actual force sensors for implementing the coordinated impedance control tasks, since we have to determine the kinematics (38) of the contacting points in the impedance control. In this section, a four-segment CDCM system (as shown in Fig. 7 ) is used to test the feasibility of the coordinated variable impedance control scheme proposed in this paper. The design parameters of the robot prototype are listed in Table 1 . Suppose the desired impedance property in operation space is given by (37) , of which the inertia matrix is supposed to be \u02dc H i = I \u2208 6 \u00d76 , and I \u2208 6 \u00d7 6 is an identity matrix. The desired stiffness matrix is \u02dc K i (t) = diag ( k 11 ,i (t ) , k 22 ,i (t ) , 0 , 0 , 0 , 0 ) and here the symbol \u201cdiag( \u2217)\u201d means a diagonal matrix associated with the given elements ( \u2217). As shown in Fig. 7 , we also suppose there are two impulse interaction forces acting on the end-segment of the CDCM, and the desired interaction forces are supposed to be F 1 (t) = [ 0 . 5 0 . 5 ] T , for t \u2208 [2.4, 4.0](s) and F 2 (t) = [ 0 . 3 0 . 3 ] T , for t \u2208 [3.2, 4.8](s). For the force acting point of F 1 , the nonzero elements of the corresponding desired stiffness matrix \u02dc K 1 (t) are given by k 11 , 1 (t) = 30 + 20 sin (3 t) and k 22 , 1 (t) = 30 + 20 cos (3 t) respectively, while for the force acting point of F 2 , the nonzero elements of the desired stiffness matrix \u02dc K 2 (t) are given by k 11 , 2 (t) = 20 + 15 sin (2 t) and k 22 , 2 (t) = 20 + 15 cos (2 t) respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000238_1.4033045-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000238_1.4033045-Figure6-1.png", "caption": "Fig. 6 Basic cones of a noncircular bevel gear", "texts": [ " The tooth profile of the cutter blades in coordinate system S2 or the tooth surfaces of flat-top generator can be presented as follows: r2\u00f0l; h\u00de \u00bcMirC\u00f0l; h\u00de \u00f0i \u00bc 1 z\u00de (7) where the coordinate transformation matrix Mi is given as Mi \u00bc 1 0 0 re cos\u00f0/i\u00de 0 1 0 re sin\u00f0/i\u00de 0 0 1 0 0 0 0 1 2 664 3 775 \u00f0i \u00bc 1 z\u00de The unit normal vector n2\u00f0l; h\u00de of the flat-top generator is represented by the equations n2 l; h\u00f0 \u00de \u00bc N2 l; h\u00f0 \u00de jN2 l; h\u00f0 \u00dej N2 l; h\u00f0 \u00de \u00bc @rC l; h\u00f0 \u00de @l @rC l; h\u00f0 \u00de @h 8>>< >>: (8) 3.2 Basic Cones of a Noncircular bevel gear. Figure 6 illustrates three basic cones of a noncircular bevel gear: pitch cone A0, root cone Af , and face cone Aa. Reference frame S0\u00f0O0 x0y0z0\u00de is fixed on the gear center and with axis z0 coincides with the axis of rotation of the gear. Hence, the pitch cone of noncircular bevel gear can be represented by vector function [11] 081013-4 / Vol. 138, AUGUST 2016 Transactions of the ASME Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/ on 01/07/2018 Terms of Use: http://www.asme" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000427_tfuzz.2018.2882170-Figure11-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000427_tfuzz.2018.2882170-Figure11-1.png", "caption": "Fig. 11. Single-link robot manipulator subject to dead-zone nonlinearity.", "texts": [], "surrounding_texts": [ "We take a single-link robot manipulator [12], [52] as the second example. Jq\u0308 +Dq\u0307 +MgL sin(q) = bDz(v) (66) where q and q\u0307 represent the position and velocity of the link, respectively. b = 2 denotes the control gain. Relevant notations used in (66) are shown in Table II. The control objective is to ensure the position of the link q can follow a given signal yr = sin(t). All the design parameters and the initializations are the same as those given in the first example, as seen in Table. I, except for c1 = 5, \u0393 = 1, \u0393\u03d1 = diag{1, 1}. For comparison, the control scheme in [13], which also considers the dead-zone compensation for nonlinear systems, is also applied to the plant in (66). Simulation results depicted in Fig. 12-Fig. 15 validate the obtained theoretical findings. The comparative results are displayed in Fig. 16-Fig. 17. In Fig. 16, when considering the time-invariant parameters, a good system performance can be also achieved under the control scheme in [13]. (The timeinvariant parameters chosen in this comparative simulation are mr(t) = 9,ml(t) = 6, br(t) = 2.5 and bl(t) = \u22122.) However, this control scheme loses its effectiveness over time when considering the piecewise time-varying parameters. Meanwhile, in Fig. 17, it is obvious that the tracking error can 1063-6706 (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. be adjusted to a more smooth and smaller region around zero under our control scheme." ] }, { "image_filename": "designv10_11_0003302_37.608535-FigureI-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003302_37.608535-FigureI-1.png", "caption": "Fig. I . Sketch showing positive directions of axes, angles, velocities, forces and moments.", "texts": [], "surrounding_texts": [ "Symbol\nX\nY\n-xS\nYS\nDefinition\nThe fixed axis on the earth due east (eating)\nThe fixed axis on the earth due north (northing)\nThe longitudinal moving axis fixed on the ship\nThe lateral moving axis fixed on the ship\nbased control [25], prediction control with a feed-forward loop [26], expert systems [27,28], predictive fuzzy control methods [29,30], and neural network techniques [31-331. A common feature of these \u201cintelligent\u201d approaches is to embed our human experiences and knowledge about ship behavior into the control strategies.\nIn this article, a multivariable neural controller is investigated for automatic berthing of a ship by the use of rudder and propeller. In comparison to the cited neural network applications [3 1-33], where neural networks learned \u201coff-line\u201d from some training data pairs pre-prepared by human operators, this article presents an \u201con-line\u201d training approach. An important advantage of such an on-line approach is the complete removal of any dependence upon the proper identification of the mathematical model expressing the dynamics of the ship, subject to some basic qualitative knowledge of ship behavior being provided. This point will be clarified later. The other advantage is that the network is trained by directly evaluating the performance error of the controller and therefore the need for off-line training and a \u201ctrainer\u201d associated with supervised control [31-331 can be removed. Furthermore, because the network training is undertaken repeatedly in each control cycle, any changes to the ship dynamics can be identified on-line, and hence the control strategy is useful for time-varying systems under changeable environmental conditions.\nThe organization of the article is as follows. In the next section, a non-linear ship model used for the berthing study is introduced. The non-linearity of the control actuators (rudder and propeller), the wind disturbances and the effect of shallow water are formulated to increase the realism and scope of the simulations. Next the design of the on-line trained neural control scheme is presented, which allows the application of directneural control for multi-input multi-output (MIMO) processes. In this MIMO marine control application, a development of a berthing route planning strategy is described to incorporate the direct neural control scheme. Automatic berthing simulations are undertaken in various environmental conditions involving\nIz\nw\nrandom wind disturbances, measurement noise, and shallow water effects. Final comments and conclusions are provided in the last section.\nMoment of inertia of ship around zs axis\nShip heading or yaw angle\nMathematical Model for Ship Berthing Simulations\nU\nV\nr\n6\nn\nThe MARAD Full-Form Ship Model Series The neural controller is designed under the assumption that an accurate measurement of the ship state (heading, position, speed, and yaw rate) can be undertaken on board ship. This is possible through the use of various navigation aids installed on board and/or on the berth, such as a gyrocompass, a rate-gyro, a Doppler log, a jetty-mounted sonar system, a global positioning system (GPS), or a theodolite positioning system (TPS). In this simulation-based research, a mathematical ship model is used to provide the ship state and to verify the performance of the controller.\nThe particular ship model used for this study is based on the Hydronautics MARAD model series [34]. The ship is considered to be a rigid body with the three horizontal degrees of freedom of surge, sway, and yaw. Ship motions in the three vertical degrees of freedom of heave, roll, and pitch are assumed to be negligible in common with most maneuvering studies. The ship motions are measured with respect to the right-handed coordinate system (xs, ys, zs), fixed on the ship, with its origin 0 located at the intersection of the longitudinal plane of symmetry and the midship\nForward ship speed (surge)\nLateral ship speed (sway)\nAngular velocity about zs axis (yaw)\nDeflection of rudder\nProDeller revolution rate\nI zs 1 The vertical moving axis fixed on the ship 1 I X G 1 Thexs coordinate of the center of gravity (C.G.) I I m 1 Mass of ship I\nI vw 1 Absolute wind speed I 1 aw 1 Absolute wind direction I I Xw 1 Fore and aft forces generated by wind I I Yw 1 Lateral forces generated by wind I 1 Nw I Moments about zs axis generated by wind I\n32 IEEE Control Systems", "Table 2. Ship Particulars\nLength\nBeam\nMean Draught\nDisplacement\nMaximum Rudder Angle\nRudder Rate\n160.93m\n23.16m\n7.47m\n16,800 tonnes\n40.0 deg\n2.5 degls\nsection, as illustrated in Fig. 1. The surge, sway, and yaw equations of motions of the ship, described with respect to the selected reference system, with the center of gravity (C.G.) corresponding to (XG, 0, 0), have the following forms:\nm(v+ur+x,Y)=f,(u,v,r,Zi,v,L,6,n)+Y,, (2)\nI,r+ mx,(V + U,) = fN(u , v, r , ti, G , i, 6, n) + N , . (3)\nThe hydrodynamic coefficients of the ship are involved in the non-linear functions fx, fy, f N , which are detailed in Reference [34]. The variables and symbols used in Equations (1-3) and in\nFig. 1 are defined in Table 1.\nIn previous studies on neural network based course-keeping and track-keeping control [ 16,241, the Hydronautics MARINER ship model [35] was used. However, the MARINER ship model has been found inappropriate in berthing simulations because some important data related to propeller operation were not available for very slow or reverse (minus) ship speed. For this reason, the new Hydronautics MARAD ship model [34] has been used for automatic berthing studies. The geometric characteristics of the ship used in the simulation is given in Table 2.\nThe Non-Linearity and Transfer Lag in Ship Control Actuators Ship control consists of providing a command rudder angle, 6\", and a command propeller revolution rate, nc. Due to the mechanical nature of the rudder and the propeller, there exist operational limits and time lags during the transmission of control signals. Therefore, the command control signals are usually not the actual control signals (6 and n) acting on the ship. In this study, a rudder limiter is presented in the form of a ramp threshold function, shown in Fig. 2, and described by the equation\nwhere y > 0 is a steady rudder rate, tk is a time interval between the k- 1 and kth control steps, and S,,, is the maximum allowable rudder angle, a value commonly referred to as the saturation level.\nTreating the propeller as a first-order system, a first order differential relationship can be applied to model how the revolution rate changes from the initial value ni-l to ni, that is, n(tk) satisfies\nIn Equation (5) , T~ is defined as the time constant; this is the time taken for n(@ to reach 63.2 percent of the full command nz (see Fig. 3). The experimental results provided by McDonald [36] show that the difference between ne , and n; corresponds to different z, values. Therefore, values of 2, in the range 5s to 15s has been used in this study.\nWind Forces and Moments The forces and moments generated by the wind acting upon the hull and superstructure of a berthing ship can have distinct influence on the motion of the ship. This is because the effectiveness of the rudder reduces significantly when the ship speed is fairly low. To establish the wind disturbance on a ship, the results of Isherwood [37] are used. The wind forces and moments are\nAugust 1997 33" ] }, { "image_filename": "designv10_11_0000645_02670836.2018.1523518-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000645_02670836.2018.1523518-Figure1-1.png", "caption": "Figure 1. (a) Schematic illustrating the geometry of the SLMbuilt component (dimensions inmm) and the locationswhere the EBSD measurements were carried out; (b) Island scan strategy.", "texts": [ " This paper aims also to highlight common trends on the evolution of texture gradients in fcc metals during SLM as a function of processing parameters, to frame the current results within this framework, and to expand the latter by adding missing data pertaining to materials processed using island scan strategies and to the presence of gradients along the build direction (BD). The alloy under investigation is an austenitic 316L stainless steel. CL20ESTM powderswere purchased from ConceptLaser (a General Electric company), and they were processed by SLM in a ConceptLaser M2 Cusing machine using the parameters summarised in Table 1. The geometry of the SLM built component is drawn schematically in Figure 1. The parts were constructed applying an island scan strategy with an island size of 5\u00d7 5mm. This strategy is a standard Concept Laser strategy to spread the heat input, and hence reduce the build-up of inherent stress. Therefore, the islands are melted in a randomised order. Furthermore, the islands shift their scan direction 90\u00b0 at each layer to avoid Table 1. SLM processing parameters LP (W) Layer thickness (\u00b5m) Scan rate (mm s\u22121) Hatch spacing (mm) 180 30 800 0.105 grooves forming. This strategy also addresses the gaps in between each layer, as the islands are shifted 1 mm in X and Y direction for each layer", " This is applied to avoid the coater knife hitting a weld path from the side, thus resulting in vibrations and uneven powder distribution. The as-fabricated specimens, hereafter termed AF, were then heat-treated at 1050\u00b0C for 1 h and water quenched. This condition will be termed HT. Themicrostructure, microtexture, and grain boundary nature of the AF and HT samples were examined by electron backscatter diffraction (EBSD) along two perpendicular planes, one parallel to the BD, termed xz plane, and one perpendicular to it (xy plane). The locations on the built part where these EBSDmeasurements were carried out are highlighted in Figure 1. It is important to note that the xz plane was examined at the midlayers, subjected to several solidification and remelting cycles, while the xy plane was examined at the top layer, subjected to one single melting and solidification cycle. EBSD was conducted using a NORDIF chargecoupled device camera in an FEI Nova NanoSEM 650 SEM using a voltage of 20 kV, and a step size of 2 \u03bcm. The orientation imaging microscopy TSL software was used for data analysis and to extract the corresponding inverse pole figure maps, direct pole figures, and misorientation distribution histograms" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003453_tsmcb.2003.818562-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003453_tsmcb.2003.818562-Figure2-1.png", "caption": "Fig. 2. Two-link robot.", "texts": [ " \u2014 For the supervisor: choose the desired attenuation level , and select the weighting matrix such that to guarantee a symmetric positive definite solution of the Riccati equation. Online processing \u2014 Solve the observer (11), and deduce the estimate state vector . \u2014 Compute using (15), from (13), and determine the control signal (9). \u2014 Update the adjustable parameters vector using (15). In this section, numerical simulations are used to illustrate the efficiency of the proposed method. Consider a two-link robot as given in Fig. 2. The dynamic equation of the two-link robot system is given as follows. (34) where and are the angular positions, is the moment of inertia, includes coriolis and centripetal forces, is the gravitational force, the applied torque vector, and the external disturbances. We have used the short hand notations and . The nominal parameters of the system are the link masses Kg, and is described as follows: and The simulation results for a sinusoidal reference trajectory, using the control law (9), are given in Figs" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000710_10407782.2019.1608777-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000710_10407782.2019.1608777-Figure7-1.png", "caption": "Figure 7. The heat source and shielding gas test. (a) The shape of the molten pool under laser stationary state. (b) The pressure distribution under the action of the shielding gas.", "texts": [ " The temperature-dependent kinematic viscosity is calculated by Eq. (7) and shown in Figure 4. The enthalpy of the discussed material is shown in Figure 5, and the specific heat can also be obtained by differentiating the enthalpy curve. Using the same method, the thermal conductivity can also be calculated and shown in Figure 6. Other parameters in the simulation are shown in Table 1. In order to verify the accuracy of the model, the heat source and shielding gas are firstly tested as shown in Figure 7. Figure 7a shows the shape of the molten pool under laser rest. It can be seen that the bath temperature exhibits a Gaussian distribution and the maximum temperature reaches 3552 K. Figure 7b shows the pressure distribution under the action of the shielding gas. At this time, the pressure applied to the center is about 65 Pa, which also shows a Gaussian distribution like the heat source. Since the process parameters used in multitrack and multilayer experiments are consistent with the single-track experiment, the numerical analysis results of the single-track experiment is compared with the experimental results to verify the accuracy of the numerical model. Using the optimized process parameters (750 W of laser power, 8mm/s of scanning speed and 12" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003652_027836499101000502-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003652_027836499101000502-Figure1-1.png", "caption": "Fig. 1. Gripper frame", "texts": [ " In this context the term displacement has a special meaning, for it refers only to the initial and final locations of the body; it is in no way concerned with any of the body\u2019s intermediate locations. Clearly there is no limit to the number of different paths that the body could sweep out, and each of these paths corresponds to the same rigid body displacement but a different rigid body motion. If we inscribe a Cartesian coordinate frame in the body, then the set of all possible displacements of the body is the set of all locations of this frame. Figure 1 shows a Cartesian frame n (normal), o (orientation), and a (approach) inscribed in the center of a (rigid) robot gripper. We denote the frame by the symbol C{3, allowing the gripper to undertake an arbitrary displacement, D, from its initial position at 19 to a final position at C{3\u2019 (Fig. 2). For the purposes of describing the displacement, we call 19 the fixed frame and C{3\u2019 the moving frame. Remark 1. The set of all isometries of [R3 forms a group. This is the so-called euclidean group, denoted by E(3)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000967_s10409-019-00914-6-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000967_s10409-019-00914-6-Figure1-1.png", "caption": "Fig. 1 Whipple bicycle in an upright, straight reference configuration (figure adapted from Refs. [12,29])", "texts": [ " Then we investigate how the circular motion is affected by the parameter of the ground surface. In Sect. 4, we discuss how to establish a reduced linearized system, then analyze the stabilities of the circular motions. We draw conclusions in Sect. 5. In this section, we will analyze the contact kinematics and local constraints of the benchmark Whipple bicycle on the ground with an arbitrary shape. Then the Lagrangian equations of the first type will be used to derive the equations of motion for the bicycle. Figure 1 shows the Whipple bicycle moving on a ground. This bicycle consists of four rigid bodies including a rear frameB, a rear wheelR, a front frameH and a front wheelF. The two frames B and H have lateral symmetries in their shape and mass distributions. The two wheels R and F are circular symmetric and make ideal knife-edge rolling contact with the ground. By completely ignoring the effects of structural compliance, joint friction and rolling friction, the Whipple bicycle can be characterized by 25 geometric and mass parameters, as shown byMeijaard et al. [12] in Table 1. We define the following coordinate systems for the bicycle: an inertial coordinate frame, FI = {O; i, j , k}, fixed on the plane, in which the i- and k-axes lie; and four body-fixed frames, Fb = {Ob; eb,1, eb,2, eb,3}, Fr = {Or ; er ,1, er ,2, er ,3}, Fh = {Oh; eh,1, eh,2, eh,3}, F f = {Oh; e f ,1, e f ,2, e f ,3}, attached to the center of mass of each body, as shown in Fig. 1. Note that the four rigid bodies of the bicycle are connected by three hinges. Before we consider the wheel contact constraints, the accessible configuration space of the bicycle in a free motion is nine-dimensional (4 \u00d7 6 \u2212 3 \u00d7 5 = 9), thus nine generalized coordinates are required. We select these coordinates as follows: the first three coordinates are related to the coordinate components, (x, y, z), of a reference point D in the frame FI . This point is located at the intersection of the steering axis and the coordinate axis O f e f ,1", " In this section, we investigate the circular solutions of the bicycle moving on a revolution surface. Without loss of generality, we specify the surface as a paraboloid of revolution, which takes amathematical formas, \u03b6 = \u03b1(\u03be2+\u03b72), where\u03b1 is a parameter of the ground surface. The circular motions of the bicycle on the surface, similar to the case of the bicycle on a horizontal plane [13,29,33], correspond to periodic orbits of theDAEs systemEq. (8). Thus, x and y vary sinusoidally and z is constant. Namely, the reference point D (see Fig. 1) traverses a circle with radius (say) R1.We designate the angular frequency of the circular motion as \u03c9, so the first Euler angle (heading) \u03c8 grows linearly with time, i.e., \u03c8(t) = \u03c9t . The secondEuler angle (roll) \u03b8 , the third Euler angle (pitch)\u03d5, the steering rotation angle \u03b4 and the wheel spin rates \u03c6\u0307r and \u03c6\u0307 f are all constants. It is worth noting that the rotations (\u03c6r , \u03c6 f ) of the two wheels relative to their respective frames are ignorable coordinates that do not appear in the Lagrangian function and constraint equations [12]" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003139_70.976011-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003139_70.976011-Figure2-1.png", "caption": "Fig. 2. Relation between jxj and the upper bound of _V .", "texts": [ " For the set-point regulation control, the value of the Lyapunov function is large at the start time and it is gradually reduced to zero because the controller is designed so that the time derivative of the Lyapunov function remains negative definite. On the other hand, for the trajectory tracking control, we start the simulation/experiment with zero error after adjusting initial conditions. The value of the Lyapunov function is zero at the start time, however, the error increases to some extent because may have any positive constant smaller than as shown in Fig. 2. This figure depicts the upper bound of versus of the equation (27). Since the performance limitation upper bounded by the inequality (25) is the convergent point as we can see in Fig. 2, the Euclidian norm of a state vector tends to stay at this point. This analysis can naturally illustrate the performance tuning. The PID gain tuning has been an important subject; however, until now, it has not been investigated very often. Recently, the noticeable tuning method was suggested as \u201csquare law\u201d in [13]. The authors showed that the square law is a good tuning method by their experiments for an industrial robot manipulator. Theoretically, we can confirm once more that the square law is a good tuning method by showing that the performance limitation of (25) can be written approximately as follows: where the square law means that the error is approximately reduced to the square times of the reduction ratio for values" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000225_amm.762.219-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000225_amm.762.219-Figure7-1.png", "caption": "Fig. 7 Kinematics schema of the motor mechanism c2", "texts": [ " \u22c5\u2212= \u22c5\u2212\u22c5\u2212= \u22c5\u2212= \u22c5\u2212= \u22c5\u2212\u22c5\u2212= \u22c5\u2212= \u22c5\u2212= \u22c5\u2212\u22c5\u2212= \u22c5\u2212= \u22c5\u2212= \u22c5\u2212\u22c5\u2212= \u22c5\u2212= \u22c5\u2212= \u22c5\u2212\u22c5\u2212= \u22c5\u2212= =\u22c5\u2212= \u22c5\u2212\u22c5\u2212= \u22c5\u2212= \u22c5\u2212= \u22c5\u2212\u22c5\u2212= \u22c5\u2212=\u22c5\u2212= \u22c5\u2212= \u22c5\u2212\u22c5\u2212= \u22c5\u2212= \u22c5\u2212= \u22c5\u2212\u22c5\u2212= \u22c5\u2212= 1010 11,1011,10 11,10 88 8989 89 7 77 7 35 55 5 44 44 4 66 66 66 33 33 3 11 1212 12 11,10 1010 1010 8 88 88 7 77 77 5 55 55 4 44 44 6 66 3 33 33 1 11 11 0 \u03d5\u03d5\u03d5 \u03d5\u03d5\u03d5 \u03d5\u03d5\u03d5 G i G iy G G ix G G i G iy G G ix G M i M M iy M M ix G i G iy G G ix G G i G iy G G ix G G i G iy G G ix G H i H iy G HG ix G G i G iy G G ix G G i G iy G G ix G JM gmymF xmF JM gmymF xmF JM gMyMF xMF JM gmymF xmF JM gmymF xmF JM gmymF xmF JM gmymF xmxmF JM gmymF xmF JM gmymF xmF M (5) Is then calculated all the forces from couplers. In the end we can determine and (three) driving forces [1-5]. In figure 5 can be monitored engine element c1 composed of kinematic elements 8-9. Determine motive power Fm1 with relations of the system 6; being two relations of calculation may be carried out a check. \u2212\u2212 =\u21d2=++\u22c5\u21d2= \u2212\u2212 =\u21d2=++\u22c5\u21d2= \u2211 \u2211 10 10 )10( 10 10 )10( sin 0sin0 cos 0cos0 10 2102 10 2102 \u03d5 \u03d5 \u03d5 \u03d5 y H iy G m y H iy Gmy x H ix G m x H ix Gmx RF FRFFF RF FRFFF (7) In figure 7 can be monitored engine element c3 composed of kinematic elements 1-2, and determine motive power Fm3 with relations of the system 8 [1-5]. + =\u21d2=++\u22c5\u2212\u21d2= + =\u21d2=++\u22c5\u2212\u21d2= \u2211 \u2211 1 1 )1( 1 1 )1( sin 0sin0 cos 0cos0 1 313 1 313 \u03d5 \u03d5 \u03d5 \u03d5 y E iy G m y E iy Gmy x E ix G m x E ix Gmx RF FRFFF RF FRFFF (8) Conclusions Forging manipulators themselves have become more prevalent in the industry today. An idea of establishing the incidence relationship between output characteristics and actuator inputs is proposed (see the relations from systems 3 and 4)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001740_j.jmapro.2021.03.008-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001740_j.jmapro.2021.03.008-Figure5-1.png", "caption": "Fig. 5. The distribution of temperature across the weld interface.", "texts": [ " < 100> in bcc and fcc metals) and they are stretched from one grain to another as long as the easy axis growth is parallel to the heat flow direction. However, the coeffect of severe plastic deformation and temperature rise during friction welding caused dynamic recrystallization in the WZ, TMAZ, and HAZ changing the morphology of the grains from columnar to equiaxed grains. Finite element analysis (FEA) was employed to examine the degree of temperature rise during friction welding, as shown in Fig. 5. The temperature distribution at the weld joint reveals that the temperature can reach as high as \u22481100 \u25e6C after two seconds in friction welding. This temperature is slightly higher than the conventional solution temperature (i.e. 1040 \u25e6C) used to homogenise the commercial 17-4PH stainless H.R. Lashgari et al. Journal of Manufacturing Processes 64 (2021) 1517\u20131528 steel. The Creq and Nieq of the current alloy was calculated according to WRC-1992 diagram and were found to be 17.034 and 8.28, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003684_ias.1992.244291-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003684_ias.1992.244291-Figure2-1.png", "caption": "Fig. 2 Structure of Proposed Motor", "texts": [ " To perform this desired function, the commutation winding should satisfy the following conditions: (1) It should have good coupling with the short pitch winding to be turned off in order to rapidly absorb the trapped energy; (2) Its self inductance should be independent of the rotor position in order to avoid the possibility of negative torque; ( 3 ) It should retain a mechanism for converting the trapped energy to mechanical energy and/or transfer this cncrgy to the field of next conducting phase. Careful study of the stator and rotor structures of VRMs leads to the finding that a full pitch winding in a 6/4 VRM (six stator poles and 4 rotor poles) whose stator pole arc is thirty degrees and rotor pole arc equal to or greater than thirty degrees, can satisfy the above conditions. Based on this concept, the motor configuration shown in Fig. 2 is proposed. The idealized winding inductances of this new motor are shown in Fig. 3. From Fig. 2 it can be seen that the full pitch winding (i.e. phase D) has good coupling with phase B which is to be turned off. This satisfies the first condition. Also from Fig. 2 it can be seen that thc reluctance of the flux path of Dhase D is constant because the total overlamed area the interaction between the currents in phase D and next phase to be turned on. This satisfies the third condition. 111. OPERATING PRINCIPLES OF THE NEW MOTOR 3.1 Excitation of the Short Pitch Windings The excitation of the short pitch windings is the same as that of conventional VRMs except the current in the winding can be turned off closer to the point of stator/rotor pole alignment for better utilization of the energy placed into the machine and therefore improved torque performance", " In terms of performance, the third approach is the best because current ig decays most rapidly in this case. After current ig reaches zero, phase B must be open circuited and phase D is short circuited. After the current in phase D decays to zero, phase D is then open circuited. 3.3 Utilization of the Trapped Energy As pointed out above, the current in the short pitch winding is transferred to the full pitch winding during the turn-off process. As a result, the main flux remains in the motor and the energy associated with the main flux is transferred from phase B to phase D. It can be seen in Fig. 2 that as the rotor rotates, the overlapped area under the stator poles of next phase (e.g. phase A) is increasing while the overlapped area under the stator poles of phase B is decreasing. As a result, part of the flux, which links winding B and D originally, is shifted from the area under stator poles of phase B to the area under stator poles of phase A. Consequently, the field energy associated with this part of the flux is transferred to the field in the region under the stator poles of phase A", " A drive system employing the new motor is being built and the measured comparisons between the performance of the two motors will be reported in the near future. VI. FUTURE RESEARCH The authors believe that research on the type of motor drives described in the paper is just beginning. For example, an extension of the concept proposed in this paper is shown in Fig. 13. the authors have proposed another motor which have two full pitch windings and two short pitch windings. The operating principles are similar to those of the motor shown in Fig. 2. The advantage of the second motor over the ACVRM described in this paper is that the slot utilization is better. The authors are conducting research on the motor shown Fig. 13 and the results will also be presented in another paper. In addition to the research mentioned above the 1, Additional converter topologies, including soft switching converters. 2. Torque ripple control. 3. Design optimization. 4. Elimination of position sensor. authors are working in the following areas: VII. CONCLUSIONS A new concept is proposed in this paper to solve the problems associated with the energy stored in the magnetic field in conventional VRMs" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000659_wrc-sara.2018.8584227-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000659_wrc-sara.2018.8584227-Figure1-1.png", "caption": "Figure 1. Sketch of the biped model. (a) Swing phase. (b) Impact phase.", "texts": [ " The biped robot appear asymmetrical gait or falls in some initial states, and the control of the biped robot is obviously * This work was supported by the National Natural Science Foundation of China (NSFC) under Grants 61503325, China Postdoctoral Science Foundation under Grants 2015M581316. The authors are with the Institute of Electric Engineering, Yanshan University, Qinhuangdao, China (e-mail: wuxiaoguang@ysu.edu.cn). continuous control problem. Therefore, we propose the DDPG to control the biped robot avoid fall over in this paper. The robot studied in this paper as shown in Fig. 1 [9]. To derive the equations of the dynamic model, several assumptions must be satisfied [10]-[12]: (1) The legs are rigid and without deformation. (2) The hip is free of damping and friction. (3) There is no relative slip between the foot and ground. (4) The impact is considered as instantaneous and completely inelastic. (5) The biped robot walks on a flat, slightly descending slope. The biped robot is composed of two straight legs with asymmetric arc feet, articulated at the hip joint H . Therefore, the biped robot possess 2 degrees of freedom, respectively located in the supporting point S and hip point H , denoted 1 and 2 " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003441_s0094-114x(02)00042-3-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003441_s0094-114x(02)00042-3-Figure2-1.png", "caption": "Fig. 2. The special case of symmetrically intersecting input and output shafts.", "texts": [ " One of the earliest known 6R linkages, the double-Hooke\u2019s-joint chain, is a hybrid of two spherical four-bars. It is a commonly applied mechanism and has significant simplifying features. Yet, to my knowledge, there is no published analysis of the loop as a 6R chain, although Ref. [14] includes a set of mobility criteria and a sample of numerically produced relationships. Instead, one encounters special-purpose analyses, founded upon the component spherical linkages, for the two particular cases of parallel (Fig. 1) and symmetrically intersecting (Fig. 2) input and output shafts. Our intention here is to provide a full six-bar formulation for this important linkage and, subsequently, to generalise it further to a less constrained loop. Our exposition will reveal the difficulties presented by displacement\u2013closure equations for loops of relatively high connectivity-sum. The analytical tools adopted here have been employed many times and appear among the cited references (for example, in Refs. [1\u20134]). We are concerned with delineating a linkage known to be mobile rather than searching for mobile solutions, so that certain simplifications can be introduced to the usual strategy", "7), that the linkage is partially locked when T4 \u00fe T5 \u00bc 0; under the prescribed constraints on angles of skew, by virtue of part-chain mobility about the connecting-rod. This circumstance obtains when the connecting-rod is directed perpendicular to the shafts. Besides the dimensional constraints specified in Section 3 above, we have the conditions a45 \u00bc 0 \u00bc T4 T5; which reduce Eq. (3.i) to a212 \u00bc 2T 2 4 \u00f01\u00fe ca45\u00de; or a12 \u00bc 2T4c a45 2 ; \u00f05:i\u00de (where we may set T4 > 0, p > a45 > 0\u00de, as is clear from Fig. 2. We select the same closure equations and variants as in the previous section. Under the present constraints, including that defined by Eq. (5.i), they are reduced to the eight respective relationships below: ch2ch3 \u00fe sh4s a45 2 \u00bc 0; \u00f05:1\u00de sh5s a45 2 \u00fe ch6ch1 \u00bc 0; \u00f05:2\u00de sh2 ch4s a45 2 \u00bc 0; \u00f05:3\u00de c a45 2 \u00fe sh6ch1 \u00bc 0; \u00f05:4\u00de ch5s a45 2 \u00fe sh1 \u00bc 0; \u00f05:5\u00de sh6sh1ca12 ch6sa12 \u00fe sh2sh3 \u00bc 0; \u00f05:6\u00de ch2sh3 \u00fe c a45 2 \u00bc 0; \u00f05:7\u00de sh6sh1sa12 ch6ca12 ch3 \u00bc 0: \u00f05:8\u00de From Eq. (5.3), sh2 \u00bc ch4s a45 2 ; ch2 \u00bc r 1 ch4s a45 2 2 1=2 ; and substitution into Eq", "8) we find, respectively, that rch4c a45 2 1 ch4s a45 2 2 1=2 \u00bc s ch5c a45 2 ca12 \u00fe sh5sa12 1 ch5s a45 2 2 1=2 \u00f05:9\u00de and rsh4 1 ch4s a45 2 2 1=2 \u00bc s ch5c a45 2 sa12 sh5ca12 1 ch5s a45 2 2 1=2 : \u00f05:10\u00de Division between these equations gives th4 c a45 2 ca12 \u00fe th5sa12 \u00bc c a45 2 c a45 2 sa12 th5ca12 ; or sa12th4th5 \u00fe c a45 2 ca12\u00bdth4 \u00fe th5 c2 a45 2 sa12 \u00bc 0: \u00f05:11\u00de We see that the general Eqs. (4.11) and (5.11) are of the same form; the latter is obtainable from the former by replacing a12=\u00f0T4 \u00fe T5\u00de by c\u00f0a45=2\u00de. Again, therefore, only the usual industrial property of parallel clevis-pins on the connecting-rod, as in Fig. 2, reduces the equation to linearity between th4 and th5. In relaxing the additional conditions of the previous two sections, we retain the selection of closure equations adopted for manipulation. They are given below: a12ch2ch3 \u00fe a45ch4 \u00fe T5sh4sa45 \u00bc 0; \u00f06:1\u00de a45ch5 \u00fe T4sh5sa45 \u00fe a12ch6ch1 \u00bc 0; \u00f06:2\u00de a12sh2 \u00fe a45sh4 T5ch4sa45 \u00bc 0; \u00f06:3\u00de T4ca45 \u00fe T5 \u00fe a12sh6ch1 \u00bc 0; \u00f06:4\u00de a45sh5 T4ch5sa45 \u00fe a12sh1 \u00bc 0; \u00f06:5\u00de T5\u00f0sh6sh1ca12 \u00fe ch6sa12\u00de \u00fe a45\u00f0sh2ch3ch4 ch2sh4\u00de \u00fe T4sh2sh3 \u00bc 0; \u00f06:6\u00de a12ch2sh3 \u00fe T4 \u00fe T5ca45 \u00bc 0; \u00f06:7\u00de T5\u00f0sh6sh1sa12 ch6ca12\u00de \u00fe a45sh3ch4 T4ch3 \u00bc 0: \u00f06:8\u00de Owing to a relative lack of simplifying properties here (Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001009_s0263574720000284-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001009_s0263574720000284-Figure8-1.png", "caption": "Fig. 8. Upper chamber mold and bottom molds. (a) Upper chamber mold. (b) Bottom mold. (c) Physical picture of mold.", "texts": [ " The robot is a composite of two silicones: liquid silicone 0 grade (more soft) and liquid silicone 16 grade (more rigid). The coefficient of silicone is shown in Table I. Due to the empty cavity inside the module, it is very difficult to design the mold in the whole sealing cavity. Based on the previous research, the upper and lower molds are adopted in this work.20, 21 Each module is made up of two different hardness silicones (upper chamber is 16 grade, bottom is 0 grade). The mold for making cavity is shown in Fig. 8. The molds are composed of upper chamber mold and bottom mold. Each set of the mold is composed of the primary mold and channel mold. The entire mold is not completely closed, and there are gaps in the edge of the molds. The functions of the gaps are diffusing the bubbles in the silicone and improving the structure quality. The molds are formed by a 3D printer, and the printed material is polylactic acid (PLA).22 The molds after 3D printing are shown in Fig. 8(c). https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0263574720000284 Downloaded from https://www.cambridge.org/core. Uppsala Universitetsbibliotek, on 15 May 2020 at 00:12:18, subject to the Cambridge Core terms of use, available at The fabrication process of the earthworm-like robot is shown in Fig. 9. The specific production processes are as follows. (1) Mix AB silicone Pour parts A and B into a plastic cup and stir for a few minutes until they are well-mixed (equal parts A and B by volume, no need to measure exactly)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001732_j.autcon.2021.103609-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001732_j.autcon.2021.103609-Figure6-1.png", "caption": "Fig. 6. Design of the manipulator arm. (a) Prismatic joints positioning sliders; (b) Electronic schematic for the slider position control.", "texts": [ " The operator has access to the remote PC, the head tracking helmet, the joystick, and the video screen, enabling the control of the robot action and the monitoring of the robot status remotely. The Robot Operating System (ROS) middleware is used as the high-level software, while several microcontroller units (MCU) are used to interface with the sensors and actuators in the system as low-level control. The main MCU is NXP MBED LPC1768. Auxiliary MCUs 1 and 2 are Arduino Nano, and MCU 3 is Arduino MEGA 2560, respectively. The main function of the robot manipulator is to provide structural attachment and kinematics for the gripper and the PPEF. As shown in Fig. 6(a), the robot manipulator has an open-chain serial configuration, with the following order: Y-slider, X-slider, Z-slider, bidirectional slider, and then branch out to the left and right linear platforms. Table 1 lists the working stroke for each individual joint. Collectively, these joints determine the final pose of the PPEF, which is mounted on top of the linear platforms. The Y-, X-, Z-, and bidirectional sliders (Igus Drylin) employ \u201cdry lubrication\u201d technology in which the moving contact between the carriage and the slider structure is facilitated by specially designed self-lubricating plastics. These sliders are coupled with their respective stepper motor using curved jaw coupling. The coupling can accommodate misalignment and is suitable for motion applications that are continuous or light to moderate in terms of duty cycle. As for the left and right linear platforms, the mechanism consists of two metallic linear guides housed in a 3D-printed structure to provide cantilever load support from the PPEF. The design avoids loading the linear actuator directly to ensure smooth motions. Fig. 6(b) shows the electronic schematic for the driving and controlling stepper motors (Nanotec PD4-N) and linear actuators (Actuonix L16) on the manipulator arm. The four stepper motors have built-in driver and controller that accept a 24-V power supply and an interface with the CANOpen bus protocol. Here, a CAN transceiver (Microchip MCP2551) is used to establish the main MCU as the master node. The physical bus is a two-wire communication, which is also known as a differential pair of transmission lines" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000617_j.ijleo.2018.05.081-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000617_j.ijleo.2018.05.081-Figure3-1.png", "caption": "Fig. 3. Temperature distribution at 370W, 1300mm/s at mid of region (a) 3, (b) 4 and (c) 5.", "texts": [ " In the current model, the heat generation history of support structure is ignored and is assumed to be at room temperature at the start of laser scanning process. The element Birth and Death technique is included in the laying of each single layer and at every sub-step within a track to change the material property of molten AlSi10Mg powder into solid as the laser progress towards the end of simulation. The time between the subsequent layer spread is ignored in the present study. The melt pool formation and the temperature distribution in the selected location of the three regions is shown in Fig. 3. As observed, the heat dissipation through a solid region 3 is found maximum among the three regions due to higher heat conductivity of solid AlSi10Mg. The high nodal temperature in region 5 is credited to heat accumulation owing to poor thermal conductivity of loose powders whereas region 4 is found to have maximum nodal temperature in between the two extreme regions. Furthermore, at the initiation of layer sintering, incomplete melting is observed as shown encircled in Fig. 3(c). In the only scanned layer above region 3, the melt pool depth was found lesser than the layer thickness and it agrees well with the previous work [25] where comparatively higher heat energy was used and melt pool depth was measured to be 43 \u03bcm in a layer thickness of 50 \u03bcm. The incomplete melting of layer above solid base facilitates an easy removal of part. The cooling rate at top surface of mid of the regions 3, 4 and 5 was found decreasing along the length of laser track and it was measured to be 4", " The nodal temperatures calculated at different monitoring locations in a single layer and along the same vertical line in the subsequently built other 2 layers are given in Table 1. The nodal temperature at the given points not only increased in the laser direction as previously discussed but also found increasing with the layer addition and correlated well with other works [3,25]. The only exception is region 3\u20134 where the temperature was found 1403.39 K lesser than the Region 3 before it. The reason is ascribed to the powders of region 2, where the accumulation of heat is noticed as the laser begin to sinter the first layer as noticed in Fig. 3(c). Temperature as high as 1459 K was recorded at the third load step which later reduces drastically due to the underlying solid surface and reduced effect of less conductive powders of region 2. The Fig. 5(b), describes the melt pool formation in the three layers at the given locations and it was found increasing as shown. Regardless of the lower nodal temperature at Region 3\u20134 of layer 1, the melt pool depth was observed larger than the region 3. The less conductive support structure melts the underlying powder over time thereby extending the depth further 10 \u03bcm from the 20 \u03bcm depth of adjacent Region 3" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001228_tvt.2020.3041336-Figure19-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001228_tvt.2020.3041336-Figure19-1.png", "caption": "Fig. 19. Flowchart for vibration calculation", "texts": [ " While for the combination method of auxiliary slots, numerous auxiliary slot combination types and slot parameters are available, and it is difficult to obtain the optimal motor model. Due to page limitation, only one auxiliary slot combination type (SARq) with specific slot parameters (r1 = 1 mm, c1 = 0.8 mm, r4 = 1 mm, and c4 = 0.8 mm) is used for verification. Optimization work of the optimal auxiliary slot types will be done in the future. The vibration calculation flowchart for the FSCW-IPM motor is shown in Fig. 19. Electromagnetic force is calculated with the 2D electromagnetic model firstly, then the stator modal analysis is performed and electromagnetic forces acting on the stator teeth are mapped into the mechanical model in form of lumped force and moment as vibration excitation. Finally, vibration harmonic response analyses are conducted using the modal superposition method. To ensure consistency of theoretical results, the same material parameters are used in all finite element analysis (FEA) models" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003818_0191-8141(88)90027-2-Figure15-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003818_0191-8141(88)90027-2-Figure15-1.png", "caption": "Fig. 15. Geometry for defining the equivalent symmetric fold for a given asymmetric fold. (a) Acute fold. (b) Obtuse fold.", "texts": [ " The relationship among the generalized style characteristics for perfect folds is still represented exactly by equation (6) and by the diagrams of the perfect fold surface in the three dimensional fold style space (Fig. 5). In this section, I derive the generalized forms of the aspect ratio/~, the bluntness ratio/~ and the bluntness/~ (note that circumflexes are used to distinguish the generalized style elements and the quantities that pertain to the equivalent symmetric folds). An equivalent symmetric fold has the same folding angle as the associated asymmetric fold. To determine the remaining two equivalent style elements (Fig. 15), extend the sides of the circumscribing quadrilateral to their mutual intersection, and construct the bisector of the resulting interlimb angle t. This line also bisects the folding angle. At the point where this bisector meets the median line M, construct a normal to the bisector. The intersections of that normal with the sides of the circumscribing quadrilateral or their extension define the inflection points fi and L on the equivalent trapezoid. The amplitude A, the half-wavelength .~/and the radius of the reference circle i0 for the equivalent trapezoid are all defined as before for symmetric folds. The closure radius of curvature r~ remains unchanged in the transformation from the asymmetric to the equivalent symmetric fold. Thus the equivalent elements of fold style are defined as before for symmetric folds: A /6 = __~ M / 3 - rc (10) /~= {~c/f,, f\u00b0rrc--3.0.co;2-4-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003179_(sici)1099-1239(19991215)9:14<1013::aid-rnc450>3.0.co;2-4-Figure2-1.png", "caption": "Figure 2. RESTORE tailless \"ghter aircraft control e!ector suite", "texts": [ " This con\"guration employs aggressive, all-aspect low observable technologies and was sized for a 1100 nautical mile high}low}low}high air-to-ground mission. The aircraft features two internal weapon bays each capable of carrying (2) GBU-27 laser guided bombs or (2) AIM-9 plus (2) AIM-120 air-to-air missiles. The RESTORE con\"guration has a complete, detailed aerodynamic database with controls consisting of elevons, pitch #aps, outboard (OB) Leading-Edge Flaps (LEFs), Spoiler-Slot De#ectors (SSDs), and All Moving wing Tips (AMTs) as depicted in Figure 2. Copyright ( 1999 John Wiley & Sons, Ltd. Int. J. Robust Nonlinear Control 9, 1013}1031 (1999) The control suite was sized during ICE investigations2 to provide su$cient control power to achieve three critical #ight conditions: Level 1 roll performance during power approach; bank angle change of 903 in 2)0 s at 303Angle Of Attack (AOA) (low-speed); bank angle change of 903 in 1)1 s at 203 AOA and 300 KCAS. The static aerodynamic force and moment data ranging from low-speed high AOA to high Mach conditions were collected during cooperative wind tunnel tests of a 1/18th scale model of the LMTAS tailless \"ghter aircraft with both National Aeronautics and Space Agency (NASA) Langley Research Center and AFRL" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000998_j.jsv.2020.115374-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000998_j.jsv.2020.115374-Figure9-1.png", "caption": "Fig. 9. Arrangement of the experimental points.", "texts": [ " When the rotational speed is after 28,000 r$min 1, especially, the proposed method is better than the method in Ref. [30]. This indicates that the cage contributes little to the radiation noise of the ACCBB. To explore the applicability of the proposed model to calculating the radiation noise of angular contact ball bearings with different dimensions, the ACCBB with 7003C is applied to a motorized spindle to further identify the reliability and accuracy of the model. The test scheme, as shown in Fig. 9, is used in this study. The motorized spindle is assembled on a distinct support, and the inner ring of the ceramic bearing rotates clockwise from the front of the motorized spindle. The test points 1 and 2 are coincident with the calculated field points, i.e. they are both located in the bearing plane, 50 mm away from the outer surface of the motorized spindle (100 mm away from the axis of the bearing). During the experiment, the sound pressures are tested using INV9206eI sound pressure sensors with sensitivities of 43" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000417_s00170-018-2799-7-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000417_s00170-018-2799-7-Figure2-1.png", "caption": "Fig. 2 Generation principle of skiving", "texts": [ " Hence, the differential rotation angle \u0394\u03c6 and linear motion \u0394F maintain the following relation: \u0394\u03c6 \u00bc \u2212 jw sin \u03b2w\u00f0 \u00de\u0394F cos \u03b2c\u00f0 \u00deRc \u00f05\u00de By now, all the kinematic parameters like nc, nw, ncf, and F can be easily identified by Eqs. (3)\u2013(5). The working principle of skiving indicates that the cutting edge Ce is conjugating with the desired machining surface Sw, and the primary motion is following to the meshing motion of cross-axis gear. Through involving the auxiliary gear rack, the generation process of skiving is briefly demonstrated as in Fig. 2, in which the external surface of workpiece generates the rack gear surface by their conjugate motion, and simultaneously, the cutter also generates the rack gear surface by their own conjugate motion. Therefore, considering all the conjugate motions relative to cutter, we can know that the external swept surface ST of the workpiece is just the external surface of the cutter part. Thus, for the intersect curveCe between ST and any given rake flank SR, it generates a curve Re on the rack gear surface, and curve Re generates a curve We on the workpiece" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000828_j.mechmachtheory.2019.103658-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000828_j.mechmachtheory.2019.103658-Figure7-1.png", "caption": "Fig. 7. Effects of different factors on the transmission error: (a) ideal conditions, (b) with tooth form deviations, (c) with tooth form deviations and contact deformation.", "texts": [ " Furthermore, the measured geometric data can also be used to generate the skin model shapes directly when analyzing a specific gear set. In this section, the effects of contact behavior between mating tooth surfaces on transmission performance are first illustrated. Then, contact behavior is calculated using the CG-FFT method to perform TCA. The tooth contact pattern and contact pressure distribution can be obtained directly from the calculation results, and the LRA strategy is adopted to calculate the transmission error. Contact deformation and contact status may have considerable effects on transmission performance. Fig. 7 shows the effects of tooth form deviations and contact deformation on transmission error. The driven gear, which is rotated by \u03b8 at a given moment, will deviate from its ideal position when tooth form deviations and contact deformation are considered. In Fig. 7 , OA represents the theoretical gear position, denoted \u03b8 in Fig. 7 (a). OB represents the position when it is affected by tooth form deviations, denoted \u03b8 f in Fig. 7 (b). OC represents the position when it is further affected by contact deformation under a given load, denoted \u03b8d in Fig. 7 (c). For the contact status, it may significantly affect the contact pressure distribution of the tooth surfaces. The desired contact status can distribute the load uniformly on the tooth surface, as illustrated in Fig. 8 (a). The tooth contact may be concentrated on one side of the tooth surface when affected by machining and assembly errors, as illustrated in Fig. 8 (b). Thus, it is important to analyze the contact behavior between mating tooth surfaces when evaluating the transmission performance" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001273_0278364920903785-Figure10-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001273_0278364920903785-Figure10-1.png", "caption": "Fig. 10. Orienting the imager to tracking an instrument with predictive filtering (mode 2).", "texts": [ " The desired pose adjustment is set equal to the difference between the current CT and the current CTTraj poses plus an additional US imager rotation or displacement command. It is not possible with the given sensing strategy to directly measure the tissue location, but it is possible to maintain the catheter\u2019s pose in the heart chamber with respect to the breathing motion disturbance. Mode 2: Instrument tracking. The US imager is rotated to track a moving target while the catheter tip position is commanded to remain constant with respect to the heart chamber (Figure 10). Maintaining US imager alignment requires coordinated motion of all 4 DOFs, and requires extensive training to perform manually. The green dotted line represents cyclical CT and Instr pose motion due to respiration only. The current expected CT pose due to breathing only is CTTraj,Current, and the current measured CT pose is CTCurrent. The yellow arrow represents the transform between the expected pose and the actual measured pose, TCT CTTraj . The current target position is InstrCurrent. The EKF is used to estimate the future target position, InstrFuture" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000716_j.mechmachtheory.2019.07.013-Figure16-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000716_j.mechmachtheory.2019.07.013-Figure16-1.png", "caption": "Fig. 16. The simulation platform of QMK50A CNC machine tool.", "texts": [ " The grinding tracks applied for the following simulation of the face gear grinding are beyond the boundary of the tooth surface of the face gear ( Fig. 14 ), in order to sufficiently grind all grid nodes on the gear tooth surface. The number of the grinding tracks for the face gear grinding of case 1 \u223c case 4 has been determined ( Fig. 15 ). Only slight difference in the number of the grinding tracks is discovered for the face gears in case 1 \u223c case 4. A simulation platform of face gear grinding based on QMK50A five-axis CNC machine tool is developed by using Vericut software ( Fig. 16 ). The relative motion coordinates between the face gear and the grinding disk wheel for the grid nodes grinding of the tooth surface of the face gear for case 1 \u223c case 4 have been obtained from the calculation of the envelope residuals of the gear tooth surfaces. Fig. 17 shows the model of the ground face gear of case 1. The partial enlargement of one ground space of the gear tooth is exhibited at the left side. The overlapping surfaces of the ground gear tooth and the theoretical gear tooth, which is generated by the geometry theory of the face gear drive, are given at the right side of Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001070_j.mechmachtheory.2020.104127-Figure14-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001070_j.mechmachtheory.2020.104127-Figure14-1.png", "caption": "Fig. 14. Experiment: (a) DWAS test setup, (b) HUST K&C test rig, (c) camber angle, and (d) toe angle.", "texts": [ " The general trends between the experimental and simulation results are the same, although the simulation curves have some discrepancies compared with the experimental results. Fig. 13 (a) shows that the simulated curve gradient is slightly smaller than experimental result during the large compression displacement of the air spring. It is possibly due to the fitting errors of the volume and effective area from experimental data. For Fig. 13 (b)-(d), there are small error in the transitory stage. They are possibly due to fitting errors of the maximum friction forces. The parameters of the air spring and bushing are shown in Table 1 . The K&C test rig (see Fig. 14 (a)-(b)) used in this study is the suspension parameter measuring device at Huazhong University of Science and Technology (HUST) [62] . The platforms are controlled by the server systems to realize displacement or force inputs. The wheel forces and moments are measured directly through force sensors. The non-contact binocular vision system (BVS) measuring the lateral, longitudinal, and vertical motion of the wheel center along with toe angle and camber angle. Camber is the angle between the top and bottom of the tire and true vertical as viewed from the front side. Toe is the measure of how far inward or outward the leading edge of the tire is facing when viewed from the top [4] . Camber and toe angle are shown in Fig. 14 (c) and (d). The BVS consists of two cameras of the same type to track the optical targets, and one base to fix the cameras. Two cameras are parallel arranged to obtain the image of external objects. Basic parameters of the BVS fulfill the requirements, i.e., on the range and the precision of K&C test. The optical targets traced are in the binocular vision coordinate system (BVCS) and need to be transferred to the vehicle coordinate system (VCS). The BVCS is referred to O c \u2212 XY Z and the VCS is referred to O \u2212 xyz" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003743_icar.2005.1507449-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003743_icar.2005.1507449-Figure3-1.png", "caption": "Fig. 3. The LARS robot and its kinematics", "texts": [ " 2(b)) of the SLU to a modified version of the LARS - a 6-DoF robot developed at IBM [23], [24]. This robot is composed from a 3 DoF X-Y-Z stage that is serially attached to a \u201cRemote Center of Motion\u201d (RCM) mechanism. This mechanism is designed to rotate the tool tip around a fixed point in space. This is a highly desirable feature for MIS where the tool is limited to a fixed fulcrum point in the patient body. The axis of rotation of the third 4520-7803-9177-2/05/$20.00/\u00a92005 IEEE rotary joint passes through this remote point. Fig. 3 presents the LARS robot and the kinematic nomenclature used for its position analysis. The following section outlines the kinematics of the SLU and the hybrid system composed from the LARS and the SLU of Fig. 4. Section III presents our approach for high-level control to support suturing in confined spaces. Section IV describes our validation setup and presents results of our experiments. Finally, section V summarizes the results of our experiments followed by conclusions. Fig. 3 and 4 show the nomenclature of LARS and SLU respectively. In this paper we assume that the SLU is attached to the LARS such that the origin of the base disk lies along this axis. We define the following coordinate frames to facilitate further discussion of the kinematics of the system: The gripper frame {g}, end disk frame {e}, snake plane frame {s}, base disk frame {b} and the world frame {w}. Without loss of generality, we can assign the frames such that the world frame coincides with the base disk frame when all the joints are at a predefined home position" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003699_j.mechmachtheory.2006.09.004-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003699_j.mechmachtheory.2006.09.004-Figure2-1.png", "caption": "Fig. 2. Coordinate system of the leg.", "texts": [ " The results show that the simplified error is small enough to introduce a more accurate dynamic model into the real-time control system. At the same time, the dynamic simulation with the inertia of legs being negligible is also performed. The 6-UPS Stewart platform-based parallel kinematic machine (XNZ63 PKM) has six degrees of freedom, and the Stewart platform has a base and a platform connected by six extensible legs with spherical joint at one end and universal joint an the other. The prototype of XNZ63 PKM is shown in Fig. 1, and one leg is shown in Fig. 2 with the associated symbols. The base coordinate system R0 is fixed on the worktable, a moving coordinate system Rp is attached to the moving platform, coordinate systems Ru and Rd are fixed on the upper and lower parts of the leg, respectively. Ruc and Rud coordinate systems, which are parallel to R0 coordinate system, are established and their origins are the centers of mass of the upper part and the lower part of the leg, respectively. R is the rotation matrix from Rp coordinate system to R0 coordinate system, pi is the position vector of the spherical joint in Rp coordinate system, t is the position vector of the origin of Rp coordinate system in R0 coordinate system, bi is the position vectors of universal joint; ui and vi are the unit vectors of the fixed axis and the rotational axis of the universal joint, respectively; eiu and eiv are the angular accelerations of the ith leg with respect to the fixed axis and the rotational axis of the universal joint, respectively; riu0 is the position vector of the mass center of the upper part of the leg in Ru coordinate system, and rid0 is the position vector of the mass center of the lower part of the leg in Rd coordinate system" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000520_tte.2019.2959400-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000520_tte.2019.2959400-Figure6-1.png", "caption": "Fig. 6. Schematic MEC model for this SynRel motor", "texts": [ " An analytical solution based on the MEC method is applied to determine the air-gap flux density of the studied SynRel motor for any rotor position and the stator phase currents. Accuracy of the analytical results is evaluated by comparing them through the FEA simulations [21]-[32]. 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. The MEC modelling of a two-pole SynRel motor is illustrated in Fig. 6. For the sake of clarity and simplicity, the case of a two-pole machine is of concern, here. As observed in Fig. 6, the stator slotting effect is neglected while allowing the uniform air-gap width. The flux barriers are numbered from 1 to 5. The whole air-gap of the motor is subdivided into ten regions, marked as 11, 12, 21, 32, 23, 34, 43, 45, 54 and 55 by the points of the intersection of the end barriers and the outer rotor periphery. For each one of the regions, an MMF source (Fij) and an air-gap reluctance (Rgij) are defined. Moreover, the reluctances Rb1, Rb2, Rb3, Rb4 and Rb5 of the five flux barriers are defined in the MEC and analytically computed by the proposed method, as discussed earlier in section III", " 1) Calculation of MMF Sources: The overall air-gap MMF field is first defined due to the stator phase currents as a function of both time and angular position through (33) [20]: \ud835\udc39(\ud835\udc61, \ud835\udf03) = \u2211 \ud835\udc64\ud835\udc5b \ud835\udc5b=0,1,2 (\ud835\udf03) \u2219 \ud835\udc56\ud835\udc5b(\ud835\udc61) (33) where, \u03b8 is the angular position (in electrical radians) measured along the mean air-gap circumference with respect to the MMF axis of phase a winding; in is the current of each phase (n=0,1,2); and wn is the winding function of phase n, which is computed according to [20]. Once the total air-gap MMF is computed, the MMF sources of the various regions, illustrated in Fig. 6, are computed as follows: \ud835\udc3911(\ud835\udc61, \ud835\udf03\ud835\udc5f) = 1 2\ud835\udefc1\ud835\udc5d \u222b \ud835\udc39(\ud835\udc61, \ud835\udf03) \ud835\udf03\ud835\udc5f+\ud835\udefc1\ud835\udc5d \ud835\udf03\ud835\udc5f\u2212\ud835\udefc1\ud835\udc5d \ud835\udc51\ud835\udf03 (34) \ud835\udc39\ud835\udc56\ud835\udc57(\ud835\udc61, \ud835\udf03\ud835\udc5f) = 1 (\ud835\udefc\ud835\udc57 \u2212 \ud835\udefc\ud835\udc56)\ud835\udc5d \u222b \ud835\udc39(\ud835\udc61, \ud835\udf03) \ud835\udf03\ud835\udc5f+\ud835\udefc\ud835\udc57\ud835\udc5d \ud835\udf03\ud835\udc5f+\ud835\udefc\ud835\udc56\ud835\udc5d \ud835\udc51\ud835\udf03, \ud835\udc56 = 1,2, \u2026 ,4, \ud835\udc57 = \ud835\udc56 + 1 (35) \ud835\udc39\ud835\udc57\ud835\udc56(\ud835\udc61, \ud835\udf03\ud835\udc5f) = 1 (\ud835\udefc\ud835\udc57 \u2212 \ud835\udefc\ud835\udc56)\ud835\udc5d \u222b \ud835\udc39(\ud835\udc61, \ud835\udf03) \ud835\udf03\ud835\udc5f\u2212\ud835\udefc\ud835\udc56\ud835\udc5d \ud835\udf03\ud835\udc5f\u2212\ud835\udefc\ud835\udc57\ud835\udc5d \ud835\udc51\ud835\udf03 (36) where, \u03b11, \u03b12, \u03b13, \u03b14 and \u03b15 are the mechanical angles of the barrier ends with respect to the rotor q-axis. 2) Computation of air-gap Reluctances: Reluctances of the MEC are computed as follows: \ud835\udc45\ud835\udc54\ud835\udc56\ud835\udc57 = \ud835\udc45\ud835\udc54\ud835\udc57\ud835\udc56 = ( 1 \ud835\udf070 ) \ud835\udc54 (\ud835\udefc\ud835\udc57 \u2212 \ud835\udefc\ud835\udc56)\ud835\udc45\ud835\udc3f , \ud835\udc56 = 1,2, \u2026 ,4, \ud835\udc57 = \ud835\udc56 + 1 (37) \ud835\udc45\ud835\udc5411 = ( 1 \ud835\udf070 ) \ud835\udc54 2\ud835\udefc1\ud835\udc45\ud835\udc3f , \ud835\udc45\ud835\udc5455 = ( 1 \ud835\udf070 ) \ud835\udc54 ( \ud835\udf0b \ud835\udc5d \u2212 2\ud835\udefc5)\ud835\udc45\ud835\udc3f (38) where, g is the air-gap length, p is the pole-pair number, R is the mean air-gap radius and L is the core length", " To assess the accuracy of the proposed mapping application in magnetic reluctance prediction, the reluctance obtained by the FE and analytical methods are compared in Table. III. As it is illustrated, the percent error between the values of the reluctances of the 1st, 2nd, 3rd, 4th and 5th flux barrier are 31, 7.2, 5.44 and 4.5. It is obvious that the proposed mapping involves a certain degree of approximation, since the barrier segments AB and GH (Figs. 3 and 4) are modelled and approximated as elliptic segments that are not perpendicular to the hyperbolic segments of the barrier. The MEC model of Fig. 6 for each one of the poles of this motor and the reluctance network shown in Fig. 7 (a) are equivalent. The MEC can be solved through electric circuit theory analysis methods [21]-[23]. The fluxes \u04241, \u04242, \u04243, \u04244 and \u04245 passing through each one of the barriers are determined as [20], [31]-[32]: \u03a61(\ud835\udc61, \ud835\udf03\ud835\udc5f) = \ud835\udc3911 \u2212 \ud835\udc39\ud835\udc52\ud835\udc5e(\ud835\udc61, \ud835\udf03\ud835\udc5f) + \ud835\udc45\ud835\udc52\ud835\udc5e\u03a65(\ud835\udc61, \ud835\udf03\ud835\udc5f) \ud835\udc45\ud835\udc5411 + \ud835\udc45\ud835\udc4f1 \u2212 \u0394\ud835\udc392(\ud835\udc61, \ud835\udf03\ud835\udc5f) + \u0394\ud835\udc393(\ud835\udc61, \ud835\udf03\ud835\udc5f) + \u0394\ud835\udc394(\ud835\udc61, \ud835\udf03\ud835\udc5f) \ud835\udc45\ud835\udc5411 + \ud835\udc45\ud835\udc4f1 (39) \u03a62(\ud835\udc61, \ud835\udf03\ud835\udc5f) = \ud835\udc39\ud835\udc61\u210e \ud835\udc46\ud835\udc35\ud835\udc45\ud835\udc61\u210e \ud835\udc46\ud835\udc35 \u2212 \ud835\udc39\ud835\udc52\ud835\udc5e(\ud835\udc61, \ud835\udf03\ud835\udc5f) + \ud835\udc45\ud835\udc52\ud835\udc5e\u03a65(\ud835\udc61, \ud835\udf03\ud835\udc5f) \ud835\udc45\ud835\udc61\u210e \ud835\udc46\ud835\udc35 + \ud835\udc45\ud835\udc4f2 \u2212 \u0394\ud835\udc393(\ud835\udc61, \ud835\udf03\ud835\udc5f) + \u0394\ud835\udc394(\ud835\udc61, \ud835\udf03\ud835\udc5f) \ud835\udc45\ud835\udc61\u210e \ud835\udc46\ud835\udc35 + \ud835\udc45\ud835\udc4f2 (40) \u03a63(\ud835\udc61, \ud835\udf03\ud835\udc5f) = \ud835\udc39\ud835\udc61\u210e \ud835\udc46\ud835\udc36\ud835\udc45\ud835\udc61\u210e \ud835\udc46\ud835\udc36 \u2212 \ud835\udc39\ud835\udc52\ud835\udc5e(\ud835\udc61, \ud835\udf03\ud835\udc5f) + \ud835\udc45\ud835\udc52\ud835\udc5e\u03a65(\ud835\udc61, \ud835\udf03\ud835\udc5f) \ud835\udc45\ud835\udc61\u210e \ud835\udc46\ud835\udc36 + \ud835\udc45\ud835\udc4f3 \u2212 \u0394\ud835\udc394(\ud835\udc61, \ud835\udf03\ud835\udc5f) \ud835\udc45\ud835\udc61\u210e \ud835\udc46\ud835\udc36 + \ud835\udc45\ud835\udc4f3 (41) \u03a64(\ud835\udc61, \ud835\udf03\ud835\udc5f) = \ud835\udc39\ud835\udc61\u210e \ud835\udc46\ud835\udc37\ud835\udc45\ud835\udc61\u210e \ud835\udc46\ud835\udc37 \u2212 \ud835\udc39\ud835\udc52\ud835\udc5e(\ud835\udc61, \ud835\udf03\ud835\udc5f) + \ud835\udc45\ud835\udc52\ud835\udc5e\u03a65(\ud835\udc61, \ud835\udf03\ud835\udc5f) \ud835\udc45\ud835\udc61\u210e \ud835\udc46\ud835\udc37 + \ud835\udc45\ud835\udc4f4 (42) \u03a65(\ud835\udc61, \ud835\udf03\ud835\udc5f) = \ud835\udc39\ud835\udc61\u210e \ud835\udc46\ud835\udc38 \ud835\udc45\ud835\udc61\u210e \ud835\udc46\ud835\udc38 + \ud835\udc45\ud835\udc4f5 (43) where, \ud835\udc39\ud835\udc61\u210e \ud835\udc46\ud835\udc38(\ud835\udc61, \ud835\udf03\ud835\udc5f) = \ud835\udc3954 \ud835\udc45\ud835\udc5454 + \ud835\udc39\ud835\udc61\u210e \ud835\udc46\ud835\udc37\ud835\udc45\ud835\udc61\u210e \ud835\udc46\ud835\udc37 \ud835\udc45\ud835\udc61\u210e \ud835\udc46\ud835\udc37 + \ud835\udc45\ud835\udc4f4 + \ud835\udc3945 \ud835\udc45\ud835\udc5445 (44) \ud835\udc45\ud835\udc61\u210e \ud835\udc46\ud835\udc38(\ud835\udc61, \ud835\udf03\ud835\udc5f) = [\ud835\udc45\ud835\udc5454 \u22121 + (\ud835\udc45\ud835\udc4f4 + \ud835\udc45\ud835\udc61\u210e \ud835\udc46\ud835\udc37)\u22121 + \ud835\udc45\ud835\udc5445 \u22121 ] \u22121 (45) \ud835\udc39\ud835\udc61\u210e \ud835\udc46\ud835\udc37(\ud835\udc61, \ud835\udf03\ud835\udc5f) = \ud835\udc3943 \ud835\udc45\ud835\udc5443 + \ud835\udc39\ud835\udc61\u210e \ud835\udc46\ud835\udc36\ud835\udc45\ud835\udc61\u210e \ud835\udc46\ud835\udc36 \ud835\udc45\ud835\udc61\u210e \ud835\udc46\ud835\udc36 + \ud835\udc45\ud835\udc4f3 + \ud835\udc3934 \ud835\udc45\ud835\udc5434 (46) \ud835\udc45\ud835\udc61\u210e \ud835\udc46\ud835\udc37(\ud835\udc61, \ud835\udf03\ud835\udc5f) = [\ud835\udc45\ud835\udc5443 \u22121 + (\ud835\udc45\ud835\udc4f3 + \ud835\udc45\ud835\udc61\u210e \ud835\udc46\ud835\udc36)\u22121 + \ud835\udc45\ud835\udc5434 \u22121 ] \u22121 (47) \ud835\udc39\ud835\udc61\u210e \ud835\udc46\ud835\udc36(\ud835\udc61, \ud835\udf03\ud835\udc5f) = \ud835\udc3932 \ud835\udc45\ud835\udc5432 + \ud835\udc39\ud835\udc61\u210e \ud835\udc46\ud835\udc35\ud835\udc45\ud835\udc61\u210e \ud835\udc46\ud835\udc35 \ud835\udc45\ud835\udc61\u210e \ud835\udc46\ud835\udc35 + \ud835\udc45\ud835\udc4f2 + \ud835\udc3923 \ud835\udc45\ud835\udc5423 (48) \ud835\udc45\ud835\udc61\u210e \ud835\udc46\ud835\udc36(\ud835\udc61, \ud835\udf03\ud835\udc5f) = [\ud835\udc45\ud835\udc5432 \u22121 + (\ud835\udc45\ud835\udc4f2 + \ud835\udc45\ud835\udc61\u210e \ud835\udc46\ud835\udc35)\u22121 + \ud835\udc45\ud835\udc5423 \u22121 ] \u22121 (49) \ud835\udc39\ud835\udc61\u210e \ud835\udc46\ud835\udc35(\ud835\udc61, \ud835\udf03\ud835\udc5f) = \ud835\udc3912 \ud835\udc45\ud835\udc5412 + \ud835\udc3911 \ud835\udc45\ud835\udc5411 + \ud835\udc45\ud835\udc4f1 + \ud835\udc3921 \ud835\udc45\ud835\udc5421 (50) \ud835\udc45\ud835\udc61\u210e \ud835\udc46\ud835\udc35(\ud835\udc61, \ud835\udf03\ud835\udc5f) = [\ud835\udc45\ud835\udc5421 \u22121 + (\ud835\udc45\ud835\udc4f1 + \ud835\udc45\ud835\udc5411) \u22121 + \ud835\udc45\ud835\udc5412 \u22121 ] \u22121 (51) \ud835\udc39\ud835\udc52\ud835\udc5e(\ud835\udc61, \ud835\udf03\ud835\udc5f) = \ud835\udc39\ud835\udc61\u210e \ud835\udc46\ud835\udc38 , \ud835\udc45\ud835\udc52\ud835\udc5e = \ud835\udc45\ud835\udc61\u210e \ud835\udc46\ud835\udc38 (52) The terms \u0394F1, \u0394F2, \u0394F3, \u0394F4 and \u0394F5 in (39) and (40), which are the MMF drops due to the flux flowing across each one of the flux barriers, are computed as follows: \u0394\ud835\udc391(\ud835\udc61, \ud835\udf03\ud835\udc5f) = \ud835\udc45\ud835\udc4f1\u03a61(\ud835\udc61, \ud835\udf03\ud835\udc5f), \u0394\ud835\udc392(\ud835\udc61, \ud835\udf03\ud835\udc5f) = \ud835\udc45\ud835\udc4f2\u03a62(\ud835\udc61, \ud835\udf03\ud835\udc5f) (53) \u0394\ud835\udc393(\ud835\udc61, \ud835\udf03\ud835\udc5f) = \ud835\udc45\ud835\udc4f3\u03a63(\ud835\udc61, \ud835\udf03\ud835\udc5f), \u0394\ud835\udc394(\ud835\udc61, \ud835\udf03\ud835\udc5f) = \ud835\udc45\ud835\udc4f4\u03a64(\ud835\udc61, \ud835\udf03\ud835\udc5f) (54) \u0394\ud835\udc395(\ud835\udc61, \ud835\udf03\ud835\udc5f) = \ud835\udc45\ud835\udc4f5\u03a65(\ud835\udc61, \ud835\udf03\ud835\udc5f) (55) The MMF drops expressed in (53), (54) and (55) can be applied to any path crossing each one of the flux barriers, because the MMF crossing each one of the barriers is independent of the path along which it is computed" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000371_j.isatra.2017.12.023-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000371_j.isatra.2017.12.023-Figure2-1.png", "caption": "Fig. 2. Arrangement of mooring lines.", "texts": [ " The mooring system is a typical part of the turret-moored FPSO, so it is necessary to establish the model of tension force exerted on the FPSO vessel from the mooring lines. The mooring system in this paper consists of 8 chain-polyester-chain mooring lines and 4 buoyancy devices in each mooring line. Because the buoyancy of buoy is far larger than the weight itself, it can reduce the tension of lines. The mooring lines are fixed from the turret of FPSO vessel to Please cite this article in press as: Wang Y, et al., Reliability-based robust and offloading vessel with unknown time-varying disturbances and j.isatra.2017.12.023 the seabed by anchors as shown in Fig. 2. Due to the influence of buoys, the mooring lines are no longer catenary as shown in Fig. 3. However, the model of tension exerted on the FPSO vessel from the mooring lines can still be established based on the classic catenary's theory. For a mooring line, the weight is far greater than the buoyancy and fluid forces exerted on the mooring line, so the influence of buoyancy and fluid forces are ignored. Then, Fig. 4 shows the forces on a mooring line's infinitesimal elementds: In Fig. 4, uj is the mass per unit length of mooring line's sectionj;4 is the angle between the mooring line microelement and the horizontal plane, and Tis the mooring line tension" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001059_j.mechmachtheory.2020.104101-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001059_j.mechmachtheory.2020.104101-Figure4-1.png", "caption": "Fig. 4. HUMA exoskeleton\u2019s 4-bar knee joint [25] .", "texts": [ " 3 ), where a crossed 4-bar mechanism, constituting a polycentric hinge, is used to closely follow the knee\u2019s ICR trajectory. It also enables a ROM of 135 \u00b0, which is comparable with a natural human knee joint [23] . Another example is a mechanism of a biomimetic 4-bar linkage knee in a knee-ankle-foot orthosis [24] . A similar mechanism is the polycentric artificial knee joint, known as HUMA, which is based on a 4-bar mechanism as a part of a lower limb exoskeleton for weight-bearing assistance ( Fig. 4 ) [25] . An analogical mechanism is applied in a bionic leg with a magneto-rheological damper [26] , and also in the Geo-Flex knee that was designed as a friction-controlled polycentric prosthesis ( Fig. 5 ) [27] . The devices that are classified into the second group are usually adjusted to the personal characteristics of the knee joint. They include, e.g. prostheses, which need to precisely reproduce human natural movements in order to avoid inflicting discomfort. These mechanisms frequently rely on the so-called \"bionic knee\" mimicking the human joint\u2019s structure in order to accurately reproduce natural movements" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003706_j.mechmachtheory.2004.02.011-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003706_j.mechmachtheory.2004.02.011-Figure2-1.png", "caption": "Fig. 2. Parameters and variables of the unbalanced mechanism.", "texts": [ " The presented method is called adaptive balancing and is developed here for two-degree-of-freedom planar articulated open kinematic chain mechanisms. Through a performed simulation, a comparison between a mechanism using the proposed method, an unbalanced one and one only statically balanced is also provided. In this section, dynamic models are presented for two-degree-of-freedom planar articulated open-loop kinematic chain mechanisms subjected to three different conditions: unbalanced, statically balanced, and adaptively balanced. Such mechanisms are composed by three links: one fixed link\u2013\u2013base\u2013\u2013and two moving ones\u2013\u2013links 1 and 2 (Fig. 2). These links are connected by two revolute joints. This mechanical system, driven by two independent actuators, can be employed as a robot manipulator for \u2018\u2018pick and place\u2019\u2019 operations. During part of its motion cycle, the payload remains temporarily attached to link 2 through the use of a gripper. In order to introduce the equations of motion, the following parameters and variables are defined \u20181 distance between revolute joint centers in link 1 (unbalanced mechanism); \u20182 distance between revolute joint center and gripper tip in link 2; \u20181c position of the center of mass of link 1 with respect to the center of the revolute joint that connects link 1 to the base (unbalanced mechanism); \u20182c position of the center of mass of link 2 with respect to the center of the revolute joint that connects link 2 to link 1 (unbalanced mechanism); m1 mass of link 1 (unbalanced mechanism); m2 mass of link 2 (unbalanced mechanism); m0 payload mass; I1 mass moment of inertia of link 1 with respect to the center of mass of the same link (unbalanced mechanism); I2 mass moment of inertia of link 2 with respect to the center of mass of the same link (unbalanced mechanism); h1 angular displacement of link 1 relative to the base; h2 angular displacement of link 2 relative to link 1; _h1 angular velocity of link 1 relative to the base; _h2 angular velocity of link 2 relative to link 1; \u20ach1 angular acceleration of link 1 relative to the base; \u20ach2 angular acceleration of link 2 relative to link 1" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001377_012102-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001377_012102-Figure4-1.png", "caption": "Figure 4. Design diagram of the GLDITM lever circuit with a four-link single-circuit lever chain: 0 - frame; 1, 2, 3 - levers", "texts": [ " Therefore, in a comparative analysis, we take all the corresponding geometrical parameters of the mechanisms to be equal and the positions of the mechanisms to be the same. That is, d4 = d5 = d6 = d7 = d- for the mechanism in Figure 2, d6 = d7 = d8 = d9 = d - - for the mechanism in Figure 3, whered4, d5, d6, d7, d8, d9 - are the reference diameters of the corresponding gear wheels. The initial values of \u03b1 and \u03c6 in two mechanisms under consideration are the same. \u03b1 is the angle of the mechanism position, \u03c6 is the angle of the position of the levers CO3 and CO5. \u0421O3 = \u0421O5, Figure 4 shows the design diagram of the GLDITM lever circuit with a four-link single-circuit lever chain, and Figure 5 shows the design diagram of the GLDITM lever circuit with a six-link doublecircuit lever chain. We willdetermine the lever circuits and the kinematic parameters of the mechanisms depending on the velocity of the centers of rotation of the driven gear wheels (VC). The kinematic parameters were determined by the centroid method. Having determined sequentially the instantaneous centers of rotation of all lever links of the mechanisms, we obtain the angular and linear velocities of the characteristic points of the mechanism links. According to the scheme shown in Figure 4 we can write: ; 3 3 CP VC (1) ; 2 2 CP VC (2) ;22 BPVB (3) ; 1 2 21 BP BP (4) ICECAE 2020 IOP Conf. Series: Earth and Environmental Science 614 (2020) 012102 IOP Publishing doi:10.1088/1755-1315/614/1/012102 ,11 APVA (5) whereCP3, CP2, BP2, BP1are determined by ;33 LCP (6) where L3 \u2013 is the length of the lever CO3 (link 3) ; 2 cos 2 sin arcsin 2 sin 1 2 d BP d CP (7) cos1 sin2 1 arccos 3L d ; 2 cos 2 sin arcsincos 1 2 d BP d BP ; (8) )cos1(21 dBP ; (9) According to the scheme shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000931_j.mechmachtheory.2019.103595-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000931_j.mechmachtheory.2019.103595-Figure5-1.png", "caption": "Fig. 5. Three configurations of 2-PrRS + PR(P)S metamorphic parallel mechanism.", "texts": [ " Suppose the cross-sectional shape of each link is circular with a maximum diameter d and the shortest distance between the centre lines of every two links is expressed by d i , then, the condition of avoiding interference of every two links is d i > d ( i = 1 , 2 , 3) (14) The architectural parameters of the metamorphic parallel mechanism with Configuration \u2160 and \u2162 are shown in Table 1 . where, b is the length of the end link, S d 0 is the length of the linear actuator when its stroke is 0, S d is the maximum stroke of all the linear actuator, S di ( i = 1,2,3) is the value of the initial, middle, and end segments of the linear actuator stroke respectively, d c is the distance between the end of the linear actuator of PR(P)S limb and the centre line of the linear actuator of PrRS limb, and the other symbols have the same meanings as before. ( Fig. 5 .) If the endpoint of the end link is specified as the reference point of the metamorphic parallel mechanism, the workspace can be analysed by the Monte Carlo method. The random value N = 30 0,0 0 0 was taken to obtain the workspace shape, as shown in Fig. 6 a. The red point area represents the workspace of configuration I, and the blue point area represents the workspace of configuration \u2162 . For comparison, the workspace of a parallel mechanism with the same parameters but no metamorphic characteristics was analysed by the same method, as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000226_j.ab.2015.12.005-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000226_j.ab.2015.12.005-Figure8-1.png", "caption": "Fig. 8. (A) Differential pulse voltammograms obtained for human blood serum (a) and after the addition of 10 mM XN, 45 mM TP, and 20 mM CAF (b) at GC/AT/ERGO electrode in 0.2 M PBS (pH 5.0). (B) Differential pulse voltammograms obtained for human urine (a) and after the addition of 5 mM XN, 45 mM TP, and 30 mM CAF (b) at GC/AT/ERGO electrode in 0.2 M PBS (pH 5.0).", "texts": [ " Determination of XN and methylxanthines in human blood serum and urine samples The practical application of the ERGO modified electrode was demonstrated by determining the concentrations of XN, TP, and CAF in human blood serum and urine samples. The serum samples were collected from a clinical laboratory. The standard addition technique was used for the determination of XN, TP, and CAF in the serum samples. The human blood serum samples were diluted 10 times using 0.2 M PBS (pH 5.0). The differential pulse voltammogram shows an oxidation peak at 0.38 for the blood serum sample (Fig. 8A, curve a). The obtained peak may be due to the oxidation of uric acid. The commercial samples of XN, TP, and CAF were spiked to the serum solution to determine them simultaneously. After the addition of 10 mM XN, 45 mM TP, and 20 mM CAF, new oxidation peaks were obtained at 0.73,1.05, and 1.31 V, whichmight be due to the oxidation of XN, TP, and CAF, respectively (Fig. 8A, curve b). The modified electrode shows good recovery for the determination of XN, TP, and CAF in human blood serum samples (see Table S3 in supplementary material). Similar recoveries were also obtained in human urine samples diluted 50 times in PBS (Fig. 8B), and the corresponding results are summarized in Table S3. These results suggest that the ERGO modified electrode can be used for the determination of XN, TP, and CAF in real samples. The electrochemical reduction of in situ generated aminotriazine diazonium cations from melamine on GC and ITO electrodes enabled a simple and efficient grafting of aminotriazine groups (AT) in one step. The graphene precursor, GO, was attached on the melamine grafted electrode via electrostatic attraction between positively charged amine groups and the negatively charged layers of GO" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001013_fitee.1900455-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001013_fitee.1900455-Figure5-1.png", "caption": "Fig. 5 A diagram showing the foot under three states (a), the length difference between the two cables calculated", "texts": [ " The forefoot cable and heel cable work with different stroke lengths at the end-effector, while the motor axis angular velocities are the same. Therefore, a tensioning device is needed to compensate for the cable length difference. A theoretical analysis was conducted to acquire the length difference between the heel cable and the forefoot cable of our exoskeleton when a human being was walking with a normal gait. The diagram presenting the relative relation between the endeffector and the lower limb is shown in Fig. 5a. OA denotes the length from the cable go-through hole in the shank mounting to the ankle rotation center, AB is the length from the ankle rotation center to the heel, AC represents the length from the ankle rotation center to the metatarsophalangeal joint, \u03b20 is the angle between OA and AB at the standing position, and the angle between OA and AC is \u03b10. Lhc and Lfc are the lengths of the heel cable and forefoot cable, respectively. \u03b8a denotes the ankle rotation angle, as defined in Section 2.1.1, the range of which can be obtained from Fig", " The two gray lines are the cables at the heel and the forefoot. In (b), the curve can be approximated to a linear function, which can be described as y=\u22122.2131x\u22120.0601 (r2=0.999 98). In (c), the four cables used for power transmission are wound on bobbins 1, 2, 3, and 4. Bobbins 2 and 3 are clockwise winding (perspective from view A) to realize dorsiflexion, and bobbins 1 and 4 are counterclockwise winding to achieve plantarflexion. References to color refer to the online version of this figure i.e., y=\u22122.2131x\u22120.0601 (r2=0.999 98), as shown in Fig. 5b. This length difference \u0394L(\u03b8a) can be used as a reference to design the tensioning device. As shown in Fig. 5c, we constructed a cable length self-tensioning device based on the above analysis. The four cables used for power transmission are wound on bobbins 1, 2, 3, and 4. Bobbins 2 and 3 are clockwise wound (perspective from view A) to realize dorsiflexion, and bobbins 1 and 4 are counterclockwise wound to achieve plantarflexion. Each bobbin has a scroll spring S and a bearing B, and they can work together to tension the cable. For instance, springs 1S of bobbin 1 and 2S of bobbin 2 are mounted in the opposite direction" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003755_j.molcatb.2003.11.008-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003755_j.molcatb.2003.11.008-Figure1-1.png", "caption": "Fig. 1. A 3D picture, not to scale, of the core of the bioreactor. Hydraulic circuits (through which the substrate solutions are re-circulated) and the common cylinder C (containing the working solution volume) have been omitted.", "texts": [ " When possible, comparison between the catalytic behaviour of soluble and insoluble laccase will be done to know the effect of the immobilisation process on the reaction rate, with particular reference to the kinetic parameters and to the pH and temperature dependence. A three-dimensional (3D) model of our laccase has been elaborated to help the choice of the amminoacidic residues to be involved in the immobilisation method and to obtain the more useful exploitation of our catalytic membrane in non-isothermal bioreactors employed in the treatment of industrial effluents polluted by phenols. The apparatus employed, shown in Fig. 1, consists of two metallic flanges in each of which it is bored a shallow cylindrical cavity, 70 mm in diameter and 2.5 mm depth, constituting the working volume to be filled with the substrate solutions. The catalytic membrane is clamped between the two flanges so as to separate and, at the same time, to connect the solutions filling the half-cells. Solutions were recirculated in each half-cell by means of a peristaltic pump through hydraulic circuits starting and ending in a common cylinder C, not represented" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001779_s10999-021-09548-8-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001779_s10999-021-09548-8-Figure4-1.png", "caption": "Fig. 4 Singularities of this parallel manipulator", "texts": [ " Ja \u00bc $rT r;14=\u00f0$rT r;14$1d\u00de $rT r;24=\u00f0$rT r;24$2d\u00de $rT r;34=\u00f0$rT r;34$3d\u00de 2 664 3 775 3 6 ; JC \u00bc $rT r;11 $rT r;12 $rT r;13 .. . $rT r;33 2 6666664 3 7777775 9 6 Therefore, the first kind of singularities happens when the determinant of the square Jacobian matrix J is zero (Gosselin and Schreiber 2016). It is consisted of the following two scenarios: (i) z = 0. It is composed of two cases, x1 6\u00bc x2 (x1\\x\\x2 or x1 [ x[ x2, these two cases are similar, only the former case is illustrated) and x1 \u00bc x2 6\u00bc x, as depicted in Fig. 4a, b. All links are constrained in the XOY plane and the moving platform gains an uncontrollable movement along Z axis under both situations. (ii) x1 \u00bc x2. It can be further divided into two conditions, x1 \u00bc x \u00bc x2 and x1 \u00bc x2 6\u00bc x, as shown in Fig. 4c, d. It is worth noting that L2 \u00bc 0 can also result in the first classification. Under the first condition, y is also equal to y1, the mobile platform can bear any external force along Z axis without actuation forces. The other case enables the mobile platform a coupled translation in workspace when all driving joints are fully locked. The second kind of singularities occurs when the determinant of the inverse Jacobian matrix J-1 is zero. In this situation, x \u00bc x1 or x \u00bc x2. These two cases are basically x1 \u00bc x \u00bc x2 for the proposed mechanism and are discussed in (ii). The combined singularity happens when both det(J) and det(J-1) are zero, which means x1 \u00bc x \u00bc x2 denoted in Fig. 4c. Under this situation, the moving platform can experience some infinitesimal motions (e.g. a motion with _x \u00bc _y) even when three actuators are locked. The three active joints can have some infinitesimal motions while the moving platform stays in a fixed position. Such singularity configurations discussed above should be avoided in the operational workspace for any industrial application by limiting motion ranges of kinematic pairs and selecting proper links dimensions (L2[ 0). Consider the inclined links (links A2A3, A4A5, B2B3, B4B5, C2C3 andC4C5) lengths of parallelogram in each chain are constant, the constraint equations of the proposed manipulator are formulated C1 \u00bc \u00f0x x1\u00de2 \u00fe z2 L2 2 \u00bc 0 C2 \u00bc \u00f0x x2\u00de2 \u00fe z2 L2 2 \u00bc 0 C3 \u00bc \u00f0y y1\u00de2 \u00fe z2 L2 2 \u00bc 0 8>< >: \u00f013\u00de For the proposed parallel manipulator, x1\\x\\x2 is employed to avoid singularities mentioned in Sect" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001067_j.mechmachtheory.2020.104108-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001067_j.mechmachtheory.2020.104108-Figure6-1.png", "caption": "Fig. 6. Relationship of internal and external meshing phase.", "texts": [ " k ( t ) = 2 k 0 L ( \u03c4 ) (20) where, k 0 is the average mesh stiffness of helical gears per unit contact line length, L ( \u03c4 ) is the total instantaneous contact line length of gear pair, which can be calculated by \u23a7 \u23aa \u23aa \u23a8 \u23aa \u23aa \u23a9 L sp ( i ) ( \u03c4 ) = [ 1 + \u221e \u2211 k =1 ( A k cos ( 2 \u03c0k\u03c4 \u2212 \u03bbsp ( i ) ) + B k sin ( 2 \u03c0k\u03c4 \u2212 \u03bbsp ( i ) ))] L m _ sp ( i ) L rp ( i ) ( \u03c4 ) = [ 1 + \u221e \u2211 k =1 ( A k cos ( 2 \u03c0k\u03c4 \u2212 ( \u03bbrp ( i ) + \u03bbsr )) + B k sin ( 2 \u03c0k\u03c4 \u2212 ( \u03bbrp ( i ) + \u03bbsr )))] L m _ rp ( i ) (21) where \u03c4 = t/ T m , T m is meshing cycle, A k , B k and L m can be calculated by \u23a7 \u23aa \u23a8 \u23aa \u23a9 A k = 1 2 \u03b5 \u03b1\u03b5 \u03b2\u03c02 k 2 ( cos ( 2 \u03c0k \u03b5 \u03b2 ) + cos ( 2 \u03c0k \u03b5 \u03b1) \u2212 cos ( 2 \u03c0k ( \u03b5 \u03b1 + \u03b5 \u03b2 )) \u2212 1 ) B k = 1 2 \u03b5 \u03b1\u03b5 \u03b2\u03c02 k 2 ( sin ( 2 \u03c0k \u03b5 \u03b2 ) + sin ( 2 \u03c0k \u03b5 \u03b1) \u2212 sin ( 2 \u03c0k ( \u03b5 \u03b1 + \u03b5 \u03b2 ))) L m = 2 b \u03b5 \u03b1 cos \u03b2b (22) In the formula, \u03bbi is meshing phase difference of meshing pair, as shown in Fig. 6 , which can be expressed by \u23a7 \u23a8 \u23a9 \u03bbsp ( i ) = dec ( z s \u03c6\u2032 sp ( i ) 2 \u03c0 ) \u03bbrp ( i ) = \u2212dec ( z r \u03c6\u2032 rp ( i ) 2 \u03c0 ) (23) where dec indicates the fractional part, Z s , Z r are the teeth number for sun gear and ring gear, respectively. In addition, meshing phase difference between external and internal meshing pairs can be expressed by t sr = C N 2 + N 1 N 2 + N 1 D v \u03bbsr = dec ( t sr T m ) (24) where C , D denote the intersection points of base circle and the connecting line gear pair center of external and internal meshing pair, respectively, N 1 , N 2 denote the tangent line between meshing line and base circle of internal and external meshing pair, respectively, v represents the meshing speed at the meshing end face, Z p is the number of star gear teeth, \u03b1sp and \u03b1pr indicate the meshing angle of external and internal meshing pairs" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003388_978-3-662-04831-3-Figure5.24-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003388_978-3-662-04831-3-Figure5.24-1.png", "caption": "Fig. 5.24: Vector loop associated with a massless spherical- spherical link", "texts": [ " 2 I - -.-- \u2022 Pr Y M Pr Y - -.-- . r.p ' l Sllli.{Jx Sllli.{Jx x (5.35c) (5.36a) (5.36b) 218 5o Model equations of planar and spatial joints with ~= AQiLi 0 (- i;/LiR 0 ALiR 0 ARL; + c;;Li 0 c;;Li 0 ALiR 0 ARL; i LiR LiR (5o36c) 5.2.1.5 Constant-distance constraint (BB5; one constrained trans lational DOF). This building block constrains the distance (C) between two points Qi and Qj located on two bodies i and j 0 The associated constraint relation will be derived from the vector loop equation (Figure 5024) rR - rR + ARLi 0 rLi - ARL; 0 rL; + rRQ30Q, = 0 PiO P;O QiPi Q;P; . or (5o37a) - R R ARLO L; ARLi Li TQ;Qi- rP;O- Tpio + 3 0 rQ;P;- 0 rQiPi' with [( R )T ( R )] 1/2 R Lo rQ;Qi 0 rQ;Qi = lrQ;QJ = lrQ:QJ = C = constant > 00 (5o37b) This provides the constraint position equation of BB5: 0 = -C + { [rR - rR + ARL; 0 rL; - ARLi 0 rLi J T (5o38a) P;O PiO Q;P; QiPi 0 [rR - rR + ARL; 0 rL; -ARLi 0 rLi J }1/20 P;O PiO Q;P; QiPi ............... '-v-' constant constant Differentiation of (5o38a) with respect to the time yields 0 = ~ 0 2 \u00b0 (r~;Q" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003438_s0921-8890(96)00049-8-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003438_s0921-8890(96)00049-8-Figure1-1.png", "caption": "Fig. 1. The robot arm and the assignment of joint angles.", "texts": [ " Since the control is bounded, the saturation function is added to the control law above as u( t ) -- sat[u(t-) + ( G 2 B 2 ) - I ( D a + dr)It=t-]. (15) The controller in (15), unlike many other sliding mode controllers uses minimum knowledge about the plant. mate information about the input gain suffices. 218 K. Erbatur et al./Robotics and Autonomous Systems 19 (1996) 215-227 3. The manipulator Table 1 The performance of the control algorithm presented in Section 2 is checked by experimental investigations on a direct drive two d of SCARA type ann sketched in Fig. 1. The dynamical equations of this manipulator are given by the following equation: M(q)ij + V(q, (t) + F = u. (16) In this expression q is the vector of joint angles ql and q2 shown in Fig. 1. u is the torque vector applied to the joints, M is the inertia matrix, V is the vector of centripetal and Coriolis forces, F stands for Coulomb friction and M and V can be written explicitly as { Pl + 2p3 cos(q2) p2 + p3cos(q2) \"~ M(q) P2 d- P3 cos(q2) P2 } (17) { --(12(2(11 + (12)P3 sin(q2) ) V(q, (1) .=- ~ (t2p 3 sin(q2) _ ' (18) where Pl = 3.1877, P2 = 0.1168 and P3 = 0.1630. These values are obtained by considering the various mass, length and inertia parameters of the arm and the direct drive motors given in Table 1 in standard units", "/Robotics and Autonomous Systems 19 (1996) 215-227 evaluate the performance of simultaneous adaptation of two parameters. By these schemes, parameters are varied continuously. By comparison with the conservative fixed parameter sliding mode approach, it can be observed that the control with adaptation has the certain advantages. Faster convergence to desired trajectories can be obtained, without the need of off-line tuning of control parameters and independent of the reference signal. Fig. 4 demonstrates the idea under the adaptation schemes for C and D matrices. The slopes of the sliding lines in Fig. 1 are varied by considering the absolute position error. The tracking performance of the sliding controller depends highly upon the value of the sliding line slope. A large value for the sliding line slope ensures good tracking performance but too large slope can cause instability. By increasing slope when the absolute error gets small, good tracking can be achieved without causing overshoot or instability. This will be carded out by fuzzy rules. The D parameter adaptation idea is illustrated on the fight-hand side in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003242_s0094-114x(00)00003-3-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003242_s0094-114x(00)00003-3-Figure8-1.png", "caption": "Fig. 8. 3-RPS spatial manipulator.", "texts": [ " For the case of the 3-PRPS hybrid manipulator, if we consider the redundant version with two extra actuators in an additional leg, we can observe that the singular and non-STLC regions are greatly reduced. This can be seen by comparing Figs. 4 and 7. In this case the force transformation matrix will be of size (6 8) and the singular regions will be the intersections of two hyper-surfaces of order 3. Numerical simulation for this mechanism were done for the parameters listed in Appendix A and results obtained for constant orientation of the output platform and at particular sections in Z-direction are shown in Fig. 7. The 3-RPS spatial manipulator shown in Fig. 8 has six output variables (three position coordinates and three orientation co-ordinates for the moving platform) and it has three degrees of freedom with three actuated prismatic joints. All the other revolute and spherical joints are passive. In this manipulator, the six output variables are not independent. The equations of motion for the 3-RPS manipulator are six second-order di erential P. Choudhury, A. Ghosal /Mechanism and Machine Theory 35 (2000) 1455\u00b114791470 equations and three algebraic constraints" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000027_s00170-016-9596-y-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000027_s00170-016-9596-y-Figure8-1.png", "caption": "Fig. 8 Contour plots of the interactive effect between laser power and scanning speed on the shrinkage ratio in Z-direction. a Layer thickness = 0.02mm. b Layer thickness = 0.03 mm. c Layer thickness = 0.04 mm", "texts": [ " The liquid phase is helpful to improve the metal liquid wetting effect between neighbor layers and thus fills pores effectively [30], thereby reducing the amount of pores in the as-processed parts. Besides, a higher energy input also causes intense evaporation in the molten pool [31]; on the one hand, it reduces the material in molten pool, thus reduces the dimensions of the processing track; on the other hand, the intense metallic vapor blow away the non-molten powder around the molten pool, forming a powder-free zone [28]. So there would be not enough powder remained for the next track, thereby, reducing the dimensional size of tracks to some extend. The contour plots in Fig. 8 depicts the interactive effects of laser power and scanning speed on the shrinkage ratio in Zdirection (layer thicknesses of 0.02, 0.03, and 0.04 mm, respectively). The general trend was that the response increases with the increasing laser power and decreasing scanning speed, but it seems that there is no recognizable range. When layer thicknesses are 0.02, 0.03, and 0.04 mm, the maximum shrinkage ratios are 2.7, 2.8, and 3.0 %, respectively, while the minimum shrinkage ratios arise in the ranges of laser power 90 W and scanning speed 700 mm/s; they are 2" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003684_ias.1992.244291-Figure13-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003684_ias.1992.244291-Figure13-1.png", "caption": "Fig. 13 Variable Reluctance Motor with Two Full Pitch Windings", "texts": [ " Certainly the results of high speed operation are close to the reality because the motors are less saturated in high speed operation. At Wisconsin, a nonlinear model is presently being developed for more accurate performance prediction. A drive system employing the new motor is being built and the measured comparisons between the performance of the two motors will be reported in the near future. VI. FUTURE RESEARCH The authors believe that research on the type of motor drives described in the paper is just beginning. For example, an extension of the concept proposed in this paper is shown in Fig. 13. the authors have proposed another motor which have two full pitch windings and two short pitch windings. The operating principles are similar to those of the motor shown in Fig. 2. The advantage of the second motor over the ACVRM described in this paper is that the slot utilization is better. The authors are conducting research on the motor shown Fig. 13 and the results will also be presented in another paper. In addition to the research mentioned above the 1, Additional converter topologies, including soft switching converters. 2. Torque ripple control. 3. Design optimization. 4. Elimination of position sensor. authors are working in the following areas: VII. CONCLUSIONS A new concept is proposed in this paper to solve the problems associated with the energy stored in the magnetic field in conventional VRMs. By retaining and utilizing the ficld energy within the machine by utilizing commutation windings, the new motors are free from current commutation problem and excitation penalty normally associated with variable reluctance motors" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000851_tia.2019.2961878-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000851_tia.2019.2961878-Figure1-1.png", "caption": "Fig. 1. (a) Schematic diagram of three-phase IPMSM with ITSF in phase-A. (b) Magnetic flux distribution in healthy and shorted winding of phase-A.", "texts": [ " The effect of ITSF on the motor operation, input/output parameters, and efficiency is analyzed using various modeling techniques. Accuracy always remains the main concern while modeling the highly nonlinear characteristic of the faulty machine. FEM-based fault modeling ensures high accuracy compared to other methods, such as field reconstruction, equivalent circuit, and FEM assisted linear machine models [10]. The equivalent circuit diagram of an IPMSM with short circuit winding in phase-A is demonstrated in Fig. 1 (a). The faulty phase is divided into healthy coils ah and faulty coils af having a resistance of Rah and Raf, respectively. The rest of the phases are modeled as single-coils with phase winding resistance (Rb,c), selfinductance (Lxx), mutual-inductance (Mxx), and the three-phase back EMFs (eabc), respectively. The induced voltage in the shorted windings (eaf) is directly related to the rotor speed and the severity of the fault. The severity of the fault \u00b5 is determined by the ratio of shorted turns Ns to the total number of turns per phase Nt", " The fault resistance is the combination of the contact resistance (Rf) and the shorted winding resistance (Raf). A large circulating or fault current if, flows through this loop which endangers the integrity of the entire system. The three-phase back-EMFs are given in (2), where \u03a6PM is the linkage flux of PM, \u03c9e is the rotor angular speed, and \u03b8e is the position of the motor. (1 ) sin( ) sin( ) sin( 2 / 3) ( 2 / 3) ah e PM e af e PM e e PM eb e PM ec e e e e (2) The magnetic flux distribution in healthy and faulty winding turns is demonstrated in Fig. 1(b) where circulating current and input-current are in the opposite phase. Thus, it generates an inverse magnetic field in the faulty slot, which opposes the main flux and consequently, the magnetic flux density of the faulty tooth reduces, while the rest of the teeth in the same phase become saturated. This phenomenon is depicted in Fig. 2 for our benchmark IPMSM with ITSF in A2 tooth. 0093-9994 (c) 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001278_j.mechmachtheory.2020.103865-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001278_j.mechmachtheory.2020.103865-Figure5-1.png", "caption": "Fig. 5. (a) Positions where the motor interferes with the left limb and the right limb, respectively, (b) the left limit, (c) the right limit.", "texts": [ " h min = h p + r 10 = \u221a r 8 2 \u2212 r 9 2 + r 10 (18) where r 8 and \u03d52 can be solved by cosine theorem according to r 3 , r 5 and r 7 . r 8 = \u221a r 7 2 + ( ad + r 2 ) 2 \u2212 2 cos ( 3 \u03c0 2 \u2212 \u03d5 2 ) r 7 ( ad + r 2 ) \u03d5 2 = a cos ( ( a \u2212 r 3 ) 2 + r 7 2 \u2212 r 5 2 2 ( a \u2212 r 3 ) r 7 ) (19) Thus, the motion range in the direction of axis z can be used as one of the evaluation indicators, as shown below. f 1 = h max \u2212 h min (20) The swing range of the robot along axis y is more closely related to the dimensional parameters of the series structure. As shown in Fig. 5 below, plane PL of moving platform is kept parallel to the coordinate plane yB 0 z . And then the distance between left and right limit points C 4 \u2032\u2032 and C 4 in the direction of axis y is taken as objective f 2 . Because of the symmetry of the structure, the dotted and solid parts in Fig. 5 are the left and right limit positions of the robot motion, respectively. Therefore, the lengths of lines A 0 C 3 and A 0 C 3 \u2032\u2032 are symmetrically equal, both equal to d ; the lengths of lines C 2 C 3 and C 2 \u2032\u2032 C 3 \u2032\u2032 are also symmetrically equal to e ; the angles B 1 A 1 A 2 and \u2220 B 2 A 2 \u2032\u2032 A 1 \u2032\u2032 are symmetrically equal, which are defined to be \u03d50 . Define the two symmetrically sharp angles formed by lines A 1 A 2 and B 1 B 2 , lines A 1 \u2032\u2032 A 2 \u2032\u2032 and B 1 B 2 both to be \u03d53 . Define the length of the limb to be q when interference occurs" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003925_tmag.2005.846262-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003925_tmag.2005.846262-Figure2-1.png", "caption": "Fig. 2. Mesh partition. (a) M-model. (b) K-model.", "texts": [ " To build the model for the simulation, the properties of the material used in the actual motor are loaded. The properties and characteristics of interest in this work are presented as follows. For M-model, 1.5 kW, 200 V, 50 Hz, 6.8 A, 4 poles, number of stator slots: 36, number of rotor slots: 44, and one slot-pitch skewing (see Fig. 1). For K-model, 100 V, 50 Hz, 4 poles, number of stator slots: 24, number of rotor slots: 34, stator winding: 66 turns, rotor bar: aluminum, and no skewing [4]. The models were created using a triangular mesh with 13 665 elements and 6907 nodes for the M-model [see Fig. 2(a)]. For the M-model, these numbers are 14 498 elements and 7333 nodes [see Fig. 2(b)]. The values obtained for the aluminum relative conductivity are for the K-model, and for the M-model. 0018-9464/$20.00 \u00a9 2005 IEEE Fig. 3 shows the measured and calculated torque and current. We can find a good agreement for the K-model and some error around 1400 min for the M-model. Here, we discuss the reason for this error. First of all, since the measured mechanical loss is 0.11 N m, it is not the reason for this error. The M-model has skewing and a stronger degree of magnetic saturation than the K-model" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003485_1.1430673-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003485_1.1430673-Figure2-1.png", "caption": "Fig. 2 \u201ea\u2026 Race finite element\u00d5ball model and \u201eb\u2026 single element with deflections", "texts": [ ", where deflection of the bearing is a result of deformation only at the ball-race contacts. However, the assumption that the inner race is rigid does not apply in auxiliary bearing applications since it is not mounted on the rotor. To calculate inner race deformation and load distribution G j I/W , a finite element model is introduced. The model uses an assemblage of beam elements, the number of which is an integer multiple of the number of balls. Element nodes are chosen to coincide with ball contact points as depicted in Fig. 2~a! so that the effect of ball reaction forces can be included through a force distribution matrix. For element nodal displacements ordered as @wy j ,wu j ,wx j ,wy j11 ,wu j11 ,wx j11# ~shown in Fig. 2~b!!, the stiffness matrix for a single inner race element is k5 EI l3 3 12 6l 0 212 6l 0 6l 4l2 0 26l 2l2 0 0 0 Al2/I 0 0 2Al2/I 212 26l 0 12 26l 0 6l 2l2 0 26l 4l2 0 0 0 2Al2/I 0 0 Al2/I 4 . (1) ology y.asmedigitalcollection.asme.org/ on 01/28/2016 Term Here E, A, I, and l are the race element Young\u2019s modulus, crosssectional area, second moment of area and length respectively. The individual element stiffness matrices are combined by considering the superposition of forces at the nodal positions of each element to give an overall race stiffness matrix K" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003594_ja0108988-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003594_ja0108988-Figure2-1.png", "caption": "Figure 2. Stick model of the catalytic triad of serine proteases with acetate hydrogen bonded to the N\u03b4-H position of imidazole. The circle identifies the substitution site in the model calculations. The charge relay was modeled for the same set of hydrogen bond partners as the iron porphine system. The model structure represents the Asp-His-Ser molecular charge relay hypothesized to account for the reactivity of serine proteases.", "texts": [ " Our approach to modeling the spectra is to use DFT to calculate vibrational spectra and potential energy surfaces for a series of trans imidazoles and imidazolates in the ironporphine-CO adduct shown in Figure 1. Figure 1 shows aspartate hydrogen bonded to the imidazole at the N\u03b4-H position. A series of hydrogen bond donors given in Table 1 were compared in order to systematically modulate the charge density on the iron. The genesis of this model is the well-studied hydrogen-bonding of Asp235 to His175 in cytochrome c peroxidase.2 This hydrogen-bond pattern presents a catalytic triad of Asp-His-Fe in peroxidases analogous to the Asp-HisSer of serine proteases shown in Figure 2. A similar motif appears in a number of enzymes, including cysteine proteases and even selenocysteine proteases and peroxidases.33,34 In the hydrolytic enzymes, the role of Asp in the triad is to increase the basicity of the imidazole ring of histidine. The \u03c3-donor strength of the histidine in turn polarizes the nucleophilic ligand (serine, cysteine, or selenocysteine) by increased hydrogen bond strength.33,34 Our study investigates the role of both \u03c3-bonding and \u03c0-bonding induced by a change in electron density on the imidazole ligand trans to bound CO. These effects are compared to a model for charge relay in serine proteases, the catalytic triad Asp-His-Ser shown in Figure 2. One significant difference between the proteases and peroxidases is the presence of the heme (here modeled by porphine). The effect of altered electron density at the heme iron is complicated by equatorial (cis) effects on the porphine ring due to changes in the iron core size. This effect is key to the effects of various proximal ligands or changes in the basicity of the imidazole of globins and peroxidases. The goal of this theoretical study is to understand the information presented by the correlation of vibrational frequencies of the \u03bdFe-CO and \u03bdCO stretching modes and the core size marker modes that consist of non-totally symmetric modes \u03bd10 and \u03bd11 as well as totally symmetric modes \u03bd2 and \u03bd3. We consider the functional relevance of \u03c3-bonding as it affects both trans and cis \u03c0-bonding by expansion of the iron core. The analogy between Asp-His-Ser and Asp-His-Fe is examined in light of the differences in \u03c0-bonding in the two systems. The extent of hydrogen bonding or deprotonation at N\u03b4 on the basicity at N\u03b5 in the Asp-His-Ser system shown in Figure 2 determines the relative energy of the N\u03b5 lone pair that is (14) Ramsden, J.; Spiro, T. G. Biochemistry 1989, 28, 3125-3128. (15) Ray, G. B.; Li, X.-Y.; Ibers, J. A.; Sessler, J. L.; Spiro, T. G. J. Am. Chem. Soc. 1994, 116, 162-176. (16) Lim, M.; Jackson, T. A.; Anfinrud, P. A. Science 1995, 269, 962- 965. (17) Laberge, M.; Vanderkooi, J. M.; Sharp, K. A. J. Phys. Chem. B 1996, 100, 10793-10801. (18) Anderton, C. L.; Hester, R. E.; Moore, J. N. Biochim. Biophys. Acta 1997, 1338, 107-120. (19) Phillips, J", " Peptidases Immune Funct. Dis. 2000, 477, 241-254. (34) Arthur, J. R. Cell. Mol. Life Sci. 2000, 57, 1825-1835. involved in a hydrogen bond with the serine hydroxyl group. For serine proteases, this hydrogen bonding interaction results in greater electron density on the catalytic serine nucleophile. Despite these differences, strong similarities emerge from the DFT calculations. One of the major similarities of the two systems that will emerge from our study is that the charge density on the oxygen atom of methanol (Figure 2), the terminal oxygen of bound carbon monoxide, or bound dioxygen (Figure 1) increases as a result of N\u03b4-H hydrogen bonding. Moreover, the serine O-H, porphine Fe-CO bond, and C-O bonds are all three weakened by increasing polarization of the imidazole in the relay. This polarization is transmitted through both \u03c3and \u03c0-effects, and our hypothesis is that the \u03c0-effect is required to achieve the type of reactivity found in peroxidases. The charge density on dioxygen increases, and the O-O bond becomes more dipolar", " Thus, equatorial and distal effects may be the principal explanation for the observed \u03c0-back-bonding correlation. Given the wealth of mutants available in the peroxidase and globin protein families it should be possible to use DFT methods to determine the relative extent of distal, proximal and equatorial contributions to the observed experimental correlation between \u03bdFe-CO and \u03bdCO. Electrostatic Correlations. In the catalytic triad of serine proteases, the effect of the charge relay is an increase in the nucleophilicity of the serine -OH group (shown as methanol in the model system) in Figure 2. The increase in the negative Mulliken charge on the serine oxygen can be seen in Table 9. Note that the negative charge on O increases proportionally to the charge on N\u03b5. The charges follow a trend consistent with a dominant contribution from \u03c3-bonding by N\u03b5 that is further corroborated by the hydrogen bonding potential energy surfaces presented below. The charge relay mechanism results in an increase in electron density on the terminal oxygen of iron-bound oxy or peroxide. The charge distributions calculated in Tables 10 and 11 using Mulliken charges support these expected trends in the ironporphine-O2 and iron-porphine-CO models", " Thus, the porphine ring is an essential mediator of the \u03c0-back-bonding effect and serves to permit a simultaneous weakening of both Fe-C and C-O bonds. The \u03c0-bonding effect more than compensates for the \u03c3-antibonding effect on the Fe-C bond, and this bond actually increases in parallel with the C-O bond length as seen in Tables 2 and 3. These predicted trends agree with calculated bond length and frequency trends and with the experimental trends in the C-O stretching frequency. Potential Energy Surfaces for the Effect of Hydrogen Bonding of Imidazole in a Charge Relay Mechanism. The Asp-His-Ser catalytic triad of serine proteases shown in Figure 2 has been studied in terms of the hydrogen bond between the serine oxygen (methanol in the model) and histidine N\u03b5 (imidazole in the model). In Figure 4, the potential energy surface for hydrogen along a CH3O-H\u201a\u201a\u201aIm f CH3O-\u201a\u201a\u201aHIm coordinate in the catalytic triad is plotted as a function of the distance from the oxygen nucleus. Stronger hydrogen bonding to N\u03b4\u2220H leads to greater basicity of N\u03b5 as indicated by the trend in the Mulliken charge in Table 9. The negative charge on the imidazolate of the IMA model shows the greatest change in electron density of N\u03b5 as well as the greatest stabilization of the hydrogen atom in the N\u03b5\u201a\u201a\u201aH-O hydrogen bond (\u224851 kcal/mol relative to methanol)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000936_j.mechmachtheory.2019.103607-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000936_j.mechmachtheory.2019.103607-Figure8-1.png", "caption": "Fig. 8. (a) Flowchart for calculating the generalized forces of a specific beam element in the global frame, schematic presentation of the helical gear-shaft model: (b) flexible beam elements based on the Lagrangian formulation, (c) fixed, (d) revolute and (e) cylindrical joints.", "texts": [ " (23) This section focuses on the modeling of shaft, which is modeled by the beam elements to improve the computational efficiency, and its connection with the gear. In this section, the 3D geometrically exact beam theory [48\u201353] is employed to simulate the dynamic behavior of shafts. In 3D geometrically exact beam theory, the objectivity of strain measures is a key issue [48\u201352] , which is guaranteed by the local frame that is introduced in each beam element. For example, for the beam element shown in Fig. 8 (b), the local frame is defined as follows. The origin O of the local frame is identical to that of the global frame, and its three base vectors coincides with those of the body-attached frame of node 1 of the beam element. The computational flowchart to obtain the generalized forces for each beam element is given in Fig. 8 (a). For the sake of simplicity, all the formulations in the subsequent sections are given in the local frame. As shown in Fig. 8 (b), the shaft is meshed into a number of Timoshenko beam elements. The deformations of shaft are described in terms of a family of its planar cross-sections ( e i 1 , e i 2 , e i 3 ) and centroids r i ( i = 1 , . . . , N, N is the number of beam nodes), which form a 3D complicated curve. Due to the effect of shear stresses, the cross-sections of Timoshenko beam are not necessarily perpendicular to the axis of centroids. A typical two-node Timoshenko beam element is shown in Fig. 8 (b). For an arbitrary node of the element, its position is denoted by the vector r , and the orientation of its cross-section is described by three base vectors e 1 , e 2 , and e 3 , which are the functions of rotation vector \u03d5, see Eq. (9) . Therefore, the generalized coordinates for a typical two-node element are expressed as q e = [ q T 1 q T 2 ]T = [ r T 1 \u03d5 T 1 r T 2 \u03d5 T 2 ]T . (24) where q i = [ r T i \u03d5 T i ] T are the generalized coordinates of node i (i = 1 , 2) . For an arbitrary point P within the given element, its location r and rotation vector \u03d5 can be calculated using Lagrangian interpolations, r = N 1 r 1 + N 2 r 2 = [ N 1 I 3 \u00d73 0 3 \u00d73 N 2 I 3 \u00d73 0 3 \u00d73 ] q e = N r q e , (25) \u03d5 = N 1 \u03d5 1 + N 2 \u03d5 2 = [ 0 3 \u00d73 N 1 I 3 \u00d73 0 3 \u00d73 N 2 I 3 \u00d73 ] q e = N \u03d5 q e , (26) where N i (i = 1 , 2) are the shape functions N 1 (\u03be ) = 1 \u2212 \u03be , N 2 (\u03be ) = \u03be , \u03be = s P \u2212 s 1 s 2 \u2212 s 1 \u2208 [0 , 1] , (27) s 1 and s 2 are the arc-length coordinates of node 1 and node 2, respectively", " Based on the principle of virtual work, the generalized inertial and elastic forces of the Lagrangian beam element can be obtained as [45] Q iner = Q t + Q r = \u2212\u03c1AL [\u222b 1 0 [ ( N r ) T N r ] d \u03be ] q\u0308 e \u2212 \u03c1L \u222b 1 0 { ( N \u03d5 )T H [ J \u02d9 \u03c9\u0304 L + \u03c9\u0304 L \u00d7 ( J \u0304\u03c9 L ) ]} d \u03be , (33) Q elas = \u2212L \u222b 1 0 [ ( \u2202 \u0304\u03b3 L \u2202q e )T \u0304L + ( \u2202 \u0304\u03baL \u2202q e )T M\u0304 L ] d \u03be , (34) which have to be transformed back to the global frame to assemble into the dynamics equations of the whole system. The connections between the helical gear and shaft or the shaft and the ground are modeled by joints, which are described with algebraic constraint equations mathematically. To couple the 3-DOF solid elements for the gear and the 6-DOF beam elements for the shaft, MPC is used to tie the entire inner-surface FE nodes of the hole to the 6-DOF floating frame of the gear. As shown in Fig. 8 (c), 0-DOF fixed joint is used to connect the helical gear and shaft, which prevents the relative movement. I- and J-markers denote the centers of the shaft and the gear, respectively, which are locked together. The six constraint equations are given as r I \u2212 r J = 0 , x T I z J = 0 , y T I z J = 0 , x T I y J = 0 , (35) where r I = [ x I y I z I ] T and r J = [ x J y J z J ] T are the positions of the I- and J-markers, respectively. A I = [ x I y I z I ] and A J = [ x J y J z J ] are the rotation matrices that represent the orientation of the I-marker and J-marker, respectively. As shown in Fig. 8 (d), the 1-DOF revolute joint between the end of shaft and ground only allows relative rotational displacement and five constraint equations are given as r I \u2212 r J = 0 , x T I z J = 0 , y T I z J = 0 . (36) As shown in Fig. 8 (e), the 2-DOF cylindrical joint between the end of shaft and ground only allows relative translational and rotational displacement and four constraint equations are given as x I \u2212 x J = 0 , y I \u2212 y J = 0 , x T I z J = 0 , y T I z J = 0 . (37) The relative rotational motion in the revolute and cylindrical joints can be eliminated by applying a motion constraint \u02d9 \u03b8 \u2212 \u03c9 0 = 0 , \u03b8 = tan \u22121 ( x T I y J x T I x J ) . (38) Predicting the contact forces between meshing teeth accurately and efficiently is necessary for the reliable simulation of helical gear dynamics, which involves the following two steps, (i) the contact detection and (ii) the evaluation of the contact forces" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001270_j.conengprac.2020.104340-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001270_j.conengprac.2020.104340-Figure1-1.png", "caption": "Fig. 1. (a) 3-D modeling of the proposed electromagnetic system and a 50 mm-diameter spherical workspace with a singularity-free field and force generation in the three green planes; singularity-force control occurs in the red areas. Calculated currents for field and force control in three basic planes (b) xy, (c) yz, and (d) zx. Calculated current and force control in the (e) out-of-plane direction, where \ud835\udefc = 45\u25e6, \ud835\udf03 = [0\u25e6, 360\u25e6], \ud835\udc35 = 30 mT, and \u2207\ud835\udc35 = 0.3 T/m.", "texts": [ " Section 4 details the achievable workspace dimensions, mechatronic component design, and system characterization. Section 5 analyzes the performance of the proposed control method in the autonomous control mode. Finally, the conclusions are presented in Section 6 and highlight the limitations and potential applications of the proposed method. The stationary EMA developed in this work consists of six electromagnetic air-filled coils in which each pair of coils is placed along three mutually perpendicular axes in Cartesian coordinate as shown in Fig. 1(a). Two circular coils (CHCx1, CHCx2) and four square coils (SHCy1, SHCy2, SHCz1, SHCz2) are fixed in pairs according to the Helmholtz coil configuration to generate an adequate magnetic field and gradient magnetic field. Square coils are placed inside the circular coils to maximize the ROI (50 \u00d7 50 \u00d7 50 mm3). The coil system specifications are shown in Table 1. At an arbitrary point P in the workspace of the stationary airfilled coil system, the magnetic field generated by each electromagnetic source, \ud835\udc35\ud835\udc5a (\ud835\udc43 ), can be precomputed individually and then linearly superposed", " (8) becomes \ud835\udc56 = C\u2020 (\ud835\udc40,\ud835\udc36)\ud835\udc37 (9) where the unit-current matrices B (\ud835\udc36), \ud835\udf15B\ud835\udc65(\ud835\udc36), \ud835\udf15B\ud835\udc66(\ud835\udc36), and \ud835\udf15B\ud835\udc67(\ud835\udc36) are obtained from the FEM model using COMSOL Multiphysics software (AC/DC module and Mathematics module). The coil\u2019s parameters such as size, turns, are provide in Table 1. The developed model is meshed with 470,363 tetrahedral elements that guarantee its convergence. The proposed coil system in this study has an orthogonal six coil configuration and aims to generate a singularity-free field for force control in the three basic planes depicted in Fig. 1(b)\u2013(d), corresponding to the three green planes shown in Fig. 1(a). Force-based position control of the object\u2019s orientation out-of-these planes (red areas in Fig. 2(a)) causes a rank-deficient problem when calculating the applied currents based on a pseudo-inverse function of the actuation matrix C (\ud835\udc40,\ud835\udc36) in Eq. (9). Decomposition of the 6 \u00d7 6 matrix C can be written as: C = 6 \u2211 \ud835\udc56=1 \ud835\udc62\ud835\udc56\ud835\udf0e\ud835\udc56\ud835\udc63 \ud835\udc47 \ud835\udc56 (10) where the left and right singular vectors \ud835\udc62\ud835\udc56 and \ud835\udc63\ud835\udc56 are orthonormal and the singular values \ud835\udf0e\ud835\udc56 are nonnegative numbers that follow the relationship \ud835\udf0e1 \u2265 \ud835\udf0e2 \u2265 \u22ef \u2265 \ud835\udf0e6 \u2265 0. The pseudoinverse of C is given by: C\u2020 = 6 \u2211 \ud835\udc56=1 \ud835\udf0e\u22121\ud835\udc56 \ud835\udc63\ud835\udc56\ud835\udc62 \ud835\udc47 \ud835\udc56 (11) Because the actuation matrix is rank-deficient, no unique solution is available for Eq. (9) as the matrix C contains very small singular values that are almost zero at some specific posture of the microobject. Division of the tiny singular values results in a severe increase in the solution of Eq. (9) with a physically higher current input to the responding coil. Fig. 1(e) illustrates the orientation-dependent singularities observed when the control direction of the magnetic object is out of the three basic planes. The regularization method has been widely used in engineering and sciences for solving the linear and non-linear ill-posed problems, such as electrical impedance tomography (Nasehi Tehrani et al., 2012), image restoration (Gu & Gao, 2009), retrieval of aerosol size distributions from multi-wavelength lidar data (B\u00f6ckmann, 2001), depth estimation (Lee, Choi, & Hwang, 2020), etc" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003207_robot.1993.291930-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003207_robot.1993.291930-Figure4-1.png", "caption": "Figure 4: Schematic of the mobile manipulator.", "texts": [ " In this subsection, we present the control algorithm for the LABMATE mobile platform. The theoretic formulation of general nonholonomic systems and its application to the LABMATE are described in [2311, which is closely related to the work in [4, 6, 14, 171. The LABMATE platform has two driving wheels (the center ones) and four passive support.ing wheels (the corner ones). The two driving wheels are independently driven by two DC motors, respectively. The following notations will be used in the derivation of the kinematic equations (see Figure 4). The derivation for the LABMATE presented here is somewhat different and simplified from the one described in [23] due to the physical limitations of the mobile plat,form. Po: Pc: Pb: Pr: d : the intersection of the axis of symmetry with the driving wheel axis; the center of mass of the platform; the location of the manipulator on the platform the reference point to be followed by the mobile plat form; the distance from Po t o Pc; There exists one nonholomic constraint, which reflects the fact that the platform must move in the direction of the axis of symmetry, i ", " Therefore, trajectory trackin of a point on the wheel axis includin Po is not possi%le as pointed out in [17]. This is clearfy due to the presence of nonholonoinic constraints. Choosing x: not equal to -d , we may decouple and linearize the system. The nonlinear feedback for achieving input-output linearlization as well as input-output decoupling is then given by [23]: U = @-'v (10) The linearized and decoupled subsystems are described by: Yl = v1 Yz = v2 3.3 Motion planning Let Bi and Li , i = 0, 1 ,2 , be the joint angles and the link lengths of the manipulator as shown in Figure 4. Also let the coordinates of the manipulator base with respect to the platform frame X c - Y e be denoted by (xi, 9;). We choose the preferred configuration of the manipulator that maximizes the manipulability measure as stated earlier. If we specify the position of the end point as the desired trajectory for the reference point, the mobile platform will move in such a way that the manipulator is brought into the preferred configuration. The manipulability measure is defined as PI w = ddet(J(8)JT(0)) (13) where 6 and J ( 0 ) denote the joint vector and Jaco- bian matrix of the manipulator", " Also notice that we do not assume any specific type of contact although a rolling contact will be preferred in our future work We apply the following explicit force control law3. There is an extensive literature regarding force control [l, 5, 9, 8, 12, 201.. The integral control was chosen due to its characteristics of a zero steady state error and a low-pass filter when a small gain is used [3, 20 . contact and avoid bounces and vibrations especially if the contact surface is rigid [la]. [181. The active damping term is effective to achieve stab / e where: { H ) = the hand coordinate system (see Figure 4) []ifp] and [ l < > : 1 \ufffd R b sin \ufffd 1 2 \u03b3 \ufffd\ufffd2 1 R2 9 > = > ; (5) The situation of the flow pattern is more complex for a spiral bevel gear. For being convenient to study, the force exerted by the flow on any elemental helical gear (see Fig. 4) is represented in differential form. Some assumptions come from Akin and Ville [10,40]\u2014namely, the air flow impinging on a tooth is deflected by the previous tooth along the direction of rotation, which approximately limits the active tooth surface by a line from the leading edge of the next tooth to the tip corner on the trailing edge of the previous tooth (Fig. 5). The following assumptions are retained: \ufffd Permanent flow; \ufffd Friction forces between fluid and tooth flanks are negligible; \ufffd Inertia forces are ignored; \ufffd Homogeneous pressure in the environment. On the basis of the Newton equation, the differential force is expressed as: dF\u00bc \u03c1UdQ (6) with: \ufffd \u03c1: density of the fluid [kg/m3]; \ufffd dQ: differential of fluid flow [m3/s]; \ufffd U: fluid flow rate [m/s]. The projections on the axis (OX and OY) in the OXY coordinate system (Fig. 4) is given as follows, respectively", " The friction forces are negligible and the ambient pressure is homogeneous, the equation of velocities is presented: U0 \u00bcU1 \u00bc U2 (9) The projection on the axis (O\u2019t) in the reference system (O\u2019nt) is put forward: \u03c1U0 sin \u03b2 0 dQ0 \u00fe \u03c1U1dQ1 \u03c1U2dQ2 \u00bc 0 (10) And: dQ0 \u00bc dQ1 \u00fe dQ2 (11) So: dQ1 \u00bc 1 2 \u00f01 sin \u03b2 0 \u00dedQ0 (12) dQ2 \u00bc 1 2 \u00f01\u00fe sin \u03b2 0 \u00dedQ0 (13) Substitute Eq. (12) and Eq. (13) into Eq. (7), it obtains: dFx\u00bc \u03c1U0 1 sin2 \u03b2 0\ufffd dQ0 (14) With: U0 \u00bc\u03c9 h r0a x 2 i dQ0 \u00bcU 0xdb\u00bc\u03c9 h r0a x 2 i xdb X. Zhu et al. Tribology International 146 (2020) 106258 x \u00bc r 0 a\u00f01 cos \u03c6\u00de: x: active tooth length as defined in Fig. 5 [m]. r0a: outside radius [m]; r0a\u00bc r0 \u00fe h* a\u00fe x1 \ufffd cos\u03b4\u22c5r0 Z h* a: addendum coefficient; x1: modification coefficient; b: width of the spiral bevel gear [m]; \u03c9: rotational speed of the spiral bevel gear [rad/s]. \u03c6 \u00bc \u03c0 Z 2 inv\u03b1p inv\u03b1A \ufffd 8 > >< > >: inv \u03b1P\u00f0\u03b4; \u03b4b\u00de \u00bc 1 sin\u03b4b arccos cos \u03b4 cos\u03b4b arccos tan\u03b4b tan \u03b4 inv \u03b1A\u00f0\u03b4a; \u03b4b\u00de \u00bc 1 sin\u03b4b arccos cos\u03b4a cos\u03b4b arccos tan\u03b4b tan\u03b4a \u03b1P;\u03b1A denotes the pressure angle at pitch point, at tooth tip, respectively [rad]. where inv \u03b1P\u00f0\u03b4; \u03b4b\u00de and inv \u03b1A\u00f0\u03b4a; \u03b4b\u00de denote the declination angle \u03b2sph at the intersection point between the pitch circle or the outside circle of the gear and the involute, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000775_tro.2019.2906475-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000775_tro.2019.2906475-Figure3-1.png", "caption": "Fig. 3. Equivalent nonlinear system.", "texts": [ " The tension in each cable can then be represented as \u03c4i = \u2212kcp\u03b4li \u2212 kcd\u03b4\u0307li, where \u03b4li = li \u2212 l0,i denotes the difference between the total length of the cable li and the nominal length of cable in the static equilibrium condition l0,i and kcp andkcd are the proportional and derivative controller gains, respectively. Similarly, suppose that the torque of each pendulum is controlled by a PD controller such that \u03c4a,i = \u2212kp\u03b8p,i \u2212 kd\u03b8\u0307p,i where kp and kd denote the pendulum controller gains. Under such conditions, an equivalent system of the CDPR can be considered as illustrated in Fig. 3 where each cable is replaced with a spring damper with kcp and kcd coefficients and the pendulums motors are replaced with a rotational spring damper with kp and kd coefficients. The system illustrated in Fig. 3 is a nonlinear system where its equivalent linearized system is shown in Fig. 4. The spring-damper in each direction is formed by projecting the spring-damping effects of the cables in those directions. Accordingly, it can be shown that kx = kcp n\u2211 i=1 c\u0302i,x ky = kcp n\u2211 i=1 c\u0302i,y k\u03b8z = kcp n\u2211 i=1 (ri,xc\u0302i,y \u2212 ri,y c\u0302i,x) (15) and kd,x = kcd n\u2211 i=1 c\u0302i,x kd,y = kcd n\u2211 i=1 c\u0302i,y kd,\u03b8z = kcd n\u2211 i=1 (ri,xc\u0302i,y \u2212 ri,y c\u0302i,x) (16) are obtained as the equivalent stiffness and damping coefficients in the planar directions of x, y, and \u03b8z , which means the CDPR is benefiting from an equivalent linear damper in any planar direction, as illustrated in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003059_10402000108982466-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003059_10402000108982466-Figure2-1.png", "caption": "Fig 2 - Schematic of flat roller profile on a flat race.", "texts": [ " D ow nl oa de d by [ U ni ve rs ity o f N ot re D am e] a t 1 4: 42 1 7 N ov em be r 20 14 Effect of Roller Profile on Cylindrical Roller Bearing Life Prediction - Part I: Comparison of Bearing Life Theories 345 TABLE 2.-MAXIMUM HERTZ STRESS-LIFE EXPONENT AS FUNCTION OF WEIBULL SLOPE FOR FOUR LIFE EQUATIONS' 'NO edge stresses assumed. *NO fatigue limit assumed, T, equal 0. contact To compare the various life theories on cylindrical bearing life prediction, we selected a simple roller-race geometry model for evaluation. The model assumes a plurality of normally loaded 12.7-mm- (0.5-in.-) diameter flat rollers running in a linear raceway having a length I L . A schematic of the roller-race model is shown in Fig. 2. The total roller length I , is equal to the roller diameter, 12.7 mm (0.5 in.). Using a closed form Hertzian solution (16) and assuming no edge stresses, normal loads were calculated for a flat roller geometry that would produce maximum Hertz stresses of nominally 1.4,1.9, and 2.4 GPa (200,275, and 350 ksi). These loads and stresses are summarized in Table 1. Load-life exponent, P Line I Point Equation Weibull S l o ~ e (Table 21 ANSI/ 1 1.11 1 6.6 1 9 1 3.33 1 3 contact For line and point contact, the maximum Hertz stress-life relationship was determined for the Weibull, LundbergPalmgren, Ioannides-Harris, and Zaretsky equations as a function of the Weibull slope or Weibull modulus" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000716_j.mechmachtheory.2019.07.013-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000716_j.mechmachtheory.2019.07.013-Figure5-1.png", "caption": "Fig. 5. Coordinate systems for face gear generation.", "texts": [ " (11) and (13) are 3 \u00d7 3 submatrices of the corresponding matrices M after removing the last column and last row. This is because the projections of the normal on each coordinate axis have no relationship with the origin of the coordinate system. Fig. 4 shows a generated conical spur involute shaper. It is visible that the tooth thickness of the conical spur involute shaper is varying from the heel end to the toe end. This makes a feasibility for the backlash modification of the face gear drive by axially moving the pinion. Fig. 5 shows a face gear which is meshing with the generating conical spur involute shaper with a shaft angle of \u03b3 m . The coordinate systems used for tooth surfaces generation of the face gear are displayed. Coordinate systems S m and S 2 belong to the being-generated face gear. The moveable coordinate system S 2 is rigidly connected to the face gear, whereas the fixed coordinate system S m is rigidly connected to the frame of the face gear. Similarly, the generating conical spur involute shaper contains a fixed coordinate system S a and a movable coordinate system S s , which are rigidly connected to the frame and the conical spur involute shaper, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000926_s00170-019-04204-0-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000926_s00170-019-04204-0-Figure7-1.png", "caption": "Fig. 7 Representative geometries, FE meshes, and boundary conditions for numerical models for type I and II experiments", "texts": [ " On the other hand, according to [18], the amount of cantilever beam distortion depends onNwhen the number of layer is small, but tends to become independent at large number ofN because the distortion curvature is related to 3 \u22c5 (N \u2212 1)/N via Eq. (1). When N = 50, the estimated curvature by Eq. (1) is only 2% smaller than for N =\u221e. Therefore, in the numerical FE simulations, the real PBF process was idealized by introducing imaginary layers by N = 10, 20, and 50 for each case. The FE calculations were performed using a commercial finite element software, ANSYS\u00aeVersion 14. Figure 7 shows the representative geometries and boundary conditions as well as FE meshes for the numerical calculations for type I and II experiments. A half of the cross-sections of type I or II specimen geometries was taken into account in the modeling process using the plane of symmetry assumptions. PLANE183 2D elements were used for the discretization under 2D plane stress condition. The mesh size was carefully selected for each model in order to have at least three elements in a layer in the thickness direction" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001200_j.procir.2020.03.100-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001200_j.procir.2020.03.100-Figure6-1.png", "caption": "Fig. 6: Block diagram of the mobile automated irrigation system (Source: Student laboratory project).", "texts": [ " In this case, sensor data is sent on intervals to the user, and the user is requested to activate the start button to switch on the system for the flow of water. Whenever system switched On or Off the pump, a message is sent to the user via GSM module, updating the status of the water pump and soil moisture. Then the similar process as in case 1 begins. The students followed the block diagram in Fig. 5, designed and built the electronics set-up of the mobile automated irrigation system is illustrated in Fig. 6. 234 Vusumuzi Malele et al. / Procedia CIRP 91 (2020) 230\u2013236 Author name / Procedia CIRP 00 (2020) 000\u2013000 5 5.3. Case 3: Mobile and Wifi Enabled Irrigation System The main element of the design consists of android enabled mobile handset, interfacing peripherals and Wifi transceiver module and controller. The android enabled mobile handsets will generate the control command signals which are supposed to be used in the system for appliance controls. This is done by using a mobile handset, analogue signal are stored in the internal memory of the IC after being digitized using ADC blocks internally" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001427_j.mechmachtheory.2021.104300-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001427_j.mechmachtheory.2021.104300-Figure4-1.png", "caption": "Fig. 4. Motion-screw systems for the output link (a) and the rod (b).", "texts": [ " With stationary injection points, the manipulator has a potential application in minimally invasive surgery (laparoscopy) though there are many kinematic designs in this field [38] . There are different methods to analyze mechanism mobility. Some of them use simple structure formulas [39] , while others examine the mechanism topology also [40 , 41] . Here we will use the screw theory approach [42] , which allows us to consider the joint axes\u2019 arrangement. First, consider output link 2 connected to base 1 by three \u201cpiercing\u201d rods 3 ignoring intermediate links 7 for a moment ( Fig. 4 , a). We can construct a motion-screw system for each of the three kinematic chains. To do this, let\u2019s consider one of the three chains and attach a reference frame to base 1 at the center of spherical joint 5 ( Fig. 4 , a). The platform motion-screw system for one kinematic chain can be written as follows: $ 1 = [ 1 0 0 0 0 0 ]T , $ 5 = [ s T 5 0 0 0 ]T , $ 2 = [ 0 1 0 0 0 0 ]T , $ 6 = [ 1 0 0 s T 6 ]T , (1) $ 3 = [ 0 0 1 0 0 0 ]T , $ 7 = [ 0 1 0 s T 7 ]T , $ 4 = [ 0 0 0 s T 4 ]T , $ 8 = [ 0 0 1 s T 8 ]T , where $ 1 , $ 2 , and $ 3 correspond to the spherical motion in joint 5; $ 4 relates to the rod\u2019s translational motion; $ 5 relates to the rod\u2019s rotation in the hole of spherical joint 5; $ 6 , $ 7 , and $ 8 correspond to the spherical motion in joint 4; s 4 \u2026s 8 are nonzero components of the screws above, s 4 being equal to s 5 ", " Moreover, any of components s 6 , s 7 , or s 8 can be a linear combination of s 4 and the other two. There is another redundant motion \u2014 the rod\u2019s rotation about its longitudinal axis. Using a universal joint on platform 2 instead of spherical joint 4 can exclude this motion. Thus, system (1) contains six linearly independent screws, and the motion of platform 2 is unconstrained. Analysis of two other kinematic chains gives an identical result. Now, let\u2019s consider a motion-screw system for each of rods 3 formed by a couple of intermediate links 7 ( Fig. 4 , b). First, we attach a reference frame to base 1 instantaneously coincident with a center of spherical joint 8 ( Fig. 4 , b). The rod\u2019s motion-screw system concerning one intermediate link is: $ 1 = [ 0 0 0 0 1 0 ]T , $ 5 = [ 1 0 0 s T 5 ]T , $ 2 = [ 1 0 0 0 0 0 ]T , $ 6 = [ 0 1 0 s T 6 ]T , (2) $ 3 = [ 0 1 0 0 0 0 ]T , $ 7 = [ 0 0 1 s T 7 ]T , $ 4 = [ 0 0 1 0 0 0 ]T , where $ 1 corresponds to the translational motion of slider 9; $ 2 , $ 3 , and $ 4 relate to the spherical motion in joint 8; $ 5 , $ 6 , and $ 7 relate to the spherical motion in joint 6; s 5 \u2026s 7 are nonzero components of the screws above. System (2) shows that any of screws $ 2 , $ 3 , or $ 4 can be a linear combination of other screws in the system" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003743_icar.2005.1507449-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003743_icar.2005.1507449-Figure9-1.png", "caption": "Fig. 9. Experimental setup showing (a) the LARS, the SLU Unit and the Optotrak and (b) a close-up of the SLU and gripper rigid body", "texts": [ " 8 presents the same simulation for the case where the suture is manipulated by the LARS while it is held by the rigid tool in Fig. 6(b). The results show that the joints of the LARS move significantly to compensate for the lack of distal dexterity. These motions are not possible for throat MIS since we have to manipulate several long tools passing through a single entry port (the patient\u2019s mouth). These results clearly indicate the importance of maintaining tool tip dexterity to avoid large motions in the proximal end of the tools. Our experimental setup consists of the LARS robot and a large model of the SLU (Fig. 9). Though the final design of the robotic system for MIS is more compact and small, our current system was easy to fabricate and served as a robust platform for initial testing of our control. Three 4-Axis LoPoMoCo [28] cards provide I/O operations of reading encoders and providing analog outputs for motor voltage control. They also have on-board power amplifiers to control low power motors. An industrial PC (Pentium-II) houses these ISA cards and is used for the servo control and user interface", " We selected the Optotrak 3020 from Northern Digital Inc. (Waterloo, Canada) to provide optical measurement of the gripper frame. The instrumentation consisted of two rigid bodies, one attached to the end of the disk of SLU, such that the reference frame of the rigid body coincided with the origin of the gripper frame. The other body was attached to the base of the robot to provide a reference for measurements. We attached six active markers to the end disk of the SLU and rotated the SLU about an arbitrary direction (Fig. 9(b)). We used least-squares fitting to determine the positions of these markers with respect to the gripper frame by fitting the 3D position readings of these markers to their respective circles of motion. Once these positions were determined we performed suturing motion and measured the 3D motion of the center of the suture. Data was collected for approximately 180 seconds with an average sampling rate of 5 Hz. Fig. 12 shows the X, Y, and Z components of pw g \u2212pw g start as measured by Optotrak" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001379_tec.2020.3030042-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001379_tec.2020.3030042-Figure3-1.png", "caption": "Fig. 3. Simplified model of enclosure.", "texts": [ " The tooth foot and tooth shoulder are respectively simplified to structure b and structure c, the density of the simplified structures are reasonably adjusted to ensure that their mass are equal to the actual ones. Accordingly, the stator core can be regarded as a cylindrical shell with additional axial combined ribs on the inner surface, as shown in Fig. 2. Actually, the stator core is fixed on the enclosure by interference fit, thus the influence of the enclosure on the natural frequencies of the stator must be considered. The structures of the stator with enclosure are complicated, and it is necessary to simplify them reasonably. As shown in Fig. 3, the enclosure can be regarded as an elastic cylindrical shell that is coaxial but unequal length to the stator core. The terminal box, cooling ribs and other structures attached to the outer surface of the frame are equivalent to cooling ribs A with uniform distribution, and the density of the equivalent cooling ribs A are reasonably adjusted to ensure that their mass are equal to the actual ones. Ignoring the influence of the stiffness of the bases, they are equivalent to the cooling ribs at the same position in the form of additional mass, which is equivalent to the cooling ribs B" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000624_1.5040635-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000624_1.5040635-Figure5-1.png", "caption": "FIG. 5. Outline of copper film formation: (a) single line (bird\u2019s eye view) and (b) multiple lines (top view).", "texts": [ " The nozzle for powder feeding is placed in the center of the head, and powder is carried from a powder container (not appeared in the figure) by argon gas flow. In order to prevent film surfaces from oxidation, the head has the shielding gas nozzle of argon flow around the powder feeding nozzle. The head is equipped on the machine with X, Y, and Z axis motion stage. The fundamental characteristics of the multiple blue DDLs were measured: the laser beam profile and the laser power. The laser beam profile and the laser power were taken using a CCD beam profiler and a power meter, respectively. Figure 5 shows the outline of copper film formation on a stainless steel plate (only two laser beams are depicted in the figure). Firstly, single film lines of copper were formed varying laser power and scanning speed of the motion stage [Fig. 5(a)]. Then, multiple lines with overlapping single lines side-by-side were formed in order to achieve the area coating of copper on the substrate [Fig. 5(b)]. The conditions of film formation are shown in Table II. Pure copper and a type 304 stainless steel plate were used as powder and substrates, respectively. Copper powder is gas-atomized powder with a mean particle diameter of 30 \u03bcm. A stainless steel plate has the dimension of 50 \u00d7 50 \u00d7 3 mm3. The substrate was placed so that the focal point of the overlapped beams was on the surface of the substrate. The optical images of every copper film surfaces and cross sections were observed by an optical microscope to investigate the film geometry and defects inside copper films. Cross sections were obtained by cutting across the film (broken line appeared in Fig. 5). Figure 6 shows the laser beam profile at the overlapped point of multiple blue DDLs. As shown in Fig. 6, the combined laser beam has the round shape and the Gaussian distribution with 0.4 mm in diameter. Figure 7 shows the output power of the multiple blue DDLs in terms of the load current in percentage. The figure shows that the laser power of the system varies linearly up to the load current of 80% and then gradually increases up to the load current of 100%. The overall output of the system is 93W" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003388_978-3-662-04831-3-Figure5.27-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003388_978-3-662-04831-3-Figure5.27-1.png", "caption": "Fig. 5.27: Spatial translational joint", "texts": [ " Q iPi '-v-\" constant Constraint velocity equations of a massless spherical- spherical link [TR -TR +ARLj \u00b7TLj -ARLi \u00b7TLi ]T PjO PiO Q jPj QiPi (5.41b) Constraint acceleration equations of a massless spherical-spherical link 5.2 Theoretical modeling of spatial joints 223 5.2.2.3 Translational joint (BB2, BB4; constrains three rotational DOFs). A joint that allows two rigid bodies i and j to perform relative translational motions in three orthogonal directions and no relative rotation to each other (Figure 5.27) is called spatial translational joint. It is modeled by a combination of building block BB4 and of a modified version of building block BB2, where the modified BB2 constrains relative rotations around the 224 5. Model equations of planar and spatial joints common body-fixed x- and y-axes, and BB4 constrains rotations around the remaining z-axis. As the modified BB2 allows relative rotations around the parallel z-axes e zQ; and e zQj of bodies i and j, the matrix A Lq j Lq i of (5.21a) is now modified to the form ( c~sa , sina , 0) - sm a , cos a , 0 0 ' 0 ' 1 (5" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000041_j.jsv.2017.01.010-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000041_j.jsv.2017.01.010-Figure1-1.png", "caption": "Fig. 1. Deformation of asperities at the point of contact during contact between smooth surface and rough surface in involute gear tooth meshing.", "texts": [ " The model has been developed on the bases of statistical concepts, Hertzian contact approach and varying sliding velocity of gear tooth mechanism, in which, rough surface has been assumed to consist of asperities whose heights ( )z varies in some statistical manner and all asperity summits have been considered as spherical and have the same characteristic radius. Let the separation between involute smooth surface of gear tooth and the reference plane in the rough surface of another gear tooth is d as shown in Fig. 1 which is constant at line of action. For the investigation of contact between the surfaces of gear teeth, those are having asperities with different summit heights, all deformable surface roughness can be considered on one surface such that it is having an asperity distribution equivalent to composite asperity height distributions of the both meshing surfaces of gears and the second surface may be considered as smooth surface. The model has been developed as shown in Fig. 1 based upon the model of Greenwood andWilliamson [28] and model of Fan et al. [25]. In Fig. 1, the contact of two surfaces of gear teeth at the point of contact has been extracted from the meshing of gears. The probability ( )P z that an asperity has a summit between z and +z dz above reference plane in rough surface is [28,31] ( ) = \u2205( ) ( )P z z dz 1 Please cite this article as: R.B. Sharma, et al., Modelling of acoustic emission generated in involute spur gear pair, Journal of Sound and Vibration (2017), http://dx.doi.org/10.1016/j.jsv.2017.01.010i where, z is the random variable for the heights of asperity summits which vary randomly, \u2205( )z is the probability density function (PDF) of the asperity height which describe the distribution and for the incorporation of all the asperities heights, it should be such that [32] \u222b \u2205( ) = ( )\u2212\u221e +\u221e z dz 1 2 When a load is applied, the smooth surface shift towards the mean level of the asperities so that, it will make contact with all the asperities for which the heights are greater than the separation i" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003131_robot.1999.770008-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003131_robot.1999.770008-Figure1-1.png", "caption": "Figure 1. 7-link planar bipedal robot model.", "texts": [ " The sloped terrain has smooth transition (such that both discrete sensors underneath the foot which has completely touched down are always turned on) and there is also no variation of terrain in the transverse direction. 2 System and Task Descriptions The control strategies studied in this paper are designated for a physical six degree-of-freedom, 7-link planar biped called Spring Flamingo. The robot has two slim legs and a body. The legs (1 kg each) are much lighter than the body (10 kg). Each leg consists of a hip joint, a knee joint and an ankle joint. All the joints are revolute pin joints with axes perpendicular to the sagittal plane. An equivalent computer model (as shown in Figure 1) was created with approximately the same configuration and mass distribution as Spring Flamingo. The detailed parameters of this model can be found in [ 11. We assume that the goal for the biped is to maintain a steady dynamic walking gait in the sagittal plane while maintaining an upright posture. We have ignored the transient problem, eg. transition from stop to walk. We also assume that the biped walking has two main phases: single support phase and double support phase. 0-7803-51 80-0-5/99 $10" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003905_1.2033899-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003905_1.2033899-Figure9-1.png", "caption": "Fig. 9 Modified Poincare maps at shaft speed with taper ball bearings", "texts": [], "surrounding_texts": [ "In conclusion, the study shows that the use of the modified Poincare map of the vibration signature can provide an effective procedure in identifying and quantifying bearing damage for prognostication applications. Specific conclusions based on the results of this study can be stated as follows: Transactions of the ASME of Use: http://asme.org/terms Downloaded F use of the modified Poincare map with vibration data for over 2000 revolutions can assure the contact of the damaged area and eliminate the problem. 3 The use the modified Poincare map can provide a dependable identification of the type of damage the number of peaks equals to the number of ball elements using relative carrier speed can provide identification of damage in the bearing race while damage in the ball element will provide an significant increase in vibration amplitude speed as well as an accurate quantification of the damage level in rolling element bearings. 4 The use of the modified Poincare map based on the shaft speed can provide a good indication of the location of the damage with reference to the shaft reference mark. 5 The use of the modified Poincare map based on the relative carrier speed can provide a better indication of the damage type and its level than those based on the shaft speed of the rolling element bearing. 6 Based on the results from this study, an interpolating algorithm can used to relate vibration amplitudes with bearing surface pitting area and depth pitting volume as failure criteria provided by bearing manufacturers ." ] }, { "image_filename": "designv10_11_0000992_j.jmbbm.2020.103733-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000992_j.jmbbm.2020.103733-Figure4-1.png", "caption": "Fig. 4. (a) Top view of the setup, (b) close-up view of the specimen in unloaded state, close-up view of (c) a subset and (d) the gage zone with paint speckle for DIC showing the initial coordinate of the subset centers, (e) 3D perspective view of the setup with transparent view of clamps, and (f) cross-section C-C view.", "texts": [ " To study the effects of \u03b8R, Ts, and porosity, a total of 8 sets of cruciform specimen were fabricated, as summarized in Table 1: \ufffd Four sets of solid specimen with \u03b8R of \ufffd45\ufffd, 0\ufffd\u201390\ufffd, 45\ufffd, and 0\ufffd and the same Ts of 0.6 mm (3 layers) \ufffd Two sets of solid specimen with Ts of 1.0 and 2.0 mm (5 and 10 layers, respectively) and the same \u03b8R of \ufffd45\ufffd (Fig. 3) \ufffd Two sets of porous specimens with \u03b8R of 0\ufffd\u201330\ufffd and 0\ufffd\u201390\ufffd and the same Ts of 2.0 mm (10 layers). Three specimens are fabricated for each set of solid and porous specimens for the biaxial test. The total number of specimens and biaxial tests is 24. The biaxial test apparatus, as shown in Fig. 4, consists of four linear actuators, marked as L1, L2, L3, and L4 (Model HS-02 by Dynamic Solution\u2122, Irvine, California) with L1 and L3 on the x-axis and L2 and L4 on the y-axis. The maximum displacement of the actuator was 60 mm. Clamps affixed to the linear actuators were used to hold the clamp zones (Fig. 1) of the specimen. Four linear actuators moved synchronously in opposing directions to pull four arms of the specimen at a slow, 2 mm/ min speed to minimize the viscoelastic effect for the quasi-static deformation (Sasso et al", ", 2009), was examined by a digital camera for strain measurement. To determine the strain at the gage zone, the displacement and deformation are acquired using the DIC method based on NCORR\u2122, a subset-based DIC prepare algorithm implemented through an opensource MATLAB\u2122 script (Blaber et al., 2015). To prepare the specimen for DIC, the powder paint was sprayed to the surface of the specimen. Sequential images of the gage zone of the specimen during loading were taken using a digital camera (Model S200 by Canon\u2122), as shown in Fig. 4e, at a frame rate of 0.25 frames per second. The image has 4000 x 3000 pixels (0.1 mm pixel spacing). The image was calibrated for lens distortion prior to the DIC Analysis. In this study, the lens distortion coefficient, k1, is 8.6 \ufffd 10 7 as determined using the method by Pan et al. (2013). As shown in Fig. 4b and d, the square gage zone of an unloaded specimen is identified. Inside the gage zone are circular subsets with radius, Sr. By selecting Sr with 35 pixels, as recommended by Blaber and Antoniou (2017), there are 625 (25 by 25) subsets inside the gage zone (which has about 179 pixels on each side). The distance between the adjacent centers of the subset is Ss, as shown in Fig. 4c. In this study, Ss \u00bc 0.7 mm. The DIC calculates the displacement vectors u and v in the x- and ydirections, respectively, for each subset. The Green-Lagrangian strains in the x- and y-directions, denoted as \u03b5L xx and \u03b5L yy, respectively and the Green-Lagrangian shear strain, \u03b5L xy, (Blaber et al., 2015), are: \u03b5L xx\u00bc 1 2 \ufffd 2 \u2202u \u2202x \u00fe \ufffd \u2202u \u2202x \ufffd2 \u00fe \ufffd \u2202v \u2202x \ufffd2\ufffd (1) K.B. Putra et al. Journal of the Mechanical Behavior of Biomedical Materials 107 (2020) 103733 \u03b5L yy\u00bc 1 2 \ufffd 2 \u2202v \u2202y \u00fe \ufffd \u2202u \u2202y \ufffd2 \u00fe \ufffd \u2202v \u2202y \ufffd2\ufffd (2) \u03b5L xy\u00bc 1 2 \ufffd \u2202u \u2202x \u00fe \u2202v \u2202y \u00fe \u2202u\u2202u \u2202x\u2202y \u00fe \u2202v\u2202v \u2202x\u2202y \ufffd (3) The Green-Lagrangian strains at the centroid in the x- and y-directions, denoted as \u03b5LC xx and \u03b5LC yy , respectively, are determined through the averaging strains in the gage zone. The average \u03b5L xx of subsets within a circular region A\u03b5 (shown in Fig. 4d) centered at the centroid and with a radius R\u03b5, is denoted as \u03b5LC xx , which represents the Green-Lagrangian strain at the centroid in the x-direction. The R\u03b5 will be determined through a convergence study. The average of \u03b5L yy for subsets within A\u03b5 denoted as \u03b5LC yy , is the Green-Lagrangian strain at the centroid in the ydirection. The averaging of A\u03b5 around the centroid can also reduce the noise during DIC measurement caused by the limited image resolution. The stretch ratio acquired from the experiment is used to determine the hyperelastic material model in Section 5", " The nominal strain is used as the independent variable when comparing the clamp force (described in Section 3.3) between the experimental measurements and the FEA results. The nominal strain in the x-direction is given by \u03b5N xx \u00bc 2(d/Li). To approximate the true stress of the specimen during biaxial testing, the clamp forces in x- and y-directions, Fx and Fy, respectively, were measured using two piezoelectric dynamometers (Model 9256C1 by Kistler, Winterthur, Switzerland), marked as D1 and D2, in x- and y-axes, respectively, as shown in Fig. 4e and f. The clamp forces, Fx and Fy, were used to calculate the apparent true stresses in x- and y-directions, \u03c3Ta xx and \u03c3Ta yy , respectively (Nolan and McGarry, 2016): \u03c3Ta xx \u00bc \u03bbC x Fx TsW and \u03c3Ta yy \u00bc \u03bbC y Fy TsW (5) The stress correction factor, S, was utilized to approximate the true stresses at the centroid, \u03c3TC xx and \u03c3TC yy , based on \u03c3Ta xx and \u03c3Ta yy (Nolan and McGarry, 2016): \u03c3TC xx \u00bc S\u03c3Ta xx and \u03c3TC yy \u00bc S\u03c3Ta yy (6) The S is dependent on the specimen geometry, clamp displacement, and linearity of the material elasticity" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000088_j.jsv.2017.12.022-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000088_j.jsv.2017.12.022-Figure2-1.png", "caption": "Fig. 2. Ease-off gear surface.", "texts": [ " The value of curvature correction Dkc equals 0 and Dkp is expressed as: DkP \u00bc 8d a2 >0 (6) in which, the value of deformation d is considered as a given value under light contact load taken from the experimental data as 0.00635 mm [4]. a is the length of ellipse long axis shown in Fig. 1(a). After curvature correction is performed on the fully conjugate gear surface along contact path, a new ease-off gear surface can be constructedwhich is 2nd order tangential to the contact path on conjugate gear tooth surface P 0. As is shown in Fig. 2, vector c and twhich are vertical to each other are the principal directions at contact point on this surface. The corresponding principal curvatures are denoted by Dkc and Dkt . The maximum normal curvature correction Dkt is along direction t which can be deduced from Dkp based on Euler's formula as follows: Dkt \u00bc Dkp sin2 a (7) where a is the angle between the tangential directions of contact path and contact line which can be represented as: cos a \u00bc c,p jcjjpj (8) Taking P 0 as the datum plane, the ease-off gear surface Q is established based on the deviation value w at all the surface points P0 of P 0 along the normal direction" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001083_s10404-019-2275-1-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001083_s10404-019-2275-1-Figure1-1.png", "caption": "Fig. 1 Schematic view of the configuration studied experimentally. A neutrally buoyant dumbbell made up of two attached spherical particles of diameters D L and D S \u2264 D L is rotated with angular velocity along its symmetry axis in a viscoelastic fluid", "texts": [ "\u00a02 we introduce the experimental setup, the dumbbells used for the locomotion, and characterise the rheological properties of the fluids used. We present our experimental results in Sect.\u00a03 and compared them with the model of Pak et\u00a0al. (2012) in Sect.\u00a04. A conclusion and perspectives are offered in Sect.\u00a05. Following the theoretical proposal put forward by Pak et\u00a0al. (2012), we conduct experiments consisting in rotating a neutrally buoyant sphere\u2013sphere magnetic dumbbell immersed in a viscoelastic fluid. The experiment is schematically represented in Fig.\u00a01. The large sphere in the dumbbell has diameter DL and the smaller one DS and the whole dumbbell rotates with angular velocity along its symmetry axis. We use the magnetic setup developed in Godinez et\u00a0al. (2012), which is a device capable of producing a magnetic field of uniform strength 6 mT and rotated mechanically. The dumbbells were placed inside a rectangular tank ( 160mm \u00d7 100mm \u00d7 100mm ) that fit into the region of uniform magnetic field inside the coils of approximately (100mm)3 in size where the test fluids were contained" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003756_bf01908876-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003756_bf01908876-Figure2-1.png", "caption": "Fig. 2. Two gears", "texts": [ " By using critical damping as a basis for determining momentary constraint forces, the objects they model via dynamic constraints smoothly fly together and remain connected. With the addition of this correction factor, Eq. 15 becomes\" The expanded Dynamics Equation with error correction _Jq[q,,]=[ _B 1 L! O J L L- (18) where: ~* = q5 (q, q', t )+ 2c~f' +fl2f_ As an illustration, formation of the expanded dynamics equation for the case of two interlocking gears is presented. This simple linkage (Fig. 2) consists of two links which rotate about parallel axes. There are two DOFs, q0 and ql. Assuming that the quantities q0, q~, q~, q], are already known, and that A and B have already been calculated, the Dynamics Equation could be used to find the motion of the two links. If, for example a torque were acting on the larger gear, it would spin but the smaller gear would remain stationary since there is no explicit relationship between the two gears. One constraint equation must be added in order to make the gears rotate according to a given gear ratio" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003218_robot.1991.131559-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003218_robot.1991.131559-Figure2-1.png", "caption": "Figure 2: The double pendulum.", "texts": [ " Use the inertia matrix attached to the moving frame, Ad\u2018, and expand it to a 4 x 4 matrix by adding a row and column of zeroes. Define = [J\u2019]w\u2019+w\u2019 x [J\u2019lw\u2019. Then, the generalized inertia forces are This equation can be written in ternis.of the generalized coordinates by substituting for d , u\u2019, and u\u2019 with the terms in Equation 10 through Equation 13. Wit,li these substitutions, Equation 18 becomes 3 Example To show that Equation 23 accurately models the dynamic properties of a rigid body, we solve a pertinent, yet relatively simple problem. The planar double pendulum, shown in Figure 2, was chosen because it is relatively simple, yet nontrivial; with some modification, it can serve as the basis for a model of a rigid body propelled by a planar robot (see Figure 3); and, by externally applying only the gravitational force, the accuracy of the solution can be verified using Conservation of Energy. [M]Q = F + h(Q, Q), (23) 3.1 Planar Quaternions where Planar quaternions are a subset of dual quaternions. &I = &2 = Q7 = Q8 = 0. (26) where [I41 is the 4 x 4 identity matrix and These constraints leave four nontrivial equations of motion, i = 3 , . . . , 6. Equation 26 trivially satisfies Equation 4 and simplifies Equation 3 to 8 [A,] = 1141 QP, i=5 and where Q; + Q: - 1 = 0. (27) h(Q, Q) = 8 [ q [J\u2019] [ q T q - 8?[GlT [Go] 4 } . { -8m[G]T[G]cio 3.2 The Double Pendulum (25) The double pendulum has two links, see Figure 2. . I Equation 23 provides a basis for solving any spatial rigid body dynamics problem. The first link is massless. I ts length is L. It rotates 01 about the fixed point, 0. The second link has mass, m , and moment of inertia, j\u2019. It rotates 02 about the center of mass, C. The position of the second link is obtained by a rotation, 81, a translation, L , along the x-axis, and a rotation, 82 . Applying Equation 1, Equation 2 and Equation 5 to this set of displacements yields the dual quaternion for the second link 81 + 02 01 + 02 Q3 = sin- , Q4 = COS- 2 \u2019 These components introduce a sixth constraint equation" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003810_027836499101000107-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003810_027836499101000107-Figure2-1.png", "caption": "Fig. 2. Two-link manipulator.", "texts": [ " l\u2019 The unknown constraint forces and moments at joint I have been eliminated. It is also true that a 1 = J 1 ij l\u2019 because the joint veloci- at UNIV OF ILLINOIS URBANA on March 5, 2013ijr.sagepub.comDownloaded from 67 tics are aH zero. Thus eq. (9) becomes: A comparison of this result with eq. (1) leads to the identification of the one-link manipulator inertia matrix as and the dynamic equation for the single-link manipulator may be written: Note that the transformation, 2x i , is required to reference all quantities to the same coordinate frame (1). Figure 2 shows a two-link manipulator formed by adding a second link to the free end of the one-link manipulator of Fig. 1. A free-body force equation may be written in Cartesian space for the second link as follows: where a2 is the spatial acceleration of link 2, f2 is the spatial force applied to link 2 by link 1, and f3 is the spatial force applied by link 2 to whatever additional link or body it contacts. Similar to the one-link case, the Jacobian matrix may be used to project the force terms onto the motion space of the two-link manipulator : The term JT f2 represents the projection of f2 onto the basis vectors of the motion space, which are expressed with respect to the coordinate system of link 2" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000572_1.4034175-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000572_1.4034175-Figure3-1.png", "caption": "Fig. 3 (a) Definition of a gauge position in the root fillet region and (b) a test pair assembled in the test machine showing some of the strain gauged teeth", "texts": [ "org/pdfaccess.ashx?url=/data/journals/jmdedb/935446/ on 01/28/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use mesh) were recorded to observe transient effects caused by the teeth having indexing errors on neighboring teeth. One of the \u201cno-error\u201d gears, gear #1 in Table 2, was strain gauged extensively using miniature gauges (HBM 1-LY11-0.3/ 120). The gauges had a gauge factor of 2.0 and a nominal resistance of 120 X. The measuring grid has a length of 0.3 mm in the active direction. Figure 3 shows the gauged gear in the test gear box meshing with another gear from Table 2. The position of the gauges represented the highest possible position below the start of active profile (SAP) without interfering with the tips of the mating gear. The signals from the gauges that passed through the slip ring were connected in quarter-bridge circuit configurations to a NI SCXI-1314 terminal block. The terminal block was then connected with a SCXI-1520 module, which is designed to process signals from Wheatstone bridge-based sensors" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000931_j.mechmachtheory.2019.103595-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000931_j.mechmachtheory.2019.103595-Figure3-1.png", "caption": "Fig. 3. Structure of the mounting body.", "texts": [ " 2 , the rR joint is mainly composed of an inner support body, a rotating shaft and an outer mount. One side of the inner support body is connected with the output end of the P pair, that is, the output shaft of the linear actuator, by a bearing. The other side of the inner support body is U-shaped and has a through hole that the rotating shaft passes through to coupled with the master link. The outer mount that two grooves is inside, is seated outside of on the inner support body. Every groove has two straight sections and one helix section (see Fig. 3 ). The rotating shaft can change its position by sliding freely along the grooves so as to alter the direction of the rotation axis of the rR joint. In order to prevent any interference with the master link, an open slot is provided in the outer mount. For ease of installation, the outer mount is divided into a mounting body, a left baffle and a right baffle. The left and right baffles are connected to the mounting body by screws. The rR joint can have various configurations as its axis can have various configurations when the rotating shaft sliding along the grooves, leading to some special and useful configuration phases of the mechanism to achieve variable mobility" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000777_tmag.2019.2905567-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000777_tmag.2019.2905567-Figure2-1.png", "caption": "Fig. 2. Diagram of the xyz coordinate system transformation.(a) xyz coordinate system transformation on the xy plane. (b) Shape of transmission line B in the xB yBzB coordinate system.", "texts": [ " One possible way to solve this problem is to conduct geometric transformation [19]. Geometric transformation mapping points to points may not make equations less complicated. Thus, the coordinate system in Fig. 1(a) needs to be transformed to simplify equations. Two principles are applied to transform the original coordinate system. 1) Ensure that transmission line i is in the xi -yi plane in the xi yi zi coordinate system. (i = A, B, and C). 2) Ensure that the xz plane and xi -zi plane share the same plane. (i = A, B, and C). Fig. 2 shows how the xByBzB coordinate system is built. In Fig. 2(a), B1 and B2 are the projections of suspension points of transmission line B onto the xy plane before tilting. B 1 is the projection of the suspension point of transmission line B onto the xy plane after tilting. xByBzB is the new coordinate system built after tilting while the yB-axis remains vertical to the ground and OB is the projection of the lowest point of transmission line B onto the xz plane after tilting. In Fig. 2(b), solid blue lines represent power transmission towers after tilting, the red line represents transmission line B, hB is the height of the lowest point after tilting, H is the height of suspension points before tilting, and HB is the height of the tilted suspension point of transmission line B. After the tower inclination, it is clear that the shape equation of transmission line B changes. In addition, the range of integration (from \u2212L/2 to L/2), h, and the point (x0, y0, and z0) in (2) also change. Section III will talk about how to calculate the changes of the shape of transmission line B, the integration range, h, and the point (x0, y0, and z0). From the geometrical relationship in Fig. 2, some quantities can be easily obtained as follows:\u23a7\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23a9 S1B = HB tan \u03b1 S2B = HB tan \u03b2 tan \u03b8B = S2B L\u2212S1B H 2 B + S2 1B + S2 2B = H 2. (3) Since the shape of the line relative to the lowest point is unaffected by the tower inclination [5], the parabolic shape can still represent transmission line B in the xByBzB coordinate system, which is expressed as yB = aBx2 B + hB (4) where xLB, xRB, and hB in Fig. 2 and aB need to be determined in order to use (2). Four equations are used to obtain them \u23a7\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 aBx2 LB + hB = HB aBx2 RB + hB = H (xLB + xRB)2 = (L \u2212 S1B)2 + S2 2B\u222b L 2 \u2212 L 2 yds = \u222b xRB \u2212xLB yBds. (5) The fourth equation in (5) means that the length of transmission line B remains the same before and after the tower tilts. In order to conduct the coordinate system transformation, the coordinate of the origin OB can be deduced by using similar triangle calculations in Fig. 2(a) xRB xLB + xRB = L 2 \u2212 x(OB) L \u2212 S1B = z(OB) S2B . (6) Here, [x(OB), y(OB), and z(OB)] is the coordinate of OB in the xyz coordinate system. Since the xz plane and xB-zB plane are on the same plane, y(OB) is zero. Once tan \u03b8B and the coordinate of the origin OB are obtained, the xByBzB coordinate system can be built accordingly. Then, (x0B, y0B, and z0B), which is the coordinate in the xByBzB coordinate system of any point (x0, y0, and z0) in the xyz coordinate system, can be calculated. y0B is equal to y0" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003855_j.mechmachtheory.2006.01.006-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003855_j.mechmachtheory.2006.01.006-Figure6-1.png", "caption": "Fig. 6. The terminal constraints exerted to the end-effector B1B2B3B4.", "texts": [ " With similar process, we can find the terminal constraints of the other three kinematic chains of the endeffector: $ r P 2B2 \u00bc \u00f0 0 0 0 cos a2 sin a2 0 \u00de \u00f040\u00de $ r P 3B3 \u00bc \u00f0 0 0 0 cos a3 sin a3 0 \u00de \u00f041\u00de $r P 4B4 \u00bc \u00f0 0 0 0 cos a4 sin a4 0 \u00de \u00f042\u00de where ai (i = 1, 2, 3, 4) is the angle from x-axis of the absolute coordinate system to the projective line of the ith kinematic chain in the plane xoy. Therefore, the terminal constraints exerted to the end-effector are four pure constraint moments, which are all perpendicular to the direction of z-axis shown in Fig. 6. The terminal constraints exerted to the end-effector are $ r E \u00bc $r P 1B1 $ r P 2B2 $ r P 3B3 $r P 4B4 2 66664 3 77775 \u00f043\u00de Obviously, 1 6 Rank\u00f0$r E\u00de 6 2. With Eq. (20), we can find the free motion(s) of the end-effector as the following two cases: (1) d \u00bc Rank\u00f0$r E\u00de \u00bc 1 In this case, there must be cos ai \u00bc 0; sin ai \u00bc 1; \u00f0i \u00bc 1; 2; 3; 4\u00de or cos ai \u00bc 1; sin ai \u00bc 0; \u00f0i \u00bc 1; 2; 3; 4\u00de \u00f044\u00de In the applicable structure shown in Fig. 4, only the first solution set of Eq. (44) is possible. Therefore, we have a1 \u00bc a4 \u00bc p 2 a2 \u00bc a3 \u00bc 3p 2 \u00f045\u00de In fact, this case is corresponding to one kind of singularities of the mechanism" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001406_tmag.2021.3057391-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001406_tmag.2021.3057391-Figure8-1.png", "caption": "Fig. 8. Comparison of model topologies. (a) Optimized model and (b) contrast model.", "texts": [ "5 mm \u2264 hPM (Thickness of PMs) \u2264 4 mm 10\u25e6 \u2264 \u03b8Alnico (Radian of Alnico) \u2264 40\u25e6 0\u25e6 \u2264 \u03b8Air (Radian of Air) \u2264 10\u25e6 10\u25e6 \u2264 \u03b8NdFeB (Radian of NdFeB) \u2264 30\u25e6 \u221220\u25e6 \u2264 \u03b1 (Current phase angular) \u2264 20\u25e6. (5) 2) Optimization Objective Functions: Maximize the average torque (T ) Minimize the torque pulsation (Tr ) Minimize the torque cost (Tc). (6) 3) Constraints: \u03b8Alnico+\u03b8Air+\u03b8NdFeB \u226465\u25e6(mechanical degrees). (7) According to the weight relationship of Tc > T > Tr , the optimal individual obtained after optimization is selected as the optimized model, as shown in Fig. 8(a). Table III shows the comparisons of design variables and objective functions before and after optimization, which indicates that optimizing the usage of Alnico and NdFeB magnets can effectively improve torque performance and reduce torque cost. To verify the effectiveness of optimization and highlight the advantages of configuring hybrid NdFeB-Alnico magnets, the comparison between the basic model, the optimized model, and the contrast model is performed by the FEM. The contrast Authorized licensed use limited to: Carleton University. Downloaded on June 03,2021 at 15:39:20 UTC from IEEE Xplore. Restrictions apply. model with only NdFeB magnets is shown in Fig. 8(b), which motor specifications are consistent with the optimized model. Fig. 9(a) and (b) show the comparison of electromagnetic torques and objective functions, respectively. The results show that the average torque of the optimized model lost 7.09%, but the torque pulsation is decreased by 83.76%, and more importantly, the torque cost is also reduced by 37.90%, when compared to the basic model. Furthermore, the torque performance of the optimized model is the same as the contrast model, while the torque cost is highly reduced by 22" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003451_robot.2001.933226-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003451_robot.2001.933226-Figure8-1.png", "caption": "Figure 8: Miniman I11 as sample positioning unit", "texts": [ " This is taken into account when calculating the robot's new moving vectors. Finally, the measured position of the gripper is also used for readjusting the parameters of the SEM when necessary, such as the triangulation line scan, the position of the ROI and the position of the SEM stage which corresponds to the area that can be scanned by the electron beam. 3. Positioning of SEM samples by mobile micro robots Simply by exchanging the manipulation unit, the microrobot MINIMAN 111 can act as a small positioning stage with five DOF. In Figure 8, the microgripper was replaced by a hemisphere with a standard sample holder in its center. 391 2 Especially in the \u201csneak mode\u201d, the robot represents a stable high resolution positioning device. Because of the direct transmission of the 6D-mouse\u2019s axes to the robot axes this setup allows a quick and convenient approaching of the desired sample position and orientation. Simply by using two Miniman 111 robots - one equipped with the hemisphere and one with a pair of tweezers - complex handling tasks with altogether ten DOF are possible" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000546_s00170-016-8533-4-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000546_s00170-016-8533-4-Figure2-1.png", "caption": "Fig. 2 Magics\u2122 setup showing the parts arrangement on the substrate plate", "texts": [ " The chemical composition of this powder is given in Table 1. Particle morphology was more or less spherical, with smaller satellite particles adhering to the bigger ones (Fig. 1). ARCAM A2 was used for manufacturing two EBM samples (45 mm wide\u00d740 mm height\u00d710 mm thick). A 10- mm thick stainless steel plate (100 mm sides) was used as a substrate during the build. More details about EBM process can be found elsewhere [3]. First, the parts were designed and saved as STL file in Magics (version 17; Materialise NV, Leuven, Belgium) software (Fig. 2). This file was then transferred to Build Assembler software (version 3; Arcam AB, M\u00f6lndal, Sweden). This particular software converts the STL geometry in to thin slices of 70 \u03bcm and writes the output as machine specific ABF file. The ABF file instructed the machine control on how to proceed with the actual part production. Figure 3 shows one of the resulting EBM part. Lasertec-40 from DMG\u2122 was used for laser experiments. This machine was equipped with the Q-switched Nd:YAG laser operating at a wavelength of 1064 nm and an average power of 100 W" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000048_tmag.2017.2698004-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000048_tmag.2017.2698004-Figure7-1.png", "caption": "Fig. 7. Configuration of the conventional VPM machine.", "texts": [ " 13\u22121=Zs), and their rotation speeds are the same, hence they can both induce back-EMFs in the outer stator windings. The back-EMF waveforms of Machine I, Machine II and the proposed machine is shown in Fig. 6. It can be seen that the back-EMF waveforms excited by Machine I and Machine II are in phase, and thus the total back-EMF of the proposed motor is the scalar sum of the back-EMFs by Machine I and II. In this part, based on 2D FEA, the proposed dual-stator VPM is compared to a conventional VPM, shown in Fig. 7. For a fair comparison, the two machines have the same stator outer diameter, stack length, heat loading, speed, etc. The detailed parameters are listed in Table II. In order to make the frequencies of the two VPM machines identical, the rotor pole pairs are kept the same. Then, based on the machine volume and heat capacity, both two machines has been optimized respectively. Next, the electromagnetic performances including back-EMF, torque density, pulsating torque, power factor, losses and efficiency are compared and analyzed" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000401_s12206-018-0611-0-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000401_s12206-018-0611-0-Figure4-1.png", "caption": "Fig. 4. (a) Tooth model and tooth cross-section; (b) cantilever beam model for the chipped tooth.", "texts": [ " 3(b)), h , xh , d and x are expressed as [26]: 1 2 1 1( )cos sinbh r a a a a= + -\u00e9 \u00f9\u00eb \u00fb (14) ( ) 2 1 2 1 sin 0 cos sin b x b r x d h r d x d a a a a a \u00a3 \u00a3\u00ec\u00ef= \u00ed \u00e9 \u00f9- + \u00a3 \u00a3\u00ef \u00eb \u00fb\u00ee (15) ( )1 2 1 1 3sin cos cosb fd r ra a a a a\u00e9 \u00f9= + + -\u00eb \u00fb (16) ( ) 1 2 3 1 0 cos sin cosb f x x d x r r d x da a a a a \u00a3 \u00a3\u00ec\u00ef= \u00ed \u00e9 \u00f9- - - < \u00a3\u00ef \u00eb \u00fb\u00ee (17) where br and fr are the radius of the basic circle and the root circle, respectively, 2a represents the half tooth angle on the base circle, and 3a is the approximated half tooth angle on the root circle. 2a and 3a are given as [26]: 2 02 inv z pa a= + (18) 2 3 sinarcsin b f r r aa \u00e6 \u00f6 = \u00e7 \u00f7\u00e7 \u00f7 \u00e8 \u00f8 (19) where z is the number of gear teeth. Fig. 4 shows the tooth model, the tooth cross-section cxs , and the cantilever beam model for the chipped tooth. As Fig. 4(a) demonstrates, the chip starts from the tip of the tooth, and the chip sizes are decided by ( , ,c c ct w l ), where ct is the chip thickness, cw is the chip width, cl is the chip length. It is observed that no tooth contact occurs in the chipped area, so the cross-section cxs becomes a composite section, denoted by A B F E D- - - - , which can be formed by the rectangle A B C D- - - minus the triangle F C E- - . Therefore, the expressions of the area cxA and area moment of inertia cxI for the cross-section cxs are different from the ones in the perfect condition", " For the rectangle A B C D- - - , rA is the area, and crI denotes the area moment of inertia about the z axis through the composite's center of gravity .co For the triangle F C E- - , tA is the area, and ctI represent the area moment of inertia about the z axis through the composite's center of gravity .co Area cxA The area cxA is expressed as: 12 2cx r t x x xA A A h w w t= - = - (20) where xt and xw represent the chip thickness and width for the cross-section cxs , respectively. Based on the cantilever beam model provided in Fig. 4(b), xt and xw are expressed as follows: ( )1a a x x c a c c c d x d xt h h h t l l \u00e6 \u00f6- - = - + - -\u00e7 \u00f7\u00e7 \u00f7 \u00e8 \u00f8 (21) c x x c ww t t = (22) where ah is half the roof chordal tooth thickness, ad is the distance from the tooth roof to the root, and ch is the distance from the chip end point to the central line. According to the properties of the involute curve (see Fig. 4(b)), ah , ad and ch are expressed as: ( )2 cos sina b a a ah r a a a a\u00e9 \u00f9= + -\u00eb \u00fb (23) ( )2 3sin cos cosa b a a a fd r ra a a a a\u00e9 \u00f9= + + -\u00eb \u00fb (24) ( ) 2 1 2 1 sin 0 cos sin b c b c c c r x d h r d x d a a a a a \u00a3 <\u00ec\u00ef= \u00ed \u00e9 \u00f9+ - \u00a3 <\u00ef \u00eb \u00fb\u00ee (25) where aa and ca can be obtained through the following equations numerically: ( ) 2 2 2b a a br r ra a+ = - (26) ( )2 3 cos sin cos . b c c c a c f r d l r a a a a a \u00e9 \u00f9+ +\u00eb \u00fb = - + (27) Area moment of inertia cxI The area moment of inertia cxI is expressed as: " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000281_s12206-016-0823-0-Figure13-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000281_s12206-016-0823-0-Figure13-1.png", "caption": "Fig. 13. Test bench.", "texts": [ "1 rad, 2.2 rad and 4.3 rad. As shown in Fig. 12(a), when the defect initial location changes, the defect causes a displacement of the excitation. However, the change in the defect initial location does not cause a change in the envelope spectrum (as shown in Fig. 12(b)). A test of the planet gear bearing defect is conducted on a wind power test platform. The test platform consists of a frequency converter, a drive motor, a speed-decreasing stage, a speed-increasing stage, a loader and a loading motor (Fig. 13). The frequency converter controls the drive motor, which drives the speed-decreasing stage to rotate. After the speed decreases, the speed increases from the speed-increasing stage. The loading motor pumps high-pressure oil into the loader to provide load. The speed-increasing stage is fabricated based on the scaled-down model of a certain wind power gearbox. The schematic of the structure of the speed-increasing stage is shown in Fig. 1. Tables 1 and 2 list the planet-stage parameters and the bearing parameters" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003622_3-540-29461-9_101-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003622_3-540-29461-9_101-Figure3-1.png", "caption": "Fig. 3. Kinematics Concept \u2013 Advanced sliding frame mechanism", "texts": [], "surrounding_texts": [ "Knowledge about the general structure of the building surface was needed before robot movement could be generated. The inputted data contains endpositions, moving distances and path characteristics. This a priori data is supplemented by online sensors which detect the facade surface and search for possible obstacles. In addition to identifying obstacles, the external sensor technology corrects the direction of motion. Sensors detect the robot\u2019s deviation from the ideal path, e.g. sensing girders or window and panel seals. The possibility of the robot colliding with open windows posed a special risk. All windows are automatically controlled and integrated in the building management control system. The robot control system communicates with the building control system to ensure windows are closed in areas being cleaned. What is more, laser scanners perform a necessary double check in case the main system has malfunctioned and a window has been left open." ] }, { "image_filename": "designv10_11_0003901_ip-b.1984.0010-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003901_ip-b.1984.0010-Figure5-1.png", "caption": "Fig. 5A Doubly-fed machine with the same primary and secondary phase-sequence", "texts": [], "surrounding_texts": [ "such fixed speed or near fixed speed operation was virtually obligatory in order for grid-connected schemes to be viable. The situation is now changing as a result of the tremendous improvements in solid state conversion technology but the cost of a 'full-power' frequency convertor is still high enough to constitute something of a disincentive to its use in wind-power schemes. The great advantage of slip-energy control schemes [2-4] is that the power rating of the convertor is much reduced, since it is only the slip power that is dealt with by the convertor. Smith and Nigim [5] have successfully implemented a slip-energy scheme using a current-source inverter. Disadvantages of inverter systems are the need for large commutating capacitors and problems of reconnection after a momentary grid interruption.\nThe work described in this paper is based experimentally on a similar slip-ring machine to that used in Reference 5. A cycloconvertor replaces the inverter, thus eliminating the need for commutating capacitors.\nAny wind-energy transducer interfaced between the turbine and the electricity grid must generate an opposing torque proportional to the square of the turbine velocity. In the experimental system, the prime mover is a DC shunt motor with constant field current and an armature current supplied by a controlled rectifier constrained to give a current proportional to the square of the motor velocity. The prime mover will only stop accelerating when its torque is counterbalanced by the transducer torque (or its internal safety current limited is reached).\nThe cycloconvertor output frequency must be related to the transducer angular velocity and the mains angular frequency by the relationship\n(1)CO2 = + where\nco2 = 2nf2\no)1 = (2)\nFor synchronous operation, the two supply frequencies cox and ft>2 rnust be completely independent, otherwise asynchronous operation will result.\nThe experimental system will operate asynchronously for sudden accelerations owing to input impulses, but mostly its operation consists of a series of synchronous steady states. Closed-loop velocity feedback constrains co2 to obey eqn. 1. However, when a state of equilibrium is achieved by torque balance, a deadband is switched into the feedback loop, and the secondary frequency co2 remains constant until either 'pull-out' torque or zero torque is reached. At pull-out torque or zero torque, the closed loop ensures a frequency change as appropriate for acceleration or deceleration. This prevents the system from drawing power from the supply in a motoring mode.\nA wind turbine has a large inertia giving a mechanical time constant of up to 100 s and the system a high source impedance. Transient instability of the kind experienced in a doubly-fed motor drive is unlikely.\nSelf starting can be achieved by removing the cycloconvertor reference signal and short circuiting the cycloconvertor output terminals. The machine then accelerates to turbine cut-in speed as an induction motor supplied by supply cot only.\n2.1 Harmonic cancellation and transient fault prevention by a double-layer winding Many commercial cycloconvertors use integral cycle blanking to prevent the simultaneous conduction of posi-\ncycloconvertor\nslip-ring machine with\ndivided winding\nFig. 2 Doubly-fed generator circuit diagram\n62 IEE PROCEEDINGS, Vol. 131, Pt. B, No. 2, MARCH 1984", "tive and negative thyristor groups. This fault condition which can be induced by a sudden gust or input power impulse gives a momentary line-to-line short circuit. In Reference 4, excess power is dumped into swamp resistors by switching to induction generation at the onset of a surge. The use of integral cycle blanking makes the cycloconvertor operate with a discontinuous circulating current which makes the harmonic content of its output dependent on the output phase angle. Continuous circulating current operation greatly reduces the harmonic content of the cycloconvertor output. The conventional way of achieving this is by the use of intergroup reactors rated at the cycloconvertor output level.\nThe system described in this paper uses the two layers of the stator as electrically separate, magnetically coupled circuits. Each thyristor group circuit is electrically separate and line-to-line short circuits are eliminated. The machine stator also fulfils the function of the intergroup reactor in maintaining continuous circulating current and eliminating harmonics. A full harmonic analysis and operational description of the divided-winding cycloconvertor system is given in a paper by one of the present authors [6]. Harmonic cancellation extends the output frequency range of the cycloconvertor up to 20 Hz, giving a system range of synchronous speed \u00b140%.\nAn important and desirable property for wind-energy generators is their ability to cope with gusts. In the scheme reported in Reference 4, a doubly-fed machine with variable-frequency rotor excitation has been used in a 250 kW installation. Here the practical limitation is the inability of the convertor to conduct the large rotorcurrent surges incurred during gusting. Exciting capacitors and a swamp resistance are used to dump the excess energy by self-excited induction generation until the gust is over. In the system described in this paper, the positive and negative thyristor group circuits of the cycloconvertor are kept electrically separate by the divided-winding arrangement. The possibility of line-to-line short circuits through the convertor is eliminated and the system is able to withstand severe input surges.\nContinuous circulating-current operation of the cycloconvertor gives considerable harmonic cancellation and eliminates all subharmonics in the cycloconvertor output voltage.\nIn the present experimental system, the use of a divided winding enforces an inverted operation of the machine with the 50 Hz supply (co^ connected to the rotor, the primary, and the lower variable frequency (co2) connected to the stator, the secondary.\n2.2 Doubly-fed machine as a generator A steady-state analysis may be based on the torque equations of Prescott and Raju [7]. Assuming the two applied voltages to be sinusoidal, these equations can be modified to form the two-axis equations of eqn. 3.\nVd!\n%\nVd2\nrt+ Lyp COyLy\nMp\nsco, M\nt + Mp COyM\nr2 + L SCOy L2\n(3)\nwhere p is the derivative operator and s is the slip defined as\nand L1, L2, rlt r2 and M have the usual meanings, and coy = IOOTT. Eqn. 3 is derived from the equivalent circuit of Fig. 3 with the machine represented in quadrature dq-axes with the rotor as the primary as shown in Fig. 4.\nThe load angle a can be considered as the leading or lagging phase displacement shown in Figs. 5A and 5B, and the voltages on the three axes are:\n- 0 0 !\nMp\n\u2014 SCO\nr2 +\nM\nL2\n2\nP\nidl'\nid2\niq2\nS = CO, \u2014 CO2\nCO,\na is positive\n1EE PROCEEDINGS, Vol. 131, Pt. B, No. 2, MARCH 1984 63", "The torque is now\na is negative\nwhere the suffixes 1 and 2 in the voltage terms correspond to the magnetic axes of the primary and the secondary, respectively.\nThe transformation co-ordinate system, defined in Appendix 7.1, results in the following expressions for the dand q-voltages:\n(6)\nInverting the matrix of eqn. 3, gives current components:\nidl = D(s) (VlAl+ V l ^ c o s a~ A* s i n a ) l\nlqi = ~/Xsj ^AlVl + V^A* COS a + A* S i n a ^\nand the primary current ix is\nh = idl + jiqi (7)\nSimilarly\nI\"2 = 7>7~; \\As vi + vi(Ai cos cc- A8 sin a)}\n{/46 yx + v2(A8 cos a + A7 sin a)}\nand the secondary current i2 is\nh = id2 + Jiq2 (8) D(s) = [rj r2 - s(xi x2 - x2)]2 + (r2 xt + sr1 x2) 2\nand At to y48 are defined in Appendix 7.2. The steady-state torque can be derived from the components of eqns. 6 and 7 as\nT = PM(iqiid2-idliJ (9)\nwhere\nP = the number of pole pairs\nM = the mutual inductance\n~ t x2 - x2)]\nx sin a \u2014 (sx2 x \u2014 r2 xj cos a)\nwhere\nK(s) = 3Px2\n\u00a9! D(s) (10)\nEqn. 10 represents the total developed torque in the doubly-fed machine. This may be expressed as two induction torques and a synchronous torque as\nwhere T7l and 7}2, the induction torques depend upon slip and are independent of load angle, and the synchronous torque 7\u0302 also depends on slip and the load angle.\nThe primary induction torque TIl is\nTh = K(s)sr2vi\nthe secondary induction torque Tl2 is\nT/2= -k{s)r,v\\\nand the synchronous torque 7\u0302 is\nU y { [ r r +\n(11)\n(12)\nTs= - x2 -\nx sin a \u2014 [sx2 rt \u2014 r2 xx] cos a} (13)\nEqns. 11-13 are modified forms of the equations given in Reference 7 expressed as functions of slip and load angle. The developed power will then be\nW = OJT = colTn + Tl2 + TJ (14)\nwhere co is the angular velocity of the machine. Care must be taken to observe the signs of the components of eqn. 14. Under certain circumstances the induction components may represent power drawn from the grid.\n2.3 System operation: characteristic modification Initial tests were carried out in open-loop operation, with manual adjustment of the secondary frequency to ensure synchronism. The induction torques are simply functions of voltage and slip, with Tl2 acting as a generating torque over the working-speed range, while Tn is a motoring torque when co < 2nfl/P and a generating torque when co > infJP.\nThe synchronous-torque component 7\u0302 makes up the difference between the torque demand of the turbine input (or prime mover) and the sum of the induction torques. Ts may be a motoring, or a generating torque. The peak synchronous torque and the magnitude of the load angle are functions of the excitation, usually defined in a doubly-fed machine as the ratio of primary induced EMF to primary applied voltage. From Reference 8, this ratio is\nn=V2col co2 (15)\nwhere N is the turns ratio. The initial results were taken with a constant excitation ratio. Fig. 6 shows T7l, 7}2 and 7\u0302 computed from eqns. 11-13 at a reduced primary voltage of 0.5 pu. It can be seen that the synchronous-torque component changes from a generating torque with a positive load angle a to a\n64 IEE PROCEEDINGS, Vol. 131, Pt. B, No. 2, MARCH 1984" ] }, { "image_filename": "designv10_11_0000336_j.optlastec.2017.07.045-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000336_j.optlastec.2017.07.045-Figure5-1.png", "caption": "Fig. 5. Mecmesin force gage 5 N", "texts": [ "5 which expresses a good quality beam. This laser beam is focused to a 50 lm spot in diameter (1/e2) by a 40 mm focal length lens. The chemical composition of solder ball is given in Table 1. Capillary inside diameter of 45 lm and capillary stand off distance of 200 lm are kept constant throughout the experimentation. A computerize controlled electronic shear test gauge manufactured by Mecmesin Limited 2016, UK is employed to these experiments. The shear speed is 200 lm/min and the load resolution is 0.001 N as shown in Fig. 5. PSA measurement is performed on GT05-0086 manufactured by Genetec Technology, Berhad Malaysia, depicted in Fig. 3(c). The experiment is conducted by the response surface methodology (RSM). This experiment is planned based on a central composition rotatable design with four factors, five levels, and full replication. The process parameters comprised of laser energy (E), wait time (W), nitrogen pressure (N), and focal position (F) are selected as the factors in the experiment. The joint shear strength and DPSA are the response of interest" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001452_tro.2021.3076563-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001452_tro.2021.3076563-Figure6-1.png", "caption": "Fig. 6. (a) Dynamic testing fixture used to characterize the vertex dynamics. (b) Top view of the vertex in the fixture. We calculated the translation velocity of the Miura vertex samples by tracking the two black dots on either side.", "texts": [ " To validate this hypothesis with the new hinge design, we constructed samples with small or large backlashes, fixed their input angle \u03b81, and excited them linearly by accelerating and then stopping them in a direction orthogonal to their base [see Figs. 6 and 7(a) and (b)]. This differs from previous papers [33]\u2013[35], in which kinetic energy came from the input velocity \u03b8\u03071 and corresponding rotation along \u03d5; these new experiments more closely resemble the motions used to transform the gripper. We built a testing device [see Fig. 6(a)] that accelerated the vertex in a spring-loaded fixture and then decelerated it with a physical block to approximate an instantaneous stop of the lower segment. The input angle \u03b81 of the lower segment was fixed by installing the vertex between a set of plates that were rigidly connected to the accelerating fixture. A high-speed camera was placed above the vertex to measure the velocity of the base [see Fig. 6(b)]. Different velocities were achieved by installing different numbers of springs in the fixture and changing their initial deflection. In some experiments, the facet inertia was modified by adding mass to the upper facets (see Table I). These parameters were chosen so that the kinetic energy of the vertex was slightly less than or greater than the transformation energy, with a difference less than 20%. This was done to test how accurate our model was; by bracketing the expected transformation point with experimental parameters on either side, the experiments would indicate that the model is accurate if we observed transformation when the kinetic energy was slightly greater than the transformation energy, and no transformation when the kinetic energy was slightly less than the transformation energy" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001344_s12555-019-0482-x-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001344_s12555-019-0482-x-Figure2-1.png", "caption": "Fig. 2. COM position.", "texts": [ " For this manipulator, the mass of motors is much greater than that of the links, which causes an uneven distribution of the mass. And the hollow structure also makes the measurement be inaccurate. In particular, the shape of the third joint is irregular such that the COM position is not easy to measure. To avoid this troublesome in the COM measurement process, some measured gravity data are used in this research to identify COM positions and to construct a dynamic model for the manipulator. In Fig. 2, li = [ px py pz 1 ]T represents the COM position w.r.t. (i\u2212 1)th coordinates, wi and vi are rotational and linear velocities of COM for the ith link, respectively. pCi = [ pCxi pCyi pCzi 1 ] is the ith COM position w.r.t. the base frame. pi\u22121 = [ pi\u22121x pi\u22121y pi\u22121z 1 ] is the origin position of (i\u22121)th coordinates. Table 1 shows the Denavit-Hartenberg (DH) parameters of the manipulator shown in Fig. 1. According to DH parameters, the homogeneous transformation matrix of the 1st coordinate is defined as follows: T 1 0 = c\u03b81 0 s\u03b81 0 s\u03b81 0 \u2212c\u03b81 0 0 1 0 0", " The total kinetic energy can then be represented as follows: K = 3 \u2211 i=1 ( 1 2 mivT i vi + 1 2 wT i RiI\u0303 iRT i wi ) , (6) where mi is the mass of the ith link, Ri is the rotation matrix between the frame fixed to the link and the base frame, and I\u0303 i is the inertia matrix for the ith link. The total potential energy of the manipulator is represented as follows: P = 3 \u2211 i=1 migT pCi , (7) where g = [0 0 9.8 0]T . Then dynamics equation of the manipulator can be derived by Euler-Lagrange equation as follows: \u03c4i = d dt ( \u2202K \u2202 \u03b8\u0307i ) \u2212 \u2202K \u2202\u03b8i + \u2202P \u2202\u03b8i . (8) To obtain the dynamic model, the COM positions pCi in (4) and (7) must be specified. The pCi in Fig. 2 can be represented as pCi = T i 0 \u00b7 l i. (9) Since T i 0 can be obtained from the kinematics, l i must be determined to derive the dynamics equations of the manipulators. 3. GRAVITY AND INERTIA COMPENSATOR DESIGN 3.1. Gravity compensation based on RBFNN In (8) gravity torque is defined as follows: gi(\u03b8) = \u2202P \u2202\u03b8i . (10) Notice that g(\u03b8i) is unknown because of the uncertain pCi . So RBFNN has been used to estimate the gravity disturbance. The structure of RBFNN is illustrated in Fig. 3. It includes three layers: input, hidden and output" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000741_s00773-019-00689-2-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000741_s00773-019-00689-2-Figure5-1.png", "caption": "Fig. 5 Implication process of a fuzzy rule", "texts": [ " 1 3 Singleton fuzzifier and product inference engine are used in this paper. The truth value of the ith rule can be obtained by the product of the membership function values in the antecedent part as where i p is the MF value of the corresponding fuzzy subset given a value of p , and i is the MF value of the corresponding fuzzy subset given a value of . Base on i , the value of KpN and KdN for each rule can be determined from the corresponding membership functions in Fig.\u00a04. Detailed implication process of a fuzzy rule is shown in Fig.\u00a05. Using the above membership functions for p and , we have the following condition: where N = 49 is the number of fuzzy rules, then the defuzzification yields the following: (26) i = i p ( p) \u22c5 i ( ), (27) N\u2211 i=1 i = 1, (28)KpN = N\u2211 i=1 i \u22c5 KpN\u22c5i, (29)KdN = N\u2211 i=1 i \u22c5 KdN\u22c5i. Here KpN.i is the value of KpN corresponding to the grade i for the ith rule, and the same definition holds for KdN\u22c5i and KdN . The actual PD control coefficient can be calculated from the following equation: (30)Kp =(Kp,max \u2212 Kp,min)KpN + Kp,min, The flowchart of the fuzzy rule-based controller can be shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003912_1.2118687-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003912_1.2118687-Figure7-1.png", "caption": "Fig. 7 The prism parallel manipulator, proposed by Herv\u00e9", "texts": [ " Thus, it follows that this Kim and Tsai modified manipulator is an exceptional manipulator of Tanev\u2019s Type, this class of platform was analyzed in Proposition 6, in Sec. 4.2, and its mobility is given by F = dim Vk m/f Aa m/f + j=1 k\u22121 i=1 rj f ji \u2212 dim Aj m/f + i=1 rk fki \u2212 dim Vk m/k = 2 + j=1 2 4 \u2212 4 = 2. The passive degrees of freedom are given by Fp = j=1 k\u22121 i=1 rj f ji \u2212 dim Aj m/f + i=1 rk fki \u2212 dim Vk m/f = j=1 2 4 \u2212 4 + 3 \u2212 3 = 0. 6.5 Herv\u00e9\u2019s Prism Robot. Consider the parallel manipulator suggested by Herv\u00e9 22 , shown in Fig. 7. The manipulator has three serial connector chains, each one formed by a cylindrical pair, a prismatic pair and a revolute pair; the axes of the cylindrical and revolute are parallel and they are not parallel to the axis of the prismatic pair. Each serial connector chain generates the Lie subalgebra asso- 216 / Vol. 128, JANUARY 2006 rom: http://mechanicaldesign.asmedigitalcollection.asme.org/pdfaccess.as ciated with the Sch\u00f6nflies group RP 4 e\u0302 j , where two of the unit vectors e\u03021 , e\u03022 , e\u03023 are equal" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000886_j.mechmachtheory.2019.03.044-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000886_j.mechmachtheory.2019.03.044-Figure3-1.png", "caption": "Fig. 3. Intersection situations of Section B: (a) edge intersection; (b) one triangle contained in the other.", "texts": [ " According to the sign of d V gi j ( d V pi j ) , the test can be divided into three cases: Case A: all d V gi j (d V pi j ) = 0 , j = 1 , 2 , 3 with the same sign; Case B: all d V gi j (d V pi j ) = 0 , j = 1 , 2 , 3 ; Case C: d V gi j (d V pi j )( j = 1 , 2 , 3) doesn\u2019t match Section A and Section B. Case A: T gi ( T pi ) lies on one side of \u03b3 i p (\u03b3 i g ) and the contact is rejected. Case B: The triangles are co-planer, and a triangle-triangle intersection test on the plane is carried out: Determine if the triangle has edges intersecting or the existence of a triangle is contained in the other. The geometric schematic is shown in Fig. 3 . (1) Let us donate the vectors: \u2212\u2192 A = V pi 2 \u2212 V pi 1 , \u2212\u2192 B = V gi 1 \u2212 V gi 2 and \u2212\u2192 C = V gi 1 \u2212 V pi 1 . The equation e \u2212\u2192 A + d \u2212\u2192 B = \u2212\u2192 C is solved by Cramer\u2019s Rule. If 0 \u2264 e \u2264 1 and 0 \u2264 d \u2264 1, then the tooth surfaces contact. Conversely, the contact is rejected. The same is done for the other edges. (2) Solve the following three equations: t 1 = \u2212\u2212\u2212\u2192 V pi 1 V gi 1 \u00d7 \u2212\u2212\u2212\u2192 V pi 1 V gi 2 t 2 = \u2212\u2212\u2212\u2192 V pi 1 V gi 2 \u00d7 \u2212\u2212\u2212\u2192 V pi 1 V gi 3 (4) t 3 = \u2212\u2212\u2212\u2192 V pi 1 V gi 3 \u00d7 \u2212\u2212\u2212\u2192 V pi 1 V gi 1 If all t k (k = 1 , 2 , 3) have the same sign, then V pi 1 is contained in T gi " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003970_j.bioelechem.2006.03.040-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003970_j.bioelechem.2006.03.040-Figure2-1.png", "caption": "Fig. 2. Cyclic voltammograms illustrating the effect of the urate anion (1.000 mM), o corresponds to UA alone and the thick line to the mixture of UA+DA; [DA]=500 \u03bc corresponds to DA alone and the thick line to the mixture of UA+DA; [DA]=490 \u03bcM", "texts": [ " Hence, it may be concluded that a single NA-coated electrode can be consecutively used for the DA detection with a good performance, i.e., with good repeatability, expressed by relatively low RSD values. The calibration experiments were performed also in the presence of excess amounts of urate and ascorbate anions, under the same experimental conditions. The calibration curves for DA in the presence of 1 mM UA revealed no statistically noticeable differences compared to those in the absence of urate. In fact, in a mixed solution of DA and UA, the urate anion is totally excluded by the NA-coated electrode and Fig. 2 gives a typical example of that feature. In fact, at the bare GCE (Fig. 2A) there was a marked interference of UA in the DA oxidation peak (which will get worse in physiological conditions where the concentration of DA is usually lower that that used in Fig. 2) whereas at the NA-coated GCE (2.6 \u03bcm) the DA oxidation peak current remained unaltered in the presence of UA (Fig. 2B). However, when AA was present in the voltammetric cell (with a concentration 0.554 mM), major alterations were noticed. Fig. 3A shows that for 50 \u03bcM DA and v=0.05 V s\u22121 a significant increment (ca. +66%) in the DA oxidation signal occurred comparing with that of DA alone associated to a pronounced decay of the corresponding reduction peak (ca. 70%). Diminishing the scan rate to 0.025 V s\u22121 leads to a slight increase of the DA oxidation current and to a large decrease (ca. 8\u00d7) in the current of the reduction of the o-quinone species (Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003733_iros.2006.282470-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003733_iros.2006.282470-Figure1-1.png", "caption": "Fig. 1. Model of a fully-actuated compass-like biped robot with flat feet. This has feet whose mass and thin can be neglected.", "texts": [ " In the second, another compasslike biped model with semicircular feet is introduced and its virtual passive dynamic walking on a level is shown. Parameter study is then performed and the gait\u2019s basic characteristics and performances such as walking speed are clarified. Throughout this paper, it is shown that energy-efficient and high-speed dynamic biped locomotion on a level can be easily realized by the effect of semicircular feet. In this section, we first introduce a fully-actuated model with flat feet and investigate its joint-torques effect. In the second, another model with semicircular feet is introduced. Fig. 1 shows a fully-actuated compass-like biped model with flat feet. This model was originally studied by Goswami et al. to stabilize the passive gait or generate a gait on a level by energy tracking control [12]. It has feet with flat feet whose mass and thin can be neglected, and the ankle-joint torques can be exerted. It is assumed that the foot of the stance-leg always touches the ground without slipping or rotating. The 1-4244-0259-X/06/$20.00 \u00a92006 IEEE swing-phase dynamic equation is given by M (\u03b8)\u03b8\u0308 + C(\u03b8, \u03b8\u0307)\u03b8\u0307 + g(\u03b8) = Su = [ 1 1 0 \u22121 ] [ u1 u2 ] (1) where \u03b8 = [\u03b81 \u03b82] T is the generalized coordinate vector, M \u2208 R2\u00d72 is the inertia matrix and C \u2208 R2\u00d72 is the Coriolis and centrifugal force matrix, and g(\u03b8) \u2208 R2 is the gravity vector, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000035_1350650116684275-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000035_1350650116684275-Figure4-1.png", "caption": "Figure 4. The finite element model of single tooth: (a) single-tooth model; (b) the convective heat transfer coefficient; (c) the friction heat flux of meshing surface.", "texts": [ " Then, the characteristic parameters of the mixture medium can be expressed as vmix lmix Pmix 2 64 3 75 \u00bc vk vo lk lo Pk Po 2 64 3 75 1 mixd mixd \u00f015\u00de where the modification factor d can be expressed as d \u00bc rc ra \u00f016\u00de where ra is the radius of addendum circle. Finite element analysis of the bulk temperature field The finite element analysis model and the boundary conditions The main content of this paper is the calculation of bulk temperature field of the gear. To save calculation time, the single-tooth model of the gear was established as shown in Figure 4. A 3D solid model was established using APDL. Eight-node hexahedron element solid70 and mapping mesh generation method were used. The surface effect element surf152 was established on the mesh surface, to which the friction heat flux was applied. In Figure 4(c), the maximum friction heat flux occurs at the meshing-in point and the minimum friction heat flux is at the pitch point. The friction heat flux firstly reduces along the meshing line, approaching to a minimum in the pitch point, and then increases. Finite element anlysis results of bulk temperature field The bulk temperature field of a single tooth based on ANSYS is shown in Figure 5. With the meshing surface comprising the highest temperature, nonmeshing surface with a lower temperature, and the wheel with the minimum temperature, there is an obvious temperature gradient in the bulk temperature field" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001258_j.isatra.2020.01.020-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001258_j.isatra.2020.01.020-Figure1-1.png", "caption": "Fig. 1. Schematic design of the rotary inverted pendulum.", "texts": [ " Section 4 expresses the control structure and theoretical aspects of the ISMC and the SDRE. Sections 5 and 6 present simulation and experimental tests with respect. Conclusions are reported in Section 7. The state-dependent Riccati equation is a model-based controller and demands a precise nonlinear model to act impressively. The non-modeled parameters play the role of uncertainty in the design which is not satisfactory; hence the uncertainty between the model and the experimental plant should be kept at a minimum level. The schematic design of the system is presented in Fig. 1. A fixed reference frame is regarded by {XYZ} on the first joint and a local frame by {xyz}, on the second joint of the system. The second frame rotates around Z , so it changes the inertia matrix of the second link during a motion. The generalized coordinates of the RIP are selected as q(t) = {q1(t), q2(t)} (rad) and Lagrange method is chosen for the derivation of the equation of motion. The first coordinate of the RIP, q1(t), presents the rotation of the motor and q2(t) presents the Please cite this article as: S" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000310_icrom.2016.7886777-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000310_icrom.2016.7886777-Figure3-1.png", "caption": "Figure 3. Human-inspired Balancing strategies", "texts": [ " The robot will fail to recover from a severe push in one step if the Capture Region doesn\u2019t have intersection with kinematic work space of swing foot and may need more steps. In the next sections we will discuss how to use the potential of CP in Push recovery controller based on the MPC scheme. The response of a human to progressively increasing disturbances can be categorized into three basic strategy: (1) ankle strategy, (2) hip strategy (3) and stepping strategy. Humans tend to use the ankle strategy in case of small pushes to bring back the CP to its desired position as depicted in Fig. 3(a). However the contact between the foot and floor is a unilateral constraint and if the ankle torque will become too large, the ZMP will be move beyond the edge of the foot and the foot will start to rotate. In case of a larger disturbance the capture point will be left the support polygon. Angular momentum of the upper body can be generated in the direction of the disturbance by applying a torque on the hip joint or arm joint as shown in Fig. 3(b). This strategy also called CMP Balancing. With increasing the disturbance the useful strategy will be steeping Fig. 3(c), however there are several situations might occur where stepping is not possible as shown in Fig. 4. In this situation the balance recovery by Hip-Ankle strategy is necessary [11]. Moreover in the situations that contact surface is small such as right side of Fig. 4, generating upper body angular momentum for balance recovery is unavoidable. In this paper the Hip-Ankle strategy is combined in single MPC scheme that will be presented in the following section. III. PUSH RECOVERY CONTROLLER Let us discretize (6), the dynamic equation of LIPM+flywheel" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000995_1464419320915006-Figure15-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000995_1464419320915006-Figure15-1.png", "caption": "Figure 15. Location of vibration acceleration nodes at housing.", "texts": [ " This is because the expression of NVH excitation source has changed after passing through the transfer path such as two-stage gear reducer and differential. Therefore, it is possible to avoid system resonance by changing the natural frequency and the mode shape of gear transmission system, thereby achieving the purpose of dynamic optimization from the perspective of transfer path. Based on this purpose, this paper further analyzes system dynamic response at bearings and housing. In order to fully reflect system dynamic response, this paper selects four nodes at housing as shown in Figure 15, which are respectively taken from the right bearing of input shaft and output shaft and two nodes at middle part of housing. Vibration acceleration responses of these nodes are calculated separately, and mean value of the responses is calculated. The results are shown in Figures 16 and 17. Effects of gear rim thickness variation on dynamic response. As shown in Figures 13 and 16, dynamic response of housing is similar to gear dynamic meshing force. With the increase of gear web thickness, dynamic response gradually tends to be consistent" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001059_j.mechmachtheory.2020.104101-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001059_j.mechmachtheory.2020.104101-Figure7-1.png", "caption": "Fig. 7. The chosen kinematic scheme of the 1 DOF knee mechanism.", "texts": [ " Design of a planar mechanism as an adjustable knee joint Developing a novel mechanism that accurately replicates the human knee joint movement, mainly by reproducing the knee\u2019s ICR trajectory, requires type synthesis to be conducted [32] . The first aim is to achieve a basic knee joint mechanism with 1 DOF that takes into account the possibility of introducing additional DOFs, which if necessary, may provide a better reproduction of the actual motion in the knee joint. In order to find the graphic forms of intermediate chains and basic schemes of potential mechanisms, the intermediate chain method from [32] is applied in this work. In the set of the found mechanism\u2019s kinematic schemes, a solution in the form as in Fig. 7 was chosen as the most appropriate and useful for adaptation to the complex knee movement. This solution is the 4-bar mechanism ( Fig. 2 ), which has already been applied for knee joint modelling. However, in this case it is further enhanced by introducing additional DOFs. The exploration process and the whole variety of achieved solutions were presented in previous work [32] . The chosen solution (that relates to Fig. 7 ) was first modified by adding prismatic joints to bars (2, 3) in order to introduce the two additional DOFs ( Fig. 8 ). However, the same motion can be achieved by applying 2-link modules that are driven by rotational motors, thus obtaining the new solution that is presented in ( Fig. 9 ). This paper is focused on the rotationally adjustable 4-bar mechanism from Fig. 9 . It has two additional DOFs (total of 3 DOFs calculated using the Kutzbach-Gr\u00fcbler equation) with rotational motors (R 1 , R 2 ) instead of cylinders (S 1 , S 2 ), which were previously used in paper [33] ", " The calculation results confirm that the chosen reference ICR trajectories are accurately matched by the new rotationally adjustable 4-bar mechanism, and also that the introduced motions, in the form of the angular velocity of the femur and its C point\u2019s displacements, are correct. However, during the simulation (Ex. 1 in Table 1 ), the reference ICR trajectory is only approximately achieved. This is due to the fact that in this trial the mechanism with the chosen optimal dimensions, but without additional DOFs (since 2-link modules are blocked), is analysed. In this case it is the same as the 4-bar mechanism in Fig. 7 that is identified to model approximately the kinematic mobility of knee. Moreover, even if the ICR trajectory could be achieved more accurately by using a mechanism with other dimensions, e.g. as shown in [24] with a mean error of 0.2 mm, the trajectory could still not be fully reproduced. Even more important is that such a mechanism would only be useful in the case of this one particular knee joint\u2019s ICR trajectory. For these reasons, by applying 2 additional DOFs, as the prismatic joints in the crossing bars, a linearly adjustable 4-bar mechanism is obtained in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001427_j.mechmachtheory.2021.104300-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001427_j.mechmachtheory.2021.104300-Figure3-1.png", "caption": "Fig. 3. Possible applications of the suggested manipulator: experiments under the water (a) and in a wind tunnel (b).", "texts": [ " Many works have studied its geometry [28] , kinematics [29] , workspaces [30 , 31] , singularities [32 , 33] , dynamics [34] , performance [35] , and optimal design [36 , 37] . Hunt has also suggested using the rods that \u201cpierce\u201d the spherical joints in his work [28] . Despite the vast amount of research for the 3-3 scheme, all these works consider the case when the drives move the rods directly. In this paper, the actuation strategy is innovative and differs from the ordinary one. The novelty leads to features of the manipulator analysis, and we will cover some of them later in this work. Fig. 3 demonstrates some applications of the suggested manipulator, including underwater experiments (a) and tests in a wind tunnel (b). With stationary injection points, the manipulator has a potential application in minimally invasive surgery (laparoscopy) though there are many kinematic designs in this field [38] . There are different methods to analyze mechanism mobility. Some of them use simple structure formulas [39] , while others examine the mechanism topology also [40 , 41] . Here we will use the screw theory approach [42] , which allows us to consider the joint axes\u2019 arrangement" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000388_j.jmapro.2018.03.046-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000388_j.jmapro.2018.03.046-Figure1-1.png", "caption": "Fig. 1. Machining specimens (a) short support; (b) tall support.", "texts": [ " In this study, the milling behavior of Inconel 718 block type supports with thin lattice walls. Standard block supports of varying height were fabricated using L-PBF and peripherally end milled to study deformation and fracture behavior, specific cutting energy, and the influence of tooth-support wall interactions on milling forces. A preliminary tool wear study was also conducted to ascertain the suitability of a TiAlN coated carbide end mill for machining Inconel 718 block supports. This tool is commonly used to machine full density Inconel 718. Machining specimens (see Fig. 1) with block supports integrated into a solid base were designed for the experiments. This design enables the use of both blocks supports and solid material for milling experiments on the same specimen. Additional solid metal, 3.175mm (0.125\u2033) in the height direction, was added to facilitate holding in a vise. The block supports were created using the build preparation software provided by Magics. The lattice pattern (see Fig. 2) was defined as a cross-hatched 2-D lattice structure with 0.8 mm hatch spacing. The lattice walls were oriented at an angle of 45\u00b0 with respect to the edges. The average wall thickness was measured to be 0.11mm using an optical coordinate measuring machine. The supports were designed to be \u201cbreakaway\u201d, which implies that the walls are narrower and weaker at the base interface. Specimens were fabricated with a support height of 2mm or 12.5 mm as shown in Fig. 1. This was done to study the effects of support height on milling behavior. It was hypothesized that taller supports would experience a greater bending moment and torsion making them more susceptible to fracture at the root. It was also hypothesized that their greater compliance may lead to a reduction in milling forces. A thin wall was added to the perimeter of the block supports for enhanced anchoring and better heat transfer during L-PBF fabrication. This was done to increase the resistance against delamination and to minimize warpage. The machining specimens were fabricated using an EOSINT M280 L-PBF machine. The default EOS process parameters were used for the EOS IN718 powder (mean size 30 \u03bcm, range: 10 \u03bcm to 60 \u03bcm). The layer thickness was 40 \u03bcm. The block supports originated at the build plate interface and were grown upward as shown in Fig. 1. The completed build was vacuum stress relieved at 1950 \u00b1 25\u00b0 F for 90+ 15/-0min per EOS recommendations. Finally the specimens were removed from the build plate using a wire EDM. Nomenclature D Diameter of the end mill R Radius of the end mill tc Chip thickness at a disk element cr Radial runout of the cutter \u03bb Angle between runout direction and tooth 1 Nt Number of teeth on the end mill ft Feed h Helix angle of the end mill dz Height of each disk element in force model Kt Specific cutting energy NKt Density normalized specific cutting energy Kr Ratio of radial to tangential cutting force doc Depth of cut VR Volume ratio of actual metal removed to swept volume for block supports The specimens were peripheral milled (climb milling) as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000048_tmag.2017.2698004-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000048_tmag.2017.2698004-Figure3-1.png", "caption": "Fig. 3. 3D structure of the rotor.", "texts": [ "org/publications_standards/publications/rights/index.html for more information. single-stator PM machine (Machine I) and a double-stator VPM machine (Machine II), shown in Fig. 2. The consequent-pole PM rotor and the outer stator compose the single-stator PM machine (Machine I). Due to the self-shielding effect of the Halbach-array magnets [10], the rotor back-iron is not essential for Machine I. The inner stator, reluctance rotor and the outer stator compose the double-stator VPM machine (Machine II). The 3D rotor structure is shown in Fig. 3. There is a magnetic bridge behind the Halbach-array PMs, and the thickness of the magnetic bridge is chosen as 0.5mm in this paper. Also, several mounting holes are punched in the rotor iron, and the rotor is supported at both ends. Then, the rotor stress analysis is also conducted. It can be seen in Fig. 4 that the maximum mechanical stress of rotor support is 0.81 MPa, which is smaller than the yield strength of the carbon steel. So the mechanical structure of the rotor is feasible. In order to make both of the magnetic fields excited by the two machines induce back-EMF in the same outer stator windings, the number of outer stator slot Zs, winding pole pair Ps, rotor PM pole pair Pr and inner stator PM pole pair Pis should satisfy: Pr \u00b1 (Pr \u2212 Pis)= Zs (1) Ps = min(Pr, Pr \u2212Pis) (2) The explanation is as follows" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001070_j.mechmachtheory.2020.104127-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001070_j.mechmachtheory.2020.104127-Figure3-1.png", "caption": "Fig. 3. Air spring.", "texts": [ " Experiments for the testing characteristic of the bushing and air spring are conducted with the MTS hydraulic tester. The sub-models (air spring model, bushing model and contact clearance model) are generated by using customized FORTRAN subroutines. The suspension model outputs the penetration depth of clearance joints and the deformations of bushings and air springs to the sub-models, and then the sub-models outputs the calculated forces to the suspension model (see Fig. 2 ). Air spring assemblies consist of the cover plate, piston, bellow and air hole (see Fig. 3 ). The total force of the air spring is the combined results of the thermodynamic force and the Berg\u2019s friction force. Note that the viscoelastic forces of the elastic parts are assumed to be zero due to the K&C test is consider as a quasi-static test. The air spring elastic force F e defined as follows [58] : P c = P \u2212 P atm (2) where P b is the gauge pressure, P is the absolute pressure in the air spring and P atm is the pressure of the atmosphere, and A e is the effective cross section area. The air spring volume V is calculated as P V n = const (3) V = V 0 ( P 0 P ) 1 n (4) where V 0 is the initial internal volume, P 0 is the initial internal pressure and n is the polytrophic coefficient" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003602_tac.2003.809800-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003602_tac.2003.809800-Figure1-1.png", "caption": "Fig. 1. Functions f (x;w), f (x;w) and f (x;w) chosen to satisfy (24)\u2013(26) for any x. That is why the illustration showsw as the only dimension of the argument.", "texts": [ " Assumption 3: There exists a function such that for any vectors and the next inequality holds (25) Assumptions 2 and 3 mean that the function is convex and the function is concave with respect to the vector . Assumption 4: For the given functions , and for any vectors and the following inequalities hold: (26) (27) In addition, there exists a constant such that (28) (29) It has been mentioned in Section II, that function can be considered as the controller . In particular, Assumption 4 holds for the sector-like monotonic functions , , with respect to the vector . The choice of functions and satisfying (24)\u2013(26) is illustrated in Fig. 1. As mentioned in Section I, we assume for the tuning criterion (30) Now, we can propose our first adaptive algorithm for the plant (22) (31) where is a positive definite matrix. In particular, if the tuning criteria , (31) becomes . (32) It is assumed that the partial derivative and, in addition, the function satisfies the local boundedness condition with respect to , . Reaching the control goal (23) with bounded for (31) and (32) is guaranteed due to the following result. Theorem 1: Suppose that for the system (22) and for the chosen macrovariable Assumption 1 holds", " If , implies that , where is a compact set, then control goal (23) is 1Function f(x;w) is said to be locally bounded if for any kxk and kwk there exist such D ( ) and D ( ) that the following holds: kf(x;w)k D ( ) +D ( ): reached in system (22) with algorithm (31) for any positive\u2013definite . Proof of this and other theorems are in Appendix 1. It is straightforward to see that any differentiable function which is monotone in satisfies the conditions of Theorem 1, i.e., for such functions and always exist (see Fig. 1). Necessity to know and may appear as too strong a restriction, but in some practical problems these functions may be chosen just as linear functions . This is indeed the case when nonlinear parameterized function is a sector like function (belonging, for example, to I and III quadrants) and monotonic with respect to its argument . We would like to stress that adaptive algorithm in a form of (31) depends on derivative explicitly and therefore we need to estimate derivative somehow in order to make this tuning scheme practically realizable" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003607_978-1-4020-2249-4_29-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003607_978-1-4020-2249-4_29-Figure2-1.png", "caption": "Figure 2. Kinematic structure of a fully-isotropic parallel manipulator with identical structural solutions for Al and A2", "texts": [ " The elementary kinematic chains A3 and A4 composing D2 have the following arrangements of joints: A3 ~-Rz-Rz) and A4 ~-Pz-Rz-Rz-Rz-Rz). The complex kinematic chain D2 is obtained by connecting A3 and A4 by the three revolute joints R2, R3 and R4 which axes are parallel with the rotation axis of the moving platform (z axis). The two examples presented in Figs.2 and 3 have: AI(J:O-2-3-4-5), A2(1:0-6-7-8-5), A3(1:0-9-10-11) and A4(1:0-12-13-14-15-16-17). The moving platform is n:17. The example presented in Fig. 2 has identical structural solutions for Al ~-Rx-Rx-Rx) and A2 (Ey-Ry-Ry-Ry). The example presented in Fig. 3 has other two distinct solutions for Al ~-Rx Pyz-Rx) and A2 (Ey-pz-Ry-Ry). An approach has been proposed for structural synthesis of a family of fully-isotropic T3Rl-type parallel manipulators. Special legs were conceived to achieve fully-isotropic conditions. As far as we are aware this paper presents for the first time fully-isotropic parallel manipulators with four degrees of mobility and a method for their structural synthesis" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003886_s11249-006-9023-x-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003886_s11249-006-9023-x-Figure7-1.png", "caption": "Figure 7. Interface film thickness normalized by the Hertzian contact radius (upper) and corresponding predicted change in viscosity due to shear rate and film thickness normalized by the bulk, low shear value (lower). The direction of motion, x, is from left to right.", "texts": [ " The EHL simulation was run initially without considering the effects of shear rate and film thickness on viscosity. Then, the wall speed and temperature input into the simulation, and the output film thickness distribution across the interface were substituted into the composite thin film viscosity model (Equation 8) in order to predict the corresponding viscosity change. The interface area film thickness and corresponding predicted change in viscosity due to thin film effects are illustrated in figure 7. The film thickness is normalized by the Hertz contact radius (137 nm) and the viscosity is normalized by the low shear, bulk viscosity of n-decane at 318 K (g0=0.71 cP). Analyses of the film thickness and viscosity contour plots indicate that the overall effects of shear rate and film thickness are to decrease viscosity in the interface area. The predicted viscosity change due to shear rate and film thickness can be evaluated using two-dimensional distributions across the interface centerlines" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003876_978-1-4612-4990-0-Figure13-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003876_978-1-4612-4990-0-Figure13-1.png", "caption": "Figure 13. Three views of a leg from the walking machine.: These projections illustrate the major mechanical features of the leg. There are three hydraulic cylinders, a pair that controls the motion of the upper segment about the universal joint and a single cylinder that moves the lower segment in and out about the knee joint.", "texts": [ "..... 12 Figure 8. It is getting more difficult to identify the waves of recoveries in this gait. .................................... 13 Figure 9. The well known alternating tripods gait. ..................... 13 Figure 10. A further reduction of drive time. .......................... 13 Figure II. Illustration of the advantage of a rear-to-front strategy over a frontto-rear strategy. ........................... 15 Figure 12. Comparison of the cockroach nervous system with a microcomputer. 16 Figure 13. Three views of a leg from the walking machine. ............... 24 Figure 14. The hydraulic ellipse. .................................... 26 Figure 15. Table showing all of the hip valve settings that are provided by the walking machine. .......................... 28 Figure 16. The limits of motion for the foot as defined by the hip joint and actuators. ................................ 29 Figure 17. The natural motions of the machine. ........................ 30 Figure 18. Single ended cylinder", " Finally, the lower cylinders on each side can be connected in a series-parallel arrangement so that all on one side are in parallel together and the two sides are in series in such a way that motion of one side results in compensating motion by the other side. The hydraulic circuits are described in considerable further detail by Sutherland [58]. The hydraulic valves are controlled by a pair of Motorola MC68000 microcomputers, while the displacements of the four pumps are controlled by the human operator who sits on a chair mounted on the frame. This machine differs from previous six legged machines in two important respects, its size and the matching of the natural motions of its legs to the natural motions of walking. Figure 13 shows a leg of the walking machine. The piston diameter of the hydraulic 24 SSA walking machine Chapter 4 cylinders is 1.5 inches and the shaft diameter is 0,625 inch. Each upper cylinder is single ended, that is, the shaft emerges from one end of the cylinder and the other end is closed. The lower cylinder is double ended, with the shaft emerging from both ends of the cylinder. The most important natural motion for walking is the drive stroke, in which a loaded leg is moved rearward. The natural motion here is a straight line stroke of the leg parallel to the desired motion of the center of gravity of the machine" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001719_j.jmapro.2021.01.029-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001719_j.jmapro.2021.01.029-Figure1-1.png", "caption": "Fig. 1. Schematic diagrams of bead modelling. (a) Self-overlapping at the corner; (b) The traditional overlapping model [9]; (c) The proposed corner cross-section model (CCM).", "texts": [ " As a structure usually requires deposition of several layers, excessive overlapping may lead to accumulating errors along the build direction, resulting in unstable deposition or entire failure after several layers. Therefore, it is very important to build a corner cross-section model based on the optimization of the process parameters at corner zones, so that the side effects of excessive self-overlapping can be eliminated or mitigated. In this study, the travelling/welding path at corners are divided into two sections, namely the travelling-in path and travelling-out path as shown in Fig. 1(a). The corner zone is defined as an area where the travelling-in path overlaps with the travelling-out path. The crosssectional profile of a single welding bead can be formulated by a parabolic function [11]. As described in the figure, the bead height, h, and bead width, w, are two important characteristics of a single bead in WAAM. The overlapping process was defined in the literature as the deposited materials overlapped when the centre distance of the adjacent paths is less than the width of the bead as shown in Fig. 1(b). The centre distance, d, between adjacent beads plays an important role in determining surface quality and smoothness of the overlapped area. In the present corner cross-section model, the self-overlapping process is considered as the overlapping of the travelling-in and travellingout beads. As the corner zone shown in Fig. 1(a), line segment AB represents the centre distance which is the function of corner angle, \u03b8, and the distance between the current travel point, A, and the turning point, PT. It can be calculated as d = 2tan(\u03b8/2)\u22c5LA (1) Where, LA is the length of segment APT representing the distance from the current cross section to the turning point. At the initial travel point, I, at corners, the centre distance has the maximum value of w. From the Eq. (1), it is clearly obtained that for a given corner angle, the centre distance reduced linearly as LA decreases, and reaches to zero when the travel point approaches the turning point", " Therefore, the overlapping process is unstable when entering the zone near turning point due to excessive overlapping. Assuming that bead overlapping process in corner zone is similar to that in normal zone as reported in the literature. So, the corner zone can be further divided into two sub-zones according to the distance far away from the turning point. It can be obtained: \u23a7 \u23aa \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23aa \u23a9 LA > d\u2217 2tan(\u03b8/2) , (stable) LA = L\u2217 A = d\u2217 2tan(\u03b8/2) , (critical) LA < d\u2217 2tan(\u03b8/2) , (unstable) (2) Where, LA* is defined as the critical length. As described in Fig. 1(a), the near turning zone is unstable and called excessive overlapping zone (EOZ), while another one is stable and called insufficient overlapping zone (IOZ). To control the forming shape at corners, the corner cross-section model focusing on the EOZ is established as described in Fig. 1(c). The flat overlapping is desired or targeted, therefore, the profile of the crosssection can be expressed as y = { h ax2 + bx + c 0 \u2264 x \u2264 tan(\u03b8/2)\u22c5LA, tan(\u03b8/2)\u22c5LA < x \u2264 w/2 + tan(\u03b8/2)\u22c5LA. (3) Where, a, b, and c are single bead model parameters referring to [7\u20139]. The process parameters of WAAM effecting the forming bead geometry are generally wire feed rate, WF, and travel/welding speed, TS. On the normal path, methods of regression analysis [9], artificial neural network [9,20], and database searching [20] have been reported to determine the optimal welding parameters according to the established single bead model", "(3), the material volume deposition rate (dV/dt) can be expressed as dV dt = Adeposit\u22c5TS(LA), LA \u2265 w 2tan(\u03b8/2) (4) Where, Adeposit represents the cross-sectional area of the deposition, TS (LA) represents the travel speed at the current cross-section which is located at the distance of LA from the turning point. On the normal path, one can obtain Adeposit = Abead = \u03c0\u22c5WF(LA)\u22c5D2 w 4\u22c5TS(LA) ,LA \u2265 w 2tan(\u03b8/2) , (5) Where, Abead is the cross-sectional area of a single bead on the normal path, D w2 is the diameter of the filler wire, and WF(LA) is the wire feed rate at the current cross-section. By inserting Eq.(5) into Eq.(4), on can obtain dV dt = \u03c0\u22c5WF\u22c5D2 w 4 , LA \u2265 w 2tan(\u03b8/2) (6) In corner zone, IOZ and EOZ have been defined above as shown in Fig. 1(a). Adeposit of IOZ is the same as that of normal path as the IOZ is not included in the proposed corner cross-section model as just stated above. Since the welding parameters are keeping constant on normal path and IOZ, one can obtain dV dt = \u03c0\u22c5WF\u22c5D2 w 4 , d\u2217 2tan(\u03b8/2) \u2264 LA < w 2tan(\u03b8/2) (7) While for EOZ, the Adeposit can be derived from Eq.(3) as: Adeposit = \u222bd/2+w/2 0 ydx = h\u22c5d/2 + Abead/2, 0 \u2264 LA < d\u2217 2tan(\u03b8/2) (8) For the single bead has the parabola profile, Abead is equal to 2wh/3. So, one can obtain the following formula for the volume deposition rate on the path dV dt = \u23a7 \u23aa \u23aa\u23a8 \u23aa \u23aa\u23a9 2\u22c5h\u22c5w 3 \u22c5TS\u22c5 [ 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001161_s12555-019-0584-5-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001161_s12555-019-0584-5-Figure3-1.png", "caption": "Fig. 3. The SEA (Series Elastic Actuator) module for the soft exosuit: (a) concept and (b) design.", "texts": [ " Actuator module To generate wire tension in the exosuit, we developed a wire-driven actuator module using Series Elastic Actuator (SEA) technology. The SEA increases compliance by attaching a spring between the actuator and load and includes a sensor for measuring spring deformation [10,11]. The basic concept of the actuator module is to give compliance to the wires through the spring. This affords the wires some flexibility during the movement of human joints, even though they are made of steel. The interaction force between the human and the robot can be determined by measuring the deformation of the spring. Fig. 3 shows the concept and detailed design of the actuator module. One motor can activate both front and rear wires. When the motor rotates, the series elastic component moves linearly along the liner shaft. The series elastic component connects the input and output parts through four compression springs. The spring constant of this mechanism owing to the four springs is 13.4 N/mm. These springs are assembled to apply a preload corresponding to 50% of the maximum deformation. The input part receives the driving force from the motor through the input wire, and the output part outputs the driving force through the front or rear wire" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000927_j.addma.2019.100818-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000927_j.addma.2019.100818-Figure4-1.png", "caption": "Fig. 4. a) Ultrasonically deposited and laser melted rectangle block for the tensile test, b) Contrast group produced by the conventional SLM approach, c) Dimensions of the tensile test sample, d) WEDM-processed tensile test samples with different track distances.", "texts": [ " The previous single layer powder deposition results indicated that the ultrasonically deposited maximum powder layer (see Table 1 and Fig. 8d) was thicker than that in the normal SLM process with powder bed spreading (i.e. 30 \u03bcm\u201350 \u03bcm [31]). The laser beam hatch distance in this experiment was thus reduced to 40 \u03bcm, in order to increase the relative laser energy deposition per unit area to melt the thicker powder layers. Three cuboid blocks were produced via ultrasonic powder deposition with powder compression according to the dimensions described in Fig. 4a. Each block was then sliced into 2 thin tensile specimens based on the geometry described in Fig. 4c, using a wire electrical discharge machining (WEDM) process. Meanwhile, four equally sized cuboid blocks, as shown in Fig. 4b were produced via the conventional soft blade powder spreading approach. The powder layer thicknesses of these four blocks were 50 \u03bcm, and the laser process parameters matched the values in Table 1. One thin tensile test specimen was collected from the center of each cuboid block and was used as the control. The final tensile test samples, shown in Fig. 4d, were prepared according to the ASTM E8-04 standard. WEDM resulted in a thin black oxidation film on the samples\u2019 surface, which was removed by polishing. The voids on the sample with a 1.0mm track distance were observed after polishing, as shown on the left side of Fig. 4d. a) 316 L powder size distribution analysis The 316 L powder size distribution was examined by a particle size analyzer (Mastersizer 3000, Malvern Panalytical Ltd). a) Single track powder deposition and single layer powder deposition A 3D non-contact profile-meter (\u03bcscan, NanoFocus AG, Germany) was employed to capture the 3D profile of the ultrasonically deposited single track powder stripes and single layer powder deposition squares in the initial loose condition and after compression. The mean powder track thickness at the centerline of each powder stripe (i" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003478_003-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003478_003-Figure3-1.png", "caption": "Figure 3. Schematic of the fabrication process. Note that the scales are distorted.", "texts": [ " Shallow and narrow V-grooves yield thin structures with small radii of curvature. The lateral projected distance of the sloped walls is larger for deep V-grooves than for shallow grooves. Therefore, deep V-grooves result in thick and robust structures but with larger radii of curvature due to the more space consuming top width of the V-grooves. A bulk micromaching process is used to form the 3D structures. The fabrication process of the self-assembly polyimide joint is described below in four sections. The sections relate to figure 3 which shows the fabrication process, schematically. (a) The fabrication process starts with a (100) silicon substrate having a 1.5 \u00b5m thermally grown silicon dioxide layer. The 30 \u00b5m deep V-grooves are formed by anisotropic KOH etching. (b) Electrical isolation of the substrate is accomplished by a new 1.5 \u00b5m thermal silicon dioxide layer. This oxide is also used as a stop layer in the following backside etch. In an example demonstrating how easy it is to realize electrical connections to an out-of-plane rotated 3D structure, a 1" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001070_j.mechmachtheory.2020.104127-Figure12-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001070_j.mechmachtheory.2020.104127-Figure12-1.png", "caption": "Fig. 12. Damper experiment (a) Test rig for damper experiment, and (b) velocity-load curve.", "texts": [ " The deformation-load static characteristic curves of air spring under different pressure are shown in Fig. 10 . Results show that the elastic stiffness increases with the increase of the internal pressure. There are four same elastomeric bushings connected to the UCA and LCA. The bushing experiment is shown in Fig. 11 . For elastomeric bushings, there exist three main deformation modes: radial, axial, and torsional [10] . Therefore, only the axial, radial and torsional modes of deformation are considered in this study. Damper experiment is conducted on the damper test rig in Fig. 12 . In the K&C test, the damper velocity is within the range \u22122.4mm/s to 2.4mm/s. The corresponding damping force is in the range of \u221218N and 66N and therefore, the damping force is relatively small and can be neglected. The identified air spring and bushing model simulation curves are compared with the experimental curves in Fig. 13 . The general trends between the experimental and simulation results are the same, although the simulation curves have some discrepancies compared with the experimental results" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000610_pedstc.2018.8343802-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000610_pedstc.2018.8343802-Figure4-1.png", "caption": "Fig. 4. Magnetic flux density distribution of the machine at the aligned position with the phase current of 25A.", "texts": [ " In order to attain the static performance of the proposed machine, a 2-D finite-element analysis is adopted. Fig. 3(a) shows the static torque profiles versus rotor position for different current values when only one phase is excited. Torque curves are obtained for 180\u00b0 elec (10.71\u00b0 mech) conduction interval. The meshing model of the structure is also shown in Fig. 3(b). One problem which comes up from the higher ranges of the excitation current is the irreversible demagnetization of the PM material. Fig. 4 shows the magnetic flux density distribution of the machine at the unaligned position for the input current of 25A. As it can be seen, the flux density in the PM is in the range of 0.5-1.3T, which is much higher than of 0.4T. Since, the phase current at normal operation is lower than 25A, there will be no irreversible demagnetization in the PMs. III. COMPARISON WITH OTHER VRMS In order to evaluate the superior operation of the machine, a comprehensive comparative study is done. Fig. 5 shows the cross section of two other MVRMs; one is the same proposed MVRM without PMs, and the other is a conventional 12/14 MVRM" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001207_052002-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001207_052002-Figure2-1.png", "caption": "Figure 2. Pressure distribution for two bearing designs Figure 3. 1 MW FlexPad bearing demonstrator [3]", "texts": [ " Figure 1 illustrates the functionality of the FlexPad called flexible arm support structure. In this concept the plain bearing segments are mounted on a special designed flexible arm. Due to the external and inner flexibility of the arm, the segment can perform a parallel displacement and follow the displacement of the shaft (Figure 1, 3) which prevents the occurrence of edge loading. The geometry of the flexible arm has amongst other parameters (arm length, inlet contour etc.) a major influence on the pressure distribution. Figure 2 shows the simulated pressure distributions of a FlexPad moment bearing with two different arm geometries. The bending stiffness of the arm of bearing A does not allow a proper alignment of the segment and high pressure peaks occur. In comparison the arm The Science of Making Torque from Wind (TORQUE 2020) Journal of Physics: Conference Series 1618 (2020) 052002 IOP Publishing doi:10.1088/1742-6596/1618/5/052002 stiffness and the inlet contour of each segment of bearing B to the right are well designed and the hydrodynamic pressure is more evenly distributed for this bearing" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000818_tie.2019.2939980-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000818_tie.2019.2939980-Figure7-1.png", "caption": "Fig. 7. FEM model", "texts": [ " Electromagnetic Analysis The electromagnetic field of the motor is solved by the transient field. Then, the Maxwell stress tensor method is used to calculate the electromagnetic force acting on the stator of the motor. The magnetic force distribution can be described as a sum of rotating waves with different spatial order and time harmonic. The radial magnetic force densities are decomposed into the truncated set of temporal and spatial Fourier coefficients. For the sake of comparison, the stator of the motor is divided into four sections in the axial direction, as shown in Fig.7. Fig.8 shows the magnetic field in the air gap along the three lines l1, l2, and l3, labelled in Fig.5. The line l1 locates in the air gap in the circumferential direction of the common motor. The line l2 locates in the air gap in the circumferential direction of the proposed motor, and The line l3 locates in the air gap in the axial direction of the PM interpoles. Fig.8 (a) denotes the magnetic field along the line l1 and l2, and Fig.8 (b) represents the magnetic field along the l3. The spatial magnetic field distribution and the electromagnetic force density can be seen in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000327_j.mechmachtheory.2017.05.014-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000327_j.mechmachtheory.2017.05.014-Figure4-1.png", "caption": "Fig. 4. The tooth number of helical curve-face gear.", "texts": [ " So, the contact point without misalignment in the meshing process of helical curve face gear pair can be discussed as follows: { f s 2 ( \u03b2s , \u03d5 s , \u03bes ) = f s 1 ( \u03b2s , \u03d5 s , \u03bes ) f s 1 ( \u03b2s , \u03d5 s , \u03bes ) = 0 f s 2 ( \u03b2s , \u03d5 s , \u03bes ) = 0 (18) And the parameters ( \u03b2s , \u03d5s , \u03be s ) for the contact point should be limited on the surfaces of the gear pair with Eq. (19) . { r 2 (2 \u2032 ) ( \u03d5 2 , \u03be2 ) = M 2 \u2032 s \u2032 \u00b7 r s (s \u2032 ) ( \u03d5 s , \u03bes ) r 1 (1 \u2032 ) ( \u03d5 1 , \u03be1 ) = M 1 \u2032 s \u2032 \u00b7 r s (s \u2032 ) ( \u03d5 s , \u03bes ) (19) And as the structure of helical curve face gear changes periodically, so any adjacent five teeth of curve face gear in half a cycle can show the characteristics in detail. The tooth number is shown in Fig. 4 . The helical curve face gear and non-circular gear are both built by the surface of the same shaper cutter. So most parameters of the curve face gear pair are decided by the shaper cutter. Some parameters of the helical curve face gear pair are shown in Table 1 . According to Eqs. (18) and (19) and with the help of MATLAB (Matrix Laboratory), the contact points can be obtained. And the function of transmission errors is shown in Eq. (20) . { \u03d5 2 = \u222b \u03d5 1 0 1 / i 12 d \u03d5 = 1 R \u222b \u03d5 1 0 r( \u03d5 1 ) d \u03d5 \u03d5 2 = \u03d5 2 \u2212 \u03d5 2 \u2032 (20) Where, \u03d5 2 \u2032 is the rotating angle with misalignment" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003122_s0094-114x(96)00033-x-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003122_s0094-114x(96)00033-x-Figure4-1.png", "caption": "Fig. 4. The RSSRR-SRR mechanism.", "texts": [ " Also, the partial derivative of the loop-closure function with respect to that particular R joint variable becomes zero. In the case of multi-loop mechanisms, singularity in one loop causes singularity of the mechanism, though the converse is not necessarily true. This fact is illustrated in the next example. For the singularity analysis of multi-loop mechanisms, we consider two examples: (1) the one-degree-of-freedom RSSR-SC mechanism shown in Fig. 3 and (2) the two-degree-of-freedom RSSRR-SRR mechanism shown in Fig. 4. 3.1.1. The R S S R - S C mechanism. Figure 3 shows the RSSR-SC mechanism with three coordinate systems, {O1}, {02} and {03}. Assuming that 01 is the actuated joint, when 0, is locked, the first link is fixed and singularity due to the spherical joint $1 is impossible. Next, we consider the possibility of singular configurations due to the spherical joint $2. We cut the mechanism at $2 and denote the point $2 of the platform as S2p and that of the link 2 as $2~. In the loop RtStS3CR1, we have three joint variables which must satisfy the corresponding loop-closure equation", " With 01 as the input, at singularity, det[J*] = 0, and we can write FC12 0 0 J det[Cz2 C33 2 C34 2 =0\" The above equation can be written in the form (22) det[A], det[B] = 0 where det[A] = Cn and det[B] = C23C34 - C24C33. Therefore, at a singularity configuration, either det[A] = 0 or det[B] = 0. On simplification; det[A] = 0 is found to be equivalent to singularity in the RtS, S2R2Rt loop and det[B] = 0 is equivalent to equation (19). It may be mentioned that det[B] = 0 or the geometric condition equation (19) does not correspond to any single loop becoming singular. 3.1.2. The RSSRR-SRR mechanism. To develop the geometric concept further, we next consider a two-degree-of-freedom R S S R R - S R R mechanism. Figure 4 shows the R S S R R - S R R mechanism with coordinate systems, {O1}, {02} and {04} attached to the three revolute joints at the base and coordinate systems {O3}, {05} attached to the revolute joints R3 and Rs. For simplicity, we assume the axes of R2 and R3 are parallel. Similarly, the axes of R4 and R5 are assumed parallel. The R S S R R - S R R mechanism has two degrees of freedom, and we assume 01 and 02 to be the actuated joints. If the inputs are locked, the joint S~ is fixed in space and cannot cause any singularity" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001348_tmrb.2020.3033020-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001348_tmrb.2020.3033020-Figure8-1.png", "caption": "Fig. 8. Illustration of the experiment platform. (a) The overall structure of DeltaMag prototype, which contains the motor module to actuate the parallel mechanism, the coil module to generate dynamic magnetic fields, and the vision module to obtain the swimmer location. \u2460 is the slide block, \u2461 is the electromagnetic coil, \u2462 is the motor, \u2463 is the stereo camera, and \u2464 is the glycerol solution tank. (b) Fabricated swimmers: the helical swimmer with a rigid resin propeller and the soft-bodied swimmer with a flexible elastomer tail, which are compared with a Hong Kong two-dollar coin. (c) Two image pairs of the helical swimmer and the soft-bodied swimmer from the stereo camera, where green boxes are tracking results.", "texts": [ " n\u03b1 = n\u22121\u03b1 + kp\u03b1\u00d7n\u03b8s + kg\u03b1 \u00d7 n\u2211 i=1 n\u03b8s n\u03b3 = n\u22121\u03b3 + kp\u03b3 \u00d7n\u03c6s + kg\u03b3 \u00d7 n\u2211 i=1 n\u03c6s (29) where kp\u03b1 and kp\u03b3 are proportionality coefficients; kg\u03b1 and kg\u03b3 are integration coefficients. These values are decided by experiments. Based on the updated yaw angle and pitch angle of the dynamic magnetic field, the real-time field vector can be further calculated through (6) and (8) for the helical swimmer and the soft-bodied swimmer, respectively. Finally, the corresponding coil actuation array can be deduced according to the field generation algorithm depicted in Section II-C. The overall system is shown in Fig. 8(a), which integrates three modules. The motor module contains three step motors (Model: NEMA17), and is controlled by a micro-controller (Model: Arduino Mega 2560). The coil module is driven by three servo-amplifiers (Model: ESCON 70/10, Maxon Inc.), and the current signal is sent by a multi-functional I/O card (Model: 826, Sensory Inc.). The vision module is composed of a shell and two USB endoscopes (Model: HK-3.9-0.1). A PMMA tank (\u03c6 290 mm \u00d7 45 mm) full of 96% glycerol solution provides low Reynolds numbers open fluid environment for swimming studies. Two scaled-up swimmers are processed as Fig. 8(b) shows. The helical swimmer has a 3D-printed resin propeller with a screw-like structure, and a cylindrical permanent magnet is inserted in the head. The magnetization of the helical swimmer is perpendicular to its long axis. The soft-bodied swimmer has a reverse-molded elastomer tail with a cone-like structure, and a disc permanent magnet is attached to the head. The magnetization of the soft-bodied swimmer is along its long axis. Fig. 8(c) shows image pairs and tracking results during experiments, which are used to rebuild the location of swimmers. Authorized licensed use limited to: Carleton University. Downloaded on May 29,2021 at 09:40:14 UTC from IEEE Xplore. Restrictions apply. The swimming characterization of two swimmers is conducted in this section, which determines the constants of the general kinematic model. To avoid severe boundary effect, each time, the swimmer swims to half height of the tank at the beginning, and then start propulsion actuated by the desired magnetic field at this altitude" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001347_s12555-020-0026-4-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001347_s12555-020-0026-4-Figure2-1.png", "caption": "Fig. 2. Schematic of the omnidirectional mobile robot.", "texts": [ " PROBLEM FORMULATION In this section, the kinematic and dynamic models of the double-frame omnidirectional mobile robot are established by using Lagrange method. 2.1. Kinematic model Under the condition of complete adsorption, the configuration of the omnidirectional mobile robot can be described by five generalized coordinates. Among them, three variables describe the position of the platform, and two variables describe the orientation of the platform. Therefore, let q = [ xc yc zc \u03b2 \u03b8s ]T , where (xc,yc,zc) are the coordinates of the center of mass Pc in the world coordinate system, and \u03b2 is the rotation angle of the platform, as shown in Fig. 2(b), \u03b8s is the angular of the robot sliding motor. Assuming the robot does not slip during the movement on the aircraft surface. The following constraint equations are true. x\u0307c cos\u03b2 = y\u0307c cos\u03b1 sin\u03b2 + z\u0307c sin\u03b1 sin\u03b2 +d\u03b2\u0307 , x\u0307c sin\u03b2 + rs\u03b8\u0307s =\u2212y\u0307c cos\u03b1 cos\u03b2 \u2212 z\u0307c sin\u03b1cos\u03b2 , (1) where \u03b1 is the dip angle, as shown in Fig. 2(a). Consider that all kinematic equality constraints are independent of time, (1) can be written A(q)q\u0307 = 0, (2) where A(q) = [ cos\u03b2 \u2212cos\u03b1 sin\u03b2 \u2212sin\u03b1 sin\u03b2 \u2212d 0 sin\u03b2 cos\u03b1 cos\u03b2 sin\u03b1 cos\u03b2 0 rs ] , (3) and rs is the radius of the sliding motor, d indicates the distance from the geometric center Po to the mass center Pc of the omnidirectional mobile robot along the positive Y \u2212axis. Let S(q) = [ S1(q) S2(q) S3(q) ] , be the full rank matrix, and the null space of A(q), that is A(q)S(q) = 0, (4) where S1(q), S2(q), S3(q) \u2208\u211c5", " It is straightforward to verify that the following matrix S(q) = rs sin\u03b2 0 0 rs cos\u03b1 cos\u03b2 \u2212sin\u03b1 0 rs sin\u03b1 cos\u03b2 cos\u03b1 0 0 0 1 1 0 0 (5) satisfies A(q)S(q) = 0. It is possible to find an auxiliary vector time function \u03bd (t) \u2208\u211c3, and \u03bd (t) = [ \u03c9s vz \u03c9r ]T , such that, for all t q\u0307 = S(q)\u03bd (t), (6) where \u03c9s is the angular velocity of sliping motor, vz is the expansion speed of a cylinder in the robot\u2019s leg, \u03c9r is the angular velocity of rotating motor. 2.2. Dynamic model The Lagrange equation is used to derive the dynamic equations of the omnidirectional mobile robot. The total kinetic energy [34] L is L = 1 2 q\u0307TM(q)q\u0307 = 1 2 mvT v+ 1 2 \u03c9 T I\u03c9. (7) In Fig. 2(a), when the outer frame adsorbs, the total kinetic energy L can be written as follows: L = 1 2 (m1 +m2)(x\u03072 c + y\u03072 c + z\u03072 c) + 1 2 Is\u03b8\u0307 2 s + 1 2 Ir(k\u03b2\u0307 )2, (8) where Is is the moment of inertia of the sliding motor rotor about the axis, Ir is the moment of inertia of the rotating motor rotor about the axis. k is the ratio coefficient between \u03b2 and \u03b8r, and k is a constant. \u03b8r is the angular of the robot rotating motor. Lagrange equation of motion for the omnidirectional mobile robot system is governed by [35] d dt \u2202L \u2202 q\u0307 j + \u2202L \u2202q j =F \u2212\u03bb1a1 j\u2212\u03bb2a2 j, j = 1,2, " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001756_j.mechmachtheory.2021.104345-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001756_j.mechmachtheory.2021.104345-Figure9-1.png", "caption": "Fig. 9. Dynamic model.", "texts": [ " The NSGA-II is very effective for many complex problems which are difficult to be solved by traditional optimization algorithms, especially for highly nonlinear multi-objective optimization problems [36\u201341] . Based on NSGA-II, the pinion modified tooth surface and corresponding optimization variables meeting functional requirements can be obtained. In general, many groups of processing parameters can be obtained after optimization. In this paper, through comparative analysis, a group of solutions with better effect is selected to verify the innovative ease-off flank modification method. According to the 8-DOF dynamic model of spiral bevel gear shown in Fig. 9 , the vibration equation shown in Eq. (38) is established, and its dynamic performance is analyzed by applying loaded transmission error excitation and meshing impact excitation in dynamic model. \u23a7 \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23a9 m 1 \u0308X 1 + c 1 x \u02d9 X 1 + k 1 x X 1 = \u2212F x m 1 \u0308Y 1 + c 1 y \u0307 Y 1 + k 1 y Y 1 = \u2212F y m 1 \u0308Z 1 + c 1 z \u0307 Z 1 + k 1 z Z 1 = \u2212F z J 1 \u0308\u03b81 = T 1 \u2212 F n r 1 + F s r 1 m 2 \u0308X 2 + c 2 x \u02d9 X 2 + k 2 x X 2 = F x m 2 \u0308Y 2 + c 2 y \u0307 Y 2 + k 2 y Y 2 = F y m 2 \u0308Z 2 + c 2 z \u0307 Z 2 + k 2 z Z 2 = F z J 2 \u0308\u03b82 = \u2212T 2 + F n r 2 \u2212 F s r 2 (38) where F s represents the impact force, and it is obtained based on impact theory shown in Section 4", " The companion shows that impact velocity and impact force of second-order spiral bevel gear before optimization are 0.6315 m/s and 5706.6 N, respectively, impact velocity and impact force of second-order spiral bevel gear after optimization are 0.5459 m/s and 4891.9 N, which are 13.56% and 14.28% lower than those before optimization. After optimization, meshing impact of second-order spiral bevel gear is reduced. When load is 1800 N \u2022m and pinion rotational speed is 20,0 0 0 r/min, based on the 8-DOF dynamic model shown in Fig. 9 , the dynamic performance of spiral bevel gear transmission is analyzed by applying LTE excitation and meshing impact excitation in the dynamic model. The dynamic response of second-order spiral bevel gear before and after optimization is analysed. The results are shown in Fig. 13 . The companion shows that the dynamic load factor of second-order spiral bevel gear before optimization is 1.0808, while the dynamic load factor of second-order spiral bevel gear after optimization is only 1.0622. After optimization, the running vibration of second-order spiral bevel gear is reduced, and its dynamic performance is improved", " During loaded transmission, the instantaneous meshing stiffness of gear transmission will also change with the mesh tooth pair number at the same time, which will cause dynamic load. To analyze the influence of dynamic load on gear transmission, dynamic load factor is introduced. Dynamic load factor reflects the vibration characteristics of gear transmission. When dynamic load factor increases, the running vibration of gear transmission is more intensive. Based on the 8-DOF dynamic model of spiral bevel gear transmission shown in Fig. 9 , the dynamic response of optimized second-order and innovative modified spiral bevel gear under the same working condition (load is 1800 Nm, and pinion rotational speed is 20 0 0 0 r/min) are compared. The results are shown in Fig. 19 . The companion shows that the dynamic load factor of innovative modified spiral bevel gear is 1.0363, which is much smaller than the dynamic load factor of optimized second-order spiral bevel gear (1.0622). Therefore, the innovative ease-off flank modification method can effectively reduce the running vibration and improve the dynamic performance of high-speed spiral bevel gear" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001760_tie.2021.3076715-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001760_tie.2021.3076715-Figure3-1.png", "caption": "Fig. 3. Schematic diagram of PMSM coupled with DC generator.", "texts": [ " The dynamic behavior of system depends upon geometrical parameters (mass polar moment of inertia), material properties (torsional stiffness and damping) and excitation source. The response becomes drastic at resonance [15] (frequency of vibration matches with natural frequency) which causes misalignment, fatigue of rotational components and generates huge acoustic noise because of severe impact loading from adjoining components. Hence it is important to analyze the vibrational behavior of system. Fig. 2 shows the pictorial view of three-phase PMSM coupled with DC generator. Schematic diagram of PMSM coupled with DC generator is shown in Fig. 3. Power is transmitted from driving shaft (S1) to driven shaft (S3) through transmission shaft (S2). Roller support (B2) is provided at midspan of S2, to avoid whirling motion which usually takes place, where the length to diameter ratio between support is high, hence transverse vibration is negligible. Oldham coupling (A) having discs (C1) and (C2) are pinned with shaft S1 and S2, respectively. Similarly, oldham coupling (B) having disc (C3) and (C4) are attached with shaft S2 and S3, respectively. Oldham couplings are used to transmit power between shafts of different diameters and different axis of rotation (in Fig. 3 all shafts are coaxial). Roller contact bearing (B1) is provided in between S1 and motor stator, similarly, at generator end, B3 is in between S3 and generator hub. An equivalent five DOF torsional lumped model is shown in Fig. 4. Five degree of freedom are chosen using effective modal mass and modal participation factor. According to it, the number of significant modes are considered in such a way that the effective mass must be atleast 95 % of actual mass [13, 17]. In present case effective mass (in rotational system polar moment of inertia), is 99 % up to first two modes" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000620_s11071-018-4338-3-Figure11-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000620_s11071-018-4338-3-Figure11-1.png", "caption": "Fig. 11 Mapping between three configurations in the continuum mechanics approach", "texts": [ " For an arbitrary point with dimensionless coordinates in the longitudinal and lateral directions \u03be and \u03b7, the position vectors of the corresponding points on the top and bottom surfaces defined, respectively, by rt , rb, and the cross-sectional thickness h\u03be are rt = S (\u03be, \u03b7, \u03b6t ) e, rb = S (\u03be, \u03b7, \u03b6b) e, h\u03be = h0 [\u03b1 (1 \u2212 \u03be) + \u03b2\u03be ] (11) where h0 is the nominal thickness before altering the element shape, and \u03b6t and \u03b6b refer to the nondimensional thickness parameterwhosedefinitionvaries with the type of element. It is clear that the thickness of the element changes linearly with respect to the length; thus, the parabolic leaf spring canbe approximatedwith linearly tapered ANCF elements. Table 2 shows examples of geometries that can be obtained using a single element of the types of elements used in this study. 5.4 ANCF modeling of the spring pre-stress In order to develop accurate representation of the leaf spring pre-stress, the three different configurations shown in Fig. 11 must be considered. These configurations are the straight configuration, the initial stressfree configuration, and the assembled pre-stress configuration. The initial stress-free configuration is a curved configuration as shown in Fig. 11. A line element dx in the straight configuration corresponds to a line element dri in the initial configuration and to a line element dr in the current configuration. The relationship between dr and dri is defined using the matrix of position vec- tor gradients J, the relationship between dr and dx is defined using the matrix of position vector gradients Je, and the relationship between dri and dx is given by the matrix Ji . One has the following relationships: dr = Jdri , dr = Jedx, dri = Jidx, J = \u2202r \u2202ri = ( \u2202r \u2202x ) ( \u2202x \u2202ri ) = JeJ \u22121 i (12) The Green\u2013Lagrange strain tensor is defined in terms of the position vector gradient matrices as \u03b5 = 1 2 ( JT J \u2212 I ) = 1 2 [ J\u22121T i ( JTe Je ) J\u22121 i \u2212 I ] (13) where Je = \u2202 (Se) /\u2202x, S is the shape function matrix, and e is the vector of nodal coordinates of the leaf spring in the current configuration", " Two initial configurations of the leaf spring can be used depending on whether or not the pre-stress is considered in the analysis, which are the configurations before and after assembly, as shown in Fig. 8a, b. Denoting the vector of nodal coordinates of the leaf spring before and after the assembly as eu and e0, respectively, the corresponding matrices of position vector gradients are denoted as Ju and J0. If the leaf spring assembly is used as the initially stress-free configuration, shown as the dashed line in Fig. 11, there will be no initial stresses. In order to account for the pre-stress caused by the assembly process, the configuration before assembly shown in Fig. 8a should be used as the initial stress-free configuration, the mapping relation is shown as the solid line arrows in Fig. 11, and thus Ji = Ju . Therefore, there exists initial stress in the configuration of the leaf spring assembly since J = JeJ\u22121 u = J0J\u22121 u and the initial strain \u03b50 = ( J\u22121T u ( JT0 J0 ) J\u22121 u \u2212 I ) /2. The difference between the assembly configuration and the un-deformed configuration ed0 = e0 \u2212 eu is used to determine the desired pre-stress value. As shown in Fig. 1, the leaf spring is connected to the chassis at one end using the shackle and at the other end using a pin joint. It is also rigidly connected to the axle at the spring seat by a set of U-bolts at the center section" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003699_j.mechmachtheory.2006.09.004-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003699_j.mechmachtheory.2006.09.004-Figure1-1.png", "caption": "Fig. 1. Prototype of XNZ63 PKM.", "texts": [ " The results show that the simplified error is small enough to introduce a more accurate dynamic model into the real-time control system. At the same time, the dynamic simulation with the inertia of legs being negligible is also performed. The 6-UPS Stewart platform-based parallel kinematic machine (XNZ63 PKM) has six degrees of freedom, and the Stewart platform has a base and a platform connected by six extensible legs with spherical joint at one end and universal joint an the other. The prototype of XNZ63 PKM is shown in Fig. 1, and one leg is shown in Fig. 2 with the associated symbols. The base coordinate system R0 is fixed on the worktable, a moving coordinate system Rp is attached to the moving platform, coordinate systems Ru and Rd are fixed on the upper and lower parts of the leg, respectively. Ruc and Rud coordinate systems, which are parallel to R0 coordinate system, are established and their origins are the centers of mass of the upper part and the lower part of the leg, respectively. R is the rotation matrix from Rp coordinate system to R0 coordinate system, pi is the position vector of the spherical joint in Rp coordinate system, t is the position vector of the origin of Rp coordinate system in R0 coordinate system, bi is the position vectors of universal joint; ui and vi are the unit vectors of the fixed axis and the rotational axis of the universal joint, respectively; eiu and eiv are the angular accelerations of the ith leg with respect to the fixed axis and the rotational axis of the universal joint, respectively; riu0 is the position vector of the mass center of the upper part of the leg in Ru coordinate system, and rid0 is the position vector of the mass center of the lower part of the leg in Rd coordinate system" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000842_j.msea.2019.138736-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000842_j.msea.2019.138736-Figure1-1.png", "caption": "Fig. 1. Illustration of slip systems in (a) BCC \u03b2 phase (b) HCP \u03b1 phase.", "texts": [ " \u03c4\u03b7 c \u00bc \u03c4\u03b7 0 \u00fe \u03c4\u03b7 H \u00fe \u03c4\u03b7 S (9) \u03c4\u03b7 H is determined by Bailey-Hirsch relation: \u03c4\u03b7 H \u00bc\u03b1*b\u03bc XN s\u00bc1 \u03a9\u03b1s ffiffiffiffiffiffi \u03c1s TS p (10) The total statistically stored dislocation density calculated using mobile dislocation density \u03c1s M and immobile dislocation density \u03c1s I : _\u03c1s M \u00bc \u03b11\u03c1s M\u03c5\u03b1 g ~l \u03b1 g 2\u03b12Rc\u03c1s M\u03c1s M\u03c5\u03b1 g \u03b13\u03c1s M\u03c5\u03b1 g ~l \u03b1 g \u00fe \u03b14 \ufffd j\u03c4\u03b1 j \u03c4\u03b1 cr \ufffdr \u03c1s I\u03c5\u03b1 g ~l \u03b1 g \u00fe X\u03b15P\u03b2\u03b1\u03c1\u03b2 M\u03c5\u03b1 g ~l \u03b1 g \u03b16Rc\u03c1s I\u03c1s M\u03c5\u03b1 g (11) _\u03c1s I \u00bc \u03b13\u03c1s M\u03c5\u03b1 g ~l \u03b1 g \u03b14 \ufffd j\u03c4\u03b1 j \u03c4\u03b1 cr \ufffdr \u03c1s I \u03c5\u03b1 g ~l \u03b1 g \u03b16Rc\u03c1s I\u03c1s M\u03c5\u03b1 g (12) The evolution law and the physical representations of the two equation above are detailed by Lyu et al. [29,40]. BCC and HCP lattice structures were employed to capture the different slip systems in dual phase Ti6Al4V. BCC is highly symmetric lattice structure with the same atom space in all unit cell dimensions. There are a total of 12 dominant {111}<110> slip systems (see Fig. 1a) in BCC phase. The HCP phase in titanium alloys has an aspect ratio of 1.587 (a/c). Three dominant slip systems families were implemented, namely Prismatic, Basal and Pyramidal (Fig. 1b). The slip systems used in the model were detailed in Table 1. A 2D 0.3 mm \ufffd 0.3 mm Voronoi tessellation microstructure containing 100 equiaxed grains (average grain size of 33.6 \u03bcm) were generated using Rhinoceros\u00ae CAD (Robert McNeel & Associates, WA, USA) with the open source Grasshopper\u00ae plugin. The CAD file was then imported into Abaqus\u00ae [41]. A custom written Python script randomly select the grains using NumPy and then converted equiaxed grains to lamellae by defining a lath substructure. Fig", " Harrison Materials Science & Engineering A xxx (xxxx) xxx Data availability The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study. Declaration of competing interest None. This publication is supported by College of Informatics and Engineering (CoEI) Postgraduate Scholarship, NUI Galway. The authors would like to thank Prof. Allison M. Beese and Mr. Alexander Wilson-Heid for providing the experimental stress-strain data used to produce Fig. 6. Appendix I Supplementary Fig. 1. Determination of yield stress at 0.2% offset in parameter sets 1 to 9. [1] M. Koizumi, FGM activities in Japan, Compos. B Eng. 28 (1) (1997) 1\u20134. [2] S. Ali, B. Ardeshir, Optimum Functionally Gradient Materials for Dental Implant Using Simulated Annealing, INTECH Open Access Publisher, 2012. [3] A. Sola, D. Bellucci, V. Cannillo, Functionally graded materials for orthopedic applications \u2013 an update on design and manufacturing, Biotechnol. Adv. 34 (5) (2016) 504\u2013531. [4] T. Niendorf, et al., Functionally graded alloys obtained by additive manufacturing, Adv" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003490_j.optlastec.2003.12.003-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003490_j.optlastec.2003.12.003-Figure2-1.png", "caption": "Fig. 2. Schematic of laser cladding on an inclined plane.", "texts": [ " The in-time motion adjustment strategy includes two parts for avoiding the defects on the upper surface and those at side surfaces, respectively. Provided the distribution of laser power is a Gaussian function as the distribution of powder concentration, its variation tendency is similar to that of powder concentration. Thus, the distribution of laser power would not be illustrated in the following. Declining of the side surface results from un(t distribution of laser power and the powder being deposited, and a4ects signi(cantly eJcient powder catchment through a coaxial nozzle. If the existing side surface is inclined as shown in Fig. 2, the powder catchment on it varies signi(cantly. Ref. [15] described the powder distribution mode of coaxial laser cladding on an inclined substrate as G = g[( h+ \u221a x2 + y2 tan ) tan ]2 \u00d7 exp \u2212 3 \u221a x2 + y2( h+ \u221a x2 + y2 tan ) tan 2 ; (x\u00a1 0); G = g[( h\u2212 \u221a x2 + y2 tan ) tan ]2 \u00d7 exp \u2212 3 \u221a x2 + y2( h\u2212 \u221a x2 + y2 tan ) tan 2 ; (x\u00bf 0); (3) where is the angle between the side surface and the horizontal. Assuming that the angle is equivalent to 45\u25e6, the powder concentration on an inclined side of the existing clad layer was calculated with Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003976_mcs.2006.1636310-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003976_mcs.2006.1636310-Figure6-1.png", "caption": "FIGURE 6 (a) An exploded view and (b) the HoTDeC thruster. The three-piece body is fitted with system components: the lower piece has all five thrusters mounted; the electronics of the hovercraft are fixed to the middle piece; the top surface protects the electronics. The lower and middle body pieces form a plenum, pressurized by the radially mounted lift thruster, which provides the air source for the hovercraft skirt. On the right is a thruster body and propeller, which are fabricated in-house using rapid prototyping methods. A small electric motor is mounted inside the back of the body to power the thruster as well as the made-in-house speed controller board.", "texts": [ " The hovercraft bodies are designed and built specifically for the testbed, and software-based design tools are used to model the geometry of the parts as well as the weight distribution. To reduce pitching and rolling, the craft is designed so that, when fully assembled, the center of mass is in the thrust plane and along the central axis of the outer body cylinder (see Figure 5). This design requires precision placement of the components inside the hovercraft. This placement is done by designing the inside body of the craft as a fixture, with machined pockets and mounting holes as can be seen in Figure 6. To accommodate the need for a lightweight body and mounting fixture design, the body of the craft is constructed from high-density foam, which is easily machined. We design the body in ProEngineer, create computer numerical control (CNC) tool paths, and machine the hovercraft in the Ford Manufacturing Laboratory at UIUC. The skirt of the craft, which is custom made for the HoTDeC system, functions similarly to conventional hovercraft skirts. Air is blown into the skirt, and the area directly under the hovercraft body becomes pressurized; air flows out from under the craft between the skirt and the floor providing an air bearing for the craft", " The skirt itself, which is made of a thin sheet of contoured plastic, is designed to maximize lift without introducing wobble instabilities. The current design, arrived at through several empirical iterations, supports a maximum payload of approximately 4.5 kg. Referring to Figure 5, the top surface of each vehicle is a lightweight cover that displays a hovercraft-identifying pattern used by the ceiling-mounted camera network. In the newest craft, the top surface is the mounting location for onboard cameras. The hovercraft thruster bodies and propellers shown in Figure 6 are custom designed and modeled using ProEngineer and experimental data to optimize thrust. These components are printed using fused deposition JUNE 2006 \u00ab IEEE CONTROL SYSTEMS MAGAZINE 59 modeling (FDM) equipment in the UIUC Ford Manufacturing Laboratory, after which thrusters are assembled by inserting small electric motors. Each assembled thruster produces a maximum thrust of 2.2 N at a maximum speed of 15,400 rpm, and has an experimentally measured speed-force relationship that is nearly quadratic" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000401_s12206-018-0611-0-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000401_s12206-018-0611-0-Figure1-1.png", "caption": "Fig. 1. Compound planetary gear set: (a) The first gear stage; (b) the second gear stage.", "texts": [ " In this paper, a gear tooth tip chipping propagation model is proposed, and the analytical equations of TVMS of a chipped gear for a compound planetary gear set are derived. Then, the TVMS reduction of sun-planet mesh pair with chipping growth on the sun gear is quantified. Four cases are simulated and analyzed to demonstrate the effects of TVMS reduction on the gear system and the theoretical fault properties of the gear system when single or multi-tooth chipping occurs on the sun gear of different gear stage. Finally, the corresponding experimental signals are analyzed to validate the theoretical derivations. Fig. 1 shows the schematic of a compound planetary gear transmission. The system consists of two gear stages: one simple and one meshed-planet. Two gear stages share one ring gear which is denoted by r . The first gear stage involves the sun gear 1s , several planet gears ip& ( 11, 2, ,i N= L , 1N is the number of planets), and the left part of the ring gear lr . The second gear stage consists of the sun gear 2s , several meshed-planet pairs \u02c6i ip p- ( 21,2, ,i N= L , 2N is the number of the meshed-planet pairs), and the right part of the ring gear rr " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001395_s12206-020-1240-y-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001395_s12206-020-1240-y-Figure5-1.png", "caption": "Fig. 5. Streamlines of oil from the stator inlet.", "texts": [ " In the crown part, approximately 96 % of the oil flows on the outer surface of the coil, and the rest is splashed out of the coil or into an empty space on the stator side. The welded part is affected by the protruding weld, and approximately 90 % of the oil flows on the outer surface of the coil. The remainder flows between the protruding weld or into the empty space on the stator side. As can be observed from the quantity and distribution of the oil streamline in Fig. 4, the welded part has lesser oil covering the outer surface of the coil in comparison with the crown part, thereby affecting the thermal distribution analysis. Fig. 5 depicts the flow path located in the stator. There are three flow paths in total. At the top, oil is injected through two inlets per flow path, and flows along the stator. The oil that flows along the flow path of the stator is integrated with the oil that flows along the coil at the bottom of the motor. One-third of the lower part of the motor is immersed in oil, which flows to the outlet at the bottom of the welded side. The temperature distribution of the coil can be observed from two perspectives" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003628_j.actamat.2004.05.011-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003628_j.actamat.2004.05.011-Figure1-1.png", "caption": "Fig. 1. (a) sample configuration and axis labels (b) 3D AFM observation of the nickel thin film after the increase of stress along the (Oy) axis. Straight-sided buckling structures arise perpendicular to the", "texts": [ " The starting pressure was 2 10 8 torr and has been maintained at 10 4 torr during deposition. The thickness of the deposited films has been measured ex situ by step height method and has been found to be about 50 nm. The as-deposited thin films present initial residual compressive and equi-biaxial stresses r0, estimated to be about 0.6 GPa by both curvature and X-ray techniques [27,28]. In order to induce delamination and then buckling in the film, the substrate has been first compressed along the (Oy) axis at room temperature and pressure (see Fig. 1(a) for specimen configuration and axes). During the uniaxial compression, external stresses (Drxx;Dryy) have been generated in the nickel thin films: Drxx \u00bc Ef Es mf ms 1 m2f rext; Dryy \u00bc Ef Es 1 msmf 1 m2f rext; \u00f01\u00de where Ei and mi are the Young\u2019s modulus and Poisson\u2019s ratio, respectively, of the material (i), rext is the external stress induced in the polycarbonate substrate during the experiment. The total stress r in the film is therefore the sum of the internal stress r0 and of the stress Dr \u00bc \u00f0Drxx;Dryy\u00de generated during the experiment. As expected, straight-sided buckling structures appear above a critical stress and are generated perpendicularly to the compression axis (Fig. 1(b)). The evolution of the straight-sided wrinkles has been then investigated using an experimental apparatus allowing the in situ atomic force microscopy (AFM) observations of sample surface during deformation [21,22]. When the external stress is released, the buckling structures evolve from straightsided to a distribution of circular blisters, called bubbles in the following, as observed in Fig. 2. Since mf < ms < 1, the release of external stresses induces a decrease of total stress in the \u00f0Oy\u00de direction and an increase in the \u00f0Ox\u00de direction of the film, from r0 \u00fe Drxx (Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003485_1.1430673-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003485_1.1430673-Figure1-1.png", "caption": "Fig. 1 \u201ea\u2026 Cross-section of rotor and auxiliary bearing and \u201eb\u2026 Contact forces for jth ball", "texts": [ " This paper extends earlier reported work by developing an analysis that couples the rotor/inner race impact and slip with inner race distortion and acceleration. Account is taken of rolling and sliding zones induced in a ball type auxiliary bearing during the impact period. Simulation studies are used to identify the influence of parameters on possible bearing damage. The techniques developed mean that a full transient simulation of the bearing system is not required. Consider an axially symmetric deep groove auxiliary bearing ~Fig. 1~a!! with a full complement of balls. Due to external rotor disturbances or component failure in the magnetic bearing system, contact of the rotor with the inner race of the auxiliary bearing occurs at a designated angular position u50. The instantaneous radial contact force acting on the inner race is W and the corresponding tangential friction force is mRW . Figure 1~b! shows the ~normal, tangential! forces acting on the j th ball, at angular position u j , as (G j I ,F j I) from the inner race and (G j O ,F j O) from the outer race. Sliding always occurs at the ball-ball contacts and so the forces from the following ( j21)th ball are (H j ,mSH j) and from the preceding ( j11)th ball (H j11 ,mSH j11). The inner race is considered to be flexible and the outer race is considered to be rigid, which is valid if the outer race is suitably constrained. All motions and deformations within the auxiliary 002 by ASME Transactions of the ASME s of Use: http://www", " Calculation of the inner race angular acceleration and slip relative to the rotor is vital for subsequent thermal analyses. In addition to the degrees of freedom used to calculate the inner race distortion an angular degree of freedom is introduced to specify rigid body 408 \u00d5 Vol. 124, APRIL 2002 rom: http://tribology.asmedigitalcollection.asme.org/ on 01/28/2016 Term angular velocity v I . Each ball has two degrees of freedom to allow circulatory motion of the center of mass and rotation about the center of mass. Ball Motion. Referring to Fig. 1~b!, the equation for the j th ball rotation about the center of mass is IBv\u0307B j5RB~FJ I 1F j O2mS~H j1H j11!!, (10) where IB52/5mBRB 2 . For a full complement of balls the circulatory velocity is the same for each ball (vC1 5 . . . 5vCN 5vC) so that the equation of circulatory motion is mBRI~11s !2v\u0307C5F j I2~112s !F j O1~11s !~H j2H j11!, (11) where s5RB /RI . For radial motion of each ball mBRIv I 2 4~11s ! 5G j O2G j I2mS~H j2H j11!. (12) If there is at least one rolling ball the angular accelerations for inner race and circulatory motion are related by v\u0307C5v\u0307 I/2(1 1s)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000008_j.mechmachtheory.2016.05.015-Figure14-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000008_j.mechmachtheory.2016.05.015-Figure14-1.png", "caption": "Fig. 14. Inverted slider-crank mechanism synthesis problem. (a) The reference linkage mechanism generating the target path at the output point. (b) D-SBM used for the mechanism synthesis with the illustration of the target path of the end-effector.", "texts": [ " Finally, we examine the motion of the synthesized D-SBM and the identified slider-crank mechanism without applying the external force Fext ,t\u204e (i.e. F0=0). (Recall that this external force was intentionally introduced to obtain the correct DOF, which is 1.) The results are shown in Fig. 13 at a number of analysis steps. This figure clearly shows that the desired mechanism is correctly synthesized by using the proposed D-SBM-based formulation. As the second synthesis problem, the synthesis of an inverted slider-crank mechanism is considered. In the Fig. 14(a), its joint types are interpreted by using the joint symbols \u2329 J\u232a and [P]. The symbol G denotes the ground and three links are identified by \u2018a\u2019, \u2018b\u2019, and \u2018c\u2019. Point and line joints are indicated by open circles and rectangles in the lower part of Fig. 14(a), respectively. All joints connecting links and the ground are revolute joints. On the other hand, the coupler link b is connected to two adjacent links through a revolute joint and a prismatic joint. The main motivation to choose this problem is to check if the proposed D-SBMbased formulation can synthesize a linkage mechanism having a prismatic joint. Because no prismatic joint has been synthesized by any of earlier gradient-based topology optimization formulations, solving this problem will justify the effectiveness of the proposed method. The target path from the end-effector of the desired linkage is illustrated in Fig. 14(b). The end-effector is assumed to be located at the center of block 2. The design domain discretization and other data are the same as those stated in the problem solved in Section 4.1 except the position of the end-effector Q. To synthesize a mechanism to generate the target path at Q within a prescribed tolerance, optimization problem (20) is solved with and without using Eq. (23). The results obtained without using Eq. (23) will be given first. Fig. 15 shows the intermediate and final configurations of the D-SBM system along with their output paths", " This means that the correct DOF (which is 1) is achieved and the desired target path is obtained by the D-SBM. To identify the linkage mechanism from the final configuration of the D-SBM, the spring stiffness values of double-springs are examined and joint types realized by different limiting stiffness values are utilized. Fig. 16(a) shows the identified linkagemechanism that consists of three rigid blocks (or links), two revolute joints, two pin-in-slot joints and a prismatic joint. The identified linkage in Fig. 16(a) is not identical to the inverted slider-crankmechanism in Fig. 14. (The kinematic interpretation of the mechanism part involving block 3 will be given below.) However, the generated path at its endeffector by the newly synthesized mechanism is virtually the same as the target path generated by the reference mechanism in Fig. 14. This is because mechanisms to generate a certain path within a tolerance are not necessarily unique. We will show later that if the additional constraint, Eq. (23), is used, it is possible to recover exactly the same mechanism as the reference one. Before presenting the result obtained with the additional consideration of Eq. (23), the motion of the synthesized mechanism in Fig. 16(a) is examined. In plotting its motion in Fig. 16(b), we considered the synthesized mechanism in Fig. 16(a) without applying the external force Fext,t\u204e", " Therefore, the rigid blocks 1 to 9 as a whole have only 1 DOF, constituting a one-DOF planar linkage. Note that the attached blocks 4, 5, and 6 do not have any effect on the output path. Let us now investigate why an apparently different mechanism in Fig. 16(a) produce virtually the same path as the reference mechanism (within the tolerance \u03b5). To this end, we examine the mechanism part involving block 3. As shown in Fig. 16(a), block 3 is connected to the ground by two pin-in-slot joints; the mechanism part simulates the motion generated by the link \u2018c\u2019 of the reference mechanism in Fig. 14(a). The two pin-in-slot joints 3\u2329yC\u03b8\u232aG and 3\u2329\u03b8Cx\u232aG of block 3 replace the revolute joint c\u2329\u03b8R\u03b8\u232aG connecting link \u2018c\u2019 of the reference mechanism and the ground G. Referring to Fig. 7(b), 3\u2329yC\u03b8\u232aG and 3\u2329\u03b8Cx\u232aG altogether form a double separated cross slider joint 3\u2329\u03b8Cx ,yC\u03b8\u232aG between block 3 and the ground. We will investigate the motion of the mechanism part involving block 3 through its instantaneous center of rotation at the initial state. Referring to the right-hand side of Fig. 16(a), the instantaneous center of rotation for block 3 connected to the ground by the pin-in-slot joint 3\u2329yC\u03b8\u232aG is on the horizontal line (dotdashed line in Fig", " Likewise, the instantaneous center of rotation for block 3 connected to the pin-in-slot joint 3\u2329\u03b8Cx\u232aG is on the vertical line (dashed line in Fig. 16(a)) passing through the pin of 3\u2329\u03b8Cx\u232aG. Therefore, the instantaneous center of rotation for block 3 is the crossing point of the two lines, marked as \u2018x\u2019 in Fig. 16(a). Apparently, the instantaneous center of rotation at the initial state is exactly at the same location as the ground revolute joint c\u2329\u03b8R\u03b8\u232aG of the reference inverted slider-crank mechanism in Fig. 14(a). Because block 3 does not rotate much during the full rotation of the input link (see Fig. 16(b)), the mechanism part involving block 3 can be considered to rotate approximately about the ground revolute joint c\u2329\u03b8R\u03b8\u232aG of the reference mechanism. This is why the synthesized mechanism by the proposed formulation yields an output path tracing the target output path within the given error tolerance even if it has a different topology from the reference linkage mechanism. The maximum value of distance error is found to be 0", " 16 yields the desired output path,we should be able to recover the same linkage mechanism as the reference mechanism which has no pin-in-slot joint. To this end, we propose to introduce an additional constraint, Eq. (23). If a smaller value of \u03b3 in Eq. (23) is used, the formation of pin-in-slot joints is more strongly suppressed. Fig. 18 shows how output paths are changed as the iteration proceeds. The results are obtained with \u03b3=0.1 in Eq. (23). Because the synthesized linkage mechanism from the converged D-SBM in this case is exactly the same as the reference mechanism in Fig. 14(a), no plot juxtaposing the synthesized mechanism with the converged D-SBM is explicitly given. This example shows that the additional constraint Eq. (23) effectively suppress the formation of pin-in-slot joints, producing simpler mechanisms whenever possible. A synthesis of a 4R four-bar mechanism has been a main subject of earlier topology optimization-based synthesis methods. In this example, we should also make sure that the proposed D-SBM method is effective in solving the synthesis of 4R four-bar mechanisms" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000628_tie.2018.2849970-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000628_tie.2018.2849970-Figure1-1.png", "caption": "Fig. 1. Basic configuration of the proposed machine and control circuit.", "texts": [ " Principle of this novel machine is illustrated in this paper and its performance is analyzed. Then time-stepping finite element method (TS-FEM) is used to analyze the transient and steady-state performance of the machine and optimize the design. Finally a prototype of the proposed machine is fabricated and the experiment results verify the validity and effectiveness of the machine design. II. BASIC MACHINE STRUCTURE AND WORKING PRINCIPLE The basic configuration of the proposed BFMPM machine is shown in Fig. 1. The novel machine consists of two rotors and one stator. The inner consequent-pole rotor is connected with wind blades and the angle of the inner rotor is adjustable with a servo motor. Two sets of stator windings are located in outer stator slots. Permanent magnets (PMs) and modulation steels are alternatively arranged on the rotors. The outer stator houses two sets of windings, named as the stator winding I and the stator winding II. The two windings are connected in series. Fig. 2 is the power flow diagram of the proposed winding power conversion system" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000621_j.matpr.2018.03.039-Figure12-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000621_j.matpr.2018.03.039-Figure12-1.png", "caption": "Figure 12 Steel Leaf Spring Deformation during Acceleration", "texts": [], "surrounding_texts": [ "Assume the vehicle is slowing down from 60 km/h to 30 km/h. Distance covered by vehicle during deceleration is assumed as 20 m. Load acting on a leaf spring:Vf 2 = Vi 2 + 2\u00d7a\u00d7d Where,Vf = Final Velocity = 30 km/h = 8.335 m/s, Vi= Initial Velocity = 60 km/h = 16.67 m/s,a = acceleration,d = distance travelled by vehicle = 20m.(8.335)2 = (16.67)2 + 2\u00d7a\u00d720,208.42 = 40a,a = 5.208 m/s2. Decelerating Force, Fd = ma,Where,m = mass of the vehicle= 2900 kg, a = acceleration= 5.208 m/s2, Fd= 2900\u00d75.208, Fd= 15110.21 N (For all four-leaf springs),For one leaf spring, Fd = 15102.32/4, Fd= 3775.58 N. Total load acting on the leaf spring is Ft = F+ Fd, Ft= 7112.25+3775.58,Ft=10887.83N. The results obtained for transient structural analysis for deceleration are shown in Figures 16-20 and listed in table 6. Table 6 Results during Deceleration Parameter Steel EN45A Carbon/Glass Composite Max Stress 415.79 MPa 545.53 MPa Max Deformation 8.9656 mm 15.005 mm Figure 16 Load during deceleration 14518 Jenarthanan M.P et al/ Materials Today: Proceedings 5 (2018) 14512\u201314519 3.4 Inference From this result, we can understand that even though deformation and equivalent stress values of Carbon/Glass Epoxy Hybrid Composite Leaf Spring increases, they are well within the safety limits." ] }, { "image_filename": "designv10_11_0003350_bio.617-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003350_bio.617-Figure3-1.png", "caption": "Figure 3. Screen-printed electrodes used for the miniaturization of the electrochemiluminescence-based sensor.", "texts": [ " , 2 The miniaturization was achieved using screen-printed electrodes instead of a glassy carbon macroelectrode. Screen-printed electrodes are small-size tools that are mass-produced at low cost and with good reproducibility according to a simple and fast method. Such tools are generally used as disposable devices and most screenprinted electrodes reported in the literature are coupled with an electrochemical detection (17). The screenprinted device used in this work was a two-electrode system consisting of a graphite working electrode and an Ag/AgCl reference electrode (Fig. 3). Choline oxidase was used as a model H2O2-generating oxidase. The enzymatic sensing layer was deposited on the working electrode surface. The enzyme was immobilized on DEAE-Sepharose beads subsequently entrapped in a PVA-SbQ layer. The experiments were initially performed in a batch system. Under optimized conditions, at 450 mV vs. Ag/AgCl, in 30 mmol/L veronal\u2013HCl buffer (pH 9), containing 50 mol/L luminol, the linear range extended from 2.10 8 mol/L to 1.10 4 mol/L choline. Many other substrates could be detected according to the same principle, using a suitable oxidase" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001324_0959651820937847-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001324_0959651820937847-Figure1-1.png", "caption": "Figure 1. Schematic diagram of the stability control system.", "texts": [ " However, mechanical systems are not ideal under real conditions, a more practical control is badly needed to deal with uncertainties in the system. Constrained tank stability control system with uncertainty Dynamic equation of the tank stability control system As the controller design object, the dynamic equation of the tank stability control system with uncertainty (including system modeling error and road excitation) can be obtained and expressed in form of equation (1) in this section. Consider the tank stability control system shown as in Figure 1. It consists of a swing part (turret) and a pitching part (barrel) attached to the pedestal (hull). Let m1 be the mass of turret, R1 be the distance between two centers of rotation of turret and barrel, also represents the radius of turret, u1 be the angular displacement of turret in the horizontal direction. m2 be the mass of barrel, R2 be the distance from the center of rotation to the muzzle, also represents the length of barrel, and u2 be the angular displacement of the barrel in the vertical direction" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003388_978-3-662-04831-3-Figure5.28-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003388_978-3-662-04831-3-Figure5.28-1.png", "caption": "Fig. 5.28: Drawings of a universal joint", "texts": [ "(x) [AQiLi 0 (- wf~R 0 ALiR 0 ARL; +ALiR 0 ARL; 0 wf~R) 0 AL;Q;] Pr(Y) [ 002]0 Constraint acceleration equations of a spatial translational joint [ 02,3 ' P?(x' y){ - ALQ;L; 0 AL;R 0 ARLi 0 [ALiLQi Pr(z)]} ' [o1,3 ' P?(x){AQiLi 0 [(ALiROARL; OAL;Q;)Pr(Y)J} 02,3 ' P?(x, y){ALQ;L; 0 [AL;ROARLi OALiLQiPr(z)J}] 01,3 ' -P?(x){ AQiLi 0 ALiR 0 ARL; 0 [AL;Q;pr(Y)J} l =: gp(P) 0 T(p) = constraint Jacobian matrix [( .. R )T (oLo )T (\"R )T (oL; )T]T r~o ' WiR ' r~o ' w0R (5.43b) (5.43c) 226 5o Model equations of planar and spatial joints 5.2.2.4 Universal joint (BBl, BB4; constrains three translational and one rotational DOF). Consider the mechanism of Figure 5028 com prising two rigid hoclies i and j connected hy a universal jointo Let Q he a point that is common to the hoclies i and j 0 Assurne that a frame LQi is fixed on hody i with dorigin Q, and with the x-axis exQi placed in the direction of the first rotation axis of the universal joint, and that a frame LQ; is fixed on hody j with origin Q, and with the y-axis eyQ;, placed in the direction ofthe second rotation axis of the universal joint, perpendicular to the first rotation axiso Consider a third frame Lk with origin Q fixed to the two (massless) rotation axes with unit vectors exK = exQi and eyK = eyQ; 0 (5" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003122_s0094-114x(96)00033-x-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003122_s0094-114x(96)00033-x-Figure5-1.png", "caption": "Fig. 5. The RPSSPR-SPR mechanism.", "texts": [ " (2) In the above situation, the partial derivative of the loop-closure function with respect to the rotation at the R joint is zero. (3) In multi-loop mechanisms, in addition to the singular configurations, resulting from condition (1), there are other singularities where condition (1) may not be true. In such situations other geometrical conditions are needed. 4. S I N G U L A R I T Y OF R P S S P R - S P R M E C H A N I S M In Ref. [16], the three-loop, three-degree-of-freedom RPSSPR-SPR mechanism of Fig. 5 has been proposed as a parallel 'wrist'. The authors have given the inverse and direct kinematics of this mechanism, however, they have not described its singularities. It is important to know the singularities of this mechanism before it can be used. In this section, we obtain the singularities of this mechanism by making use of the approach described in Sections 2 and 3. We choose the geometry and the coordinate systems used in Ref. [16]. The chosen geometry causes loss of generality to some extent but makes the expressions much simpler" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000936_j.mechmachtheory.2019.103607-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000936_j.mechmachtheory.2019.103607-Figure1-1.png", "caption": "Fig. 1. Typical modeling methods for the helical gear system: (a) the analytical method, (b) the nonlinear FE models, and (c) the model order reduction method (Craig\u2013Bampton method).", "texts": [ " Therefore, an accurate and high-efficiency prediction of the dynamic behavior of helical gear-shaft systems is necessary for reliable and cost-effective gearbox design [12] . To achieve this, 3D models of the helical gears and shafts and the interaction between the gear pair need to be established. Gear-shaft systems can be modeled by formulations of varying sophistication [16\u201318] . Shafts had been represented by simple lumped springs [18] and complex finite elements [16,17] . Gears had been modeled as rigid disks, and the interaction between gear pair was simulated by the spring-damper element using analytical methods [19] , as shown in Fig. 1 (a). However, analytical methods with so many simplifications are not able to compute the complex dynamic responses for gears with complicated 3D geometry, such as multi-tooth-face contacts and uneven tooth-load distribution. On the other hand, the traditional finite element (FE) method provides an effective approach to obtain the gear meshing stiffness, nodal displacement and stress distribution under static conditions, where highly-refined meshes typically assigned for contact areas are computationally feasible [20] . In Ref. [21] , only the gear teeth in meshing areas are finely meshed in static contact simulation to save computational costs. However, in dynamic conditions, all gear teeth will come into contact during revolutions, therefore, highly-refined meshes are required for all teeth of helical gears, as illustrated in Fig. 1 (b). Consequently, the application of FE method in dynamic contact analysis of helical gears may boast of large degrees of freedom (DOFs) that can be more than 10 6 [22] . When several gears in a drive train with thousands of possible contacts are considered simultaneously in one simulation, the FE method prevents sufficiently long analysis time using an acceptable computational effort. To further improve the computational efficiency, the model order reduction (MOR) technique has been introduced to reduce the DOFs of the helical gear", " [25] , the original elastic nodal DOFs were spanned by a certain set of eigenmodes which satisfy the geometric boundary conditions but do not satisfy the dynamic boundary conditions imposed by the gear meshing forces. As a result, eigenmodes with eigenfrequencies up to 80kHz were needed to precisely compute the local deformations and stresses in the contact area, making the MOR technique still computationally expensive. The Craig\u2013Bampton method is another widely used MOR formulation [26] , which uses static shape vectors combined with vibration modes to approximate the deformation of a flexible body, as shown in Fig. 1 (c). This method fulfills the dynamic boundary conditions and static completeness which guarantees the same level of accuracy in static solutions with the original FE model. However, the addition of static shape vectors for each possibly-loaded boundary DOF in the helical gear will result in a very high-dimensional model that cannot be calculated due to limited amounts of working memory. In contrast, omission of these static shapes, though computationally efficient, will lead to the inaccurate recovery of local dynamic stresses in the contact area [24] " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000020_s1052618816040026-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000020_s1052618816040026-Figure4-1.png", "caption": "Fig. 4.", "texts": [ " Consequently, the groups of screws make it possible to solve the problem of determining the kinematic screws that transfer a parallel-structure robot to neighboring singular positions, as well as determining the screw groups that withdraw the robot from the singular positions. We show that there is a correlation between the parameters of the kinematic gradient screw \u03a9* and the coordinates of mount points Ai of the kinematic coupling chains for a singular position. Let us vary the position vectors r1(5 \u00d7 10\u20131, 0, 0) and r2(\u20135 \u00d7 10\u20131, 0, 0) of mount points A1 and A2 (Fig. 4) for the singular position under consideration when three forcing screws E1, E2, and E3 lie on the same plane; the rest of the position vectors are invariable. The axes of forcing screws E1, E2, and E3, like the previous case, intersect at a point coinciding with the point of the origin. Determinant ( ) composed of the Plucker coordinates of the forcing screw axes is also zero. According to the algorithm, we find the withdrawing gradient screw that has the following form: \u03a9*(0, \u20132828 \u00d7 10\u20133, 2828 \u00d7 10\u20133, 0, 0, 5657 \u00d7 10\u20133)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003912_1.2118687-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003912_1.2118687-Figure3-1.png", "caption": "Fig. 3 A parallel manipulator without relative motion between the platforms and without self-motion", "texts": [ " This criterion for computing the passive degrees of freedom has the advantage of being independent of whether or not Vj m/f = Aj m/f j = 1,2,\u2026,k . Of course, if in the position analyzed any one of the serial connecting chains happens to be in a singular configuration the dimension of the infinitesimal mechanical liaison may be affected and the computation of the number of degrees of freedom may produce incorrect results. In this final section, the results developed in this contribution will be applied to a series of interesting examples of parallel manipulators. 6.1 Fixed Platform Without Self-Motion. Figure 3 shows a parallel platform, in which there is no relative movement between the moving and fixed plataforms, this class of platforms was analyzed in Sec. 3. Each serial connecting leg is formed by three revolute pairs whose axes are parallel. Therefore, the closure algebra associated with each leg are given by Aj m/k = ple\u0302j ; namely, they are the subalgebras associated with planar subgroups. Moreover, the set e\u03021 , e\u03022 , e\u03023 is linearly independent. Furthermore, Aa m/f = j=1 3 Aj m/f = 0 . Therefore, there is no relative movement between the fixed platform and the moving platform" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001781_s12046-021-01650-z-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001781_s12046-021-01650-z-Figure1-1.png", "caption": "Figure 1. Axial flux permanent magnet machines: (a) one stator and one rotor; (b) two stators and one rotor, [5].", "texts": [ " In high-performance drive systems, PMSM is usually used and is characterised by smooth motion through the entire range of motor speeds, total torque control at zero rpm, and rapid acceleration and deceleration. PMSMs are classified as radial flux machines and axial flux machines based on flux paths. Flux flows from rotor to stator in the radial direction through the air gap in radial flux machines and vice versa. The machines are similarly designed to flow in the shaft\u2019s axial direction and are referred to as axial flux machines [1\u20137]. One rotor and two stators are axial flux devices, figure 1, which have a back-iron in the stator but do not have a back-iron in the rotor. The multi stator axial flux machine\u2019s power density is better than the single-stator unit with uneven forces [4]. The radial field machines, however, are notable for their ease of manufacturing and assembly; and hence their disproportionate attractiveness and market existence [5]. Thermal analysis and cooling solutions have to be identified to enhance the life period of the electric machine. The voltage unbalances in the air gap produces negative *For correspondence sequence voltage that rotates flux against rotor rotation, helping to create high currents" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000520_tte.2019.2959400-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000520_tte.2019.2959400-Figure3-1.png", "caption": "Fig. 3. GH at flux barrier which is considered as segment GH' that orthogonally intersects flux barrier hyperbolic borders at points G and H'", "texts": [ " The rotor structure of a SynRel motor with a generic represented hyperbolic flux barrier is shown in Fig. 2. According to this modelling, the machine rotor is of center O and radius R and the barrier borders AG and BH lie on hyperbolas \u03931 (with center O and foci F1) and \u03932 (with center O1 and foci F1) which intersect the circumference having radius R-\u03b4 and center O at points A, B and G, H. Barrier contours AB and GH are approximated as elliptic segments that are perpendicular to the hyperbola AG at points A and G (Fig. 3). Hence, each flux barrier is described by the geometric parameters of \u0394, h, \u03b4, \u03b5, \u03b1, where \u03b1 is the angle between the horizontal line passing through points O and D and the line connecting O to the central point of segment GH and angle \"\u03b3\" is defined as a deviation angle around \"\u03b1\", which is approximated from (1). According to the above assumptions and introducing a Cartesian reference frame having the axes x, y and its origin in O, the coordinates of any generic points of the plane, i.e., A, B, D and E are expressed as: \ud835\udefe = \ud835\udc60\ud835\udc56\ud835\udc5b\u22121 ( \ud700 2\u2044 \ud835\udc45 )~ \ud700 2\ud835\udc45 (1) \ud835\udc65\ud835\udc34 = (\ud835\udc45 \u2212 \ud835\udeff)\ud835\udc50\ud835\udc5c\ud835\udc60(\ud835\udf0b \u2212 \ud835\udefc + \ud835\udefe), \ud835\udc66\ud835\udc34 = (\ud835\udc45 \u2212 \ud835\udeff)\ud835\udc60\ud835\udc56\ud835\udc5b(\ud835\udf0b \u2212 \ud835\udefc + \ud835\udefe) (2) \ud835\udc65\ud835\udc35 = (\ud835\udc45 \u2212 \ud835\udeff)\ud835\udc50\ud835\udc5c\ud835\udc60(\ud835\udf0b \u2212 \ud835\udefc \u2212 \ud835\udefe), \ud835\udc66\ud835\udc35 = (\ud835\udc45 \u2212 \ud835\udeff)\ud835\udc60\ud835\udc56\ud835\udc5b(\ud835\udf0b \u2212 \ud835\udefc \u2212 \ud835\udefe) (3) \ud835\udc65\ud835\udc37 = \u2212\ud835\udc45 + \u2206 + \u210e, \ud835\udc66\ud835\udc37 = 0, \ud835\udc65\ud835\udc38 = \u2212\ud835\udc45 + \u2206, \ud835\udc66\ud835\udc38 = 0 (4) Note that the assumption (\u03b5\u00abR) holds true in (1)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000219_j.conengprac.2015.12.007-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000219_j.conengprac.2015.12.007-Figure1-1.png", "caption": "Fig. 1. Pratt & Whitney PW4084 turbofan engine.", "texts": [ " The overshoot of fan speed will lead to fluctuation in propulsion and hence jerking of the airplane, which is undesirable in consideration of comfort, let along the waste of fuel and the reduction of efficiency. Therefore, it is practically important to avoid speed overshoot of the fan. This is easy for a single-spool turbofan engine because the fan speed is directly determined by the fuel flow. For a two-spool turbofan engine like the Pratt & Whitney PW4084 turbofan engine (Spang & Brown, 1999) shown in Fig. 1, however, the overshoot-free regulation task becomes complicated, because the speed of the fan, i.e., the speed of the low-pressure shaft, is affected not only by the fuel flow but also by the speed of the highpressure shaft. Traditionally, overshoot is avoided at the expense of rapidity. How to ensure rapid as well as overshoot-free response theoretically is a meaningful yet difficult problem, and it is even harder in the absence of appropriate system model. To the best knowledge of the authors, no relevant results have been reported up to now" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000755_tac.1960.6429294-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000755_tac.1960.6429294-Figure2-1.png", "caption": "Fig. 2-Argument and magnitudes of (s;-s,).", "texts": [ ", Polytechnic l nst, of Brooklyn, Brooklyn, N. Y., Rept. No. R-449-55; 1955. 9 H. Ur, \"Geometrical Properties of Root Loci,\" M.S. thesis, Purdue University, Lafayette, Ind.; August, 1956. '; 0 always holds. Namely, Eq. (23) always makes sense in Case II. 3.1.3. Case III: \u03c6 (t) \u2208 ( \u03c6, \u03c6 ) and \u03c6\u0302 (t +\u2206tmax) \u2208 ( \u03c6, \u03c6 ) Obviously, since \u03c6 (t) \u2208 ( \u03c6, \u03c6 ) and the output constraint violation is not predicted, the system will normally tracking the desired trajectory \u03c6d in this case (\u03c3\u03c6 = 6). It is noticed that Case III may occur when the situations (b) and (d) in Fig. 4 are activated. While at this moment, since \u03c6d could beyond the output constraints, the tendency of the new output constrained trajectory will violate the output constraints again, which may cause frequent switching. For avoiding this phenomenon, the switching mode \u03c3\u03c6 = 5 is ntroduced. Then, \u03c6\u0307\u03c3\u03c6 ,s and \u03c6\u03c3\u03c6 ,s can be obtained by \u03c6\u0307\u03c3\u03c6 ,s (t) = { 0, if \u03c3\u03c6 = 5 \u03c6\u0307d (t) , if \u03c3\u03c6 = 6 (25) \u03c6\u03c3\u03c6 ,s (t) = { \u03c6\u03c3\u03c6 ,s (t \u2212\u2206ts) , if \u03c3\u03c6 = 5 \u03c6d (t) . if \u03c3\u03c6 = 6 (26) Summarily, \u03c6\u0307\u03c3\u03c6 ,s(t) and \u03c6\u0308\u03c3\u03c6 ,s(t) are computed as follow: \u03c6\u0307\u03c3\u03c6 ,s(t) = \u23a7\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8\u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 c1, if \u03c3\u03c6 = 1 c2, if \u03c3\u03c6 = 2 \u03c6\u03073,s (t) , if \u03c3\u03c6 = 3 \u03c6\u03074,s (t) , if \u03c3\u03c6 = 4 0, if \u03c3\u03c6 = 5 \u03c6\u0307d (t) , if \u03c3\u03c6 = 6 (27) \u03c6\u0308\u03c3\u03c6 ,s(t) = \u23a7\u23aa\u23a8\u23aa\u23a9 0, if \u03c3\u03c6 = 1, 2, 5 \u03c6\u03083,s (t) , if \u03c3\u03c6 = 3 \u03c6\u03084,s (t) , if \u03c3\u03c6 = 4 \u03c6\u0308d (t) ", " Thus, y\u03c3 ,s = [\u03c6\u03c3\u03c6 ,s, \u03b8\u03c3\u03b8 ,s, \u03c8\u03c3\u03c8 ,s, Z\u03c3Z ,s] T , y\u0307\u03c3 ,s = [\u03c6\u0307\u03c3\u03c6 ,s, \u03b8\u0307\u03c3\u03b8 ,s, \u03c8\u0307\u03c3\u03c8 ,s, Z\u0307\u03c3Z ,s] T and y\u0308\u03c3 ,s = [\u03c6\u0308\u03c3\u03c6 ,s, \u03b8\u0308\u03c3\u03b8 ,s, \u03c8\u0308\u03c3\u03c8 ,s, Z\u0308\u03c3Z ,s] T denote the output constrained trajectory and its first and second derivatives, respectively. Lemma 2. If the output constrained trajectory, its first and second derivatives are calculated by (27)\u2013(29), there must exist a positive constant B0 such that \u03a00 = {( y\u03c3 ,s, y\u0307\u03c3 ,s, y\u0308\u03c3 ,s ) : y\u03c3 ,s2 + y\u0307\u03c3 ,s2 + y\u0308\u03c3 ,s2 \u2264 B0 } . (31) w b ( w o t t S w w S w a Proof. Considering (15), we have \u03c6\u03c3\u03c6 ,s \u2208 (\u03c6, \u03c6) when \u03c3\u03c6 = 1, 2. According to the definition of the switching algorithm, the minimum interval time of the switching algorithm is \u2206tmin, which satisfies \u2206tmin \u2264 \u2206t\u03c6 by (17). As shown in Fig. 4, hen \u03c3\u03c6 = 3, 4, the value of \u03c6\u03c3\u03c6 ,s, which can be presented as the tangent of the imaginary circular obstacle, will not eyond the output constraints during every \u2206tmin second in geometry. Namely, \u03c6\u03c3\u03c6 ,s \u2208 [\u03c6, \u03c6] when \u03c3\u03c6 = 3, 4. If \u03c3\u03c6 = 6, we obtain that \u03c66,s = \u03c6d (t) \u2208 [\u03c6, \u03c6]. If \u03c3\u03c6 = 5, \u03c65,s will hold at the previous value, which is also within the interval [\u03c6, \u03c6]. Summarily, combining with (29) and Assumption 3, we have \u03c6\u03c3\u03c6 ,s(t) \u2208 [\u03c6, \u03c6] \u2286 [\u2212\u03b41, \u03b41] for all t > 0. When the switching mode \u03c3\u03c6 = 3, 4, \u03c6\u0307\u03c3\u03c6 ,s can be presented as the slope of the tangent of the imaginary circular obstacle" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000914_j.measurement.2019.06.045-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000914_j.measurement.2019.06.045-Figure4-1.png", "caption": "Fig. 4. Reverse calculation of gear base circle center.", "texts": [ " The coordinates of the gear base circle center O0 ex1; ey1;0 in the RCS is calculated by the least squares equation, which is established by the geometric relationship between the tooth profile measurement points and the gear base circle center. The calculation flow chart is shown in Fig. 3. When the direction vector s \u00bc vx;vy;1 of the geometric center axis of the gear is given, the transformation relationship between the RCS and the MCS is shown in Eq. (8). X1 Y1 Z1 1 2 6664 3 7775 \u00bc MY MX A X Y Z 1 2 6664 3 7775 \u00f08\u00de where \u00f0X1;Y1; Z1\u00de is the coordinates in RCS. The reverse calculation of gear base circle center in the RCS O1 X1Y1Z1 is described in Fig. 4. If any two measurement points Pi0\u00f0xi0; yi0\u00de and Pij\u00f0xij; yij\u00de are on one involute, the corresponding involute starting angles of the two points hi0 and hij are the same [18]: hi0 \u00bc hij. In order to determine the geometric center coordinates O0 ex1; ey1;0 in the RCS, the least squares equation is established as F ex1; ey1 \u00bc min Xm i\u00bc1 Xn j\u00bc1 Dij 2 \u00f09\u00de where Dij(rad) is the variation between the starting angles of the involutes of the tooth profile measurement points Pij\u00f0xij; yij\u00de and Pi0\u00f0xi0; yi0\u00de in the RCS and obtained as: Dij \u00bc hij hi0 \u00f010\u00de where i is the number of involutes, i = 1, 2" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001184_j.measurement.2020.108198-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001184_j.measurement.2020.108198-Figure3-1.png", "caption": "Fig. 3. Loading of an angular ball bearing.", "texts": [ " 1 shows the procedure of the diagnostics. The main contributions of the work are as follows: The bearing is angular contact type ball bearing but in the other studies, bearings are deep groove ball bearings as mentioned before. Loading of the bearing is applied with the help of four screws tightened by a torque meter which were forced a disc onto the inner race therefore it changes to radial loading and axial loading simultaneously. Fig. 2 shows the disk which presses on to the inner race and the place of the screws and Fig. 3 shows the decomposition of the load into radial and axial loadings. The radial loading due to of this disk, is constant (the amount of tightening of the screws is constant therefore the loading is constant) but the axle has some mass so that it becomes semiconstant. Whilst in other researches because of the bearings type which was deep groove ball bearings, so they were loaded in the loading zone defined by Hertzian contact theory. Fig. 4 shows the combination of the constant loading and the loading zone of the Hertzian contact theory" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001756_j.mechmachtheory.2021.104345-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001756_j.mechmachtheory.2021.104345-Figure3-1.png", "caption": "Fig. 3. Concave TE curve.", "texts": [ " Secondly, the contact pattern on pinion tooth surface and the modification curve along the instantaneous meshing line of pinion tooth surface is preset according to the design requirements. Thirdly, the correction value of pinion auxiliary tooth surface along the instantaneous meshing line is calculated, and it is superimposed on pinion auxiliary tooth surface, then pinion ease-off target surface satisfy the functional requirements is obtained. Lastly, pinion modified tooth surface and corresponding processing parameters that can precisely satisfy the predesigned meshing performances is worked out. The geometric shape of concave TE curve is shown in Fig. 3 , where \u03d51 is pinion rotation angle, and \u03b4 is TE amplitude. There are five control points on the TE curve: points A and B are the entrance and exit meshing point, and their corresponding amplitude of TE are \u03b4A and \u03b4B . Points C and D are two peaks of TE curve. Point M is reference point. The detailed introduction of concave TE curve is provided in [29] . The concave TE curve is defined as follows: { \u03c62 = \u03c62 M + Z 1 Z 2 \u03d5 1 M + \u03b4\u03c62 \u03b4\u03c62 = c 0 + c 1 \u03d5 1 M + c 2 \u03d5 2 1 M + c 3 \u03d5 3 1 M + c 4 \u03d5 4 1 M + c 5 \u03d5 5 1 M + c 6 \u03d5 6 1 M + c 7 \u03d5 7 1 M (1) where c i (i = 1 , 2 , " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001089_tia.2020.3046195-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001089_tia.2020.3046195-Figure1-1.png", "caption": "Fig. 1. Location of water jacket in the 48-V MGU.", "texts": [ " Side-by-side comparison of these three concepts for a given application should be of interest in light of the fact that the two existing cooling designs that are already in production are less effective than the proposed design. A prototype machine with the proposed cooling jacket is made and its performance was validated through thermocouple measurements and infrared (IR) thermography to validate the thermal flow analysis and the temperature distribution of the motor. The application provides forced liquid cooling through stator water cooling jacket enclosed between inner and outer shells of the 48-V MGU, as shown in Fig. 1. The gap between the outer shall and rib is one of the design parameters for optimization of the jacket. Three common solutions are investigated using CFD analysis. The first concept that is shown in Fig. 2(a) features easy manufacturing. It is a hollow jacket, which encompasses the stator and allows the coolant water to circulate along the circumference of the machine. In the second concept, the flow of coolant is interrupted by axial channels and ribs, as shown in Fig. 2(b). Similar to the circumferential cooling jacket design, the axial rib jacket follows a design that is also in production by a tier-one supplier and is thus assumed to be optimized for mass production" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001034_tie.2020.3009578-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001034_tie.2020.3009578-Figure1-1.png", "caption": "Fig. 1. A 24-slot Nr-pole F2Ay-OW-SWFFSM with virtual coils. (a) The cross-section of topology. (b) The vectors distribution of fundamental flux-linkages of virtual coils.", "texts": [ ", can be selected more effectively and accurately. In order to solve this problem, a new auxiliary evaluation variable called the internal distribution coefficient (IDC) of armature coils, which is proportional to the fundamental amplitude of corresponding open-circuit flux-linkage of armature coil, is proposed in this paper. Meanwhile, an approach based on the virtual coils\u2019 flux linkages is proposed in this paper to achieve the IDCs of armature coils in these 3-phase 24-slot F2Ay-OW-SWFFSMs. As shown in Fig.1 (a), the virtual coils, Si (i=1, 2, \u2026,24), are concentratedly wound on each stator tooth, and both the number of turns and winding directions of them are the same as corresponding armature coils. Consequently, the flux-linkages of armature coils can be equivalent to the sum of corresponding virtual coils\u2019 flux-linkages when the slight magnetic flux leakages between stator teeth are neglected. Fig.1 (b) shows the vectors distribution of fundamental flux-linkages of virtual coils. Due to the opposite polarity of adjacent two field coils, the vc can be given by 2r vc s N N (13) Hence, the phase relations between random vectors in Fig.1 (b) can be obtained. On the basis of above analysis, the IDCs of armature coils with different coil pitches, KIDC, in these 24-slot F2Ay-OW-SWFFSMs can be defined as follows: 1 1 max sin 4 2 cos max 2 sin 2 y ajc sj j vc IDC ajcs y K (14) while sj represents the fundamental flux-linkage of virtual coil Sj (j=1,2\u2026, y). Authorized licensed use limited to: CMU Libraries - library.cmich.edu. Downloaded on August 18,2020 at 09:24:07 UTC from IEEE Xplore. Restrictions apply" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001041_j.ijmecsci.2020.106020-Figure14-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001041_j.ijmecsci.2020.106020-Figure14-1.png", "caption": "Fig. 14. Schematic illustration of the displacement of the axes for shaving the face gear.", "texts": [ "2 , a seven-five axis machine tool with a horizontal shank was selected based on the existing condition of the laboratory, and its layout structure is shown in Fig. 13 . The axes required for the spur face gear shaving motion include the movable axes X, Y, Z and the rotational axes A, C . The movable axes Y and Z realize the radial feed of the shaving cutter, the movable axis X enables the spur face gear to move along its axial direction, and the rotational axes A and C perform the task of cutting the materials. Geometric relations are established based on the structure of the machine tool in Fig. 14 , where \u0394S x and \u0394S z are the displacement variation of the shaver cutters along the X -axis and Z -axis of the machine tool, respectively. S y is the displacement variation of the spur face gears along the Y -axis of the machine tool. H f is the tooth depth of the spur face gears, and \u0394R is the tooth width of the spur face gears. Then, these geometric relations can be expressed as in Eq. (24) based on the geometric transformation and gear meshing principles. \u23a7 \u23aa \u23aa \u23a8 \u23aa \u23aa \u23a9 \u0394\ud835\udc46 \ud835\udc65 = \u0394\ud835\udc45 cos \ud835\udefd 0 \u2264 \ud835\udc46 \ud835\udc66 \u2264 \ud835\udc3b \ud835\udc53 \u0394\ud835\udc46 \ud835\udc67 = \u0394\ud835\udc45 sin \ud835\udefd \ud835\udf19\ud835\udc60 \ud835\udf19\ud835\udc53 = \ud835\udc41 \ud835\udc53 \ud835\udc41 \ud835\udc60 = \ud835\udc5a \ud835\udc60\ud835\udc53 (24) The linkage of the axes can be achieved by the motion control equations above, and the whole tooth flank can be obtained simultaneously with the axial feed" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003131_robot.1999.770008-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003131_robot.1999.770008-Figure5-1.png", "caption": "Figure 5. Geometric constraint to calculate h h ~ , during downslope walking: (a) case 1; (b) case 2.", "texts": [ " By geometric consideration, the hip height limit hlimi, is computed by Equation (4): hbm,, = ,/- - r tan p (4) where 1, +1, is the total length of the leg (excluding the foot); ,b is the slope gradient; and r = s1 cos p + 1, . A factor kheighr is multiplied to the height limit hlimir to give the desired height of the hip from a global slope, h& kherghr is typical chosen to be around 0.85. For larger slope variations, it should be smaller. For the downslope, depending on the swing leg's touch-down location, both the back supporting leg during the double support phase and the swing leg during the single support phase may reach singular configuration as shown in Figure 5(a) and Figure 5(b), respectively. In the algorithm, we have set the swing leg to touch down when the vertical projection of the hip is between both legs. For such strategy, the case depicted in Figure 5(b) can occur and the corresponding height limit hlimir is computed as in Equation (5): hl,m,, = /= + r, tan p (5 ) where r, = 0 . 5 ~ ~ cos . The minimum of the computed hip height limit hlimit between Equations (4) and (5) is used to compute the desired hip height hd during the downslope walking. These equations can also be used for level walking where ,!3 is zero. This subsection considers transitional walking from level to slope ground and from slope to level ground, where the slope can be either ascending or descending" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000628_tie.2018.2849970-Figure13-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000628_tie.2018.2849970-Figure13-1.png", "caption": "Fig. 13 Prototype of the BFMPM machine and test bench. (a) Prototype of the BFMPM machine. (b) Test bench of the BFMPM machine.", "texts": [ " Finally, the total back-EMF is dramatically decreased when the inner rotor position is 150o electric degree. These simulation results verify the correctness of the analysis model mentioned in section II and prove the effectiveness of the proposed BFMPM machine for the various-speed constant-amplitude voltage operation in wide speed range. IV. PROTOTYPE AND EXPERIMENTAL RESULTS In order to verify the effectiveness of the novel machine, a prototype is manufactured and a test bench is designed to simulate the real working condition. Fig. 13 (a) shows the prototype of the BFMPM machine. The cup-shaped middle rotor consists of the modulation steels and PMs. The modulation steels of the middle rotor consist of silicon lamination to reduce the eddy current loss caused by the magnetic field harmonics and these laminations are fixed by two non-magnetism end rings as shown in Fig. 13. Two windings, power winding 1 and power winding 2 are mounted on the stator. Power winding 1 is an integral-slot distributed winding with 2 pole pairs. Power winding 2 is a fractional-slot concentrated winding with 13 pole pairs. The test bench consists of two servo machines and the prototype of BFMPM machine. Servo I connects with the inner rotor and controls the rotor position to regulate the phase difference between two windings. Servo II coupled with the middle rotor is designed to simulate the winding turbine and regulates the rotating speed" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000620_s11071-018-4338-3-Figure10-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000620_s11071-018-4338-3-Figure10-1.png", "caption": "Fig. 10 Physical interpretationof the slope coordinates inANCF element", "texts": [ " While ANCF elements can be used to represent nonlinear geometry, linearly tapered elements are used in this investigation in order to provide simple and clear demonstration of how the ANCF position vector gradients can be used to obtain the desired shapes. Stretch and shrinkage of the element cross section can be conveniently realized by changing the norm of the gradient vectors [34,35]. For example, tapering an ANCF element in the z direction can be achieved by simplymultiplying the gradient vector rz by scaling factors \u03b1 and \u03b2 at the first and second element node, respectively, as shown in Fig. 10. For an arbitrary point with dimensionless coordinates in the longitudinal and lateral directions \u03be and \u03b7, the position vectors of the corresponding points on the top and bottom surfaces defined, respectively, by rt , rb, and the cross-sectional thickness h\u03be are rt = S (\u03be, \u03b7, \u03b6t ) e, rb = S (\u03be, \u03b7, \u03b6b) e, h\u03be = h0 [\u03b1 (1 \u2212 \u03be) + \u03b2\u03be ] (11) where h0 is the nominal thickness before altering the element shape, and \u03b6t and \u03b6b refer to the nondimensional thickness parameterwhosedefinitionvaries with the type of element" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003469_095440602761609434-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003469_095440602761609434-Figure1-1.png", "caption": "Fig. 1 Hertzian pressure distribution for a nite line contact", "texts": [], "surrounding_texts": [ "The variation in density of the lubricant with pressure is de ned by Dowson and Higginson [9] as r 1 aPPh 1 bPPh 4 where a and b are constants, dependent upon the properties of the uid. The values used in the current analysis are 5 83610\u00a110 and 1 68610\u00a19 respectively, which are based on mineral oils." ] }, { "image_filename": "designv10_11_0003302_37.608535-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003302_37.608535-Figure9-1.png", "caption": "Fig. 9. Setting desired ship heading vi.", "texts": [ " Specifically, the selected berthing route is partitioned into several segments to provide a discrete set of desired headings,y(; see Fig. 8 (here i= 0 to 6). Theintermediate desired heading within a segment, designated vf , is determined from the linear correction function U:,.,\", $1. In Equation (43), xk E [x1-], xz] is the current x coordinate of the ship, whereas yt, and yf are respectively the initial and final planned tangent values for segment i . Now consider the situation where the ship is not on the desired route, but at a point (xk, yk); see Fig. 9. In this case, the new desired heading y~,\" is obtained from the equation (44) where and 4 = Y k - Y , . (46) As illustrated in Fig. 9, the yri obtained from Equation (44) can help to direct the off-track ship back to the desired route, because > y~: when the ship is above the desired route and tpf < when the ship is below the desired route. August 1997 39 2. The Setting of (x,\", y,\") Values. When the ship is off the planned route and located at (xk, y k ) , see Fig. 10, a new desired intermediate position (x,\", y,\") is automatically generated. To achieve a smooth response, it is not necessary or desirable to direct the ship toward the point Q, which corresponds to the minimum distance between the current ship position and the planned route" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000674_s1560354718070122-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000674_s1560354718070122-Figure2-1.png", "caption": "Fig. 2. Roller Racer on a plane.", "texts": [ " 7\u20138 2018 and gyrostatic torque) of the system which arise in real situations where the specified periodic change in the configuration variable is achieved. The dynamics of the Roller Racer in which \u201cdynamical\u201d control is implemented by using external torque (gyrostatic torque) or by using the prescribed time dependence of the mass distribution has not been investigated. 2. EQUATIONS OF MOTION Consider the problem of the motion of the simplest wheeled vehicle, the Roller Racer, on a plane. The Roller Racer consists of two coupled platforms which can freely rotate in a horizontal plane independently of each other (see Fig. 2). Each platform has a rigidly attached wheel pair consisting of two wheels lying on the same axis. We define three coordinate systems: \u2014 an inertial coordinate system Oxy; \u2014 a noninertial coordinate system C1x1y1, attached to the first platform, with origin C1 at the center of mass of the wheel pair. We assume that the axes C1x1 and C1y1 are directed, respectively, along a tangent and a normal to the plane of the wheels; \u2014 a noninertial coordinate system C2x2y2, attached to the second platform, with origin C2 at the center of mass of the wheel pair", " 7\u20138 2018 \u2014 for the first wheel pair: r\u0307 + \u03c8\u0307(c1n1 \u2212 b1\u03c41) + h1\u03c6\u030711\u03c41 = 0, r\u0307 + \u03c8\u0307(c1n1 + b1\u03c41) + h1\u03c6\u030712\u03c41 = 0, \u03c41 = ( cos\u03c8, sin\u03c8 ) , n1 = ( \u2212 sin\u03c8, cos\u03c8 ) , \u2014 for the second wheel pair: r\u0307 + (\u03d5\u0307(t) + \u03c8\u0307)(c2n2 \u2212 b2\u03c42) + h2\u03c6\u030721\u03c42 = 0, r\u0307 + (\u03d5\u0307(t) + \u03c8\u0307)(c2n2 + b2\u03c42) + h2\u03c6\u030722\u03c42 = 0, \u03c42 = ( cos(\u03d5(t) + \u03c8), sin(\u03d5(t) + \u03c8) ) , n2 = ( \u2212 sin(\u03d5(t) + \u03c8), cos(\u03d5(t) + \u03c8) ) , where \u03c6ij are the angles of rotation of the wheels, h1 and h2 are the radii of the wheels on the first and the second platform, b1 and b2 are the distances from the point of contact of the wheel to the center of mass of the corresponding wheel pair, and c1 and c2 are, respectively, the distances from the center of each wheel pair to the attachment point of the platforms (see Fig. 2). Multiplying the equations for the first and the second wheel pairs by n1 and n2, respectively, we obtain relations without the angles of rotation of the wheels: \u2212x\u0307 sin\u03c8 + y\u0307 cos\u03c8 + c1\u03c8\u0307 = 0, \u2212x\u0307 sin(\u03d5(t) + \u03c8) + y\u0307 cos(\u03d5(t) + \u03c8) \u2212 c2(\u03d5\u0307(t) + \u03c8\u0307) = 0. (2.1) These relations mean that the projection of the velocity of the center of mass of each wheel pair C1 and C2 onto the direction perpendicular to the plane of the corresponding wheel is equal to zero. The angles of rotation of the wheels are defined in terms of quadratures by means of x(t), y(t), \u03c8(t) [8]: h1\u03c6\u030711 = b1\u03c8\u0307 \u2212 x\u0307 cos\u03c8 \u2212 y\u0307 sin\u03c8, h1\u03c6\u030712 = \u2212b1\u03c8\u0307 \u2212 x\u0307 cos\u03c8 \u2212 y\u0307 sin\u03c8, h2\u03c6\u030721 = b2(\u03d5\u0307(t) + \u03c8\u0307)\u2212 x\u0307 cos(\u03d5(t) + \u03c8)\u2212 y\u0307 sin(\u03d5(t) + \u03c8), h2\u03c6\u030722 = \u2212b2(\u03d5\u0307(t) + \u03c8\u0307)\u2212 x\u0307 cos(\u03d5(t) + \u03c8)\u2212 y\u0307 sin(\u03d5(t) + \u03c8)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000884_s40997-019-00290-3-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000884_s40997-019-00290-3-Figure1-1.png", "caption": "Fig. 1 Schematic of planetary gear transmission", "texts": [ " For discussing the effect of the flexibility on the dynamic characteristics of the planetary gear transmission system, in this paper, a rigid-flexible coupled dynamic model of the planetary gear transmission system was developed considering the flexible internal ring gear, flexible shaft, time-varying meshing stiffness and static transmission error excitation. The flexibility of the internal ring gear is based on the shell theory. The dynamic characteristics of the planetary gear transmission system, such as the distribution of dynamic stress and deformation on the pitch line and tooth root of the ring, were investigated. A schematic of the planetary gear transmission system as a research object including a rotating carrier C, five planet gears P1,P2,P3,P4,P5 , a sun gear S and a fixed internal ring gear R is shown in Fig.\u00a01. The basic parameters of the planetary gear transmission system, which are from a 5-MW wind turbine gearbox, are listed in Table\u00a01. The time-varying meshing stiffness and the static transmission errors were determined according to the references (Zhai et\u00a0al. 2016; Sun et\u00a0al. 2015). The modeling methods for the components of planetary gear transmission system are shown in Table\u00a02. The flexible internal ring gear and sun shaft are modeled using the shell theory and finite element method, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000690_s11012-019-00973-w-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000690_s11012-019-00973-w-Figure1-1.png", "caption": "Fig. 1 Spiral bevel gear pair", "texts": [ " It establishes a mathematical model for the computerized numerically controlled cradle-style pinion generator by considering these design parameters: tool parameters, initial machine settings and polynomial coefficients of the auxiliary tooth surface correction motion. To solve the polynomial coefficients, an optimal model was suggested. The tooth surface correction method has served as a basis for the modification of high-contact-ratio (HCR) spiral bevel gears, i.e., the higher-order transmission error (HTE), which is drawn on the function-oriented design. Figure 1 shows a portrait of spiral bevel gear pair. It is assumed that the translational degrees of freedom (DOF) for the considered bevel gears are restricted in all directions by means of bearings. Both gears are free to rotate about their axes. By applying Lagrange formulation [17\u201322], the equation of motion of the system is achieved: I1\u20ach1 \u00fe Cmrb1\u00f0rb1 _h1 rb2 _h2 _e\u00de \u00fe kmrb1f \u00f0rb1h1 rb2h2 e\u00de \u00bc T1 I2\u20ach2 Cmrb2\u00f0rb1 _h1 rb2 _h2 _e\u00de kmrb2f \u00f0rb1h1 rb2h2 e\u00de \u00bc T2 \u00f01\u00de where I1, I2 rotary inertia of pinion and gear, rb1, rb2 base radii of pinion and gear, h1 angular displacement for the for driver, h2 angular displacement for the driven, T1 constant driver torque and T2 constant breaking torque, k time-varying meshing stiffness, c damping coefficient between the meshing gear teeth of the pairs" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001755_lra.2021.3071952-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001755_lra.2021.3071952-Figure2-1.png", "caption": "Fig. 2. A schematic diagram of a PNA with geometrical parameters.", "texts": [ " In practice, the acceleration generally fluctuates with the persistent disturbance, which in turn incurs a large gain of the proportional term. It will increase the possibility of input saturation and degrade the control performance correspondingly. IV. VERIFICATION Attributed to the concavo-convex multicavity structure, the soft PNA features have a fast response and long life span. Therefore, the actuator has received notable attention due to its potential application in the field of soft gloves and grippers [16], [31]\u2013[33]. The schematic diagram in Fig. 2 shows the initial state and full-size geometrical parameters of the PNA. As shown in Fig. 2, H,W , and L are the total height, width and length of the PNA, respectively. H1, H2, and H3 are the heights of the top wall, the exterior wall and the bottom wall, respectively. W1,W2 are the widths of the anterior and exterior wall, respectively. To mimic a human finger, the parameters of the actuator are set as W = 0.015m,W1 = 0.003m,W2 = 0.002m, H1 = 0.007m, H2 = 0.003m, H3 = 0.011m, L = 0.128m,m = 0.04 kg. In addition, the desired trajectory is chosen as qd(t) = 0.9\u2212 0.8 cos(0.6t) (rad) such that q\u0307d(t), q\u0308d(t) are all known and Bd = 1" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001379_tec.2020.3030042-Figure18-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001379_tec.2020.3030042-Figure18-1.png", "caption": "Fig. 18. Finite element model of entire motor except rotor.", "texts": [ " 17, the asymmetry of the end cover of the motor in both the axial and radial directions is large, and its natural frequencies are difficult to obtain by the analytical calculation. The modal shapes and corresponding natural frequencies obtained by the FEM are shown in Tab. VIII, respectively. It can be seen that the each order modal frequency of the end cover under free vibration is greater than that of other parts of the motor. Therefore, the end cover cannot be easily ignored in the modal analysis of the motor. The finite element model of the entire motor except the rotor is shown in Fig. 18. The modal shapes of the entire motor are relatively complex, and the deformation of each component is different. Therefore, it is difficult to determine the specific order of the modal shape. The modal shapes and corresponding natural frequencies of the entire motor are shown in Tab. IX, respectively. It can be seen that the existence of the end cover will limit the radial deformation of the stator to a certain extent, so the radial natural frequencies of the entire motor will become larger. The modal shapes of the entire motor are far more than a TABLE VIII NATURAL FREQUENCIES OF END COVER Order 2nd 3rd 4th m=0 Modal shapes Results/Hz 1186" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000983_j.precisioneng.2020.02.007-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000983_j.precisioneng.2020.02.007-Figure1-1.png", "caption": "Fig. 1 Schematic diagram and coordinate systems of internal gear Sw (Ow-XwYwZw) and skiving tool St", "texts": [ " The surface of gear flank was extracted from cloud points of cutting edge based on Z-map method. Fast Fourier transform (FFT) analysis was used to clarify the influence of eccentricity error on the surface roughness profile. Influences of eccentricity error and feed rate on the surface roughness profile of gear tooth were investigated with proposed model, followed by the experimental verification. Three coordinate systems were used to establish the relative movements of the cutting tool and workpiece by the matrix transformation and calculation. As shown in Fig. 1, global coordinates O-XYZ, and two local coordinate systems, Ot-XtYtZt, Ow-XwYwZw, are fixed on the cutting tool and workpiece, respectively. The relative shaft angle \u03a3 between axes of cutting tool and workpiece is located in the XZ plane of global coordinates O-XYZ and can be calculated by: (1)\u03a3 = \ud835\udefd\ud835\udc61 + \ud835\udefd\ud835\udc64 Where \u03b2t and \u03b2w refer to the helix angle of cutting tool and workpiece, respectively. The vector between the original points Ow and Ot is referred to as the vector a in the global coordinate system", " Similarly, right edge Edgerf of skiving tool can be expressed by: (5)\ud835\udc38\ud835\udc51\ud835\udc54\ud835\udc52\ud835\udc5f \ud835\udc53 = \ud835\udc47 -1 \u2219 [ \ud835\udc5f \u2219 (\ud835\udc50\ud835\udc5c\ud835\udc60\ud835\udf03 + \ud835\udf03 \u2219 \ud835\udc60\ud835\udc56\ud835\udc5b\ud835\udf03) -\ud835\udc5f \u2219 (\ud835\udc60\ud835\udc56\ud835\udc5b\ud835\udf03 \u2015 \ud835\udf03 \u2219 \ud835\udc50\ud835\udc5c\ud835\udc60\ud835\udf03) 0 1 ] Thus, the intial cutting edge Edget i of one cutter tooth can be expressed by: (6)\ud835\udc38\ud835\udc51\ud835\udc54\ud835\udc52\ud835\udc56 \ud835\udc61 = [\ud835\udc38\ud835\udc51\ud835\udc54\ud835\udc52\ud835\udc59\ud835\udc53 \ud835\udc38\ud835\udc51\ud835\udc54\ud835\udc52\ud835\udc5f \ud835\udc53] Next, the transformation matrix are used to position the initial cutting edge in the O-XYZ coordinate system using tool setting parameters. Based on the location, rake angle and shaft angle of skiving cutter, the cutting edge can be calculated by adding Trt, Trake and Tincl, respectively, as following equation: (7)\ud835\udc38\ud835\udc51\ud835\udc54\ud835\udc52\ud835\udc5c = \ud835\udc47\ud835\udc56\ud835\udc5b\ud835\udc50\ud835\udc59 \u2219 \ud835\udc47\ud835\udc5f\ud835\udc61 \u2219 \ud835\udc47\ud835\udc5f\ud835\udc4e\ud835\udc58\ud835\udc52 \u2219 \ud835\udc47 \u20151 \ud835\udc5f\ud835\udc61 \u2219 \ud835\udc38\ud835\udc51\ud835\udc54\ud835\udc52\ud835\udc56 \ud835\udc61 Where (8)\ud835\udc47\ud835\udc5f\ud835\udc61 = [1 0 0 \ud835\udc5f\ud835\udc61 0 1 0 0 0 0 0 0 1 0 0 1 ] (9)\ud835\udc47\ud835\udc5f\ud835\udc4e\ud835\udc58\ud835\udc52 = [\ud835\udc50\ud835\udc5c\ud835\udc60\ud835\udefe 0 \u2015\ud835\udc60\ud835\udc56\ud835\udc5b\ud835\udefe 0 0 1 0 0 \ud835\udc60\ud835\udc56\ud835\udc5b\ud835\udefe 0 0 0 \ud835\udc50\ud835\udc5c\ud835\udc60\ud835\udefe 0 0 1 ] 5 (10)\ud835\udc47\ud835\udc56\ud835\udc5b\ud835\udc50\ud835\udc59 = [1 0 0 0 0 \ud835\udc50\ud835\udc5c\ud835\udc60\ud835\udf00\ud835\udc61 \u2015\ud835\udc60\ud835\udc56\ud835\udc5b\ud835\udf00\ud835\udc61 0 0 0 \ud835\udc60\ud835\udc56\ud835\udc5b\ud835\udf00\ud835\udc61 0 \ud835\udc50\ud835\udc5c\ud835\udc60\ud835\udf00\ud835\udc61 0 0 1 ] Where and t are the rake and inclination angles of rake face of cutter (see Fig. 1(b)), respectively. For calculating the cloud points of cutting edge during cutting, the workpiece is fixed and the relative movement of the edge of the cutting tool edge Edgew t after a specific time t can be calculated by adding some translation matrices as the following equation: (11)\ud835\udc38\ud835\udc51\ud835\udc54\ud835\udc52\ud835\udc64\ud835\udc61 = \ud835\udc47\ud835\udc61\ud835\udc5f\ud835\udc4e\ud835\udc5b\ud835\udc60 \u2219 \ud835\udc47\u03a3 \u2219 \ud835\udc47\ud835\udc5f\ud835\udc5c\ud835\udc61 \u2015 \ud835\udc64 \u2219 \ud835\udc47\ud835\udc5f\ud835\udc5c\ud835\udc61 \u2015 \ud835\udc61 \u2219 \ud835\udc38\ud835\udc51\ud835\udc54\ud835\udc52\ud835\udc5c Where: (12)\ud835\udc47\ud835\udc5f\ud835\udc5c\ud835\udc61 \u2015 \ud835\udc61 = [cos (\ud835\udf14\ud835\udc61\ud835\udc61) \u2015\ud835\udc60\ud835\udc56\ud835\udc5b(\ud835\udf14\ud835\udc61\ud835\udc61) sin( \ud835\udf14\ud835\udc61\ud835\udc61) cos (\ud835\udf14\ud835\udc61\ud835\udc61) 0 0 0 0 0 0 0 0 1 0 0 1 ] (13)\ud835\udc47\ud835\udc5f\ud835\udc5c\ud835\udc61 \u2015 \ud835\udc64 = [ cos (\ud835\udf14\ud835\udc64\ud835\udc61) \ud835\udc60\ud835\udc56\ud835\udc5b(\ud835\udf14\ud835\udc64\ud835\udc61) \u2015sin( \ud835\udf14\ud835\udc64\ud835\udc61) cos (\ud835\udf14\ud835\udc64\ud835\udc61) 0 0 0 0 0 0 0 0 1 0 0 1 ] (14)\ud835\udc47\u03a3 = [1 0 0 0 0 \ud835\udc50\ud835\udc5c\ud835\udc60\u03a3 \u2015\ud835\udc60\ud835\udc56\ud835\udc5b\u03a3 0 0 0 \ud835\udc60\ud835\udc56\ud835\udc5b\u03a3 0 \ud835\udc50\ud835\udc5c\ud835\udc60\u03a3 0 0 1] (15)\ud835\udc47\ud835\udc61\ud835\udc5f\ud835\udc4e\ud835\udc5b\ud835\udc60 = [1 0 0 \ud835\udc53(1) 0 1 0 \ud835\udc53(2) 0 0 0 0 1 \ud835\udc53(3) 0 1 ] Where f = [fax, fay" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001061_j.measurement.2020.108492-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001061_j.measurement.2020.108492-Figure1-1.png", "caption": "Fig. 1. Offset misalignment in (a) Radial, (b) Axial directions; Angular misalignment (c) perpendicular to plane of action and (d) in plane of action.", "texts": [ " Misalignment results in scuffing failure on the pinion addendum and gear dedendum regions due to limited lubricant in the overstress region. At the end of the test, all the four seals appears safe, while the coupling spiders damage seriously. Gearbox is an important power transmission device in various applications including automotive, wind turbine, electric overhead crane, machine tool, sugar industry, and material handling equipment etc. Gearbox failure due to misalignment is a serious issue. It observes to be the second most killer of a gear set. Parallel, radial and angular misalignments occur in meshing gears as shown in Fig. 1. Few examples of gearbox failure due to misalignment are overhang-meshing gears, deflection of pinion or gear shaft supported between the bearings, poor adjustment of bearings, bearing wear, poor foundation and assembly error etc. Above cited reason of misalignment results in malfunction of the gearbox. Deflection of shaft causes imperfect meshing of gears, bearing overstress, and seal wear etc. The overloaded contact area results in wear, pitting, scuffing and breakage of gear\u2019s teeth etc. Gearbox consists of gear, bearing, and rotor as the primary loading components, and failure of one component affects others and may lead to gearbox breakdown" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001584_tmech.2021.3068622-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001584_tmech.2021.3068622-Figure2-1.png", "caption": "Fig. 2. Kinematic model of the DAR", "texts": [ " if the robot loses tension on reaching a singular position or if the rope is broken. The DAR is a mobile robot moving 2-DOF due to the pulling action of two flexible nylon fiber ropes. Therefore, the vibration applied to the robot body can be classified into two types: kinematic and rope vibrations. In this section, the vibration of the DAR is analyzed that generated by the flexible rope using kinematic models. The kinematic model of the robot utilizing elastic massless two ropes is presented in Fig. 2. The position vectors of the moving robot are as follows: \ud835\udc5d \u20d7\u20d7\u20d7\u20d7 = \ud835\udc34\ud835\udc56\u20d7\u20d7 \u20d7 \u2212 \ud835\udc5e\ud835\udc56\u20d7\u20d7 \u20d7 \u2212 \ud835\udc11\ud835\udc67\ud835\udc5f\ud835\udc56\u20d7 , \ud835\udc56 = 1, 2 (1) \ud835\udc99 = \ud835\udc5d \u20d7\u20d7\u20d7\u20d7 = [ ]T, ?\u0307? = \ud835\udc09?\u0307? , \ud835\udc09 = [\u2212\ud835\udc62 \u20d7\u20d7\u20d7\u20d7 T \u2212\ud835\udc62 \u20d7\u20d7\u20d7\u20d7 T ] T (2) where \ud835\udc5d \u20d7\u20d7\u20d7\u20d7 is the position vector of DAR, \ud835\udc34\ud835\udc56\u20d7\u20d7 \u20d7 is the anchor position vector, \ud835\udc5e\ud835\udc56\u20d7\u20d7\u20d7 is the rope vector, \ud835\udc11\ud835\udc67 is the robot's rotation matrix, \ud835\udc5f\ud835\udc56 \u20d7 is the revolute joint vector from the body frame origin (o), ?\u0307? = [\ud835\udc5e \ud835\udc5e ] T, is joint velocity vector and \ud835\udc09 is the Jacobian matrix between the Cartesian space (global frame O) and joint space" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003007_s0142-1123(98)00077-2-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003007_s0142-1123(98)00077-2-Figure5-1.png", "caption": "Fig. 5. Contact fatigue test rig. TR=test roller, LR=load roller, OS=oil supply and LC=load cell.", "texts": [ " The machine was selected for this testing for its capability of performing tests with parameters similar to those experienced by a gearwheel flank in an automotive gearbox. Before selecting this rig a literature study [1] was made and from this it was concluded that the SKF-ERC test rig was suitable mainly due to the high speed, the simple test geometry, the flexible drive system and the flexible lubrication system. The lubrication system on the SKFERC rig was deemed suitable as it is filtered, temperature controlled, and it can be used with added contamination in the lubricant. The test rig used for this study is of the roller-to-roller type as shown in Fig. 5. The test rig is shown with the front bearings and covers removed to expose the test cell with the test and load ring mounted in place. Visible in the figure is also part of the lubrication and drive system. The test cell where the testing takes place is shown schematically in Fig. 6. The test cell consists of two rings. A large ring which is the load-ring, i.e. a ring that is used to apply load to the specimen tested, and a small test ring that is the specimen tested. To ensure an even pressure on the rings a camber with a radius of 30 mm is ground on the load ring" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000620_s11071-018-4338-3-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000620_s11071-018-4338-3-Figure8-1.png", "caption": "Fig. 8 The leaf spring before and after assembly. a Leaves before assembly. b Assembled leaf spring", "texts": [ " The leaves are clamped together by the center bolt, and the leaf spring assembly is fixed to the spring seat by a set of U-bolts, while the spring seat is rigidly attached to the axle. The leaf spring is connected to the chassis using the shackle at one end and a pin joint at the other end. The shackle can have a small rotation to allow for small longitudinal translation of the spring with respect to the chassis. Leaf springs are designed to have pre-stress in order to reduce the stress of the master leaf when the spring is mounted on the vehicle. This pre-stress can be achieved by changing the leaf curvature during the assembly process, as shown in Fig. 8a. Specifically, nips between the adjacent leaves, below the master leaf, are formed by successively reducing the radius of curvature of the leaves, as shown in Fig. 8a [1]. Therefore, when the leaves are clamped together, as shown in Fig. 8b, the master leaf is subjected to a bending preload opposite in direction to that caused by the vehicle load, resulting in overall reduction of the spring bending stress during the vehicle operation. To extend the life cycle of the leaf springs, they are usually designed based on the concept of the uniform strength beam. Depending on if the thickness or width of the leaf is kept constant in the ideal model, the designed leaf spring can be classified as a uniformthickness leaf spring or a parabolic leaf spring, respectively", " One has the following relationships: dr = Jdri , dr = Jedx, dri = Jidx, J = \u2202r \u2202ri = ( \u2202r \u2202x ) ( \u2202x \u2202ri ) = JeJ \u22121 i (12) The Green\u2013Lagrange strain tensor is defined in terms of the position vector gradient matrices as \u03b5 = 1 2 ( JT J \u2212 I ) = 1 2 [ J\u22121T i ( JTe Je ) J\u22121 i \u2212 I ] (13) where Je = \u2202 (Se) /\u2202x, S is the shape function matrix, and e is the vector of nodal coordinates of the leaf spring in the current configuration. Two initial configurations of the leaf spring can be used depending on whether or not the pre-stress is considered in the analysis, which are the configurations before and after assembly, as shown in Fig. 8a, b. Denoting the vector of nodal coordinates of the leaf spring before and after the assembly as eu and e0, respectively, the corresponding matrices of position vector gradients are denoted as Ju and J0. If the leaf spring assembly is used as the initially stress-free configuration, shown as the dashed line in Fig. 11, there will be no initial stresses. In order to account for the pre-stress caused by the assembly process, the configuration before assembly shown in Fig. 8a should be used as the initial stress-free configuration, the mapping relation is shown as the solid line arrows in Fig. 11, and thus Ji = Ju . Therefore, there exists initial stress in the configuration of the leaf spring assembly since J = JeJ\u22121 u = J0J\u22121 u and the initial strain \u03b50 = ( J\u22121T u ( JT0 J0 ) J\u22121 u \u2212 I ) /2. The difference between the assembly configuration and the un-deformed configuration ed0 = e0 \u2212 eu is used to determine the desired pre-stress value. As shown in Fig. 1, the leaf spring is connected to the chassis at one end using the shackle and at the other end using a pin joint" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001289_ab818b-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001289_ab818b-Figure8-1.png", "caption": "Figure 8. (a) Schematic representation of continuous inkjet printing (CIJ) and (b) Drop-on-demand printing (DOD).", "texts": [], "surrounding_texts": [ "(Re) number and the square root of the Weber (We) number, and is independent of fluid velocity (Z) is given in Eq. 4.\n( ) ( ) ( ) ( ) [ ] / / rg h = =Ohnesorge Oh number Z a N N 4 1 2 Re We 1 3\nThe printable fluid should have a Z value between 1 and 10 (e.g. must be Z > 2), which can avoid the primary drop, followed by secondary (satellite) drop, during the printing and it is necessary for particularly drop-on-demand (DOD) printing technique.98\nThe choice of suitable print head diameter and size of the nanoparticles is very important as the formulation ink contains the dispersed nanoparticles, which should be smaller than that of the print head, about 50 \u03bcm in size. In order to prevent the clogging, printing instability, and agglomeration eventually blocking at the nozzle, the size of the nanoparticles should meet the size a minimum 1/50 of the print head diameter.99\nThe next important parameter to optimize is the formation of inkjet droplets. In general fluid dynamics describes the property of ejected droplets that can land over the surface of the substrate and their behavior with the substrate during printing. The more conscious factor is the distance between the substrate and the print head, which guarantees to have homogenous high-resolution print. When the substrate is close to the print head, it causes secondary droplets, which may be scattered and affect the homogeneity of the final print feature due to its primary droplets pressure. In addition, the final printable nanoparticles ink properties might be depending on its substrate surface energy and also its viscosity and surface tension.100\nCoffee ring effect and curing time is yet another parameter need to be optimized. The printable ink contains a dispersed nanoparticle, which may evaporate and leaves as a ring-like structure on its surface perimeter that they termed as \u201ccoffee-ring effect.\u201d This is due to its viscosity and solute transport property, interplaying during the droplet land on the surface and that has dried by solvent motion occurred around the substrate. This phenomenon may also be affecting the homogeneity of inkjet printing droplets and this effect need to overcome. Similarly, it is necessary to freeze the ink droplets within its geometry too quickly. In order to reduce the coffee-ring effect, the solvent should possess the properties of both boiling point and heat of vaporization higher than that of water and within a maximum of 5 min it has to promote adhesiveness on the substrate.101,102\nScreen printing.\u2014Figure 5 represented the evolution of printing technology since its first invention. Inkjet and screen-printing have grown up tremendously in the 18th and 19th centuries. Screenprinted device (Fig. 6) principally contains a component of (1) substrate with printer stage, (2) stencil with meshes, (3) formulated functional ink, (4) squeegee, (5, 6) separation with transfer desired pattern, (7) area masked by a dielectric material, and (8) prepared individual electrode. To fabricate the electrode; initially, the stencil with mesh used for penetration of ready-mix is\nsqueegeed on the substrate. This resulted dried electrode was separated, followed by forming the predefined structure onto the surface. This printed electrode is being used in the electrochemical experiment instead of a noble metal electrode. Indeed, using this technique, the carbon paste electrode has an emphasis to develop cheap and affordable cost electrodes. The printed electrode circuits can be fabricated through different approaches such as pad printing, roll to roll and screen printing. Among this technique, the screenprinted electrode had the ability towards commercial production of large-scale reproducible electrode that revolutionized in order to\nJournal of The Electrochemical Society, 2020 167 067523", "compromise the distance from the laboratory to implementation in industries.103\u2013105 Consequently, the glucose sensor market has incorporated with the screen-printed electrode. With the advent of this, an individual can be able to measure their serum glucose level at home along with instant precious results The screen-printed electrode offers a significant sensitivity, higher signal-to-noise ratios, require a minimum quantity of sample volumes and owns the ability to replace the conventional solid-state electrodes and can able to use for multiple analysis using one electrode106,107 (Fig. 7).\nInkjet printing.\u2014Inkjet printing is presently an extensive personal printing gadget. However, this inkjet printer is widely used in the commercial application of graphics and other traditional uses.108 Moreover, it has great attention in the recent era for the fabrication of electronic gadgets like transparent displays, micro-fluids device, disposable, flexible and wearable electronics devices. Further their prototype for biosensor and tissue engineering are leading application area.109 Inkjet printing can be separated into two types based on their mechanism of which generates the droplets and typically termed as \u201ccontinuous inkjet printing (CIJ)\u201d and \u201cDrop-on-demand (DOD)\u201d (Figs. 8a and 8b). DOD printing is the most dominant printing technique due to its smaller size in print head in the range of 20\u201350 \u03bcm, which can print graphics and text content in a precious manner.110\u2013112 However, in the CIJ printing, it generates drops at the\nrate in the region of 20\u201360 kHz and typically drop velocity to be >100 m s\u22121 at the print head. So that the CIJ generates continuous ink drops by charging the device with the pressurized flow even where the print is not necessary.113 These unnecessary drops are collected in the gutter using the charged deflectors in which this recycled ink is not applicable for material science application in terms of contamination risks. The droplet controlled only while steering a drop in the flight or position of the substrate, whereas in the second process is the binary printing technique, it may be deposited on the substrate or recycled in the gutter. Hence CIJ is potentially inefficient method. And also, it has hindrance like Rayleigh instability, pressure, smaller print head, bigger droplet formation, and cannot control the drops and position. These factors are considered during the printing, so that, the DOD printing ensured a highly precise technique compare to that of CIJ printing.114 DOD system assured to generate the droplets at the rate of 1\u201320 kHz. These droplets are formed through propagating the pulse by which is controlling the drop size and ejection velocity by the management of pressure pulse when it should exceed a threshold level in the print. It can also ensure to control via static pressure for the formation of meniscus by the surface tension at the nozzle to further construct the pattern on the surface of the substrate.113,115,116\nPaste or ink formulation.\u2014Paste(inkjet) printable functional material, should possess the suitable paste(ink) formulation which can able to deposit or print upon the surface of the substrate. However, the conductive ink formulation is for conventional graphics paste or ink. The paste or ink should have good adhesion against the specifically targeted substrate and high resolution, low printer maintenance, lifetime stability, and good printability.117,118 Hence, the formulation adapts conductive ink should have the properties of viscosity, surface tension, wettability and adhesion to provide superlative printing performance by adjusting to the substrate. For instance, in the subject to the formulated ink, the viscosity should be in the range of 8\u201315 cP for the piezoelectric printer head, whereas below the 3 cP viscosity for the thermal inkjet printing and approximately \u223c70,000 cP for screen printing.\nA two-dimensional material with a single layer of nanosheets has a thickness of 0.34 nm as an interplanar spacing. Moreover, graphene nanosheets have intrinsic in-plane conductivity with Fermi velocity and varying its sheet resistance with respect to the number of layers.119 Pristine graphene (PG) can be produced with various methods by mechanical, liquid-phase exfoliation,120 chemical vapor deposition (CVD), solvothermal synthesis, chemical crosslinking of polycyclic compounds, thermal decomposition, probe sonication,and electrochemical exfoliation.121 Dispersion of pristine graphene is generally prepared in the presence of organic\nJournal of The Electrochemical Society, 2020 167 067523", "solvents of cyclohexanone, terpinol, N-methylpyrrolidone, 1,3- dimethyl-2-imidazolidinone, o-dichlorobenzene, ascorbic acid, and ethanol.122 In order to obtain a stable inkjet printable ink, it is formulated using various stabilizing agents such as: polycyclic aromatic hydrocarbon, surfactants like sodium dodecyl sulfate (SDS), Sodium deoxycholate, sodium cholate and sodium dodecylbenzene sulfonate (NaDDBS), Triton X-100, Tween 20, Tween 80, and CTAB; polymers such as PVP and PVA; and ethyl cellulose.123 However, graphene oxide (GO) contains hydroxyl, epoxy, carbonyl, and carboxylic groups.124 This can easily dispersible in non-polar solvents like water, and polar solvents such as N,N-dimethylformamide (DMF), N-methyl-2-pyrrolidone (NMP), isopropanol, and ethylene glycol used to prepare stable dispersion without any stabilizers.125 Compared to pristine graphene (PG), GO have advantages due to high dispersion with the loading range of 0.002\u20130.1 wt%.123,126\nDiabetes Mellitus is one of the metabolic diseases and the percentage of people affected by diabetes mellitus are increasing worldwide every day, which causing life-threatening and impeding conditions of cardiac, nervous, renal, ocular, cerebral, and peripheral vascular diseases. Perhaps the treatment of diabetes has turned out to be a more sophisticated science, including self-testing and monitoring in compact size and accurate analysis followed by an uninterrupted glucose monitoring device. There are four generations of enzymatic based glucose sensors. First-generation depends on oxygen as co-substrate in order to catalytic regeneration of the FAD center. In continuation of that, mediators (e.g. redox mediators) and mediators\u2019 free sensors (e.g. electrons transfer between the enzyme and the electorate) were developed by second and third-generation of glucose sensors, respectively. Hence, enzymatic based glucose biosensor has its own advantages and disadvantages.127,128 The nonenzymatic electrode is the fourth generation glucose sensor that has the potential towards directly oxidize glucose in the sample. Despite this, the problem associated with this is the lack of selectivity, slow kinetics, pH, and fouling by real sample constituents at the electrode, that tactic has prevented from practical sensor application. The electrochemical analysis is the major technique that has played a vital role since the discovery of glucose sensor. It is due to the combination of specificity and stability against the glucose oxidase for the fabrication of electrochemical detection of glucose using SPEs evolving, recently. The first paper-based microfluidic device is introduced by Henry group at Colorado State University using electrochemical measurements.129 In 2013, Maatanen et al. fabricated first inkjet printed paper based electrochemical glucose sensors with the modification of electrode surface.130 Then, in 2015, Costa et al. executed the fully inkjet printed carbon ink based MWCNT for paper based electrochemical sensor for detection of metal (Fe2+) ion.131 More recently screen or inkjet printed electrode were playing an extensive vital role in glucose sensor with low cost, disposable, environmentally degradable, high through put sensitivity, selectivity and stability, and handheld in size for real-time quick analysis. And also, carbon derived (e.g. graphene, graphene oxide, reduced graphene oxide, graphene nanoribbons) nanomaterials and their nanocomposite (e.g. with a combination of metal, metal oxides and polymers) have greater attention in the recent days. This is because of ease to achieve desired functionalization on the surface of the nanocomposite which is due to its higher surface to volume ratio. The screen-printed novel graphene nanoplatelets-iron phthalocyanine incorporated on conducting hydrogel for the amperometric glucose sensor. The screen-printed electrode of PAA/GPL-FePc/ GOx-CH shows the higher electrocatalytic activity of 0.26 V by Cyclic Voltammetry (CV) technique.132 Hence, it is ensured that, the enhancement in the redox reaction might be due to the preferred orientation of GOx upon the FePc site over the hydrogel of PAA-VS-PANI/GPL-FePc/GOx-CH. Equations 5\u20137 depicts the details of an amperometric response of glucose oxidation.\n( ) ( ) [ ] + + + + GO GAD glucose O GO FDH gluconolactone H O 5 x 2 x 2\n2 2\n[ \u2010 ( ) ] ( ) [ \u2010 ( ) ]\n( ) [ ] + + + + + + 2 GPL Fe III Pc GO FADH H O 2 GPL Fe II Pc GO FAD O 2H 6 x 2 2 2\nx 2\n[ \u2010 ( ) ] [ \u2010 ( ) ] [ ] + + + - H2 GPL Fe II Pc 2 2 GPL Fe III Pc 2e 7\nThe glucose of GOx (FAD) was converted into gluconolactone and H2O2 generated by an enzyme-catalyzed reaction by diffusion mechanism through the solution. FePc was used as a mediator for transferring the electron in between the GOx and the electrode via the reduction of the enzyme, estimated with sensitivity of 18.11 \u03bcAmM\u22121 cm\u22122 by H. Al-Sagur et al. In another study, bismuth (III) oxide decorated graphene nanoribbons electrode were fabricated for enzymatic glucose biosensor with modified SPCE/GNR/Bi2O3 electrode to increase the electrical conductivity. The CV response of this material was examined with an increase in the concentration of H2O2 which is directly proportion to its oxidation current. The Amperometry detection of glucose on SPCE/CNR/Bi2O3/GOx/Naf electrode was developed in order to observe the electrochemical response of glucose and extended to the study of quantification of glucose content in real samples of honey, blood serum, and urine samples.133 To further enhance the response of glucose at ultrasensitive, a screen-printed 3D copper oxide and copper oxide/graphene assembly has been utilized. As a consequence, electrochemical oxidation was ascribed in the occurrence of glucose in which it has been catalytically oxidized through Cu (III) into the form of gluconic acid as a by-product of Cu (II) species on the CuO/SPGE electrode. The CuO/few-layer graphene/SPGE shows a higher electron transfer rate at fabricating electrode is evident from its surfaces controlled electrochemical oxidation capability. The amperometric results of modified CuO/few-layer graphene/SPGE shows an enhancement in electrocatalytic performance with an effective higher electron transfer rate from the glucose and also in human serum samples.134 The electrochemical response of H2O2 can be attained via inkjet maskless lithography (IML) using high-resolution graphene films. The IML fabricated electrode was further used to detect the H2O2 by CV and amperometric method. The acquired CV and amperometric result provide the evidence of electrocatalytic oxidation peak with the linear increasing concentration of H2O2 with quick response time.135 Moreover, the Platinum modified/rGO/Poly (3-aminobenzoic acid) film modified (GOx-Pt/rGO/P3ABA) screen-printed carbon electrode for amperometric showed that. the addition of PtNPs in the presence of rGO exhibits electrocatalytic properties towards sensing H2O2. The fabricated Pt/rGO/P3ABA electrode also exhibits a significant charge transfer effect between the electrode/electrolyte interfaces and offers noble sensitivity towards the detection of glucose. This electrode also studied for a real sample of human serum, exhibited a clinically measurable signal.136 The Impedimetric detection method is recently showed highly precious and accurate determination of glucose. Using modified rGO/APBA (reduced graphene oxide and Amino phenylboronic acid) screen printed electrode impedimetric spectra studies were observed for blank and human serum samples of blood glucose. The impedance spectra changed at lower frequencies, due to interaction between the glucose and the modified rGO/APBA screen-printed electrode. During the monitoring of glucose in the real human blood sample, often the changes in the lower frequencies have been observed. Moreover, there is a complex compound present in the human serum, the results show good linearity and sensitivity with the detectable limit with glucose specific detection against various analytes137 and the detailed comparison on the previous literature related to glucose sensor is given in Table I.\nJournal of The Electrochemical Society, 2020 167 067523" ] }, { "image_filename": "designv10_11_0003566_0094-114x(94)90031-0-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003566_0094-114x(94)90031-0-Figure5-1.png", "caption": "Fig. 5. Four basis screws ~ c i a t e d with the displacement of a point.", "texts": [ " ks k6 + n 0 0 i --/(5 0 (22) where x = tan(O0/2), and kt, i -- !, 2 . . . . . 6, are functions of the known constants, i.e. functions of r, = (a, b, c) and rj = (d, e , f ) : kl = (d - a)/2, k2 = ( e - b ) / 2 , k 3 = ( f - c)/2, k, = ( f + c)/2, ks = - (e + b ) / 2 , ke -- (d + a)/2. From equation (22), we know that the screw g0 belongs to a 4-system. This agrees with the fact that Qo 3 possible screws exist. The four basis screws Sot, SO2, SO3 and S~, given in equation (22), are illustrated in Fig. 5. So, is a screw with infinite pitch, and its axis passes through R, and Rj. SO, represents a pure translation of the body. SO2, S0~ and So, are screws with zero pitch, and their axes are parallel to the axes of the reference frame and pass through the midpoint of the segment between R, and Rj. Note that, with the new definition of pitch, a zero pitch finite twist may indicate a screw displacement with a 180 \u00b0 rotation and a finite translation. In what follows, we show that any screw of the 4-system can displace the specified point from its initial to its final position" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003388_978-3-662-04831-3-Figure6.7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003388_978-3-662-04831-3-Figure6.7-1.png", "caption": "Fig. 6.7: Translational damper between points P ; and P j of bodies i and j", "texts": [ " Then F i acts in the direction of eji and Fj acts in the direction of ( -eji)- 6.1 Constitutive relations of planar external forces and torques 247 2. For (R.ji - R.jiO) < 0 the two bodies are pushed and the spring is under compression. Then Fi acts in the ( -eji) direction, and Fj acts in the eji direction. The deformed length .eji of the spring and the associated unit vector eji are computed by (6.6) , (6.7) , and (6.8). 6.1.3.2 Translational damper. Given a translational (point-to-point) damper between the bodies i and j , as shown in Figure 6.7. The damper force on body i is defined as Fi = di \u00b7 fji \u00b7 eji , di > 0 (linear damper) (6.11a) or as Fi = di (iji) \u00b7 eji, di: IE.1 ---+ IE.1 (nonlinear damper), (6.11b) with with di > 0 as damping coefficient, di(-) as damper characteristic, and with (6.12a) and dn as defined in (6.6). Computation of the time derivative 248 6. Constitutive relations of planar and spatial external forces and torques ~ (t2 ) = 2 \u00b7 fji \u00b7 fji = ~ [(dL; )T \u00b7 (dj i)Li] (6.12b) dt J\u2022 (6.12a) dt J' = 2. (dL! )T . (Li(l') = 2" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003879_j.wear.2004.11.018-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003879_j.wear.2004.11.018-Figure2-1.png", "caption": "Fig. 2. Configuration scheme of a linear guideway.", "texts": [ " Secion 4, which forms the bulk of this paper, then validates hese theoretical considerations on a test set-up and correations of the equivalent damping ratio are established with espect to bearing design parameters. Finally some concluions and directions for further research are highlighted in ection 5. . Equivalent damping ratio of a linear ass\u2013spring\u2013damper system A linear guideway system allows one degree of freedom DOF), the feed direction (X), and \u2018blocks\u2019 the remaining five, he bearing DOFs (normal (X), lateral (Y), yaw (MC), pitch MB), and roll MA) (see Fig. 2). Such a linear guideway can e modeled as a mass moving in one direction with friction orces between the mass and the fixed ground. If the system is linear, the problem reduces to considering a ingle DOF (SDOF) mass\u2013damper\u2013spring (m\u2013c\u2013k) system in n a linear system, \u03b6 is constant. In a \u2018linearized\u2019 equivalent f a non-linear system, \u03b6 will generally depend on the oscilation amplitude and/or frequency. This \u2018equivalent\u2019 \u03b6 will e analyzed for systems with hysteretic friction in the next ection. . Equivalent damping ratio of a mass on a hysteretic pring This section first briefly characterizes the hysteretic fricion that is dealt with in this paper" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000625_j.jmatprotec.2018.06.027-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000625_j.jmatprotec.2018.06.027-Figure4-1.png", "caption": "Fig. 4. A schematic of processing parameters. Black and grey circles indicate operation spots of a pulsed laser. Grey circles refer to the previous layer and black ones refer to the current layer.", "texts": [ " The spread powder layer is scanned by the laser beam according to the pre-sliced CAD model. The building platform descends for delivering a new layer of powders, and the procedure is repeated until the part is built in its entirety. In order to produce pores with different morphologies, various exposure times (ETs), i.e. 40, 60, and 80 \u03bcs, were used to produce the samples. ET refers to the time duration that a laser dwells on one spot. It directly controls the laser energy to the metal powders. The definition of the laser processing parameters is schematically shown in Fig. 4 and their values are listed in Table 1. The 316 L stainless steel powders used in the research are spherical in shape, ranging from 15 \u03bcm to 45 \u03bcm with a mean diameter of 30 \u03bcm. The material composition of 316 L stainless steel is shown in Table 2. The samples produced for material characterizations were 10mm\u00d710mm\u00d710mm cubes. A CM sample, which was produced from wrought bar materials after hot rolling (hardness\u223c250 HV), was also investigated in terms of material phase and microstructures for comparison purposes" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001777_j.mechatronics.2021.102595-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001777_j.mechatronics.2021.102595-Figure2-1.png", "caption": "Fig. 2. The coordinate system for the calibration of CDPRs.", "texts": [ " (15) To prevent the algorithm from entering an infinite loop iteration, the termination criterion of the iterative identification is set to \ud835\udf43\ud835\udc58 = \ud835\udc99\ud835\udc58 \u2212 \ud835\udc99\ud835\udc58\u22121, (16) which stops when \u2016\ud835\udf43\ud835\udc58\u2016 \u2264 10\u22124 is satisfied. The calibration of the coordinate system parameters only requires the external measurement device to measure the end-effector position, which can improve the applicability of this method. The calibration method is described in detail as follows. The coordinate system of CDPRs has been described in Fig. 2. The pose of base frame {\ud835\udc42} in the world frame {\ud835\udc4a } can be defined as \ud835\udc4a \ud835\udc42 \ud835\udc7f = \ud835\udc4a \ud835\udc42 \ud835\udc91,\ud835\udc4a\ud835\udc42 \ud835\udf53]\ud835\udc47 , where \ud835\udc4a \ud835\udc42 \ud835\udc91 and \ud835\udc4a \ud835\udc42 \ud835\udf53 denote the position and orientation from he base frame to the world frame, respectively. Moreover, {\ud835\udc42\u2032} and {\ud835\udc38\u2032} denotes the actual pose of the frame system in the world frame which obtained by identification. The purple dashed arrow indicate the vector of actual pose and the black solid arrow indicate the vector for the theoretical pose. The position of the end-effector frame {\ud835\udc38} in the mobile platform frame {\ud835\udc40} can be defined as \ud835\udc40 \ud835\udc38 \ud835\udc91" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001009_s0263574720000284-Figure14-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001009_s0263574720000284-Figure14-1.png", "caption": "Fig. 14. Schematic diagram of axial cross-sectional length under air pressure.", "texts": [ " Under the premise of not damaging the cavity and the cavity is not leaking, the ultimate air pressure of the single module is 17\u201318 kPa and the elongation at this air pressure is about 60%. When the one-link is combined with three modules, the single module cannot expand to the bottom due to internal compression. When the internal air pressure increases, the deformation of the crosssection is hindered and the module is elongated axially. Formulas (7\u201310) are as follows to study the utmost length of the single module under the baffle. As shown in Fig. 14, when not inflated, L1 is defined as the length of a half-wave plate in the upper corrugated cavity. After inflating, the length becomes L2 due to the axial force. So the (L2 \u2212 L1) is the https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0263574720000284 Downloaded from https://www.cambridge.org/core. Uppsala Universitetsbibliotek, on 15 May 2020 at 00:12:18, subject to the Cambridge Core terms of use, available at elongation of half-wave plate. If there are a half-wave plates, the total elongation can be estimated as L" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003220_tmag.2003.816500-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003220_tmag.2003.816500-Figure1-1.png", "caption": "Fig. 1. Cross section of PMSM.", "texts": [ " Most of the analysis was done on motor magnetics alone. Usually, this kind of motor is operated under inverter supply and various control circuits, therefore, the finite-element analysis of the motor requires inclusion of the voltage source inverter circuit as an integral part of modeling of the motor. By using circuit analysis, the voltage source inverter model can be included into the finite-element electromagnetic analysis simultaneously. The cross section of the PMSM with cage bars is shown in Fig. 1. The geometry and the magnetic circuit of the machine are very complicated and it is further complicated by the use of rotor cage bars for self starting which in turn requires accurate modeling. In this paper, the dynamics of the self-starting PMSM is studied by using a coupled time-stepping FEM method. In order to guarantee a good compromise between computing time and accuracy of results, two-dimensional FEM models combined with equivalent rotor bar circuits are used in the computation. The parameters of end effects due to stator windings and rotor end rings obtained by analytical methods are also included in the circuits [4]" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003131_robot.1999.770008-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003131_robot.1999.770008-Figure7-1.png", "caption": "Figure 7. Sequence for level-to-downslope transition.", "texts": [ " We now consider the level-to-downslope and upslopeto-level transitions. During the level-to-downslope transition, the biped executes the usual walking control for single support phase until the swing time has expired. When the swing time expires, if the swing foot has not touched down, the biped will exert a preset downwards force exerted at the swing leg\u2019s ankle so that the swing foot will continue on its way down. The downward force will cause the swing leg\u2019s ankle to penetrate through a virtual surface (which is the global slope) (see Figure 7(a)). When the virtual surface is penetrated, the biped recomputes the gradient of the global slope based on the instantaneous position of the swing leg\u2019s ankle (see Figure 7(b)) and adjusts the desired hip height accordingly. This is a continuous process. After the swing leg has touched down, the state machine will switch to the double support phase and the biped will compute the intermediate global slope (see Figure 7(c)). In this phase, the biped will compute the desired hip height based on the global slope. The swing leg of the next single support phase will also follow this global slope. The biped then goes through the whole sequence (Figure 7) again before both feet are on the same slope. The strategy for the level-to-downslope transition can also be applied to the upslope-to-level transition. For both the level-to-downslope and upslope-to-level transitions, we have to control the swing leg so that it will not hit the ground prematurely. To avoid such an event, the desired lift height for the swing leg is set to a value which will enable it to clear all the edges of the level-todownslope and upslope-to-level transitions. This is based on the assumption that we know the maximum change in the gradients for each slope transition" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000368_j.matpr.2017.11.685-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000368_j.matpr.2017.11.685-Figure1-1.png", "caption": "Fig. 1: Schematic Diagram of Rotating Biological Contactor (RBC).", "texts": [ " In rotating biological contactor, disc biomass is liable for the degradation of organic materials [Ghawi and Kris 2009]. Rotating biological contactor consist a different size glass container called reactor and a series of circular disks of polymer materials like polystyrene, polyvinyl chloride, polyethylene and acrylic plastic. These discs are submerged in wastewater and rotated through it. These discs are mounted on horizontal shaft and rotated by a variable-speed electric motor. RBC consist single or multiple stage (shown in Fig. 1). There are many parameters affecting RBCs performance like organic loading, hydraulic loading, biomass, rotational speed, wastewater temperature, staging, RBC media, Dissolved oxygen levels and medium submergence. 2.1 Wastewater All the chemicals used in the study were of analytical grade and used without further purification. The synthetic wastewater was made by dissolving the phenol (concentration in 50-1000 mg/L) in distilled water. 4220 Saraswati Rana et al./ Materials Today: Proceedings 5 (2018) 4218\u20134224 2", "2 Seed Sludge Activated sludge was collected from sewage treatment plant located in Bhopal, India. The sludge was first screened for the removal of coarse and bigger particles and then it was aerated for 1\u22122 d. It was transferred into the reactor and aerated again for 3\u22125 d for acclimatization of the sludge with the wastewater. 2.3 Fabrication of RBC unit A lab-scale RBC was fabricated with an acrylic plastic transparent sheet having 5 litre working volume. A schematic experimental setup is shown in Figure 1. This reactor consists of 6 discs, each having 10 cm diameter. The discs were mounted on a shaft of Stainless steel, geared with a rotational speed of 5 to 50 rpm by an electric motor. The shaft passed through the center of each disc and was mounted on the bearing attached to the ends of the wastewater container and the submergence of the discs was 40 percent. The addition of feed and the wasting of sludge were done with peristaltic pumps. Mixed liquor suspended solid (MLSS) concentration was controlled between with a sludge age of approximately 20 d" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000560_s00170-016-8857-0-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000560_s00170-016-8857-0-Figure5-1.png", "caption": "Fig. 5 Machine-tool setting for pinion tooth-surface finishing on CNC generator", "texts": [ " (c) The following convergence criterion should be satisfied for the objective function and separately for all parts of the objective function: f mp\u00f0 \u00deiter\u2212 f mp\u00f0 \u00deiter\u22121 f mp\u00f0 \u00deiter\u22121 \u2264\u0394 f pmax imp\u00f0 \u00de pmax0 imp\u00f0 \u00de iter \u2212 pmax imp\u00f0 \u00de pmax0 imp\u00f0 \u00de iter\u22121 pmax imp\u00f0 \u00de pmax0 imp\u00f0 \u00de iter\u22121 \u2264\u0394p \u0394\u03c62max imp\u00f0 \u00de \u0394\u03c62max0 imp\u00f0 \u00de iter \u2212 \u0394\u03c62max imp\u00f0 \u00de \u0394\u03c62max0 imp\u00f0 \u00de iter\u22121 \u0394\u03c62max imp\u00f0 \u00de \u0394\u03c62max0 imp\u00f0 \u00de iter\u22121 \u2264\u0394\u03c6 \u00f018\u00de (d) The convergence criterion is set to\u0394f=\u0394p=\u0394\u03c6=0.001. If the convergence criterion is fulfilled the iterations are stopped, the optimal values of manufacture parameters are obtained. The CNC machine for generation of spiral bevel and hypoid gears is provided with six degrees-of-freedom for three rotational motions (\u03b8, \u03b6, and \u03b7), and three translational motions (X, Y, Z, Fig. 5). The six axes of CNC generator are directly driven by the servo motors and able to implement prescribed functions of motions. The face-hobbing method requires simultaneous six-axis control (the face-milling method requires only five-axis control). The following coordinate systems are applied to describe the relations and motions in the CNC generator (Fig. 5): Coordinate systems Kt(xt, yt, zt) and Ki(xi, yi, zi) are rigidly connected to the head cutter and the pinion/gear, respectively. The coordinate transformations between the basic and auxiliary coordinate systems are defined by the following equations: r!t0 \u00bc Mt\u22c5 r!t \u00bc cos\u03b8 sin\u03b8 0 0 \u2212sin\u03b8 cos\u03b8 0 0 0 0 0 0 0 0 0 1 2 664 3 775\u22c5 r!t \u00f019\u00de r!i0 \u00bc Mti0\u22c5 r!t0 2 3 r!i \u00bc Mi\u22c5 r!i0 \u00bc cos\u03b7 0 sin\u03b7 0 0 1 0 0 \u2212sin\u03b7 0 cos\u03b7 0 0 0 0 1 2 664 3 775\u22c5 r!i0: \u00f021\u00de The coordinate transformation from system Kt (attached to the head-cutter) to system Ki (attached to the pinion/gear) performs the following equation: r" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001395_s12206-020-1240-y-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001395_s12206-020-1240-y-Figure2-1.png", "caption": "Fig. 2. Experiment: (a) stator and coil; (b) schematic.", "texts": [ " These values were obtained experimentally. In this study, the motor was tested to confirm the temperature distribution. The driving conditions of the motor were the same as the numerical analysis conditions. The rotation speed of the drive motor was 12000 rpm and rated power was 52.5 kW. The motor was run with continuous power. The temperature and flow rate of the oil injected into the stator and coil were 80 \u00b0C and 10 LPM. The temperature was measured at six points on the crown part and five points on the welded part. Fig. 2(a) is the stator and coil of the motor used in the experiment, with the thermocouple for temperature measurement attached to the outside of the coil. Fig. 2(b) depicts a schematic of experiment. The cooling oil is supplied by the pump. The temperature of the supplied oil is controlled by coolant and a heat exchanger. The temperature of the coolant is controlled by the chiller. The motor is controlled using an inverter. Fig. 3(a) depicts the temperatures obtained from the experimental and numerical analysis of the coil crown part. The temperature is normalized using the equation: * max TT T = (9) where maxT is the maximum temperature of each case. In the crown part, six points were monitored" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003171_s0378-4371(02)00503-4-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003171_s0378-4371(02)00503-4-Figure1-1.png", "caption": "Fig. 1. The three speeds c1;2;3 of the splay-concentration waves for wavevectors oriented at an angle to the z-axis are given by the radial distances of the curves from the origin (a schematic sketch).", "texts": [ " DeEning to be the angle between the wavevector and the 1 One could in principle imagine purely nematic phases made of paired-up, oppositely directed polar particles, or vector phases made of V-shaped pairings of apolar particles. ordering direction, we End: (i) a pair of bend-twist waves with waves peeds cbt( ) = (v1 \u00b1 v2) cos ; (1) where v1 and v2 are phenomenological constants of order the SPP drift speed v0, and (ii) three splay-concentration waves whose speeds ci for i = 1 to 3 are more simply understood from Fig. 1 than from an equation. The above wavespeeds are of course calculated at lowest order in wavenumber, neglecting viscous damping which arises at the next order. This is acceptable for schools of small Esh, i.e., small enough to keep the Reynolds number from reaching the turbulent range and yet large enough that viscosity does not dominate totally. Experiments on bacterial suspensions are, however, likely to be in the Stokesian limit Re qa 1, where Re= v0a= is the Reynolds number of an SPP of size a in a &uid with kinematic viscosity ", " Bend and twist (\u2207 \u00d7 n\u22a5) of the axis of orientation couple to vorticity (\u2207 \u00d7 u\u22a5) in the &uid &ow, as can be seen by taking the curl of (3) and (4). This results in propagating bend-twist waves with speeds given by Eq. (1). Without hydrodynamic &ow, these degrees of freedom would relax in a purely diDusive manner. 3 If instead we take the divergence of (3) and (4) we see that splay (\u2207 \u00b7n\u22a5), in-plane expansion (\u2207 \u00b7 u\u22a5) and concentration &uctuations c combine to yield three wavelike eigenmodes whose speeds as a function of direction are illustrated schematically in Fig. 1. In the simplifying limit 1=$=0, they can be seen as the coupled dynamics of splay and in-plane expansion, accompanied by simple advection of the concentration by the mean drift. Having discussed the propagating modes, let us turn next to the instabilities we mentioned in Section 1.2. The equations of motion for an SPP nematic suspension follow from (3)\u2013(5) upon setting v0 = 1 = $ = 0, i.e., restoring z \u2192 \u2212z invariance. A little algebra then shows that the squares of the splay-concentration wavespeeds vanish for = =4, which means the speeds themselves are imaginary (signalling an instability) either just above or just below 45\u25e6, depending on the sign of some phenomenological parameters" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003674_robot.2000.845294-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003674_robot.2000.845294-Figure5-1.png", "caption": "Figure 5 - Linear Combinations of Generalized Errors in Prismatic Joints", "texts": [ " The bottom figure shows that the same end-effector errors can be reproduced by a specific combination of the translational error e2 and the rotational error e5 of frame i. To obtain the same end-effector errors, it is required that q2 = qi-l)5 . and q5 = qi-lb in this case (see the relationship between E' and E in Appendix A). If joint i is prismatic, then Equations (9-10) are also valid. These combinations simply state that the effects of the generalized errors along the X and Y axes of frame i-1 can always be reproduced by a combination of the three translational generalized errors of frame i (see Figure 5) . This is always true for prismatic joints, since such joints only move along the Z-axis of frame i-1 (using the D.H. frame definition). 3.3 Partial Measurement of End-Effector Pose The linear combinations of the columns of the Identification Jacobian matrix J, shown in Equations (7- 10) are obtained when both position and orientation of the end-effector are considered. In the case where only the end-effector position is measured, its orientation can take any value, resulting in additional linear combinations" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003810_027836499101000107-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003810_027836499101000107-Figure1-1.png", "caption": "Fig. 1. One-link manipulator.", "texts": [ " In addition, some of the projected terms may be directly related to the dynamic equations of the original smaller chain and the torque (force) vectors at the joints. Thus the dynamic properties of the new link may be combined with those of the original chain to give the dynamic equations of the total configuration. From these equations, the inertia matrix of the augmented system is easily identified. To begin the development of the Structurally Recursive Method, a one-link manipulator, as shown ine Fig. 1, is examined. A free-body force equation may be written for the single link as follows: where is the spatial acceleration of link 1, f, is the spatial force applied to link 1 by the base, and f2 is the spatial force applied by link 1 to whatever additional link or body it contacts at the origin of coordinate frame 2. The terms of this equation are written as quantities in Cartesian space. In order to identify the manipulator inertia matrix, the equation must be transformed to joint or motion space, as in eq", " It is also true that a 1 = J 1 ij l\u2019 because the joint veloci- at UNIV OF ILLINOIS URBANA on March 5, 2013ijr.sagepub.comDownloaded from 67 tics are aH zero. Thus eq. (9) becomes: A comparison of this result with eq. (1) leads to the identification of the one-link manipulator inertia matrix as and the dynamic equation for the single-link manipulator may be written: Note that the transformation, 2x i , is required to reference all quantities to the same coordinate frame (1). Figure 2 shows a two-link manipulator formed by adding a second link to the free end of the one-link manipulator of Fig. 1. A free-body force equation may be written in Cartesian space for the second link as follows: where a2 is the spatial acceleration of link 2, f2 is the spatial force applied to link 2 by link 1, and f3 is the spatial force applied by link 2 to whatever additional link or body it contacts. Similar to the one-link case, the Jacobian matrix may be used to project the force terms onto the motion space of the two-link manipulator : The term JT f2 represents the projection of f2 onto the basis vectors of the motion space, which are expressed with respect to the coordinate system of link 2" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003113_15209150050194233-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003113_15209150050194233-Figure1-1.png", "caption": "FIG. 1. Schematic of a Lexan chamber used for the isolation of glucose oxidase held together by stainless-steel screws. The inside contains the GOD enzyme, protected by polycarbonate membranes coated with Nafion or left without it.", "texts": [ "2 mg of bovine serum (Sigma) were dissolved in 1 mL of glutaraldehyde prepared solution. After stirring the suspension for 5 minutes, 50 mL were placed on top of an 11-mm-diameter nylon mesh. This mesh was sandwiched between two 10-mm pore polycarbonate membranes (Millipore, Bedford, MA) that had been dip-coated with Nafion or that had been left without Nafion. These components were placed in a 13-mmdiameter Lexan chamber. Two stainless-steel screws were put in place, to hold the chamber together (Fig. 1). Lexan was the material of choice for this study, as it is a derivative of polycarbonate and can withstand high temperatures. Stainless-steel screws were used to hold the chambers together. The chambers, including the GOD and polycarbonate membranes within them, were sterilized by heat at a temperature of 120\u00b0C for 1 hour. This method of sterilization simultaneously cured the Nafion membranes, while still preserving the enzyme activity.15 As a previous study showed, Nafion calcifies both in vitro and in vivo" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003737_cdc.2003.1272286-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003737_cdc.2003.1272286-Figure3-1.png", "caption": "Fig. 3: Differentiator convergence", "texts": [ "5 in order to provide some time for the differentiator convergence. The integration was carried out according to the Euler method (the only reliable integration method with discontinuous dynamics), the sampling step being equal to the integration step t = 10 . In the absence of noises the tracking accuracies 101 5 3.12.10-\u2019, / U / 5 1.4.10 , 161 5 0.011 were attained. The car trajectory, 3-sliding tmcking sign(z, - vo) +z2, 4 4 deviations, steering angle and its derivative I are shown in Fig. 2a, h, c, d respectively. It is seen from Fig. 3c that the control U remains continuous until the entrance into the 3-sliding mode. The steering angle 0 remains rather smooth and is quite feasible. with t = loJ the tracking accuracies 5 2.5.10-\u2019, / a I 5 2.4.10J, ] U / _< 0.11 were attained, which corresponds to the asymptotics stated in Theorem 5 . Convergence of the differentiator outputs to the directly calculated derivatives of u is demonstrated in Fig. 3. In the presence of output noise with the magnitude 0.01m the tracking accuracies In1 5 0.04, I a I 5 0.2, I U I 5 1.8 were obtained. With the measurement noise of the magnitude 0.1 the accuracies changed to In1 5 0.4, 16 I 5 0.9, I Cr I 53.2 which corresponds to the asymptotics stated by Theorem 4. The performance of the controller with the measurement error magnitude O.1m is shown in Fig. 4. It is seen from Fig. 4c that the control U is continuous function off. The steering angle vibrations have magnitude of about 12 degrees and frequency 1 which is also quite feasible" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003242_s0094-114x(00)00003-3-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003242_s0094-114x(00)00003-3-Figure5-1.png", "caption": "Fig. 5. Three-degree-of-freedom planar redundant manipulator.", "texts": [ " The regions where the STLC condition is violated along with the workspace boundary are shown on the right-hand side of Fig. 4. It can be seen that the non-STLC regions are surrounding the singular zones. P. Choudhury, A. Ghosal /Mechanism and Machine Theory 35 (2000) 1455\u00b114791468 If an additional actuated leg is added to the 3-DOF planar manipulator shown in Fig. 1, then we have the case of a redundant parallel manipulator with m> n. The equations of motion for the planar redundant manipulator shown in Fig. 5 are M \u00c8t a Z HF 14 where the block elements of the mass matrix M are M11 MpE2 X4 i 1 Qi M12 MT 21 \u00ff MpR? X4 i 1 Qiqi? ! M22 Ip Mp \u00ff R2E2 \u00ff RRT X4 i 1 qT i?Qiqi? and P. Choudhury, A. Ghosal /Mechanism and Machine Theory 35 (2000) 1455\u00b11479 1469 Z 2666664 Mp \u00ff o2R\u00ff g X4 i 1 Ui \u00ffMpR g X4 i 1 qi Ui 3777775 H s1 s2 s3 s4 q1 s1 q2 s2 q3 s3 q4 s4 f f1 f2 f3 f4 T In the above equation, Z is the column vector containing the centripetal, Coriolis and other non-linear terms, H is the force transformation matrix and vector f denotes the input actuations" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003052_s101890050039-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003052_s101890050039-Figure1-1.png", "caption": "Fig. 1. Geometrical characteristics of a set of parallel surfaces (see text).", "texts": [ " Another elementary result is that parallel surfaces have the same centers of curvature M and P at all their intersections \u00b5 with the same normal: the principal radii of curvature are the signed lengths \u00b5M and \u00b5P , and \u03c3M = 1/\u00b5M , \u03c3P = 1/\u00b5P the principal curvatures at \u00b5. The centers of curvature M and P describe two surfaces which are the envelopes of the normals and which are called the focal surfaces FM and FP of the set of parallel surfaces Li. At the contact of a layer Li with the focal surfaces, one of the radii of curvature vanishes (the curvature is infinite); henceforth the focal surfaces are the sets of singular points of the geometry of parallel layers, Figure 1. As a matter of fact, this situation is reminiscent of the propagation of light rays in an isotropic medium, i.e. one of constant index of refraction, in the approximation of geometrical optics: the light rays being the analogs of the normals to the layers, the surfaces of equal phase the analogs of the layers, and the caustics \u2014where the light intensity diverges\u2014 the analogs of the focal surfaces \u2014 where the free energy density diverges. This is the reason why focal surfaces (2D defects) degenerate into focal lines (1D defects) in smectics of SmA and SmC type", " Since they coincide, C \u2032 1 and C \u2032 2, being on the same cone, have two intersections, P and Q. In other words, two FCDs that have one common generatrix and two contacts on their generating conics, obey l.c.c. The law of corresponding cones leads to the geometrical construction of Figure 3. If two conics are coplanar, the triples F1, M , F \u2032 2, and F \u2032 1, M , F2, are aligned; F1, F2, F \u2032 1, F \u2032 2, are the foci of C1 and C2. Point A is the common projection of the two intersections P and Q of C \u2032 1 and C \u2032 2. Figure 1 of reference [7] illustrates l.c.c. in the coplanar case for a photograph by C. Williams. Figure 4 restitutes in 3D the continuity of cyclides along the generatrices of contact in the case of two incomplete FCDs obeying l.c.c. The points of contactM and P are the centers of curvature of the Dupin cyclides passing through all the points \u00b5 on the segment MP , whether they are considered to belong to one FCD or to the other. Therefore \u03c3M \u2261 \u03c31,M = \u03c32,M , \u03c3P \u2261 \u03c31,P = \u03c32,P , where \u03c3M = 1/\u00b5M , \u03c3P = 1/\u00b5P are the principal curvatures at \u00b5; \u00b5M and \u00b5P are signed lengths", " of the disorientation \u03c9) there are 2 solutions in b/\u03bb which make the derivative vanish. The solution with the smaller, microscopic b/\u03bb is a maximum, while the other one is a minimum. This is the valid solution; it varies rather quickly with e (or \u03c9). The residual area is large for small disorientations \u03c9, and the energy is small; at \u03c9 = 0, the \u201cresidual\u201d area invades the whole boundary. It is only for very large disorientations that the residual area becomes microscopic. At large disorientations, the residual areas are relaxed by curvature walls. It is visible in Figure 1 that the layers of a complete FCD can be geometrically prolongated outside the FCD by two sets of parallel planar layers, perpendicular to the generatrices (i.e. to the asymptotic directions of the FCD) and limited to the grain boundary. Each of these layers is tangent to a Dupin cyclide all along the circle of contact, so that we expect that the physical realization of this particular geometry would not be too costly. In fact, the energy cost has two origins: the curvature walls in the residual regions (the layers do not abut abruptly on the grain boundary), and a mismatch in curvatures of the Dupin cyclides and the layers outside the FCD-Is" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000281_s12206-016-0823-0-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000281_s12206-016-0823-0-Figure2-1.png", "caption": "Fig. 2. The nonlinear bearing dynamics model.", "texts": [ " The gearbox is composed of two parallel-axis gear systems and a planetary gear train. The bearings in a parallel-axis gear system are generally installed on the gearbox. The outer raceway of the bearings remains fixed and stationary, whereas the inner raceway of the bearings rotates with the drive shaft. Conversely, the outer raceway of the bearings of the planet gears in a planetary gear train rotates with the planet gears, and the inner raceway is connected to the planet gear shafts and remains stationary. Fig. 2 shows the schematic picture of the planet bearings in the planetary gear train. In this study, a nonlinear bearing dynamics model with two degrees of freedom is employed ( , s sb b x y ), as shown in Fig. 2. The model considers the radial clearance of the bearings ( r C ), and the nonlinear contact force between the balls and the inner and outer rings along the directions of sb x and sb y axes ( , Bx Byi i S S F F ) are calculated based on the Hertz contact theory [15]. According to the Hertz contact deformation theory [15], Bxi S F and Byi S F can be expressed for the condition of no de- fects ( ) 1 cos Bxi z S b k k k k F k \u03bb\u03c4 \u03b4 \u03b8 = =\u2211 (1) ( ) 1 sin Byi z S b k k k k F k \u03bb\u03c4 \u03b4 \u03b8 = =\u2211 (2) where z represents the total number of balls; b k represents the deflection coefficient of the load; \u03bb represents the deflection index of the load ( 3 / 2\u03bb = for a ball bearing) [15]", " The k \u03c4 represents the operator for determining the contact condition of the k th ball, which can expressed as follows 1 0 0 0 k k k \u03b4 \u03c4 \u03b4 > < = (3) where k \u03b4 represents the contact deformation of the k th ball. The contact deformation of the k th ball at k \u03b8 can be ex- pressed as ( ) ( )( )cos sin si sik b k b k r \u03b4 x \u03b8 y \u03b8 C= + \u2212 (4) in which sib x and sib y represent the displacements of the inner ring relative to the outer ring of the i th planet bearing in the sb x direction and the sb y direction, respectively. The r C represents the radial clearance of the bearing, k \u03b8 represents the angle of the center of the k th ball (as shown in Fig. 2), and can be expressed as follows at time t (the time is beginning when the center of the first ball is on the sb x axis) ( )2 1 k pc k w t z \u03c0 \u03b8 \u2212 = \u00d7 + (5) where pc w represents the rotational speed of the cage, which can be expressed as ( )1 / 2 1 cos pc out b d w w D \u03b1 = \u00d7 \u00d7 + \u00d7 (6) in which out w represents the rotational speed of the outer ring of the bearings, which is consistent with the rotational speed of the planet gears ( ). p w d represents the diameter of the balls. D represents the pitch diameter of the bearings", " The d \u03b8 represents the angle between the starting location of the defect and the ball adjacent to the defect in a direction that is opposite to the rolling direction, and can be expressed as 1d D k \u03b8 \u03b8 \u03b8 \u2212= \u2212 (12) where D \u03b8 represents the starting location of the defect. 1k \u03b8 \u2212 represents the position angle of the ball adjacent to the defect in a direction that is opposite to the rolling direction (as shown in Fig. 3). It is assumed that the rotational direction of the planet bearing is consistent with the rotational direction shown in Fig. 2 (counterclockwise). The supporting shaft of the inner raceway of the bearings of the planet gears are fixed to the planet carrier. The inner raceway only revolves around the sun gear and does not self-rotate during operation. The angle by which the ball rotates relative to the inner raceway within time t can be expressed as (in the range of 0 2\u03c0\u2212 ) ( ) ( )( )/ 2 / 2 2 c pc pc w t w t\u03b8 \u03c0 \u03c0 \u03c0 = \u00d7 \u2212 \u00d7 \u00d7 (13) where [] represents the rounding sign. Thus, k h can be expressed as (14) where i represents the number of ball which adjacent to the defects in the direction opposite to the rolling direction at the initial time and k \u03b8\u2206 represents the position angle of the k th ball relative to the i th ball along the direction opposite the rolling direction, which can be expressed as follows ( ) ( ) 2 2 2 . k i k i k z k i i k z \u03c0 \u03b8 \u03c0 \u03c0 = \u2212 > \u2206 \u2212 \u2212 < (15) Assuming the rotational direction of the bearings of the planet gears is consistent with the schematic in Fig. 2 (counterclockwise). The outer raceway not only has self-rotates with the planet gears but also revolves around the sun gear with the planet gears. The rotational speed of the outer raceway is higher than the rotational speed of the cage. In the bearing system shown in Fig. 2, the balls rotate clockwise relative to the outer raceway. The angle by which the ball rotates relative to the outer raceway within time t can be expressed as follows (in the range of 0-2 \u03c0 ): ( ) ( ) ( )( / 2 ( ) / 2 ) 2 . c out pc out pc w w t w w t\u03b8 \u03c0 \u03c0 \u03c0 = \u2212 \u00d7 \u2212 \u2212 \u00d7 \u00d7 (16) According to Eq. (6), ( ) out pc w w\u2212 can be expressed as ( )( )( ) 1 / 2 1 / cos . out pc out b w w w d D \u03b1\u2212 = \u00d7 \u00d7 \u2212 \u00d7 (17) Here, k h can be expressed as . (18) The gear-bearing coupling dynamics model is based on the bending-torsion coupling dynamics model of planetary gear trains [26]" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003594_ja0108988-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003594_ja0108988-Figure1-1.png", "caption": "Figure 1. Stick representation of the imidazole carbonmonoxy iron porphine adduct with acetate hydrogen bonded to the N\u03b4-H position of imidazole. The circle identifies the substitution site in the model calculations. The charge relay is modeled by replacing acetate by a range of hydrogen bond partners given in Table 1. The model structure represents the Asp-His-Fe catalytic triad found in peroxidase enzymes.", "texts": [ "3 In peroxidases, where imidazole is polarized by the electrostatic interactions with aspartate or other protein residues, the fine-tuning of reactivity by changes in electrostatic environment is a major determinant of the electron density on the bound oxy or peroxy species. A charge relay involving hydrogen bonding has been suggested in cytochrome c peroxidase, sulfite reductase, and CooA.2,4,6 The specific mechanism for control of histidine reactivity and stability is apparent in the hydrogen bonding to the N\u03b4-H hydrogen of histidine in globins, oxidases, peroxidases, and a large number of other heme enzymes.7 Figure 1 shows a proposed charge relay derived from studies of peroxidases where aspartate (modeled as acetate) forms a strong hydrogen bond to the N\u03b4-H position of histidine (modeled as imidazole) to form an Asp-His-Fe charge relay. Distal effects are also important, and these enzymes typically have appropriate histidine or arginine side chains capable of controlling the protonation state of bound intermediates;8-13 however, distal effects are not included in this study. The present study addresses the proximal effect of such a charge relay on electronic structure by connecting vibrational spectroscopic data from studies of the carbonmonoxy adducts to a bonding picture relevant for the proximal charge relay in histidine-ligated heme enzymes", "1021/ja0108988 CCC: $20.00 \u00a9 2001 American Chemical Society Published on Web 11/21/2001 is inert, and yet Fe-CO and C-O stretching bands observed in resonance Raman and infrared (IR) spectra1,11,14-21 serve as sensitive probes of the electrostatic environment in a range of heme proteins including peroxidases, oxidases, monooxygenases, prostaglandin synthase, and globins.19,22-26 Calculated substituent effects can be divided into trans-effects (proximal), cis-effects (equatorial), and distal effects (see Figure 1). Recently, semiempirical calculations have been applied to the study of proximal/distal side effects using a point charge model,11 and density Functional theory (DFT) calculations of model meso-substituted porphines have been used to model equatorial substituent effects.27A number of studies have also addressed various aspects of hydrogen bond effects on the distal side.28-32 The calculated effects agree with the experimentally determined inverse correlation of Fe-CO and C-O stretching mode frequencies known as \u03c0-back-bonding", " The present density functional theory (DFT) study of the effect charge relay on the C-O potential surface addresses the nature of the trans-effect due to hydrogen bond interactions with N\u03b4-H of the proximal imidazole by comparison with experimental data on the vibrational frequencies of both inplane and axial ligand modes. Our approach to modeling the spectra is to use DFT to calculate vibrational spectra and potential energy surfaces for a series of trans imidazoles and imidazolates in the ironporphine-CO adduct shown in Figure 1. Figure 1 shows aspartate hydrogen bonded to the imidazole at the N\u03b4-H position. A series of hydrogen bond donors given in Table 1 were compared in order to systematically modulate the charge density on the iron. The genesis of this model is the well-studied hydrogen-bonding of Asp235 to His175 in cytochrome c peroxidase.2 This hydrogen-bond pattern presents a catalytic triad of Asp-His-Fe in peroxidases analogous to the Asp-HisSer of serine proteases shown in Figure 2. A similar motif appears in a number of enzymes, including cysteine proteases and even selenocysteine proteases and peroxidases", " 2000, 57, 1825-1835. involved in a hydrogen bond with the serine hydroxyl group. For serine proteases, this hydrogen bonding interaction results in greater electron density on the catalytic serine nucleophile. Despite these differences, strong similarities emerge from the DFT calculations. One of the major similarities of the two systems that will emerge from our study is that the charge density on the oxygen atom of methanol (Figure 2), the terminal oxygen of bound carbon monoxide, or bound dioxygen (Figure 1) increases as a result of N\u03b4-H hydrogen bonding. Moreover, the serine O-H, porphine Fe-CO bond, and C-O bonds are all three weakened by increasing polarization of the imidazole in the relay. This polarization is transmitted through both \u03c3and \u03c0-effects, and our hypothesis is that the \u03c0-effect is required to achieve the type of reactivity found in peroxidases. The charge density on dioxygen increases, and the O-O bond becomes more dipolar. The net effect is to increase the charge on the terminal oxygen (i", "48,49 All calculations were carried out on the SGI/ Cray Origin 2000 and IBM SP supercomputers at the North Carolina Supercomputer Center (NCSC). A numerically tabulated basis set of double-\u00fa plus quality was employed as described in the Supporting Information. The geometry optimizations were carried out until the energy difference was less than 10-6 a.u. on subsequent iterations. Following geometry optimization the Hessian matrix was constructed by finite difference. Calculations on the M1 model were carried out using Gaussian98 at the NCSC.50 The M1 model consists of the imidazole-iron-CO moieties in Figure 1 with the porphine ring replaced by four amidinato (-NH2 -) groups (see Supporting Informa- (35) Choi, S.; Spiro, T. G.; Langry, K. C.; Smith, K. M.; Budd, L. D.; LaMar, G. N. J. Am. Chem. Soc. 1982, 104, 4345-. (36) Feitelson, J.; Spiro, T. G. Inorg. Chem. 1986, 25, 861-865. (37) Hu, S.; Smith, K. M.; Spiro, T. G. J. Am. Chem. Soc. 1996, 118, 12638-12646. (38) Li, X. Y.; Czernuszewicz, R. S.; Kincaid, J. R.; Su, Y. O.; Spiro, T. G. J. Phys. Chem. 1990, 94, 31-47. (39) Ghosh, A.; Bocian, D. F. J", " Table 1 gives the dihedral angles for the imidazole ligands, porphine geometry changes, and the hydrogen bonding geometry of N\u03b4-H of the various hydrogen-bond-forming moieties (H2O, CH3COO-, CH3CONHCH3). The Np-Fe-N\u03b5-C\u03b4 dihedral angles for the imidazole were initially at 0\u00b0 prior to geometry optimization (except in the IM45 structure where the dihedral angle \u03c4 was set to 45\u00b0 at the outset of the geometry optimization). [The following abbreviations have been used for atoms in the structure shown in Figure 1: Np, pyrrole nitrogen of the porphine ring; N\u03b5, the nitrogen of imidazole that is bonded to Fe; N\u03b4, the nitrogen of imidazole the is protonated; C\u03b4, the carbon of imidazole bonded to N\u03b5 and N\u03b4.] Since the imidazole ligands were not constrained in the calculations performed here, there are a variety of dihedral angles \u03c4 in the different species as seen in column 2 of Table 1. The imidazole ligand to iron shows modest rotation in the IM, IMA, IMH2O, and IMAH2O models (column 2, Table 1). However, when a larger, more polarizable group hydrogen bonds to N\u03b4-H the dihedral angle increases (column 2, Table 1)", " For example, a comparison of a simple model for Im-Fe-CO with four amidinato groups instead of a porphine molecule was carried out using both MP2 and BLYP calculations for both a neutral and anionic imidazole (analogous to IM and IMA with four NH2 \u03b4- groups instead of porphine). The Fe-Np, Fe-N\u03b5, Fe-C, and C-O distances are given in Table 8. Both the MP2 and BLYP calculations agree that both the Fe-C and C-O bonds increase as the ligand becomes more basic. This trend is the same as that found for the GGA and BLYP porphine models studied here (Figure 1 and Table 2). While the agreement in terms of structure is encouraging, it does not prove that CI has been adequately treated. It has been suggested that CI is necessary to correctly determine the energy level of the N\u03b5 lone pair in heme enzyme model calculations.65,66 However, the excellent agreement of the in-plane vibrational modes (Figure 3) and correct relationship of \u03bdCO with experimental trends (Tables 3, 5, and 12) are a good indication that the DFT approach provides reasonable treatment of the ground-state vibrational modes of interest", " The comparison of the serine protease catalytic triad with peroxidase models serves to underscore the fact that \u03c3-bonding contributions from the imidazole are important in both. Furthermore, as we have seen above, \u03c0-bonding effects must be considered in the peroxidase model, while these do not appear to play a major role in the serine protease catalytic triad. The potential energy surfaces for both Fe-CO and C-O bond dissociation have been studied for the iron-porphine-CO model molecules shown in Figure 1. Figure 5 shows the potential energy surface for the Fe-CO coordinate. The ordering of the effect on binding is the same as for the Asp-His-Ser model above. The trend indicates that increased basicity trans to the CO ligand weakens the Fe-CO bond, but the effect is significantly smaller than for the deprotonation of the serine hydroxyl shown in Figure 4. The negatively charged model adducts IMA, IMAH2O, and IMACET weaken the trans FeCO bond to the greatest extent (\u22483 kcal/mol). The hydrogen bonding ligands show small effects on trans CO bonding (e" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003566_0094-114x(94)90031-0-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003566_0094-114x(94)90031-0-Figure1-1.png", "caption": "Fig. 1. Screw triangle associated with incompletely specified displacement problems.", "texts": [ " When three positions of a body, Y~, :~;, and Y-k, are specified, there are three corresponding screws, S 0, S# and S j , but only two of them are independent. These three screws and their normals form a spatial figure known as a MMY lqj2--a screw triangle. It is well known that in the screw triangle the normals to the screw axes are displaced from one another by distances and angles that correspond to one-half the screw translations and rotations. The approach used in Tsai and Roth [3] for incompletely specified displacement problems involves constructing a special screw triangle (illustrated in Fig. 1) by decomposing the screw S~ for the incompletely specified displacement into two screw displacements: They first determine a unique screw, L#, which will displace the specified element(s) of the body from its initial to its final position. Second, they describe the rest of the possible displacements in terms of a single incompletely determined screw, N~. It has free parameters, which, depending on the case, can be the rotation ~,~, the translation ,l~, or the direction cosines of the screw axis for N~" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000638_icra.2018.8460838-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000638_icra.2018.8460838-Figure3-1.png", "caption": "Fig. 3. Quadrotor body axes (subscript b), global axes (subscript g), interim yaw axes (subscript c), and second angle axes (subscript csa, with angle \u03b3). East, North, Up (ENU) convention.", "texts": [ " The first singularity is a fundamental limitation of the transformation, founded on the notion that the desired thrust direction sets the quadrotor attitude. The second singularity, and the sensitivity of states near this singularity, needs to be managed robustly. A thorough description of the differential flatness transformation can be found in references such as [10] and [11]; we repeat the main steps here. The starting assumption is that the thrust vector of the quadrotor sets the direction of the z body axis, zb (see Fig. 3). Hence, from a planned trajectory that gives the desired acceleration x\u0308sp, we get the thrust vector (T), that sets the direction of the zb: T = x\u0308sp \u2212 e3g (1) zb = T ||T|| (2) Here, g is the acceleration due to gravity, and e3 the global z unit vector. The first type of singularity occurs in Eq. 2 when the thrust magnitude is zero. The desired yaw angle, \u03c8sp sets the vector xc: a unit vector in the xy plane pointing in the desired heading direction. The cross product of zb with xc gives an orthogonal vector, yb, that represents the y body axis direction", " Mellinger\u2019s approach has been used very effectively for autonomous navigation in ships [2], and through indoor environments [12], however only with moderate roll or pitch angles. Mellinger and Loianno only demonstrate roll in isolation, and do not exceed 90\u25e6, therefore they do not operate near the sensitive regions of the transformation. Thomas [15] uses a method that enables orientations holding at 90\u25e6 for an extended period, and extending past 90\u25e6, with flight demonstrations of a quadrotor perching on both vertical surfaces and the underside of inclined surfaces. To move away from the singularity (see Fig. 3), their approach employs an additional working angle, \u03b3, to rotate the xc vector in the vertical plane: xc = [ cos(\u03c8) cos(\u03b3), sin(\u03c8) sin(\u03b3), sin(\u03b3) ] (7) This moves xc away from the xy plane to avoid being parallel with zb. While their approach moves the location of singularity, it does not remove it. Thomas\u2019 demonstrations show the effectiveness of their approach, however the examples only operate with one axis of rotation (pitch), rather than the full range of quadrotor motion. D. Inverted flight None of the previous work described above have demonstrated highly-aggressive flight with 360\u25e6 rotations through inversion" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003084_6.1998-4357-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003084_6.1998-4357-Figure3-1.png", "caption": "Fig. 3 Vector diagram explaining how the velocity Vg of the hub point g& is calculated. The linear velocity of the helicopter CG is vb IB and its angular velocity is WJB. All velocities are measured in body coordinates. For clarity in the figure, lateral motions are neglected.", "texts": [ " The constants \u2014hr and tT are the offsets of the rotor from the helicopter's center of gravity in the x and z directions respectively; the rotor hub is in-line with *In some countries, people prefer the yaw and the roll controls switched (type I). t Strictly speaking, R is the rotor span, excluding the rotor hub length. However, since the model helicopter's rotor blade remains nearly rigid due to its short length (0.4 to 0.8 meter), high rotor speed (1300 to 1900 rpm), and hingelesshub design, R is assumed to be the distance between the rotor axis and the rotor tip. the CG in the y direction. The geometry is sketched in Figure 3. vg = W/B X + R\u2022IB (2) where, RTIB IB = \u2014 ip sin 6 0 cos + -ij) cos sin 8 \u20146 sin + TJJ cos cos 8 x (3) The advance ratio, /z, which is the airspeed component parallel to the rotor disk, is the magnitude of the first two elements of v^, and the descent ratio, i/, which is the airspeed component perpendicular to the rotor disk, is the magnitude of the third element v = (4) (5) The rotor solidity, a, is the ratio between the rotor blade area and the rotor disk area. It indicates how \"solid\" the rotor disk is,16 and is taken to be the number of blades (2) times the area of a rotor blade (2cR) divided by the area defined by the rotor disk 2c The inflow ratio, A, is the net value of the descent ratio v and the induced air velocity, the velocity of the air through the rotor blade, Vj" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003133_tec.2002.801731-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003133_tec.2002.801731-Figure1-1.png", "caption": "Fig. 1. Cross-section of the studied machine.", "texts": [ " Using a DSP board (TMS320C31), a rotor-oriented vector control is achieved. Experiments are carried out for transient operations and are compared with the simulation in the case of unsaturated and saturated conditions. The simulation shows the importance of using a saturated model to obtain a good agreement of results when they are compared to the experimental ones. 0885-8969/02$17.00 \u00a9 2002 IEEE II. MODELING The cross\u2013section of the stator and rotor structure of the studied synchronous reluctance machine is shown in Fig. 1. The stator is made with symmetrical three-phase windings and the rotor contains a squirrel cage. For the modeling, magnetic hysteresis, the skin effect (in the rotor bars) and iron losses are neglected. The air-gap magnetomotive forces are assumed to be sinusoidally distributed. The two-axis representation of the electrical equivalent machine is given in Fig. 2. The voltage equations of the two-axis representation written in the rotor reference frame are (1) (2) (3) (4) The stator and rotor flux linkage in equations (1)\u2013(4) are related to the currents as follows: (5) (6) (7) (8) Introducing magnetizing currents and in the two\u2013axis, stator flux linkages become with (9) with (10) Usually, total inductances are split up into a leakage and magnetizing component" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001089_tia.2020.3046195-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001089_tia.2020.3046195-Figure5-1.png", "caption": "Fig. 5. Simplified stator windings model.", "texts": [ " Downloaded on May 14,2021 at 13:37:14 UTC from IEEE Xplore. Restrictions apply. Laboratory technical reports [21]\u2013[23] based on the thermal performance benchmarking of the Nissan LEAF motor [24]. The anisotropic thermal conductivity of the winding slot part is treated as 0.99 W/mK in radial and angular directions and 292 W/mK in axial direction [21]. Two of the thermal resistance values, the slot liner to stator and stator to inner shell, have been revised to 0.0025 and 0.0003, respectively, calibrated by the measurements in this study. Fig. 5 shows a simplified stator winding with specified heat loses and thermal conductivity in its slot (red) and end turn (blue) regions. Slot fill factor is the ratio of the cross-sectional area occupied by copper wire inside the stator slot to the total amount of available space in the bare slot. The fill factor of 0.4474 is determined by the measurement and therefore an effective density of the windings is set to 4000 kg/m3 in the simulations. From the manufacturing standpoint, one parameter that was found to potentially have a major impact on the characteristics of cooling jackets is the size of the existing gap between the jacket ribs and the outer shell of the motor housing" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001273_0278364920903785-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001273_0278364920903785-Figure2-1.png", "caption": "Fig. 2. Joint inputs and corresponding tip motions adjust the US imaging plane.", "texts": [ " In this work, we present our system as the third flexible manipulator in vivo motion compensation system overall and the first in vivo motion compensation system to accurately and automatically steer a cardiac catheter. The techniques demonstrated here are applicable to cyclical physiological motion compensation in other organ systems and with other flexible manipulators as well. We apply this technology to cardiac US catheters (also known as intracardiac echocardiography (ICE) catheters), which are specialized catheters featuring an US transducer in the distal tip. US catheters are steered by adjusting four degrees of freedom (DOFs) at the control knob (Figure 1), resulting in catheter tip motions shown in Figure 2. US catheters enable enhanced intra-procedural imaging of working instruments and cardiac structures, such as catheter ablation lesion formation (Cooper and Epstein, 2001; Dravid et al., 2008; Epstein et al., 1998; Marrouche et al., 2003; Ren and Marchlinski, 2007), but manual navigation of US catheters is difficult in terms of the physical and cognitive burden on the clinician. Manual US catheter steering requires significant training. As a result, US catheters are typically only used for the most critical phases of a procedure, such as transseptal puncture (Jongbloed et al" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003807_j.euromechsol.2005.11.001-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003807_j.euromechsol.2005.11.001-Figure4-1.png", "caption": "Fig. 4. One-translational and two-rotational DOFs asymmetrical PKM.", "texts": [ " That mechanism uses one planar-spherical limb and two other limbs, each of which generates the 5-DOF product of G(x) and R(N,y) motions. Another example of planar-spherical limb is shown in Fig. 3(b). The equivalent generators of planar-spherical kinematic bonds are described online (Herv\u00e9, 2003). In this family of mechanisms, two limbs produce G(x)RN,y) and a third limb produces G(y)S(N). One can readily show G(x)R(N,y) \u2229 G(y)S(N) = T (z)R(N,x)R(N,y). The last proposed family is represented here by the mechanism of Fig. 4. It uses two limbs that are similar to the ones used in Fig. 3(a) and the third limb generates T (z)S(O). Notice, however, that this mechanism cannot be actuated using the three P joints. Remarks. \u2022 Among the three limbs, two limbs have the same architecture and produce the same motion type. Only two limbs with distinct architectures are sufficient to realise the kinematic constraint of the platform motion in each of the PKMs proposed. However, three limbs are used to ensure that there is one actuator per limb" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003084_6.1998-4357-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003084_6.1998-4357-Figure1-1.png", "caption": "Fig. 1 The coordinates defined. The orientat.ion variables, roll, pitch, yaw (<\u00a3, 6,0) and the position variables (x, y, z) are relative to the body frame (fixed to the helicopter).", "texts": [], "surrounding_texts": [ "had a faster response. Another group from Caltech2 did a similar identification and designed a LQR controller. The realtime control and data acquisition ran on the PC, which hosted the pulsewidth modulated IO board and Polhemus sensor board.3 Again, the controller showed good performance only for pitch and roll response. Yaw response was poor for the same reason as above. Significant improvement on the yaw response was achieved when a separate loop shaping controller based on a lead-lag design was implemented.\nFuzzy Control Dr. Sugeno from the Tokyo Institute of Technology4 has had a considerable amount of success in flying the model helicopter for commercial purposes. The project's goal was to develop a controller for an unmanned helicopter that can operate under hostile conditions. The control system was designed using fuzzy control theory. The integrated control system, ranging from low level basic flight modes to high level supervisory control, takes a human voice as its input. Because human language voice commands are naturally imprecise or 'fuzzy,' the fuzzy logic framework was a good fit. The primary issue here was to design a controller that can easily include qualitative information as well as quantitative information. Some pre-experiment simulation was done on a Silicon Graphics IRIS workstation and a PC. The fuzzy controller rules were first constructed with the help of a actual human pilot's experience and knowledge. The rules were then tested and reformulated using the simulator. The helicopter was equipped with various sensors such as camera, gyroscope for 3D acceleration, Doppler speedometer, magnetic compass, laser altimeter, and GPS.\nUnmanned Aerial Vehicle Competition The annual unmanned aerial vehicle competition has been organizing a number of universities to complete a task of recognizing and moving an object to a designated target. So far, the competitors have typically been concentrating on the sensory issues such as the image processing, with a lesser emphasis on the control problems. Among the participating universities, USC used a concept called \"behavior based control\",5'6 which implements a number of complex tasks with a collection of simple, interacting behaviors in parallel. Their approach seeks to use a behavioral based approach as a structure to unify navigation, motor control, and vision. This approach was inspired by the distributed yet unified control of biological systems. To maintain the safety of the helicopter, the lower-level behaviors\nmay 'negotiate' with a mid-level to satisfy both sets of behavioral criteria. They claim this approach was useful in building an integrated control system; an open issue is the determination of a set of rules and principles for creating behaviors. The MIT, Boston University and Draper Lab team7 was successful in building an autonomous model helicopter designed to hover, fly around, and recognize five randomly placed drums during the 1996 International Aerial Robotics Competition. The system consisted of the helicopter with various sensors such as GPS, IMU, altimeter, and compass, as well as a ground control station, a vision processor, and a safety pilot. The control system is divided into four closed loops.for roll, pitch, yaw, and collective/throttle with integrators to eliminate steady state errors. Pre-determined trim positions were used on those loops. They used relatively simple control laws to minimize the development time and be flexible to the changes in helicopter configuration. Again, their research effort was concentrated more on the sensor issues and the interactions between the various components than on the control structure itself.\nOther UAV\nThe Naval Research Lab8 has designed an airplane style UAV which is intended to be a missile decoy. It has an electric motor for a nose mounted propeller, three fiber-optic rate gyro sensors for the pitch, roll, and yaw axes, a barometric altimeter, and a pitot-static airspeed sensor. All the actuator dynamics are based on linear dynamic equations, and the single-axis control law is used for attitude and altitude control. From the launch through the cruise transition phase, the trajectory is based on a first-order linear fit to find the desired pitch angle profile based on 6DOF simulation. The reference pitch position is time-scheduled to follow the nominal trajectory. Various parameters are based on a wind tunnel experiment. Although the paper did not address the issues regarding how the aircraft would follow the pre-planned trajectory once it reached the cruise phase in satisfying the specific mission goal, it demonstrated the potential capability of the craft as a missile decoy.\nIn terms of UAV control, Kaminer et al.9 pointed out that under a shifting wind disturbance, the traditional control scheme, in which the guidance and control parts are separate, may be inadequate to satisfy the precise tracking and frequent heading change necessary. To solve this problem, they examined a guidance and control scheme where the two are combined, so that the guidance law becomes an integral part of the feedback control system. With", "such design specifications as zero steady state error and certain bandwidth requirements, they devised a state-space coordinate system in which the linearization of the plant along a reference trajectory is time-invariant. This realization results in trajectories that consist of straight lines, arcs of circles of constant radii, and any combinations thereof. The control system itself is an LQR design. Their simulation showed a good result for an aircraft following a descending helical trajectory. However, the scheme only applies to certain specific trajectories as mentioned above, so it remains uncertain how useful the technique could be to a real system.\nSikorsky Aircraft10 has been developing a saucertype VTOL UAV called Cypher to meet various civil and military requirements. It has two counterrotating, 4 ft long, coaxial, four-bladed main rotors shrouded by the 6.5 ft diameter main frame. Similar to a helicopter, it uses collective and cyclic pitch control for movement, powered by a 60 hp rotary engine. Sensors include radar, gyros, accelerometer, GPS, video camera, etc. To achieve a simple operator/vehicle interface, the operator is only required to send out basic maneuver commands such as takeoff, hover, cruise, desired heading, etc. Linear state space models are used to develop control laws and to determine specifications for servo and sensor bandwidths. The vehicle successfully demonstrated reconnaissance and surveillance capability, and is being improved to accomplish such tasks as mine-deploying and scouting missions. The vehicle is not yet completely autonomous nor is it capable of following a pre-determined trajectory.\nOther research At Purdue,11 a student derived the dynamic equation of a model helicopter's vertical motion using blade element theory. For the experiment, a model helicopter was affixed on a stand to let it move only vertically. Uncertain parameters were estimated by interpolating the results from number of experiments with different parameters. After linearizing the dynamic model around the hover condition, controllers were designed using full state feedback poleplacement, LQR, and neural network techniques. All the controllers showed satisfactory performance.\nFuruta et al.12 derived a mathematical model of a model helicopter fixed on a stand, free to rotate around the pitch, roll, and yaw axis. Conservation of angular momentum was used to obtain the model. Realizing that the model helicopter is hard to control manually, they designed a stable tracking controller using the state space method. This stabilizing control input is then used to compare and validate the\nderived mathematical model with the experimental result. They realized that to be able to control the model helicopter in a full 6DOF situation, they need to expand the model to other degrees of freedom including the vertical motion. The model they derived was based on the full-scale helicopter modeling because they modeled a flapping rotor hub with spring, without explicitly taking the flybar into account.\nAzuma13 from University of Tokyo derived a mathematical model of a rigid rotor system. In this rotor system, each rotor blade is hinged but is spring loaded. He carefully derived a equation of motion using complex variables considering how different flapping stiffness affects the response of the system. Since this model does not take the dynamics of the helicopter as a whole, the validity of the model has not been fully proven.\nMathematical model In this section, we will derive the dynamic equations of motion for the model helicopter including its actuator dynamics. We will use results from rigid body dynamics,15 as well as basic aerodynamics and helicopter theory.14'16\nModel vs. full scale helicopters Before deriving the model helicopter dynamics, it is important to consider the differences between a full-scale helicopter and a model helicopter. First of all, a model helicopter has a much faster timedomain response due to its small size. Therefore, without employing an extra stability augmentation device, it would be extremely difficult for a human pilot to control it. A large control gyro with an airfoil, often referred to as a flybar, is almost always used nowadays to improve the stability characteristic around the pitch and roll axes and to minimize", "the actuator force required. Also, the tail rotor control for the model helicopter is assisted by an electronic gyro to further stabilize the yaw axis. Most full scale helicopters do not have such a control gyro on the rotor system. The large inertia of the rotor and fuselage and the flapping rotor hinge provide adequate stability.\nSecondly, most model helicopters do not have a flapping hinge on the rotor to maximize the control power. Full scale helicopters often use either a free flapping rotor hinge or a spring-mounted hinge; these are usually absent on a model helicopter.\nRigid Body Equations We will model the helicopter as a rigid body moving in space. As shown in Figure I, we use the variables (x, y, z) to represent the position of the helicopter in body coordinates. We use the variables () to represent the roll, pitch, and yaw angles of the helicopter with respect to the body coordinates. Because it is a rigid body, the helicopter's position and orientation in body coordinates will always be zero; however, the velocity and acceleration expressions are greatly simplified by using these coordinates. We will assume the rotor system is completely rigid (there is no aeroelasticity effect), and that the the airfoil is symmetric and non-twisted. The aerodynamic interaction between the rotor and the fuselage is neglected. The aerodynamic expressions are based on 2-D analyses. This type of modeling is often called level-1 modeling and is appropriate for low bandwidth control and to observe the parametric trends for flying qualities and performance studies.14\nThe standard rigid body dynamical equation will be used to model the motion of the helicopter in its environment. The state vector q = (x,y,z,4>,6,tl;)T contains the position and orientation information for the helicopter. Expressing the equation in coordinates gives15\n\"1/3x3 0 0 I 9 =\nMe-'. '. - Kg^\n(1)\nThe rotation matrix Rjg transforming the inertial coordinates into body coordinates using yaw-pitchroll (ZYX) Euler angles is given by\nRIB =\ncos ip \u2014 sin ip 0 cos 8 0 sin 8 sin^ cos ill 0 0 1 0\n0 0 1 -sin9 0 cosfi\n1 0 0 0 cos 4> ~ sin 4> 0 sin (j> cos \nThe cross \"x\" notation is used to represent the skewsymmetric cross-product matrix. For a vector a = [d a2 as]T,\nax = 0 \u2014as 02\nas 0 \u2014ai \u201403 ai 0\nThe rotational inertia matrix of the helicopter is given by\nThe terms on the right-hand side of the rigid body equation (1) include both the applied forces and disturbances. The D terms represent drag forces; these will be treated as disturbances in our model. The mass of the helicopter is given by m, and the fuselage inertias are Ixx, Iyy, Izz. Terms such as Ixy and Iyz are zero due to the symmetry of the helicopter with respect to the x-z plane. Although Ixz is nonzero, because the helicopter is not symmetric with respect to the x-y plane, it is typically much smaller than the other terms. We have included it in the model for completeness. The rotor rotational inertia is Ir. The rotor angular velocity is \u00a32, and the offset between the rotor axis and the helicopter's center of gravity is ir. Usually this offset is expected to be zero for better handling quality. Nevertheless, we will assume this quantity is non-zero for generality. The gravitational acceleration constant is g. It is assumed that the helicopter's center of gravity is in-line with the rotor axis laterally.\nThe four independent inputs are T, the net thrust generated by the rotor, and M$,Me,M$, the net moments acting on the helicopter, which are applied by a pilot. The mechanisms for creating these inputs will be described in the following section. The torque applied by the motor, Tm, is related to the thrust T and cannot be controlled independently. The electronic gyro acts as a damper on the yaw motion; we will use a simple linear model, Kgi{> for this gyro, although more sophisticated (PI controlled) gyros have recently become available.\nModel helicopter actuation A model helicopter moves forward when a pitching moment is first applied and the fuselage is tilted" ] }, { "image_filename": "designv10_11_0001465_s42235-021-0063-6-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001465_s42235-021-0063-6-Figure1-1.png", "caption": "Fig. 1 Fabrication of helical microstructures. (a) Schematic of the melt spinning; (b) device and (c, d) parameter control of the constant-helix-angle enwinding; (e) device and (f) parameter control of the constant-pitch enwinding.", "texts": [ " Polylactic acid (glass transition temperature approximately 55 \u02daC) was used as a matrix. NdFeB magnetic particles (5 \u03bcm in average diameter) were added into the molten polymer and dispersed mechanically. The mass ratio of particles to polymer was 3/25. When spinning, the molten polymer was extruded through the spinneret into the air below the solidification temperature of the polymer. The solidified polymer was taken up at a significantly higher velocity than that of the mean extrusion, resulting in the drawing of the filament, as schematically shown in Fig. 1a. The steady-state ratio of extrusion to take up area is called the draw ratio, to within the approximation that polymer density is independent of temperature, the draw ratio is equal to the ratio of taking up to extrusion velocity[34]. In this experiment, the diameters of fibers were adjusted by the velocity ratio. The obtained fiber was enwound on a metal micro-mandrel to form a helical structure. Both cylindrical mandrel and conical mandrel were used to obtain straight and conical helical microstructures, respectively", " The inner diameter and taper angle of the helix were determined directly by the mandrel, while the pitch or helix angle was related to the enwinding. We proposed two enwinding methods to fabricate a helix with a certain helix angle or pitch, and the two methods can produce different forms of conical helixes. The constant-helix-angle enwinding method is shown in Figs. 1b \u2013 1d. The metal micro-mandrel is fixed on a motorized rotary stage. A tensioned fiber with an end fixed on the rotary stage passes through a fixed hole in the distance (Fig. 1b). When the enwinding begins the mandrel is rotated around its axis by the rotary stage. The fiber and the mandrel surface come into contact, forming an initial helix angle between the fiber and the mandrel axis (Fig. 1c). Then the fiber is enwound to form a helical micro-structure. Since the distance L between the hole and the helical microstructure is much longer than the distance D between the ends of two fiber segments S0 and S1, the angle between two segments is approximately 0\u02da (Fig. 1d). The two segments keep parallel, resulting in the helix angle of each small segment on the helix is the same as the initial helix angle . Therefore, the precondition of the constant-helix-angle enwinding is a long enough distance L. The angle can be controlled by adjusting the position of the fixed hole. The constant-pitch enwinding method is shown in Figs. 1e and 1f. The difference with the constant-helix-angle enwinding is that the hole which the fiber passes through is fixed on a precision motorized linear stage (Fig. 1e). At the edge of the hole, the fiber forms a corner point that can move with the linear stage along the axis of the mandrel, as shown in Fig. 1f. During the enwinding process, the rotary stage and the linear stage move synchronously. The corner point moves away from the mandrel at a constant speed. The fiber is enwound to form a helical structure. The target pitch can be calculated by: m t ,vp n (1) where pt is the target pitch (m), n is the rotating speed of the rotary stage (rs\u22121), and vm is the moving speed of the linear stage (ms\u22121). Contrary to the constant-helix-angle enwinding, the precondition of the constant-pitch enwinding is to keep a small distance between the corner point and the mandrel surface to ensure the accuracy of the pitch" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003855_j.mechmachtheory.2006.01.006-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003855_j.mechmachtheory.2006.01.006-Figure7-1.png", "caption": "Fig. 7. The terminal constraints exerted to the end-effector B1B2B3B4.", "texts": [ " Therefore, the kinematic screws of kinematic chain P1B1 can be rewritten as $ actu P 1B1 \u00bc $2 $3 $4 $5 2 6664 3 7775 \u00f048\u00de Therefore, the reciprocal screws of kinematic chain P1B1 can be gained: $ r1 P 1B1 \u00bc \u00f0 0 0 0 cos a1 sin a1 0 \u00de $ r2 P 1B1 \u00bc \u00f0 cos a1 cos b1 sin a1 cos b1 sin b1 L sin b1 x1 sin b1 x1 sin a1 \u00fe L cos a1\u00f0 \u00de cos b1 \u00de ( \u00f049\u00de With similar processes, we can find the terminal constraints of the other three kinematic chains of the end- effector in the same Cartesian coordinate system: $r1 P 2B2 \u00bc \u00f0 0 0 0 cos a2 sin a2 0 \u00de $ r2 P 2B2 \u00bc \u00f0 cos a2 cos b2 sin a2 cos b2 sin b2 L sin b2 x2 sin b2 \u00f0x2 sin a2 L cos a2\u00de cos b2 \u00de ( \u00f050\u00de $r1 P 3B3 \u00bc \u00f0 0 0 0 cos a3 sin a3 0 \u00de $ r2 P 3B3 \u00bc \u00f0 cos a3 cos b3 sin a3 cos b3 sin b3 L sin b3 x3 sin b3 \u00f0x3 sin a3 L cos a3\u00de cos b3 \u00de ( \u00f051\u00de $ r1 P 4B4 \u00bc \u00f0 0 0 0 cos a4 sin a4 0 \u00de $ r2 P 4B4 \u00bc \u00f0 cos a4 cos b4 sin a4 cos b4 sin b4 L sin b4 x4 sin b4 x4 sin a4 \u00fe L cos a4\u00f0 \u00de cos b4 \u00de ( \u00f052\u00de Therefore, when the actuations are assigned to the four sliders, the terminal constraints exerted to the endeffector are four pure constraint forces along the individual axes of the limbs, and four pure constraint moments, which are all perpendicular to the direction of z-axis in the absolute coordinate system shown in Fig. 7. The terminal constraints exerted to the end-effector under the given actuations are $ r E \u00bc $ r1 P 1B1 $r1 P 2B2 $ r1 P 3B3 $r1 P 4B4 $ r2 P 1B1 $ r2 P 2B2 $r2 P 3B3 $ r2 P 4B4 2 66666666666666664 3 77777777777777775 \u00f053\u00de Obviously, the number of DOFs of the end-effector can be calculated with M \u00bc 6 d \u00bc 6 Rank\u00f0$r E\u00de. From the above analysis, we know that the four pure moments can prevent the end-effector from rolling about x-axis and y-axis in the absolute coordinate system provided that Eq. (45) did not hold" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000755_tac.1960.6429294-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000755_tac.1960.6429294-Figure6-1.png", "caption": "Fig. 6-(a) Loci for K of constant magnitude and phase. (b) Loci for K with constant real and imaginary parts.", "texts": [ " After ap plication of l'Hospital's Theorem, F M = - (42) m MUll = F(~) + 2F,,(~) + Fuu(~). (43) m uu mum (47)T(s, k). acK 1 - Kb T=--- SENSITIVITY CAUSED BY LARGE VARIATIONS IN PARAMETERS Consider the transmission T of the graph shown in Fig. 7. Since only the derivatives of F appear in the formulas derived and since the derivative of a constant is zero, all results obtained remain valid. If K varies in such a way that either its real or imagi nary parts are constant, the loci of interest are mapping of lines in Fig. 6(b). F is then derived from K itself. The most common root locus corresponds to the real axis which is a grid line in both Fig. 6(a) and 6(b). Hence, F can be derived for this case from either K or log K as is done in the examples. (41) (44) 1Muu(G, 0) = - Fuu(G, 0). 3 F = m(u, v)M(u, v) = 0 m(O, 0) = mv(O, 0) = M(G, G) = M,,(G, G) = O. because of choice of coordinates The branch tangent to the u axis is described by Evaluation of the derivatives of F is carried out as be fore and examples appear again in Appendix I. (48) (49) 1 ilK K 1- Kob 1---- 1 ---= SKT = S. 1- Kob T To Let K = Ko+ilK and T(K o) = To. Then, But, Hence, (45) (46a) (46b) 1 r" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003673_s0022-460x(03)00760-0-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003673_s0022-460x(03)00760-0-Figure3-1.png", "caption": "Fig. 3. (a) A cantilever helical rod; (b) type of dynamic loads.", "texts": [ " Forty steps of integration are used in the analysis. The Durbin\u2019s inverse Laplace transform [35,36] is applied for transformation from the Laplace domain to the time domain. Example. A cantilever helical rod is now considered. The parameters used in this example are those used in Ref. [34] for the elastic material. Various dynamic loads are applied on the free end of the rod. Material and geometrical properties are: d \u00bc 12 cm; a \u00bc 25:522834 ; a \u00bc 200 cm; E \u00bc 2:06 1011 N=m2; r \u00bc 7850 kg=m3 and n \u00bc 0:3 (see Fig. 3). Various dynamic loads with amplitude Po \u00bc 106 N are applied vertically at the free end of the rod. A time increment Dt of 20 ms is used in the calculations. An internal damping coefficient g \u00bc 0:02 is used for all cases. It is well documented that increasing the damping coefficient decreases the amplitude of the dynamic response [9,11]. Non-dimensional vertical displacement at the free end and non-dimensional shear force bending moment at the fixed end, are shown in Figs. 4a\u2013d and 5a\u2013d for different loading cases" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001756_j.mechmachtheory.2021.104345-Figure16-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001756_j.mechmachtheory.2021.104345-Figure16-1.png", "caption": "Fig. 16. The finite element analysis model of spiral bevel gear.", "texts": [ " To ensure the tooth surface accuracy, based on tooth surface equation, the finite element mesh model of tooth surface is built by rotating and arraying the position coordinates of discrete points of tooth surface, and the tooth surface obtained by this method can meet the requirements of high accuracy. The solid model of gear and pinion is constructed with the discrete points, and then gear and pinion are placed in the same meshing coordinate system based on the principle of coordinate transformation to complete the assembly of spiral bevel gear. The seven-tooth FEA model of spiral bevel gear shown in Fig. 16 is obtained, and the assembly accuracy meets the requirements. Based on the seven-tooth FEA model of spiral bevel gear, the LTE of second-order spiral bevel gear is carried out. And Figs. 14\u201315 and Table 4 show FEA results. The companion shows that although two methods obtain slightly different LTE amplitudes of second-order spiral bevel gear, the variation of LTE curve is basically the same; optimized second-order spiral bevel gear has a lower LTE amplitude than unoptimized second-order spiral bevel gear" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001732_j.autcon.2021.103609-Figure17-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001732_j.autcon.2021.103609-Figure17-1.png", "caption": "Fig. 17. Path of bristles during circumference covering, showing examples of left bristle having lower path resolution and lesser push-in depth, while right bristle having higher path resolution and more push-in depth. (a) Ideal case. (b) Diameter of bristles reduced during polish work. (c) Misalignment due to slight symmetrical deviation. (d) Irregular pipe surface.", "texts": [ " The trajectory points are calculated by the Robot PC, which is K.H. Koh et al. Automation in Construction 125 (2021) 103609 reprogrammable with operator inputs. The time interval between calculated points is 0.25 s. When the operator has aligned the bristle pair against the pipe tangent, the location of the center axis for the pipe is known if the pipe diameter is entered correctly. An unused bristle will have a diameter of 25.4 mm, which will gradually decrease due to wear and tear. As illustrated in Fig. 17, the points on the circular path around the pipe circumference are calculated based on the radius, the push-in depth of the bristle (usually <4 mm), and the resolution. Resolution refers to density of the points that cover the circular path and is optimized experimentally. A low resolution will result in unsatisfactory coverage, while a high resolution will require more time. Despite the known geometrical adjustments, unknown factors, which alter the contact condition between the pipe surface and the bristles, remain, including the bristle wear and tear during the polish process, the imperfect alignment of the bristle pair against the pipe symmetrically, and the irregularities on the surface, such as bumps, creases, rusts, and debris" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003807_j.euromechsol.2005.11.001-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003807_j.euromechsol.2005.11.001-Figure1-1.png", "caption": "Fig. 1. Member of the first one-rotational and two-translational DOFs asymmetrical PKM family.", "texts": [ " Each of the first two families provides the platform with one-rotational-two-translational DOFs and each of the second two families provide the platform with one-translational-two-rotational DOFs. All the PKMs presented here have three limbs to allow the actuators to be placed on the machine base. The planar PKM is a commonplace one-rotational-two-translational DOFs PKM. This is not the one presented here though as this family is fairly well established (Tsai, 1999; Merlet, 2000). Instead the rotation axis is selected to be not normal to the translation plane. Fig. 1 depicts a PKM that provides one-rotational and two-translational DOFs. Using Lie group theory, one can demonstrate the full-cycle mobility of that mechanism as follows. The first limb generates the product G(x)R(O,y). O is a point of the axis of rotation and belongs to the moving platform. The second limb generates the same motion set. The third limb generates G(z)R(A,y)R(B,y). Using group algebraic properties of motions sets, one can show that G(z)R(A,y)R(B,y) is equal to G(z)G(y) by elimination of the redundancy of the square of G(z) \u2229 G(y) = T (x) in the product G(z)G(y)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000088_j.jsv.2017.12.022-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000088_j.jsv.2017.12.022-Figure1-1.png", "caption": "Fig. 1. The fully conjugate gear surface and its projection; (a) Tooth surface of P 1, P 0 and P 2 (b) Projection plane of surface P 0.", "texts": [ " The position vector and normal vector of pinion tooth surface are represented as follows: r1 \u00bc r up; qp n1 \u00bc n up; qp (1) in which, up and qp denote the parameters of generating pinion surface corresponding to the length of generating line and rotation angle of head-cutter [4]. The function of TM between gear and pinion is described as: 42 \u00bc 420 \u00fem12\u00f041 410\u00de \u00fe d42 d42 \u00bc Xn i\u00bc0 ai\u00f041 410\u00dei \u00f0i \u00bc 0;1; :::;n\u00de (2) Here, 41 and 42 stand for the rotation angles of gear and pinion around their axis, and 410 and 420 are the initial rotation angles, respectively. m12 is the theoretic transmission ratio or the tooth number ratio. d42 is the unloaded TE, ai is the corresponding coefficients. Fig. 1(a) shows the generating process of the pinion surface and the corresponding conjugate gear surface. P 1 denotes the pinion tooth surface represented in pinion coordinate system S1\u00f0X1;Y1; Z1\u00dewhile P 0 designates the fully conjugate gear tooth surface with P 1 according to the generating movement TM, which is represented in gear coordinate system S2\u00f0X2;Y2; Z2\u00de. The fully conjugate gear tooth surface P 0 with predesigned TM can be represented as follows: r0 up; qp;f1 \u00bc M01r1 up; qp n0 up; qp;f1 \u00bc M01n1 up; qp n1,V 01 \u00bc 0 (3) In which, M01 means the equivalent matrix for transforming from the pinion coordinate system S1\u00f0X1;Y1; Z1\u00de to the gear coordinate system S2\u00f0X2;Y2; Z2\u00de", " Therefore, the position of calculation point should be determined from working condition and meshing performance. Surface P 2 represented in gear coordinate system S2\u00f0X2;Y2; Z2\u00de is the desired tooth profile. In order to ensure that P 2 is in point contact with P 1 along the predesigned contact path, the curvature correction on surface P 0 is performed to obtain predesigned TM. The orientation of contact path is one of the critical factors of meshing performance which has close relation with overlap ratio. It should be predetermined according to the requirements of running performance. Fig. 1(b) shows the projection of conjugate surface P 0 rotating around its own axis. On the projection plane, calculation point M0 is selected as the origin of discrete coordinate system SOT, and the direction of X axis is along the pitch cone. The predesigned line L going through point M0 in angle G with X axis is selected as the contact path. Several contact points on L marked with symbol M m; M m\u00fe1; :::; M0; ::: ;Mm 1;Mm are selected as the calculation points to determine the TE function. S0\u00f0s; t\u00de and P0\u00f0x0; y0; z0\u00de denote the points on the projection plane and surface P 0 respectively. The coordinate relation between S0 and P0 can be derived as: 2 4 s t 1 3 5 \u00bc \u00bdM20 2 64 x0 up; qp ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi y20 up; qp \u00fe z20 up; qp q 1 3 75 (4) inwhich, \u00bdM20 is thematrix of coordinate transformation from coordinate systemUOV to XOY . As illustrated in Fig.1(a), every point along special contact path Lc on surface P 0 is determined uniquely which is corresponding to the points along line L. The curvature correction value is the relative normal curvature of the two surfaces, namely induced curvature. In order to ensure the correct TM along the predesigned contact path between gear and pinion teeth, the flank correction approach should be performed on the area of conjugate surface P 0 other than contact path. In order to avoid surface interference and meet contact strength requirements, the curvature correction along the tangential direction of contact path should equal to zero, while that along other directionsmust be greater than zero. Vector c is the tangential direction of contact path Lc and p is the instantaneous contact line at calculation point M0 shown in Fig. 1(a). Symbol Dkc and Dkp are used to denote the relative normal curvature along the direction c and p respectively. p can be determined by the following expression [36]: p \u00bc k1vV 01 \u00fe t1vn1 V01 \u00feu01 n1 (5) in which, k1v ; t 1 v are the curvature and torsion of pinion tooth surface P 1 along the direction of relative velocity V01. The value of curvature correction Dkc equals 0 and Dkp is expressed as: DkP \u00bc 8d a2 >0 (6) in which, the value of deformation d is considered as a given value under light contact load taken from the experimental data as 0.00635 mm [4]. a is the length of ellipse long axis shown in Fig. 1(a). After curvature correction is performed on the fully conjugate gear surface along contact path, a new ease-off gear surface can be constructedwhich is 2nd order tangential to the contact path on conjugate gear tooth surface P 0. As is shown in Fig. 2, vector c and twhich are vertical to each other are the principal directions at contact point on this surface. The corresponding principal curvatures are denoted by Dkc and Dkt . The maximum normal curvature correction Dkt is along direction t which can be deduced from Dkp based on Euler's formula as follows: Dkt \u00bc Dkp sin2 a (7) where a is the angle between the tangential directions of contact path and contact line which can be represented as: cos a \u00bc c,p jcjjpj (8) Taking P 0 as the datum plane, the ease-off gear surface Q is established based on the deviation value w at all the surface points P0 of P 0 along the normal direction" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003511_s0094-114x(00)00024-0-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003511_s0094-114x(00)00024-0-Figure3-1.png", "caption": "Fig. 3. Relationship between the worm and cutting blade coordinate systems.", "texts": [ " 2(c) and (d), which can be represented as follows rt r2 1 \u00ff s2 n 4 sin2 b1 r \u00ff sn 2 tan a1 ; 2 where r1 is the pitch radius and sn the normal groove width of the produced worm. The ZN-type worm is cut by a straight-edged cutting blade placed on its groove normal plane. Therefore, the ZN-type worm surface is the locus of the cutting blade, and the worm surface geometry depends on the design parameters of the cutting blade and on machine-tool settings. The ZN-type worm cutting mechanism can be simpli\u00aeed by considering the relative motion of a straight-edged cutting blade performing a screw motion along the worm rotation axis. As shown in Fig. 3, coordinate system S1 X1; Y1;Z1 is associated with the worm surface, and coordinate system Sf Xf ; Yf ;Zf is the reference coordinate system; Z1-axis is the rotation axis of the worm. The locus of the cutting blade can be represented in coordinate system S1 by applying the following homogeneous coordinate transformation matrix equation x1 y1 z1 1 2664 3775 sin u1 sin u1 cos b1 \u00ff sin u1 sin b1 0 \u00ff sin u1 cos u1 cos b1 cos u1 sin b1 0 0 sin b1 cos b1 \u00ffP1u1 0 0 0 1 2664 3775 xc yc zc 1 2664 3775; 3 where parameter P1 is the lead-per-radian revolution of the worm surface, and u1 the rotation angle of the worm in relative screw motion" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001068_j.jmatprotec.2020.116935-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001068_j.jmatprotec.2020.116935-Figure1-1.png", "caption": "Fig. 1. Schematic diagram of the electronic imaging system used in an EBSM machine.", "texts": [ " The in-situ experiment was conducted to demonstrate the in-process monitoring. Signal fusion was performed to investigate the feasibility of defect identification with the dual-detector detection system. The electronic imaging system was designed to monitor the layerwise fabrication of EBSM process by detecting the emitted electrons like SEs and BSEs. These electrons deliver topographic information of the target surfaces since their yield and spatial distribution relate to the target surface topography. Fig. 1 shows the dual-detector electronic imaging system. The imaging system consists of two detectors and current amplifiers, a multi-channel data acquisition card, and an industrial personal computer. The detectors are made of copper. The electrons with initial velocity vectors confined in the detection solid angle are collected. Besides, the two detectors were specifically arranged to improve the system sensitivity to surface topography. First, the detectors were mounted close to the build platform to collect more SEs" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001578_j.addma.2021.101954-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001578_j.addma.2021.101954-Figure1-1.png", "caption": "Fig. 1. Schematic of the uniaxial tensile test samples.", "texts": [ " The average values for a minimum of three measurements were reported along with the measured error. The as-built cube samples were designated as LPBF-AB, while the heat-treated ones as LPBF-HT. It is noteworthy that the heat-treatment process applied to all samples in the current study was heating to 490 \u25e6C for 6 h and aircool in the oven [28]. Uniaxial tensile test samples were machined out of additively manufactured round bars based on the E8/E8M ASTM standard [30]. A minimum of three tests was applied for each set of uniaxial test specimens. Fig. 1 shows a tensile test coupon, schematically, and the dimensions are shown in Table 3. A quasi-static strain rate of 9 \u00d7 10\u2212 3 s\u2212 1 was implemented on an Instron 1332 universal hydraulic machine equipped with a 25 mm extensometer. The samples were designated based on the building direction (BD) and heat-treatment. The LPBF-AB-H represents the 18Ni-300 maraging steel sample in the as-built condition manufactured in the horizontal direction, while the LPBF-AB-V represents the same sample printed in the vertical direction" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003490_j.optlastec.2003.12.003-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003490_j.optlastec.2003.12.003-Figure1-1.png", "caption": "Fig. 1. Schematic of laser cladding for RM.", "texts": [ " The results of the experiments veri(ed the e4ects of in-time motion adjustment on dimensional accuracy and surface (nish. ? 2003 Published by Elsevier Ltd. Keywords: Laser cladding; In-time motion adjustment; Dimensional accuracy; Surface (nish; Defect Laser cladding is a material processing technique in which a laser is used as a heating source to melt metal powder to be deposited on a substrate. This technique is being applied as a rapid manufacturing (RM) process to generate a part point-by-point and layer-by-layer as shown in Fig. 1. It has been introduced as a means of creating functional metal parts with near-net shape geometries and has a signi(cant advantage over traditional RP techniques due to direct fabrication of a near-net shape part compared to the two-step process involving an intermediate step of mould preparation in conventional RP techniques. Development e4orts are being conducted in research centers throughout the world [1]. However, it is inadequate to consistently regulate part quality due to defects occurring during laser cladding, such as declining of side surfaces, undulation and roughness on the upper surface or at the side surfaces" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001280_j.jmapro.2020.02.045-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001280_j.jmapro.2020.02.045-Figure6-1.png", "caption": "Fig. 6. (a) The components were sectioned in two parts: the lower one in which the inner zone corresponds mostly to the up-skin and the upper area in which the internal part corresponds to the down-skin. Non-self-supporting areas highlighted in yellow for three different angle thresholds for the self-supporting condition: (b) R = 30 mm, (c) R = 40 mm, and (d) R = 50 mm (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).", "texts": [ " The reason is that the energy value depends on the numerical combination of the process parameters (laser power, scan speed, hatching distance and layer thickness). The same value can be obtained with different process parameters leading to different results [26,28,32]. Surely, the formation of spatter and dross is due to the high laser absorption factor of the powder compared to the solid metal of the part. Moreover, some areas in the prototypes with R = 40 and 30 mm has required supports having angles less than 35\u00b0. Fig. 6 shows the upper area of the component in which the internal part corresponds to the downward facing surfaces. The images are obtained by using Materialize's Magics software. This software is widely used in PBF processes to orient components and to insert supports. If 45\u00b0 is selected as the threshold angle for the self-supporting condition, the components with R = 40 and 30 mm require supports in the surfaces and edges that are highlighted in yellow in Fig. 6(b) and (c)). If the threshold angle is gradually reduced, it turns out that no edge is highlighted for both the components when the angle is smaller than 37\u00b0. The component with R = 50 mm already at 45\u00b0 has all internal selfsupporting surfaces, whilst only the edges are non-self-supporting areas. For achieving the self-supporting condition also for the edges, it would be necessary to decrease the threshold angle to 23\u00b0, but this value is much lower than the limit for AlSi10Mg alloy (30\u00b0), thus making edges inaccurate" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000560_s00170-016-8857-0-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000560_s00170-016-8857-0-Figure1-1.png", "caption": "Fig. 1 Hypoid gear hobbing", "texts": [ " The optimization is based on machine tool setting variation on the cradle-type generator conducted by optimal polynomial functions and on optimal head-cutter geometry. In the second step, an algorithm is developed for the execution of motions on the CNC hypoid generator using the relations on the cradle-type machine. Effectiveness of the method was demonstrated by using a face-hobbed hypoid gear example. Significant reductions in the maximum tooth contact pressure and in the transmission errors were obtained. An imaginary generating crown gear is used to generate the tooth surface of the face-hobbed hypoid pinion and gear teeth (Fig. 1). To obtain the pinion/gear tooth surface in the generating process, the work gear is rolled with the imaginary gear (Fig. 1). Figure 1 shows the relative position between the headcutter and the generating crown gear. The machine tool settings are the radial machine tool setting (e), the tilt angle of the cutter spindle with respect to the cradle rotation axis (\u03ba), the swivel angle of cutter tilt (\u03bc), and the tilt distance from tilt centre to reference plane of head-cutter (hd). The tooth surface of the imaginary generating crown gear is obtained by coordinate transformations from the coordinate system Ke(xe,ye,ze) (attached to the head-cutter) to coordinate system Kc(xc,yc,zc) (attached to the imaginary generating crown gear) by applying the following equation (based on Fig. 1): r!c \u00bc M c4\u22c5M c3 e; ig1 \u22c5M c2 \u03bc;\u03ba; hd\u00f0 \u00de\u22c5M c1 rt0\u00f0 \u00de\u22c5 r!e \u00bc M ec\u22c5 r!e \u00f01\u00de Matrices Mc1, Mc2, Mc3, and Mc4 are presented in Ref. [32]; r!e is the radius vector of the blade profile points (Fig. 2). In the tooth surface generating process, the work gears are rolled with the imaginary generating gear (Figs. 1 and 3). The coordinate system Kc(xc,yc,zc) is attached to the generating crown gear; the coordinate systems K1(x1,y1,z1) and K2(x2,y2,z2) are attached to the pinion and gear, respectively. The teeth surfaces of the pinion and of the gear are defined by the following system of equations: r", " 0 @ 1 A it ;iz\u00f0 \u00de : \u00f012\u00de An optimization method is applied to systematically define optimal head-cutter geometry and machine tool settings to simultaneously minimize maximum tooth contact pressure and angular displacement error of the driven gear. The proper manufacture variables, objective function, and constraints needed to be defined. The following manufacture parameters are taken as the basis of the proposed optimization formulation: the radii of the head-cutter blade profile (rprof1 and rprof2, Fig. 2), the difference in head-cutter radii for the manufacture of the contacting tooth flanks of the pinion and the gear (\u0394rt0), tilt (\u03ba) and swivel (\u03bc) angles of the cutter spindle with respect to the cradle rotation axis (Fig. 1), tilt distance (hd), variation in the radial machine tool setting (\u0394e, Fig. 1), and variation in the ratio of roll in the generation of pinion tooth-surface (\u0394ig1). The variations of the tilt and swivel angles, tilt distance, radial machine tool setting, and the ratio of roll are conducted by polynomial functions of fifth-order: \u03ba \u00bc c10 \u00fe c11\u22c5 \u03c8c1\u2212\u03c8c10\u00f0 \u00de \u00fe c12\u22c5 \u03c8c1\u2212\u03c8c10\u00f0 \u00de2::::\u00fe c15\u22c5 \u03c8c1\u2212\u03c8c10\u00f0 \u00de5 \u03bc \u00bc c20 \u00fe c21\u22c5 \u03c8c1\u2212\u03c8c10\u00f0 \u00de \u00fe c22\u22c5 \u03c8c1\u2212\u03c8c10\u00f0 \u00de2::::\u00fe c25\u22c5 \u03c8c1\u2212\u03c8c10\u00f0 \u00de5 hd \u00bc c30 \u00fe c31\u22c5 \u03c8cl\u2212\u03c8c10\u00f0 \u00de \u00fe c32\u22c5 \u03c8cl\u2212\u03c8c10\u00f0 \u00de2::::\u00fe c35\u22c5 \u03c8cl\u2212\u03c8c10\u00f0 \u00de5 \u0394e \u00bc c40 \u00fe c41\u22c5 \u03c8c1\u2212\u03c8c10\u00f0 \u00de \u00fe c42\u22c5 \u03c8c1\u2212\u03c8c10\u00f0 \u00de2::::\u00fe c45\u22c5 \u03c8c1\u2212\u03c8c10\u00f0 \u00de5 \u0394ig1 \u00bc c50 \u00fe c51\u22c5 \u03c8c1\u2212\u03c8c10\u00f0 \u00de \u00fe c52\u22c5 \u03c8c1\u2212\u03c8c10\u00f0 \u00de2::::\u00fe c55\u22c5 \u03c8c1\u2212\u03c8c10\u00f0 \u00de5 \u00f013\u00de where \u03c8c1 is the angle of rotation of the imaginary generating crown gear in pinion tooth surface generation", "001492 \u22120.001442 \u03bc 0 0 \u22120.001958 0.003917 0.005750 \u22120.003583 hd 0.07170 0 0.001667 \u22120.081333 0.014167 0.019167 \u0394e 0.01517 0.001167 0.003533 0.001917 0.003583 0.003583 \u0394ig1 0 0 \u22120.001667 0.001667 0.048333 0.011667 m31 \u00bc sin\u03b6\u22c5sin\u03b7\u22c5cos\u03b8\u2212cos\u03b7\u22c5sin\u03b8 m32 \u00bc sin\u03b6\u22c5sin\u03b7\u22c5sin\u03b8\u00fe cos\u03b7\u22c5cos\u03b8 m33 \u00bc \u2212cos\u03b6\u22c5sin\u03b7 m34 \u00bc sin\u03b7\u22c5 X \u22c5sin\u03b6 \u00fe Z\u22c5cos\u03b6\u00f0 \u00de\u2212Y \u22c5cos\u03b7 The location and the orientation of the tool with respect to the pinion/gear are given in coordinate systems that are represented for a conventional, cradle-type generator (Fig. 1). An algorithm will be developed for the execution of motions on the CNC generator using the relations valid for the cradle-type machine. This algorithm is based on the conditions that the relative position of the axes of the head-cutter and the pinion rotations, zt0 and yi0, and the axial relative position of the head cutter and the pinion/gear should be the same whether the pinion/gear is cut on a cradle-type or a CNC hypoid generator. To ensure the same relative position of the two axes, zt0 and yi0, on both the cradle-type and CNC hypoid generating machines, the elements of the coordinate transformation matrices should be equal" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001280_j.jmapro.2020.02.045-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001280_j.jmapro.2020.02.045-Figure5-1.png", "caption": "Fig. 5. Deviation color maps with regard to the accuracy of the two parts of the prototypes: (a) R = 50 mm, (b) R = 40 mm, (c) R = 30 mm.", "texts": [ " [23], in order to minimize cable movements and, thus, minimizing measurement errors. A number of 256 averages has been considered so as to guarantee a dynamic range of 90 dB that is necessary to carefully measure the out-of-band rejection of the components. The measured performances are compared to the predicted values in Table 2. The accordance is rather good confirming the manufacturing quality of the integrated components for all the three values of radius. The result of the deviation analysis between the STL model and the model produced by the L-PBF process is shown in Fig. 5. The accuracy of the internal channels is confirmed by the color maps of the deviations of the scanned components from the STL model, for which the gaussian distribution has a standard deviation of approximately 0.04-0.07 mm. In particular, the internal areas have an average deviation of about 0.08 mm, 0.046 mm and 0.023 mm from the CAD model for the R of 50 mm, 40 mm and 30 mm, respectively. This deviation is not due to the socalled \u201cstaircase effect\u201d, typical of some additive technologies, but by the dross formation", " (1), it can be easily inferred that the length Lo increases when the inclination angle \u03b8 decreases. This aspect can give rise to a very evident staircase effect, which negatively affects the quality of the protruding structures. For a layer thickness of 30 \u03bcm and an angle of 30\u00b0 (i.e., the minimum angle for self-supporting surface in AlSi10Mg alloy), the length Lo is equal to 17 \u03bcm which is less than the diameter of the melt pool (about 200 \u03bcm [26]). This value suggests that the error cannot be attributed to the staircase effect. From the stereomicroscope images of Fig. 5, it can see that the deviation occurs on some edges of the overhanging areas. Overhangs necessarily involve the fusion on the powder, which has starkly different material properties than its bulk counterpart. The heat conduction rate may be hundred times smaller than bulk conduction [27], resulting in a much larger melt pool than the one obtained on an already melted layer. Because the powder particles are random packaged, inducing a variable thermal conductivity, melt pools sink deep into the powder and with recoater blade pressure and capillary forces at play, solidify into an extremely rough surface with large deformities called \u201cdross\u201d" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001280_j.jmapro.2020.02.045-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001280_j.jmapro.2020.02.045-Figure2-1.png", "caption": "Fig. 2. (a) Traditional WR51 waveguide subsystem; (b) redesigned WR51 waveguide component integrated.", "texts": [ " Three prototypes with different bending/twisting radii (R = 50 mm, 40 mm, and 30 mm) have been manufactured in AlSi10Mg alloy through L-PBF. First, the components have been tested at an electromagnetic level, and the results, already published in a previous study [12], are summarized in Section 4. Then, the prototypes have been cut in order to analyze the internal structure of the channels and to correlate the electromagnetics performances with the surface characteristics. The Ku/K-band WR51-waveguide system shown in Fig. 2(a) has been selected as a relevant benchmark in order to assess the capability of the L-PBF process to reduce the mass and to miniaturize dual-band dual-polarization waveguide antenna-feed chains [12]. The standard architecture of the WR51-waveguide system shown in Fig. 2(a) consists of a 50-mm long bend, a twist with a length of 80 mm, and a straight 47-mm long section implementing the pass-band filter. These dimensions are needed in order to guarantee the typical electromagnetics requirements set by satellite telecommunications. The architecture of the integrated component is shown in Fig. 2(b), and it cannot be easily produced in a single part through conventional processes (turning, milling, or electric discharge machining). Indeed, the design of this component has been carried out by exploiting the free-form capability of additive technology. Specifically, the L-PBF process has been considered, because it allows the development of metal components already assembled with high density (> 99.5 %), good tensile strength and hardness [13\u201316], and a much lower surface roughness than that obtainable by another PBF process, namely the electron beam melting (EBM) [17\u201320]. With the aim of investigating the miniaturization capabilities offered by the L-PBF process, the integrated component of Fig. 2(a) has been designed for three different values of the bending/twisting radius, that is R equal to 50 mm, 40 mm and 30 mm (Fig. 3). It has to be pointed out that R = 30 mm is the minimum length sufficient to allocate the filter, i.e. the bend and twist are fully merged in the filter without any additional mass or envelope. The three components have been electromagnetically designed and simulated by combining the method described in Peverini et al. [21] and CST Microwave Studio. The CAD model has been converted into a STL file in which the deviation control and the angle control [22] have been chosen, so as to reduce the approximation error and to make the discrepancies negligible between the electromagnetics responses of the two models" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001059_j.mechmachtheory.2020.104101-Figure15-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001059_j.mechmachtheory.2020.104101-Figure15-1.png", "caption": "Fig. 15. A scheme for Eq. (7) and for finding the ICR trajectory.", "texts": [ "01 s, and therefore its coordinates are determined as follows: C Z ( t i ) = C Z ( t i \u22121 ) + s Z ( t ) C Y ( t i ) = C Y ( t i \u22121 ) + s Y ( t ) (5) In order to calculate displacements s ( Figs. 13 and 14 ), the vector product of angular step \u03d5i carried out in time t, and the calculated lever arm r i defined in Eq. (6) , were used. r Z (t) = C Z (t \u2212 t) \u2212 IC R Z (t) r Y (t) = C Y (t \u2212 t) \u2212 IC R Y (t) (6) Furthermore, using numerical data from the ADAMS simulations for the positions and velocities of the femur points (B, C), the ICR position was computed according to the scheme presented in Fig. 15 and Eq. (7) . General functions of the straight lines were identified as being perpendicular to the velocity vectors of points B and C, and they also crossed through these points. Solving the system of these two equations using determinants enabled the ICR point as the intersection point of the two straight lines to be found. IC R Z = W Z W m = \u2212P B v YC + P C v Y B v ZB v YC \u2212 v ZC v Y B IC R Y = W Y W m = \u2212P C v ZB + P B v ZC v ZB v YC \u2212 v ZC v Y B (7) where: P B = \u2212 ( v ZB Z B + v Y B Y B ) P C = \u2212 ( v ZC Z C + v YC Y C ) and: The results of the four performed types of simulations are listed in Table 1 together with the acquired numerical values that are further shown in the plots of Figs. 16 to 19 . In order to obtain the driving forces of the mechanisms\u2019 motors, a vertical force V = 1 kN ( Fig. 11 ) is assumed on the femoral link, simulating human body weight. For both mechanisms (the rotationally adjustable 4-bar mechanism in Fig. 11 and the linearly adjustable 4-bar mechanism in Fig. 8 ), and in all simulations, the calculations are performed to find the ICR trajectory according to the previously described procedure ( Fig. 15 and Eq. (7) ). Fig. 16 shows the Walker et al. trajectory (I) and the two example trajectories (II, III \u2013 the named boundary trajectories) in order to cover a range of possible paths. This is due to the fact that the knee joint\u2019s ICR trajectory is different for each individual person. The performed simulations can be summarised as follows: \u2022 Ex.1 \u2013 the Walker et al. trajectory ( Fig.16 -I) is used asthe reference for the4-bar mechanism with the optimal dimensions and rotationally adjustable 4-bar mechanism, and also with the optimal dimensions, but with 1DOF (additional DOFs are blocked), \u2022 Ex" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000716_j.mechmachtheory.2019.07.013-Figure11-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000716_j.mechmachtheory.2019.07.013-Figure11-1.png", "caption": "Fig. 11. Envelope residual on face gear tooth surface.", "texts": [ " Envelope residuals on the face gear tooth surface will be generated at the area between the contiguous grinding tracks by using the grinding method proposed in this paper. The envelope residuals must be strictly controlled since it\u2019s a major index of gear surface finish. A discrete mathematical method for calculating the envelope residuals of the face gear is presented in this section. And based on this, a numerical model for determination of the rotation angles \u03c8 s \u2217 of the reference shaper (further determining the grinding tracks of the disk wheel) is established, aiming to satisfy the prescribed processing precision for face gear grinding. As shown in Fig. 11 , 1 and 2 are contiguous grinding tracks on the tooth surface of the face gear. Surfaces g 1 and g 2 are formed by the grinding disk wheel as it moves along the grinding tracks 1 and 2 , respectively. e is the intersection line of surfaces g 1 and g 2 . Let us consider now two generic points M 1 and M 2 , which will be ground by the grinding disk wheel, are located at two contiguous nodes of the same radii of the aforementioned discretization grid. Envelope residual of point T , which lies on the intersection line e and has the same radius with point M 1 (or M 2 ), is defined as the deviation of this point to the theoretical tooth surface of the face gear, and is represented by \u03bb in Fig. 11 . In this paper, the envelope residual \u03bb of point T is assumed to be the maximum residual between the two being-generated points M 1 and M 2 of the gear tooth surface. The envelope residuals of the gear tooth surface are only considered above the tangent line between the working surface and the fillet surface of the face gear. In order to obtain the envelope residual \u03bb of the intersection point T , the coordinates of point T must be calculated initially. The positioning of the disk wheel in coordinate system S of the face gear has been determined for the grinding of 2 points M 1 and M 2 of the gear surface by application of the algorithm proposed in Section 3 ", " The coordinates of point T can be obtained in coordinate system S 2 as: { r ( g1 ) 2 ( u ( 1 ) sg , \u03b8 ( 1 ) g ) = r ( g2 ) 2 ( u ( 2 ) sg , \u03b8 ( 2 ) g )( x ( g1 ) 2 )2 + ( y ( g1 ) 2 )2 = ( R T ) 2 (33) where, r 2 ( g 1) and r 2 ( g 2) are instantaneous tooth surface equations of the grinding disk wheel in coordinate system S 2 at the position of points M 1 and M 2 , respectively. x 2 ( g 1) denotes the coordinate x of vector r 2 ( g 1) . Eq. (33) contains four equations with four unknowns. The position vector of point T represented in coordinate system S 2 of the face gear can be determined from the solution of equation: r T = r ( g1 ) 2 ( u ( 1 ) sg , \u03b8 ( 1 ) g ) (34) The point W on the gear tooth surface is supposed to be the projection of point T along the normal direction of the tooth surface of the face gear ( Fig. 11 ). The surface parameters of point W are taken as u s w , l s w , \u03c8 s w . The unit normal n 2 ( u s w , l s w , \u03c8 s w ) of point W of the gear tooth surface is parallel to a vector formed by the difference of the position vector of points T and W . Then the following equations are satisfied: { ( r 2 ( u w s , l w s , \u03c8 w s ) \u2212 r T ) \u00d7 n 2 ( u w s , l w s , \u03c8 w s ) = 0 f s 2 ( u w s , l w s , \u03c8 w s ) = 0 (35) Based on the coordinates of the intersection point T on the intersection line e and the corresponding projection point W of point T on the gear tooth surface" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003252_la9808519-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003252_la9808519-Figure1-1.png", "caption": "Figure 1. Electrochemical cell used for cyclic voltammetry, electrochemical impedance, and electroreflectance spectroscopy measurements. The gold working electrode is mounted in a Teflon sleeve that gives an exposed area of about 0.32 cm2 (6.35 mm diameter); the platinum sheet counter electrode area is about 30 cm2; the overall height of the working chamber is 4.5 cm; working and reference electrodes are fixed in place by tight press-fit; in electroreflectance measurements, illumination is done with a 100-W xenon-arc light source directed at 15\u00b0 from the normal to the working electrode. The remaining parts of the ER apparatus are described in ref 4. All potentials measured with this device are reported relative to the saturated Ag/AgCl reference electrode potential.", "texts": [ " N-Acetyl-L-cysteine (NAC; CAS # 616-91-1) was obtained from Sigma (Product #A8199) and used without further purification. Gold electrodes were made from polycrystalline 99.99% purity gold rod purchased from Alpha (Ward Hill, MA). Potassium dicyanoaurate (I) from Aldrich (Milwaukee, WI) was 98% pure. Water for all experiments was purified on a Milli-Q system (Millipore). Instrumentation. All electrochemical and spectroelectrochemical measurements were performed using the quartz halfcylindrical cell shown in Figure 1. The three electrodes mounted into the cell were a saturated Ag/AgCl reference electrode (Abtech, Yardley, PA), a platinum sheet counter electrode with total area of more than 30 cm2, and a gold rod working electrode fitted into a Teflon holder with a geometric area of 0.32 cm2. Working electrode potentials for linear ramp, direct, and alternating current were controlled by an EG&G potentiostat (10) Niaura, G.; Gaigalas, A. K.; Vilker, V. L. J. Electroanal. Chem. 1996, 416, 167. (11) Willit, J. L", " Next, the electrode was washed with water and electrochemically cleaned by potential cycling at the same conditions described prior to electrodeposition of the fresh gold layer. After the freshly prepared electrode was washed with water, it was modified with thiol by immersion for 30 min into a solution of about 5 mM NAC in 0.2 M phosphate buffer, pH 7. After extensive water washing, a 30 mL aliquot of 0.5 mM cytochrome c solution in 0.01 M phosphate buffer was placed on the gold surface for 15 min at +4 \u00b0C. Another water wash was followed with placement of the electrode into the electrochemical cell shown in Figure 1. Measurement Procedures. All electrochemical and electroreflectance measurements were performed in 0.01 M phosphate buffer (pH 7.4, ca. 20 \u00b0C) which was deoxygenated by continuous argon bubbling before and during measurements. Prior to determining heterogeneous electron-transfer rate parameters by cyclic voltammetry, the solution resistance was evaluated by using the measurement procedure available with the EG&G potentiostat in IR compensation mode. This solution resistance measurement was repeated 7-10 times, resulting in mean values ranging from 260 to 680 W, depending on the distance between reference and working electrodes" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003160_cdc.1999.830084-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003160_cdc.1999.830084-Figure2-1.png", "caption": "FIGURE 2.", "texts": [ " Note that the distribution spanned by { Y2) is also geodesically invariant. Thus, if we consider the system as having only the input Y2, it is (%dyn, %ki,)-reducible to 1 m r = 0 = 0 , \\ir = 0. However, this system is obviously not locally controllable. It is also clear that with just the input vector field Y1, the robotic leg is not (%&, %ki,)-reducible to a kinematic system. 5.2 Upright rolling disk Here we consider a uniform disk rolling upright without slipping on a flat surface orthogonal to the direction of gravity (Figure 2). We use coordinates (n,y ,O,$) as indicated in the figure. We denote by m the mass of the disk, r the radius of the disk, J the moment of inertia about the z-axis, and I the moment of inertia about its centre of mass in the direction of a line orthogonal to its face. For this example, we must use an affine connection which is not Levi-Civita, but which is computed using the methodology of Lewis [ 2 ] , to which we refer for the details. Here we merely record that the non-zero Christoffel symbols are given by and the input vector fields by l a y2 = -- " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003388_978-3-662-04831-3-Figure1.4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003388_978-3-662-04831-3-Figure1.4-1.png", "caption": "Fig. 1.4: Examples of simple mechanisms including joints", "texts": [], "surrounding_texts": [ "8 1. Introduction", "1.4 Prototype applications of rigid-body mechanisms 9", "10 1. Introduction" ] }, { "image_filename": "designv10_11_0001348_tmrb.2020.3033020-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001348_tmrb.2020.3033020-Figure1-1.png", "caption": "Fig. 1. Conceptual illustration of mobile-coil system with respect to the patient, demonstrating a magnetic microswimmer propels in the urinary system. Visual feedback is expected to be obtained by an eye-in-hand ultrasound probe.", "texts": [ " The conventional approach is to enlarge the workspace by fabricating bulky coils and powering high currents, which has some limitations, such as frequency concerns and cost problems [29], [30]. To break the increase of the control distance with the workspace, the concept of mobile coils was proposed [31]. Several studies have explored the idea of connecting an electromagnet with a serial robotic manipulator [32], [33], however, the problem of multiple coils implementation still exists. Herein, this article reports a system with parallel mobile coils, DeltaMag. A conceptual configuration with respect to the patient is shown in Fig. 1. In addition, the motion control of magnetic microrobots needs to be explored [34]. Owing to the existence of boundary effect and other factors, swimmers often drift from the desired path in open-loop actuation; hence, closed-loop control is widely used to improve tracking performance [35]. For instance, planar closed-loop control of a sperm-shaped microrobot was accomplished under microscopic guidance by Khalil et al. [16]. Xu et al. [36] realized closed-loop 2D path following of magnetic helical swimmers by 3D pose estimation" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000936_j.mechmachtheory.2019.103607-Figure15-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000936_j.mechmachtheory.2019.103607-Figure15-1.png", "caption": "Fig. 15. (a) The numerical contact bands in the pinion, where L 1 , L 2 , and L 3 are the theoretical contact lines, (b) the engagement and tooth-change process of 15 pairs of teeth for the pinion, and the influences of \u201ctooth-change\u201d thresholds on (c) DTE ( \u03b8c \u2212 \u03b8t ) of the pinion center, (d) von Mises stress of point 7 of tooth 1 of the pinion. For clear illustration, the meshing-out (blue dot-dash line) and meshing-in (red dot-dash line) moments are shown in two insets. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)", "texts": [ " 3 (a), the simulation is performed by applying a rotational velocity \u03c9 = \u221210 \u00d7 step (0 , 0 , 0 . 1 , 1) RPM to D of the gear shaft and a resistant torque M = \u2212500 \u00d7 step (0 , 0 , 0 . 1 , 1) Nm to B of the pinion shaft. The acceleration time is 0.1s and total simulation time is t = 3s, which approximately covers the engagement process of 15 teeth. In this example, the nodes of three pairs of tooth-faces are defined as boundary nodes, i.e., tooth-faces 1B, 2B, and 3B of the pinion and tooth-faces 1A, 2A, and 3A of the gear. Fig. 15 (b) shows the engagement and tooth-change process of 15 pairs of teeth for the pinion, where the x -axis is the normalized time t\u0304 = \u03b8( t ) / ( 2 \u03c0/z ) that represents the number of rotation teeth and y -axis is the tooth index. To achieve continuous rotation, the tooth-change process, which will update the tooth-faces in the \u201cpotential contact area\u201d, has to be implemented during each engagement. Therefore, the tooth-change threshold t c , which determines the instants to implement tooth-change process, has to be carefully selected for smooth and accurate dynamics results", " DTE is defined as the difference between the actual position and the theoretical position that the gear would occupy if the gear teeth are considered perfect and rigid, which is an important parameter in the study of gear vibration and noise [12] . According to the theory in Section 2.1.3 , the tooth-change threshold t\u0304 c should be set within (0.1841, 1) for a smooth \u201ctooth-change\u201d as the theoretical contact ratio of the helical gear pair is 2.1841. Therefore, six toothchange thresholds t\u0304 c = 0 . 1 , 0 . 2 , 0 . 3 , 0 . 4 , 0 . 5 , 0 . 6 are chosen to investigate its effect on the smoothness of \u201ctooth-change\u201d process. Fig. 15 (c) shows the DTE ( \u03b8c \u2212 \u03b8t ) of the pinion center, where \u03b8 c and \u03b8 t are the actual and theoretical angular positions of pinion center. It can be seen that the results of t\u0304 c = 0 . 4 , 0 . 5 , 0 . 6 are in very good agreement with each other. In contrast, the sudden non-physical increase of DTE can be observed for t\u0304 c = 0 . 1 , 0 . 2 , 0 . 3 , where the \u201ctooth-change\u201d instants are prior to the meshing-out of the previous tooth. This means that the contact tooth-face pairs are changed to the subsequent three even though the first tooth-face pair is still in contact, and the resulting loss of contact forces gives rise to this sudden increase of DTE. Fig. 15 (d) depicts the time history of von Mises stress in point 7 of tooth 1 of the pinion. It is noticed that the results of von Mises stress are similar to those of the DTE \u00e2 the results of t\u0304 c = 0 . 4 , 0 . 5 , 0 . 6 are almost the same but the sudden non-physical increase can be found for t\u0304 c = 0 . 1 , 0 . 2 , 0 . 3 . Hence, appropriate selection of \u201ctooth-change\u201d instants can eliminate the non-physical phenomenon in the \u201ctooth-change\u201d process. It is also noted that no obvious oscillations are observed for t\u0304 c = 0 . 4 , 0 . 5 , 0 . 6 , which verifies the effectiveness of prediction values of generalized coordinates in our time integration algorithm. It is worth mentioning that the numerical \u201ctooth-change\u201d window is approximately within (0.4, 1), which is different from the theoretical range (0.1841, 1). This phenomenon is caused by the shapes of contact area between meshing gears, which are actually contact bands [60] , not the theoretical contact lines, as shown in Fig. 15 (a). Theoretically, for the sake of simplicity, the contact line assumption is used to derive the contact ratio of any helical gear pair. However, as a matter of fact, the contact lines are actually a series of bands, whose widths are larger than zero. The width of contact bands is determined by the applied torque and contact stiffness between gear pair, which results in the difference of \u201ctooth-change\u201d thresholds between numerical analysis and theory. As illustrated in Fig. 3 (a), the model is the same as the one studied in Section 3" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000225_amm.762.219-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000225_amm.762.219-Figure2-1.png", "caption": "Fig. 2 Cinematic schema of a forging manipulator main mechanism", "texts": [ " Introduction A railbound forging manipulator is presented in the fig. 1. All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, www.ttp.net. (#91177438, University of British Columbia, Kelowna, Canada-09/06/17,00:46:53) The kinematic chain plan (the kinematic diagram) of the main mechanism, which fall within a single plane or in one or more of the other plane parallel to each other, is presented in the fig. 2 [1- 5]. Nomenclature c1 - lifting hydraulic cylinder; c2 - the buffer hydraulic cylinder; c3 - leaning hydraulic cylinder; l1, l2, l3 \u2013 variable lengths; A-L \u2013 linkages; A, B, K, F \u2013 fixed linkages; \u03d51, \u03d53, \u03d56, \u03d58, \u03d510 - variable angles; a-g \u2013 constant lengths; xB, yB, xA, yA, xK, yK, xF, yF \u2013 constant coordinates; \u03b2, \u03b8, \u03d54 \u2013 constant angles; \u03d5 - an angle which must be maintained constant (\u03d5=\u03c0-\u03b8) to keep permanently the segment GM horizontally. Fm1, Fm2, Fm3 \u2013 the driving forces of the mechanism" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000620_s11071-018-4338-3-Figure26-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000620_s11071-018-4338-3-Figure26-1.png", "caption": "Fig. 26 Configuration of the suspension system at the time point of largest deformation. a Leaf spring configuration. b Axle articulation. c Shackle RN coordinate frame. d Different penetrations at the edges", "texts": [ " The vertical upward impact load Fd associated with the unilateral bump is applied on the corresponding central segment of the leaf spring and the other side is applied with Fst to simulate the case of axle articulation when the vehicle passes a bump on one side of the vehicle. The vertical displacement of the center node of the impacted leaf spring is shown in Fig. 25. It can be noted that the largest deformation appears at around t = 0.086 s and the corresponding configuration of the leaf spring is shown in Fig. 26a, while the axle articulation is shown in Fig. 26b. Obvious rotation of the shackle can be seen in Fig. 26c. Due to the twisting of the leaf spring, different penalties at the contact points on the edges can be seen in Fig. 26d. It can be seen from Fig. 25 that while the SSM implementation can still alleviate the locking in the case of the dynamic analysis of axle articulation and produces larger displacement than GCM implementation, it cannot give a solution close to the HOBE42 solution. This is due to the large twisting distortion of the leaf spring associated with the axle articulation loading condition. Because of the linear interpolation in the beam cross-sectional direction, the low-order beam cannot capture the nonlinear distribution of the torsional deformation" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003448_1.1539514-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003448_1.1539514-Figure2-1.png", "caption": "Fig. 2 Static equilibrium on base and moving platform", "texts": [ " This geometrical interpretation is correct in a coordinate system having its origin attached to the moving platform. In this representation each row of the Jacobian matrix is a function of wRpui and the direction numbers of l\u0302i , which are both functions of the moving platform position. 2.1 The Lines of the Jacobian Matrix in World Coordinate System. Consider another representation of the Jacobian matrix in the form: Jb Tt5Fb (5) where Fb5@fb T ,mb T#T represents the wrench exerted by the base rather than the moving platform on the environment, Fig. 2. By using simple statics equations and representing Fb by Fe one obtains: At5BFe (6) where: A5F l\u03021 \u00af l\u03026 b13 l\u03021 \u00af b63 l\u03026 G B5F I 0 @p3# IG (7) I2333 unit matrix bi2position vector of the spherical joint of the ith prismatic actuator at the base in W coordinate system. @p3#2skew-symmetric matrix representing vector multiplication. 34 \u00d5 Vol. 125, MARCH 2003 rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 08/23/20 @p3#5F 0 2pz py pz 0 2px 2py px 0 G (8) Equations ~5! and ~6! yield: JT5B21A (9) Where B21 is given by: B215F I 0 @2p3# IG (10) Contrary to wRpui , which is a varying vector in W, the vector bi is constant in W" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003129_iecon.2000.973184-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003129_iecon.2000.973184-Figure5-1.png", "caption": "Figure 5: Accumulation error and modification of the estimated position", "texts": [ " In Spur, the commands to control the robot move along the straight line, rotation or stop are provided. A central controller called the master module whieh controls of the total motion of the robot, keeps a map of the building and path data. The master module get the estimated position from vehicle control module and sends a vehicle commands based on the present position and path data. An accumulation error exists in the estimated position by the vehicle control module, and it may cause the trouble. (Figure 5-a) To adjust error in the estimated position, the robot use the landmark and map. The robot detects the landmark using its own external sensors, and compares with the landmark model given in the map. so that it recognizes and calculate error position and modifies it. In case when flat walls exist in the robot environment in the building, the robot uses them as the landmark. which is detected by the ultra sonic sensor. (Figure 5-b) For the case in which no sufficient number of walls are existing in the environment. The artificial landmarks are prepared. The non-contact-type ID card (Figure 6) were used as an artificial landmark. which can give the global position information. ID cards are laid under the carpet. (Figure 7) The ultrasonic sensors are also used to detect the obstacles. The bumper and touch sensors can detect the obstacles too. The robot has an environment map, and the information of landmark for positioning" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003422_00207170210156161-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003422_00207170210156161-Figure1-1.png", "caption": "Figure 1. Schematic representation of the two-link planar arm.", "texts": [], "surrounding_texts": [ "the \u00aenal population are further improved by using a local search routine. The estimated global minimizer h \u00a4 for the optimization problem (38) is given by the individual that strictly satisfy all the semi-in\u00aenite constraints and has the best \u00aetness over all the iterated generations. For the problem at hand, this means that the estimated global minimizer satis\u00aees with certainty all the limits imposed on the joint torques and torque derivatives.\nProblem (15) is a di cult one because the constraints (16) and (17) are in general non-linear and non-convex with respect to both arguments t and h and moreover they are of semi-in\u00aenite type, i.e. inequalities must hold for any value of t in the continuous interval \u20300; hi\n\u0160. In the pertinent mathematical literature, problem (15) is characterized as a generalized semi-in\u00aenite problem (see, for example, Reemtsen and Ruckmann 1998) and the known algorithms to solve it can only determine local solutions. It is worth stressing that when a given h 2 B is o ered, checking with certainty its feasibility with respect to constraints (16) and (17) can be solely ascertained by using a deterministic global approach. This explains why, in many cases, using popular optimizers (such as the Matlab optimizer that is based on sequential quadratic programming) for di cult problems, the found `optimal\u2019 solution is not even feasible (i.e. useless from a practical standpoint) and to overcome this \u00afaw many arti\u00aeces (ad hoc discretizations, smoothings, etc.) and repeated trials are necessary to hopefully arrive at an acceptable solution (cf. \u00a7 4.1). On the contrary, the new idea developed with the proposed approach combining a stochastic global optimization technique, speci\u00aecally a genetic algorithm, with a deterministic global method, an interval procedure, provides an estimated global solution that is feasible with certainty.\nRemark 1: The interval procedure computing the penalty terms F\u2026\u00bci k \u2026h\u2020\u2020 and F\u2026~\u00bci k \u2026h\u2020\u2020 uses `inclusion functions\u2019 relative to \u00bd i k \u2026t; h\u2020 and _\u00bd i k \u2026t; h\u2020 respectively (see, for example, Ratschek and Rokne (1988) or Hansen (1992) for the speci\u00aec concept of inclusion function). Hence, it is necessary or appropriate the symbolic computation with respect to the arguments t and h of the torques and their derivatives along each spline segment. On the practical side, this can be e - ciently organized using a recursive code scheme. Starting with the iterative solution of the tridiagonal system (9) we use slack variables for the spline expression (2) and its derivatives (21), (22) and (23) and plug them into the dynamics expressions (12) and (14). To e ectively evaluate these expressions we use the recursive Newton\u00b1Euler formulation (see Sciavicco and Siciliano (2000) that also reports the related computational complexity analysis) for the torque dynamics and the extension of this formulation (deduced with an auto-\nmatic di erentiation approach) for the torque derivative dynamics.\nRemark 2: From a computational complexity viewpoint, problem (15) is NP-hard and any algorithm aiming at \u00aending with certainty the exact global solution with arbitrary prespeci\u00aeed precision (i.e. an overall purely deterministic global method) would su er the so-called curse of dimensionality. Only really trivial problems could be solved by such an algorithm and no signi\u00aecant robotics application, such as those proposed in \u00a7 4, could be addressed. As known, Goldberg (1989), using a genetic algorithm to search on an ndimensional space, such as B in our hybrid approach, alleviates the curse of dimensionality permitting to obtain good estimates of global minimizers even when n is relatively large. A complete description of the proposed genetic/interval algorithm is reported in Guarino Lo Bianco and Piazzi (2001 a). In the same paper, several semi-in\u00aenite test problems are formulated and solved with numerical details.\n4. Examples\nTwo examples are exposed in this section. The \u00aerst one concerns a simple two-link planar arm. It has been mainly proposed to compare the results obtained with the genetic/interval algorithm with those obtained with a standard algorithm for semi-in\u00aenite optimization. The second example takes into account an actual manipulator. The dynamics of a Puma 560 manipulator is used to plan an optimal minimum-time trajectory. The purpose is to demonstrate that the proposed approach can be fruitfully used with non-trivial problems.\n4.1. A planar two-link robot arm\nFor a two-link (m \u02c6 2) planar arm with revolute joints, the task is to plan, under given dynamic constraints (limited torque and torque derivative), a minimum-time trajectory whose possible path is sketched in \u00aegure 1. More precisely, the distal end of the arm has to cross some via points (s \u02c6 10 and n \u02c6 11), given by their cartesian coordinates (see the \u00aerst two columns of table 1). By solving the inverse kinematics these cartesian via points are converted into the joint via points reported in the last two columns of table 1. Note that the second and the penultimate knots have not been imposed, being associated to the two free joint displacements. The joint variable vector is q :\u02c6 \u2030q1 q2\n\u0160T and belongs to the joint-space work envelope Q :\u02c6 \u20300; \u00ba=2\u0160 \u00a3 \u2030\u00a1\u00ba; 0\u0160. Under the hypothesis of masses concentrated at the distal end of each link the following dynamics equations can be derived (Craig 1989, p. 204).\nD ow\nnl oa\nde d\nby [\nU Q\nL ib\nra ry\n] at\n0 0:\n52 0\n8 N\nov em\nbe r\n20 14", "\u00bd1 \u02c6 m2l22\u2026 q1 \u2021 q2 \u2020 \u2021 m2l1l2 cos \u2026q2 \u2020\u20262 q1 \u2021 q2 \u2020\n\u2021 \u2026m1 \u2021 m2 \u2020l21 q1 \u00a1 m2l1l2 sin \u2026q2 \u2020 _q 2 2 \u00a1 2m2l1l2 sin \u2026q2 \u2020 _q1 _q2 \u2021 m2l2g cos \u2026q1 \u2021 q2 \u2020 \u2021 \u2026m1 \u2021 m2 \u2020l1g cos \u2026q1 \u2020\n\u00bd2 \u02c6 m2l1l2 cos \u2026q2 \u2020 q1 \u2021 m2l1l2 sin \u2026q2 \u2020 _q 2 1\n\u2021 m2l2g cos\u2026q1 \u2021 q2 \u2020 \u2021 m2l 2 2 \u2026 q1 \u2021 q2 \u2020\nwhere m1 and m2 are the links masses, g is the gravity acceleration, and l1, l2 are the links lengths. For the example at hand the following values have been adopted: g \u02c6 9:8 m/s 2 , l1 \u02c6 1:0 m, l2 \u02c6 0:5 m, m1\n\u02c6 15:0 kg and m2\n\u02c6 7:0 kg. By direct derivation of the above dynamics equations, the following expressions for the torque derivatives are obtained\n_\u00bd1 \u02c6 m2l 2 2 \u2026 ___q1 \u2021 ___q2 \u2020 \u2021 \u2026m1 \u2021 m2 \u2020l21 ___q1\n\u2021 m2l1l2 cos \u2026q2 \u2020 \u20302 ___q1 \u2021 ___q2 \u00a1 _q 3 2 \u00a1 2 _q 2 2 _q1 \u0160 \u00a1 m2l1l2 sin \u2026q2 \u2020\u20304 q1 _q2 \u2021 2 _q1 q2 \u2021 3 q2 _q2 \u0160 \u00a1 l1g\u2026m1 \u2021 m2 \u2020 sin \u2026q1 \u2020 _q1 \u00a1 m2l2g sin \u2026q1 \u2021 q2 \u2020 \u2026 _q1 \u2021 _q2 \u2020\n_\u00bd2 \u02c6 m2l 2 2 \u2026 ___q1 \u2021 ___q2 \u2020 \u2021 m2l1l2 cos \u2026q2 \u2020\u2030 ___q1 \u2021 _q2 _q 2 1 \u0160\n\u00a1 m2l2g\u2026 _q1 \u2021 _q2 \u2020 sin \u2026q1 \u2021 q2 \u2020 \u2021 m2l1l2 sin \u2026q2 \u2020\u20302 _q1 q1 \u00a1 q1 _q2 \u0160\nThe vector of the interval times that parameterizes the cubic spline trajectory is h :\u02c6 \u2030h1 h2 \u00a2 \u00a2 \u00a2 h11 \u0160T 2 B :\u02c6 \u20300:02; 10:0\u016011 (it has been \u00aexed \u00b8 \u02c6 0:02 s). Consider the arm at rest in the initial and \u00aenal positions (i.e. v 0 \u02c6 v 11 \u02c6 0; a 0 \u02c6 a 11 \u02c6 0) and by virtue of Property 2, problem (15) admits a solution if a > \u2030maxq2Q fg1 \u2026q\u2020g maxq2Q fg2 \u2026q\u2020g\u0160T \u02c6 \u2030249:9 34:3\u0160T Nm\nand b > \u20300 0\u0160T. Then, a minimum-time trajectory planning is sought by \u00aexing a \u02c6 \u2030260 50\u0160T Nm, and b \u02c6 \u2030300 200\u0160T Nm s \u00a11 . The optimization problem is solved by using two di erent algorithms: the genetic/ interval algorithm developed by the authors and the algorithm for semi-in\u00aenite optimization provided by the Matlab Optimization Toolbox (Grace 1994). The results, given by the estimated minimizers, are reported in table 2. A single result is proposed for the genetic/ interval algorithm owing to its capability to converge to an estimated global minimizer (see the \u00aerst column of table 2) whereas three di erent results are shown for the Matlab algorithm. Indeed, the Matlab algorithm for semi-in\u00aenite optimization, as well as almost all the standard algorithms, normally converges to local solutions depending on the chosen starting point h0. De\u00aened h0 :\u02c6 \u2030\u00b2 \u00b2 \u00a2 \u00a2 \u00a2 \u00b2\u0160T, the three solutions found by the Matlab algorithm refer to the following starting points: \u00b2 \u02c6 10 (the far end of B), \u00b2 \u02c6 5 (the middle point of B) and \u00b2 \u02c6 1. The total travelling times for the four cases\nD ow\nnl oa\nde d\nby [\nU Q\nL ib\nra ry\n] at\n0 0:\n52 0\n8 N\nov em\nbe r\n20 14", "are reported in the last row of table 2. The total travelling times obtained with \u00b2 \u02c6 10, \u00b2 \u02c6 5 and \u00b2 \u02c6 1 are respectively 13.3%, 7.8% and 1.0% greater than the corresponding minimum-time obtained by means of the genetic/interval algorithm. Many tries can be experimented by running the Matlab optimizer with other di erent starting points. For example, when \u00b2 is chosen too small, such as \u00b2 \u02c6 0:02, the Matlab algorithm stops by warning that it is unable to \u00aend feasible solutions.\nSome tests have been done to check the actual feasibility of the solutions. The solution found by the genetic/interval algorithm is indeed feasible while all the solutions found by the Matlab algorithm are actually unfeasible. Sometimes the constraints are only slightly violated but sometimes a consistent error is detected. For example, the solution corresponding to \u00b2 \u02c6 1 (see \u00aegure 2) produces a torque derivative minimum on the \u00aerst joint equal to \u00a1316.04 Nm/s, i.e. the constraint violation is equal to a 5.3% excess. What\u2019s going on? Simply the Matlab algorithm evaluates the semi-in\u00aenite constraint functions on a grid of values chosen over the time intervals \u20300; hi \u0160, i \u02c6 1; 2; . . . ; n. The grid thickness is chosen on the basis of heuristic rules. Hence the feasibility of the minimizer is not guaranteed with certainty and, on the contrary, the probability to violate the imposed limits is high when the involved functions are not continuous. This is the case for the torque derivative functions.\nThe optimal torque and torque derivative pro\u00aeles evaluated by the genetic/interval algorithm are plotted in \u00aegure 3. These plots makes evident that, at joint 1, both the torque and torque derivative constraints are active. The resulting path in Cartesian plane is shown in \u00aegure 4 where the crosses denote the assigned via points.\nFigure 2. The `optimal\u2019 derivative pro\u00aele for the \u00aerst joint of the two-link arm evaluated by the Matlab Optimization Toolbox. The semi-in\u00aenite constraint is violated inside the area evidenced by the circle.\nFigure 3. Estimated optimal torque and torque derivative pro\u00aeles found by the genetic/interval algorithm for the two-link arm.\nD ow\nnl oa\nde d\nby [\nU Q\nL ib\nra ry\n] at\n0 0:\n52 0\n8 N\nov em\nbe r\n20 14" ] }, { "image_filename": "designv10_11_0000281_s12206-016-0823-0-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000281_s12206-016-0823-0-Figure4-1.png", "caption": "Fig. 4. A sun-planet gear mesh.", "texts": [ " The model considers the effect of the gravity of each component, the time-varying meshing stiffness and the backlash. The displacements of the sun gear, the planet carrier and the ring gear in the transverse (x) direction, longitudinal (y) direction and torsional (u) direction can be expressed as ( ), , , , l l l x y u l s c r= , respectively. The displacements of each planet gear in the transverse (x) direction, longitudinal (y) direction and torsional (u) direction are expressed as , , i i i x y u . Fig. 4 shows a sun-planet gear mesh, the meshing force between the sun gear and the ring gear and each of the planet gears ( ( ), ijp F j s r= ) can be expressed as i i i ijp jp j jp F k h \u03b4= (19) where ijp k ( ,j s r= ) represents the meshing stiffness between the sun gear and the ring gear and the i th planet gear (as shown in Fig. 4), and ( ) ijp t\u03b4 ( ,j s r= ) represents the relative deformation between the sun gear, the ring gear and the i th planet gear, which can be expressed as (20) where s \u03b1 and r \u03b1 represent the pressure angles of the sun gear and the ring gear, respectively. isp pi s \u03d5 \u03d5 \u03b1= \u2212 and irp pi r \u03d5 \u03d5 \u03b1= + ( pi \u03d5 represents the relative position angle of each planet gear) (as shown in Fig. 4). The ij h represents the operator for determining the gear tooth contact condition, which can expressed as follows ( ) ( ) 1 0 0 0. i i i jp j jp t h t \u03b4 \u03b4 > < = (21) The coupling dynamics model (as shown in Fig. 5) considers the supporting force of the bearings of the planet gears as the nonlinear exciting force of the system. The forces between the carrier, the i th planet and the bearing of the i th planet are shown in Fig. 6. The contact deformation of the bearing of each planet gear can be calculated based on the displacements of the planet gear and the planet carrier", " T c c c r r r s s s N N N x y u x y u x y u x y u x y u= \u22efq (23) ( )g tF is gravity excitation, can be expressed as ( ) [ , ,0, , ,0, , ,0, cx cy sx sy rx ryg g g g g g g t F F F F F F=F 1 1 2 2 , ,0, , ,0, , , ,0] p x p y p x p y p x p yN N g g g g g g F F F F F F\u22ef (24) where ( ) ( ) , ,x y g c g c F m gsin w t c s r F m gcos w t \u2206 \u2206 \u2206 \u2206 = \u2212 \u2206 = = \u2212 (25) ( ) ( ) 1 2 , , ,x y g c N g c F m gsin w t p p p F m gcos w t \u03d5 \u03d5 \u2206 \u2206 \u2206 \u2206 \u2206 \u2206 = \u2212 + \u2206 = = \u2212 + \u22ef (26) where c w represents the rotational speed of the planet carrier and \u03d5\u2206 represents the position angle of the planet gear (Fig. 4). ( )z tF is the excitation force caused by planet bearing, could be expressed as ( ) 1 1 , , ,0,0,0,0,0,0, , ,0, , ,0 z u t F F F F F F F = \u22ef N Ncx cy c px py px py F (27) where , cx cy F F and cu F represent the interactive force between the bearing of each planet gear and the planet carrier, as shown in Fig. 6. Due to the angle ( ip \u03d5 ) between the coordinate axes of each planet gear ( mbi x , mbi y ) and the coordinate axes of the planet carrier ( c x , c y ) (as shown in Fig. 6), , cx cy F F and cu F can be expressed as ( ) ( ) ( ) ( ) 1 1 1 cos sin si " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001563_s00170-021-07221-0-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001563_s00170-021-07221-0-Figure6-1.png", "caption": "Fig. 6 Position angle of balls", "texts": [ " The rotor eddy current loss of the permanent magnet synchronous motor is expressed as Hr \u00bc \u03c1rl\u222cJ 2ds \u00f024\u00de whereHr denotes the eddy current loss of rotor; \u03c1r and l are the resistivity of the rotor material and the axial length of the rotor, respectively; J denotes the induced eddy current density; and s represents the cross-sectional area of the rotor. As a crucial parameter in the thermal network model, the frictional heat generated by the bearing should be considered and calculated accurately. The definition of the position angle for the bearing balls is shown in Fig. 6, and the position of ball and the inner and outer rings before and after loading is illustrated in Fig. 7.Without loss of generality, the curvature center of the bearing outer raceway is assumed to be fixed in this work. Under the action of force F = [Fx, Fy, Fz, Mx, My], the relative displacement \u03b4 (\u03b4 = [\u03b4x, \u03b4y, \u03b4z, \u03b8x, \u03b8y]) in the bearing occurs. In consideration of frictional heat, the thermal displacement u (u = [ua, ur]) in the bearing is generated. At high speed, the centrifugal displacement uc is produced by the bearing" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003388_978-3-662-04831-3-Figure6.2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003388_978-3-662-04831-3-Figure6.2-1.png", "caption": "Fig. 6.2: Gravitational field acting on a body in the ( -eyR) direction", "texts": [ "1 (Characterization offorces and torques): The action of a force on a body is uniquely characterized by the amplitude, direction, and line of action of the force (force arrow). Attachment points of forces arenot needed. The action of a torque on a body is uniquely characterized by the amplitude and direction of the torque ( torque arrow). Lines of action and attachment points of torques are not needed. 6.1.1 Gravitational force (weight) In this context the gravitational field will be assumed to act in the negative eyR direction (Figure 6.2). Then the weight Fwi of a body i is Fwi = -mi \u00b7 g \u00b7 eyR or R ( 0 ) Fw = ' -mi \u00b7g = constant, (6.3a) with g as the gravitational constant. Since the line of action of Fwi meets the center of mass Ci of body i , the force Fwi does not generate a moment with respect to C;; i.e. , M L i -o c iwi = \u00b7 6.1.2 Applied force and moment (6.3b) Consider a force represented by an arrow F i of length Fi through the point P; on body i (Figure 6.3). Then 242 6. Constitutive relations of planar and spatial external forces and torques (6" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000346_j.mechmachtheory.2017.09.013-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000346_j.mechmachtheory.2017.09.013-Figure2-1.png", "caption": "Fig. 2. Constructing process of 5R SLOL.", "texts": [ " In this section, we combine multi Bennett linkages, overlap the links with same parameters, then eliminate the overlapped links, fix part of the coincident joints, and translate the rest coincident joints to the single joints, then a new 5R or 6R kinematic chain is obtained. Using screw theory to analyze the mobility of the kinematic chain, the chain with one DOF is the SLOL, which we want to construct. The detailed process is shown as blow. 3.1. Type synthesis of 5R SLOL Take two Bennett linkages ABCF and C \u2032 F \u2032 ED, which have the following relationship, { a I = a II \u03b1I = \u03b1II (4) where I and II indicate the linkages ABCF and C \u2032 F \u2032 ED. Combine the two Bennett linkages and overlap the link CF and C \u2032 F \u2032 as shown in Fig. 2 , then eliminate the overlapped link CF and C \u2032 F \u2032 , fix the coincident joints F and F \u2032 , translate the coincident joints C and C \u2032 to a single joint, thus the link AF and F \u2032 E become to one rigid link AE, link BC and C \u2032 D are connected by the joint C, we get a single loop kinematic chain ABCDE. In Fig. 2 , solid line indicates the link, cylinder indicates the joint, dashed line indicates the overlapped link. In order to define the DH parameters of the linkages and denote the motion screw of the joint, we use the arrow to indicate the positive direction of the revolute joint. Now we analyze the mobility of the kinematic chain ABCDE by screw theory. As kinematic chain ABCDE is constructed by two Bennett linkages I and II, so we have, $ C = $ C \u2032 , $ F = $ F \u2032 (5) In the two Bennett linkages, we have, { m I ( $ A \u2212 $ C ) = l I ( $ B \u2212 $ F ) m II ( $ C \u2032 \u2212 $ E ) = l II ( $ F \u2032 \u2212 $ D ) (6) where m I , l I , m II , l II denote the length of the diagonal line of linkages I and II", " After the similar construction, we have that, the length between joints A and E is not zero but equals d AE = | b I \u2212 b II | , the offsets of joints A and E equal zero, the twist of new link EA is \u03b1EA = \u03b2II \u2212 \u03b2I . In Fig. 8 , the thick dash line indicates the coincident part of links AF and EF \u2032 . From the above analysis we conclude that the angle K has no effect on the DOF of the linkage. So we can apply the four configurations to the construction process of the 5R SLOL, then we get four configurations of the 5R SLOL. Except for the general form shown in Fig. 2 (c), there are still three special forms of the 5R SLOLs with zero joint offset. As the linkages with zero joint offset have more excellent deployability, we would synthesize the three special forms. Firstly we apply the configuration II to the construction process, and obtain a 5R SLOL ABCDE, we define it as 5R-A form. Then we apply the configurations III and IV to the construction process, and get another two 5R SLOLs. The added constraints of the 5R SLOL are shown in Table 1 , the construction process is shown in Table 2 " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001773_tte.2021.3085367-Figure21-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001773_tte.2021.3085367-Figure21-1.png", "caption": "Fig. 21. The prototype of the investigated HMC-VFMM. (a) Components. (b) Test rig.", "texts": [ " Due to the investigated machine features a triangle flux barrier design in the rotor core, a stress analysis of the rotor structure is necessary. Fig. 20 illustrates the stress distributions of the machine at the speeds of 1500rpm and 10000rpm. It can be seen that the maximum stress occurs at the sharp corner of the triangle flux barrier, and the maximum stresses at 1500rpm and 10000 rpm are 0.38Mpa and 19.42Mpa respectively, which is much lower than the threshold value of 440 MPa. The stator/rotor assemblies of the manufactured prototype are depicted in Fig. 21. Furthermore, in no-load condition, the analytically predicted and experimentally measured back-EMF waveforms are compared in Fig. 22. It demonstrates that the analytically predicted solutions agree well with the experimental results, which confirms the accuracy and effectiveness of the proposed hybrid field analytical method. Fig. 23 compares the output torques of the prototype under different q-axis currents. It can be seen that the proposed method always exhibits slightly higher torque than the FE results when the q-axis currents less than 9A (rated current is 7" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003551_0094-114x(95)00101-4-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003551_0094-114x(95)00101-4-Figure2-1.png", "caption": "Fig. 2. The Standford Arm.", "texts": [ " A comparison between this methodology with those presented in [35] allows a better understanding of the meaning of coefficient Di, D;j, D~j k there presented as the result of mathematical derivation and whose meaning can be explained in term of W, H, L and d matrices. 4. OPEN LOOP EXAMPLE In order to show the practical use of the methodology, let us consider the problem of writing the kinematic and dynamic equations of the Standford Arm, having six degrees of freedom with five revolute joints and one prismatic, whose initial position is drawn in Fig. 2. The kinematics section describes how you can write the position matrices, the relative and absolute velocity and acceleration matrices, while the dynamics section describes how to write the inertia matrix and the dynamic equilibrium. We describe the joint space coordinates by the vector Q .=- [ , .9, , oa2, d3, ~,, ~95, ~96] t. 4. I. Kinematics In this example the reference frames of the links are placed according to Denavit and Hartenberg. Then the matrices that describe the relative position matrices of the links are MO, | Cl 0 - Sl 0 S~ 0 Ci 0 0 - 1 0 0 ", " The absolute position matrix of any link of the robot can be evaluated as usual as Mo, i = M0.1Mi,2\"'\" Mi i.i Matrices L in relative frame have the form PL for prismatic joints and rL for revolute joints as shown in equation (1). Remembering the relation between matrices W, H and L the relative velocity and acceleration matrices between contiguous links with revolute pairs, joints i = 1, 2, 4, 5, 6 in our example, are 0 - q ; 0 ! 0 r c); 0 0 0 w,_,.,._,,= 0 o _o H;_. ld(;_ o - - 0 - - b--i--6-and for the prismatic pair, joint 3 in Fig. 2, are - 0 ~ - q , o o _1 o o o - 0 0 0 0 - 6 . . . . 0 - - 6 . . . . ~ - 0 0 0 0 = 0 0 0 0 W2'3(2) __0 __0 _0 _0_3 0 0 0 0 H2,3(2) 0 0 0 0 0 0 0 0 = 0 0 0 q3 -~) - U - b - - - b - where q; is the ith free coordinate of the joint and ~\u00a2, ~/its time derivatives. To obtain the absolute velocity and acceleration matrices of the links we use the velocity composition rule and the Coriolis theorem, Wo.g(o) = Wo,y ~(o) + Wj_ Ly(o) Ho4(o) = Ho.j_ ,(o) + 2Wo, j_ ~(o)Wj_ ~,j(o) + Hi_ I,Ao) (l 1) in which the relative velocity and acceleration matrices are referred to the absolute frame (0)", " The weight action matrix ~ may be evaluated by means of the gravity acceleration matrix, inertia matrix and the Skew operator by the formula ~ito) = Skew(Hg~o)Jito)). The total action matrix ~o.i on each link can be found starting from the end effector, the only link on which the external force acts (known), calculating the inertial action matrix, summing the total action matrix of the successive link and summing the weight action matrix \u00a2'i = ~ i + \u00a2'i+l + ~i It is very hard to write the dynamic relation of the manipulator in Fig. 2 in symbolic form, so this part is presented only in numeric form in Section 6 which outlines the easy implementation of the presented formulation. 5. C L O S E D L O O P E X A M P L E In this section we present an application of the methodology applied to the closed loop system in Fig. 3, writing the kinematic and dynamic equations. We describe the joint space coordinate by 598 Giovanni Legnani et al. the vector Q = [~tt, a2, ~3, a]. Using the local flame of the fourth link shown in Fig. 3 and letting ci = cos(zti) and si = sin(~J the relative position matrices are: ] V l o , I = cl - s ~ 0 l llc, I sl cj 0 l l js l 1 0 0 1 , 0 " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001070_j.mechmachtheory.2020.104127-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001070_j.mechmachtheory.2020.104127-Figure1-1.png", "caption": "Fig. 1. Revolute clearance joints and flexible bushings in the double wishbone air suspension.", "texts": [ " The DWAS is more common on the bus and heavy-duty truck front suspensions. The suspension consists of the upper control arm (UCA) and lower control arm (LCA) connecting the frame through flexible bushings and to the upright (UP) through revolute joints, which also determine the mechanism articulation. The struts, comprising an air spring and damper are mounted to the upright. During K&C measurements, the knuckle (KN) is restrained by the steering tie rod because the steering wheel was blocked. Fig. 1 shows the schematic structure of the DWAS model where there are three joints with clearances: Upper revolute joint (URJ), lower revolute joint (LRJ) and kingpin revolute joint (KRJ). The DWAS nonlinear multi-body dynamic model is built in ADAMS/VIEW and the subroutines are written by FORTRAN. Experiments for the testing characteristic of the bushing and air spring are conducted with the MTS hydraulic tester. The sub-models (air spring model, bushing model and contact clearance model) are generated by using customized FORTRAN subroutines" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000024_c6sm01781a-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000024_c6sm01781a-Figure9-1.png", "caption": "Figure 9. Sketch of the stick-slip behavior due to the discrete nature of the nature, in stage II of the DN composite under uniaxial tension.", "texts": [ " As a result, the composite will have very limit stretchability even if the mesh could fragment into a number of islands. The role of interlayer sliding in the DN composite is similar to that of the pullout of the 2nd network from the damaged 1st network in a DN gel.27 Accompanied by the damage evolution in stage II, a DN composite should experience some stick-slip-like events, each of which corresponds to a drop in stress due to the rupture of one mesh island, followed by an increase due to the sliding and reloading of the tape layer under the cracked region, as shown by the schematic stress-stretch curve on Fig. 9. The peak stress is obviously bounded by peaks , and the discrete increment in the overall stretch is associated with the length of sliding sL related to the overall size of the sample D : DLss 2 , where s is the average stretch in the tape at the sliding zones (A, B, D). Given that the resultant force transferred by a sliding zone is *f , we can obtain the approximate scaling law for the average stretch Hfs * , with being a numerical factor. In reality, the damping caused by the viscoelasticity of the tape or the interlayer adhesion will smooth out the stick-slip events and result in a plateau of almost constant stress. The plateau stress plateaus can be estimated from an energy perspective, e.g. by achieving the same area below the stress-stretch curve, as sketched in Fig. 9. Neglecting the stiffness change caused by the mesh fracture, we A mesh island (1st) Continuous Tape (2nd) A B C D Sliding Figure 8. Sketch illustrating the interaction between the mesh and the tape. The membrane force/stress distribution in the mesh and tap e layers. The mesh acts like the 1st network in a DN gel, while the tape acts like the 2nd network. Page 6 of 8Soft Matter S of tM at te r A cc ep te d M an us cr ip t Pu bl is he d on 2 3 Se pt em be r 20 16 . D ow nl oa de d by U ni ve rs ity o f C al if or ni a - Sa n D ie go o n 27 /0 9/ 20 16 0 7: 53 :5 0", " A lower sliding stress corresponds to a larger sliding zone, and thus a lower plateau stress plateaus as given approximately by Eq. (4). On the other hand, if the sliding stress is high, although a higher plateau stress can be reached, the ultimate overall stretch is reduced. Therefore, an intermediate interlayer sliding stress is preferred for the DN composite to achieve optimal toughness. Here, we take the values measured from independent experiments done over the mesh and tape individually: -1Nm 1170k , -1* Nm 420f , and kPa 38 , and plot the peak and plateau stresses given by Eqs. (2) and (4) in Fig. 9. The unknown ratio DLs , together with the numerical factor , is taken to be a fitting parameter for the plateau stress. It is found that when the value 01.0DLs is taken, the plateau stress predicted by theory matches well with that measured, as shown by Fig. 10. In stage III, as all mesh islands are smaller than sL2 , the maximum membrane force in the mesh is always lower than f . Therefore, no further damage will take place in the mesh layer, and the deformation is manifested by the interlayer sliding and the stretching of the tape layers" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001228_tvt.2020.3041336-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001228_tvt.2020.3041336-Figure1-1.png", "caption": "Fig. 1. Structure of the FSCW-IPM motor.", "texts": [ " Despite the rotor along with stator slot-opening optimization that helps reduce torque ripple and radial force [24], the reduced radial force and vibration sources are not described in detail while the average torque is not discussed. In this paper, a single-layer FSCW-IPM motor with unequal W Authorized licensed use limited to: Cape Peninsula University of Technology. Downloaded on December 18,2020 at 15:42:30 UTC from IEEE Xplore. Restrictions apply. 0018-9545 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. width stator teeth is analyzed. Its cross-section is shown in Fig. 1 and the specification parameters are presented in Table I. As the motor has 20 slots and 18 poles, the lowest non-zero order spatial harmonic of electromagnetic force is 2. The generation of low-order radial force can be determined by the combination of slot and pole [25] and explained modulation of stator slot [26]. Since vibration magnitude of the motor is inversely proportional to the 4th power of the spatial order of radial force [13], [27], [28], the 2nd order spatial harmonic serves as the main parameter for the vibration optimization", " Due to the symmetry of rotor structure, there are two basic types of auxiliary slots on the rotor, namely notching on q-axis and d-axis, respectively. The auxiliary slot parameters are shown in Fig. 5 (a): they are auxiliary slot depths c1, c2, and 1/2 widths r1, r2 on q-axis and d-axis. To enhance fault tolerant capability and reduce cogging torque of FSCW-IPM motor, the unequal stator tooth width structure with single-layer concentrated winding are adopted. The armature-teeth are winding-wound teeth, while fault-tolerant teeth are winding-free teeth, as shown in Fig. 1. Therefore, there are two basic types of auxiliary slots on the stator, namely notching on armature-teeth and fault-tolerant teeth, as shown in Fig. 5 (b). The parameters c3, c4, r3, and r4 represent depths and 1/2 widths of auxiliary slots on fault-tolerant-teeth and armature-teeth, respectively. To simplify the presentation of auxiliary slots, auxiliary slots on q-axis and d-axis are abbreviated as Rq and Rd, respectively. Auxiliary slots on the armature teeth and fault-tolerant teeth are abbreviated as SA and SF respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001059_j.mechmachtheory.2020.104101-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001059_j.mechmachtheory.2020.104101-Figure3-1.png", "caption": "Fig. 3. A crossed 4-bar knee joint - Kin-Com [23] .", "texts": [ " This research activity proves that the knee joint\u2019s complex motion is currently known to be important aspect of biomechanics. Moreover, there are several solutions of mechanisms in orthotic devices that are capable of closely imitating the knee joint\u2019s movement with quite good accuracy, as is the case in [23] . The above-mentioned knee joint devices may be classified into two categories with regards to the criteria of their functionality. The first group includes devices that are adjustable and intended for individuals who satisfy a determined range of anatomical conditions. An example is Kin-Com ( Fig. 3 ), where a crossed 4-bar mechanism, constituting a polycentric hinge, is used to closely follow the knee\u2019s ICR trajectory. It also enables a ROM of 135 \u00b0, which is comparable with a natural human knee joint [23] . Another example is a mechanism of a biomimetic 4-bar linkage knee in a knee-ankle-foot orthosis [24] . A similar mechanism is the polycentric artificial knee joint, known as HUMA, which is based on a 4-bar mechanism as a part of a lower limb exoskeleton for weight-bearing assistance ( Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001070_j.mechmachtheory.2020.104127-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001070_j.mechmachtheory.2020.104127-Figure6-1.png", "caption": "Fig. 6. DWAS model: (a) Flexible model of the DWAS, and (b) first order natural shapes of suspension supporting components.", "texts": [ " The dynamic correction coefficient \u03bcd is given by \u03bcd = \u23a7 \u23a8 \u23a9 0 , | v t | \u2264 v s | v t | \u2212v s v d \u2212v s , v s < | v t | < v d 1 , | v t | \u2265 v d (25) where v s and v d are given tolerances (bounds) for the relative tangential velocity at the contact point of the surfaces. In the DWAS model, the UCA, LCA, UP and KN are modeled with finite elements to consider flexibility. The meshes of the 3D CAD models are generated in HYPERMESH. The flexible model of DWAS is created through inserting the MNF files from HYPERMESH for flexible components into ADAMS, as shown in Fig. 6 (a). The suspension supporting components material is structural alloy steel with Young\u2019s modulus 206GPa, Poisson\u2019s ratio 0.32 and Density 7.9g/cm 3 . A free modal analysis of the structure is performed by means of FEM. The first order natural modal shapes of the suspension supporting components are shown in Fig. 6 (b). The first three natural frequencies of supporting components are shown in Fig. 7 . Results show that the lowest natural frequency is for the LCA, while the highest value is for the SP. The model parameters A e , V, F b , F g , x 2 are identified on the basis of bench tests for the air spring and bushing components. The air spring and bushing experiment were carried out as shown in Figs. 8 and 11 . For the air spring component, the elastic stiffness K e can be obtained through Eqs. (5), the air spring effective area A e and volume V need to be identified" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000992_j.jmbbm.2020.103733-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000992_j.jmbbm.2020.103733-Figure1-1.png", "caption": "Fig. 1. (a) Shape and geometrical parameters of a four-arm cruciform biaxial test specimen, (b) the initial shape prior to biaxial elongation with square gage zone area, and (c) the deformed shape of gage zone during biaxial elongation testing for the solid specimens.", "texts": [ " Journal of the Mechanical Behavior of Biomedical Materials 107 (2020) 103733 measurements, material constants, and FEA validations as well as summarizes the effects of silicone AM process parameters on the silicone AM material stress-strain curves. The room-temperature-vulcanizing (RTV) silicone (737 Neutral Cure Sealant by Dow Corning\u2122, Midland, Michigan) was the material selected in this study. This silicone has a high viscosity of 45 Pa\u22c5s at 27 \ufffdC and a tack-free time of 14 min to maintain the shape during extrusionbased AM (Plott and Shih, 2017). After curing, the maximum elongation is over 300% with a tensile strength of 1,206 kPa and a Shore A hardness of 33 (Dow Corning Corporation, 2016). As shown in Fig. 1a, the cruciform specimen has four arms, four clamped zones, one square gage zone in the middle. This shape was proposed by Bell et al. (2012) to allow for large deformation in the gage zone while minimizing the deformation at four arms of the specimen during the biaxial test. The xy coordinate system is centered at the centroid of the gage zone. The specimen will be clamped in the four clamped zones with the width A and depth D. The distance of the clamp edge is B. The overall length of the specimen is Lt and the initial unclamped region length is Li \u00f0 \u00bc Lt 2D\u00de, also illustrated in Fig. 1a. The length of the square gage zone is G \u00bcW\u00fe 2r r ffiffiffi 2 p , where W is the narrowest width of the arm and r is the fillet radius. In this study, A \u00bc 50 mm, D \u00bc 13.5 mm, B \u00bc 5 mm, Lt \u00bc 87 mm, and Li \u00bc 60 mm. The W and r are determined by the shape selection method described in Appendix B. The clamp jaws are 55 mm wide (allowing 2.5 mm on each side for the expansion of the specimen during clamping) and 16.2 mm deep (allowing 2.7 mm for the expansion of the specimen during biaxial testing). The experimental setup for AM of four cruciform specimens (TAZ 5 by Lulzbot, Loveland, Colorado) is shown in Fig", " Three specimens are fabricated for each set of solid and porous specimens for the biaxial test. The total number of specimens and biaxial tests is 24. The biaxial test apparatus, as shown in Fig. 4, consists of four linear actuators, marked as L1, L2, L3, and L4 (Model HS-02 by Dynamic Solution\u2122, Irvine, California) with L1 and L3 on the x-axis and L2 and L4 on the y-axis. The maximum displacement of the actuator was 60 mm. Clamps affixed to the linear actuators were used to hold the clamp zones (Fig. 1) of the specimen. Four linear actuators moved synchronously in opposing directions to pull four arms of the specimen at a slow, 2 mm/ min speed to minimize the viscoelastic effect for the quasi-static deformation (Sasso et al., 2008). The synchronous movement of four linear actuators ensures the center of the specimen remains almost stationary during the biaxial test. The gage zone, the region of interest of the specimen (Esc\ufffdarpita et al., 2009), was examined by a digital camera for strain measurement", "8 mm2 for specimens with \u03b8R of 0\ufffd\u201390\ufffd and 0\ufffd\u201330\ufffd, respectively. The effects of \u03b8R (0\ufffd\u201390\ufffd and 0\ufffd\u201330\ufffd) on the porous specimen stress-strain curve will be presented in Section 6.8. Fig. 8 shows the deformation of the specimen (TS \u00bc 0.6 mm and \u03b8R \u00bc \ufffd45\ufffd) and distribution of the Green-Lagrangian strains, \u03b5L xx and \u03b5L xy, in the gage zone based on the DIC process, described in Section 3.2, during biaxial testing with d from 0 to 38 mm (\u03bbC x \u00bc 2 is expected at d \u00bc 38 mm). The gage zone was expanded from a square (Fig. 1b) to a circular shape (Fig. 1c) due to non-uniform strain distribution in the arm of the specimen. At the maximum displacement (d \u00bc 38 mm), the specimen had the largest deformation, as shown in Fig. 8d. The maximum \u03b5L xx (\u00bc 2.08) was located on both ends of the x-axis in the deformed gage zone. The difference between the maximum and center \u03b5L xx in the gage zone varied from 25% to 40% depending on d. The maximum \u03b5L xy at any given displacement was located at the four corners of the gage zone. The center of the deformed gage zone had \u03b5L xx of 1", "1 Specimen Shape Selection Method Since there is no ASTM or ISO standard for the shape of a cruciform specimen for the biaxial test, the specimen shape needs to be determined. There are four key prior studies on the shape of the cruciform specimen (Duncan et al., 1999; Hamdi et al., 2006; Seibert et al., 2014; Shim et al., 2004). Seibert et al. (2014) proposed that the specimen shape should maximize the uniformity of the specimen strain. Duncan et al. (1999) found slippage at the clamps during testing must be minimized as it could produce an incorrect strain measurement. In this section, the cruciform specimen shape is determined by selecting W and r (shown in Fig. 1) with: 1) uniformly distributed strain and 2) the maximum principal stretch ratio below the failure stretch ratio. The uniformity of the strain distribution in the gage zone was evaluated using the degree of efficiency, \u03b7, which is defined as the ratio between the stretch ratio in the x-direction at the centroid, \u03bbC x , to the stretch ratio in the x-direction at the narrowest width of the specimen arm, \u03bbW x (Seibert et al., K.B. Putra et al. Journal of the Mechanical Behavior of Biomedical Materials 107 (2020) 103733 2014): \u03b7\u00bc \u03bbC x \u03bbW x (B", " Since the silicone AM material can elongate more than 300% (Plott and Shih, 2017), \u03bbUTS was set to about 4. During biaxial testing, \u03bbMax can be located at either the fillets or the arms of the specimen where the principal stretch ratio of the specimen is the highest. The upper and lower bounds of W and r were identified for the specimen shape selection. The lower bound of W was 5 mm to allow at least 5 by 5 mm gage zone area for the DIC measurement (based on a study by Bell et al. (2012)). The upper bound of W was 50 mm which is the width of the clamp zone, the A shown in Fig. 1. The lower bound of r was 1 mm to avoid material buildup at the corner of the specimen due to over extrusion during the AM process (Plott and Shih, 2017). The upper bound of r was 5 mm since r needs to be smaller or equal to the distance of the clamp edges (B in Fig. 1) to avoid unclamped material in the clamp zone when W is at the upper limit. An iterative design process was implemented to generate specimen shapes. This process starts with the smallest W (5 mm) and r (1 mm) to minimize the clamp forces (reducing slippage caused by thinning at the clamped region (Shim et al., 2004). FEA is used to identify the location and magnitude of \u03bbMax the specimen during biaxial testing. The boundary condition described in Section 4 and the Yeoh material model described in Appendix A will be utilized for the FEA" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000806_s12666-019-01785-y-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000806_s12666-019-01785-y-Figure7-1.png", "caption": "Fig. 7 X-component of stress: a at the beginning of simulation and b at simulation time of 0.009375 s", "texts": [ " Besides, stress in the Z-direction is much higher than X- and Y-direction stresses. This is due to the TGM explained above which leads to the expansion along the direction of heat source (Z-direction). The temperature gradient in build direction of the powder layer is much higher than the gradients in the width and length directions, as heat transfer in build direction is restricted by the low thermal conductivity of the powder layers. This higher temperature gradient results in a higher level of residual stress in the Z-direction. Figure 7 shows the X-component of stress contour for the model with 800 mm/s scan speed and 400 W laser power at the simulation times of 0 and 0.009375 s, when laser goes to the centre of the first track. It can be observed that the tensile stress is usually surrounded by a large compressive stress. It can be explained by TGM that the area with the high temperature has the tensile stress to generate an expansion, while the adjacent cool material has the compressive stress to constrain this expansion. Further, at the beginning of the heating, the surrounded unheated powder and the environment have a relatively low temperature which causes a large temperature gradient at the start point [9]" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000390_asjc.1817-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000390_asjc.1817-Figure2-1.png", "caption": "Fig. 2. The PVTOL aircraft in the presence of crosswind. [Color figure can be viewed at wileyonlinelibrary.com]", "texts": [ " The terms J and L are the inertia and the distance from the rotor to the center of mass,respectively. The terms \u00a9 2018 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd f1T = f1 + fw1 and f2T = f2 + fw2 represent the forces applied to PVTOL, where f1 and f2 are the trust produced by the rotors and fw1 and fw2 correspond to the crosswind forces. The parameter \ud835\udf00 defines the coupling between the rolling moment and the lateral acceleration. In general, this parameter is very small, not well-known, and frequently neglected. Fig. 2 depicts a schematic of the PVTOL aircraft. To simplify the forthcoming developments, we introduce the following transformations x = X g y = Y g u1 = f1T +f2T mg u2 = (f1T \u2212f2T )L J w1 = fw1 +fw2 mg w2 = L(fw1 \u2212fw2 ) Jg . Assuming \ud835\udf00 = 0, the model (1) can be rewritten as x\u0308 = \u2212 sin(\ud835\udf03)(u1 + w1); y\u0308 = cos(\ud835\udf03)(u1 + w1) \u2212 1; ?\u0308? = u2 + w2. (2) It is worth noting that neglecting the crosswind effect in the above model leads to the same model considered in [45]. The control problem for the PVTOL aircraft under crosswind is defined as follows Control Problem: Let the PVTOL model (2) under crosswind effects" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001465_s42235-021-0063-6-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001465_s42235-021-0063-6-Figure9-1.png", "caption": "Fig. 9 Effect of the surface and the conical shape of conical helixes. (a) The generation of the lateral force: the resistance near the surface is more significant than that far away from the surface, resulting in a lateral force. The shape of the conical helix leads to the uneven distribution of lateral forces, generating a torque, which converts part of the lateral force into forwarding propulsion in head-forward swimming (b) and makes part of the screw propulsion contribute to drift in tail-forward swimming (c).", "texts": [ " This might be related to the low Reynolds number environment[26], where the role of time becomes negligible, and reciprocal motion results in little net movement. Therefore, the velocities in the two swimming directions are almost the same. When swimming near a surface, the conical helix exhibited a unique behavior with a smaller drift in head-forward swimming. Xin et al. also reported this phenomenon[40]. This is likely to be related to the surface effect and the unique conical shape. As shown in Fig. 9a, when the helix rotates, the resistance near the surface is more significant than that far away from the surface, resulting in a lateral force perpendicular to the helix axis and parallel to the surface. This caused the drift of straight helixes[41]. However, for a conical helix, the larger diameter of the tail produces a greater lateral force than the head. This creates a torque that makes the axis of the conical helix oblique. During the head-forward movement, the helix is inclined at a negative deviation angle by the torque (Fig. 9b). Part of the lateral force is converted into forwarding propulsion. In contrast, when moving in the opposite direction, the torque inclines the helix at a positive angle, makes the part of the propulsion contribute to drift (Fig. 9c). For conical helixes, the smaller drift in near-wall swimming along their sharp end is conducive to their precise locomotion control[40]. Their unique conical shape may make them have the potential to perform special tasks, such as large taper angle conical helixes for holding and transporting cargo, conical helixes with a sharp end for drilling through tissues, etc. In this study, we proposed a new method for fabricating and programming shape memory helical microswimmers based on polylactic acid to realize the incorporation of SMPs in helical microswimmers" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000820_tec.2019.2941935-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000820_tec.2019.2941935-Figure2-1.png", "caption": "Fig. 2. Machine regions and non-overlapping winding configurations", "texts": [ " In this method, the motor cross section is divided into an appropriate number of sub-regions. TABLE I PARAMETERS OF THE CASE STUDY Parameters Unit Symbols Values Bottom slot radius (mm) \ud835\udc45\ud835\udc60\ud835\udc59 18 Slot opening radius (mm) \ud835\udc45\ud835\udc60\ud835\udc5c 29 Stator radius (mm) \ud835\udc45\ud835\udc60 31 Magnet radius (mm) \ud835\udc45\ud835\udc5a 32 Rotor back iron radius (mm) \ud835\udc45\ud835\udc5f 38 Motor axial length (mm) \ud835\udc59\ud835\udc60 100 Slots angle (rad) \ud835\udeff 0.42 Slot opening angle (rad) \ud835\udefd 0.21 Magnet arc to pole pitch ratio \ud835\udefc\ud835\udc5d 0.85 Iron rotor groove arc per pole pitch ratio \ud835\udefc\ud835\udc5f 0.85 Number of coil turns \ud835\udc41\ud835\udc61 62 PMs relative permeability \ud835\udf07\ud835\udc5f \ud835\udc43\ud835\udc40 1.05 PM remanent flux density (T) \ud835\udc35\ud835\udc5f\ud835\udc52\ud835\udc5a 1 Fig. 2 illustrates these sub-regions indexed sl, so, a and m denoting slot, slot-openings, air-gap and magnets, respectively. Table I lists the parameters of the case study. Two types of non-overlapping windings are applied in the proposed outer-rotor motor. Since the permeability of cores is considered infinite, the number of sub-domains with nonoverlapping winding alternate winding teeth is equal to 2Q+p+1 (p sub-regions for PMs, Q sub-regions for slots, Q sub-regions for slot openings and 1 sub-region for air-gap) where p is the number of PMs and Q is the number of stator slots" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001079_j.apor.2020.102404-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001079_j.apor.2020.102404-Figure1-1.png", "caption": "Fig. 1. Surface vessel motion coordinate frames.", "texts": [ " This composite hierarchical anti-disturbance control structure provides computational efficiency and is conducive to practical applications. The remainder is structured as follows. Section 2 presents the vessel motion mathematical modelling. Section 3 details the DP composite hierarchical control design. Section 4 provides simulations and comparisons. Section 5 gathers concluding remarks and future work. To describe the surface vessel\u2019s motions, the north-east frame OX0Y0Z0 and the vessel-fixed frame AXYZ are illustrated in Fig. 1. Both the X0Y0 and XY planes are parallel to the water surface. The north-east frame OX0Y0Z0 denotes an inertial coordinate frame. The north-east frame\u2019s origin O is set as the vessel reference point. The axis OX0 directs to the north, the axis OY0 directs to the east, and the axis OZ0 points towards the earth center. The vessel-fixed frame AXYZ fixes to the moving surface vessel. The vessel-fixed frame\u2019s origin A is located at the vessel centreline in a distance from the vessel gravity center. The axis AX directs from the aft to the fore, the axis AY directs to the starboard as well as the axis AZ directs from the top to the bottom" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000030_rcs.1786-Figure15-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000030_rcs.1786-Figure15-1.png", "caption": "FIGURE 15 The 3D modeling of Blocker 1 and Blocker 2 (on the left) and Pinning (on the right)", "texts": [ " Figure 14 shows the implementation of our operating theater with its different robotic arms, the patient\u2019s limb modeling and the surgical bed. The mechanisms used in our operating theater are B\u2010BROS1, B\u2010BROS2 and P\u2010BROS. They are all ABB\u2019s IRB 120 robots.65,66 \u2018Blocker 1\u2019 is the tool used to block the patient\u2019s limb at the humerus and lately unblock it according to coordinates computed by the blocking module. To reduce the fracture and block the limb at forearm, \u2018Blocker 2\u2019 is used according to coordinates received from the reduction module. Blocker 1 and Blocker 2 have the same 3D modeling illustrated in Figure 15. \u2018Pinning\u2019, as its name suggests, is the tool used to perform pinning at the patient\u2019s elbow according coordinates computed by the pinning module. Its 3D modeling is also shown in Figure 15. To simulate the progress of the surgery on the patient\u2019s limb, we model the latter as illustrated in Figure 16. It is modelled by a mechanism that rotates about the X axis (in red). B\u2010BROS1 module describes the behavior of the robotic arm B\u2010BROS1 and how it blocks the patient\u2019s limb at the humerus and unblocks it once the surgery is completed. Thus, this module features two procedures: (i) B_BROS1_humerusBlock (): it blocks the arm at a distance of y + 100 mm where y is the coordinate on Y axis of the intersection point of the humeral palette and its median" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003774_j.na.2005.05.028-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003774_j.na.2005.05.028-Figure2-1.png", "caption": "Fig. 2. The behavior of the vector fields onM0 for u= 0.", "texts": [ " (37) We have Mu = {(x1, x2) \u2208 R2/x1 = \u2212x32} (38) The two systems (36) and (37) are transverse to Mu except on the common singularity (0, 0). At the points solution to the following equations: { x1 = \u2212x32 , x2(1 \u2212 3x42 + 3x2u)= 0. (39) The dynamics of the two subsystems are tangent toMu, the vector fields of the two subsystems at these points have two nonnull components along the axis x1 and x2 and therefore, the discrete state is observable. For example foru=0 these points are givenbyp1= ( \u2212 1 33/4 , 1 31/4 ) and p2 = ( 1 33/4 ,\u2212 1 31/4 ) ; the vector fields of subsystems 1 and 2 are tangent to M0 (see Fig. 2). Therefore, the discrete state is observable for any switch function. In this section,we give a linear example in order to illustrate our algebraic and geometrical methods. Let us consider the mechanical system described in Fig. 3. The linear hybrid model of the plant under investigation is as follows: for z2(t) 0: m1z\u03081 = \u2212 1z1 + 2(z2 \u2212 z1)+ 1(z\u03072 \u2212 z\u03071)+ u and m2z\u03082 = \u2212 2(z2 \u2212 z1)\u2212 1(z\u03072 \u2212 z\u03071) (40) for z2(t)> 0: m1z\u03081 = \u2212 1z1 + 2(z2 \u2212 z1)+ 1(z\u03072 \u2212 z\u03071)+ u and m2z\u03082 = \u2212 2(z2 \u2212 z1)\u2212 1(z\u03072 \u2212 z\u03071)\u2212 2z\u03072" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001464_j.jsv.2021.116360-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001464_j.jsv.2021.116360-Figure4-1.png", "caption": "Fig. 4. The FEM analysis of simulated gearbox: (a) geometric model of two-stage gear transmission system, (b) mesh stiffness of gear pair, (c) theoretical frequency spectra of all bearing dynamic forces, (d) constructed vibration signals on two measuring points.", "texts": [ " The gear mesh stiffness is different for different positions of gears in a mesh cycle. Hence, both gears are rotated parametrically to compute the variation of gear mesh stiffness in a mesh cycle. Since bearings are used to support the rotors, the modeling of bearing is achieved by getting the equivalent constants of stiffness kb and damping cb. Dynamic modeling of the whole gear transmission system is shown in Fig. 3. Based on the above dynamic modeling method, the three-dimensional geometry of two-stage gear transmission system is shown as Fig. 4(a). All shafts have the same dimensional parameters with cross sectional diameter of 40 mm and length of 600 mm, and have the same material characteristic of structural steel. They are supported by bearings. All bearings are assumed to be isotropic and have constant equivalent stiffness of 107N \u22c5 m\u2212 1 [33]. The equivalent damping of bearings and mesh damping of gears are ignored. All gears are assumed to be rigid, and their meshing characteristics are expressed by calculating the periodically time-varying mesh stiffness, as shown in Fig. 4(b). A constant load torque of 20N \u22c5 m is applied to the driven shaft. Table 1 provides detailed parameters. The generalized alpha method is used to solve time-dependent problems, and different bearing dynamic force components can be obtained by extracting the response of the corresponding shaft end center. In this case, twelve theoretical bearing dynamic forces of six bearings (considering x and z components in each bearing) can be calculated as shown in Fig. 4(c). The frequency components mainly include shaft frequencies, side-band frequencies generated by modulation between the shafts and two gear pairs, and subharmonic frequencies generated by the nonlinearity contained in the model. The process of impact vibration being transmitted to the housing through the bearings approximately follows the linear relationship [34], therefore the dynamic responses of gearbox can be reconstructed by simultaneously applying all of the calculated bearing dynamic forces to corresponding positions of the housing as shown in Fig. 4 (d). It can be found that vibration response signals of the measuring points contain all components of the bearing dynamic forces, and also contains other components such as housing X. Yu et al. Journal of Sound and Vibration 511 (2021) 116360 modal frequencies. Affected by structure transfer paths of the housing, the amplitude of each signal component has been changed significantly. In order to verify the effectiveness of bearing dynamic force identification, the structure transfer function matrix shown in Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003805_881587-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003805_881587-Figure2-1.png", "caption": "Figure 2. CFR-48 Engine Build Schematic", "texts": [ " Use of the lexan sleeve precluded firing of the engine and operation at higher speeds. Additional characteristics of the engine are listed In Table 1. The cylinder sleeve was lubricated via two air-assisted nozzles which spray Bore Stroke Piston Displacement Compression Ratio Cylinder Wall Thickness Piston Ring Pack Lubricant 10.16 cm 10.06 cm 0.82 1 4.5:1 1.90 cm GM 10012045 GM 10012809 (A) 15W-40 881587 3 the oE and air mixture directly on the sleeve; the engine build and lubrication method are shown in Figure 2. The optics were installed in the horizontal plane 5.5 cm below the top of the piston Cat TDC), with the incident beam normal to the major-thrust face of the cylinder. The height of the illuminated position on the cylinder determines the crank, angle position at which the piston and rings cross the laser beam. These positions are required for interpretation of recorded data, and their use will become apparent in the section discussing calibration methods. face of the cylinder wall is illuminated" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001441_tmag.2021.3081186-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001441_tmag.2021.3081186-Figure3-1.png", "caption": "Fig. 3. d/q-axis magnetic flux path of the proposed motor.", "texts": [ " BV-04 2 The explosive view of the AFPM machine investigated in the paper with 48-slot/8-pole is shown in Fig. 2 (a), which belongs to the axial-flux topology with single-stator doublerotor, and the prototype is shown in Fig. 2 (b). The rotor uses segmented skewing PMs, which can effectively mitigate the cogging torque, suppress the torque ripple of the machine [9]. In addition, by introducing the SMC cover on the surface of PMs, the eddy current loss is effectively reduced, and the reluctance torque is improved. Fig. 3 shows d/q-axis magnetic flux path of the proposed motor. The d-axis magnetic flux path passes through SMC cover, PMs, stator and rotor, while the q-axis magnetic flux path is formed by crossing the stator and rotor. There is also another machine. ( PMF \u2014magnetomotive force of PM, PMR \u2014equivalent magnetic reluctance of PM pole, SR \u2014magnetic reluctance of stator, RYR \u2014magnetic reluctance of rotor yoke, SMCR \u2014magnetic reluctance of the SMC cover, airgapR \u2014the magnetic reluctance of air-gap.) Authorized licensed use limited to: UNIVERSITY OF WESTERN ONTARIO" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003511_s0094-114x(00)00024-0-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003511_s0094-114x(00)00024-0-Figure4-1.png", "caption": "Fig. 4. Coordinate systems among the worm, worm gear and oversize hob cutter.", "texts": [ " Therefore, the surface and normal vector equations of the oversize hob cutter can be obtained by replacing the subscripts 1 with o in Eqs. (4) and (8). As mentioned therein before, in order to produce a point-contact worm gear set, the worm gear is usually cut by an oversize worm-type hob cutter. The mathematical model of the worm gear can be obtained by considering the locus of the oversize hob cutter together with the equation of meshing between the oversize hob cutter and worm gear. The cutting/meshing mechanism of a worm gear set is shown in Fig. 4. The coordinate system, S1 X1; Y1; Z1 is associated with the worm, So Xo; Yo;Zo is associated with the oversize hob cutter and S2 X2; Y2;Z2 is associated with the worm gear; and the \u00aexed coordinate systems Sw Xw; Yw; Zw ; Sh Xh; Yh; Zh and Sg Xg; Yg; Zg are the reference coordinate systems for the worm, oversize hob cutter and worm gear, respectively. Axes Z1; Zo and Z2 are the rotation axes of the worm, oversize hob cutter and worm gear, respectively. Parameters c and c1, measured from Z2-axis to Zh-axis and Zw-axis, are crossed settingangles of the oversize hob cutter and worm, respectively. Parameters S and SN are the shortest center-distances measured from the rotation axis of the worm gear to that of the oversize hob cutter and worm, respectively. The shortest center-distance can be expressed by equations: S ro r2; and SN r1 r2; 9 where ro; r1 and r2 are the pitch radii of the oversize hob cutter, worm and worm gear, respectively. Rotation angles / and /g, as shown in Fig. 4(b) and (c), are associated with the rotation angles of the oversize hob cutter and worm gear, respectively, during the cutting process. Rotation angles /1 and /2, shown in Fig. 4(d) and (e), are associated with the rotation angles of the worm and worm gear, respectively, during the meshing process. Since the oversize hob cutter and the produced worm gear remain in conjugation motion during the cutting process, rotation angles / and /g can be related by the equation /g Nh Ng /; 10 where Ng and Nh are the tooth numbers of the worm gear and oversize hob cutter, respectively. The locus of the oversize hob cutter represented in coordinate system S2 can be obtained by applying the homogeneous coordinate transformation matrix equation R2 M2o Ro ; 11 where R2 and Ro are the locus equations of the oversize hob cutters represented in coordinate systems S2 and So, respectively", " (18), the closed-form equation of meshing between the oversize hob cutter and the worm gear can be expressed as follows: lo 1 2 a \u00ff b b2 \u00ff 4 a c p ; 20 where a a1 sin / \u00ff uo a2 cos / \u00ff uo ; b b1uo b2 sin / \u00ff uo b3uo b4 cos / \u00ff uo b5; c c1uo c2 sin / \u00ff uo c3uo c4 cos / \u00ff uo c5; a1 mgh sin ao sin bo sin c; a2 mgh cos ao sin c; b1 \u00ff mghPo sin2 ao sin bo cos bo sin c; b2 mgh rt sin bo \u00ff Po cos bo sin c S cos c cos bo sin ao cos ao; b3 mghPo sin ao cos ao cos bo cos c; b4 mgh Po sin c \u00ff S cos c sin2 ao sin bo cos bo 1 \u00ff cos2 ao rt sin c ; b5 sin2 bo \u00ff cos2 ao cos2 bo 1 \u00ff \u00ff mgh cos c Po sin2 ao cos2 bo \u00ff \u00ff 1 mghS sin c; c1 mghP 2 o cos ao sin c; c2 rt cos bo \u00ff Po sin bo mghS sin ao cos c; c3 rt cos bo Po sin bo mghPo sin ao sin c; c4 PoS cos c \u00ff r2 t sin c mgh cos ao; c5 Po 1 \u00ff \u00ff mgh cos c \u00ff Smgh sin c rt cos ao: Therefore, the mathematical model of the worm gear surface cut with an oversize hob cutter can be obtained by considering Eqs. (13) and (20) simultaneously. TCA of the worm and worm gear can be simulated by considering the meshing mechanism of worm gear sets as shown in Fig. 4. If the worm rotates about its rotation axis through an angle /1, the worm gear will rotate about its rotation axis through an angle /2. Parameter SN is the shortest distance between the worm axis Z1 and worm gear axis Z2, and c1 is the crossed setting-angle of these two axes. To perform TCA on the worm gear set, position vectors and normal vectors of the matting worm and worm gear surfaces must be expressed in the same reference coordinate system, say coordinate system Sw Xw; Yw;Zw , as shown in Fig. 4(a). According to Fig. 4 and the coordinate transformation method, the position vector and normal vector of the worm surface, represented in coordinate system Sw, can be obtained as follows: x1 w A1 cos /1 \u00ff u1 B1 sin /1 \u00ff u1 ; y1 w A1 sin /1 \u00ff u1 \u00ff B1 cos /1 \u00ff u1 ; 21 z1 w C1 \u00ff P1u1; N 1 yw E1 cos /1 \u00ff u1 \u00ff D1 sin /1 \u00ff u1 ; N 1 yw D1 cos /1 \u00ff u1 E1 sin /1 \u00ff u1 ; 22 N 1 zw Nz1: Similarly, the position vector and normal vector of the worm gear surface, represented in coordinate system Sw, are obtained as follows: x2 w x2 cos /2 \u00ff y2 sin /2 SN ; y2 w x2 sin /2 y2 cos /2 cos c1 \u00ff z2 sin c1; 23 z2 w x2 sin /2 y2 cos /2 sin c1 z2 cos c1; N 2 xw Nx2 cos /2 \u00ff Ny2 sin /2; N 2 yw Nx2 sin /2 \u00ff Ny2 cos /2 cos c1 \u00ff Nz2 sin c1; 24 N 2 zw Nx2 sin /2 \u00ff Ny2 cos /2 sin c1 Nz2 cos c1: In the meshing process, worm and worm gear surfaces are in continuous tangency at every contact point", " Some major design parameters of the worm gear set are given as follows: (1) Tooth number of the worm and oversize hob cutter N1 1 tooth; (2) Module of the worm and oversize hob cutter m 8:5 mm/tooth; (3) Crossed setting-angle of the worm c1 90\u00b0; (4) Pitch diameter of the worm d1 79:5 mm; (5) Half-apex blade angle of the straight-edged cutting blade is a 20\u00b0; (6) Pitch diameter of the oversize hob cutter d1 85:00 mm. The oversize hob cutter is based on the concept that the tooth widths of the worm and hob cutter are equal in their normal sections on the pitch cylinder. In order to satisfy this criterion, the setting angle c of the oversize hob cutter in the cutting process must be set smaller than that of the worm in the meshing process (i.e., angle c1), as shown in Fig. 4(a), and it can be expressed by: c c1 \u00ff b1 bo 89\u00b03505900; 31 where b1 and bo are the lead angles of the worm and oversize hob cutter, respectively. According to the developed mathematical model of the worm gear set, a three-dimensional computer graphic of the ZN-type worm gear set is shown in Fig. 5. Based on the developed mathematical model of the worm gear set, the contact surface topology method and TCA computer simulation programs, the bearing contact of worm gear sets can be obtained. Fig. 6(a)\u00b1(c) show the bearing contacts on the worm gear surfaces when pitch diameters of the oversize hob cutter are 85" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001377_012102-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001377_012102-Figure6-1.png", "caption": "Figure 6. Design scheme of the gear circuit GLDITM with a four-link single-circuit lever chain: 0 - frame; 1, 2, 3 - levers; 4, 5, 6, 7 - gearwheels", "texts": [ " 5, we can write: ; 5 5 CP VC (10) ; 4 4 CP VC (11) ;44 BPVB (12) ; 1 4 41 AP BP (13) ,11 APVA (14) where - CP4, CP5, BP4, AP1 are determined by 55 LCP ; (15) ICECAE 2020 IOP Conf. Series: Earth and Environmental Science 614 (2020) 012102 IOP Publishing doi:10.1088/1755-1315/614/1/012102 whereL5 \u2013 is the length of the lever\u0421\u041e5 (link 5) \u0421P4= ; )4sin( 2sin d (16) ; )sin( cossin2 4 d d BP (17) dAP 1 ; (18) The gear circuits of the GLDITM are solved after solving the lever circuits of the GLDITM, using the obtained formulas. Fig. 6 shows the design diagram of the gear circuit of the GLDITM with a fourlink single-circuit lever chain, and Figure 7 shows the design diagram of the gear circuit of the GLDITM with a six-link double-circuit lever chain. Sequentially determining the instantaneous centers of rotation of gear wheels, we determine the angular velocity of the driven gear wheel 7 with a four-link single-circuit lever chain - \u03c97 and the angular velocity of the gear wheel 9 with a six-link double-circuit lever chain - \u03c99. According to the scheme shown in Figure 6 we can write: CP VC 7 7 ; (19) Where P7C is defined by determining the instantaneous centers of rotation P4, P5, P6, P7 of links 4, 5, 6, 7, respectively. The angular velocities of the gear wheels 4, 5, 6, 7 relative to the instantaneous centers of rotation and the linear velocities of the characteristic points of the mechanism K, A, E, B, F \u2013 VK4 , VA, VE5 , VB, VF6 and the angular velocities of links 5, 6, 7 \u2013 \u03c95, \u03c96, \u03c97, are determined similarly having previously solved the triangles P5AE, P6BE, P6BF, P7FC" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003018_s0013-4686(99)00183-8-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003018_s0013-4686(99)00183-8-Figure2-1.png", "caption": "Fig. 2. A selection of data from Fig. 1 plotted as a function of [PO3\u00ff 4 ]tot at pH 7.3 for \u00aexed [H2O2]bulk: (^) 5 mM, (Q) 12 mM, (R) 19 mM, ( ) 26 mM, (q) 33 mM and (.) 40 mM.", "texts": [ " It is also possible that the rate constant k2 may increase with [PO3\u00ff 4 ]tot. However, this could not fully account for the bu er concentration dependence since if N were to remain constant while k2 increases, then increasing [PO3\u00ff 4 ]tot would result in saturation occurring to the same extent with [H2O2] in each curve in Fig.1 (although the current at saturation would be greater at higher [PO3\u00ff 4 ]tot). To assist with interpretation of the bu er concentration dependence a selection of the data presented in Fig. 1 is shown as a function of [PO3\u00ff 4 ]tot in Fig. 2. In addition to displaying the previously noted trend that rate increases with [PO3\u00ff 4 ]tot, a number of signi\u00aecant features are evident in this view of the data. First, the relative increase in response with [PO3\u00ff 4 ]tot is greater for higher [H2O2]. For example, for 5 mM H2O2 the response increases by a factor of 1.9 from 25 mM to 100 mM phosphate, whilst for 40 mM H2O2 the factor is 3.5 increase over the same range of [PO3\u00ff 4 ]tot. We ascribe this to a balance of equilibria between formation of the binding site from some precursor and the binding of H2O2 to the active site according to reaction (1)", " The new term (K 0BS[PO3\u00ff 4 ]tot,bulk) \u00ff1 is likely to dominate the contribution from the terms K4[O2] and K5[H +] leading to j k2NK1 H2O2 1 K4 O2 1 K 0BS PO3\u00ff 4 tot,bulk K1 H2O2 1 K5 H k2=k3 ! : 13 low precision results for K4 and K5. This situation would not be ameliorated by varying rotation rate since there are no mass-transport considerations for phosphate. Another major concern is that the possibility of higher phosphate species forming as described in reaction (7) would prevent reliable optimization. Linked to our hesitation to undertake optimization is our \u00aenal observation that we make for the data presented in Fig. 2. If simple formation of the binding site were to occur according to reaction (6) and the species PtBS were requisite for any oxidation of H2O2, then a response would not be expected in the absence of phosphate. Extrapolation of the data presented in Fig. 2 does not satisfactorily indicate whether this is the case. We were unable to conduct rotating disc electrode experiments for [PO3\u00ff 4 ]tot < 2 mM whilst maintaining full iR compensation due to increased electrolyte resistance. It is for this reason that this [PO3\u00ff 4 ]tot region was explored using microelectrodes where iR artifacts do not prevail. Furthermore, the loss of rotation rate dependence information is not an issue since quantitative analysis was deemed to be futile and furthermore, the decrease in O2 and H+ inhibition a orded by hemispherical di usion is advantageous in clarifying the dependence on bu er concentration" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001207_052002-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001207_052002-Figure9-1.png", "caption": "Figure 9. Preliminary design of a plain bearing in moment design for large turbines", "texts": [ " After demonstrating the functionality of the FlexPad concept in demonstrator tests for a small 1 MW turbine in an earlier project, the next step is to transfer this bearing concept to moment bearings for larger plant sizes (up to 6 MW). In comparison to other bearing concepts the moment bearing offers the advantage of a compact design. This compact design is achieved by a large shaft diameter, which leads to high demands on manufacturing accuracy and high costs for the currently used roller bearings. In contrast to roller bearings, these disadvantages do not apply to plain bearings in such an extent, since plain bearings can be segmented. The preliminary design of a segmented plain bearing in moment design is shown in Figure 9. This bearing concept was inspired by commercially available rolling bearings in moment design (e.g. SKF Nautilus), which are used in wind turbines up to 6 MW [12]. The Science of Making Torque from Wind (TORQUE 2020) Journal of Physics: Conference Series 1618 (2020) 052002 IOP Publishing doi:10.1088/1742-6596/1618/5/052002 This design consists of a non-rotating outer ring, the segments mounted on the outer ring and the rotating hollow shaft. The plain bearing segments are designed to ensure parallel displacement of the sliding surface under axial and radial loads as well as under bending moments" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001781_s12046-021-01650-z-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001781_s12046-021-01650-z-Figure2-1.png", "caption": "Figure 2. Applications of the PMSM: aerospace applications [A][20]; hybrid electric cars [B][21]; light aircraft electric motor [C][22]; 1000W motor for motorcycle [D][23]; hero electric twowheeler [E][24]; hybrid aircraft electric motor [F][25]; PMSC electric motor [G][26].", "texts": [ " High-speed PMSM machines are essential prime movers in turbines, generators, compressors, spindles, aero chargers, and aviation applications [16]. The permanent magnet synchronous motor with higher efficiency, higher reliability, and higher torque density is the best bet for wind turbine generators, electric shipboard propulsion motors, belt transmission motors in mines, and ball mill motors [17]. PMSM is also used for an in-wheel electric vehicle (EV) application [18]. Permanent-magnet synchronous motors (PMSMs) are also used in whole electric aircraft [19], figure 2 [20\u201326]. PMSM losses are categorized as core losses, mechanical losses, stray losses, and Cu losses. Core losses occur in the stator core of the PMSM, the core loss is assorted as eddy current and hysteresis loss. Mechanical losses are assorted as windage loss and bearing friction loss, figure 3. Similarly, the copper losses depend upon the flow of current in the armature winding. These losses lead to high temperatures in PMSM under high-speed operational conditions. Investigation on the thermal behaviour of the motor shows that these losses are accounting for 10-20% of the entire power input [14, 27, 28]" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001267_j.jclepro.2020.120491-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001267_j.jclepro.2020.120491-Figure5-1.png", "caption": "Fig. 5. Stress deformation and strain at the extreme position of the ankle bone robot\u2019s ankle joint.", "texts": [ " Therefore, it is reasonable to analyze the strength of the ankle joint structure under this extreme working condition. The same is true for a standard adult male with a height of 175 cm and a weight of 74 kg. The weight of the ankle joint component is 2 kg. Based on the ANSYS software, the human foot exerts a certain force on the bone ankle joint component in the direction perpendicular to the vertical axis of the human lower limb. At its extreme position, the strength analysis results are shown in Fig. 5. It could be seen from the analysis results that the exoskeleton ankle joint component also uses 6061 aluminum alloy as the main material satisfies the requirement under the ultimate stress condition, that is, the design is reasonable. The underactuated robotic ankle exoskeleton described herein is a highly compliant structure based on an underactuated 3-RRS spherical parallel mechanism. As shown in Fig. 6, the structure body is connected by three dynamic and static platforms through three identical branches" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003733_iros.2006.282470-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003733_iros.2006.282470-Figure2-1.png", "caption": "Fig. 2. Relations between generalized virtual gravity vectors at CoM and joint torques. The equivalent transformed torque of the hip-joint torque u2 yields the central force.", "texts": [ " (4) can be rearranged as fg = Jg(\u03b8)\u2212T ([ 1 0 ] u1 + [ 1 \u22121 ] u2 ) = mbu1 M\u0394g [ sin \u03b82 cos \u03b82 ] \u2212 rgu2 \u0394g rg rg =: f1 + f2 (5) where rg := |rg| and \u0394g := det(Jg) = \u2212mb(mH l + ma + ml) sin(\u03b81 \u2212 \u03b82) M2 . (6) Note that Eq. (5) is written in the form consisting of two unit vectors. f g has a singularity of \u03b81 = \u03b82, and thus it is unadvisable to examine the torque distribution effect based on this approach. The ratio of |f1| to |f2| is, however, kept finite regardless of the singularity so long as both u1 and u2 are not zero. Eq. (5) shows that the ankle-torque effect f1 yields being parallel to the swing leg and that of the hip-torque f2 yields central force as shown in Fig. 2. This can be also understood from the angular momentum point of view. Let L [kg\u00b7m2/s] be angular momentum of the robot, and its time-derivative satisfies the relation L\u0307 = u1 + MgXg. (7) Since only u1 appears in this equation, it can be found that the equivalent transformed force vectors of all joint torques except ankle\u2019s should yield in the direction of rg; they are parallel to rg as seen from f2 \u2208 span {rg} in Fig. 3. Only u1 directly affects L\u0307. It is true that, as seen from Fig. 2, the two force vectors must be exerted suitably to drive the CoM forward, but why is the ankle-torque required much more than hip-torque one? In order to prove this question, let us consider the following condition |f1| |f2| = mb|u1| Mrg|u2| = 1 (8) which means the condition that the ankle-torque effect f1 is the same as the hip-torque one. The torque ratio is then TABLE I PHYSICAL PARAMETERS mH 10.0 kg m 5.0 kg a 0.5 m b 0.5 m arranged as |u1| |u2| = Mrg mb = (mb)\u22121 ( (mH l + ma + ml)2 + m2b2 \u22122mb(mH l + ma + ml) cos \u03b8H)1/2 \u2265 mH l + 2ma mb = Ml mb \u2212 2" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003706_j.mechmachtheory.2004.02.011-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003706_j.mechmachtheory.2004.02.011-Figure4-1.png", "caption": "Fig. 4. Parameters and variables of the adaptively balanced mechanism.", "texts": [ " In the general case, the coefficients of kinematic variables and gravitational terms are the following D11 \u00bc m1\u2018 2 1c \u00fe I1 \u00fe m2\u00f0\u201821 \u00fe \u201822c\u00de \u00fe I2 \u00fe m0\u00f0\u201821 \u00fe \u201822\u00de \u00fe m2B\u00f0\u201821 \u00fe \u201822B\u00de \u00fe m1B\u2018 2 1B \u00fe 2\u20181 cos h2\u00f0m2\u20182c \u00fe m0\u20182 m2B\u20182B\u00de \u00fe m2I\u00f0\u2018212B \u00fe \u201822I\u00de \u00f030\u00de D12 \u00bc m2\u2018 2 2c \u00fe I2 \u00fe m0\u2018 2 2 \u00fe m2B\u2018 2 2B \u00fe \u20181 cos h2\u00f0m2\u20182c \u00fe m0\u20182 m2B\u20182B\u00de m2I\u2018 2 2I rT \u00f031\u00de D111 \u00bc 0 \u00f032\u00de D112 \u00bc D121 \u00bc \u20181 sin h2\u00f0m2\u20182c \u00fe m0\u20182 m2B\u20182B\u00de \u00f033\u00de D122 \u00bc D112 \u00f034\u00de D1 \u00bc g cos h1\u00f0m0\u20181 \u00fe m2I\u201812B \u00fe m1\u20181c \u00fe m2\u20181 m1B\u20181B \u00fe m2B\u20181\u00de \u00fe g cos\u00f0h1 \u00fe h2\u00de \u00f0m2\u20182c \u00fe m0\u20182 m2B\u20182B\u00de \u00f035\u00de D21 \u00bc D12 \u00f036\u00de D22 \u00bc m2\u2018 2 2c \u00fe I2 \u00fe m0\u2018 2 2 \u00fe m2B\u2018 2 2B \u00fe m2I\u2018 2 2I r 2 T \u00f037\u00de D211 \u00bc \u20181 sin h2\u00f0m2\u20182c \u00fe m0\u20182 m2B\u20182B\u00de \u00f038\u00de D222 \u00bc 0 \u00f039\u00de D212 \u00bc D221 \u00bc 0 \u00f040\u00de D2 \u00bc g cos\u00f0h1 \u00fe h2\u00de\u00f0m2\u20182c \u00fe m0\u20182 m2B\u20182B\u00de \u00f041\u00de where \u201812B is the distance between the center of the revolute joint that connects the rotor to link 1 and the center of revolute joint that connects link 1 to the base; \u20182I is the position of both compensation masses m2I=2 with respect to the center of revolute joint that connects the rotor to link 1; and rT is the transmission ratio (Fig. 4). For the sake of clearness, gear (or pulley) masses are not explicitly included in presented equations. The three conditions for the adaptive balancing are m2\u20182c \u00fe m0\u20182 m2B\u20182B \u00bc 0 \u00f042\u00de m0\u20181 \u00fe m2I\u201812B \u00fe m1\u20181c \u00fe m2\u20181 m1B\u20181B \u00fe m2B\u20181 \u00bc 0 \u00f043\u00de m2\u2018 2 2c \u00fe I2 \u00fe m0\u2018 2 2 \u00fe m2B\u2018 2 2B \u00fe \u20181 cos h2\u00f0m2\u20182c \u00fe m0\u20182 m2B\u20182B\u00de m2I\u2018 2 2I rT \u00bc 0 \u00f044\u00de Substituting the calculated compensation inertias m1B;m2B and m2I in Eqs. (30)\u2013(41), D11 \u00bc m1\u2018 2 1c \u00fe I1 \u00fe m2\u00f0\u201821 \u00fe \u201822c\u00de \u00fe I2 \u00fe m0\u00f0\u201821 \u00fe \u201822\u00de \u00fe m2B\u00f0\u201821 \u00fe \u201822B\u00de \u00fe m1B\u2018 2 1B \u00fe m2I\u00f0\u2018212B \u00fe \u201822I\u00de \u00f045\u00de D12 \u00bc 0 \u00f046\u00de D111 \u00bc 0 \u00f047\u00de D112 \u00bc D121 \u00bc 0 \u00f048\u00de D122 \u00bc D112 \u00f049\u00de D1 \u00bc 0 \u00f050\u00de D21 \u00bc D12 \u00f051\u00de Table Geom \u20181 ( 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001228_tvt.2020.3041336-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001228_tvt.2020.3041336-Figure5-1.png", "caption": "Fig. 5. Parameters of auxiliary slots on the rotor and stator. (a) rotor. (b) stator.", "texts": [ " According to the structures of stator and rotor and winding pattern of FSCW-IPM motor, four basic auxiliary slot types are proposed. Effects of the auxiliary slot parameters on cogging torque, torque average, torque ripple, and the radial force spatial harmonic magnitude are investigated. The characteristics of different combined types of auxiliary slots are analyzed and compared. Due to the symmetry of rotor structure, there are two basic types of auxiliary slots on the rotor, namely notching on q-axis and d-axis, respectively. The auxiliary slot parameters are shown in Fig. 5 (a): they are auxiliary slot depths c1, c2, and 1/2 widths r1, r2 on q-axis and d-axis. To enhance fault tolerant capability and reduce cogging torque of FSCW-IPM motor, the unequal stator tooth width structure with single-layer concentrated winding are adopted. The armature-teeth are winding-wound teeth, while fault-tolerant teeth are winding-free teeth, as shown in Fig. 1. Therefore, there are two basic types of auxiliary slots on the stator, namely notching on armature-teeth and fault-tolerant teeth, as shown in Fig. 5 (b). The parameters c3, c4, r3, and r4 represent depths and 1/2 widths of auxiliary slots on fault-tolerant-teeth and armature-teeth, respectively. To simplify the presentation of auxiliary slots, auxiliary slots on q-axis and d-axis are abbreviated as Rq and Rd, respectively. Auxiliary slots on the armature teeth and fault-tolerant teeth are abbreviated as SA and SF respectively. The combined auxiliary slots are also abbreviated, for example, the abbreviation SARq is the combination type of auxiliary slots SA and Rq" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003706_j.mechmachtheory.2004.02.011-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003706_j.mechmachtheory.2004.02.011-Figure6-1.png", "caption": "Fig. 6. Possible architecture for the mechanism balanced according to the proposed method.", "texts": [ " Second, the position of the second actuator can also be altered. The shaft of this actuator may be connected to the rotor shaft instead of being directly coupled to link 2. This measure will result in a reduction of driving torque by a factor of 0:5\u00f01\u00fe 1=rT\u00de. One undesirable consequence is that driving power for that actuator will increase by a factor of 0:5\u00f01\u00fe rT\u00de. So, there must be a trade-off between lower compensation inertia and higher driving power, when choosing an adequate value for the transmission ratio. The Fig. 6 shows how the mechanism will look like after making the necessary modifications required for the adaptive balancing. Future works will be concentrated on the generalization of the adaptive balancing to any kind of open-loop mechanism, planar or spatial, with different joint types and n degrees of freedom. Such a balancing should be achieved under the presence of perturbation forces of different natures, not only due to payload weight, but also generated when robot gripper holds a workpiece (machining forces)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000327_j.mechmachtheory.2017.05.014-Figure24-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000327_j.mechmachtheory.2017.05.014-Figure24-1.png", "caption": "Fig. 24. The experimental meshing.", "texts": [ " But the trend for the change of theoretical analysis is the same with FEM analysis and the maximum error is 6.54%. During the FEM analysis, there will be some errors, which are caused by 3D model and assemble of gear pair. And taking those errors into consideration, the maximum error 6.54% can be accepted. 6. Experiment The experiment is operated at the State Key Laboratory of Mechanical Transmission of Chongqing University. The noncircular gear was mounted on the drive shaft with helical curve face gear mounted on the driven shaft, shown in Fig. 24 . The errors of alignment e, q and \u03b3 are represented by the adjustment of the relative position of drive shaft and driven shaft. Because of the variable transmission ratio of this helical face gear pair, the surface of every tooth is not the same to either adjacent one in half a cycle. And a half cycle with five teeth of the helical curve face gear should be taken into consideration to get the principle of tooth contact completely. The experimental area are not the same with theoretical result completely, because of the misalignment during experimental meshing" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000792_978-981-13-9539-0_7-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000792_978-981-13-9539-0_7-Figure1-1.png", "caption": "Fig. 1. Instrumented IMU device", "texts": [ " It is worth noting, although limited studies have been conducted with regards to skateboarding, nonetheless, other sporting activities that have used IMU sensors, as well as machine learning, has been well-documented [5\u201312]. This paper aims at evaluating a number of machine learning models based on selected IMU signals in classifying Ollie, Kickflip, Shove-it, Nollie and Frontside 180 tricks. This outcome of this investigation may serve useful to a more objective based evaluation by the judges as well as providing a means for skateboarders to further improve their performance. Figure 1 depicts the design of the instrumented IMU device modelled using CATIA. The casing of the device is printed using a Zortrax M200 Plus 3D printer. The material selected for printing the instrumented IMU device is Acrylonitrile butadiene styrene (ABS) owing to its desirable mechanical properties, primarily high impact strength and good shock absorbing as the device will be prone to impacts and shocks from the tricks. The instrumented IMU consists of an IMU unit (MPU6050), a Bluetooth Module (HC05), a microcontroller (Arduino Pro Mini) as well as a 3" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003134_robot.1991.131621-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003134_robot.1991.131621-Figure2-1.png", "caption": "Figure 2 : The position vector of the origin of the link 5 frame, P5, is uniquely determined by the given position vector, p8, and the approaching vector, 0 8 , of the end-effector: P5 = Pa - d8 ' 0 8 . Note that P5 is not a function of 85", "texts": [ " The upper arm is structuredin the form of roll(2)-pitch(Y)-yaw(X)-roll(2) with the rotational axes, 2, X, Y, and Z , being orthogonal to each other and intersecting at the common point. The upper arm is mainly responsible for orienting the end-effector. The 2 - X - Y - Z structure for orientation is very flexible and versatile, allowing the arm to choose one of the following wrist configurations with 3 joints: X - Y - 2 and 2 - X - Y as implemented for the wrist of the T3 robot, or 2 - X - 2 and 2-Y-Z as implemented for the wrist of the PUMA robot. The kinematic configuration of the AA1 arm is illustrated in Fig.2, and fully described by the Denavit-Hartenberg paramet,ers as shown in Table 1. 3.2 Decomposition of Kinematic Equations for Redundancy Distribution Let us consider that a task point is given in the Cartesian space in the form of a homogeneous transformation, T 8 , of the endeffector frame (refer to Fig.2): where pg = [ps2., pay, p82IT represents the position of the orb gin of the end-effector frame w.7.t. the base frame, and ng = [ n a ~ , ~ a y , n 8 t ] ~ ~ 08 = [O8z,08yr'%zIT, m d a s = [ a 8 ~ , ~ 8 y t a 8 z ] ~ represent respectively the normal vector, the orientation vector and the approaching vector of the end-effector frame w.r.t. the base frame. Since T8 = A l ( 8 1 ) A 2 ( 8 2 ) . . . A s ( 8 8 ) , where A i ( & ) represents the homogeneous transformation from the link i - 1 frame to the link i frame, each element of ne, 08, a8 and pa, is in general a function of 81, 82, 8 3 , 8 4 , 85, 86, 87 and 88. To obtain the \"parameterized\" inverse kinematic solution based on the direct algebraic manipulation of (18) is not recommended due to the complexity involved as well as the lack of a physical insight on the solution. Therefore, we decompose (18) into subsets of kinematic equations based on the analysis of arm geonietry[7], prior to the derivation of the \"parameterized\" inverse kinematic solution, as follows: 1) As shown in Fig.2, let us first determine the position of the origin of the link 5 frame, Op5, ur.7.t. the base frame, OP5 = P8 - d8 ' a8 (19) Note that Op5 is a function of only 81, 8 2 , 83 and 8 4 , since 85 does not affect O p g , such that OP5 = 5 ( 8 1 , 8 2 , 8 3 1 8 4 ) (20) 2) Once Op5 is obtained by (19), then 84 can be determined directly from Op5, independent of 01, 8 2 , and 8 3 . As shown in Fig.2, 2 2 , 2 4 , 2 3 and 2 4 are perpendicular to 23 (zl = 22 x 2 3 , 24 = z 3 x 24) and, therefore, are on the same plane. Thus, the angle between 22 and 2 4 , L ~ 7 , 2 4 , becomes 84 - 180\u00b0, because L2224 = L x 3 1 4 - L 2 3 2 2 - L ~ 4 x 4 and 1 x 3 1 4 = O4 and L x ~ z ~ = LZ424 = goo. Now, if we form a triangle AABC, as shown in Fig.3, then Lm,m = l 8 O o - (84 - 180O) = 360\u00b0 - 8 4 , and the length of three sides are given by - - AB= d 3 , B C = d5 - AC = I I Op5 - dr . a011 dz + dz - 2d3d5cos(360\u00b0 - 84) = E2 (21) Therefore, 6'4 can be obtained by applying the cosine rule to the triangle AABC defined above: (22) 3) Once 84 is obtained, we can compute 81, 82 and 83 from (20) by O p5 = " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001207_052002-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001207_052002-Figure5-1.png", "caption": "Figure 5. Preliminary design of a FlexPad bearing for a three-point suspension", "texts": [ " Since in a three-point suspension the non-torque loads are absorbed in the gearbox as second bearing point, the gearbox performs a small vertical and horizontal displacement. In case of designing a plain bearing for this arrangement, the displacement of the gearbox has a great influence on the load distribution in the main bearing and needs to be considered in the EHD simulation. The Science of Making Torque from Wind (TORQUE 2020) Journal of Physics: Conference Series 1618 (2020) 052002 IOP Publishing doi:10.1088/1742-6596/1618/5/052002 For this boundary condition a preliminary design of a conical FlexPad bearing was derived (see Figure 5). The geometry of this preliminary design is derived from the geometry of spherical roller bearings. This double conical bearing design has a mean diameter of 890 mm and consists of 32 equal pads, 16 on each side, that are connected to the bearing housing via the previous described doubleflexible support structure. By designing the number of bearing segments two contradictive effects need to be considered. On the one hand the number of segments cannot be too low because in this case some segments are just partially located in the loaded zone and a parallel displacement of the bearing segment cannot take place", " On the other hand, an increasing number of bearing segments leads to higher manufacturing and assembly costs. In the former research project WEA-GLiTS simulations have shown, that 16 pads at each cone are a good compromise to fulfil the mentioned requirements. Finally, the optimal number of pads is dependent on numerous aspects, e.g. bearing size, operating conditions, manufacturing and assembly possibilities. EHD-Model In order to conduct an EHD simulation for the presented preliminary design in Figure 5 first a multibody simulation model needs to be set up. This model consists of two flexible bodies, namely the main shaft and the main bearing. To reduce the number of degrees of freedom (DOF) a mixed modal/static reduction is performed. For the shaft in total 50 modes are considered in the simulation. For the plain bearing segments, a staggered reduction is conducted. During this procedure, the modes are calculated one after the other for each segment. This ensures that there is no need to consider an extremely large number of global modes for the deformation of each segment and for each segment the same number of DOF is considered", "1088/1742-6596/1618/5/052002 scaled with a scaling factor up to this turbine size. This procedure is sufficiently accurate for the feasibility study in this paper, because for the evaluation of the load distribution it is not the exact level of the loads but rather the combination of the individual non-torque loads that is important. The input parameters are summarized in the following table. As result of the conducted simulation Figure 6 shows the calculated hydrodynamic pressure distribution for the geometry shown in Figure 5 in a three-dimensional plot. For a better clarity just the hydrodynamic pressure distribution on each segment without the shaft and the bearing are shown. First off all it can be concluded that no pressure peaks due to edge loading occur which is an indication that the sliding segments can perform a properly parallel displacement. The left plot shows the hydrodynamic pressures from the view in downwind direction and reveals the loaded zone of the bearing. Due to the radial force Fz in negative z-direction the bottom segments are more loaded than the upper ones" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000343_ec-03-2017-0086-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000343_ec-03-2017-0086-Figure1-1.png", "caption": "Figure 1. Normal section of the rack cutter for involute FS generation", "texts": [ " Finally, the main conclusions of this study are drawn in Section 5. In this study, the FS exhibits involute tooth profile which can generated by a straightedged rack cutter based on the theory of gearing. Then, the conjugate geometry of CS is derived as an envelope of the loci of tooth profiles of the FS being driven by the elliptical WG. In this section, first the mathematical model of the straight-edged rack cutter was developed. Then the mathematical model of the involute FS was derived based on the theory of gearing and the generatingmechanism. Figure 1 depicts the normal section of the straight-edged rack cutter used to generate the involute FS. The rack cutter comprises two regions: straight-edged region and rounded-tip region, which are used to generate the involute region and the fillet region of the involute FS, respectively. According to the illustration depicted in Figure 1, the mathematical model of the rack cutter can be expressed in coordinate system Sa (Xa, Ya) in the following: Study of a harmonic drive 2109 D ow nl oa de d by S ou th er n C ro ss U ni ve rs ity A t 0 6: 17 2 0 O ct ob er 2 01 7 (P T ) where i = 1 or 2, i = 1 denotes the straight-edge region and i = 2 denotes the rounded-tip of the rack cutter. The mathematical model of regions 1 and 2 of the rack cutter can be expressed as follows: Straight-edge region: R 1\u00f0 \u00de a \u00bc x 1\u00f0 \u00de a y 1\u00f0 \u00de a 1 8>>< >>: 9>>= >>; \u00bc \u00f0L1cosa1 hf\u00de 6\u00f0L1sina1 hftana1 b 1 8>< >: 9>= >; (2) where L1 is the position parameter of straight edge, andM0M1 \u00bc L1; a1 denotes the normal pressure angle;symbols ha, hf and b are addendum, dedendum and half-tooth space of the rack cutter, and b \u00bc pmn 4 ; The upper sign and lower sign in \u201c6\u201d represent the left and right sides of the rack cutter, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001089_tia.2020.3046195-Figure11-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001089_tia.2020.3046195-Figure11-1.png", "caption": "Fig. 11. Predicted temperature distribution of three cooling jackets. (a) Circumference. (b) Axial. (c) Spiral.", "texts": [ " Due to the air gap between the stator and rotor, the temperatures of rotor and permanent magnet take a much longer time of 2400 s to reach the steady state. Fig. 10 shows the maximum temperature histories of windings, stator, rotor, magnets, and coolant with the three jacket concepts at flow rate of 3 LPM. The spiral jacket gives the lowest maximum windings temperature of 156.7 \u00b0C, whereas the axial and circumference jackets have their maximum temperatures of 162.2 \u00b0C and 171.8 \u00b0C, respectively. Fig. 11 shows the predicted temperature distribution of three cooling jackets. The circumference jacket gives the highest temperature because of low convection heat transfer coefficient, comparing to the axial and spiral jackets. Predicted peak temperature distributions across the motor components under the transient operation are displayed in Fig. 12. According to Figs. 9 and 12, the spiral jacket results in lower temperatures across various motor component when compared to other two concepts. Authorized licensed use limited to: Central Michigan University" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001319_tec.2020.3007802-Figure10-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001319_tec.2020.3007802-Figure10-1.png", "caption": "Fig. 10. The radial vibration of mode 2 caused by: (a) Second order force, (b) Tenth order force. (c) Fourteenth order force, (d) All force", "texts": [ " In order to separate the radial force density, a 2-D fast Fourier transform (FFT) analysis can be performed in space and time domains. Fig.8 shows the waveform at one instant and its spatial harmonic spectrum of radial magnetic force density with twice the fundamental frequency. From Fig.8 (b), it can be seen that the amplitudes of decomposed 2-order and 10-order components are 785.6 N/m2 and 15280 N/m2 respectively, and their waveforms are shown in Fig.8 (a). Then, these forces will exert on the stator, as shown in Fig.9. Fig.10 presents the vibration caused by these forces. 0 60 120 180 240 300 360 -30000 -20000 -10000 0 10000 20000 30000 F o rc e d e n s it y ( N /m 2 ) Rotor position (Mech.degree) All order 2 order 10 order 14 (a) Authorized licensed use limited to: University of Exeter. Downloaded on July 16,2020 at 00:15:50 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. It can be shown from Fig.10 that both of the 2-order, 10-order and 14-order force densities can cause the 2nd mode vibration, and the maximum value of the surface vibration of the stator at 100Hz are 0.00181, 0.0128 and 0.00064 m/s2 respectively. The 2nd mode vibration caused by the 10-order force density is 7.07 times of that by the 2-order force density, which is consistent with the result of 1.0/0.14=7.14 in Fig.3. When all the forces are loaded, the vibration amplitude of the motor is 0.01286 m/s2, and it can be seen that it is mainly excited by the 10-order force", " The rotation frequency fr=nr/60 is 10 Hz, and the fundamental frequency (pnr/60) is 50Hz, so the dominating frequency components in Fig.15 are 2npfr as 100Hz, 200Hz, 300Hz, 400Hz, and 500Hz. The measured and simulated 100Hz acceleration of the motor are 0.0136 m/s2 and 0.0128 m/s2 respectively, which is consistent with each other. The obvious 2nd mode deformation can be seen in Fig.16, which is at 100Hz and is extracted from the fifteen accelerometers. This matches well with the FEM results illustrated in Fig.10. B. Integer Slot PM Motors This 6p/36s experimental motor is shown in Fig.14 (b). In Fig.17, the measured and simulated vibration acceleration of the integer slot PM motor is presented as the speed is 1500r/min. The rotation frequency fr is 25Hz, and the 1st slot frequency (Zfr) is 900Hz. The measured and simulated vibration acceleration of the motor at 900Hz are 0.172m/s2 and 0.187m/s2 respectively, which is consistent with each other. The vibration mode shape which is extracted from the relative phase of the vibrations of fifteen accelerometers is drawn in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003464_910858-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003464_910858-Figure6-1.png", "caption": "Fig. 6: Squared vibration signals of 40 cycles comprising different excitation causes", "texts": [], "surrounding_texts": [ "combustion process. These knock related pressure vibrations can be isolated by high-pass filtering (right hand side of the figure) and further processed in the time domain. The increasing knock intensity of the cycles from the bottom to the top is indicated by the different pressure amplitudes. The frequency spectra of the cylinder pressure signals (in the center of the figure) exhibit high levels at the combustion chamber resonance frequencies beyond 5 kHz.\nIn fig. 3 cylinder pressure frequency spectra of knocking combustion are presented. They were selected from consecutive working cycles at stationary engine conditions (4500 RPM, MOT) and are arranged in the order of their knock intensity. The first cavity mode (6 kHz) responds with its amplitude to knock most intensively. But typically the higher harmonics are responsible for the excitation of structure vibrations and thus can serve better for knock detection.\nThe resonance frequencies depend on the dimensions of the combustion chamber and on the sound velocity of the cylinder charge. For simple cylindrical chamber geometries the frequency calculation procedure is easy. The arguments of the relative maxima and minima of the different orders of the Bessel functions determine the cavity mode frequencies. More complex geometries of the combustion chamber must be treated by finite element method calculations.", "Fired Cylinder Pressure Engine\n4500 RPM 3 0 2. Resonance W O T dB -\nI I I I I I I J I J I I\nI I Structure I I - Vibration\n30 dB\nStructure Engine Block Response\n, Transfer Function Measurement\n4 8 12 16 kHz 24", "Signal Shape\n0 25 'CA 50\nIntegration Rect i f ied Squared $ 1 /,/=-I:\n15 kHz\n15 kHz\n6 kHz\nFig. 8: Approaches of knock intensity evaluation: integration of rectified and squared signal\nshows the difference between the two approaches of knock intensity evaluation: integration of the squared and the rectified signals in a predertermined time window. It comes evident that integration of the squared signal (window energy) fits the characteristics of the typical knock induced vibration signal better than integration of the rectified signal (window integral). Typically the knock related structure vibration trace starts immediately with high amplitudes at the occurrence of the in-cylinder pressure shock waves and decays corresponding to an e-function. This characteristic is also exhibited by the knock induced high frequency cyl inder pressure component (see fig . 2)\nFig. 9 quantifies on the basis of an example the advantage of the signal squaring method compared to the rectifieing method. The difference of knock valuation between both approaches is shown as a function of the window energy. At the borderline energy level the squaring method is more sensitive by 0.4 refered to the mean values of window energy and window integral.\n$2000 Q, 4500 RPM Heavy 5 m2/s3 /Knocking 3 Cycle\n0 200 380 Consecutive Working Cycles The valve closing impacts depend on the valve clearance which determines the velocity at the lift-off instant from the cam. In a mechanical valve train the clearance varies according to the thermal conditons especially of the cylinder head and the valve stem. A valve train with hydraulic lash adjusters is very sensitive concerning the closing velocity due to the dynamic behavior of the\n. . . high pressure element. So the valve closing 0.8- , 1 2 3 G/rrT 4 . . . . . I i . . . . . . impacts occur with very different intensity Knock which complicates the knock detection. Rectified : Borderline . . . . . . . . . . . . . . . . . . . . Window Integral1 . . . . . . . . . . . . . . . . . Fig. 7 shows the influence of the valve . . . . . . . , . . . . . . -11 - ..... . . . . . . . . . . . . . . . clearance on the amplitude of the excited . . . . . . . a'\n- I . . . . , ,w:::.:,: * * *\nSquared: structure vibration. The different excitation ilko' 1 . . . . . potency as well as the different pulse *i:::.:.: Window Energy E ,ky : ...:::;;; . . . . . occurrence time has to be considered for the , . . Coefficient assessment of knock detection interference by ........... of Correlation the valve train.\n0.0 I , , , , , ,\nDetermination of Knock Intensity 0 200 m2/s3 400\nKnock detection reliability is increased by knock intensity evaluation on basis of the Fig. 9: Advantage of the signal squaring squared structure vibration signal. Fig. 8 method" ] }, { "image_filename": "designv10_11_0001562_tii.2021.3064576-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001562_tii.2021.3064576-Figure1-1.png", "caption": "Fig. 1. Structure of the two PCM units used in this work. (a) Prototype of the PCM. (b) Cross-section in the X-Y plane.", "texts": [ " Downloaded on June 29,2021 at 16:30:51 UTC from IEEE Xplore. Restrictions apply. 1551-3203 (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. A PCM made of PMAs and designed by the Intelligent Robotics Lab, Northeastern University, China, is employed for the following experiments. A brief description of the PCM is illustrated below. The PCM prototype, composed of two units, is exhibited in Fig. 1(a). Both units are built upon the PMAs and have a clover-shaped exterior. Fig. 1(b) depicts the PCM concentric structure of the two units. Within each unit, the outer layer is built upon three identically contractile PMAs spaced at 120 intervals, and the inner layer is made from one extensor PMA installed in a central position. Moreover, each unit is separated by nylon cable ties and arranged by a 25 mm spacing to guarantee uniformity in motion. When different contractile PMAs are inflated or deflated with the air pressure, bending motion in different directions is accomplished at each unit", " Inflating actuator 1 allows the first unit to bend in the negative Y-axis direction with zero rotation around the longitudinal axis. Along the same line, the positive Y-axis direction is introduced at the second unit to inflate actuators 2 and 3. Three contractile PMAs can be filled to gauge pressures of 0\u2013500 kPa (0\u20135 bar) in each unit. We utilize pressures of 0\u2013260 kPa (0\u20132.6 bar) gauge for the following experiments, as there are pinching effects at higher pressures. To further demonstrate the effectiveness of the presented control strategy, experiments were performed using the PCM (see Fig. 1(a)) with the presented experimental setup (see Fig. 2). Although current research based on dynamic models of PCMs opens the door for developing control strategies, these models possess relatively large computational complexity. As noted in [1], [3], [5], model-based control strategies for PCMs remain in the nascent stage, and thus, model-free control strategies overwhelmingly dominate practical applications of PCMs because of their effectiveness and simplicity. In the following experiments, we compare the presented control strategy with model-free adaptive control (MFAC) approach" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003831_j.snb.2006.08.042-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003831_j.snb.2006.08.042-Figure1-1.png", "caption": "Fig. 1. Structure of the Pt plasma-deposited electrode.", "texts": [ " Compared ith conducting polymers, which are used as enzyme dopng membranes in numerous biosensor reports, non-conducting olymers provide favorable qualities such as the capability to oad controlled amounts of enzyme, the ability to form thin and niform films, nonpoisonous to enzymes and the ability to filter lectro-active interferents. For example, Miao et al. selectively eviewed the recent progresses in the development of ampermetric biosensors based on various types of non-conducting Actua p o g o s o t e b t s l a e t a l i t F a a s b I e u m l c m p [ p i e P t p f 2 2 p u p f c U w p K r w w a 2 w t M S P s w c s 3 r t a T i whole area except the circular shaped working, counter and reference electrodes were printed with a polyurethane-based insulator. The structure of the electrode used in this study is depicted in Fig. 1. J.H. Han et al. / Sensors and olymers of phenol and its derivatives, phenylenediamines, and veroxidized or electroinactive polypyrroles; these sensors in eneral exhibit favorable permselective properties against varius interferents, but with limited linear range and use life [22]. Application of an outer membrane is necessary to improve ensor linearity and lifetime. For the fabrication of an in vivo r ex vivo glucose monitoring device, one of the strategies is he use of a suitable outer membrane on the GOx immobilized lectrode" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000606_j.triboint.2018.02.028-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000606_j.triboint.2018.02.028-Figure1-1.png", "caption": "Fig. 1. The model of \"through\" type defects of roller bearing.", "texts": [ " To provide the foundation for accurate defect diagnosis and life prediction of roller bearings, the defected roller bearing model considering the characteristics of contact type and natural defects is required. Defects of roller bearing is considered as the depression due to material spalling. The assumption that defects extend axially throughout the rollers or raceways is widely adopted in modeling of defected roller bearings. Rollers passing over such \u201cthrough\u201d type defect will go into the defect depression, which will result in additional displacement and curvature variations as shown in Fig. 1. Through the introduction of the contact load change due to additional displacement and the Hertz contact stiffness change due to curvature variations [7,8[7,8] into bearing ). 4 February 2018; Accepted 22 Febru dynamic model, the vibration response of defected roller bearing can be modeled. Several researchers analyzed the vibration response of roller bearing with different width of \u201cthrough\u201d type defect [9], and proposed the measuring technique of defect width based on decomposition using wavelet transform [10,11]" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003052_s101890050039-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003052_s101890050039-Figure5-1.png", "caption": "Fig. 5. Tilt grain boundary a) curvature wall; b) dislocations wall; c) FCD wall.", "texts": [ " Therefore we take the total core energy as equal to twice the ellipse core energy: fcore = 8aK1E ( e2 ) . (2c) In the case of a TFCD (e = 0), the total energy scales as the radius of the focal circle. Recall: the complete elliptic integral of the first kind is given by K(x) = \u222b 1 0 (1 \u2212 t2)(1 \u2212 xt2)\u22121/2 dt, and the complete elliptic integral of the second kind by E(x) =\u222b 1 0 (1\u2212 t2)\u22121/2(1\u2212 xt2)1/2 dt. In smectics, tilt grain boundaries with a disorientation angle \u03c9 can be achieved according to three different geometries: curvature walls, according to a model by de Gennes [11], (Fig. 5a), dislocation walls (Fig. 5b); FCD walls (Fig. 5c). We consider here the case of FCD-split walls. The boundary is packed with ellipses of equal eccentricities e(\u03c9) = sin \u03c9 2 and parallel long axes, and the hyperbolae have consequently parallel asymptotes. The angle between the asymptotes measures the disorientation between the two grains, since the layers are perpendicular to the asymptotic directions. The \u201ccommon vertices\u201d are at infinity on both sides and the domains are complete, Figure 6; l.c.c. is obeyed, since any pair of domains in contact at any point M on both ellipses carries the same pair of vertices P and Q at infinity" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003727_j.aca.2004.09.003-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003727_j.aca.2004.09.003-Figure1-1.png", "caption": "Fig. 1. FIA\u2013ECL determination set-up for METH.", "texts": [ " The volume of the hin layer cell was about 1.5 l. A three-electrode system as used for potentiostatic control of the electrolytic sysem. The working electrode was an ORMOSILs-modified lassy carbon disk (22.1 mm2). The counter electrode set t the outlet consisted of a stainless-steel pipe, and the eference electrode was Ag/AgCl (saturated KCl solution). he CHI 800 Electrochemical Analyzer taken as potentiotat was used for electrolysis. ECL intensity was observed hrough an IFFM-D FIA Luminescence Analyzer (Ruimai o., China). As shown in Fig. 1, a flow injection system equipped with Rheodyne 7125 sample injector (Cototi, CA, USA, 20 l) nd an injection loop of 20 l was comprised. All the pH mea- er was about 2 \u00d7 10 Torr, and the energy scales were alibrated using copper. Survey spectra were collected with a ass energy of 30 eV, and a pass energy of 15 eV was used for oth core and valence band spectra. Spectra were calibrated y taking the Cls peak due to residual hydrocarbon as being at 84.6 eV. The sample was examined at two different takeoff ngles, 90\u25e6 and 30\u25e6, with respect to the sample surface" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000086_978-3-319-69050-6_17-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000086_978-3-319-69050-6_17-Figure5-1.png", "caption": "Fig. 5 3D printing on textile process: a Schematic sketch of 3D printing on textile process and b 3D print on textile", "texts": [ " For adhesion between fabric and polymer, it is necessary to have sufficient porosity\u2014too little and the polymer simply forms a film on the surface\u2014too much, and there is little textile in the final product. Fabric with variable porosity which can be controlled through pre-tensioning, such as knits, make them quite suitable for use. When 3D printing on textiles using the FDM method, the plastic is extruded onto and into the textile through the printer nozzle as shown both schematically and photographically in Fig. 5. The mechanical connection between the printed plastic and the textile to be printed on is created by the infiltration of the molten polymer around the fabric threads and the subsequent hardening of the plastic when it cools [2, 3]. A photomicrograph showing the infiltration of polymer through a knitted fabric is presented in Fig. 6. There may also be a chemical bond between the textile fiber and the printed polymer, depending on the particular materials used and the surface treatments on the fabric" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003235_1.1332398-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003235_1.1332398-Figure2-1.png", "caption": "Fig. 2 Geometrical consideration of the nonlinear EHD model", "texts": [ " For the sake of completeness and to ensure the continuity of the lubrication regime a hyperbolic load variation function is fitted to Eq. ~2!. Figure 1 shows a map of W\u0304i against hG i for a range of h\u0304 i values. It covers both HD and EHD regimes. The model described in this work assumes a total deflection d i in the contact angle direction of the ith ball, comprising the total elastic deflection de ~includes the inner and outer races and thus the total film thickness hi!. Under initial conditions ~see Section 6.1! all contacts suffer universal deflection, Fig. 2, given by d05de1h0 . (7) If the center-line of the shaft undergoes a general movement a component of which is rd in the normal direction of the ith contact and with respect to its frame of reference O, the following total deflection relation results Fig. 2 d i5de12hi1rd . (8) It should be noted that in a lubricated bearing, the ball/raceway contacts are separated by two layers of oil film. Due to the difference in curvature between the ball and the respective raceways, each layer may operate in a different regime of lubrication. To simplify the analysis in this model the difference in curvature between the ball and the surrounding raceways is ignored, thus making the two layers geometrically identical ~i.e., 2hi!. Using the normalized groups in Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001429_lra.2021.3068951-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001429_lra.2021.3068951-Figure1-1.png", "caption": "Fig. 1. Uncertainty in contact interactions", "texts": [ " Let the discrete time EKF of the state deviations \u03b4x\u0302t take the form of the second row of (14), then following [22] the error dynamics \u03b4et+1 = \u03b4xt+1 \u2212 \u03b4x\u0302t+1 is given by \u03b4et+1 = (At \u2212GtFt) \u03b4et + Ct\u03c9t \u2212GtDt\u03b3t (19) This is the simplest estimator of choice and can be replaced with any other estimator as long as it can be written locally as a linear dynamical system. The optimal estimation gains are then given by Gt = At\u03a3tF T t ( Ft\u03a3tF T t +Dt\u0393tD T t )\u22121 (20) where \u03a3t is the error dynamics covariance. As legged robots have a free floating base modeled as an SE(3) element, the proper Lie group operations must be utilized during the propagation of the covariance of the local error dynamics. A full treatment of EKFs on Lie groups can be found in [31]. Consider a robot during a dynamic contact scenario as depicted in Fig. 1. A control algorithm computes actuation torques based on the perception of the robot\u2019s own states along with its surrounding environment. Both the perception of the robot environment and its states are susceptible to sensor noise and perception errors, introducing uncertainty in the measurements. We propose to model the contact uncertainty as an uncertainty at the tip of the swing foot \u0393c as shown in the ellipsoid in Fig. 1. This has the advantage of avoiding the need to keep track of the environment model or the next contact location in the state vector. We then map this uncertainty back to the space where the full state covariance matrix \u0393fs is defined. Adding both covariances results in the total uncertainty in the contact interaction. A deviation in the swinging end-effector of the robot can be linearly mapped to a deviation in its state vector through[ \u03b4p \u03b4p\u0307 ] = [ Js 0 J\u0307s Js ] \ufe38 \ufe37\ufe37 \ufe38 As [ \u03b4q \u03b4v ] (21) whereJs is the jacobian of the swinging foot", " A linear spring damper contact model is used for the simulations with an explicit Euler integration scheme [33] at a time step \u03b4tsim = 1\u00d7 10\u22124 s with a spring stiffness parameter of k = 1\u00d7 105 N/m and a spring damping parameter of b = 3\u00d7 102 Ns/m. The coefficient of static friction used in simulation is \u03bc = 0.7. The simulated feedback control frequency runs at 1 kHz and the discretization step for the optimal control problems is set to \u03b4topt = 1\u00d7 10\u22122 s. Moreover, the legs of the robot will be referred to as FL,FR,HL,HR denoting FrontLeft, FrontRight, HindLeft and HindRight respectively. Each leg of the robot in turn consists of three joints as it can be seen in Fig. 1. For all the experiments, the same cost function, weights and reference trajectories are used for both DDP and Risk Sensitive Control. All the planning and control is designed for perfectly flat floor in all three experiments. This results in the same whole body trajectories xt and the same feedforward torque control profiles \u03c4 for both DDP and Risk Sensitive control in each experiment. The sensitivity parameter is set to \u03c3 = 10 for the Risk Sensitive solver, leaving the uncertainty models as the only variable in the experiments", " For all the experiments presented, the uncertainty parameters can be described as follows. The process noise \u03a9t = diag(1\u00d7 10\u22126) through out the whole experiment. The full state measurement noise \u0393fs = diag(5\u00d7 10\u22123) for all the experiments. \u0393c = 0 during any lift off phase of the foot. For the landing phase \u0393c is increased to 5\u00d7 10\u22124 for the diagonal elements corresponding to p and 1\u00d7 10\u22124 for the diagonal elements corresponding to p\u0307. In this experiment, the task is to swing a single leg forward with a maximum height of 10 cm and a step length of 8 cm similar to what is shown in Fig. 1. A 3 cm high block is added at the next contact location to simulate an unpredicted contact of 9.2% of the total leg length. The contact with the block occurs at t = 0.43 s whereas the contact with flat ground was planned for t = 0.55 s. The first uncertainty model, Risk-Uniform, is simply a diagonal matrix with equal variance on all of its entries. In the second uncertainty model, Risk-SwingJoints, the variance terms on the joints of the swinging foot are increased. In the third model, Risk-Unconstrained, we add a contact noise term similar to (22) without using the nullspace projection due to the active contacts" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001080_j.mechmachtheory.2020.104153-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001080_j.mechmachtheory.2020.104153-Figure9-1.png", "caption": "Fig. 9. Working process of the VSA. The upper four graphs represent the stiffness regulation at equilibrium position; the lower four graphs represent the working state when an external torque \u03c4 ext is applied.", "texts": [ " The pivot is inserted into the linear guide rail of the guide bar and can slide along the rail when an external load is applied on the load side link of the actuator or the crank length is adjusted by the stiffness motor. The guide bar is connected to the load side link through a revolute joint and is constrained by a customised torsion spring. The load side link is connected to the support base and crank through revolute joints. A mechanical limit is used to constrain the actuator deflection. Two encoders are used to measure the position of the actuator and the torsion spring deflection angle. The working process of the VSA is presented in Fig. 9 . When the load side of the actuator is at the equilibrium position where no external load is applied, the stiffness can be regulated or held without providing any resistant force theoretically. The upper four graphs in Fig. 9 represent the stiffness modulation process at the equilibrium position by adjusting the length of the crank. When the pivot is aligned with the rotation axis of the crank ( Fig. 9 (a1)), the apparent stiffness is zero; when the pivot is aligned with the guide bar rotation axis ( Fig. 9 (d1)), the apparent stiffness reaches infinity theoretically. When an external load is applied on the load side of the actuator, a deflection angle \u03b8 occurs. Then, the rotational angle \u03b8l of the load side link is derived as the sum of the principal motor drive angle \u03b8m and the deflection angle \u03b8 . The lower four graphs in Fig. 9 represent the working states when an external load \u03c4ext is applied. The deflection angle \u03b83 in high stiffness situation is smaller than the deflection angle \u03b82 in small stiffness situation. Compared with the VSAs that can theoretically achieve an infinite stiffness range in the literature, e.g., AwAs-II, vsaUT-II, and SVSA, the proposed VSA can achieve a more compact structure due to the use of only one linear torsion spring in the mechanism. Furthermore, a torsion spring without any preloading is used in the proposed VSA; hence, all the energy stored in the spring can be used for the passive deflection, and the energy capability of the VSA can be improved" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000560_s00170-016-8857-0-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000560_s00170-016-8857-0-Figure3-1.png", "caption": "Fig. 3 Generation of pinion and gear tooth-surfaces by the imaginary crown gear", "texts": [], "surrounding_texts": [ "The proposed optimization procedure relies heavily on the loaded tooth contact analysis for the prediction of maximum tooth contact pressure and transmission errors. The load distribution and transmission error calculation method employed in this study were developed by the author of this paper and can be described as follows. In the applied load distribution calculation, it is assumed that the point contact under load is spreading over a surface along the \u201cpotential\u201d contact line, which line is made up of the points of the mating tooth surfaces in which the separations of these surfaces are minimal, instead of assuming the usually applied elliptical contact area. The investigations have shown that in the case of relatively small tooth surface modifications the assumption of an elliptical contact area causes false results. The load distribution calculation is based on the conditions that the total angular position errors of the gear teeth being instantaneously in contact under load must be the same, and along the potential contact line (contact area) of every tooth pair instantaneously engaged, the composite displacements of tooth surface points\u2014as the sums of tooth deformations, tooth surface separations, misalignments, and composite tooth errors\u2014should correspond to the angular position of the gear member. Therefore, in all the points of the instantaneous potential contact lines, the following condition should be satisfied: \u0394\u03c62 \u00bc \u0394\u03c6 d\u00f0 \u00de 2 \u00fe\u0394\u03c6 k\u00f0 \u00de 2 \u00bc \u0394yn rD \u22c5 r! a!0 \u22c5 e! r! \u00fe\u0394\u03c6 k\u00f0 \u00de 2 \u00f03\u00de where \u0394yn is the composite displacement of contacting surfaces in the direction of the unit tooth surface normal e!, r! is the position vector of the contact point, and rD is the distance of the contact point to the gear axis, and a! 0 is the unit vector of the gear axis. The composite displacement of the contacting surfaces in contact point D, in the direction of the tooth surface normal, can be expressed as \u0394yn \u00bc w zD\u00f0 \u00de \u00fe s zD\u00f0 \u00de \u00fe en zD\u00f0 \u00de \u00f04\u00de where zD is the coordinate of point D along the contact line, w(zD) is the total deflection in point D, s (zD) is the relative geometrical separation of tooth-surfaces in pointD, and en(zD) is the composite error in point D, that is the sum of manufacturing and alignment errors of pinion and gear. The total deflection in point D is defined by the following equation ([34, 35]) w zD\u00f0 \u00de \u00bc Z Lit Kd zD; zF\u00f0 \u00de\u22c5p zF\u00f0 \u00de\u22c5 dz\u00fe Kc zD\u00f0 \u00de\u22c5p zD\u00f0 \u00de \u00f05\u00de where Lit is the geometrical length of the line of contact on tooth pair it, Kd(zD, zF) is the influence factor of tooth load acting in tooth-surface point F on total composite deflection of pinion and gear teeth in contact point D. Kd includes the bending and shearing deflections of pinion and gear teeth, pinion and gear body bending and torsion, and deflections of supporting shafts. A finite element computer program is developed for the calculation of bending and shearing deflections in the pinion and gear. Kc(zD) is the influence factor for the contact approach between contacting pinion and gear teeth, i.e., the composite contact deformation in point D under load acting in the same point, p (zF) and p (zD) are the tooth loads acting in positions F and D, respectively. As the contact points are at different distances from the pinion/gear axis, the transmitted torque is defined by the equation T \u00bc Xit\u00bcNt it\u00bc1 Z Lit r F \u22c5 p! zF\u00f0 \u00de\u22c5 t!0F \u22c5dz \u00f06\u00de where rF is the distance of the loaded point F to the gear axis, t ! 0F is the tangent unit vector to the circle of radius rF, passing through the loaded pointF in the transverse plane of the gear, and Nt is the number of gear tooth pairs instantaneously in contact. The load distribution on each line of contact can be calculated by solving the nonlinear system of Eqs. (3\u20136). An approximate and iterative technique is used to attain the solution. The potential contact lines are discretized into a suitable number of small segments, and the tooth contact pressure, acting along a segment, is approximated by a concentrated load, \u0394 F ! , acting in the midpoint of the segment. By these approximations, Eqs. (3, 4, and 6) become \u0394\u03c62 \u00bc \u0394yn it ;iz\u00f0 \u00de\u22c5 r! a!0 \u22c5 e! rD\u22c5 r! 0 B@ 1 CA it ;iz\u00f0 \u00de \u00fe\u0394\u03c6 k\u00f0 \u00de 2 it\u00f0 \u00de \u00f07\u00de \u0394yn it ;iz\u00f0 \u00de \u00bc w it ;iz\u00f0 \u00de \u00fe en it ;iz\u00f0 \u00de \u00fe s it ;iz\u00f0 \u00de \u00f08\u00de T \u00bc Xit\u00bcNt it\u00bc1 Xiz\u00bcNz it\u00f0 \u00de iz\u00bc1 r F it ;iz\u00f0 \u00de\u22c5 \u0394 F ! it ;iz\u00f0 \u00de\u22c5 t ! 0F it ;iz\u00f0 \u00de \u00f09\u00de where w it ;iz\u00f0 \u00de is the total displacement in the midpoint of segment iz on tooth pair it, \u03b6 \u00bc arccos t13\u00f0 \u00de; \u03b6 \u00bc arc sin t23\u00f0 \u00de : is the concentrated load acting in the midpoint of the segment, it is the identification number of contacting tooth pair, iz is the segment identification number on tooth pair it, and Nz it\u00f0 \u00de is the number of segments on the contact line of tooth pair it. The total displacement is defined by the expression w it ;iz\u00f0 \u00de \u00bc wt it ;iz\u00f0 \u00de \u00fe wc it ;iz\u00f0 \u00de \u00fe wgs it ;iz\u00f0 \u00de \u00f010\u00de where wt it ;iz\u00f0 \u00de is the composite bending and shearing deflection of pinion and gear teeth, wc it ;iz\u00f0 \u00de is the composite contact deformation of pinion and gear teeth, and wgs it ;iz\u00f0 \u00de is the deflection due to pinion and gear body bending and deflection of the supporting shafts. The tooth deflections are obtained by the following summation wt it ;iz\u00f0 \u00de \u00bc Xiz1\u00bcNz it\u00f0 \u00de iz1\u00bc1 K p\u00f0 \u00de d it ;iz1\u00f0 \u00de \u00fe K g\u00f0 \u00de d it ;iz1\u00f0 \u00de \u22c5\u0394F it ;iz1\u00f0 \u00de: \u00f011\u00de The compliances K p\u00f0 \u00de d it ;iz1\u00f0 \u00de and K g\u00f0 \u00de d it ;iz1\u00f0 \u00de of the pinion and the gear are determined by the finite element method. The actual load distribution, defined by the values of concentrated loads \u0394 F ! it ;iz\u00f0 \u00de, acting in the midpoints of the seg- ments of the potential contact lines, is obtained by using the successive-over-relaxation method. In every iteration cycle, a search for the points of the potential contact lines that could be in instantaneous contact is performed. For these points, the following condition should be satisfied \u0394yn it ;iz\u00f0 \u00de\u2264 \u0394\u03d52\u2212\u0394\u03d5 k\u00f0 \u00de 2 it\u00f0 \u00de r! a!0 \u22c5 e! rD\u22c5 r! 0 @ 1 A it ;iz\u00f0 \u00de : \u00f012\u00de" ] }, { "image_filename": "designv10_11_0000620_s11071-018-4338-3-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000620_s11071-018-4338-3-Figure9-1.png", "caption": "Fig. 9 Two types of leaf spring based on two uniform strength beam concepts. a Uniform-thickness multi-leaf spring. b Parabolic leaf spring", "texts": [ " 8b, the master leaf is subjected to a bending preload opposite in direction to that caused by the vehicle load, resulting in overall reduction of the spring bending stress during the vehicle operation. To extend the life cycle of the leaf springs, they are usually designed based on the concept of the uniform strength beam. Depending on if the thickness or width of the leaf is kept constant in the ideal model, the designed leaf spring can be classified as a uniformthickness leaf spring or a parabolic leaf spring, respectively. The uniform-thickness leaf spring is shown in Fig. 9a. In the multi-leaf spring, the leaves with different curvatures are clamped together and the adjacent leaves contact along the full longitudinal length due to the assembly pre-stress. By contrast, the other method is to vary the thickness of the leaves, rather than the width, with respect to the length of the leaf in order to obtain uniform stress throughout the leaf spring. This spring type is called the parabolic leaf spring and is shown in Fig. 9b. In practice, the thickness of the center clamped segment, which is rigidly connected to the spring seat, is constant. Unlike the uniform-thickness multi-leaf spring, the parabolic leaf spring normally has only one or two leaves because even one single parabolic leaf can function as a uniform strength beam. The weight of the parabolic leaf spring is therefore less than that of the uniform-thickness multi-leaf spring for the same stiffness. In practice, to increase the stiffness of the leaf spring, parabolic leaf springswith two leaves are commonly used, and a rubber or plastic spacer is often inserted between adjacent leaves at the ends to separate them and reduce the interleaf friction. As shown in Fig. 9b, there are gaps between leaves in the assembly and the leaves initially contact only at the two edges, unlike the uniform-thicknessmulti-leaf spring in which the leaves can have distributed contact along the length of the leaves. As a result, the friction between the parabolic spring leaves is much less than that in the uniform-thickness leaf spring, improving stability and ride comfort. Because the parabolic leaf spring has advantages of light weight and weak interleaf friction, it is widely used in modern suspension systems" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003138_pesc.1996.548674-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003138_pesc.1996.548674-Figure9-1.png", "caption": "Fig. 9. Refractive action along LT given a diode boundary", "texts": [ " In a refractive case, in the (1 ,O) configuration the state might hit 6 to the right of the intersection of cs and 6. It then slides along 6 toward the origin until it hits cs. We will call this point the successor 0,. At oo the family of on-trajectories (0,l) will become valid. If a stable sliding mode is present, the converter will move toward xa. If the: action with respect to cs is refractive, the state moves away from both (T and 6. Thus the switching is refractive with respect to 0. This behavior is shown in Fig. 9. If the next (0,IJ trajectory redirects the state to cs (Fig. 9a), the converter leaves discontinuous mode, Theorem 2 is satisfied, and stability can be concluded. If, however, the next (0,l } trajectory leads the state to 6 (at the point 6, in Fig. 9b), the sliding mode along 6 will bring the state to o,, again. Hence Theorem 2 is violated: s , ,~ is not smaller than s,. The converter will operate along a stable limit cycle, and indeed does not meet the definition of large signal stability. Theorem 5: A converter such as a buck, boost, or buckboost circuit with two states, with an active switch controlled by a stable stationary, straight line boundary, and with a diode boundary will be large signal stable if for a successor 6, there is no successor 6 , that is not reached via a sliding mode on the diode boundary" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001379_tec.2020.3030042-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001379_tec.2020.3030042-Figure4-1.png", "caption": "Fig. 4. Axial vibration diagram of elastic beam.", "texts": [ " Generally, the complex boundary conditions of the structure will make the calculation complicated when directly solving the motion differential equations of the structure, and it is difficult to get accurate results. Therefore, some research start from the perspective of energy conservation to solve the vibration characteristics of the elastic structure. Afterwards, the process of solving the natural frequencies by the energy method is expounded based on the simple-supported elastic beam, as shown in Fig. 4. EI(x) and \u03c1(x) are the axial distribution of the elastic modulus and density of the beam, respectively. The displacement function of axial vibration of an elastic beam can be expressed as , siny x t y x t (1) where y(x) is the function of modal shape related to the position, \u03c9 and \u03b1 are the vibration angular frequency and the relative position angle. The potential energy and kinetic energy of the simple-supported elastic beam can be expressed as 2 2 20 2 2 2 20 , 2 sin 2 L L EI x y x t PE dx x t y x EI x dx x (2) 2 0 2 2 2 0 , 2 cos 2 L L x y x t KE dx t t x y x dx (3) Ignoring the damping of the elastic beam, Umax=Tmax can be obtained from the energy conservation of the system, thus the Rayleigh quotient expression of the simply-supported elastic beam can be described as discrete orthogonal functions, scilicet 1 1 2 2 1 tN Nt Nt i i i y x c x c x c x x c \u03c7 (5) where Nt is the number of functions in the orthogonal function cluster, the orthogonal function cluster \u03c7 and the weighting coefficient c are 1 2, , , , ,i Ntc c c cc (6) T 1 2, , , , ,i Nt \u03c7 (7) Substituting (5) into (4), the simplified Rayleigh quotient expression can be obtained as T 2 T cKc cMc (8) The Rayleigh quotient takes the extreme value of the weighting coefficient c, then T T T T 2 T cMc cKc cKc cMc c c 0 c cMc (9) where the specific elements of the stiffness matrix K and the mass matrix M are 22 2 20 L ji ij xx k EI x dx x x \u03c7\u03c7 (10) 0 L ij i jm x x x dx \u03c7 \u03c7 (11) Simplifying (9) according to the related theory of matrix calculation, the characteristic equation of natural frequencies of the elastic beam can be expressed as 2 0K M c (12) Consequently, the vibration displacement of continuous systems can be discretized based on Galerkin discretization, and the characteristic equation of natural frequencies of elastic beams can be obtained by energy conservation" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000879_j.apor.2019.01.030-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000879_j.apor.2019.01.030-Figure5-1.png", "caption": "Fig. 5. The illustration of EBS LOS based guidance method.", "texts": [ " The updated weights are used in the Eq. (5) to estimate the rudder angle to control the ship sailing on the desired yaw angle. The response of the ship\u2019s motions would be used in the next recursive loop. More details about the design of UKF RBFNN control strategy can be seen in [40]. Moreover, the trajectory tracking involves automatic calculation of the heading angle by collecting instant positions and using it to determine the dynamic heading, which is achieved by using the EBS LOS guidance algorithm (see Fig. 5).This algorithm is implemented by introducing a virtual circle with radius RLOS (normally 2 times of ship\u2019s length) to get the intersection nearby the waypoint p x y( , )k k k1 1 1+ + + Based on the calculated LOS point p x y( , )LOS los los and the ship\u2019s current position p x y( , )ship , the dynamic LOS desired course angle xd and the trajectory tracking deviation E0 can be calculated by the following equations: x tan y y x x ( )d los los 1= (6) E y y cos x x sin( ) ( ) ( ) ( )k k k k0 = (7) In order to numerically evaluate the performance of the control system, the cost function of yaw tracking error denoted by CYaw and the cost function of rudder actions denoted by CRudder were adopted in this study [41]" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003664_s0043-1648(02)00241-7-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003664_s0043-1648(02)00241-7-Figure1-1.png", "caption": "Fig. 1. The test apparatus.", "texts": [ " In our previous work, Category I, the normal load, L, which compressed the rider specimen against the slider specimen, was so high that the portion of L carried by the fluid was small [6]. Here, the functional relationship between machinery component wear and entropy is further explored within the framework of irreversible thermodynamics. The emphasis of the present paper is on cases where the fluid carries a large portion of L. We refer to this regime as Category II, which includes the limiting case where the fluid carries all of L and consequently we have zero wear. Fig. 1 is a schematic representation of the central portion of the apparatus. The apparatus contains a precision, high-speed rotating shaft mounted on ball bearings. The shaft is driven by a dc motor, which is isolated to insure that motor vibrations are not transferred to the test shaft. A magnetic speed pickup measures the shaft\u2019s velocity. The shaft is partially immersed in a fluid lubricant. The lubricant is drawn in between a slider and rider component-pair and is circulated by means of a peristaltic pump" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001427_j.mechmachtheory.2021.104300-Figure14-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001427_j.mechmachtheory.2021.104300-Figure14-1.png", "caption": "Fig. 14. Calculation of point A j coordinates using polar coordinates r and \u03b4 on the example of the kinematic chain with j = 1.", "texts": [ " Using expression (48) , we can find the coordinates of point A j corresponding to the singular position. Later we will see how to use the obtained coordinates in the workspace analysis. Let\u2019s consider the procedure to find these coordinates on an example for point A 1 . We can use the following method for any other kinematic chain in the same manner. Suppose we know the values of generalized coordinates q 1 and q 2 . In subsection 3.2 , we have found that point A 1 would stay on circle for the fixed values of q and q ( Fig. 14 ). 1 1 2 Radius r and coordinates p M of the circle center M in the base frame { GL } in general (non-symmetrical) case can be found from the following expressions: r = 2 \u221a p ( p \u2212 L AS1 ) ( p \u2212 L AS2 ) ( p \u2212 L S1 S2 ) L S1 S2 , (49) p M = p S1 + L S1 M L S1 S2 ( p S2 \u2212 p S1 ) , (50) where half-perimeter p of triangle S 1 S 2 A 1 and lengths L S 1 S 2 and L S 1 M of the triangle base S 1 S 2 and its segment S 1 M are: p = 1 2 ( L AS1 + L AS2 + L S1 S2 ) , (51) L S1 S2 = | p S2 \u2212 p S1 | , L S1 M = \u221a L 2 AS1 \u2212 r 2 . (52) Expression (12) allows us to find coordinates p S 1 and p S 2 of points S 1 and S 2 . Since point A 1 belongs to circle 1 , it is convenient to describe its position p A 1 using polar coordinates r and \u03b4 ( Fig. 14 ): p A 1 = p M + r ( v 2 cos \u03b4 + v 3 sin \u03b4 ) , (53) where v 2 and v 3 are a couple of orthonormal vectors, defining plane 1 of circle 1 . There are many ways to place v 2 and v 3 in plane 1 . We will use the one where vector v 2 and unit vector z 1 , pointed along axis O 1 Z 1 of frame { O 1 }, lie in a common plane. Setting another unit vector v 1 normal to plane 1 and directed from S 1 to S 2 ( Fig. 14 ), we obtain the following expressions: v 1 = p S2 \u2212 p S1 L S1 S2 , v 3 = v 1 \u00d7 z 1 | v 1 \u00d7 z 1 | , v 2 = v 3 \u00d7 v 1 . (54) Now, consider singularity (48) when A 1 S 1 is perpendicular to z 1 . In this case, expression (48) will have the form: ( p A 1 \u2212 p S1 ) T z 1 = 0 . (55) Substituting (53) and (12) into (55) with the fact that v 3 is perpendicular to z 1 , after rearranging the terms, we will get the expression for cosine of \u03b4, corresponding to the singular configuration: cos \u03b4 = q 1 + ( p O 1 \u2212 p M ) T z 1 v T 2 z 1 r , (56) where p is a known and constant vector that contains the coordinates of O in { GL }", " In this study, we will consider only the constraints (43) \u2013(45) and the singularity (48) , neglecting other singular configurations. This type of workspace is very common for parallel manipulators, and there are various methods to find it [1] . Here we will use a straightforward and intuitive geometrical approach [1 , 59] that consists in the following steps: 1) Find spaces { A j } of possible locations for points A j . As we saw earlier in the forward kinematics section, with the specified values of generalized coordinates q i , each of the three points A j lies on circle j ( Fig. 14 ). If we vary the values of q i between their minimum and maximum values, we will get a set of circles for each point A j , which represents the possible locations of point A j . If we apply the constraint for angle \u03b2Si , the set of circles will become the set of arcs { A j }. In this step, we also calculate the coordinates of points A j , which correspond to singular configurations (48) , according to the above algorithm. 2) Find spaces { B j } of possible locations for points B j . Now, given the set of arcs { A j } for each point A j , it is not difficult to determine the locations of points B j , using the fact that points A j , B j , and C j belong to a common line for each kinematic chain" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000356_j.ifacol.2017.08.1823-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000356_j.ifacol.2017.08.1823-Figure1-1.png", "caption": "Fig. 1. Schematic Representation of the ith Fixed-Pitch Actuator Module \u2212 A fixed-pitch propeller (black) is coupled to an electric motor (grey). Given a rotation speed \u03c9i, a resulting thrust force fAi and torque \u03c4Ai are generated in the center of pressure (orange).", "texts": [ " By taking into account the masses and moments of inertia of all the payload modules, it is possible to define the body reference frame FM so that the origin coincides with the center of mass (CoM) of the UAV and the body axes are aligned 4 with the principal axes of inertia. The overall mass and moment of inertia of the UAV will be denoted by m and IM , respectively. An actuator module is a module of the UAV able to generate forces and torques. In this paper we will assume that an actuator module is always a motor-driven fixedpitched propeller of negligible mass 5 . As illustrated in Fig. 1, each actuator module is characterized by its own local reference frame FAi, such that the origin coincides with the aerodynamic center of pressure (CoP). The forces and torques generated by the ith propeller can be locally obtained as fAi = [ 0 0 \u2212cLi ] \u03c92 i , \u03c4Ai = [ 0 0 \u2212sicDi ] \u03c92 i , (1) respectively, where cLi > 0 and cDi > 0 are the positive aerodynamic lift and drag coefficients, si \u2208 {\u22121,+1} denotes the spin direction of motor i (i.e. si = \u00b11 implies that the motor is spinning around \u00b1z\u0302Ai), and \u03c9i is the rotational speed", " By taking into account the masses and moments of inertia of all the payload modules, it is possible to define the body reference frame FM so that the origin coincides with the center of mass (CoM) of the UAV and the body axes are aligned 4 with the principal axes of inertia. The overall mass and moment of inertia of the UAV will be denoted by m and IM , respectively. 2.2 Actuator Modules An actuator module is a module of the UAV able to generate forces and torques. In this paper we will assume that an actuator module is always a motor-driven fixedpitched propeller of negligible mass 5 . As illustrated in Fig. 1, each actuator module is characterized by its own local reference frame FAi, such that the origin coincides with the aerodynamic center of pressure (CoP). The forces and torques generated by the ith propeller can be locally obtained as fAi = [ 0 0 \u2212cLi ] \u03c92 i , \u03c4Ai = [ 0 0 \u2212sicDi ] \u03c92 i , (1) respectively, where cLi > 0 and cDi > 0 are the positive aerodynamic lift and drag coefficients, si \u2208 {\u22121,+1} denotes the spin direction of motor i (i.e. si = \u00b11 implies that the motor is spinning around \u00b1z\u0302Ai), and \u03c9i is the rotational speed", " As a result of these physical limitations, the control inputs are subject to the actuator saturation constraints 6 umin < ui(t) < umax, \u2200i \u2208 {1, . . . , NA}. (4) 2.3 Dynamic Equations To take advantage of the decoupling between the translational and rotational dynamics, it is customary to control the UAV in the body reference frame FM relative to the 4 Please note that orientation of the body axes can be changed without any loss of generality. 5 We assume that its mass is accounted as a payload module. 6 Without loss of generality, in this paper the actuator constraints are considered the same for all NA actuator modules. Fig. 1. Schematic Representation of the ith Fixed-Pitch Actuator Module \u2212 A fixed-pitch propeller (black) is coupled to an electric motor (grey). Given a rotation speed \u03c9i, a resulting thrust force fAi and torque \u03c4Ai are generated in the center of pressure (orange). inertial reference frame FI . The UAV dynamics are obtained by writing the Newton-Euler equations of motion 7 based on Hahn (2002), I x\u0308\u03c9 +C(x\u0307\u03c9)x\u0307\u03c9 = g +B(x\u03c9)u, (5) where x\u0307\u03c9 := [p\u0307T I ,\u03c9 T M ]T is the vector of linear and angular velocities" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003218_robot.1991.131559-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003218_robot.1991.131559-Figure3-1.png", "caption": "Figure 3: An open chain planar robot holding a workpiece.", "texts": [ "of the generalized coordinates by substituting for d , u\u2019, and u\u2019 with the terms in Equation 10 through Equation 13. Wit,li these substitutions, Equation 18 becomes 3 Example To show that Equation 23 accurately models the dynamic properties of a rigid body, we solve a pertinent, yet relatively simple problem. The planar double pendulum, shown in Figure 2, was chosen because it is relatively simple, yet nontrivial; with some modification, it can serve as the basis for a model of a rigid body propelled by a planar robot (see Figure 3); and, by externally applying only the gravitational force, the accuracy of the solution can be verified using Conservation of Energy. [M]Q = F + h(Q, Q), (23) 3.1 Planar Quaternions where Planar quaternions are a subset of dual quaternions. &I = &2 = Q7 = Q8 = 0. (26) where [I41 is the 4 x 4 identity matrix and These constraints leave four nontrivial equations of motion, i = 3 , . . . , 6. Equation 26 trivially satisfies Equation 4 and simplifies Equation 3 to 8 [A,] = 1141 QP, i=5 and where Q; + Q: - 1 = 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003710_0957-4158(92)90043-n-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003710_0957-4158(92)90043-n-Figure6-1.png", "caption": "Fig. 6. Blower performance map.", "texts": [ " This can be done by using the coordinates on the wall and model geometry as shown in Fig. 5. The angles of or, /3, 7 and 6 are measured by the sensors and h and ! are calculated from these angles. If the frictional coefficient /~ is assumed, the required negative pressure in the sucker can be estimated by combining Figs 4 and 5, i.e. F/W or I~F/W in Fig. 4 can be determined by h and ! in Fig. 5, which gives the minimum required sucking force. The minimum required pressure Po(Po = F/S, where S is the base area of the sucker) can be given on the blower performance map, shown in Fig. 6 as an example. On the other hand, just after a cup is fixed on the wall, the negative pressure is measured, which is P in Fig. 6 for example. It gives a little larger value than P0. The input voltage of the blower, V, must be increased to V = V1 to get a certain pressure margin. But in this case it is important to know whether P is on curve A or B. If it is on B, the pressure margin M = P/Po, is less than that on A. The difference between A and B depends on the leakage of sucking air. If M is not enough, the fixing position on a wall has to be changed. To get the same pressure margin for the different leakage conditions, the higher input voltage is required for the larger air leakage" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001427_j.mechmachtheory.2021.104300-Figure10-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001427_j.mechmachtheory.2021.104300-Figure10-1.png", "caption": "Fig. 10. Mechanism velocity analysis for a single kinematic chain.", "texts": [ " Given a tolerance of 1 \u00d7 10 \u20136 as the stopping criterion, convergence has been reached after four iterations, as shown in Table 2 . This procedure can be also applied for trajectory calculation, taking the calculated platform coordinates on the current step as an initial guess for the next step. This section studies the relations between the output link velocities and the velocities of the other bodies, especially the sliders. Suppose that angular velocity \u03c9 pl and linear velocity \u03c5O of point O pl describe the platform motion ( Fig. 10 ). Our task is to find a connection between these two vectors and the sliders\u2019 velocities \u02d9 q = [ \u0307 q1 . . . \u02d9 q6 ] T . Let\u2019s consider one of the kinematic chains (calculations for the other ones will be the same). The velocity of point B j can be found as: \u03c5Bj = \u03c5O + \u03c9 pl \u00d7 OB j = \u03c5O \u2212 ( OB j ) \u03c9 pl = [ I 3 \u00d73 \u2212 ( OB j )][\u03c5O \u03c9 pl ] , (26) where OB j is a vector from point O pl to B j ; is a skew-symmetric matrix representation of a vector. We can express this velocity as the sum of two components ( Fig. 10 ): \u03c5Bj = \u03c5\u2016 Bj + \u03c5\u22a5 Bj , (27) where \u03c5\u2016 Bj and \u03c5\u22a5 Bj are projections of \u03c5Bj on rod B j A j and the plane, perpendicular to it, respectively. Given \u03c5Bj from (26) , these projections will have the following form: \u03c5\u2016 Bj = 1 L 2 ABj BA j BA T j \u03c5Bj = P BAj \u03c5Bj , (28) \u03c5\u22a5 Bj = \u03c5Bj \u2212 \u03c5\u2016 Bj = ( I 3 \u00d73 \u2212 P BAj ) \u03c5Bj , where BA j is a vector pointed from B j to A j ; P BAj = 1 L 2 ABj BA j BA T j is a projection matrix. Next, since rod A j B j is a rigid body, we can use the relations: \u03c5\u2016 Aj = \u03c5\u2016 Bj , (29) \u03c5\u22a5 Aj = \u2212\u03c5\u22a5 Bj L ACj L BCj , where \u03c5\u2016 Aj and \u03c5\u22a5 Aj are projections of the point A j velocity on rod B j A j and the plane, perpendicular to it, respectively; L ACj and L BCj are the lengths of the rod\u2019s corresponding fragments. Total velocity \u03c5Aj of point A j is the sum of two components in (29) , and it will have the following form after substitution of (28) and rearranging the terms: \u03c5Aj = \u03c5\u2016 Aj + \u03c5\u22a5 Aj = 1 L BCj ( L ABj P BAj \u2212 L ACj I 3 \u00d73 ) \u03c5Bj . (30) We can use the same approach and consider the equality between velocities\u2019 projections of points A j and S i on interme- diate link A j S i . These projections can be found as follows ( Fig. 10 ): \u03c5Aji = 1 L 2 ASi SA i SA T i \u03c5Aj = P SAi \u03c5Aj , (31) \u03c5\u2016 Si = 1 L 2 ASi SA i SA T i \u03c5Si = P SAi z i \u02d9 qi , where \u03c5Aji is a projection of vector \u03c5Aj on intermediate link S i A j ; \u03c5\u2016 Si is a projection of the point S i velocity \u03c5Si on the same intermediate link; SA i is a vector pointed from S i to A j ; P SAi = 1 L 2 ASi SA i SA T i is a projection matrix; z i is a unit vector directed along axis Z i of frame { O i } ( Fig. 10 ). Equating the expressions above to each other, we will get: P SAi z i \u02d9 qi = P SAi \u03c5Aj . (32) To find \u02d9 qi , we can take the norm of both sides of (32) : ( P SAi z i ) T P SAi z i \u02d9 q 2 i = ( P SAi \u03c5Aj )T P SAi \u03c5Aj . (33) Opening the parentheses with the fact that P SAi z i = 1 L 2 ASi ( SA i \u00b7 z i ) SA i , P SAi \u03c5Aj = 1 L 2 ASi ( SA i \u00b7 \u03c5Aj ) SA i , (34) SA T i SA i = L 2 ASi = 0 , (33) will take the following form: ( SA i \u00b7 z i ) 2 \u02d9 q2 i = ( SA i \u00b7 \u03c5Aj )2 , (35) from which \u02d9 qi = SA i \u00b7 \u03c5Aj SA i \u00b7 z i = 1 SA i \u00b7 z i SA T i \u03c5Aj " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000889_j.compstruct.2019.04.063-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000889_j.compstruct.2019.04.063-Figure5-1.png", "caption": "Fig. 5. An application in the form of a vehicle suspension system \u2013 quarter car model.", "texts": [ " 11b can be used to generate stiffness characteristics, for potential use in vehicle suspension. Fig. 12 shows load carrying capacity of three such spring where number of stacked units used vary from 10 to 17. The load-deflection curves are based around typical linear, helical spring\u2019s stiffness values of 30 kN/m. The curves are such that they provide varying stiffness at low and high deflections. Stiffness at higher deflections is expected to influence the vehicle body motion i.e. the motion of ms in Fig. 5. Fig. 13 shows normalised force and acceleration responses that influence handling and ride comfort of a vehicle. The velocity normalised tyre force in Fig. 13a shows two peaks \u2013 one due to the vehicle bounce mode at lower frequency and the second one, the wheel hub mode. Ideally, the flatter the curve the more consistent is the tyre force. The Belleville stacks produce massive improvement by reduced force variation at the vehicle bounce mode, but show some deterioration nearer wheel hub mode. There is a huge potential in tuning nonlinear stiffness to optimise performance throughout the frequency range" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003674_robot.2000.845294-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003674_robot.2000.845294-Figure3-1.png", "caption": "Figure 3 - Linear Combination of Translational Generalized Errors", "texts": [ " Each equation associates a generalized error from link i-1 with a combination of errors from link i that result in end-effector errors in same magnitude and direction. Since it is not possible to distinguish the amount of the error contributed by each generalized error, these errors associated with link i-1 are indistinguishable. Equation (7) reflects the fact that the translational error along the Z-axis of frame i-1 has the same effect as a 361 1 combination of the translational errors along the Y and Z axes of frame i (see Figure 3). This relation is easily explained by the fact that the skew angle a, between the axes of joints i-1 and i is constant. Equation (8) states that the rotational error along the Zaxis of frame i-1 has the same effect as a combination of the rotational and translational errors along the Y and Z axes of frame i. For simplicity, a planar manipulator is used to explain this combination (see Figure 4). The top figure shows the end-effector translational and rotational errors AXt and AXr caused by the rotational generalized error qi" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001052_s00170-020-06061-8-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001052_s00170-020-06061-8-Figure3-1.png", "caption": "Fig. 3 Simple helical springs fabricated using the tradition spring manufacturing process [29]", "texts": [ " To investigate the behavior of variable dimension helical spring\u2013based periodic lattice structures, each designed spring was repeated in two dimensions to model larger spring-based structures employed in many industries, such as for footwear and sleeping mattresses. The designed and additively manufactured structures can be seen in Fig. 2. Simple helical springs with uniform design parameters are being fabricated using traditional manufacturing processes at high volumes; however, these simple helical springs are not optimal in energy absorption and other mechanical properties (Fig. 3). Therefore, the variable dimension helical springs need to be designed but more complex to be manufactured using traditional manufacturing methods [29]. Thus, the application of AM is crucial for fabricating these intricate geometries helical springs with variable design parameters as shown in Fig. 2 and Table 1. The samples were constructed using AM (Fig. 2) with polyamide (PA12) material powder on a high-speed MJF 4200 series 3D printer [30] in the High-Speed 3D Printing Research Center at the National Taiwan University of Science and Technology" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000048_tmag.2017.2698004-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000048_tmag.2017.2698004-Figure1-1.png", "caption": "Fig. 1. Configuration of the proposed VPM machine.", "texts": [ " In addition, authors in [8] develops a multi-pole dual-stator VPM machine with high torque capability by incorporating the merits of fractional-slot concentrated-windings and VPM structure. Furthermore, high temperature superconducting bulks are also employed in [9] to enhance the flux modulation effect of the iron teeth and thus improving the torque density of VPM machines. As aforemen- tioned, high torque density is always desirable in VPM machines. So in this paper, in order to improve the torque performances of conventional VPM machines, a novel dualstator VPM machine will be presented and analyzed. The structure of the proposed machine is shown in Fig. 1. It has two stators and a sandwiched rotor. The outer stator is a conventional stator with three-phase windings and semi-closed slots, and the inner stator has an iron core and PMs mounted on the surface of it. The rotor has a consequent-pole structure with Halbach array PMs. The magnetization directions of the PMs are also illustrated in Fig. 1. The proposed dual-stator VPM machine can be regarded as a superposition of two machines: a I Manuscript received March 19, 2017. Corresponding author: Dawei Li (email: daweili@hust.edu.cn). Digital Object Identifier inserted by IEEE 0018-9464 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. single-stator PM machine (Machine I) and a double-stator VPM machine (Machine II), shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003597_s11661-002-0376-y-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003597_s11661-002-0376-y-Figure1-1.png", "caption": "Fig. 1\u2014Electron beam solid freeform fabrication apparatus.", "texts": [ " EAGAR, Thomas Lord Profes- process uses a layer-by-layer approach similar to that of sor of Materials Engineering and Engineering Systems, is with the Depart- many rapid prototyping techniques. Deposition of metal is ment of Materials Science and Engineering, Massachusetts Institute of accomplished by feeding wire into a melt pool maintainedTechnology, Cambridge, MA 02139. Manuscript submitted May 22, 2001. on the surface of the previous layer by an electron beam METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 33A, AUGUST 2002\u20142559 (Figure 1). Appropriate positioning of the part during deposi- et al.[6] The output of these calculations is the average energy loss per unit of path length experienced by an incident elec-tion of each layer makes production to near-net shape possible. tron, also referred to as the stopping power of the material for electrons with a given initial energy. For Alloy 718, theThe EBSFF process addresses most of the quality problems of the conventional ingot-processing route. The stopping power varies from 2.819 MeV-cm2/g at 100 kV to 1" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003023_s0168-874x(97)81968-3-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003023_s0168-874x(97)81968-3-Figure7-1.png", "caption": "Fig. 7. Separation distances of the pairs of teeth adjacent to the contacting pair.", "texts": [ " (2) Because the tooth deflection of plastic spur gear is larger than that of steel spur gear, the influence of the premature and/or delayed meshing of teeth should be considered for plastic spur gears. Accordingly, a modification of the existing method has been derived for plastic spur gars, and verified by the multi-tooth contact analysis. This modified method can be used to study the minimization of static transmission errors of molded spur gears with parametric tooth profiles. The authors would like to thank the National Science Council of Republic of China for the financial support of this study through contract NSC-83-0422-E110-003. Appendix Refer to Fig. 7, the separation distances of the pairs of teeth adjacent to the contacting pair are calculated by the following procedures geometrically. For the adjacent pair of teeth before the contacting pair, the position vector of any point on the tooth profile of the driven gear is expressed as Pa = Pay = / s i n ~b2 c o s ~b 2 J - Rp2 - e b 2 t~ sin ~ + F Rp2 sinq52 + Rb2~bcos(~ -- ~b2) ,-], (A.1) L C -- Rp2 c o s (~2 - - Rb2 ~b s in(~ - ~b2)J 2rt where (])2 = - - ~ - - (1 - - X) Z2\" The subscript 2 denotes the driven gear", " In addition, q~ is the rotation angle from the pitch point, and ~ is the pressure angle. C is the center distance of two gear axes. x represents the distance from the pitch point to the contact position normalized by the base pitch, and Z is the tooth number. Assume the tip of the driving tooth will come into contact with the flank on the driven tooth, the ~b of the contact point on the driven tooth can be solved from Pa~ + PaZy = R21, (a.2) where the subscript 1 represents the driving gear, and Ra is the radius of the addendum circle. Then, as shown in Fig. 7, 7~ = t an - 1 _ _ _ - - Pax (A.3) Pay ' 2n (p~ = (1 - x) ~1 + inv ~ - inv qSal, where C a l = COS 1 Rbx inv ~ = tan ~ -- ~. (A.4) R a 1 The separation distance of the adjacent pair of teeth before the contacting pair is defined as E\u00b0ep = Rbl(]Ja - - (~0a)\" (A.5) F o r the adjacent pai r of teeth beh ind the con tac t ing pair, the angle of the tip of the dr iven t o o th defined in Fig. 7 is ca lcula ted by 2re /3\u00a2 = (1 + x) Z22 + inv ~ - inv q~a2, where \u00a2a2 = COS-1 Rb2 (A.6) Ra2 \" Assume the tip of the dr iven t o o t h is the con tac t point . T h e n ~0\u00a2 = s in - 1 Ra2 sin fie Re ' and where Rc = x / C 2 --[- R22 -- 2CRa2 cos fie 27t 7c = (1 + x) -~--- - inv ~ + inv \u00a2\u00a2, L1 (A.7) where ~bc = cos -1 Rbl (A.8) Rc The separa t ion dis tance of the adjacent pair of teeth beh ind the con tac t ing pair is def ined as (A.9) E~p = Rbl(7 e -- q~e). [1] M.D. Gafitanu, Contributions to the study of the influence of the number of teeth on the loading capacity of polyamide gears, Rev" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003388_978-3-662-04831-3-Figure5.16-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003388_978-3-662-04831-3-Figure5.16-1.png", "caption": "Fig. 5.16: Drawings of (relative) translational joints", "texts": [ " The constraint position equations of the translational Joint are obtained from the requirements that this joint does not allow relative rotations of the two bodies i and J; i.e., 194 5o Model equations of planar and spatial joints '1/Jij := '1/Ji - '1/Ji = c'l/J = constant or (5o15a) A ' 3 = = constant L 0 L . ( cos '1/Jij , - sin '1/Jij ) sin '1/Jij , cos '1/Jij ' but only relative translations along a common axis, where the latter require ment can be mathematically modeled as followso Consider the geometrical situation of Figure 5o16a with noncoincident points Si, Qi, and Sj, Qj on the hoclies i and j, respectively, located on a common straight line that de fines the direction of the relative translation of the bodieso Then the vectors ti := rsiQi and rs;Q; must remain collinear as well as the vector dji := rs;Qi where the vector rs;Qi is assumed tobe nonzeroo The above requirement can be written in terms of the orthogonality relation or (R 0 tLi)T 0 dl:.i = 0 \u2022 ]2 with and R := ( 01 : -01 ) 0 tfij_ := R 0 tfi Taking into account the vector loop equation (Figure 5o16a) R R dR R R R 0 Tpio + TQiPi + ji- Ts;Q; - TQ;P; - TP;O = yields (5o15b) (5o15c) 5.1 Theoretical modeling of planar joints 195 196 5o Model equations of planar and spatial joints This provides, together with (5o15c) and (5o15a), the constraint position equa tions (5o16a) and '1/Ji- '1/Jj = c,p = constanto (5o16b) 5.1.2.4 Combined orientation/partial-position constraint. Combined relative orientationfpartial-position constraints are theoretical models of rack-and-pinion mechanisms and cam followers (Figure 5017) 0 For the rack and-pinion mechanism of Figure 5o17a, the noslippage condition guarantees identical velocities of bodies 1 and 2 at their contact point Ao Then (5o17a) with R as the radius of the piniono This provides the constraint position equation Y~1o- Y~1 o(O) = -R ('lj;2- 'I/J2(0)) (5o17b) with y~10 (0) and 'I/J2(0) as starting conditions of y~10 and 'I/J2o 5" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000536_s11370-015-0180-3-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000536_s11370-015-0180-3-Figure4-1.png", "caption": "Fig. 4 Impression drawing of the 7-DOF space manipulator", "texts": [ " In order to ensure the strength of joint 4, its value should be far away from the 30\u25e6 of singular points. At the same time, it as far as possible maintains the large range of working space. That is why the range limit of joint 4 is among the 30\u25e6\u2013150\u25e6. And the other joints should be far away from the 10\u25e6 of singular points. This study is a basic research component of a national space manipulators project. To verify the suitability of the methods proposed earlier, it will be applied to 7-DOF space manipulators in a microgravity environment, as shown in Fig. 4, where the kinematics are similar to the structure in Fig. 1. In the task that needs to be simulated, the end-effectormust handle equipment while attached to a satellite carrier, which is a typical task for space manipulators. Some of the parameters related to the manipulators are shown in Tables 2 and 3. The simulation environment is MATLAB 2013a using the toolbox \u201cSpacedyn\u201d programmed by Shimizu et al. [26]. The parameters of the 7-DOF manipulator which are related to Table 1 are as follows: dbs = 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000004_1.4033611-Figure16-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000004_1.4033611-Figure16-1.png", "caption": "Fig. 16 Stephenson chains with seven prismatic joints", "texts": [], "surrounding_texts": [ "[1] Crossley, F. R. E., 1965, \u201cPermutations of Kinematic Chains With Eight Mem- bers or Less From Graph Theoretic View Point,\u201d Developments in Theoretical and Applied Mechanics, Vol. 2, Pergamon Press, Oxford, UK. [2] Freudenstein, F., and Dobrjanskyj, L., 1964, \u201cOn a Theory of Type Synthesis of Mechanisms,\u201d 11th International Congress of Applied Mechanics, Springer, Berlin, Germany, pp. 420\u2013428. [3] Woo, L. S., 1967, \u201cType Synthesis of Plane Linkages,\u201d ASME J. Eng. Ind., 89(1), pp. 159\u2013170. [4] Manolescu, N. I., 1973, \u201cA Method Based on Baranov Trusses and Using Graph Theory to Find the Set of Planar Jointed Kinematic Chains and Mechanisms,\u201d Mech. Mach. Theory, 8(1), pp. 3\u201322. [5] Fang, W. E., and Freudenstein, F., 1990, \u201cThe Stratified Representation of Mechanisms,\u201d ASME J. Mech. Des., 112(4), pp. 514\u2013519. [6] Kim, J. T., and Kwak, B. M., 1992, \u201cAn Algorithm of Topological Ordering for Unique Representation of Graphs,\u201d ASME J. Mech. Des., 114(1), pp. 103\u2013108. [7] Shin, J. K., and Krishnamurty, S., 1994, \u201cOn Identification and Canonical Numbering of Pin Jointed Kinematic Chains,\u201d ASME J. Mech. Des, 116(1), pp. 182\u2013188. [8] Shin, J. K., and Krishnamurty, S., 1994, \u201cDevelopment of a Standard Code for Colored Graphs and Its Application to Kinematic Chains,\u201d ASME J. Mech. Des., 116(1), pp.189\u2013196. [9] Ding, H., and Huang, Z., 2009, \u201cIsomorphism Identification of Graphs: Especially for the Graphs of Kinematic Chains,\u201d Mech. Mach. Theory, 44(1), pp. 122\u2013139. [10] Nie, S., Liao, A., Qiu, A., and Gong, S., 2012, \u201cAddition Method With 2 Links and 3 Pairs of Type Synthesis to Planar Closed Kinematic Chains,\u201d Mech. Mach. Theory, 47, pp. 179\u2013191. [11] Yan, H.-S., and Kuo, C.-H., 2006, \u201cTopological Representations and Characteristics of Variable Kinematic Joints,\u201d ASME J. Mech. Des, 128(2), pp. 384\u2013391. [12] Ding, H., and Huang, Z., 2007, \u201cThe Establishment of the Canonical Perimeter Topological Graph of Kinematic Chains and Isomorphism Identification,\u201d ASME J. Mech. Des., 129(9), pp. 915\u2013923. [13] Ding, H., Yang, W., Huang, P., and Kecskem ethy, A., 2013, \u201cAutomatic Structural Synthesis of Planar Multiple Joint Kinematic Chains,\u201d ASME J. Mech. Des., 135(9), p. 091007. [14] Uicker, J. J., and Raicu, A., 1975, \u201cA Method for the Identification of and Recognition of Equivalence of Kinematic Chains,\u201d Mech. Mach. Theory, 10(5), pp. 375\u2013383. [15] Mruthyunjaya, T. S., and Raghavan, M. R.,1979, \u201cStructural Analysis of Kinematic Chains and Mechanisms Based on Matrix Representation,\u201d ASME J. Mech. Des., 101(3), pp. 488\u2013494. [16] Yan, H. S., and Hall, A. S., 1981, \u201cLinkage Characteristic Polynomials: Definition, Coefficients by Inspection,\u201d ASME J. Mech. Des., 103(3), pp. 578\u2013584. Journal of Mechanical Design AUGUST 2016, Vol. 138 / 082301-7 Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jmdedb/935363/ on 01/27/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use [17] Yan, H. S., and Hall, A. S., 1982, \u201cLinkage Characteristic Polynomials: Assembly Theorems Uniqueness,\u201d ASME J. Mech. Des., 104(1), pp. 11\u201320. [18] Yan, H. S., and Hwang, W. M., 1983, \u201cA Method for the Identification of Planar Linkage Chains,\u201d ASME J. Mech. Transm. Autom. Des., 105(4), pp. 658\u2013662. [19] Sunkari, R. P., and Schmidt, L. C., 2006, \u201cReliability and Efficiency of the Existing Spectral Methods for Isomorphism Detection,\u201d ASME J. Mech. Des., 128(6), pp. 1246\u20131252. [20] Hasan, A., Khan, R. A., and Mohd, A., 2007, \u201cA New Method to Detect Isomorphism in Kinematic Chains,\u201d Khamandu J. Sci. Eng. Technol., I(III), pp. 1\u201311. [21] Quist, F. F., and Soni, A. H., 1971, \u201cStructural Synthesis and Analysis of Kinematic Chains Using Path Matrices,\u201d 3rd World Congress for Theory of Machines and Mechanisms, pp. D213\u2013D222. [22] Agrawal, V. P., and Rao, J. S., 1985, \u201cIdentification of Multi-Loop Kinematic Chains and Their Paths,\u201d J. Inst. Eng., 66, pp. 6\u201311. [23] Agrawal, V. P., and Rao, J. S., 1989, \u201cIdentification and Isomorphism of Kinematic Chains and Mechanisms,\u201d Mech. Mach. 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C., 1988, \u201cComparison of Plane and Spatial Kinematic Chains for Structural Error Performance Using Pseudo Hamming Distances,\u201d Indian J. Technol., 26, pp. 155\u2013160. [30] Rao, A. C., and Varada Raju, D., 1991, \u201cApplication of the Hamming Number Technique to Detect Isomorphism Among Kinematic Chains and Inversions,\u201d Mech. Mach. Theory, 26(1), pp. 55\u201375. [31] Hamming, R. W., 1950, \u201cError Detecting and Error Correcting Codes,\u201d Bell Syst. Tech. J., 29(2), pp. 147\u2013160. [32] Rao, A. C., and Rao, C. N., 1993, \u201cLoop-Based Pseudo-Hamming Values I: Testing Isomorphism and Rating Kinematic Chains,\u201d Mech. Mach. Theory, 28(1), pp. 113\u2013127. [33] Rao, A. C., 1997, \u201cHamming Number Technique. I: Further Applications,\u201d Mech. Mach. Theory, 32(4), pp. 477\u2013488. [34] Ambekar, A. G., and Agrawal, V. P., 1986, \u201cOn Canonical Numbering of Kinematic Chains and Isomorphism Problem: Max Code,\u201d ASME Paper No. 86- DET-169. [35] Ambekar, A. G., and Agrawal, V. P., 1987, \u201cCanonical Numbering of Kinematic Chains and Isomorphism Problem: Min Code,\u201d Mech. Mach. Theory, 22(5), pp. 453\u2013461. [36] Tang, C. S., and Liu, T., 1993, \u201cThe Degree Code: A New Mechanism Identifier,\u201d ASME J. Mech. Des., 115(3), pp. 627\u2013630. [37] Mruthyunjaya, T. S., 2003, \u201cKinematic Structure of Mechanisms Revisited,\u201d Mech. Mach. Theory, 38(4), pp. 279\u2013320. [38] Ding, H., Huang, P., Yang, W., and Kecskem ethy, A., 2016, \u201cAutomatic Generation of the Complete Set of Planar Kinematic Chains With Up To Six Independent Loops and Up To 19 Links,\u201d Mech. Mach. Theory, 96 pp. 75\u201393. [39] Ding, H., Huang, P., Liu, J. F., and Kecskem ethy, A., 2013, \u201cAutomatic Structural Synthesis of the Whole Family of Planar 3-Degrees of Freedom Closed Loop Mechanisms,\u201d ASME J. Mech. Rob., 5(4), p. 041006. [40] Sandor, G. N., and Erdman, A. G., 1988, Advanced Mechanism Design: Analysis and Synthesis, Vol. 2, Prentice-Hall, New Delhi, India, Chap. 1. [41] Crossley, F. R. E., 1966, \u201cOn an Unpublished Work of Alt,\u201d J. Mech., 1(2), pp. 165\u2013170. [42] Rao, A. C., and Nageswara Rao, C., 1989, \u201cIsomorphism Among Kinematic Chains With Sliding Pairs,\u201d Indian J. Technol., 27, pp. 363\u2013365. 082301-8 / Vol. 138, AUGUST 2016 Transactions of the ASME Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jmdedb/935363/ on 01/27/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use" ] }, { "image_filename": "designv10_11_0000621_j.matpr.2018.03.039-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000621_j.matpr.2018.03.039-Figure5-1.png", "caption": "Figure 5 Static Load Figure 6 Mesh Diagram", "texts": [ "P et al/ Materials Today: Proceedings 5 (2018) 14512\u201314519 2.2 Material Properties Material originally used for this leaf spring[6] is spring steel EN45 [2], Mechanical properties of steel EN45 are listed in Table 2. Jenarthanan M.P et al / Materials Today: Proceedings 5 (2018) 14512\u201314519 14515 fixed end, all translations are constrained as well as rotations except z-axis. In Shackle end, translation along x-axis and rotation along z-axis are released while all other DOFs are arrested. Assume Leaf Spring is in static loading condition shown in Figure 5 (without speed factor) and analyze Total Deformation and Von-Mises Stress values of both Steel and Hybrid Composite Leaf Spring. [7] Load Calculation: Weight of Vehicle, W1= 2150 Kg,Additional Weight (Passengers and Luggage), W2= 750 Kg. Total Weight, W= 2900 Kg. Load Acting on Leaf Spring, F= m\u00d7a F= 2900\u00d79.81 F= 28449 N (For all four-Leaf Springs): F= 7112.25 N (For one Leaf Spring) Then the assembly is meshed to for finite elements (Figure 6). Then the setup is solved for Total Deformation and Von-Mises Stress for both Steel Spring and Hybrid Composite [10]" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003601_icsmc.1999.812540-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003601_icsmc.1999.812540-Figure1-1.png", "caption": "Figure 1: Coordinate frames of the biped robot", "texts": [ " In typical human locomotion, leg muscles are repeatedly hardened and relaxed depending on the gait phase and result in very soft contacts with the ground. Using the same idea, the parameters of the impedance control are modulated depending on the its gait phase in order to have stable contacts. The dynamics of the biped robot is described in Section 2. The impedance controller and the impedance modulation strategy are presented in Section 3. Section 4 is devoted to the on-line trajectory generator. Section 5 describes simulations, followed by conclusions in Section 6. 2 Dynamics of Biped Robot The biped robot used in the paper is shown in Figure 1. It has 3 degrees of freedom in each leg. Biped, robots are different from the typical manipulators in that they have no fixed contact points with the ground, and the constraints between the feet and the ground change repeatedly as they walk. Actuator dynamics and friction forces in each joint are all ignored in the following equation of motion. The dynamics of lV - 960 the biped robot used in the paper is described by H,qc + Gca0 + D,h, + n, = rc (1) Huq, + G,aO + D,h, + nu = r, (2) QcQc + Ququ + Rao + Pch, + g = 0 (3) where q E R3, a0 E R6, and h E R6 are the joint acceleration, acceleration of the base link, and constrained force, respectively; H E are inertia matrix of the leg chain, the matrix which denotes the dynamic effects of the base link to each link chain, and a Jacobian, respectively; n E R3, Q E R6x3, P, R E and g E R6 are Coriolis and centripetal term, gravitational effects, the matrix denoting the dynamic effects of the link chains to the base link, the matrix denoting the dynamic effects of the constrained force to the base link, the inertia matrix of the base link, and a term including the gravitational effects of the base link" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000931_j.mechmachtheory.2019.103595-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000931_j.mechmachtheory.2019.103595-Figure4-1.png", "caption": "Fig. 4. Schematic representation of 2-PrRS + PR(P)S metamorphic parallel mechanism.", "texts": [ " For ease of installation, the outer mount is divided into a mounting body, a left baffle and a right baffle. The left and right baffles are connected to the mounting body by screws. The rR joint can have various configurations as its axis can have various configurations when the rotating shaft sliding along the grooves, leading to some special and useful configuration phases of the mechanism to achieve variable mobility. The following study will reveal the configurations of the mechanism in accordance with the three phases of motion of the rR pair. As described in Fig. 4 , the reference coordinate system O-XYZ is set up at the midpoint of the bottom edge of the fixed platform triangle, which is the intersection point of three actuator axes. The Y -axis points to the vertex of the fixed triangle base, the Z -axis points upward along the vertical direction, and the X-direction is generated by the right-hand screw rule. A moving coordinate system o 1 -x 1 y 1 z 1 is set up on the point o 1 , which is the centre point of the mobile platform triangle. In the original position, the x 1 , y 1 , and z 1 axes are coincident with the X, Y, and Z axes, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003215_s0003-2670(98)00469-3-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003215_s0003-2670(98)00469-3-Figure4-1.png", "caption": "Fig. 4. Absorption spectra of HPPA corresponding the pH variation of the medium. Nitric acid and sodium hydroxide were for pH adjustment.", "texts": [ " The \u00afuorescence intensity was assumed to be maximum at pH 11. When the pH was lower than 11, the \u00afuorescence intensity was reduced according to the degree of the acid dissociation of HPPA. The \u00afuorescence was generated from an anionic form of the product which has lost a phenolic hydrogen ion. The \u00afuorescence intensity has been proposed to increase with an increase in electron density in the aromatic rings of the product [6]. Therefore, the acid dissociation constant of HPPA was evaluated by measuring the absorbance \u00afuctuation at 240 nm. Fig. 4 shows the absorption spectra of HPPA corresponding to the pH variation of the medium. The acid dissociation constant of HPPA was estimated from the experimental results to be pK1<1 and pK2 10.3. On the other hand, when the pH was beyond 11, the \u00afuorescence intensity was decreased due to the loss of activity of the immobilized enzyme. The decrease of activity of the immobilized enzyme is caused by a change of the structure of the enzyme occurring in the preparation of the immobilized enzyme. Therefore, the reaction pH was set at 11 with 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001747_tro.2021.3062306-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001747_tro.2021.3062306-Figure6-1.png", "caption": "Fig. 6. Setting an initial estimate for the sensor poses using RVIZ interactive markers. In (a), the hand camera pose is being adjusted, while in (b), the hand camera and the world camera pose are being adjusted. (a) Eye-on-hand. (b) Joint-hand-base.", "texts": [ "list=PLQN09mzV5mbKL orTuKpb9EmfL_SFAF7nQ Authorized licensed use limited to: Miami University Libraries. Downloaded on June 15,2021 at 23:23:13 UTC from IEEE Xplore. Restrictions apply. in (10) or (11). To initialize camera-related transformations, we developed an interactive tool, which creates an RVIZ interactive marker associated with each sensor. It is then possible to move and rotate the markers and position the sensor at will. This provides a simple interactive method to easily generate plausible first guesses for the poses of the sensors. Some examples of this procedure are depicted in Fig. 6. Concerning the atomic transformations associated with the calibration pattern [pat T\u0302 base i in (10)], these are initialized by defining a new branch in the transformation tree, which connects the pattern to the frame to which it is fixed, e.g., for the eye-onhand case, it is base T\u0302 pat i = baseArgb opt i \u00b7 rgb optT pat i (16) where rgb optTpat i is estimated by solving the perspective-n-point for the detected pattern corners [28], [29], and baseArgb opt i is the aggregate transformation computed by deriving its topology from the tf tree and using the initial values for each atomic transformation in the chain" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003733_iros.2006.282470-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003733_iros.2006.282470-Figure6-1.png", "caption": "Fig. 6. Relation between the hip-joint torque and the generalized virtual gravity vector at CoM. The robot must walk only by central force, but the rolling effect enables to overcome the unreasonableness.", "texts": [ " The ZMP then travels forward monotonically in the sole under the assumption of \u03b8\u03071 > 0. If setting the origin of X-Z plane as the contact point of the sole with the ground when \u03b81 = 0, the X and Z positions of the contact point are then expressed as R\u03b81 [m] and 0 [m], respectively. Here let us consider the inverse transformation of uH to f g. It yields f g = Jg(\u03b8)\u2212T [ 1 \u22121 ] uH = uH \u0394g ([ R\u03b81 0 ] \u2212 rg ) , (18) and we can find that the same result is obtained as the fully-actuated case as shown in Fig. 6; fg yields a vector from stance-leg\u2019s contact point with the ground to the CoM position (central force). Also in this case unreasonableness arises, nevertheless, the robot can exhibit VPDW on a level. This implies that the rolling effect is important to create a stable gait and dramatically increases the stable domain. Note that, as seen from Fig. 5 (a), \u03b8\u03071 > \u03b8\u03072 is always achieved, or the singularity \u03b8\u0307H = 0 is automatically avoided without any additional control. In the all simulations of this paper, the automatic singularity avoidance is observed", " The results will be reported in a future paper. In this paper, the effect of semicircular feet on dynamic biped locomotion has been investigated through numerical simulations. A fully-actuated case has also been discussed and its torque distribution mechanism has been investigated. By the effect of semicircular feet, high-speed and energyefficient biped gaits have been generated without concerning the ZMP condition. The rolling motion can overcome the unreasonableness of underactuation as depicted in Fig. 6 and help to generate a stable limit cycle. The results of this paper imply that the knack of biped gait generation is not kicking the floor but rolling on the floor. The most important factor in biped gait generation is not what control or desired trajectories are applied to the walking robot but whether the foot shape is circular or not. If this hypothesis is true, the case with more complicated biped models, such as models with knees or upper body, becomes also possible without any additional control strategies" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003238_s0022-0728(98)00049-7-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003238_s0022-0728(98)00049-7-Figure2-1.png", "caption": "Fig. 2. Oxidative electropolymerization of 2 (1 mM) in CH3CN+0.1 M TBAP by repeated potential scans between 0 and 0.70 V at a glassy carbon electrode (diameter 5 mm); dashed line, a scan between 0 and 1.37 V; scan rate, 0.1 V s\u22121.", "texts": [ " The resulting enzyme electrodes were thoroughly rinsed in distilled water and incubated for 30 min in stirred phosphate buffer (pH 6.5) at 20\u00b0C before use. 3.1. Electrochemical polymerization of 2 The electrochemical behaviour of the amphiphilic pyrrole lactobionamide 2 in argon -purged CH3CN+ 0.1 M TBAP, was investigated by cyclic voltammetry on a glassy carbon electrode. Upon oxidative scanning the cyclic voltammogram for 2 displays an irreversible oxidation peak at 1.2 V due to the oxidation of the pyrrole unit [40] (Fig. 2). Repeatedly scanning the potential between 0 and 0.7 V induces the appearance and the growth of a reversible oxidation wave around 0.23 V, which is in good agreement with the reported E1/2 values for poly(N-alkylpyrroles) [40]. This indicates the formation of an electropolymerized film on the host matrix. However, we previously reported that the enzyme immobilization in poly(amphiphilic pyrrole) leads to biosensors in which the enzymatic reaction, rather than substrate mass transport, is the rate-limiting step [42\u201344]" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001009_s0263574720000284-Figure18-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001009_s0263574720000284-Figure18-1.png", "caption": "Fig. 18. Different group in two-links earthworm-like robot.", "texts": [ " Uppsala Universitetsbibliotek, on 15 May 2020 at 00:12:18, subject to the Cambridge Core terms of use, available at where \u03b3 is defined as the reciprocal of the arc radius after bending. The bending translation could be regarded as the rotation about z-axis with curvature angle \u03b8 and the rotation about y-axis with orientation angle \u2205. d is defined as the diameter of robot. li is the length of the one-sided cavity in the ith group. The bending section could be considered as a perfect arc of circle whose length is L. In Fig. 18, there are three modules in one-link and six modules in two-links and the same straightline module is defined as a group.25 The inflation condition is defined as state 1, the normal condition is defined as state 0, and the deflation condition is defined as state -1. If the earthworm-like robot crawls in two-dimensional space (x-y plane), the robot cannot rotate around the y-axis during crawling, so the orientation angle \u2205 is 0. The deviation angle \u03b1 of the seven different inflation and deflation combinations in the x and y plane coordinates is recorded in Table II" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000775_tro.2019.2906475-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000775_tro.2019.2906475-Figure5-1.png", "caption": "Fig. 5. CAD model of platform with attached multiaxis reaction system prototype.", "texts": [ " 4, will be dissipated to reach the static conditions, which, based on Theorem 1, means the asymptotic stability conditions for the whole nonlinear system, as illustrated in Fig. 2, are satisfied. It is worth mentioning that (33) shows a specific condition of the systems parameters where an uncoupled vibrational mode shape can happen in out-of-plane directions of z and \u03b8x without stimulating the pendulum mechanism to suppress the system energy. However, the condition of (33) can be easily violated in the CDPR design for all points of the workspace. In order to validate the proposed reaction system, a prototype (see Fig. 5) was built and tested using the test setup shown in Fig. 6. The setup consisted of a 12-cable, planar CDPR, originally presented by Mendez in [23]. Cable lengths were controlled by four identical dc motors attached to the fixed frame. A detailed discussion of the CDPR mechanical design and its merits can be found by referring to [23]. Two identical pendulum actuators were designed and built as part of the requirements for the reaction system proposed in Section III. Each actuator consisted of a direct drive Beckhoff AM8131 dc motor with absolute encoders, a mount plate, a pendulum shaped load mass, and a coupler to fix the load mass to the motor shaft" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003855_j.mechmachtheory.2006.01.006-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003855_j.mechmachtheory.2006.01.006-Figure4-1.png", "caption": "Fig. 4. A spatial parallel mechanism made up of 4-PUU.", "texts": [ " (35) indicates that the end-effector BC can make a free rotation about a line passing through point \u00f0 xB yB 0 \u00de with a direction \u00bd 0 0 1 , which is just its self-rotation axis\u2014z 0-axis shown in Fig. 2. So, the end-effector only has one rotational DOF about z 0-axis; and as a result, we can only either select pair B or select C as the actuation. In application, this mechanism can be utilized as an adjustable bearing. 3.2. Analysis on the mobility properties of the end-effector in a 4-PUU spatial parallel mechanism A spatial parallel mechanism, shown in Fig. 4 [6], is made up of 4-PUU (one prismatic pair and two universal pairs) kinematic chains. To investigate the mobility properties of the end-effector, we first decompose the spatial parallel mechanism to be four kinematic chains connecting the end-effector with the fixed guides and then analyze the reciprocal screws (terminal constraints) of each kinematic chain according to the above analysis steps. Assume that the distance between the two guides is 2L, the x-axis of the fixed Cartesian coordinate system (fixed coordinate frame) shown in Fig. 4 is superimposed with the middle line of the two guides, and y-axis and z-axis are all perpendicular to the guides. Therefore, the Cartesian coordinates of slider Pi (i = 1, 2, 3, 4) can be denoted as P 1\u00f0 x1 L 0 \u00de; P 2\u00f0 x2 L 0 \u00de; P 3\u00f0 x3 L 0 \u00de; P 4\u00f0 x4 L 0 \u00de We first analyze kinematic chain P1B1 in the fixed Cartesian coordinate system shown in Fig. 4. In Fig. 5, x 0, y 0 and z 0 are parallel to the corresponding axes of the fixed one shown in Fig. 4. B1P is the projection of B1 in xoy plane, and OB1P is the projective line of OB1 in xoy plane. b1 is the angle from line OB1P to line OB1, a1 is the angle from x axis to line OB1P. The Plu\u0308cker coordinates of slider P1 are $1 \u00bc \u00f0 0 0 0 1 0 0 \u00de The universal pair P1 can be decomposed as two orthogonal rotational pairs, the direction vectors of which are denoted by e1 u and e2 u individually. Where e1 u is parallel to z-axis and as a result has the form of e1 u \u00bc \u00bd 0 0 1 , e2 u can be found by the following formula: e2 u \u00bc P 1B1P ", " Therefore, the terminal constraints exerted to the end-effector are four pure constraint moments, which are all perpendicular to the direction of z-axis shown in Fig. 6. The terminal constraints exerted to the end-effector are $ r E \u00bc $r P 1B1 $ r P 2B2 $ r P 3B3 $r P 4B4 2 66664 3 77775 \u00f043\u00de Obviously, 1 6 Rank\u00f0$r E\u00de 6 2. With Eq. (20), we can find the free motion(s) of the end-effector as the following two cases: (1) d \u00bc Rank\u00f0$r E\u00de \u00bc 1 In this case, there must be cos ai \u00bc 0; sin ai \u00bc 1; \u00f0i \u00bc 1; 2; 3; 4\u00de or cos ai \u00bc 1; sin ai \u00bc 0; \u00f0i \u00bc 1; 2; 3; 4\u00de \u00f044\u00de In the applicable structure shown in Fig. 4, only the first solution set of Eq. (44) is possible. Therefore, we have a1 \u00bc a4 \u00bc p 2 a2 \u00bc a3 \u00bc 3p 2 \u00f045\u00de In fact, this case is corresponding to one kind of singularities of the mechanism. The free motions the end-effector gains in this case can be obtained by solving $ r E $ F1 E \u00bc 0 $F1 E \u00bc $1 E $ 2 E $3 E $ 4 E $ 5 E 2 66666664 3 77777775 \u00f046\u00de where $ 1 E \u00bc 1 0 0 0 0 0\u00f0 \u00de $2 E \u00bc 0 0 1 0 0 0\u00f0 \u00de $ 3 E \u00bc 0 0 0 1 0 0\u00f0 \u00de $ 4 E \u00bc 0 0 0 0 1 0\u00f0 \u00de $ 5 E \u00bc 0 0 0 0 0 1\u00f0 \u00de (2) d \u00bc Rank\u00f0$r E\u00de \u00bc 2 The free motions the end-effector obtained in this case can be similarly solved: $F2 E \u00bc $2 E $ 3 E $4 E $ 5 E 2 66664 3 77775 \u00f047\u00de From the above analysis, we can find that the end-effector at least has the motions represented by $ F2 E . When a1 \u00bc a4 \u00bc p 2 and a2 \u00bc a3 \u00bc 3p 2 , the end-effector gains one more rotation $ 1 E. That is, the end-effector at least has M \u00bc Rank\u00f0$F2 E \u00de \u00bc 4 DOFs, whose mobility properties are depicted by $ F2 E \u2014one rotational DOF about z-axis and three independent translational DOFs along the coordinate axes in a real three-dimensional space. If we select the four sliders shown in Fig. 4 as the actuators, the $ Fn1 E can be analyzed as follows: When the actuations are given, the four sliders will be seen as fixed pairs. Therefore, the kinematic screws of kinematic chain P1B1 can be rewritten as $ actu P 1B1 \u00bc $2 $3 $4 $5 2 6664 3 7775 \u00f048\u00de Therefore, the reciprocal screws of kinematic chain P1B1 can be gained: $ r1 P 1B1 \u00bc \u00f0 0 0 0 cos a1 sin a1 0 \u00de $ r2 P 1B1 \u00bc \u00f0 cos a1 cos b1 sin a1 cos b1 sin b1 L sin b1 x1 sin b1 x1 sin a1 \u00fe L cos a1\u00f0 \u00de cos b1 \u00de ( \u00f049\u00de With similar processes, we can find the terminal constraints of the other three kinematic chains of the end- effector in the same Cartesian coordinate system: $r1 P 2B2 \u00bc \u00f0 0 0 0 cos a2 sin a2 0 \u00de $ r2 P 2B2 \u00bc \u00f0 cos a2 cos b2 sin a2 cos b2 sin b2 L sin b2 x2 sin b2 \u00f0x2 sin a2 L cos a2\u00de cos b2 \u00de ( \u00f050\u00de $r1 P 3B3 \u00bc \u00f0 0 0 0 cos a3 sin a3 0 \u00de $ r2 P 3B3 \u00bc \u00f0 cos a3 cos b3 sin a3 cos b3 sin b3 L sin b3 x3 sin b3 \u00f0x3 sin a3 L cos a3\u00de cos b3 \u00de ( \u00f051\u00de $ r1 P 4B4 \u00bc \u00f0 0 0 0 cos a4 sin a4 0 \u00de $ r2 P 4B4 \u00bc \u00f0 cos a4 cos b4 sin a4 cos b4 sin b4 L sin b4 x4 sin b4 x4 sin a4 \u00fe L cos a4\u00f0 \u00de cos b4 \u00de ( \u00f052\u00de Therefore, when the actuations are assigned to the four sliders, the terminal constraints exerted to the endeffector are four pure constraint forces along the individual axes of the limbs, and four pure constraint moments, which are all perpendicular to the direction of z-axis in the absolute coordinate system shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000973_s12541-019-00312-9-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000973_s12541-019-00312-9-Figure2-1.png", "caption": "Fig. 2 Swing leg and its dynamic model", "texts": [ " In manual training, the therapists only guide patient\u2019s legs in swing phase. Similarly, the assistance of swing phase is only considered in this paper. A patient-cooperative control method is adopted in the swing phase. Before establishing the dynamic model of the exoskeleton swing phase, some assumptions are proposed. (1) The motion of exoskeleton only exists in sagittal plane. (2), The feet of exoskeleton are considered as concentrated masses at the end of shank in dynamic model. The swing leg and its dynamic model are shown in Fig.\u00a02. The center of mass for every segment of the leg can be obtained in the reference coordinate x-o-y. The Lagrange method is used for gaining the dynamic equations of the exoskeleton swing phase. The dynamic equations of swing phase can be described as follows. where = [ 1 2] , 1 and 2 are angular positions for the hip and knee joint separately. ( ) is the symmetric definite inertial matrix. \ud835\udc02(\ud835\udc2a, ?\u0307?) is the Coriolis and centrifugal matrix. ( ) is the gravitational matrix. is the control input vector of hip and knee joints" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001009_s0263574720000284-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001009_s0263574720000284-Figure2-1.png", "caption": "Fig. 2. Single module model diagram in solid works. (a) External structure. (b) Internal structure. (c) Angle.", "texts": [ " Therefore, the materials are highly elastic polymer materials. Silicone and rubber materials meet these design requirements. (2) Under the action of air pressure, the earthworm-like soft robot can be bended and stretched by the special corrugated structures and the regular extension and contraction gaits. Based on the current designs of the soft robot, a modular design is adopted in this paper. The functions of the earthworm-like robot are proposed as follows. 2.2.1. Single module bending function. The single module is shown in Fig. 2. The length of the single module is 55 mm, the outside diameter is 32 mm, and the angle is 120\u25e6 (Fig. 2(c)). As shown in Fig. 2(b), the structure of a single module, like a corrugated tube, and its interior is interconnected cavity. The physical picture of the single module is shown in Fig. 3. https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0263574720000284 Downloaded from https://www.cambridge.org/core. Uppsala Universitetsbibliotek, on 15 May 2020 at 00:12:18, subject to the Cambridge Core terms of use, available at The structure of soft manipulator or soft crawling robot is shown in Fig. 4. The upper chamber is mainly composed of corrugated shapes, with low hardness and high elongation material" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001348_tmrb.2020.3033020-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001348_tmrb.2020.3033020-Figure2-1.png", "caption": "Fig. 2. Modular diagram of DeltaMag, where special points are labeled to show assembly. (a) Design of the motor module. O is the center of baseplate; E is the center of endplate; D is the center of magnetic swimmer; \u03b6 is the preassigned control distance; qi is the displacement of ith slide block; Mi and Ai are the center points of ith pair of parallel linkages connected with the endplate and the corresponding slide block, respectively. {O} is the world coordinate frame and {E} is the endplate coordinate frame. (b) Design of the coil module. Ci is the proximal center of ithelectromagnetic coil. {Ci} is the ith coil coordinate frame. (c) Design of the vision module. {K} is the stereo camera coordinate frame, which is further illustrated in Fig. 6.", "texts": [ ", n or pB A, where A and B of the latter are start and end points of the vector); matrices utilize uppercase bold font (e.g., Q); functions adopt fraktur font (e.g., f). Except for particular illustration, right superscript designates reference frame, which is omitted when refers to the word coordinate frame; right subscript indicates index; left superscript represents the number of iterations, which is given when necessary. The motor module mainly contains a parallel mechanism that is actuated by three step motors, as shown in Fig. 2(a). We assume that the motors execute given motion instructions precisely. During operation, the endplate center E keeps above the magnetic swimmer D over a stated control distance \u03b6 . The baseplate center O is the origin point of the world coordinate frame {O}. Since the endplate keeps parallel with the baseplate during actuation, all point coordinates labeled in the diagram can be derived using structure parameters and geometric relationships when a targeted location of E is assigned. Thus, the motor actuation array Q can be further deduced by: Q = [ q1 q2 q3 ]T = f(xe, ye, ze,P) (1) Authorized licensed use limited to: Carleton University", " where qi is the displacement of the ith slide block (i = 1, 2, 3); f is a function representing the inverse kinematics of the parallel mechanism, a detailed derivation of which can refer to [42]; P = {|AiMi|, |EMi|, . . . } is a set denoting mechanism parameters. The parallel mechanism drives the endplate to the target position, which also carries the coil module and the vision module close to the controlled device during motion. The coil module includes three separated electromagnetic coils that are integrated with the parallel mechanism, as shown in Fig. 2(b). The poses of all coils change with the movement of the parallel mechanism that are derivable according to the inverse kinematics, based on which twice coordinate transformations are included in the field generation algorithm. The swimmer position DCi under the ith coil coordinate frame {Ci} can be computed by: ( xCi d , yCi d , zCi d ) = gi(xd, yd, zd, \u03b6,P) (2) where gi refers to a group of formulas calculating converted coordinates of the swimmer for the ith coil; zCi d equals to zero because of the designated {Ci} frame", " The magnetic field generated by each coil is proportional to the actuation current, and the total magnetic field obeys superposition principle; therefore, to produce a desired magnetic field Bd, the coil actuation array I is calculated as follows: I = [i1 i2 i3]T = [ RC1 BC1 1 RC2 BC2 2 RC3 BC3 3 ]\u22121 Bd (4) where ii is the flowing current of the ith coil. D. Vision Module and Stereo Location The vision module incorporates a self-made stereo camera, which is fixed at the center of the endplate, and the eye-in-hand configuration enlarges the visible region without sacrificing the imaging accuracy. Although several advanced stereo cameras are commercially available in the market, they can hardly be utilized in our system due to unmatched size and/or unsuitable working distance. The vision module is shown in Fig. 2(c), which consists of two identical fixed-focus endoscopes and a 3D-printed shell. The image distance of each camera ranges from 20 mm to 80 mm, and the baseline distance is set according to the human binocular vision system [43]. The design parameters of the stereo camera are as follows: the diameter of a single camera is 3.9 mm, the baseline distance is 8 mm, and the outer diameter of the stereo camera is 13 mm. The intrinsic and extrinsic parameters of the vision module are calibrated by MATLAB 2016b (MathWorks, Inc" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003235_1.1332398-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003235_1.1332398-Figure3-1.png", "caption": "Fig. 3 Angular contact ball bearing under combined load", "texts": [ " (8) It should be noted that in a lubricated bearing, the ball/raceway contacts are separated by two layers of oil film. Due to the difference in curvature between the ball and the respective raceways, each layer may operate in a different regime of lubrication. To simplify the analysis in this model the difference in curvature between the ball and the surrounding raceways is ignored, thus making the two layers geometrically identical ~i.e., 2hi!. Using the normalized groups in Eq. ~5!, the total deflection for the ith contact as shown in Fig. 3 is obtained as d\u0304 i52 h\u03040h\u0304 i1H F A\u0304 sin a01Z\u0304 l1 d\u0304 2 ~f\u0304 cos u i1w\u0304 sin u i!G 2 1@~ A\u03041 d\u0304e!cos ap1X\u0304 l cos u i1Y\u0304 sin u i# 2J 1/2 2A\u0304 . (9) In Eq. ~9! the subscripts i and l for the ball to races\u2019 contacts and the center movements for the left bearing can be replaced by the corresponding quantities denoted by j and r for the right bearing ~see Section 5!. 160 \u00d5 Vol. 124, JANUARY 2002 rom: http://tribology.asmedigitalcollection.asme.org/ on 01/28/2016 Term The corresponding contact angle relation is tan a i5 F A\u0304 sin a01Z\u0304 l6 d 2 ~f\u0304 cos u i1w\u0304 sin u i" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001572_tmech.2021.3067335-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001572_tmech.2021.3067335-Figure1-1.png", "caption": "Fig. 1. Bending motion comparison between the conventional rolling joint and CMRJ under an external load. Bending motion of the conventional rolling joint in the (a) lateral direction and (b) 45\u00b0 diagonal direction. (c) Bending motion of the CMRJ in the 45\u00b0 diagonal direction.", "texts": [ " To verify the performance of the new manipulator, we used an optimized motion estimation analysis (OMEA) method to predict the cable tension, as well as the shape and tip position. The rest of this paper is organized as follows. Section 2 introduces the concept and structure of the CMRJ. Section 3 describes the OMEA for the CMRJ. Section 4 presents the performance validation of the CMRJ using both OMEA and the prototype. Section 5 discusses the experimental results, and Section 6 presents the conclusions. A rolling joint consists of multiple rigid segments and a thin cable [Fig. 1(a)]. Rolling joints for MIS should work well in surgical operations such as resection and suturing, even under external loads from reaction forces at the surgical site. The force advancing under the external load, the bending force, is produced by the joint moment, which is determined by multiplying the actuating tension times the distance between the actuating cable and rotation center of the joint. Therefore, the bending force can be increased by increasing the cable tension or the distance between the actuating cable and rotation center of the joint. However, the cable tension and distance have their respective limitations\u2014the breaking strength and rolling joint diameter. When an external load acts on the tip of a rolling joint in the diagonal direction, the upper and lower actuating cables pull the segment to generate a bending force against the external load [Fig 1(b)]. The tension required to create the bending force is distributed over the lengths of the two cables, reducing the Authorized licensed use limited to: Carleton University. Downloaded on May 27,2021 at 11:52:50 UTC from IEEE Xplore. Restrictions apply. 1083-4435 (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. > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 3 overall cable tension. However, the positions of the actuating cables are located 45\u00b0 above and below the direction of the external load, so that any loss exists in the diagonal direction. We present a CMRJ with a linear guide in the segment for cable movement [Fig. 1(c)]. When the CMRJ bends in the diagonal direction, the cable moves in the bending direction through the linear guide. This movement helps the cables generate a bending force without loss. As the bending force increases, the CMRJ can bend further under the same external load. As a result, the CMRJ improves the workspace of the manipulator in the diagonal direction while reducing the cable tension, compared with the conventional rolling joint. We designed a linear guide for the cable movement segment (see Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003471_027836499601500204-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003471_027836499601500204-Figure5-1.png", "caption": "Fig. 5. Conservative support polygon.", "texts": [ " The mapping module then combines the images to construct a terrain elevation map, and returns the map to the footfall planning module. The footfall planner uses a neural network to evaluate the terrain map, estimating the goodness of each foot-sized patch in terms of stability and traction. The gait planner then chooses the best footfall location within the specified region. After setting a leg move, the gait planner finds the maximum body move that follows along the arc, one that does not violate limits on leg motion, and keeps the Ambler\u2019s center of gravity within the conservative support polygon (CSP) (Fig. 5). This guarantees that the Ambler won\u2019t tip over even if any single leg fails. The gait planner then forwards the chosen leg move to the leg-recovery planner, which plans a fast trajectory that avoids terrain collisions. The chosen leg and body moves are then forwarded to the real-time controller module. Concurrently, if the end of the arc has not been reached, the gait planner qtarts planning the next pair of leg and body moves. The real-time controller generates leg move trajectories that are linear in joint space, coordinating the leg joints so that all motions start and end simultaneously", " Stack reachability constraint. are fixed, the planner determines how far each stack can move along the arc before reaching a kinematic limit (Figure 11A). The second constraint is based on stability. To be statically stable, the rover\u2019s center of mass must lie within the support polygon formed by the convex hull of the feet. For added safety, we insist that the Ambler always lie within the conservative support polygon (CSP), which is defined as the intersection of all five-legged support polygons (see Fig. 5) (Mahalingam and Whittaker 1989). Thus, if the Ambler remains within the CSP, any one leg can fail, and the vehicle will still remain statically stable. The gait planner finds where the body travel intersects the leading edge of the CSP and uses this as an additional constraint on body motion. The minimum motion determined by the kinematic and support constraints is then chosen as the next body move. This planning suffices for movement in the horizontal plane. To plan vertical movements, the planner obtains a terrain map from the perception system of a region in the direction of travel" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003405_j.1460-2687.2002.00093.x-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003405_j.1460-2687.2002.00093.x-Figure1-1.png", "caption": "Figure 1 Club (C1\u2013C3) and clubface (F1\u2013F4) markers tracked by the video collection system to determine the location of the clubface and a reference point near the centre of the club (\u02dc) in the global coordinate system. A transformation matrix relating the club and clubface markers enabled only C1\u2013C3 to be present during data collection.", "texts": [ " In order to maximize accuracy, the cameras focused on a space that gave video images from the bottom half of the swing, centred on the region of ball strike. These camera locations provided 15\u201325 images during the swing, including data before and after impact with the ball. During the swing, the video analysis system tracked the locations of three spherical reflective club markers (C1\u2013C3) that were placed on the clubhead and shaft and which were used to predict four clubface marker locations during the swing. The three club markers (Fig. 1) defined a local coordinate system based in the club. As the markers were made of lightweight wood and the ping-pong balls were attached using titanium fasteners, the markers did not add significant mass to the clubs. In order to locate the clubface marker locations relative to 66 Sports Engineering (2002) 5, 65\u201380 \u2022 2002 Blackwell Science Ltd the club and shaft markers, four reflective markers (F1\u2013F4, Fig. 1), were placed on the clubface and filmed during a special calibration procedure (the clubface markers were only in place during the initial calibration; see Fig. 1). The clubface calibration defined a clubface coordinate system, and a transformation matrix was determined between the club and clubface coordinate systems. The locations of the four clubface markers in the global coordinate system were predicted using the 3-D clubhead and shaft marker locations in the global coordinate system and the transformation matrix between the club and clubface coordinate systems. Determination of impact time and location A linear interpolation between two frames of video data was used to identify the specific time and location of impact with the ball" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001434_tia.2021.3075424-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001434_tia.2021.3075424-Figure1-1.png", "caption": "Fig. 1. Cross-section of tested IPMSM.", "texts": [ " 2 2 2 r T r in dqs dqs r dqsr T r r T r T r r T r s dqs dqs dqs sh r dqs dqs dqs dqs P d R dt i v i i i i L i J\u03bb i \u03b3 (14) The first term is a resistive loss, and the second term is the variation of the magnetic energy according to dq-currents, which is already formularized in (11). A portion of the last term is used to change W, which can be seen as the internal energy of an IPMSM, and the remainder is converted into mechanical power. The result of dividing the last term by the mechanical speed is identical to Te1 + Te2, but Te3 does not appear since it comes from the variation of W inside IPMSM. Fig. 1 shows the cross-section of the tested IPMSM, of which nominal parameters based on the FEA model are shown in Table I. FEA is performed on JMAG Designer 18.0. Fig. 2 shows torque waveforms from FEA with two MTPA operating points; the average torque, \ud835\udc47 , follows the torque command, Te *. Note that each torque component is calculated by (13) with \ud835\udecc\ud835\udc51\ud835\udc5e\ud835\udc60 \ud835\udc5f and W obtained from FEA. As shown in Fig. 2, the sum of three components, \u03a3Te, exactly matches to the output torque from FEA. As shown in Fig. 2(c), even if dq-currents are constant, the torque waveforms have the (6n)th-order harmonics" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000971_1077546319896124-Figure14-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000971_1077546319896124-Figure14-1.png", "caption": "Figure 14. Test system for dynamic characteristics of the gear pair.", "texts": [ " The distance of sensors to the gear center is the radius of the base circle, so the measured acceleration directly reflects the value of the torsional vibration of the gear in the direction of meshing line. Two signals are sent out by the collector ring and are converted by a charge amplifier and analog-to-digital converter. The real waveform of relative torsional vibration of the gear pair is obtained by subtracting each other after sampling by using the computer. Then the relative vibration acceleration spectrum of the gear pair is obtained by the fast Fourier transformation (FFT) analysis. The testing system for dynamic characteristics of the gear pair are shown in Figure 14. The result is shown in Figure 15. As can be seen from Figure 15, the meshing frequency and its frequency doubling are the vibration signals generated during the gear meshing process. Because of the existence of axle frequency modulation signal, there are abundant side frequencies in meshing frequency and its frequency doubling accessories, but the amplitude of side frequencies is low, which indicates that the vibration of gear meshing frequency is mainly responsible for meshing excitation. The peak value of the meshing frequency is prominent in the power spectrum of ideal gear meshing, but its harmonic amplitude is small" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000059_s40870-017-0122-6-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000059_s40870-017-0122-6-Figure4-1.png", "caption": "Fig. 4 Specimen designs for Kolsky bar experiments in (a) compression; and (b) tension. (Unit: mm except for the thread size in inch)", "texts": [ "\u00a03a) and those reported for 1 3 traditional (low power) LENS\u00ae processes [3]. Finally, the AM steel has substantial sub-grain structure (Fig.\u00a0 3e, f), which indicates a high dislocation density. Both AM and wrought 304L stainless steels were machined with electric discharge machining (EDM) into two different specimen geometries. The compression specimens were cylindrical with a diameter of 6.35\u00a0 mm and a height of Ls = 3.18\u00a0mm. The tensile specimens were made into a cylindrical dog bone shape with a 3.18\u00a0 mm gage diameter and a Ls = 6.35\u00a0mm gage length. Figure\u00a04 shows the schematic drawings for both compression and tensile specimens. Each compression specimen was sandwiched between the incident and transmission bars for dynamic compression tests. The tensile samples were directly threaded into the ends of the incident and transmission bars for dynamic tensile tests. Dynamic compressive and tensile experiments were performed with Kolsky compression and tension bars, respectively. Figure\u00a05 shows a schematic of the Kolsky compression bar apparatus. In this study, the Kolsky compression bar system was made of Maraging C350 steel and had a common diameter of 19", "\u00a0(2)]; whereas the strain history was calculated with the laser measurements by using the following equation [31, 32], where is the relative displacement across the front and back ends of the specimen, as measured by the laser extensometer; y is the relative displacement across the front and back ends of the specimen when the dynamic yield strength is reached; y is the dynamic yield strength of the tested material; and c\u2032 is the correction factor for specimen strain calculation at gage section. According to the specific (5)\ud835\udf00 = \u23a7 \u23aa\u23a8\u23aa\u23a9 c \ufffd \ud835\udeff Ls \ufffd \ud835\udf0e \u2a7d \ud835\udf0ey \ufffd \ud835\udeff\u2212(1\u2212c\ufffd)\ud835\udeffy Ls \ufffd \ud835\udf0e > \ud835\udf0ey \ufffd design of the tensile specimen shown in Fig.\u00a0 4b, the correction factor, c\u2032, has been determined as 0.62 in this study [32]. Figure\u00a011 shows the calculated stress and strain histories in the tensile specimen subjected to a dynamic tensile load. Similar to the compression test, the nearly linear strain rate in the specimen indicates a nearly constant strain rate of 2900\u00a0s\u22121 during dynamic tensile loading. Following the same procedure, the AM 304L stainless steel and wrought material listed in Table\u00a0 1 were dynamically characterized in compression and tension" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003882_s10458-006-9004-3-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003882_s10458-006-9004-3-Figure1-1.png", "caption": "Fig. 1 Schematic illustration of the task geometry as a section, of length L, of a longer pipe, with radius R. Fluid flows in the positive x-direction with average velocity vavg. The gray area is the target region on the surface of the pipe", "texts": [ ", chemical receptors allowing the robots to detect it when they physically are in contact with the target area. We examine the rate at which robots find the target, the energy they use and the false positive rate. Table 1 lists the physical parameters involved in this task. Small vessels have diameters up to several tens of microns, and lengths of about a millimeter. We focus on a short segment in the middle of such a vessel to avoid considering fluid dynamics from vessel branching at the ends. Figure 1 shows the geometry of our task: a segment of the vessel of length L with a target region on the wall emitting a chemical into the fluid. Robots continually enter one end of the vessel with the fluid flow. The robot density corresponds to 1012 robots in the entire 5-l blood volume of a typical adult, an example of medical applications using a huge number of microscopic robots [23]. In spite of this large number, the robots use only about 10\u22123 of the vessel volume, far less than the 20\u201340% occupied by blood cells", " Furthermore, if robots have the sensing ability to detect the wall, they could slow down as they approach the wall. At any rate, the robot speed v0 in Table 2 is likely below the speed at which collisions with the vessel walls cause damage [24]. Nevertheless, as with other safety issues of microscopic robots, experimental evaluation will be necessary and the control choices for the robots should minimize the potential for injury while successfully performing their tasks. The target geometry considered above, shown in Fig. 1, is only one possible arrangement for the target in the vessel wall. To examine the robustness of the control approaches, this section describes results for additional situations. The controls described above using communication involve passive motion once a robot reaches the wall. Such robots will find the target only if they reach the wall at or upstream of the target. These responding robots move toward the wall before encountering detectable chemical concentrations. Thus the robots lack a guide to the best locations on the wall. With the axially symmetric geometry of Fig. 1, such guidance is not needed: any point on the wall upstream of the target moves passively to the target. However, if the target does not wrap around the vessel some upstream locations will not lead to the target. To examine the behavior in this case, we consider a target with the same surface area as in Fig. 1 but oriented lengthwise along the vessel. A specific example is a target extending only 1/3 of the way around the vessel and with three times the length, i.e., 90 \u00b5m, along the vessel. In this case, the chemical spreads around the vessel as it moves downstream. Table 4 shows the resulting behaviors. For Brownian motion alone, the robots find the target only about 65% as often as for the equivalent area target wrapped around the vessel. Given the fairly small displacements during the time the robot passes the target, this reduction can be understood as due to only 1/3 the vessel wall having the target, but the target being 3 times longer so robots spend 3 times as long passing it, increasing the Brownian displacement by a factor of \u221a 3", " For the circulatory system, flow is generally faster in larger vessels, implying the total cross section of the smaller branches exceeds that of the larger vessel. Quantitatively, branching vessels roughly conserve the sum of the cubes of their diameters [57]. For a split into two branches of equal diameters shown in Fig. 9, the corresponding radius of the larger vessel is 3\u221a2 R, with modestly faster fluid flow. In the figure, the branches have angles \u00b120\u25e6 with respect to the larger vessel. The target area is the same length as in Fig. 1 and wraps around the upper vessel. The gradient following and communication controls respond differently depending on the direction of flow. When the flow is from the smaller vessels into the larger one (\u201cmerging\u201d) the communication protocols have little effect on the number of robots reaching the target: those protocols rely on robots moving to the wall upstream of the target and then moving passively until they reach the target. Since the branch is downstream of the target in this case, robots entering the larger vessel are already downstream of the target and their response to the acoustic signals leads them to the wall of the larger vessel and hence away from the target" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000795_s00170-019-03928-3-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000795_s00170-019-03928-3-Figure3-1.png", "caption": "Fig. 3 Model diagram and a sketch of form angle. a \u03b8 = 0\u00b0. b \u03b8 = 30\u00b0. c \u03b8 = 60\u00b0. d Sketch", "texts": [ " This paper combined various process parameters in Table 3 named F series of the SLM-316L HMDS and \u03c9 between 22.3 and 333.3 J/mm3 to explore the process parameters of forming the high-density (more than 99%) 316L HMDS. After determining the optimal \u03c9 formed the high-density 316L HMDSs, considering the influence of the hatch space (scanning speed) and form angle on the microstructure and mechanical properties of the SLM-316L HMDS, the angle between the plane of the substrate and the center line of the SLM-316L HMDS was the form angle (\u03b8) as shown in Fig. 3. Using the process parameters in Table 4 named S series of the SLM-316L HMDS, the SLM-316L HMDSs were manufactured for density measurements, microstructure analysis, and mechanical property testing. The cross section of the 316L HMDS was taken along the OXZ plane parallel to the building direction as shown in Fig. 4. The springs were prepared according to the standard metallographic Table 1 Chemical composition of gas-atomized 316L powder (wt%) C Si Mn S P Cr Ni Mo Fe \u2264 0.03 \u2264 1.0 \u2264 2.0 \u2264 0.01 \u2264 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003007_s0142-1123(98)00077-2-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003007_s0142-1123(98)00077-2-Figure6-1.png", "caption": "Fig. 6. The test cell.", "texts": [ " The lubrication system on the SKFERC rig was deemed suitable as it is filtered, temperature controlled, and it can be used with added contamination in the lubricant. The test rig used for this study is of the roller-to-roller type as shown in Fig. 5. The test rig is shown with the front bearings and covers removed to expose the test cell with the test and load ring mounted in place. Visible in the figure is also part of the lubrication and drive system. The test cell where the testing takes place is shown schematically in Fig. 6. The test cell consists of two rings. A large ring which is the load-ring, i.e. a ring that is used to apply load to the specimen tested, and a small test ring that is the specimen tested. To ensure an even pressure on the rings a camber with a radius of 30 mm is ground on the load ring. Both rings are independently driven from the same motor with a system of gearwheels and belts which enables the operator to set the amount of slip to the desired value by changing gears in the drive system. The range of slip ratios that can be used is from +10% to 250%" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003489_bf02672536-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003489_bf02672536-Figure1-1.png", "caption": "Fig. 1--Experimental setup for the absorption measurements during single laser tracks.", "texts": [ "ne than those which have been observed at lower basicities, as shown in Figures 2(b) and (c). Figure 1 provides an indication of the influence of temperature on the distribution of antimony. At basicities of 0.818 and below, temperature has an almost negligible influence on Lsb. That trend is reversed at a basicity of one, as shown in Figure 1 (c). The data in Figure 1 (c) reveals that at 1450 ~ the distribution of Sb between metal and slag is similar to that experienced at the same temperature but lower basicities. However, increasing the temperature to 1500 ~ or 1550 ~ while maintaining a constant basicity of one, yields substantial increases in Lsb. The distribution of antimony between slag and metal tends to decrease with increasing concentration of Sb in the metal phase, except at 1550 ~ and a basicity of one (Figures l(c) and 2(c)). At the conditions mentioned, the Lsb increases rapidly with the antimony content in the metal", " Extrapolating this cooling curve back to the time the laser was switched off, to, gives the temperature the sample would have reached had all the absorbed energy been evenly distributed throughout the volume of the sample, T(to) , assuming negligible heat losses during the very short heating period. Therefore, the temperature rise of the sample, (T ( to ) - _ T a ) , allows the determination of the mean absorption/3 through f~ = mcp[T( to ) - Ta] [4] P~'i with P being the laser power and ri the interaction time ( i . e . , the sample length divided by the travel speed of the laser). The experimental setup is shown schematically in Figure 1. Experiments were conducted on machined ingots of eutectic A1-Cu 33 wt pct, previously cast using 99.99 pct pure aluminum and copper. The samples were polished with SiC 1000 grit paper and then ultrasonically cleaned in alcohol in order to obtain the same surface quality for all experiments. The surface roughness of the specimens was measured to be approximately 1 ~tm R~ (mean roughness DIN 4768). For the temperature measurements, two K-type thermocouples were spotwelded onto the back of the samples with wires 0", "6/xm), producing a near top hat mode, was used as a power source, and the samples were moved with a numerically controlled X-Y table. The laser processing parameters are given in Table I. The power impinging on the workpiece was determined using power meters. The beam was focused, thus concentrating as much as possible the laser energy on the liquid rather than on the solid. Under the processing conditions used, no visible plasma was observed. Figure 2 shows the temperatures recorded using the configuration shown in Figure 1.* The time at which the *The time difference that appears between the two thermocouples (about 0.5 seconds) during the heating period is related to the integration time of the voltmeter and not directly to the scanning speed (0.5 m/s). The difference between the maximum temperatures recorded is a combined effect of the positioning of each thermocouple and of the integration time. This fact, however, has no influence on the results. sample had cooled to a nearly isothermal state (defined as a temperature difference between the thermocouples of less than 1 ~ determined t~" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001041_j.ijmecsci.2020.106020-Figure13-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001041_j.ijmecsci.2020.106020-Figure13-1.png", "caption": "Fig. 13. Structure of the machine tool applied for shaving the face gear.", "texts": [ " These steps alternate until the entire gear is machined, and the rotary speed of the tool can reach 4000 r / min . The comparison experiment for spur face gear grinding is set up under the same processing parameters to analyse the shaving effect on the tooth surface quality. The specific experimental steps are shown in Fig. 12 . 5.2. Movement equations of the cutter points According to the requirements of machining movement described in Section 2.2 , a seven-five axis machine tool with a horizontal shank was selected based on the existing condition of the laboratory, and its layout structure is shown in Fig. 13 . The axes required for the spur face gear shaving motion include the movable axes X, Y, Z and the rotational axes A, C . The movable axes Y and Z realize the radial feed of the shaving cutter, the movable axis X enables the spur face gear to move along its axial direction, and the rotational axes A and C perform the task of cutting the materials. Geometric relations are established based on the structure of the machine tool in Fig. 14 , where \u0394S x and \u0394S z are the displacement variation of the shaver cutters along the X -axis and Z -axis of the machine tool, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001551_j.triboint.2021.106901-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001551_j.triboint.2021.106901-Figure2-1.png", "caption": "Fig. 2. The sketch of the solution for ultrahigh-speed ball-on-disc friction testing.", "texts": [ " With regard to the vibration, both the preparation and clamping of the disc will induce the eccentric mass. The vibration caused by the eccentric mass of disc after clamping in high sliding speed would also worse the stability of the ball disc friction test. According to the above analysis, the key to improving the sliding speed is to reduce the end run-out of disc and the vibration. Therefore, the combined solution of on-line precision cutting and in-situ dynamic balance is proposed, as shown in Fig. 2. The perpendicularity error between the end face and the rotation axis of the disc, and the flatness error of end face are inevitable in the disc preparation process. Additionally, the perpendicularity error between the end face and the rotation axis could also be induced when the disc is clamped in the tribometer. The perpendicularity and flatness error would cause the end run-out during the tribology test, which could be almost completely eliminated by the on-line precision cutting after the clamping" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000346_j.mechmachtheory.2017.09.013-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000346_j.mechmachtheory.2017.09.013-Figure9-1.png", "caption": "Fig. 9. Constructing process of 6R-U SLOL.", "texts": [ " There are four constructing methods in total, including three Bennett linkages arranged in a straight line and combined unilaterally, three Bennett linkages arranged in a straight line and combined bilaterally, three Bennett linkages arranged in L shape, four Bennett linkages arranged in net shape. The detailed process is shown as below. 3.2.1. Three Bennett linkages arranged in a straight line and combined unilaterally Take three Bennett linkages ABCH, C \u2032 H \u2032 G \u2032 D \u2032 , GDEF with the following parameters, { a I = a II = a III \u03b1I = \u03b1II = \u03b1III (25) where I, II, III indicate the linkages ABCH, C \u2032 H \u2032 G \u2032 D \u2032 , GDEF. Then we arrange the three linkages in a straight line and combine them unilaterally, as shown in Fig. 9 . Eliminate the coincident links CH, C \u2032 H \u2032 , DG, D \u2032 G \u2032 , fix the coincident joints H, H \u2032 , G \u2032 , G, translate the coincident joints C, C \u2032 to a single joint C and joints D, D \u2032 to a single joint D, then we obtain a new single loop kinematic chain ABCDEF. Now we take mobility analysis to the kinematic chain ABCDEF. In the kinematic chain ABCDEF, there exists the following relation for the coincident joints, \u23a7 \u23aa \u23a8 \u23aa \u23a9 $ C = $ C \u2032 $ D = $ D \u2032 $ G = $ G \u2032 $ H = $ H \u2032 (26) For the three Bennett linkages which are used to construct the kinematic chain ABCDEF, there exist the following screw motion equations, { m I ( $ A \u2212 $ C ) = l I ( $ B \u2212 $ H ) m II ( $ C \u2032 \u2212 $ G \u2032 ) = l II ( $ H \u2032 \u2212 $ D \u2032 ) m III ( $ G \u2212 $ E ) = l III ( $ D \u2212 $ F ) (27) Substitute Eq", " (29) , we have d = 5 (30) The mobility of ABCDEF is calculated as, M = d(n \u2212 g \u2212 1) + g \u2211 i =1 f i + v = 5 \u00d7 (6 \u2212 6 \u2212 1) + 6 + 0 = 1 (31) In the motion of kinematic chain ABCDEF, the above equations remain unchanged, so it is a 6R SLOL, which is defined as 6R-U SLOL, this kind of constructing method is feasible. This 6R SLOL is also the general form of the 6R Goldberg linkage [4,13] . A 3D model of a 6R-U SLOL is shown in Fig. 10 . The singular state analysis of 6R-U SLOL is similar to the 5R SLOL, we would take it in another study. In the synthesis process of 6R-U SLOL in Fig. 9 , we apply the configuration I to the combining parts 1 \u00a9 and 2 \u00a9, so there exist offsets for the joints A and F. In order to obtain the linkages with excellent deployability, we apply other configurations to the construction process and get several configurations for the 6R-U SLOL with zero joint offset. The added constraints of the 6R-U SLOL are shown in Table 3 , the construction process of 6R-U SLOL is shown in Table 4 . For the linkages in Table 4, 6 R-U-A SLOL is the basic form of 6R Goldberg linkage [4,13] ", " For the 6R-U-C SLOL, the configuration in Table 4 is the case when b III < b I + b II . When b III > b I + b II , it is also a 6R 6-bar linkage, only the length of link AF changes. For the 6R-U-F, the configuration in Table 4 is the case when b I < b II , b III < b II , the other configurations are similar. 3.2.2. Three Bennett linkages arranged in a straight line and combined bilaterally When three Bennett linkages are arranged in a straight line to construct a 6R SLOL, there is another constructing approach other than the approach shown in Fig. 9 . In this approach the three Bennett linkages are combined bilaterally, which is shown as below. For the three Bennett linkages ABCH, C \u2032 H \u2032 G \u2032 D \u2032 , GDEF, we have that { a I = a II = a III \u03b1I = \u03b1II = \u03b1III (32) Where I, II, III indicate the linkages ABCH, C \u2032 H \u2032 G \u2032 D \u2032 , GDEF. Eliminate the overlapped links CH,C \u2032 H \u2032 ,DG,D \u2032 G \u2032 , fix the coincident joints H, H \u2032 , D, D \u2032 , translate the coincident joints C, C \u2032 to a single joint C and joints G, G \u2032 to a single joint G, then we obtain a new single loop kinematic chain ABCEFG" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003284_0094-114x(94)90025-6-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003284_0094-114x(94)90025-6-Figure7-1.png", "caption": "Fig. 7. The manipulator in the position when the faces of the base pyramid 102 and the top pyramid 708 are in contact.", "texts": [], "surrounding_texts": [ "(i) When the vector S, rotates through an angle ~0t the top pyramid rotates about the vector Ss, which remains stationary. (ii) When the vector Ss rotates through an angle q>2 the top pyramid rotates about the vector S~, which remains stationary. (iii) When the vector S~ rotates through an angle ~o~ the top pyramid rotates about the vector S~, which remains stationary. it follows, that any given set of angles ~o~, ~o 2, \u00a2P3 determine the position of the platform. An algorithm to determine the vectors $7, SB and S~ is now given. (i) Set the angle ~o t . The top pyramid rotates about the vector S,. After a new vector position S 4 is determined, the cosine of the angle between the vectors $4 and Ss is given by d,.a= L,I.t + M, Ms + N, Ns. The relationships between the vectors S, and S~, S7 and Sa, $4 and S~ are given in detail by [8]. Using PREB3 module determines the position of the vector S~ via the vectors $4 and Ss. Following this the same module PREB3 can be used to determine the position of the vector $9 via the vectors $7 and $1. (ii) Set the angle \u00a2~2. The top pyramid rotates about the vector Sg. After a new vector position Ss is determined, the cosine of the angle between the vectors Ss and S~ can also be determined. Then the PREB3 module can be used to determine the position of the vector Ss, via the vectors $s and $9. It is important to note that the direction cosines of the vector $9 are known from (i). Then the PREB3 module determines the vector $7 via the vectors $4 and $9. (iii) Set the angle ~03. The top pyramid rotates about the vector $7. After a new vector position $6 is determined the cosine of the angle between $6 and $7 can also be determined. Then the PREB3 module determines the new position of the vector $9 via the vectors S 6 and S~. The direction cosines of the vector S~ are known from (ii). And, finally, the PREB3 module determines the vector Ss via the vectors $7 and S~. Therefore, using the above procedure one can specify the vectors $7, Ss and $9 using the three given angles ~os, ~o~, and ~03. It is clear from the algorithm, that there is no need to introduce an additional variable and to solve a non-linear equation to determine unknown vectors. The solution is thus obtained without iteration. 128 RAuu 1. At.tz~ et al. AS mentioned above, the moving coordinate system O, X~ Y, Z~ is connected rigidly to the top platform and hence the positions of the axes Oi X,, O~ Y, and O~ ZI can be determined. Since all of the revolute joints move on the same sphere with radius R3 we can obtain their coordinates from the following relations. x ~ = x o - R 3 L , y , = y o - R ~ M , z ~ = z o - R 3 N , . where i -- 7, 8, 9. The direction cosine of the side 7-8 is determined from the equations, L~4 = (x, - xT)/6.s, M74 = (ys - y~)/l~.s, N,4 = (:. - z,)/17.s. The direction cosines of the sides 7-9 and 8--9 are analogously determined. Then using the PREB3 module the direction cosine of the vector S,3 using S~2 and S,o is determined. The axes O, XI, O, g, are determined by using the pair of vectors ($12, $10), and the axis O, Zj is simply determined by using OI X, and O, F,. The coordinates of O, are obtained from the expressions Xo, = x T - R2L,3, Yo, = y T - RzM,3 , Zo, = z T - R2N,~ where R 2 is the radius of the circle passing through the points 7, 8, 9 (see Fig. 2). This completes the forward displacement analysis. It is interesting to note that rotating the input links with the same angular speeds that the platform makes rotation about the axis O, Z, and the same time remaining parallel to the plane of the base pyramid. 3. NUMERICAL VERIFICATION OF RESULTS A mechanism was chosen with sides 1|.2 : */2.3 : 1;.3 : 17.s : Is., : 17.9 : 145 cms. The remaining parameters can be determined using Fig. 3 which illustrates the base pyramid only since the calculations for the upper pyramid are identical to those for the base pyramid. From Fig. 3, R~ = !,.2 cos 45 \u00b0. The radius of the circumscribing circle of the pyramid base is, R, = (!1.2/2)(1/cos 30 \u00b0) and, RI - - R2. An in-paralkl spherical manipulator 129 The radius of the sphere r = OOt is given by \u2022 and, cos ~z = R,/R3 = i / 2 cos 30 \u00b0 cos 45 \u00b0, cos ~'3 = r / R = (R~ - RZ)'rz/il.2 cos 45 \u00b0, cos ~, = \u2022/R3 cos 45 \u00b0. The coord inates o f the base po ints are 1002 .53 ;0 ;0 ) , 2(0;0; 102.53), 3(0; 102.53;0). The d i rec t ion cosines o f the revolute j o i n t axes are S t { l ;O ;O } , Sz{O;O; ! } and S3{O; I ; 0 } . The leg lengths are it., = 12.3 = 13.6 =/4.7 = ls.s = !~., -- 145 cms. The cosines of the fixed angles are . Transactions of the ASAE \u00a9 2000 American Society of Agricultural Engineers 0001-2351 / 00 / 4306-1415 1415VOL. 43(6): 1415-1419 A pivoting test frame was constructed with a radius (l) of 2.34 m from the pivot point to the axle center (fig. 1). The drop mechanism used in the vertical free vibration tests consisted of a steel base plate with an inverted U-shaped bracket with two tabs to support the axle. The distance from the base plate to the tabs was 0.45 m, which placed the axle center 0.47 m from the base plate. The tabs were just long enough to support the axle without causing initial upward movement of the tire when the mechanism pivoted to drop the tire. The axle, when resting on the tabs, was in contact with a switch that initiated data acquisition at the instant the tire was dropped", " After oscillations had fully decayed, the final axle height was measured for each test to determine the equilibrium deflection. Vertical load and equilibrium deflection were regressed to fit equation 1. Stiffness was determined from the non-rolling equilibrium load deflection data in the same manner as the static load-deflection data. The generally accepted vertical model for a tire consists of a spring and viscous damper in parallel. Assuming that stiffness and damping coefficients are constant values and that damping is entirely viscous, the equation of motion for the test frame and tire/wheel system shown in figure 1 can be represented by equation 3. This equation is valid for small values of \u03b8, where sin \u03b8 can be approximated by \u03b8. For oscillatory (underdamped) motion, the general solution to the homogenous portion of this equation of motion is shown in equation 4, where the angular displacement is a function of time (Thomson, 1988). The equilibrium position is determined by the vertical load (L) on the tire for the given inflation pressure. The measured angular position versus time data were regressed to equation 4, which typically yielded coefficients of determination exceeding 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000327_j.mechmachtheory.2017.05.014-Figure22-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000327_j.mechmachtheory.2017.05.014-Figure22-1.png", "caption": "Fig. 22. Contact stress nephograms of helical curve face gear pair.", "texts": [ " FEM analysis During the meshing process, the contact ratio of helical curve face gear pair is ranging from 1.3 to 2.5, so the FEM analysis of helical curve face gear pair will be divided into single meshing and double meshing. The FEM analysis in this paper was obtained with \u03d5 1 = \u22120 . 01 \u03c0 , Fig. 21 (a) shows the analysis with single meshing and Fig. 21 (b) shows the analysis with double meshing. With the help of ANSYS, the contact stress can be shown on the surface of helical curve face gear with single meshing and double meshing. As Fig. 22 (a) and (b) shown, the contact area on the surface of helical curve face gear are appeared at the inner part of tooth. The area is ellipse at every moment and the errors for the theoretical contact stress compared with FEM analysis are shown in Fig. 23 . From Fig. 23 , the theoretical contact stress is different from FEM analysis during the meshing process. But the trend for the change of theoretical analysis is the same with FEM analysis and the maximum error is 6.54%. During the FEM analysis, there will be some errors, which are caused by 3D model and assemble of gear pair" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003388_978-3-662-04831-3-Figure5.31-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003388_978-3-662-04831-3-Figure5.31-1.png", "caption": "Fig. 5.31 : Vector diagram of a translational (prismatic) joint", "texts": [ ",Lj ALjR ARLi AL;LQo - 3 o WLjR o o o , + ALQ3L3 0 WL3 0 WLj 0 ALjR 0 ARL; 0 AL;LQ; L 3R LjR -2 0 ALQ3L3 0 WL3 0 ALjR 0 ARL; 0 c;;L; 0 AL;LQi LjR L;R + ALQjLj 0 ALjR 0 ARL; 0 c;;L; 0 c;;L; 0 AL;LQ; 0 L;R L;R 5.2.2.7 Prismatic joint (BB2, BB3, BB4; constrains three rota tional and two translational DOFs). A prismatic joint between bodies i and j constrains three rotational DOFs and two translational DOFso Two rotational DOFs around the x- and y-axes are constrained by the modified BB2 (cfo Equation 5.42b)o The remaining rotational DOF around the z-axis is constrained by BB40 The two translational DOFs in the y- and z-directions are constrained by BB3 (Figure 5031)0 5.2 Theoretical modeling of spatial joints 235 This provieles the following moclel equations of a prismatic joint that may also be consiclered as a combination of the model equations of a translational joint (modified BB2, BB4) with the model equations of BB3. Constraint position equations of a prismatic Joint P? (x, y) ( ALQ; L; . A L ; R . ARLi . ALi LQ 1 )Pr(z) P?(x) (AQiLi. ALiR . ARL; . AL;Q;) Pr(Y) (5.51a) Constraint velocity equations of a prismatic Joint 236 5o Model equations of planar and spatial joints pT(x y)( -ALQ;L; owL; OAL;ROARL; OAL;Lq, r ' L;R +ALQ;L; 0 AL;R 0 ARL; 0 wf~R 0 AL;Lq, )Pr(z) P" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0002457_gsecongeo.18.6.575-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0002457_gsecongeo.18.6.575-Figure8-1.png", "caption": "Fig. 8\u2022 represents a parallel fold drawn for simplicity as a", "texts": [], "surrounding_texts": [ "Since T is constant we get on integrating- s\u2022 -- s-- T\u2022. (2) This shows that between any two points where the dip is zero the lengths of any two strata are the same, such as between the parallel ends bounding the fold, or between anticline and anticline or syncline and syncline. Or what is the same thing the equation indicates that parallel folds are the result of action between vertical parallel ends and can. therefore be ascribed to tangential forces. The last statement needs to be modified by defining more closely what is meant by parallel folds in this paper. To be truly parallel the center of curvature (Z in Fig. 80) must lie outside the fold or no closer than the periphery of the lowest or uppermost bed in the system. If the center of curvature enters the bed a discontinuity occurs, meaning a different system of folds. From Equation (2) we get the important slip relation s\u2022- s =- T\u2022 which measures the relative slip between the bedding planes, as follows' Point _//, for instance, in Fig. 80 measures the end of s\u2022 and C the end of s. Had there been no sl\u2022p between the bedding planes _//would have coincided with B. That is arc .,4B represents the amount of tangential slip with reference to C and is measured by the value T\u2022, where the angle \u2022 is expressed in radians. SURFACE TYPES OF FOLDING. 583 series of circles of different radii. The curved line or slip line LMN was a straight vertical line when the strata were horizontal before folding. The shaded portion shows the relative slip with reference to point L. Thus M has slipped a distance QM, and N a distance PN measured foma line drawn normal to the dip at L. The position of the slip line was calculated from Equation (2).. If a thick book is first marked with straight vertical lines and then folded it can be made to approach the conditions of parallel folding. Features to be noted regarding parallel folds are as follows: I. The deformation is due primarily t'o slipping shearing and flow along the bedding planes. 2. The dips are constant along any radial line so long as the center of curvature remains outside the fold under consideration. 3- The dips on an anticline become steeper with vertical depth. On a rectangular similar fold the dips are vertically the same throughout. 4. It seems reasonable to assume that the amount of frictional heat generated by the folding is proportional to the slip, T\u2022. That is, the greater the dip the greater the amount of heat liberated, increasing to a maximum in the case of overturning. Since there is no slip on the anticlines or synclines where the dip is zero, these portions of the fold are relatively free of such heat, as in the case of similar folds. 5. Under certain conditions the various bent layers of a parallel fold may be under neutral surface conditions, each developing an individual neutral surface, and each bed so formed separated from its neighbor by the usual slipping plane. NEUTRAL SURFACE FOLDS. In this type the deformation does not occur primarily by means of floq or slipping as in the previous cases but theoretically at least by the actual elongation or contraction of the components of the rock. Thus in Fig. 82 abcd represents a block of flat strata, dT an elementary true thickness and oo' a surface through the center of gravity. The block is now folded so that oo' has 584 \u0153. L. the radius r0. The rock grains above oo' are then in tension, those below in compression and dT has become apparent thickness dr; the length ab is stretched to a'b' and length cd contracted F\u2022[G. 82. Deformation of a strata block according to the neutral surface law. to c'd'. The length oo' remains the same and being the locus of no deformation and no stress is here called the neutral surface. This type of folding is therefore essentially one of bending. The mathematical relations for this are that ab.dT = radr.. Since ab = roa we get rodT = rdr. Integrating this we obtain r \u2022 -- 2 ro T q- C. For convenience measuring T from the neutral surface oo', we get that when r -- to, T = o and c = r% so that the formula becomes r'= ro: q- 2 ro T. (3) The apparent hickness t is expressed by 2rot \u2022-- r-- r0-- -- \u00df r-T- r0 On the usual assumption tl\u2022at the compression and tension stresses are proportional to the contraction and elongation of any arc of radius r, it can be shown that the stresses along any face c'oa' vary at a linear rate. The face oc' is longer than face oa', consequently the total compression on the former exceeds the total tension on the latter. That is, the forces form an unbalanced SURFACE TYPES OF FOLDING. 585 couple which, taken in conjuction with the opposing or balancing forces on an adjacent face, can be resolved into a component acting a16ng the radius r. If we have a series of anticlines and synclines, the stresses, together with the radial components, are a maximum on the anticlines and synclines, and all vanish on the limbs between at the point of inflection, or the point where the curvature disappears. On an anticline the radial component would be directed upward, and on the succeeding syncline downward, so that there would be a tendency for the radial forces to balance along the course of a series of folds. In the case of an isolated dome formed under the neutral sur- face law, with fiat strata on all sides, the existence of the radial component might be the basis for interpreting the uplift as arising from vertical forces. Such a hypothesis would imply extreme coherence and elasticity of the strata in order for the doming to draw in the ends by stretching without rupture. This condition is conceivable if the bottom of the periphery of the dome floats on a friction reducer such as molten rock associated with a laccolith intrusion. It is not the intention to limit laccolith domes to neutral surface folding or vice versa by this statement. As a general occurrence neutral surface folds are probably the result of tangential movement. At the upper and lower limits of a bed folded according to the neutral surface law we have r\u2022: X/ro 2 + 2rot for the boundary of the tension side and r: = X/ro :m 2rot for the boundary of the compression side." ] }, { "image_filename": "designv10_11_0001061_j.measurement.2020.108492-Figure13-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001061_j.measurement.2020.108492-Figure13-1.png", "caption": "Fig. 13. Dismantle damage Taper roller bearing (32206).", "texts": [ ") as predicted by vibration analysis are also confirmed by visual and microscopic examinations of dismantle gearbox and its components as shown in Fig. 12. As hypothesized that the misalignment in gearbox (drive end) should severely affect the right-side taper roller bearing (32206) and gear contact; experimental findings observe similar type of failure behaviour. On visual inspection of gearbox, the right-side taper roller bearing (32206) is severely damage and severe wear marks are observed on almost all the mating gears teeth surfaces. Dismantle front rotor sub-assembly and the zoom pictures of rightside bearing are shown in Fig. 13. Several pits are observed on all the roller surfaces and inner cone. The damage rollers badly deform (shape) bearing cage, and at few locations, metal deformation (or roller impression) is observed due to the roller pressing against cage under misalign load. Several wear marks and pits are also observed on the inner cup surface due to roller damage. Bearing failure also affects gear transmission, contact patch area and its location as shown in Figs. 14 and 15. The contact patch impression (red mark) clearly indicates the bearing misalignment effect on gear transmission" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000621_j.matpr.2018.03.039-Figure15-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000621_j.matpr.2018.03.039-Figure15-1.png", "caption": "Figure 15 Carbon/Glass Leaf Spring Von-Mises Stress during Acceleration", "texts": [], "surrounding_texts": [ "Assume the vehicle is slowing down from 60 km/h to 30 km/h. Distance covered by vehicle during deceleration is assumed as 20 m. Load acting on a leaf spring:Vf 2 = Vi 2 + 2\u00d7a\u00d7d Where,Vf = Final Velocity = 30 km/h = 8.335 m/s, Vi= Initial Velocity = 60 km/h = 16.67 m/s,a = acceleration,d = distance travelled by vehicle = 20m.(8.335)2 = (16.67)2 + 2\u00d7a\u00d720,208.42 = 40a,a = 5.208 m/s2. Decelerating Force, Fd = ma,Where,m = mass of the vehicle= 2900 kg, a = acceleration= 5.208 m/s2, Fd= 2900\u00d75.208, Fd= 15110.21 N (For all four-leaf springs),For one leaf spring, Fd = 15102.32/4, Fd= 3775.58 N. Total load acting on the leaf spring is Ft = F+ Fd, Ft= 7112.25+3775.58,Ft=10887.83N. The results obtained for transient structural analysis for deceleration are shown in Figures 16-20 and listed in table 6. Table 6 Results during Deceleration Parameter Steel EN45A Carbon/Glass Composite Max Stress 415.79 MPa 545.53 MPa Max Deformation 8.9656 mm 15.005 mm Figure 16 Load during deceleration 14518 Jenarthanan M.P et al/ Materials Today: Proceedings 5 (2018) 14512\u201314519 3.4 Inference From this result, we can understand that even though deformation and equivalent stress values of Carbon/Glass Epoxy Hybrid Composite Leaf Spring increases, they are well within the safety limits." ] }, { "image_filename": "designv10_11_0000084_icacci.2017.8125901-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000084_icacci.2017.8125901-Figure2-1.png", "caption": "Fig. 2. Dynamics of 2-DOF Helicopter [12].", "texts": [ " The elevation of the nose over the pitch axis is controlled by the front propeller and the rotational motion around the yaw axis is controlled by the back propeller. The voltages across the pitch and yaw motors are \u00b124V and \u00b115V respectively. The pitch angle \u03b8 and the yaw angle \u03c8 represent two degrees of freedom. When the nose of helicopter goes up, we get \u03b8 > 0, and the yaw axis becomes positive when the rotation of helicopter is in the clockwise direction [12]. The helicopter model dynamics is shown in Fig. 2. The thrust forces Fp and Fy are applied across the pitch and yaw axis respectively. The torques act at a distance rp and ry from the respective axis. The gravitational force Fg pulls down the helicopter nose. The center of mass acts at l distance from the pitch axis along the helicopter body length. The position of center of mass is obtained by transformation of coordinates and is given as Xc = l cos\u03b8 cos\u03c8, Yc =\u2212l cos\u03b8sin\u03c8, Zc = l sin\u03b8 , where l is the distance between the center of mass and the intersection of the pitch and yaw axes" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001377_012102-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001377_012102-Figure1-1.png", "caption": "Figure 1. Scheme of the roller pair, in which the center of the movable working shaft moves along an arc of a circle: 1- rotating working shaft; 2- movable working shaft; 3- lever; 4 - the material being processed; O1, O3, O5- axes of rotation", "texts": [ " As noted earlier, GLDITM with a six-link double-circuit lever chain and GLDITM with a four-link single-circuit lever chain in roller machines with a roller module of the third type can lead to an additional angle of rotation of one working roll against another working roll, depending on the change in their interaxle distance. The magnitude of these additional angles of rotation is different in two GLDITM used in roller modules of the third type under other similar geometrical parameters. Therefore, the purpose of the paper is to determine which one of these mechanisms provides the least additional angle of rotation under other similar geometrical and kinematic parameters. Figure 1 shows a diagram of a roller pair, the center of the movable working shaft of which moves along a circular arc (roller module of the third type). In this roller pair, one of the working shafts (1) rotates on the axis (O1) forming a rotational pair with the frame (0), and the second working shaft (2) rotates on the axis (O2), which is pivotally connected to the frame by means of a lever (3) along the O3 axis. In the roller machines built according to this scheme, at the moment of change in interaxle distance (O1O2), the center of rotation of the movable working shaft (O2) moves in an arc-like manner relative to the center of O3 along an arc of a circle with a radius equal to the lever length (3)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001194_j.jclepro.2020.123307-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001194_j.jclepro.2020.123307-Figure1-1.png", "caption": "Fig. 1. Schematic diagram of the HDMR technology.", "texts": [], "surrounding_texts": [ "The conventional manufacturing approaches for metal components such as smelting, forging, and machining play a dominant role in environmental impacts. For instance, the industry contributes (directly and indirectly) approximately 37% of the global CO2 emissions in 2013 (Worrell, 2016). Research by the national bureau of China indicates that the industrial sector made up a relatively significant share for 68% of the energy expended in 2016 (National Bureau of Statistics (NBS), 2016). In the last few decades, sustainability has attached great attention to the industry. The conventional techniques like smelting, and forging are now regarded unsustainable due to the atmospheric, terrestrial, and aquatic pollution caused by the humongous equipment, as well as the low utilization of fossil fuel and material (An et al., 2018; Morrow et al., 2007). As the conventional approaches are so crucial in the field of energy consumption, various efforts have been conducted towards sustainable manufacturing. In the casting industry of iron and steel, strategies including updating the furnace control systems, adjusting the production structure by replacing natural gas-fired furnaces with capable induction furnaces, and switching to clean fuels are adopted to save energy and reduce emission (An et al., 2018; Carbontrust.com, 2011; Unver and Kara, 2019). Furthermore, the methods of optimization for systemic metabolic behaviors also produce a favorable outcome (Zhao et al., 2019, 2018, 2015). In the rolling and forging industry, strategies that substituting flywheels, clutch, and brake with servo motors and adopting more reasonable production schedules have beneficial effects. However, the primary causes of tremendous energy consumption, especially the enormous forging machine, repeated heating processes, and massive waste material are still inextricable. Hence, significantly distinctive and powerful methods to save energy are urgently desired. Additive manufacturing (AM) technology is a direct layer-wise fabricating technology according to the 3D digital model, which differs from the conventional subtractive and mass conserving approaches(Bandyopadhyay and Heer, 2018; Livesu et al., 2017). AM produces objects directly by progressively joining the feedstock of powder and wire from bottom-up without tools or dies. It makes a breakthrough to fabricate geometrically sophisticated and multifunctional gradient components that could not be manufactured through traditional manufacturing techniques ordinarily and changes the way to design and fabricate. What\u2019s more, AM is a rapid prototyping approach by integrated equipment, which shows significant potential in the reduction of material waste, process time, cost, energy consumption, and carbon emission for the small scale production of complex components due to the principle of layer building (Frazier, 2014)(Duflou et al., 2017). It\u2019s indicated that AM technologies have been widely accepted in multiple fields, including aerospace, shipbuilding, motor vehicles, electronics, and healthcare (DebRoy et al., 2018; Li et al., 2019; Mary Kathryn Thompson, 2016). And it plays a remarkable role in improving material utilization, reducing life-cycle impacts, energy consumption, and emissions (Le Bourhis et al., 2013; Runze Huang Matthew Riddle, 2015). The sustainability and environmental performance of AM processes have been investigated in recent years(Ford and Despeisse, 2016). Kellens et al. (Kellens et al., 2017) provided a comprehensive overview of the current studies analyzing the environmental dimensions of AM, encompassing life cycle stages from material production to the part manufacturing and use phase up to the waste treatment of the AM production waste. Cruz Sanchez discussed the recycling processes of AM technologies and the connections between circular economy and distributing recycling(Cruz Sanchez et al., 2020; de Azevedo et al., 2020). As a newly popular approach and a promising substitute, the AM techniques are always in comparison with the conventional ways. Despite the above advantages and the growing applications, the efficiency in the throughput is not entirely satisfactory due to the low productivity caused by the limited layer height. In consequence, the specific energy consumption (SEC) of current AM systems was indicated to exceed conventional manufacturing processes such as machining, casting, or injection molding in mass production scales(Duflou et al., 2012a, 2012b; Yoon et al., 2014). However, this related expression maybe not absolute because it depends on the specific application and different AM methods. Yoon (Yoon et al., 2014) compared the AM approach with conventional bulk-forming and subtractive processes in terms of specific energy consumption and concluded that AM technology is suitable for the fabrication on a small scale. Ingarao (Ingarao et al., 2018) provided a comprehensive comparison for aluminum components made by turning, forming, and Selective Laser Melting (SLM) 3 processes and pointed out that AM technique is preferable only in specific scenarios like high complexity shapes or significant weight reduction. Thomas concluded that current AM technology is cost-effective for small batches customized production of strong light-weight products with continued centralized manufacturing(Thomas and Gilvert, 2014). The existing researches mainly focused on the macro description of environmental impacts and the cost of AM technology. Nevertheless, the research on modeling the processes is insufficient. In most cases, the energy-consuming performance is obtained by the power measurement in the process. Baumers implemented a tool for the estimation of process energy flows in a direct metal laser sintering (DMLS) system by multiplying the energy consumption rate with the total time(Baumers et al., 2012). Paul presented a mathematical analysis to calculate the necessary laser energy expenditure for manufacturing simple components using SLS by a function of the total area of sintering with the part geometry, slice thickness, and the build orientation(Paul and Anand, 2012). Furthermore, most of the comparisons between AM and traditional approaches in the previous studies are performed on the hypothesis of similar performance and quality. Whereas, it should be noted that looseness and defects by the anisotropy from layer fabricating would result in unsatisfactory mechanical properties. AM technologies may not perform an equivalent as conventional methods in mechanical quality and efficiency (Lewandowski and Seifi, 2016). YiZhu(Jia et al., 2018) associated the energy spending with mechanical performance in SLM and indicated that superior tensile strength deserves more energy consumption. Hence, the comparison of energy consumption could be more meaningful and convincing only when the quality of the two approaches at the same level. Hybrid deposition and micro rolling (HDMR) is a hybrid approach combining in-situ rolling with wire and arc additive manufacture (WAAM), which can fabricate components of wrought quality with fantastic energy and material consumption. Mathematical modeling for energy consumption is still inadequate for AM processes, which motived this research to characterize the HDMR process and developed an energy consumption model. In this research, a more concrete estimation model for the HDMR technique based on the two main processes of depositing and rolling in terms of active work was contributed, which could indicate the energy efficiency clearly during the manufacturing process. For demonstration, we monitored the energy consumption of a Ti-6Al-4V component during the process as a reference. Additionally, we worked out the energy consumption of this part in the conventional way according to the recommended equipment and process route. A comprehensive comparison between HDMR technology and conventional forging methods is performed in energy consumption, mechanical properties, and manufacturing process. This document is organized in the following manner. Section 2 contains the brief introduction and energy modeling of the HDMR process. In Section 3, we conducted a case study and estimated the energy consumption with a measurement by power meter as a reference. A comparison of the HDMR approach and the conventional manufacturing methods in environmental aspects is discussed in Sections 4. Section 5 concludes the present and future work of this article. 2. Methodology and energy model 2.1 HDMR technology The HDMR technology is a novel direct metal manufacturing technique for middle to large near-net-shape components with high dimensional accuracy and perfect mechanical quality by applying in-site continuous rolling pressure in the depositing process(Zhang et al., 2013, 2016). It selects electric arc as the heat source and metal wire as the feedstock, which outstands in low cost and high efficiency. Compared with powder-feed AM approaches, wire-feed approaches have a more satisfactory deposition rate (several kgs/h) and material usage efficiency (approaching 100 pct). Additionally, wire feedstock is usually one order of magnitude cheaper (Mary Kathryn Thompson, 2016). Hence, HDMR is regarded as a promising approach to fabricate medium to large components integrally. The HDMR process is illustrated in Fig .1, the welding arc generated under the high-energy current melts the feeding metal wire with the substrate or previously deposited layer and deposits layer by layer along a defined path according to the pre-sliced CAD model. Whilst the micro-roller moves synchronously right behind the welding torch to apply continuous pressure on the top surface of the semi-solid material near the molten pool. The thermocycling caused by the heat of the next layer will promote microstructure recrystallization and generate unbalanced stress. The dendrite or columnar grains produced in the depositing process would be broken into short crisscross grains under the plastic deformation by in-situ hot rolling, which would increase the mechanical properties. The 4 stress state would be improved at the same time. Additionally, milling is coupled to fabricate complex geometries, interior features, and smooth surfaces. 2.2 Energy consumption modeling for HDMR Aiming at characterizing the energy consumption of the HDMR process quickly and approximately, we try to divide the consumed energy into two main parts. One is the active energy required to fulfill the direct functions, and another is the auxiliary energy cost on the indirect technical functions of the equipment. Specifically, the active energy is usually determined theoretically in terms of physical shape and state, which represents the minimum energy demanded in the process. Mostly, the active effects in the HDMR approach are composed of the melting of the feeding wire to liquid drops and the plastically rolling deformation of the deposited beads. The auxiliary energy depends on the machinery and equipment to conduct the active works. The total energy consumption could be divided into depositing energy, rolling energy, and the energy consumed by the machine tool according to the producing principle, which can be interpreted as equation 1 shows. EHDMR=Edepositing+Erolling + Emachine tool (1) In the depositing process, the welding arc generated under the high-energy current melts the feeding metal wire to be the droplets, which are deposited layer by layer. However, the heat produced by the welding arc couldn\u2019t be completely absorbed because of the heat loss through radiation, convection, electrode heating, and heat conduction in the TIG torch. The energy efficiency of the power supply is defined as the ratio of arc energy delivered to the substrate and the total arc energy input from the power supply, and it doesn\u2019t vary significantly within the range of different process parameters(DuPont and Marder, 1995; Joseph et al., 2003). Hence, the energy required in the depositing process could be determined as follow: Edepositing= \u00b7m\u00b7\u2206t+ m / (2) \u2014 Specific heat capacity of the feeding material; \u2014 Specific latent heat capacity of the feeding material; m \u2014 Mass of the depositing material; \u2206t \u2014 Temperature difference to the melting point; \u2014 Energy efficiency of the power supply; As for the deforming process, the micro roller scrolls synchronously along the cladding route right behind the welding torch and squeezes the cross-section of the semi-solidified bead from the parabola to the drum(Ding et al., 2016; Fu et al., 2017). The rise and fall of the roller are driven by a sever motor. Therefore, the energy cost on the rolling process is determined by the active work and the energy efficacy of the executing motor. The deformation work by rolling is estimated by the integral of the deformation resistance and the reduction of the rolled beads. By referencing the plane-strain upsetting, we proposed an equivalent calculation method to estimate the plastic deformation work. In the slab rolling(Lihua Lv, 2007), the deformation work Wdeformation to press a slab from the dimension of L\u00d7B\u00d7H to l\u00d7b\u00d7h could be evaluated by the integration of the deformation force Px, the horizontal cross-sectional area Fx and the vertical displacement of dhx. Wdeformation= - PxFx H h dhx=2\u03c3sV ln H h + 1 8 b h - B H (3) 5 F \u2014Area of the horizontal cross-sectional, V/hx; P \u2014 Simplified average unit deformation force on the contact surface, 2 1 + \u00d7 ; \u2014 Yield strength of the material; As the bead is depressed, material on the top of the bead goes down under the rolling pressure, accompanied by sideways displacement. To simplify the estimation, we hypothesize the complex slip in multi-direction during the rolling process to vertically downward slip. And, the vertical reduction of the rolled beads in the rolling process equals the reduction of the peaks of the beads. Considering that the profile of the bead before and after rolling could be accurately fitted through parabola functions and isosceles trapezoid respectively. To perform the calculation, an equivalent method was proposed to simplify the beads to the cuboid with the equivalent size. The height of the equivalent cuboid equals to the original height of the beads in view of the start and end position of the rolling process. The equivalent width of the rectangles can be deduced based on the principle of constant area respectively. In consequence, the equivalent width of the beads to be rolled and rolled are 2W/3 and (w1+w2)/2 respectively. Erolling=2\u03c3sV ln H h + 1 8 b h - B H / (5) B \u2014 Equivalent width of the bead before rolling, B = 2/3W; b \u2014 Equivalent width of the bead after rolling, b = (w1+w2)/2; V \u2014 Volume of the depositing bead; \u2014 Energy efficiency of the rolling motor; However, the relative motion between the subtract and the welding torch is the basis of additive manufacturing. The remaining energy besides the above factors was consumed to carry out the active work. The energy consumed to drive the machine tool for depositing and rolling could be estimated according to the average operating power and the traveling time by: Emachine tool =Pptp/\u03b73 (6) Pp \u2014 Average power to drive the machine tool; tp \u2014 Traveling time of the depositing process; % \u2014 Energy efficiency of the machine tool; V \u2014 Volume of the depositing bead; \u2014 Energy efficiency of the rolling motor; 6 3. Experiment 3.1 Case introduction Currently, titanium is the most popular material in the aerospace industry for the remarkable performance in specific strength, fracture toughness, corrosion, resistance, and lightweight. However, the manufacturing of titanium components is costly in terms of purchase cost, energy consumption, machinability, and material utilization (Williams et al., 2015). Industries like aerospace are now embracing AM technology for the superiority of sustainability, integrality, and rapidity. In this paper, we performed a case study for the fabrication of a Ti-6Al-4V thin-wall load-bearing wrought component. This component is characterized by the cross shape with four blades and a central hole. Every blade is vertical to each other and possesses a structure of thin wall with the diverse cross-section features and the stiffeners on various locations. The 3D model is demonstrated with the dimensional annotations in Fig. 3. Fig. 3. Sketch of the Ti-6Al-4V thin-wall component 3.2 System set up The HDMR system investigated in this paper is illustrated in Fig.4. It consists of a five-axis machine tool, a welding system, an argon gas protection system, and an industrial control system. The working size could be as large as about 2800mm by 1500mm by 900mm. The gas protection system covers the fabrication unit with a closed chamber for some unique material like titanium and super alloy, which have a strict requirement for the air composition. This system capitalizes on the flexibility afforded by the five-axis machine tool, which is reformed with the welding torch and micro roller fixed coaxially on the shell of the spindle. The rolling pressure is adaptive to different materials and is modified by the force sensor located on the roller rack. 7 This part was deposited with the welding machine EWM Tetrix 551. A torch stand-off distance of 8mm was applied, and \u03c61.2 mm Ti-6Al-4V wire was fed at the angle of 30\u00b0 into the arc. The oxygen content and water content was kept below 15ppm and 50ppm by diluting and purifying the closed chamber, which was filled with 99.9% argon. Table 1 lists the adopted parameters for Ti-6Al-4V in this depositing experiment, which is obtained from a serious of optimal experiments. Table 1 Optimized depositing parameters for HDMR Process parameter Value Power supply Tungsten Inert Gas Welding Gas flow rate (L/min) 10 Average current (A) 160-170 Average voltage (V) 13.3-13.7 Travel speed (m/min) 0.13 Wire feed speed (m/min) 2.4 Overlap rate (%) 30 3.3 Energy consumption of HDMR The HDMR process starts depositing along the tangential direction based on a steel cylindrical substrate, which would be sheared off from the finished part in the end. Subsequently, the deposition of the blades is symmetrically conducted to avoid unbalanced thermal stress and deformation. Milling is called when the junction has different features and uneven surfaces. Thermal monitoring is applied to capture the surface temperature behavior of the deposited area by using infrared thermography. The nominal active energy consumption is estimated via summing up the melting heat in the welding process and the deforming work in the rolling process. (1) The molten heat of the Ti-6Al-4V wire while welding each bead at a melting point is estimated by the thermodynamic formula as following: Edepositing=& \u00b7\u2206t+ / =7.42\u00d7105kJ \u2014 Average power to drive the machine tool; \u2014 Specific latent heat capacity of Ti-6Al-4V,3.7-5.0 kCal/g; & \u2014 Mass of the deposited blank, 36kg; \u2206' \u2014Temperature difference to the melting point, 1640\u2103; \u2014The melting efficiency, 0.7-0.8 in gas tungsten arc welding (GTAW). (2)The workability, namely \u03c3s, of Ti\u20136Al\u20134V under hot compression conditions, is determined with the temperature range and strain rate range(Bruschi et al., 2004; Gao et al., 2019; Park et al., 2002). The active deformation energy can be estimated by formula (5) with the sizes of the WAAM and HDMR bead listed in Table 2: Erolling=2\u03c3sV ln H h + 1 8 b h - B H / =3.73\u00d7103kJ \u03c3s \u2014Yield strength of Ti-6Al-4Va at 800\u2212900\u2103 with the strain rate of 0.2 s-1,200-250Mpa; V \u2014Volume of the deposited blank, 5.49\u00d710-3m3; \u2014 Mass of the deposited blank, 36kg; \u2206' \u2014The energy efficiency of the servo motor, 0.8-0.9; traveling time of depositing could be derived through the mass of the blank and the feeding speed of the \u03c61.2mm wire. In the depositing process of this part, the trajectory of the machine tool is mainly made up of a linear shift by a single axis, which is driven by 8 a sever motor with the rated power of 3kw. Considering the additional modules like the air conditioner, lightings, sensors, and fans, the energy efficiency of the machine tool is regarded as 0.4-0.5 approximately. The additional energy of the HDMR system could be estimated by formula as follows: Emachine tool=Pptp/\u03b73=1.08\u00d7106kJ Pp \u2014Average power to drive the platform, 2.4 kW; tp \u2014Basic depositing time, 1.8\u00d7105s; % \u2014Energy efficiency of the machine tool, 0.3-0.4; The total energy consumed in the HDMR process is estimated to be 18.2\u00d7105kJ, and the corresponding specific energy consumption (SEC) equals 5.06\u00d7104 kJ/ kg. 3.4 Verification of the energy model For the precise estimation of energy consumption for this specific HDMR equipment, the electricity consumption of the manufacturing process was measured and recorded with a digital multi-purpose power meter (YOKOGAWA wt1800, Japan). The purpose of this measurement was to confirm the agreement between the proposed HDMR power model and experiments. This power meter was configured to a 1s measurement cycle, and the accuracy can be 0.05% of the range. The set up of the experiment is illustrated in Fig. 5. Three voltage probes and three current clamps were connected to the system\u2019s three-phase power supply. The power meter collected the current and voltage for power analysis and transmits them to the computer for recording. Fig.5. Diagram of the connection of power meter Since the total time of the manufacturing process is too long to keep the power meter running all the time. Thus, we analyzed the actual specific energy consumption according to the process of depositing typical features of the \u201cI\u201d cross joint. The power curve while alternately depositing the four blades in one layer is illustrated in Fig.6. In this layer, each leaf was deposited of 0.104 kg Ti-6Al-4V wire with an energy consumption of 5.94\u00d7103 kJ, which is calculated from the processing time and power measurements through the in-depth approach. We forecast the SEC of the whole process as the average SEC of one layer based on the assumption that the 9 manufacturing process is uniformly stable. Consequently, the actual SEC of component fabricating for this HDMR system is estimated to be 5.71\u00d7104 kJ/kg, which is close to the estimated value of the proposed model, with a deviation of 11.4%. Fig.6. The power profile while depositing\u201cI\u201d cross joint" ] }, { "image_filename": "designv10_11_0001267_j.jclepro.2020.120491-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001267_j.jclepro.2020.120491-Figure3-1.png", "caption": "Fig. 3. Schematic diagram of 3-RRR, 3-RRS spherical parallel mechanism.", "texts": [ " Since there are many different types of structures in the underactuated spherical parallel structure, it is necessary to further select various spherical parallel mechanisms according to actual design requirements: 1) With high flexibility, it could realize flexible pose transformation in space; 2) Ensure that the overall structure does not interfere with the human body during the movement, and is easy to use; 3) Ensure the overall structure\u2019s compactness and reduce the overall structure\u2019s space volume; 4) Try to ensure the symmetry of the structure, which could effectively reduce the subsequent design and production difficulty. The 3-RRR spherical parallel mechanism and the 3-RRS spherical parallel mechanism in the underactuated spherical parallel mechanism are initially selected as the prototypemechanism of the exoskeleton ankle joint components, as shown in Fig. 3. Themoving and static platforms are connected by three identical branches, and the active pair is located on the same static platform. The main difference is the type of connection pair used. The 3-RRR spherical parallel mechanism a single branch consists of three rotating pairs. 3-RRS spherical parallel mechanism a single branch consists of two rotating pairs and one spherical pair. Considering structural flexibility requirements of exoskeleton use, this paper chooses 3-RRS spherical parallel mechanism as the prototype mechanism of exoskeleton robot ankle joint components" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003625_robot.2000.846403-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003625_robot.2000.846403-Figure3-1.png", "caption": "Figure 3. Family of dexterity ellipsoids: a - at a singular configuration, b - far away from singularities.", "texts": [ " Using the definition (17), we have computed instantaneous dexterity ellipsoids for the double pendulum mounted atop of the unicycle. To this aim we have fixed the links' lengths of the double manipulator as Z1 = 2, 12 = 1, and selected different configurations (u1,2~2,21,22) and times of motion T . The results are presented in figures 3, 4 and 5 below, demonstrating the relevance of our dexterity ellipsoids as a tool for the dexterity assessment of mobile manipulators. Notice, that at the singular configuration (figure 3 a)) the dexterity ellipsoid has degenerated to an ellipse. Figure 4 a) shows that at T = 0 the dexterity of the mobile double pendulum simply reduces to the manipulability of the double pendulum itself, that is always singular in the 3-dimensional taskspace. The dexterity measure increases along with the time of motion. 4 Conclusion By making use of control-theoretic methods we have proposed in this paper a collection of new tools facilitating the kinematic analysis of mobile manipulators. They include the kinematics, the analytic Jacobian, the dexterity matrix, the dexterity measure and the manipulability ellipsoid" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000074_j.ifacol.2017.08.1338-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000074_j.ifacol.2017.08.1338-Figure1-1.png", "caption": "Fig. 1. Quadcopter system.", "texts": [ " Therefore, the Newton-Euler rotation equation is given by: I \u2212\u0307\u2192 \u2126 + \u2212\u2192 \u2126 \u00d7 (I \u2212\u2192 \u2126) = \u03c4, (4) where \u03c4 [\u03c4\u03c6 \u03c4\u03b8 \u03c4\u03c8] gathers the roll, pitch, yaw torques, and I = diag{Ixx, Iyy, Izz} represents the inertia tensor. Gathering (3) and (4) we can write the dynamics of the quadcopter in an extended form:[ x\u0308 y\u0308 z\u0308 ] = [ 0 0 \u2212g ] + 1 m [ c\u03c6s\u03b8c\u03c8 + s\u03c6s\u03c8 c\u03c6s\u03b8s\u03c8 \u2212 s\u03c6c\u03c8 c\u03c6c\u03b8 ] T, (5a) \u2126\u0307x \u2126\u0307y \u2126\u0307z = (Iyy \u2212 Izz)I \u22121 xx \u2126y\u2126z (Izz \u2212 Ixx)I \u22121 yy \u2126z\u2126x (Ixx \u2212 Iyy)I \u22121 zz \u2126x\u2126y + I\u22121 xx \u03c4\u03c6 I\u22121 yy \u03c4\u03b8 I\u22121 zz \u03c4\u03c8 , (5b) In terms of the angular velocity \u03c9i of the ith rotor (i \u2208 {1 \u00b7 \u00b7 \u00b7 4}) configured as in Figure 1, the thrust T and angle torques \u03c4 used in (5) are given by: T = KT (\u03c9 2 1 + \u03c92 2 + \u03c92 3 + \u03c92 4), \u03c4\u03c6 = LKT (\u2212\u03c92 2 + \u03c92 4), \u03c4\u03b8 = LKT (\u2212\u03c92 1 + \u03c92 3), \u03c4\u03c8 = b(\u2212\u03c92 1 + \u03c92 2 \u2212 \u03c92 3 + \u03c92 4), (6) where b, L and KT are constants of the quadcopter frame assumed known. Remark 1. The linear relationship (6) shows that we can choose either [T \u03c4\u03c6 \u03c4\u03b8 \u03c4\u03c8] or [\u03c91 \u03c92 \u03c93 \u03c94] to be the input of quadcopter system. Hereinafter, we will make use of both of them for flat output representation and fault events analysis. 1 Note that, in order to write in a more compact way we have used in (1) \u2032c\u2032 and \u2032s\u2032 to denote the cos(\u00b7) and sin(\u00b7) functions, respectively", " Therefore, the Newton-Euler rotation equation is given by: I \u2212\u0307\u2192 \u2126 + \u2212\u2192 \u2126 \u00d7 (I \u2212\u2192 \u2126) = \u03c4, (4) where \u03c4 [\u03c4\u03c6 \u03c4\u03b8 \u03c4\u03c8] gathers the roll, pitch, yaw torques, and I = diag{Ixx, Iyy, Izz} represents the inertia tensor. Gathering (3) and (4) we can write the dynamics of the quadcopter in an extended form:[ x\u0308 y\u0308 z\u0308 ] = [ 0 0 \u2212g ] + 1 m [ c\u03c6s\u03b8c\u03c8 + s\u03c6s\u03c8 c\u03c6s\u03b8s\u03c8 \u2212 s\u03c6c\u03c8 c\u03c6c\u03b8 ] T, (5a) \u2126\u0307x \u2126\u0307y \u2126\u0307z = (Iyy \u2212 Izz)I \u22121 xx \u2126y\u2126z (Izz \u2212 Ixx)I \u22121 yy \u2126z\u2126x (Ixx \u2212 Iyy)I \u22121 zz \u2126x\u2126y + I\u22121 xx \u03c4\u03c6 I\u22121 yy \u03c4\u03b8 I\u22121 zz \u03c4\u03c8 , (5b) In terms of the angular velocity \u03c9i of the ith rotor (i \u2208 {1 \u00b7 \u00b7 \u00b7 4}) configured as in Figure 1, the thrust T and angle torques \u03c4 used in (5) are given by: T = KT (\u03c9 2 1 + \u03c92 2 + \u03c92 3 + \u03c92 4), \u03c4\u03c6 = LKT (\u2212\u03c92 2 + \u03c92 4), \u03c4\u03b8 = LKT (\u2212\u03c92 1 + \u03c92 3), \u03c4\u03c8 = b(\u2212\u03c92 1 + \u03c92 2 \u2212 \u03c92 3 + \u03c92 4), (6) where b, L and KT are constants of the quadcopter frame assumed known. Remark 1. The linear relationship (6) shows that we can choose either [T \u03c4\u03c6 \u03c4\u03b8 \u03c4\u03c8] or [\u03c91 \u03c92 \u03c93 \u03c94] to be the input of quadcopter system. Hereinafter, we will make use of both of them for flat output representation and fault events analysis. 1 Note that, in order to write in a more compact way we have used in (1) \u2032c\u2032 and \u2032s\u2032 to denote the cos(\u00b7) and sin(\u00b7) functions, respectively. \u03c93 \u03c43 \u03c91 \u03c41 \u03c94 \u03c44 \u03c92 \u03c42 BxBy Bz f4 f3 f2 f1 Fig. 1. Quadcopter system. 2.3 Wind perturbation model We will add to the translation dynamics in (3) an air perturbation force \u2212\u2192 FD. The force triggered by the quadcopter motion and external wind (Fox and McDonald, 1994) is modeled as follows: \u2212\u2192 FD = 1 2 CD\u03c1|\u2212\u2192Vr|A \u2212\u2192 Vr, (7) where \u03c1 is the surrounding fluid density, CD is the drag coefficient, \u2212\u2192 Vr = \u2212\u2192vw \u2212 \u03be\u0307 is the vector of relative motion between the wind speed \u2212\u2192vw and the quadcopter velocity \u03be\u0307. The projected area A is calculated by the following relation: A = Ax \u2223\u2223\u2223\u2223\u2223 \u2212\u2212\u2192 IxB \u2212\u2192 Vr |\u2212\u2192Vr| \u2223\u2223\u2223\u2223\u2223+Ay \u2223\u2223\u2223\u2223\u2223 \u2212\u2212\u2192 IyB \u2212\u2192 Vr |\u2212\u2192Vr| \u2223\u2223\u2223\u2223\u2223+Az \u2223\u2223\u2223\u2223\u2223 \u2212\u2212\u2192 IzB \u2212\u2192 Vr |\u2212\u2192Vr| \u2223\u2223\u2223\u2223\u2223 , (8) where Ax, Ay, Az, which depend on the designed structure of the quadcopter, describe the projected areas into YZ, XZ, and XY planes of the BF" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001059_j.mechmachtheory.2020.104101-Figure14-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001059_j.mechmachtheory.2020.104101-Figure14-1.png", "caption": "Fig. 14. Model for calculating the C point movement.", "texts": [], "surrounding_texts": [ "After the optimisation process, assumptions and equations are introduced in order to design a model with imposed movement for carrying out simulations. In the simulations, the angular velocity of femur movement is no longer considered constant. The movement is divided into 3 phases, namely: accelerating phase (T), phase of movement with constant velocity (8T), and decelerating phase (T) - a combined total time of 10T = 17 s. By integrating the acceleration\u2019s equation, which considers half of the sinusoid [44] , solutions are obtained in the form of angular velocity as Eq. (2) and angular displacement as Eq. (3) . On their basis, the final form of the driving position function is determined as knee (t) in Eq. (4) . For part of the position function, referring to the motion phase with constant velocity \u03c9 const , the values of the angular position are calculated as the sum of the angular position in the preceding time point and the product of the constant rotational speed and time step t ( Eq. (4) ). In order to obtain a continuous angular velocity function, the value of \u03c9 const has to be equal to the result of Eq. (2) at the end of the accelerating phase - therefore T ( \u03c9 const = \u03c9 (T) = \u03b1T / T rad/s). Eq. (3) is used to obtain the angular position functions for the other two phases \u2013 the acceleration and deceleration parts of the final function ( knee (t) in Eq. (4) ). \u03c9 (t) = \u2212 \u03b1T 2 T cos ( \u03c0 t T ) + \u03b1T 2 T (2) where \u03b1T \u2013 angle of rotation in the considered phase of movement, T \u2013 time of the movement in the considered phase, t \u2013 time. \u03c6( t ) = \u2212 \u03b1T 2 \u03c0 sin ( \u03c0 t T ) + \u03b1T 2 T t + C 1 (3) The values of integration constants C 1 (0 and 4 \u03b1T respectively for the acceleration and deceleration parts in Eq. (3) ), and later of the angle \u03b1T \u2248 0.2327 rad, are calculated on the basis of the boundary conditions and the requirement of the continuous angular displacement function, with details being given in [33] . \u03c6acc (t) = \u2212 \u03b1T 2 \u03c0 sin ( \u03c0 t T ) + \u03b1T 2 T t, since \u03c6acc (0) = 0 \u03c6const ( t i ) = \u03c6i \u2212 1 + \u03c9 const \u2217 t \u03c6dec (t) = \u2212 \u03b1T 2 \u03c0 sin ( \u03c0 t T ) + \u03b1T 2 T t + 4 \u03b1T since \u03c6dec (9 T ) = \u03c6acc (T ) + \u03c9 const \u2217 (9 T \u2212 T ) knee (t) = { \u03c6acc (t) f or 0 \u2264 t \u2264 1 . 7 s \u03c6const ( t) f or 1 . 7 \u2264 t \u2264 15 . 3 s \u03c6dec ( t) f or 15 . 3 \u2264 t \u2264 17 s (4) Using Eq. (4) , the value of the angular position \u03d5(t) is computed and thefemur angular displacement function is set in ADAMS, as shown in Fig. 12 . For the case of a 4-bar mechanism with additional DOFs, the position of the ICR should not be considered coincident with the intersection point of the crossed elements, which was assumed in [31] for simplification purposes. As a consequence, in further simulations, calculations are carried out in order to obtain data suitable for imposing the motion in the ADAMS model, and also to enable the movement to be performed for a required ICR trajectory. The reference ICR trajectory is converted to the trajectory of one of the femur element\u2019s points \u2013 the C point with a time step of 0.01 s ( Figs. 10 and 13 ). The calculations during the simulations are performed with a sampling frequency of 100 Hz. The position of point C is calculated according to Eq. (5) , as the sum of its position in the preceding time point and its linear displacement s calculated for time step t = 0.01 s, and therefore its coordinates are determined as follows: C Z ( t i ) = C Z ( t i \u22121 ) + s Z ( t ) C Y ( t i ) = C Y ( t i \u22121 ) + s Y ( t ) (5) In order to calculate displacements s ( Figs. 13 and 14 ), the vector product of angular step \u03d5i carried out in time t, and the calculated lever arm r i defined in Eq. (6) , were used. r Z (t) = C Z (t \u2212 t) \u2212 IC R Z (t) r Y (t) = C Y (t \u2212 t) \u2212 IC R Y (t) (6) Furthermore, using numerical data from the ADAMS simulations for the positions and velocities of the femur points (B, C), the ICR position was computed according to the scheme presented in Fig. 15 and Eq. (7) . General functions of the straight lines were identified as being perpendicular to the velocity vectors of points B and C, and they also crossed through these points. Solving the system of these two equations using determinants enabled the ICR point as the intersection point of the two straight lines to be found. IC R Z = W Z W m = \u2212P B v YC + P C v Y B v ZB v YC \u2212 v ZC v Y B IC R Y = W Y W m = \u2212P C v ZB + P B v ZC v ZB v YC \u2212 v ZC v Y B (7) where: P B = \u2212 ( v ZB Z B + v Y B Y B ) P C = \u2212 ( v ZC Z C + v YC Y C ) and:" ] }, { "image_filename": "designv10_11_0000536_s11370-015-0180-3-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000536_s11370-015-0180-3-Figure2-1.png", "caption": "Fig. 2 Schematic of the 7-DOF structure", "texts": [ ", Lee and Bejczy [4] proposed an approach for representing the redundancy of manipulators, Tondu [16] suggested that joints 1 and 3 appear to be the best choices for parameterizing the redundancy, andYu [17] utilized joint 7 as the redundant joint. However, it is not possible to uniquely determine the redundant joint angle based on other joints because there are nonlinear relationships between the joints of 7-DOFmanipulators.A previous study [15] also addressed the concept of \u201cself-motion,\u201d i.e., the upper arm and the forearm can revolve around the line between the shoulder and wrist even if the position and orientation of the end-effector are fixed. As shown in Fig. 2, the reference plane is determined by the upper arm and forearm when joint 3 is zero (at this point, the manipulator is equal to a 6-DOF manipulator and the reference plane is unique). As defined above, the plane of the upper arm and forearm can rotate around the axis fixed by the shoulder and wrist. After rotation, the new plane is called the arm plane and \u03c8 is used to define the angle of the distance between these two planes: the arm angle. Therefore, we can represent the rotation matrix of each joint in the following form: bRs = 0R1 \u00b7 1R2 \u00b7 2R3 sRe = 3R4 eRt = 4R5 \u00b7 5R6 \u00b7 6R7", " Step 5: Determine the intersection of every feasible range of \u03c8 and separate the singular point from this set. Step 6: Select an optimal solution that can makes \u03b4q as close to zero as possible using the traditional method so the speed of the joints satisfies the Trapezoidal Planning Law. In the S-R-S space manipulator, the working space is determined by the length of upper arm and forearm [25]. Hence, the length of l2 and l4 can be determined when the operation space of end manipulator is known. From the Fig. 2, it is can be seen that the length of l2 and l4 is only related to the joint 4 with the certain working space of manipulator. While the determination of joint 3 is at least considering three factors: (1) the angle of joint 4 should be as far as possible close to the position of reasonable stress; (2) keeping away from the singular point and limit; (3) as far as possible to make the working space of manipulator large. In this paper, joint 4 has been analyzed. The singular points of joint 4 are only 0\u25e6 and 180\u25e6" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003686_bf01578534-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003686_bf01578534-Figure2-1.png", "caption": "Fig. 2a, b. a Cross-section with N1 = N 2 , b Model corresponds to the half stator slot pitch", "texts": [ " (1) We assume that there is only radial heat dissipation through the frame surface. We also neglect axial thermal currents from and towards the windings ends. For symmetry reasons, the number of rotor slots N2 is set equal to the number ofs ta tor slots N1. This means that 118 Archly fiir Elektrotechnik 77 (1994) we keep the actual radial dimensions of the rotor, while the tangential dimensions are modified in proport ion to ratio NdN2. The same modification is also applied to the cross-sections of slots and teeth (Fig. 2 a). For the temperature computation one may change the shape of the slots in order to get a coincidence of their sides with radii and arcs of the grid, and in fact we do so. This change has a negligible effect on copper temperatures and the whole temperature distribution. Because of symmetry, only the section which corresponds to the half stator slot pitch is dealt with, i.e. we consider an angle of 180~ (Fig. 2b). The insulation between the copper windings and the c o r e consists of: a. the slot insulation, b. the air gap between the slot insulation and the laminations, c. the insulation varnish of the windings, and d. the air gaps between the conductors. All these insulations are replaced by an equivalent thermal conductivity: dl + d2 + d3 2 = (2) dt d2 d3 where dl is the thickness of the slot insulation, d2 is the thickness of air gap between the slot insulation and the laminations and d3 is the thickness of an equivalent layer corresponding to the insulation varnish of the windings and the air gaps between the conductors and 21, 22, 23 are the corresponding thermal conductivities", " The heat diffusion equation in a two dimensional problem concerning a homogeneous and isotropic medium with constant thermal conductivity coefficient reads: V2 T + 0 _ l O T (4) 2 a at where: T = temperature, K, t = time, s, 2 = thermal conductivity coefficient, W/m 9 K, O = strength of heat source (copper losses) per unit volume, W/m 3, a = 2/Ocp, thermal diffusivity, m2/s, r = mass density, kg/m a, cp = specific heat at constant pressure, J/kg\" K. Because of the absence of tangential heat flux on boundaries OA and OB (Fig. 2 b), the Neumann boundary condition, i.e.: 2 V T . e = 0 (5) is applied on OA and OB, where e is the unit vector normal to these boundaries. On the outer surface the boundary condition is: 2 g r . n + c f f T - T~) = 0 (6) where: n = (nx, n S the unit vector normal to outer surface, c~ = heat transfer coefficient, W/m 2 - K, T~ = surrounding temperature, ~ The initial condition is T(t = 0) = T o . (7) As it is shown in Fig. 3 the machine cross-section has been divided into 35 regions. There are 7 homogeneous regions: laminations of stator and rotor, copper windings of stator and rotor, insulation of stator and rotor windings and air gap" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001070_j.mechmachtheory.2020.104127-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001070_j.mechmachtheory.2020.104127-Figure5-1.png", "caption": "Fig. 5. The revolute clearance joint in a multi-body system.", "texts": [ " Unlike the traditional Berg\u2019s friction model, the maximum friction force F g varies with the displacement excitation x . The maximum friction force F g can be obtained by curve fitting. F g = g 1 x 3 + g 2 x 2 + g 3 x + g 4 (9) where g 1 , g 2 , g 3 and g 4 polynomial coefficients. Finally, the friction displacement x 2 can be determined as x 2 = F g ( x 0 ) K max \u2212 K e ( x 0 ) (10) where K max is the maximum tangent stiffness when x is infinitely close to x 0 and K e is the elastic stiffness. To investigate the joint effects, the mathematical model of a revolute joint is shown in Fig. 5 . The journal part j with radius R j is located inside of the bearing part i with radius R i . xy represents the global coordinate system. Point O j and O i are the centers of the journal and bearing. The eccentricity vector e can be determined as e = r O j \u2212 r O i (11) where r O j and r O i are the center positions of the journal and the bearing respectively in the global reference frame of xy . The relative penetration \u03b4 is evaluated as \u03b4 = {| e | \u2212 c, | e | > c 0 , | e | \u2264 c (12) where c is the clearance" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000016_icuas.2016.7502576-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000016_icuas.2016.7502576-Figure2-1.png", "caption": "Fig. 2. Graphical representation of rotor frames FRi. The red dots denote the rotor CoMs. Modified image, original taken from [5].", "texts": [ " The body-fixed frame is defined as FB = {M,XB , YB , ZB}, with origin M coinciding with the vehicles CoM, XB pointing forward, ZB pointing down and YB pointing right, see Fig. 1. To investigate the effect of propeller tilt on maneuverability, a right-handed orthogonal rotor frame of reference, FRi = {Oi, XRi, YRi, ZRi}, is introduced for i = 1, 2, .., 6. Origin Oi is at the CoM of the ith rotor, where it is assumed that this coincides with the center of spinning. ZRi coincides with the rotors spinning axis and points downward, YRi points inward and XRi points left, perpendicular to both the other axis. An illustration of FRi is given in Fig 2. To initiate the analysis that follows, the geometrical parameters of the considered hexarotor model are specified. For this, a conventional hexarotor configuration was kept in mind, see Fig. 1. Here, all six rotors are coplanar and vehicle leg ri corresponds to the ith rotor, with i = 1, 2, .., 6. Moreover, the legs are lifted upward under a fixed dihedral angle \u03c8dih. In addition, |r1| = |r2| = .. = |r6| = lt. If these legs are projected onto the XBYB plane, three additional design parameters are revealed: the angle between the projections of r1 and r2, denoted by \u03b1, and the angle between the projections of r2 and r3, denoted by \u03b2", " FTi , is directed along the negative ZRi -axis. A common way, see e.g. [4], [8], [9], to model FTi is by assuming a quadratic relationship between generated thrust FTi and rotor speed, in the following way: FTi = cF\u03a9 2 i , with cF > 0 [Ns2] a thrust constant, specific to the rotor and \u03a9i [rad/s] the spinning velocity of the ith rotor. Correspondingly, the resulting thrust force vector in the body-fixed frame is: FTi B = TBRi FTi Ri \u2208 R 3\u00d71 = TBRi [ 0 0 \u2212cF\u03a9 2 i ]T , for i = 1, 2, .., 6 (4) Referring to Fig. 2, it is assumed that the point of application of FTi is Oi. Hence, the six thrust forces cause a resultant moment MT around the body-fixed axes, equal to: MT = 6\u2211 i=1 ( rBi \u00d7 FTi B ) \u2208 R 3\u00d71 (5) , where MT is in [Nm] and rBi [m] is the moment arm and is found from the hexarotor geometry, see Sec. II. Furthermore, a so-called reaction torque, which is equal in magnitude and opposite in direction to the motor torque, is exerted on the motor as a result of Newton\u2019s third law. Since the rotors are mounted firmly on the hexacopter frame, the reaction torque is imparted on this frame" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000030_rcs.1786-Figure16-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000030_rcs.1786-Figure16-1.png", "caption": "FIGURE 16 Limb 3D modeling", "texts": [ " To reduce the fracture and block the limb at forearm, \u2018Blocker 2\u2019 is used according to coordinates received from the reduction module. Blocker 1 and Blocker 2 have the same 3D modeling illustrated in Figure 15. \u2018Pinning\u2019, as its name suggests, is the tool used to perform pinning at the patient\u2019s elbow according coordinates computed by the pinning module. Its 3D modeling is also shown in Figure 15. To simulate the progress of the surgery on the patient\u2019s limb, we model the latter as illustrated in Figure 16. It is modelled by a mechanism that rotates about the X axis (in red). B\u2010BROS1 module describes the behavior of the robotic arm B\u2010BROS1 and how it blocks the patient\u2019s limb at the humerus and unblocks it once the surgery is completed. Thus, this module features two procedures: (i) B_BROS1_humerusBlock (): it blocks the arm at a distance of y + 100 mm where y is the coordinate on Y axis of the intersection point of the humeral palette and its median. Figure 17 illustrates how the blocking is performed, (ii) B_BROS1_humerusUnblock (): it releases the patient\u2019s limb once the fracture treatment is completed" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001293_tie.2020.2984460-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001293_tie.2020.2984460-Figure3-1.png", "caption": "Fig. 3: Voltage vector representation in the uvw- and dq-frame.", "texts": [ " 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. the electrical angular velocity, \u03c9m is the mechanical angular velocity and np is the pole pair number of the machine. The angles \u03b8U and \u03b8 := \u03b8r + \u03b8U are the phase angles of the fundamental voltage vector uks,1(\u03b1) in the dq- and uvwframe, respectively, as depicted in Fig. 3. Based on Fig. 3, the fundamental voltage vector is given by uks,1(\u03b1):= ( uds,1(\u03b1) uqs,1(\u03b1) ) = ( a1(\u03b1) cos \u03b3(\u03b1)+b1(\u03b1) sin \u03b3(\u03b1) a1(\u03b1) sin \u03b3(\u03b1)\u2212b1(\u03b1) cos \u03b3(\u03b1) ) . (6) The angle \u03b3(\u03b1) represents the phase angle of the vectors a1(\u03b1) := (a1(\u03b1) cos \u03b3(\u03b1), a1(\u03b1) sin \u03b3(\u03b1))> and b1(\u03b1) := (b1(\u03b1) sin \u03b3(\u03b1),\u2212b1(\u03b1) cos \u03b3(\u03b1))> (with amplitudes a1(\u03b1) and b1(\u03b1), respectively) in the dq-frame and is given by tan \u03b8U = uqs,1(\u03b1) uds,1(\u03b1) (6) = a1(\u03b1) sin \u03b3(\u03b1)\u2212 b1(\u03b1) cos \u03b3(\u03b1) a1(\u03b1) cos \u03b3(\u03b1) + b1(\u03b1) sin \u03b3(\u03b1) \u21d2 \u03b3(\u03b1) = arctan ( a1(\u03b1) sin \u03b8U + b1(\u03b1) cos \u03b8U a1(\u03b1) cos \u03b8U \u2212 b1(\u03b1) sin \u03b8U ) , (7) where arctan(y/x) returns the four-quadrant inverse tangent tan\u22121 of y and x (see Matlab function atan2(y, x) [18])" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000746_jsen.2019.2960926-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000746_jsen.2019.2960926-Figure7-1.png", "caption": "Fig. 7. Structure of the developed slave robot (a) Overall structure (b) Detailed structure of the slave manipulator.", "texts": [ " 6, the angels of the handle and the MEMS gyroscope at time T are respectively defined as \u03b2 and \u03b1. The angels of the handle and the MEMS gyroscope at time T\u2019 are respectively defined as \u03b2\u2019 and \u03b1\u2019. The relationships between \u03b1, \u03b1\u2019, \u03b2 and \u03b2\u2019 can be obtained according to geometric principle: + 90 (5) '+ ' 90 (6) Subtracting the above two formulas: ' ' (7) So the rotational angle displacement of the handle is ' , which is equal to the rotational angle displacement of the MEMS gyroscope ' . The structure of the slave robot is shown in Fig.7. The slave manipulator is designed to mainly realize axial and rotational movements of the catheter. The whole slave manipulator is assembled onto a pair of supporting arms. The supporting arms are linked with a T-style guider. The T-style guider is a standard connector of clinical operating table. A liner actuator is assembled between the supporting arm and the slave manipulator. The supporting arm and the linear actuator have the ability to adjust the slave manipulator position and posture with 3 DOF (degree of freedom). The detailed structure of the slave manipulator is shown in Fig. 7(b). The motor (SGMJV-01ADE6S with controller SGDV-R90A01B) and a ball screw fixed with the baseplate are used to generate linear motion of the components assembled on its sliding block. It consists mainly of the servo motor (EC-max16 with manipulator Maxon 1558-1748 (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. > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 6 epos2 50/2, reduction ratio 84:1), a pair of herringbone gears, and a designed catheter rear-end clamping device" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003989_0278364906065826-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003989_0278364906065826-Figure1-1.png", "caption": "Fig. 1. Conceptual image of stiffness imagers.", "texts": [ " These studies, however, focus on the stiffness or impedance at a local point. As far as we know, there is no work discussing the methodology for obtaining global information for stiffness distribution. Several studies discuss robotic endoscopes (Ikuta, Tsukamoto, and Hirose 1998; Takemura, Harada, and Maeno 2002; Simaan, Taylor, and Flint 2004; Cepolina, Challacombe, and Michelini 2005). While most studies try to increase the degrees of freedom to improve dexterity, there is no work combining endoscopes with a non-contact stiffness imager. Figure 1 shows a conceptual diagram of stiffness imagers where (a) and (b) are contact type and non-contact type, respectively. Suppose that various ring patterns are projected onto an environment as shown in Figure 1(a) where a piece of stiff material is included within the object. When we push the object with our finger tip, each circle will be deformed to a non circular shape depending upon the size and the stiffness of the piece as shown in Figure 1(a), while a uniform material results in a circular shape. Through observation of the ring patterns, we can visually recognize whether a stiff part exists or not, and if this is the case where it is and how large it is. As shown from this example, this type of sensing can be conveniently utilized for an object where the surface deforms not only at the force application point but also in the surrounding area due to the surface tension, e.g. human skin. This is the basic concept of the Stiffness Imager. The sensing system as shown in Figure 1(a), however, includes a blind spot where a part of the view is blocked by the finger. Such an occlusion can be completely avoided by utilizing a flow based force impartment, such as either an air jet or a water jet, as shown in Figure 1(b) where a flow is given to the environment through the small hole at the center of the lens. This method avoids at James Cook University on March 16, 2015ijr.sagepub.comDownloaded from direct contact and is especially useful in medical applications. We would like to note that using ring patterns is just an example and there are many variations for showing the stiffness distribution. We would also like to note that a precise stiffness distribution is not always necessary in medical applications, instead, a displacement distribution during a force impartment is often sufficient" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003122_s0094-114x(96)00033-x-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003122_s0094-114x(96)00033-x-Figure1-1.png", "caption": "Fig. 1. The RSSR mechanism. Xl, X2", "texts": [ " The number of actuated joints is equal to f and is smaller than the total number of joints j in the mechanism. In order to obtain the values of the ( j - f ) passive joints, one has to use the loop-closure constraint equations. To arrive at the 'simplest' form of the loop-closure equation one has to use the geometry of the mechanism and the nature of the joint. We illustrate the method of obtaining the 'simplest' form of the loop-closure equation with the help of a familiar RSSR mechanism. In an RSSR mechanism, as in Fig. 1, f is 2. If we neglect the rotational degree of freedom of the S - - S link about itself, then the mechanism has one degree of freedom. We assign coordinate systems {Ol}, {02} as shown in Fig. 1 and denote the coordinates of the centres of the two spherical joints by tSl and 2S2, respectivelyi'. The position vectors tSt and 2S2 can be written by inspection as tSl=[l lcos01 llsin01 0 1] T 2S2 = [/2 cos 02 /2 sin 02 0 l] r. (2) The position vector of the centre of the spherical joint, S~, can be written in the coordinate system {05} as ~s, = [RI'S, (3) where JR] is a known 4 x 4 transformation matrix relating coordinate systems {Or} and {02}. i'Tbe leading superscript denotes the coordinate system in which the position vector is described and the following subscript denotes the number of the spherical joint" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001344_s12555-019-0482-x-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001344_s12555-019-0482-x-Figure1-1.png", "caption": "Fig. 1. The structure of the manipulator.", "texts": [ " In Section 3, the design process of the RBFNN-GIC is described in detail and the traditional method of LMS is also briefly introduced. This section also contains a comparison of simulated gravity-fitting surfaces. In Section 4, the design of a PD controller with the proposed compensation scheme is presented. Section 5 provides a discussion to show the superiority of the proposed RBFNN-GIC against the conventional LMS-GIC. Finally, a conclusion is given in Section 6. 2. PROBLEM STATEMENTS The structure of the manipulator used in this research is shown in Fig. 1. To improve the tracking accuracy and stability of the manipulator, this study designed a PD controller with GIC. The rotation axis of joint 1 is perpendicular to the ground. The rotation axis of joints 2 and 3 are parallel to the ground. Therefore, the influence of gravity occurs only on joints 2 and 3, which should be compensated for by maintaining a stable posture. For the precise motion of the manipulator, not only gravity but also inertia terms must be compensated. To obtain the inertia, the COM should be known", " To avoid this troublesome in the COM measurement process, some measured gravity data are used in this research to identify COM positions and to construct a dynamic model for the manipulator. In Fig. 2, li = [ px py pz 1 ]T represents the COM position w.r.t. (i\u2212 1)th coordinates, wi and vi are rotational and linear velocities of COM for the ith link, respectively. pCi = [ pCxi pCyi pCzi 1 ] is the ith COM position w.r.t. the base frame. pi\u22121 = [ pi\u22121x pi\u22121y pi\u22121z 1 ] is the origin position of (i\u22121)th coordinates. Table 1 shows the Denavit-Hartenberg (DH) parameters of the manipulator shown in Fig. 1. According to DH parameters, the homogeneous transformation matrix of the 1st coordinate is defined as follows: T 1 0 = c\u03b81 0 s\u03b81 0 s\u03b81 0 \u2212c\u03b81 0 0 1 0 0.1 0 0 0 1 , (1) where c\u03b8i and s\u03b8i represent cos\u03b8i and sin\u03b8i, respectively. The homogeneous transformation matrix of the 2nd coordinate is defined as follows: T 2 0 = c\u03b81c\u03b82 \u2212c\u03b81s\u03b82 s\u03b81 0.2c\u03b81c\u03b82 c\u03b82s\u03b81 \u2212s\u03b81s\u03b82 \u2212c\u03b81 0.2c\u03b82s\u03b81 s\u03b82 c\u03b82 0 0.1+0.2s\u03b82 0 0 0 1 . (2) The homogeneous transformation matrix of the 3rd co- ordinate is defined as follows: T 3 0 = c\u03b81c\u03b823 \u2212c\u03b81s\u03b823 s\u03b81 p3x c\u03b823s\u03b81 \u2212s\u03b81s\u03b823 \u2212c\u03b81 p3y s\u03b823 c\u03b823 0 p3z 0 0 0 1 , (3) where \u03b823 = \u03b82 + \u03b83, p3x = 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003296_robot.2000.845354-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003296_robot.2000.845354-Figure3-1.png", "caption": "Figure 3: Structure of the Knee Transmitter", "texts": [ " The pelvis tilt will prove also very useful in walking down and up stairs, by reducing the load of support ankle and knee while allowing the swing leg to recover the contact faster. A frontal view of the pelvis is given in figure 2. 3.2 Transmitters Five joints are equipped with classical HarmonicDrive Gears: the 3 rotations of vertical axes Z6, Z9 and 215 and the 2 hip adduction/abduction rotations, 27 and 28 (see figure 1). The 10 other joints use as transmitters screw-nuts with satellite rollers combined with rod-crank systems (figure 3). The nut with satellite rollers is inserted in a slider which is guided by four rollers that can move along a straight beam. The rotation of the screw produces the translation of the slider, which itself pushes or pulls on two rods acting on an arm of the adjacent limb. These nuts with satellite rollers allow a high accuracy with low friction, and give a good reversibility to the system: for example the torque due to the weight of the leg when it is horizontal is enough to make it moving. The obtained reduction ratio is variable, while high torque and high velocities can be transmitted (see next section)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000328_j.msea.2017.05.052-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000328_j.msea.2017.05.052-Figure1-1.png", "caption": "Fig. 1. \u201cComb-like\u201d structure in as-produced state (a) and samples for FCG testing after EDM cutting (b).", "texts": [ " \u2022 Layer thickness: 50 \u00b5m. \u2022 Distance between lines: 160 \u00b5m To qualitatively determine Re solubility ratio and select optimal SLM parameters, the analysis of binarized SEM/BSE sample crosssection images registered with three magnification levels has been used. Additionally, X-ray fluorescence (XRF) analyzes were made with the Bruker S4 Explorer device usage for determining Re content in finally produced samples. Final samples for mechanical testing were cut out from the produced \u201ccomb-like\u201d structures (see Fig. 1) by means of Electro Discharge Machining (EDM). Two geometries of mini-samples for tensile tests (with 5 and 10 mm gauge section length) and one type of samples with notches for Fatigue Crack Growth (FCG) rate tests (see Fig. 2b) with 4\u00d74 mm gauge section have been prepared. Each type of samples was produced in 0\u00b0, 45\u00b0 and 90\u00b0 orientation to the basal X-Z plane, according to a scheme presented in Fig. 2a. The laser beam was oriented parallel to Y axis during the manufacturing process. Half of the total number of produced samples underwent heat treatment (HT) designed for Inconel 718 alloy (1 h solutioning in 1100 \u00b0C, 8 h ageing in 720 \u00b0C, cooling to 620 \u00b0C (100 \u00b0C/h) for 10 h ageing and finally cooling in water) while the other half remained in the initial state (no heat treatment \u2013 NHT)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000620_s11071-018-4338-3-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000620_s11071-018-4338-3-Figure6-1.png", "caption": "Fig. 6 Quasi-static simulation of the leaf spring assembly process. a Stress-free configuration. b Initial configuration e0 before inner loop of static analysis. c Final equilibrium configuration ei after inner loop of static analysis", "texts": [ " These gaps lead to the problems of inaccurate point cloud meshes as previously mentioned. Instead of scanning the assembled leaf spring using the existing scanning technology, two alternate approaches can be used. The first ismanual measurements of points on the assembled leaf spring, and the second is an iterative numerical procedure. Both methods have shown to produce similar results in this investigation. The iterative numerical procedure can be used to obtain the pre-stressed reference configuration (assem- bled spring) shown in Fig. 6c from the stress-free configuration of the leaves before assembly, shown in Fig. 6a, by simulating the quasi-static process of assembly numerically. As shown in Fig. 6b, the initial leaf spring assembly configuration is acquired by clamping the two leaves together at the center clamped segment. The initial penalty \u03b40 at the two end contact elements can be obtained to start the iteration to determine the final equilibrium leaf spring assembly configuration as shown in Fig. 6c. The normal contact force Fn j,i at contact point i of element j can be expressed in terms of the penetration \u03b4 j,i between the contact surfaces as Fn j,i = K0\u03b4 j,in j,i , where K0 is the current penalty contact stiffness coefficient and n j,i is the corresponding normal vector. As shown in the flowchart of Fig. 7, the iterative algorithm consists of two loops: the outer and inner loops. The purpose of the outer loop is to adjust the current contact stiffness coefficient K0 according to the obtained equilibrium configuration ei to ensure convergence to the desired value of the penetration \u03b4tol" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003876_978-1-4612-4990-0-Figure11-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003876_978-1-4612-4990-0-Figure11-1.png", "caption": "Figure 11. Illustration of the advantage of a rear-to-front strategy over a front-to-rear strategy.: Each pie wedge represents the drive phase of one leg. The foot travels down the curved arc from top to bottom, with the hip joint at the point of the wedge. Each labeled region within the wedges, two per wedge, is named with the initial letter of the name of the leg that is recovering while that leg is moving over that portion of its drive stroke. For example, the middle and rear legs are much farther apart during the recovery of the front leg and thus provide much more stable support with the rear-to-front strategy than with the front-to-rear strategy. The left group of pie wedges illustrates the rear-to-front strategy and the right group shows the front-to-rear strategy. This illustration is drawn for the gait of Figure 7.", "texts": [ " With a rear-to-front strategy the base of support for the animal is larger than with a front to-rear, thus increasing its margin of stability, because when a rear leg is recovered the front leg on the same side is still in the early part of its drive. By contrast, in a front-to-rear strategy the recovery of the rear leg comes during a later part of drive of the front leg so that the support is closer to the center of gravity and hence the stability is less. The contrast between the two strategies is illustrated in Figure 11. Section 2.2 Rear-to-front waves 13 Rear-to-front waves can also describe the walking of quadrupeds. In fact many quadrupeds exhlbit the follow-the-Ieader strategy fairly clearly. Cats, when walking slowly, place their rear feet as closely as possible to the positions of the front feet. Casual observations by the author show that even when an animal is galloping the successive pairs of footprints are remarkably close together, indicating that this strategy is never completely abandoned. 2.3 Why insect gaits are not discrete Early work on quadruped walking [43] identified a small number of discrete gaits" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000391_s00170-018-1895-z-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000391_s00170-018-1895-z-Figure7-1.png", "caption": "Fig. 7 Layering of the thin-walled part with unequal thickness Fig. 8 Segmentation of the unequal width and equal height track", "texts": [ " The integral term of the controller in Eq. (5) feeds back the total height error E, as shown in Fig. 6c. The total height error E increased fast after each step of excitation, and this can be compensated after several layers. Both the actual deposition height and total deposition height were controlled to be stable and convergent in several layers. The overshoots and rates of convergence in Fig. 6a, c can be adjusted by changing the control parameters. A basic variable width structure is shown in Fig. 7: a thinwalled part with unequal thickness accumulated by several variable width tracks. For the deposition of this kind of structure, only when the deposition heights in different width positions are controlled to be equal, the deposition process can continue with good accuracy. Therefore, deposition height control is essential in variable width deposition. The laser spot diameter in Fig. 2 is the major influence factor of the cladding track width. With matched laser powers in different widths, the cladding track width was controlled using the open-loop method", " (17) contains both the difference in total actual deposition heights and the difference defocus distances between adjacent segments. The scanning speed vtrans_i is calculated as the resultant motion of the X and Z directions: vtrans i k \u00fe 1\u00f0 \u00de \u00bc vi k \u00fe 1\u00f0 \u00de ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u0394x2trans i k \u00fe 1\u00f0 \u00de \u00fe\u0394z2trans i k \u00fe 1\u00f0 \u00de p \u0394xtrans i k \u00fe 1\u00f0 \u00de \u00f018\u00de A thin-walled unequal width part was designed (Fig. 7). The designed total length was 86 mm, and the designed (desired) total height was 18.26 mm. The part was divided into seven segments with a length of 11.7 mm for each segment. Each transition segment was 0.3 mm long. The defocus distance varied from \u2212 8 to \u2212 2 mm, with laser spot sizes varied from 4.9 to 1.6 mm and \u0394d = 1 mm. Both sides of the part have a 1 mm length slowdown of scanning speed to avoid collapse at the ends. Table 3 shows the parameters and measured data of these segments. Seven PI controllers were designed for these seven segments, and scanning speed v was the single control input" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003449_87.556029-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003449_87.556029-Figure1-1.png", "caption": "Fig. 1. Inverted pendulum apparatus.", "texts": [ " To provide a performance benchmark with respect to robustness, a direct comparison was made against linear quadratic (LQ) control. In this section, the inverted pendulum apparatus will be briefly described and the models for the system will also be given. Finally, the nature of the robustness tests will be outlined. A. Inverted Pendulum Application The inverted pendulum is a challenging control problem. The pendulum is hinged to the top of the wheeled cart, or the gantry crane, that travels along a track as shown in Fig. 1. The cart and the pendulum are constrained to move in the vertical plane. There are four measured states: the horizontal position, the velocity of the cart, the angle between the pendulum and the vertical, and the angular velocity. A microcomputer with an 80 386 microprocessor was used for control and data acquisition purposes. An eight-input/two-output LABMASTER AD/DA board was used with 12-bit resolution and 0.025% accuracy on the input channels. The sampling time was 0.01 s as dictated by the speed limitations of the data acquisition board" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003224_0921-8890(95)00019-c-Figure10-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003224_0921-8890(95)00019-c-Figure10-1.png", "caption": "Fig. 10. MAP vectors for some common \"Life\" forms.", "texts": [ " The metric below this defines negative survival aspects and defines devices that must be moved, fed, and protected from outside sources. A good biological example of a uniform MAP- (MAP-negative) metric would be a bird's egg, and a good technical example of would be a personal computer. As suspected, the MAP represents a survival space upon which can be measured not just biomorphs but most simple biological organisms, machines, and even children's toys. As such the MAP is useful to see how biomorphic mechanisms rate against these other biomimetic devices. A MAP diagram showing some common survival vectors is detailed in Fig. 10. The vertex of each triangle converges at the point where a particular creature's survival scale is measured. As the three main MAP vectors abound in fuzzy logic connections, for many creatures there are half and quarter way points along each. For example, most plants are harder than the immediate objects in their vicinity, but do not use flight-or-hide behavior against aggression. This would give them a P0 rating if it were not for the chemical a n d / o r thorn defenses most plants employ, which raises them to a P1" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003566_0094-114x(94)90031-0-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003566_0094-114x(94)90031-0-Figure3-1.png", "caption": "Fig. 3. Screw triangle associated with the displacement of a line.", "texts": [ " Substituting equations (7) and (8) into the above equation gives / c, c2 '~_ ( c , x , qx2'~_ = + 0' Let $3 also be written in the form of equations (6), I x s So2, where x3 ffi tan(~b\u00a2~/2), and ~0~ is the value for the free parameter for obtaining ~3. Setting the above two equations equal, we have 1 cl c2 f(x3) \u2022 f (x , ) 4 f (x2) ' (9) x3 c,x, c2x2 (10) f(x~) \u2022f(x,) 4 f(x2)\" Dividing equation (I0) by equation (9) yields a unique x3: cj xl f (x2) + c2x2f(xt ) x3 = c , f (x z) + ezf(x,) Therefore, for any given cj and c2, we obtain a unique unit screw belonging to the screw system (a 2-system) for displacing the two specified points from their initial to their final positions. 3.2. A line As shown in Fig. 3, let Li be the line of interest. We are interested in finding all the possible screws that will displace the line to a second position, L s. We specify the direction-cosine vector of L . n. the direction-cosine vector of L s, n s, the position vector of a point on L . e~ and the position vector of a point on L s, e s. The free parameters are chosen to be qk 0 and ,t0, which are, respectively, the rotation and translation parameters of the incompletely determined screw, N 0. According to Tsai and Roth [3], the analytic expressions for the resultant screw are le = k~n0tan-~ + l0 tan ~-~ + " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000971_1077546319896124-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000971_1077546319896124-Figure7-1.png", "caption": "Figure 7. Dynamic model of a helical gear pair considering tooth surface friction.", "texts": [ " The mathematical description is as follows 8>>>>< >>>>: min X2n\u00fe1 j\u00bc1 Xj \u00bdF \u00bdp \u00fe \u00bdZ \u00fe \u00bdd \u00fe \u00bdX \u00bc \u00bdw \u00bde T \u00bdp \u00fe X2n\u00fe1 \u00bc P s:t; pj; dj; Z; Xj \u2265 0 pj \u00bc 0; or dj \u00bc 0 (4) Detailed solution of LTCA of a helical gear pair can be found in Fang (1997a, 1997b). In addition, about the introduction of LTCA can also be found in Li (2002) and Wang et al. (2012). By solving equation (4), the normal displacements [Z] of contact position in one mesh period are obtained. The time-varying meshing stiffness is calculated by normal force divided by normal displacement. An 8-degree bending-torsion-shaft coupled vibrating system is considered in Figure 7, which is represented as f\u03b4g \u00bc f x1 y1 z1 \u03b81 x2 y2 z2 \u03b82 gT (5) 4.1.1. Calculation of the sliding friction coefficient. In this article, the formula of sliding friction coefficient comes from Xu et al. (2007). It is represented as \u03bc \u00bc ef \u00f0SR;Ph;v0;S\u00dePb2 h jSRjb3vb6e vb70 Rb8 (6) f \u00f0SR;Ph; v0; S\u00de \u00bc b1 \u00fe b4jSRjPh log10\u00f0v0\u00de \u00fe b5e jSRjPh log10\u00f0v0\u00de \u00fe b9e S (7) The precise determination of parameters in formulas (6) and (7) is the key for accurate calculation of the sliding friction coefficient. In the article, partial parameters are calculated according to the results of TCA, LTCA, and dynamic analysis", " According to Figure 8, the calculation of arm of friction force are represented as 8>< >>: s1 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0r01 \u00fe r02\u00de2 \u00f0r1b \u00fe r2b\u00de2 q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r22a r22b q \u00fe r1bw1t \u03bb s2 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0r01 \u00fe r02\u00de2 \u00f0r1b \u00fe r2b\u00de2 q s1 \u03bb\u00bc y1 \u00fe \u03b81r1 y2 \u03b82r2 ey (12) The clearance function f can be expressed as fij\u00f0y\u00de \u00bc 8< : y b\u03be y > b\u03be 0 y \u2264 jb\u03be j y\u00fe b\u03be y< b\u03be (13) The backlash fhy also satisfies the aforementioned formula. In the direction of radius and axis, the dynamic meshing forces are respectively represented as F1v \u00bc cos \u03b2 kfhv\u00f0y1 \u00fe \u03b81r1 y2 \u03b82r2 e\u00de \u00fe c _y1 \u00fe _\u03b81r1 _y2 _\u03b82r2 _e (14) Fz \u00bc sin \u03b2 k\u00bdz1 z2 \u00f0y1 \u00fe \u03b81r1 y2 \u03b82r2\u00detan \u03b2 e \u00fe c _z1 _z2 _y1 \u00fe _\u03b81r1 _y2 _\u03b82r2 tan \u03b2 _e (15) According to Figure 7, the dynamic formulas are represented as m1\u20acx1 \u00fe c1x _x1 \u00fe k1xf1x\u00f0x1\u00de \u00bc \u03c7\u03bcF1y (16) m1\u20acy1 \u00fe c1y _y1 \u00fe k1yf1y\u00f0y1\u00de \u00bc F1y (17) m1\u20acz1 \u00fe c1z _z1 \u00fe k1zf1z\u00f0z1\u00de \u00bc Fz (18) I1\u20ac\u03b81 \u00fe F1yr1\u03b4 s1\u03c7\u03bcF1y \u00bc T1 (19) m2\u20acx2 \u00fe c2x _x2 \u00fe k2xf2x\u00f0x2\u00de \u00bc \u03c7\u03bcF1y (20) m2\u20acy2 \u00fe c2x _y2 \u00fe k2yf2x\u00f0y2\u00de \u00bc F1y (21) m2\u20acz2 \u00fe c2z _z2 \u00fe k2zf2z\u00f0z2\u00de \u00bc Fz (22) I2\u20ac\u03b82 F1yr2b \u00fe s2\u03c7\u03bcF1y \u00bc T2 (23) A helical gear pair is taken as an example to verify the proposed dynamic model. Relative parameters of the helical gear pair are shown in Table 1. Through the calculation of TCA of a helical gear pair, the contact path on the tooth surface can be determined" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003827_tmag.2006.879068-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003827_tmag.2006.879068-Figure3-1.png", "caption": "Fig. 3. Axially-laminated rotor.", "texts": [ " The brass interpole lamination-retaining pieces, as conductors, were also treated in the same manner. III. EXPERIMENTAL SETUP The 2/6 pole test machine was set up; it was rewound from a four-pole axially-laminated synchronous reluctance motor. This was fabricated from the stator of a 7.5-KW induction machine. It was connected to a load machine via a torque transducer. Four-quadrant operation was possible with the load machine. The test machine specification is given in Table I and a picture of the rotor is shown in Fig. 3. It was found that the slots in the stator were small because two single-layer windings had to be inserted, so that the electric loading was limited. However, this study was to assess the rotor losses, which are a function of flux (and hence voltage) so the test machine served its purpose. The machine was supplied from a 50-Hz three-phase autotransformer to the two-pole winding. While no feedback control system was set up, the machine could be run with a resistive load on the six-pole winding. The machine could also be run from two three-phase autotransformers at 1500 r/min [which corresponds to 50 Hz on each supply according to (1)]; the speed control of the load machine did tend to drift terms of rotor angle leading to the system oscillating between generating and motoring, but with care, the system could be stabilized for a few seconds and the relevant parameters logged via a power analyzer and oscilloscope" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003652_027836499101000502-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003652_027836499101000502-Figure2-1.png", "caption": "Fig. 2. Displacement offraine 19 to frame ~\u2019.", "texts": [ " Clearly there is no limit to the number of different paths that the body could sweep out, and each of these paths corresponds to the same rigid body displacement but a different rigid body motion. If we inscribe a Cartesian coordinate frame in the body, then the set of all possible displacements of the body is the set of all locations of this frame. Figure 1 shows a Cartesian frame n (normal), o (orientation), and a (approach) inscribed in the center of a (rigid) robot gripper. We denote the frame by the symbol C{3, allowing the gripper to undertake an arbitrary displacement, D, from its initial position at 19 to a final position at C{3\u2019 (Fig. 2). For the purposes of describing the displacement, we call 19 the fixed frame and C{3\u2019 the moving frame. Remark 1. The set of all isometries of [R3 forms a group. This is the so-called euclidean group, denoted by E(3). By &dquo;group&dquo; we mean a group in the mathematic sense (see appendix C), so for Remark 1 to hold, the four group properties must hold. These are (1) closure under composition, (2) association, (3) the existence of an inverse, and (4) the existence of an identity. The composition of two displacements, Da and Db, is itself clearly a displacement; hence the set of rigid body displacements is closed under composition", " The importance of the finite screw in the context of the euclidean group is discussed in sections 3 and 4. 2.1. Two Matrix Representations of the Euclidean Group Here we briefly review two matrix representations of E(3) that have found application in robot kinematics. They are (1) the group of 4 x 4 homogeneous coordinate transformation matrices and (2) the group of 3 x 3 dual-number orthogonal matrices. The 4 x 4 matrix representation of E(3) describes how points transform under a rigid displacement. Under the rigid body displacement D, depicted in Figure 2, the point P = (x, y, z) is transformed into the point P\u2019 = (x\u2019, y\u2019, z\u2019) where d = (dn dy, dz) gives the coordinates of the origin of frame ~\u2019 in frame ~, and the matrix R E SO(3) gives the orientation of 16\u2019 in ~. As is shown in Denavit and Hartenberg (1955) and Bottema and Roth (1979) (and indeed in many other places), equation (3) can be written as a 4 x 4 matrix The 4 x 4 matrix of equation (4) is the basis of the unified description of the lower kinematic pairs introduced in Denavit and Hartenberg (1955)", " The point S is a repeated eigenvector, so we have identified the four isotropic points of D. The displacement D leaves three lines in [R3 unaltered. These are the finite screw axis and the imaginary tangent lines T, and Tl. In the mechanical world the only isotropic line of significance is that of the finite screw axis. In general this is the only real isotropic line of the displacement D. Suppose that we wish to effect a displacement by a finite screw motion (for example, the displacement that takes frame 16 into ~\u2019, depicted in Figure 2); then it is necessary to specify (1) the axis of the screw, $~, ; (2) the angle rotated, 0; and (3) the distance translated, T. We shall now show that it is possible to express these three parameters in terms of the nine elements of the matrix A that describes the displacement. The reduction of an orthogonal matrix of general form to one of a special form can be effected by a similarity transformation (Ayres 1962). We can make use of the properties of similarity transformations to reduce any matrix A E SOD(3) to a matrix of the form where matrix B E OD(3), and the matrices A and BAB&dquo;\u2019 are said to be similar or equivalent", " This requires the specification of the A matrices for all points along the path of the finite screw motion. From equation (35), the infinitesimal screw that generates the motion is and by equation (26), the finite twist about the screw $ through an angle 4> (where 0 ~ ~ ~ 0) is where 0 = g + gT/0. Expanding the exponential and noting Z\u20192\u2019t -\u2019\u2019 - (- I)(\u2019- ~2 and i2n = I ~ , I I.- - 1........ð.&dquo;&dquo;II - . _ - - Equation (37) gives a concise formulation of the displacement matrix describing the location of the moving frame ~\u2019 in the fixed frame 19 (see Fig. 2), at each point of a finite screw motion. This parameterization is given directly in terms of the angle of rotation 4J. Note that for 4J = 0 the matrix N( 4J) = E, and for 0 = 0 the displacement matrix lV( 9) = A, as expected. In robotics it is usual to refer the location of the gripper frame to some fixed base frame 7A, usually located at the base of the manipulator. If the location of frame 19 in 26 is given by the matrix B, then by the group property of composition, the location of the moving ~6\u2019 in frame 91, is given by ~V(<~)F" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000334_icra.2017.7989292-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000334_icra.2017.7989292-Figure1-1.png", "caption": "Fig. 1. Elastic wire handling by a manipulator with a six-axis force/torque sensor at its wrist based on the proposed shape estimation method. Note that, in this case, the grasped end of an elastic rod is the base end.", "texts": [ " Moreover, the required calculations are very simple owing to deep understanding of robot manipulator kinematics, and thus we can compute the rod shape in real-time. We show experimental results in order to validate our proposed method. The contribution of this paper is considered to be as follows: \u2022 A real-time spatial shape estimation method of an elastic rod has been proposed. The method can be useful for a one-dimensional elastic rod handling by a robot manipulator equipped with a six-axis force/torque sensor at the wrist (as shown in Fig. 1). \u2022 Experimental data shown in this paper will be useful for future benchmarks of similar kinds of spatial shape estimation techniques without occlusions. \u2022 The proposed real-time spatial shape estimation method is an illustrative application example of the discretized Kirchhoff elastic rod model, which is valuable in continuum/soft robotics research. The major limitations of the proposed shape estimation method include 1) no unknown external contact or forces along the rod, 2) necessity of the accurate model for good estimation accuracy, and 3) necessity of an appropriate sixaxis force/torque sensor" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001560_s00170-021-07375-x-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001560_s00170-021-07375-x-Figure2-1.png", "caption": "Fig. 2 The schematic of the build direction, torch direction of the single strut", "texts": [ " Thus, strut-like substrates consisting of several layers need to be deposited before starting to fabricate wire structures. Due to unavoidable interferences in the physical welding process, layers with abnormal shapes may occasionally appear, as shown in Fig. 1. For the experiments conducted in this work, these samples (which lie significantly outside of the average data range) will be excluded to reduce errors and improve the model accuracy. A schematic diagram describing the build direction and torch direction of a wire structure is shown in Fig. 2. During the deposition, the torch direction always remains parallel with the build direction of the strut. During each welding period, the torch remains stationary at a certain distance from the deposition point, referred to as the contact tip to work distance (ctwd). A strut with an inclined build direction will feature a certain slope k between the two layers Lm and Ln. The torch direction will also have an inclined angle \u03b1m (relative to the ground), defined as: \u03b1m \u00bc tan\u22121 Lnz\u2212Lmz Lnx\u2212Lmx \u00bc tan\u22121km \u00f02\u00de It is worth noting that for these non-vertical struts, \u0394h is not measured vertically upward along the z-axis direction but follows the build direction of the strut with the slope km. The alteration point highlighted in Fig. 2 is used to distinguish when the build direction of the strut varied so that the torch can adjust its direction accordingly. In situations where the build direction changes smoothly with the Bezier curve, no alteration point is required. The geometric data required for these calculations can be readily obtained from CAD data. This point defined zones where an adaptive slicing process is required, which is detailed in the following sections. Experiments are carried out employing the robotic WAAM system, as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001311_j.mechmachtheory.2020.103978-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001311_j.mechmachtheory.2020.103978-Figure8-1.png", "caption": "Fig. 8. Anthropomorphic 9-DOF manipulator.", "texts": [ " A circle centred at [0 0 900] T mm and parallel to X \u2212 Y plane with a radius R = 450 mm is used as the desired path for the second scenario. Fig. 4 and Fig. 5 show a straight-line tracking where the spherical wrist is oriented down and up, respectively. Fig. 6 shows the tracking of a circular path with simple configuration vectors, while Fig. 7 shows the tracking with complex configuration vectors. We can also implement other scenarios such as obstacle avoidance and joint limit avoidance. An anthropomorphic 9-DOF manipulator is shown in Fig. 8 . The dimensions of the workspace and configuration space are R 6 and R 9 , respectively. Therefore, three elbow joints have to be fixed to reduce the 9-DOF redundant manipulator to 6-DOFs one. Here, besides the joint \u03b82 , the joints \u03b85 and \u03b86 are parameterized through clustering in workspace and configuration space. The remaining joints \u03b81 , \u03b83 , \u03b84 , \u03b87 , \u03b88 , and \u03b89 will be calculated by using Paul\u2019s method. Let U 0 be the matrix defining the position and orientation of the EE. Here, the center of the spherical wrist is 0 7 and its position is denoted by 0 P 7 " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000946_rpj-02-2019-0035-Figure14-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000946_rpj-02-2019-0035-Figure14-1.png", "caption": "Figure 14 Two deposition orders (a) sequentially, (b) symmetrically", "texts": [ " Rotate angle is positive when the cross-vector points to Y ! ; otherwise, it is negative (Figure 13). To decrease the deformation and thermal stress of part, a 3D transient thermal stress finite element (FE) analysis model was built to find an optimal deposition order for six blades. A Additive manufacturing Rui Wang, Haiou Zhang, Wang Gui-Lan and Xushan Zhao Rapid Prototyping Journal Volume 26 \u00b7 Number 1 \u00b7 2020 \u00b7 49\u201358 deposition layer varying from radius 60 to 63mm was analyzed after the centroid cylinder was already fabricated. Figure 14 shows the two deposition orders. Order 1 is sequential deposition (Figure 14(a)), and Order 2 is symmetrical deposition (Figure 14 (b)). The experiment material is stainless steel (316L), and the temperature-dependent material properties are given in Figure 15. The deposition parameters are shown inTable I. The hemispherical heat source model proposed by Goldak et al. (1984) is selected. The power density (W/m3) distribution about the welding time t (s) and position (x, y, z) is described as follow: q x; y; z; t\u00f0 \u00de \u00bc 6 ffiffiffi 3 p Q R3p ffiffiffiffi p p e 3x2=R2 e 3y2=R2 e 3j 2=R2 (4) where Q is the energy input rate (W ), R is the radius of the hemisphere (m), j = z \u2013 vt and v is the welding speed (m/s)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001427_j.mechmachtheory.2021.104300-Figure11-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001427_j.mechmachtheory.2021.104300-Figure11-1.png", "caption": "Fig. 11. Examples of singularities: a) B j coincides with C j \u2014 different configurations of the links are possible (two of the kinematic chains omitted and the rod shortened for clarity); b) S i A j is perpendicular to the linear guide \u2014 \u03c5Si has no projection on intermediate link S i A j and can be nonzero even for the motionless output link.", "texts": [ " (33) Opening the parentheses with the fact that P SAi z i = 1 L 2 ASi ( SA i \u00b7 z i ) SA i , P SAi \u03c5Aj = 1 L 2 ASi ( SA i \u00b7 \u03c5Aj ) SA i , (34) SA T i SA i = L 2 ASi = 0 , (33) will take the following form: ( SA i \u00b7 z i ) 2 \u02d9 q2 i = ( SA i \u00b7 \u03c5Aj )2 , (35) from which \u02d9 qi = SA i \u00b7 \u03c5Aj SA i \u00b7 z i = 1 SA i \u00b7 z i SA T i \u03c5Aj . (36) Combining Eqs. (26) , (30) , and (36) in a single one, we will get: \u02d9 qi = 1 L BCj ( SA i \u00b7 z i ) SA T i ( L ABj P BAj \u2212 L ACj I 3 \u00d73 )[ I 3 \u00d73 \u2212 ( OB j )][\u03c5O \u03c9 pl ] . (37) Analyzing the expression above, we can instantly identify two cases corresponding to mechanism singular positions. The first one becomes when the platform joint B j coincides with the base joint C j ( Fig. 11 , a). When this occurs, the value of L BCj equals zero, and the slider velocity \u02d9 qi is undetermined. The other case corresponds to the configuration when intermediate link S i A j is perpendicular to the linear guide ( Fig. 11 , b) \u2014 the dot product in (37) becomes equal to zero, and \u02d9 qi tends to infinity. Eq. (37) can also be written in the following well-known form: \u02d9 qi = J i ( X ) [ \u03c5O \u03c9 pl ] \u21d2 \u02d9 q = J ( X ) V , (38) where J ( X ) is a mechanism Jacobian matrix, each row J i ( X ) of which is calculated according to (37) ; V is a six-dimensional vector, combining the linear and the angular velocities of the platform. The Jacobian matrix depends on the manipulator configuration, that can be determined in advance using the inverse kinematics" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001338_icra40945.2020.9197094-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001338_icra40945.2020.9197094-Figure2-1.png", "caption": "Fig. 2. (a) Motion capture marker layout on the operator\u2019s upper body. (b) Commands used to control the robot based on direction of movement. (c) The original reference system is transformed to be aligned with the plane where the markers CH1, CH2, and ABD lie, with origin at CH1.", "texts": [ " We used the PhaseSpace Impulse X2E (phasespace.com) system to track the operator\u2019s movements. This accurate optical tracking mechanism was used in order to test the effectiveness of the interface while avoiding the performance limitations of other types of sensors. In practice, other tracking systems could be employed. Our motion capture setup includes six lightweight-lineardetector cameras monitoring seven active LED markers placed on the forearm and the chest of the operator. The gestures are tracked in real time at 270 Hz. As shown in Fig. 2(a), the Body Interface exploits four markers on the operator\u2019s forearm for gesture recognition (two on the elbow EL1 and EL2, two on the wrist WR1 and WR2), and three on the operator\u2019s chest to create a body centered reference system (CH1, CH2, and ABD). The operator\u2019s gestures are mapped to the kinematics of the robot through our custom Gesture Interpreter Tool (GIT). The GIT recognizes three types of commands: grow/retract, steer left/right/backwards/forwards, and rotate the end effector. One command of each type can be given simultaneously. The communication with the robot\u2019s microcontroller is realized via a serial port at 66 Hz. The specific mapping between the gestures and commands can be customized based on the application. Fig. 2(b) shows one proposed mapping, used to control a soft robot hanging from the ceiling and growing in the direction of gravity. Moving the forearm above and below the operator\u2019s transverse plane (forearm flexion/extension) will make the robot retract and grow, respectively; whereas all the movements parallel to the transverse plane are mapped as steering movements (forearm back and forth and medial/lateral rotation, respectively backwards/forwards and left/right); finally, pronosupination defines the end effector rotation", " During calibration, the offset between \u03b8P and the starting orientation of the end effector is stored to assure the operator\u2019s comfort during the teleoperation. 2) Reference System Alignment: In order to properly retrieve the data, the GIT needs to define a body centered reference system. The three chest markers allow the operator to be aligned to the motion capture reference system, resulting in an interface that is independent of the operator\u2019s 727 Authorized licensed use limited to: Carleton University. Downloaded on September 21,2020 at 01:36:48 UTC from IEEE Xplore. Restrictions apply. pose in space. As shown in Fig. 2(c), the frame defined by the calibration of the Motion Capture system \u3008xMC, yMC, zMC\u3009 is transformed into the reference system of the operator \u3008xOP, yOP, zOP\u3009, such that the coordinates of the markers are expressed with reference to the latter. In particular, CH1, CH2, and ABD define a plane, which the GIT transforms to be lying on the xOP-yOP plane, with CH1 placed at the origin of the new reference system. The operator can therefore control the robot in whatever body pose is most comfortable. We built a soft growing robot specifically for manipulation tasks" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001379_tec.2020.3030042-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001379_tec.2020.3030042-Figure8-1.png", "caption": "Fig. 8. Modal shapes of stator core under free vibration.", "texts": [ " In order to ensure that the mechanical performance parameters used in the analytical calculation are consistent with that of the laminated stator prototype, the density of the stator core is determined by measuring the mass and volume of the prototype, and the radial and tangential elastic modulus are obtained by changing it in the 3D finite element model until the simulation results converges to the measured value with the axial modal order m=0. The selection of the axial elastic modulus is referred to [26] and [28]. Based on the above methods, the mechanical performance parameters of the stator core are finally determined: density \u03c11=7600kg/m3, elastic modulus Er=E\u03b8=195GPa, Ez=49GPa, shear modulus Gr\u03b8=76.77GPa, Grz=G\u03b8z=28GPa, and Poisson\u2019s ratio \u03bcr\u03b8=\u03bcrz=\u03bc\u03b8z=0.27. The modal shapes of the stator core under free vibration obtained by the FEM are shown in Fig. 8, where s represents that the vibration amplitude changes uniformly along the axial direction, that is, the axial modal order m=0, and r represents the axial modal order m=1. The calculation results of the natural frequencies corresponding to the different modal shapes with different equivalent structures are shown in Tab. III and Tab. IV. The teeth are respectively equivalent to simple structure a, combined structure of a and b, combined structure of a and c and combined structure of a, b and c in method I to IV, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000020_s1052618816040026-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000020_s1052618816040026-Figure2-1.png", "caption": "Fig. 2.", "texts": [ " Considering possible movements that lead to neighboring singular positions, one can see that, having found only one degenerate configuration, one can determine five\u2014for a six-degree robot\u2014infinitely close similar configurations. Therefore, the singular zone or surface is five-dimensional. If the parallel-structure robot has W degrees of freedom, its singular surface is (W \u2013 1)-dimensional. Let us consider a numerical example. We have a robot in the singular position. The coordinates of mount points Ai and Bi are represented in fixed coordinates (Fig. 2) by vectors ri, \u03c1i (i = 1, \u2026, 6) and are written as follows: r1(0, 0, 0) = r2 = r3, r4(\u20131, 1, 0), r5(\u20131, \u20131, 0), r6(0, \u20131, 0); \u03c11(1, 0, 0), \u03c12(\u20131, 0, 0), \u03c13(0, 1, 0), \u03c14(\u20131, 1, \u20131), \u03c15(\u20131, \u20131, \u20131), and \u03c16(1, \u20131, \u20131). All distances between the corresponding points of the base and the output link equal . Determinant (U) composed of the Plucker coordinates of the forcing screw axes has the following value: According to Eqs. (3), the gradient screw was obtained as \u03a9*(0, 0, 0, 0, 0, 2828 \u00d7 10\u20133). Analysis of the gradient screw components shows that movement along the axis z equal to 2828 \u00d7 10\u20133 will result in the fastest withdrawal from the singularity position" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003737_cdc.2003.1272286-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003737_cdc.2003.1272286-Figure1-1.png", "caption": "Fig. 1 : Kinematic car model", "texts": [], "surrounding_texts": [ "Theorem 5. Let 7 > 0 be the constant input sampling interval and the noises be absent. Then the fallowing inequalities are established infinite time for some positive constants pi\n(0 r - i la 1 0 . Lemma 2. Let 1 5 i 5 r-2, then for any positive p i , yi with sufticiently large p,, > 0 and sufticiently small yeI> 0 the inequaliry\nprovides for the finite-lime establishment and keeping of the inequaliry\nla(O + pi N < r - i ) / ( r - i + ~ ) y, 1 ( r - i ) / ( r - i+ l )\nProof. Consider the point set a = {(a, a , ..., a )I jYI,rl 5 E,} for some fixed E, > 0. Simple calculations show that R c a, with small E, where R, is defined by the inequality\nla(!) + p i N(r-I) / (r- i+l) y, 1 4 ~ ~ ( r - ; ) / ( ~ - i + l )\nThat implies in its tum $. < a i $+ , where $., $+ are homogeneous fUnctions of a, 6, ..., a of the weight r - i. Restricting $. and $+ to the homogeneous sphere a'\" +\n= I , where p is the least multiple of 1, 2, ..., r - i, achieve some continuous on the sphere functions and 41,. Functions and can be approximated on the sphere by some smooth functions 4,. and $,+ from beneath and from above respectively. Functions and $I,+ are extended by homogeneity to the (0 smooth homogeneous functions @. and @+ of a,&, ..., a of the weight r - i, so that R c R, = {(a, 6 , ..., ai')) @. 5\na @+I.\n(0\n(0 .\n( i )\n(r-i-I)/(,-<) y, < ,-z-l)/(,-I) Id\"') + pel N;,, , A - Yi t i N:,\n,-I,, I-1.7 Yi N;-1,7 (0\n,-1.r ,.I? ,-I,, ( i )\n(0\na pilr-1) ( I ) P/(,.i) + ...+ (a )\n(9\nThe condition lYi,,l t E, is assured outside of Prove now that R, is invariant and attracts the trajectories with large p,I. The \"npper\" boundary of Cl, is given by the equation x+ = 0'' - O+ = 0. Suppose that at the initial moment x+ > 0 and, therefore, Yi,, 2 5. Takiig into account that b+ is homogeneous and, according to Lemma 1, b+5\n~ ; ; - i - l Y ( r - I ) and Irr+l< K, Nt, for some K, K~ > 0, achieve differentiating that\n(,- I- I) /( ,- i) '\n,-i-I)/(,-i)\ni+ < (-Pi+, E, + Y~+J Ni,, - Q +\n5 (+*I 5 + YHI + K) 4 Hence x+ vanishes in finite time. Thus, the trajectory inevitably enters the region R, in finite time. Similarly, the trajectory enters 0, if the initial value of rr, is negative and, therefore, 'PI,, < - E,. Obviously, C l 2 is invariant.\nChoosing @. and @+ sufficiently close to $. and $+ on the homogeneous sphere and p,I large enough, achieve due to Lemma 1 the statement of Lemma 2..\nSince No,, = lal, q0,, = a, Lemma 2 is replaced by the next simple Lemma with i = 0. Lemma 3. The inequality 16 + p,lal sign a1 < yll$l)\" provides with 0 5 yI< PI for the establishment injhtie time and keeping of the identity a = 0.\nThe proof of the Theorem is now finished by the similar proof that for any small y > 0 with sufficiently large a the inequality Id\"') + p,.] 'f,.2r I < y Nfi2,, is estahlished in finite time and kept afterwards. W\nOther proofs are standard, follow the proofs of the analogous theorems from [S, 9, IO]. and %e based on the homogeneity reasoning. Consider, for example, Theorem 4.\nDenote E,, = z, - a . Taking into account 7 E [-E, E] and form (7) of the differentiator achieve\nU = - a s i g n ( ~ ' , , , , ( ~ b , 6 + 5 , , ... P +5,.J),\n(,.I)/, .\n112\n(1)\n(11) (,-I)\neo E -&I &,+[-E, E] I(rly'sign(b+[-E, El) + Cl, SI E - & 1 b+ [-E, \u20ac11 ( r2) i r . Slgn(b+ [-E, El) + 52 , ... (12) L E -L I 50+ [-E, EI Ibsign(%+ [-E, ED+ 5,.,, E,,-l B -Ll sign&+ [-E, E]).\nDynamics (12) of the differentiator is independent of the system dynamics (lo), (11). Thus, with E = 0 derivative deviations Si vanish in finite time [lo]. Hence, trajectories of (10) - (12) converge to 0 in finite time with E = 0 (Theorem 1).\nIt is easy to see that with E > 0 the transformation 0) r i ( i )\n(t,a , C i ) H ( K f , ~ a ,K'%,~), i=O ,..., r-1 (13)\ntransfers trajectories of (10) - (12) into trajectories of (10) - (12) but with the changed noise magnitude K'E. This", "homogeneity implies the desired asymptotics of the residual attracting set [9, lo].\nI . Simulation example: car control\nConsider a simple kinematic model of car control x =ucoscp, y =vsinip, (p = viitan e, e=u ,\nwhere z and y are Cartesian coordinates of the rear-axle middle point, cp is the orientation angle, v is the longitudinal velocity, 1 is the length between the two axles and 0 is the steering angle (Fig. I). The task is to steer the car ftom a given initial position to the trajectory y = &), while Ax) and y are assumed to be measured in real time.\nDefme\nu = y - &).\nLet U = comt = 10 d s , I = 5 m, &) = 10 sin(O.05~) + 5, x = y = cp = 0 = 0 at f = 0. The relative degree of the system is 3 and 3-slidmg controller P 3 can he applied here. It was taken a = 0.5, L = 100. The resulting output-feedback controller (7), (8) is\n2i3 -1\u20187 2i3. U = - 0.5 [H+ 2 (H+ I ZOi\nio = Yo, vo = - 9 1 zo - Is Slgn(Z0 - 0) + ZI,\nI zI+ I z0i SWZ, I 1\u201d U3 -1R\n[z2+ 2 (M+ I z0l ) (zl+ I zolMsign zo 11. m . 112 , i, = uI, vI = - 15 I zI - uol\ni, = - 110 sign@, - vI).\nMark that the differentiator parameter L = 100 is deliberately enlarged in order to provide for faster convergence and higher robustness with respect to sharp commands caused by possible measurement errors (otherwise L = 22 would he sufficient in the absence of sampling noises). The control was applied only from f = 0.5 in order to provide some time for the differentiator convergence.\nThe integration was carried out according to the Euler method (the only reliable integration method with discontinuous dynamics), the sampling step being equal to the integration step t = 10 . In the absence of noises the tracking accuracies 101 5 3.12.10-\u2019, / U / 5 1.4.10 , 161 5 0.011 were attained. The car trajectory, 3-sliding tmcking\nsign(z, - vo) +z2,\n4\n4\ndeviations, steering angle and its derivative I are shown in Fig. 2a, h, c, d respectively. It is seen from Fig. 3c that the control U remains continuous until the entrance into the 3-sliding mode. The steering angle 0 remains rather smooth and is quite feasible.\nwith t = loJ the tracking accuracies 5 2.5.10-\u2019, / a I 5 2.4.10J, ] U / _< 0.11 were attained, which corresponds to the asymptotics stated in Theorem 5 . Convergence of the differentiator outputs to the directly calculated derivatives of u is demonstrated in Fig. 3.\nIn the presence of output noise with the magnitude 0.01m the tracking accuracies In1 5 0.04, I a I 5 0.2, I U I 5 1.8 were obtained. With the measurement noise of the magnitude 0.1 the accuracies changed to In1 5 0.4, 16 I 5 0.9, I Cr I 53.2 which corresponds to the asymptotics stated by Theorem 4. The performance of the controller with the measurement error magnitude O.1m is shown in Fig. 4. It is seen from Fig. 4c that the control U is continuous function off. The steering angle vibrations have magnitude of about 12 degrees and frequency 1 which is also quite feasible. The performance does not change when the frequency of the noise varies in the range 100 - 100000.\nThe performance of the standard 3-sliding controller [8- 101 in the absence of noises is demonstrated in Fig. 5 . The advantages of the new controller are obvious (compare Figs. 2d, 5h). Simulation shows that the standard controller is also much more sensitive to the parameter choice.", "A new arbitraq-order sliding mode controller is proposed. It is actually only the second know family of such controllers. It is also a sliding-mode controller of a new type, because it provides for sliding motion on a manifold of codimension higher than 1 by means of control continuous everywhere except this manifold. As a result the chattering effect of such a controller is significantly reduced.\nThe real-time exact differentiator [lo] of the appropriate order is combined with the proposed controller providing for the full SISO control based on the input measurements only, when the only' information on the controlled uncertain process is actually its relative degree. The obtained controller is locally applicable to generalcase weakly-mini\"-phase SISO systems; it is also globally applicable if the relative degree is constant and few boundedness restrictions hold globally. In the absence of noises the resulting accuracy is proportional to z', T being a sampling period and r being the relative degree. That is the best possible accuracy with discrete sampling and discontinuous control [6]. Artificially increasing the relative degree, arbitrarily smooth control may be produced, which totally removes the chattering effect.\nWhile the sensitivity of the higher-order differentiation to input noises grows severely with the differentiation order [7], the sensitivity of the proposed controller to the higherorder derivative estimation errors decreases exactly in the same proportion. That results in the acceptable performance of the proposed output-feedback controller.\nBoth the proposed controller and its output-feedhack version are very robust with respect to measurement noises. The simulaiion shows thai it is probably the first praciically applicable ou fpu t-feedback r-sliding controller with r > 2. The direct measurements of successive output derivatives can be avoided. Only boundedness of the measurement noise is needed, no frequency considerations are relevant.\n[l] G. Bartal i , A. Ferrara, A. Levant, E. Usai. On second order sliding mode controllers. Variable Structure Systems, Sliding Mode and Nonlinear Control (Lecture Noies in Contr. andInz Science, 247, (K.D. Young and U. Ozguner (Ed)), pp. 329-350, Springer-Verlag. London, 1999. [2] C. Edwards, S. K. Spurgeon. Sliding Mode Control: Theory and Applications, Taylor & Francis, 1998 [3] A.F. Filippov. Di@erential Equations wiih Discontinuous Righi-Hand Side, Kluwer, Dordrecht, the Netherlands, 1988. [4] L. Fridman, Singularly pemrbed analysis of chattering in relay control systems, IEEE Trans. on Aufomaiic Control, vol. 47(12), pp. 2079-2084,2002 [SI A. Isidori. Nonlinear Control Sysrems, second edition, Springer Verlag, New York, 1989. [6] A. Levant (L.V. Levantovsky). Sliding order and sliding accuracy in sliding mode control, Iniernaiional Journalof Control, 58(6), pp.1247-1263, 1993. [7] A. Levant. Robust exact differentiation via sliding mode technique, Auiomatica, 34(3), pp. 379-384, 1998. [SI A. Levant. Universal SISO slidmg-mode controllers with finite-time convergence, IEEE Trans. on Automatic Control, vol. 46(9), pp. 1447-1451,2001. [9] A. Levant. Universal output-feedback SISO controller, Proc. of the 15th IFAC Congress, July 2002, Barcelona, 2002. [IO] A. Levant, Higher-arder sliding modes, differentiation and output-feedback control, International Journal of Control, 76 (9/10), pp. 924-941,2003. [ I l l L. Rosier, Homogeneous Lyapunov function for homogeneous continuous vector field. System and ControlLeffers, 19, pp. 467-473, 1992. [12] J.-J. E. Slotine, and W. Li, Applied Nonlinear Conirol (London: Prentice-Hall, Inc.) , 1991 [13] V.I. Utkin. Sliding Modes in Optimization and Control Problems, Springer Verlag, New York, 1992. [14] A.S.1 Zinober, (Ed.). Variable Structure and Lyupunov Control, Springer-Verlag. Berlin, 1994." ] }, { "image_filename": "designv10_11_0003448_1.1539514-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003448_1.1539514-Figure1-1.png", "caption": "Fig. 1 Typical Stewart-Gough manipulator", "texts": [ " Manuscript received December 2000; revised February 2002. Associate Editor: S. K. Agrawal. Copyright \u00a9 2Journal of Mechanical Design rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 08/23/20 matics matrix. Finally, an example of this singularity for a planar 3 degrees-of- freedom redundant parallel robot is presented in a stiffness modulation singular position. 2 Jacobian Formulation Consider a general Stewart-Gough type parallel manipulator subject to a wrench Fenv5@fenv T ,menv T #T applied by the environment, Fig. 1. Let the position/orientation vector of the moving platform relative to world coordinate system be X 5@x ,y ,z ,ux ,uy ,uz# T, where x, y, z are the Cartesian coordinates and ux , uy , and uz are three orientation variables of the moving platform, and let x\u0307 denote the end effector twist and q\u0307 the corresponding active joints\u2019 rates. For parallel manipulators, the commonly used expression of the Jacobian matrix is: q\u03075Jx\u0307, S Ji j5 ]qi ]x j D (1) which is the inverse of that of serial manipulators\u2019: x\u03075Jq\u0307, (Ji j 5]xi /]q j)", "org/about-asme/terms-of-use Downloaded F Using the loop closure method @19#, or the static equilibrium method @4,9,10#, along with Eqs. ~1! and ~2!, respectively, yields the commonly used formulation of the Jacobian matrix. J5F l\u03021 T ~wRpu13 l\u03021!T ] ] ] l\u03026 T ~wRpu63 l\u03026!T G (3) where l\u0302i denotes a unit vector along the ith active prismatic joint pointing from its joint at the base to its joint at the moving platform. The platform-attached and the base-attached coordinate systems are referred to by the letters P and W, respectively, Fig. 1. Accordingly, wRp is the rotation matrix from P to W, and ui is the constant position vector of the ith joint in P, Fig. 1. In order to interpret the Jacobian matrix as lines, the following basic definitions of line geometry are reviewed. A given sextuplet of numbers @ lvx ,lvy ,lvz ,lmx ,lmy ,lmz# T represents a line in space only when it belongs to a five-dimensional quadratic manifold called the Grassmannian @1,20#, the Plu\u0308cker hypersurface @21,22# or Klein quadric @6,20# or, in other words, it fulfils Eq. ~4!. 1vx1mx11vy1my11vz1mz50 (4) Observing Eq. ~3!, it is clear that the rows of the Jacobian are the Plu\u0308cker ray coordinates of lines along the prismatic actuators" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000236_imece2015-52165-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000236_imece2015-52165-Figure1-1.png", "caption": "Figure 1- Meshing scheme used for CFD", "texts": [ " c) The effective thermal conductivity of the powder bed, was calculated based on method that thermal conductivity is dependent to the gas filled the chamber. The equation would be summarized as follow: \ud835\udc58\ud835\udc5d = \ud835\udc58\ud835\udc60(1 \u2212 \ud835\udf19) (3) In Eq. (6), \ud835\udc58\ud835\udc5d and \ud835\udc58\ud835\udc60 are respectively thermal conductivity of powder bed and solid materials. Also porosity of powder bed, \ud835\udf19, can be written as: \ud835\udf19 = \ud835\udf0c\ud835\udc60 \u2212 \ud835\udf0c\ud835\udc5d \ud835\udf0c\ud835\udc60 (7) where \ud835\udf0c\ud835\udc60 and \ud835\udf0c\ud835\udc60 are densities of solid material and powder bed. The effective thermal conductivity was assigned to powder and substrate was modeled separately Figure 1. A triangular meshing scheme was used for the numerical investigation. To increase the accuracy and reduce the simulation time, a finer mesh was used near the laser path as shown in Figure 2. It is assumed that only powder bed transfer heat through environment. The heat transfers through convection and radiation mechanisms. Also initial temperature of the powder bed and substrate is uniform. Laser would warm up the powder bed until it reaches the melting point. After that it would absorb the energy" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003084_6.1998-4357-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003084_6.1998-4357-Figure5-1.png", "caption": "Fig. 5 The basic structure of the model helicopter's cyclic control system. The flapping angle of the flybar, /?, is the angle of the flybar with respect to the body coordinate frame attached to the rotor hub. It is zero when the flybar is perpendicular to the rotor axis. Ball joints are shown as \"o\", and fixed joints are shown as \"\u2022\". The cyclic pitch input to the main rotor blade is controlled by the combination of the Bell input from the swashplate and the Hiller input from the flybar.", "texts": [ " Flybar dynamics The dynamics of the rotor and the flybar are the most significant nonlinearities involved in the creation of the forces and moments on the helicopter. The actuator dynamics include as states the flapping angle and velocity (/?, /?) of the flybar and the position and angular velocity (\u00a3, Q) of the main rotor blade. As mentioned before, the flybar plays a major role in augmenting the stability of the helicopter. This system is often called as a Bell-Hiller mixer, because it takes advantage of two different cyclic control systems, as shown in Figure 5. Cyclic control is the mechanism by which the rotor blade's pitch is changed in a rotation so that an unequal distribution of the lift applies a moment around the rotor hub. This moment then provides pitch and roll attitude control as depicted in Figure 2. The Bellmixer allows the blade pitch to be changed directly from the cyclic servo actuator. It is fast in response, but lacks stability. Meanwhile, the Hiller-mixer allows the pitch of the flybar to be changed instead of the pitch of the blade", " The flybar then flaps, and this flapping motion causes the pitch of the main blade to change. There is a direct relationship between the cyclic input applied to the main blades 6cyc (which is .the function of stick commands 6s and 6$) and the cyclic angle of the rotor blades 8cyc. A similar relationship exists between the cyclic input applied to the flybar Sfiy and the flapping angle of the flybar /?. The orientation of the main blade is given by f. Note the 90\u00b0 phase difference between 6cyc and S/iy, due to the geometry of the rotor/flybar assembly sketched in Figure 5. (7) (8) An important assumption at this point is that the rotor system does not apply reaction forces back to the actuators, including the flybar (the flybar is considered to be another actuator to the main blades). This is equivalent to assuming the actuators are able to apply infinite amount of forces to the airfoils. We also neglect the influence of /i and v on the flybar due to its relatively small wing surface. When a cyclic input is applied by the pilot, the flybar creates lift which tilts the flybar disk", "16 2ir i-R = 5/7m Jo Jo r sin \u00a3 dL We assume that the rotor angular velocity is constant; thus \u00a3 = Qi. The lift element equation is similar to the flybar lift used in equation (10). dLm = -f ecyc - cdr - sin^ - - cost (13) The induced air velocity V{ must be derived empirically.16 However, it is usually of similar magnitude around the rotor disk, especially in hover or lowvelocity motions. It therefore has little effect on the net moment on the helicopter; we will assume that it is negligible in calculating dLm. From Figure 5, there are two different kinds of inputs which affect Qcyc: a direct input by the pilot and an indirect input by the flybar. The geometry of the hub linkages indicate that 6cyc will be the weighted sum of these two inputs. Jcyc \"eye (14) The expression for the rotor thrust T is wellknown in the literature.17 The constant tip loss factor B takes into account the fact that a finite length rotor blade would lose some of the lift generated due to the wing tip vortex effect;16 we will use the value B = 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001060_j.isatra.2020.09.011-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001060_j.isatra.2020.09.011-Figure1-1.png", "caption": "Fig. 1. Holonomic kinematic model of the bevel-tipped flexible needle showing insertion and rotational velocities i1 and i2 . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)", "texts": [ " Assumptions of the present study In this work, the following assumptions are considered: \u2022 Needle path is assumed to be anatomical obstacle-free in this study. \u2022 Disturbances considered here are matched and bounded. \u2022 The study is performed without considering the dynamic needle-tissue interaction force modeling. .2. Kinematic model of flexible bevel-tipped needle In our study, we have used the generalized non-holonomic nicycle model proposed by Webster et al. [7]. As shown by the odel depicted in Fig. 1, frame Q (at the needle tip) is referenced ith respect to the base frame P. Here, angle \u03b8 is the turn angle f the front wheel angle made by frame Q depending upon the inertion length and bevel angle. The distance between the frames and P attached to the front and back wheels is represented by 1. When we rotate the needle in a controlled fashion, it follows straight-line path, but without rotation, it naturally moves up nd down, as shown in Fig. 1. The POSE of frame Q is given by, PQ = [ RPQ pPQ 0 1 ] \u2208 SE(3) (1) 1 = p\u03071i1 + p\u03072i2 (2) where p\u03071 = [0, 0, 1, 0, k, 0]T (associated with insertion velocity) p\u03072 = [0, 0, 0, 0, 0, 1]T (associated with rotational velocity). The needle is moving ahead along the z-axis due to insertion velocity i1, and by the rotational velocity i2, the needle is moving up and down within the x-z plane due to the rotation around y-axis. The insertion (along the z-axis) and movement (around y-axis) jointly are evident in Fig. 1. In our methodology, we have considered the rotational velocity as the primary one causing the needle to spin thereby advancing in a straight line (indicated as straight needle without deflection (blue colored)), that needs to be controlled to keep in the desired x\u2212 z plane and the insertion velocity as the secondary input which is considered constant from the entry point to the target. In order to define the orientation between the frames P and Q, we have utilized the Z-X-Y fixed angles as generalized coordinates for parameterizing the rotation matrix RPQ " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000056_j.talanta.2015.05.044-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000056_j.talanta.2015.05.044-Figure5-1.png", "caption": "Fig. 5. The inter-day study of 10 mg mL 1 of five parabens in 0.05 M phosphate buffer solution (pH 6):acetonitrile (60:40, %v/v) on G/PVP/PANI nanocompositemodified SPCE.", "texts": [ " The intra-day precision of 30 measurements was evaluated to ascertain the stability of this proposed method. It was found that the obtained peak currents did not significantly change in repeated measurements with the relative standard deviation (RSD) in the range of 3.42\u20137.20% for all five parabens. In addition, the inter-day precision was also investigated for 3 days with the same electrode. It was found that the modified electrode can be used more than 3 days because the sensitivity did not significantly change as shown in Fig. 5. Eventually, the proposed method using the G/PVP/PANI nanocomposite-modified SPCE coupled with HPLC was applied to simultaneously detect five parabens in real samples. A soft drink and a cosmetic product were selected as a model of sample because they were reported to have a chance to contaminate with parabens. The chromatogram in Fig. 6(A) of the soft drink sample apparently showed no sign of any paraben. Therefore, the soft drink sample was spiked with standard parabens at a concentration of 5 mg mL 1 to investigate the accuracy of this proposed method from the recovery by the standard addition method and the typical chromatogram of the spiked sample is shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000631_j.ymssp.2018.07.027-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000631_j.ymssp.2018.07.027-Figure1-1.png", "caption": "Fig. 1. The twin-rotor helicopter model made by Quanser company.", "texts": [ " A new overlapping technique for algebraic differential estimation is discussed. Based on the new resetting and overlapping strategy, the algebraic differential estimator is designed to calculate the derivatives of output signals. The numerical and experimental results of LQR and OFLC for the 2-DOF helicopter are presented. The comparison is done between two control strategies. The Quanser 2-DOF laboratory helicopter consists of a helicopter model mounted on a fixed base with two propellers that are driven by DC motors. The system is shown in Fig. 1. The front propeller controls the elevation of the helicopter pitch angle, and the back propeller controls the side to side motion of the helicopter yaw angle. The pitch h and yaw w angles are measured using high-resolution encoders. The pitch encoder and motor signals are transmitted via a slip ring, which eliminates the possibility of wires tangling and allows the yaw angle to rotate freely 360 degrees. The mathematical model of the 2-DOF helicopter is obtained based on the following conventions [38]" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003168_1521-3935(20011001)202:14<2926::aid-macp2926>3.0.co;2-3-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003168_1521-3935(20011001)202:14<2926::aid-macp2926>3.0.co;2-3-Figure2-1.png", "caption": "Figure 2. X-ray diffraction patterns at room temperature of EM3-T2.5 with the beam a) perpendicular to the surface of the elastomer film (y-axis), b) parallel to the axis of stress during synthesis (z-axis) and c) perpendicular to the other axes (x-axis); d) schematic drawing of the coordinate system of the sample.", "texts": [ " Trifunctionally V3-Crosslinked Systems Because of the perpendicular orientation of the mesogenic groups with respect to a mechanical field for the corresponding linear polymer melt the same orientation is expected for the elastomers. It can be assumed, that a negative order parameter within microscopic domains does not exist, because for similar polymers always positive order parameters are reported in literature. In the following, the ordering direction of the mesogenic groups is referred to as the director of the single domains, as usual. The X-ray diffraction pattern of EM3-T2.5 with 2.5% crosslinker concentration (Figure 2a), with the beam perpendicular to the surface of the elastomer film (y-axis) shows a broadened wide angle reflection with an intensity maximum at the meridian. The axis of stress (z-axis) is parallel to the meridian. Since the stress is parallel to the meridian, the director orientation is perpendicular to the external stress, as expected (Weak small angle reflections on the equator are due to some smectic fluctuations and are neglected because of their small intensity.) The question arises, whether the director of the single domains is planar oriented, having all directions in the plane perpendicular to the axis of stress (xy-plane), or homogeneously oriented, forming a classical monodomain, due to additional restrictions, e.g. surface effects. Therefore X-ray scattering experiments with the beam parallel to the axis of stress (z-axis) (Figure 2b) and parallel to the x-axis, perpendicular to the other directions, (Figure 2c) are carried out (for the different directions refer to Figure 2d). The diffraction pattern with the beam parallel to the axis of stress (z-axis) is similar to the pattern with the beam perpendicular to the elastomer surface (y-axis). The meridian is perpendicular to the elastomer surface here (yaxis). But with the beam parallel to the x-axis a halo can be observed. Its azimuthal intensity distribution shows slight maxima, that are neglected in comparison to the distinct maxima for the other directions. The azimuthal intensity distribution of all directions is summarised in Figure 3" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001760_tie.2021.3076715-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001760_tie.2021.3076715-Figure9-1.png", "caption": "Fig. 9. Geometrical projection of lumped element-2 (Scale 1:1).", "texts": [], "surrounding_texts": [ "Geometrical parameters of PMSM and DC generator of experimental setup is given in Table III, which is used for natural frequency and mode shape calculations [30]. Geometrical projections of lumped elements 2, 3 & 4 are shown in Figs. 9, 10 & 11 which is required for inertia and stiffness matrix calculations. Further, damping and excitation torque is required for time response of torsional vibration of system. Authorized licensed use limited to: Carleton University. Downloaded on May 30,2021 at 21:54:56 UTC from IEEE Xplore. Restrictions apply. 0278-0046 (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. 7 Stiffness of any shaft under torsion is given by GiJi/Li, where Gi is Shear modulus of shaft and coupler (for stainless steel (Grade-304), Gi is 77\u00d7103 MN/m2). The material of shaft and coupler is steel having density of 7780 kg/m3 [31]. Ji is an area polar moment of inertia given by \u03c0di 4/32, where di is diameter of shaft and Li is the length of element. By using spring series addition and geometrical properties, equivalent mass polar moment of inertia and equivalent torsional stiffness for elements 2, 3 & 4 are calculated and given in Table IV, respectively." ] }, { "image_filename": "designv10_11_0003990_ias.2006.256728-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003990_ias.2006.256728-Figure7-1.png", "caption": "Fig. 7 Prototype 22-pole, 24-slot modular PM machine mounted on test rig", "texts": [ " Further, it should be noted that although the amplitudes of the high-order time harmonics is relatively low, they may induce significant vibrations. 0 2000 4000 6000 8000 10000 12000 14000 16000 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Frequency (Hz) N or m al is ed ra di al fo rc e de ns ity (N /m 2 ) f = 733.33 2f 3f 4f Fig. 6 Time harmonic distribution of radial force density at \u03b8s = 0 and full-load The foregoing analysis of the vibration characteristics of a modular PM machine has been validated by measurements on the prototype 22-pole, 24-slot machine which is shown in Fig. 7 together with its test rig. The machine is connected to a 4- quadrant DC power supply via a three-phase diode bridge rectifier and was operated as a generator. Fig. 8 shows a typical phase current waveform. An accelerometer was mounted on the machine housing to measure vibrations under various operating conditions. Fig. 9 (a) shows the measured vibration spectrum on no-load at a rotor speed of 2000 rpm, which is around the middle of the operating speed range for the particular modular machine which is under consideration" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003608_9783527618811-Figure2.3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003608_9783527618811-Figure2.3-1.png", "caption": "Fig. 2.3 Scale definition for spacecraft with solar panels.", "texts": [ " Let miri = \u222b Bi r dm mi = \u222b Bi dm ci = r\u0304i \u2212 r\u03041 I(r1,B) = I(r1,B1) + n \u2211 i=2 { I(ri,Bi) + mi[c2 i I \u2212 ci \u2297 ci] } Finally, we must choose a basis for the representation of I(ri,B). Let us use a principal axis basis for B1. Let e(i) be a principal axis basis for Bi and let e(i) = e(1)Ri. Then I(ri,Bi) = e(i)Ii\u03b5 (i) = e(1)RiIiR t i \u03b5 (1) no summation Therefore, the representation of the inertia tensor in the chosen reference frame is I(r1,B) = e(1) { I1 + n \u2211 i=2 [ RiIiR t i + mi(ct i ci I \u2212 cic t i) ]} \u03b5(1) (2.16) Example 2.1 Let us calculate the inertia tensor for the spacecraft with solar panels illustrated in Fig. 2.3. We will consider the body to be a cylinder and the two panels to be rectangular hexahedra, all of uniform density and of the dimensions indicated in Fig. 2.3. Let the x-axis be the axis of the panel passing through the center of the b\u2212\u2212c face and the y-axis the symmetry axis of the cylinder. Choose the x-axis to be a principal axis for the cylinder. Let the panels each be inclined at angles \u03c0/2\u2212 \u03b8 to the generators of the cylinder. Let B1 be the cylinder and B2, B3 the (identical) panels. Elementary calculations provide I1 = 1 12 m1 3R2 + H2 0 0 0 3R2 + H2 0 0 0 6R2 and I2 = I3 = 1 12 m2 b2 + c2 0 0 0 a2 + c2 0 0 0 a2 + b2 The translations from the center of mass of B1 to the centers of mass of B2 and B3 are c2 = (R + 1 2 a)e1 and c3 = \u2212(R + 1 2 a)e1 and the rotation matrices are R1 = R2 = 1 0 0 0 cos \u03b8 \u2212 sin \u03b8 0 sin \u03b8 cos \u03b8 Now we can assemble the inertia matrix as given by (2" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000108_tec.2018.2820083-Figure16-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000108_tec.2018.2820083-Figure16-1.png", "caption": "Fig. 16. Deformation when applying 1200Hz radial force and bending moment together", "texts": [ " For bending moment, the 2.5N concentrated force is applied on the edge of the pole to create moment. In order to balance the pole, the bending moment caused by the concentrated force is equivalent by the force couple F as shown in Fig. 10. The value of F is set to 1.25N, which is half of 2.5N. For the frequency of force, two typical frequencies are used, 1200Hz and 2500Hz, which are close to the two modal natural frequencies of pulsating modal and bending modal shape obtained from modal test in the section V. Fig. 16, 17 and 18 show the deformation response of the stator caused by radial force and bending moment together, radial force only, and bending moment only, respectively, where the frequencies of radial force and bending moment are 1200Hz. Fig. 19, 20 and 21 show the corresponding results when the frequencies of radial force and bending moment are 2500Hz. In these figures, the situation is 1=9 , and only the two instants are shown when the deformation are maximum. From Fig. 17 and Fig. 18, it can be seen that the maximum deformation of the bending mode is nearly 10 times higher than that of the pulsating mode" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000346_j.mechmachtheory.2017.09.013-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000346_j.mechmachtheory.2017.09.013-Figure8-1.png", "caption": "Fig. 8. Configuration IV for the combination of two Bennett linkages.", "texts": [ " After the similar construction we have that the length of link AE equals zero, the joints A and E becomes to a U joint, the angle from joints A to E equals \u03b2I \u2212 \u03b2II . In Fig. 7 , thick dash line indicates the coincident links AF and EF \u2032 . (IV) In this configuration, we have K = 0 and b I = b II , then links AF and EF \u2032 are in a straight line but their length are not equal. After the similar construction, we have that, the length between joints A and E is not zero but equals d AE = | b I \u2212 b II | , the offsets of joints A and E equal zero, the twist of new link EA is \u03b1EA = \u03b2II \u2212 \u03b2I . In Fig. 8 , the thick dash line indicates the coincident part of links AF and EF \u2032 . From the above analysis we conclude that the angle K has no effect on the DOF of the linkage. So we can apply the four configurations to the construction process of the 5R SLOL, then we get four configurations of the 5R SLOL. Except for the general form shown in Fig. 2 (c), there are still three special forms of the 5R SLOLs with zero joint offset. As the linkages with zero joint offset have more excellent deployability, we would synthesize the three special forms" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001410_j.mechmachtheory.2021.104291-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001410_j.mechmachtheory.2021.104291-Figure1-1.png", "caption": "Fig. 1. Noise: Generation, transmission and radiation .", "texts": [ " In a second step, the developed methodology is tested and validated against established research and software tools. On this basis, a comparison and discussion of some modeling details is finally given. \u00a9 2021 Elsevier Ltd. All rights reserved. In addition to power density, reliability and efficiency, noise is always a major factor for a successful gear design. The time varying gear mesh stiffness along the path of contact leads to oscillating forces on the shafts and bearings. These vibrations are finally transmitted to the casing and radiate air borne noise, see Fig. 1 . As a result, the technical design of the actual gear mesh is well known as the most decisive criterion for noise generation in a gearbox. Even with today\u2019s computer power, a complete elastic simulation of this dynamic rolling process - e. g. with a standard finite element solver - is still extremely inefficient. Therefore, the computational determination of the fluctuating gear mesh stiffness and its subsequent implementation into a total system analysis is highly relevant. Finding an appropriate methodology sufficiently compromising accuracy and computation time is quite challenging and has been a research topic for decades" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001595_j.ijsolstr.2021.111075-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001595_j.ijsolstr.2021.111075-Figure2-1.png", "caption": "Fig. 2. Solution of the pure deformation of a bar element.", "texts": [ " The detailed derivation process of the particle internal force generated by the deformations of the bars is given by Yu et al. (2011), and a brief summary is given as follows. Because the particle internal force vector fbara generated by the deformation of bars is related only to the pure deformation, the rigid body translation u1 and rigid body rotation Dh of the bar element must be removed from the relative displacement of the bar element. The solution of the pure deformation of a bar element 1\u20132 is depicted in Fig. 2. Here, 1a 2a and 1b 2b are the spatial positions of bar element 1\u20132 at time ta and tb, respectively, where 1a 2a is the reference configuration, and 1 is the reference particle. The displacement of particle 1 is taken as the rigid body translation of bar element 1\u20132. The spatial position of 1b 2b after the fictitious reverse rigid body translation u1 is 10 20. The relative it cell of the Miura pattern. (c)The unit cell of the Miura pattern is discretized into displacement between particle 2 and particle 1 is presented as follows: g2 \u00bc u2 u1 \u00f06\u00de where u1 and u2 are the displacement vectors of particle 1 and particle 2 during ta tb" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003516_s0378-4371(02)01260-8-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003516_s0378-4371(02)01260-8-Figure8-1.png", "caption": "Fig. 8. A bent strip.", "texts": [ " Inserting this in the bending energy, we /nd Eb \u223c .2=w. Now using w \u223c .\u22121=3 we infer Eb \u223c .7=3. The scaling of the stretching ridge width as we move from the vertex to mid-ridge is also of interest. We consider a stretching ridge on an elastic membrane of thickness h as before. The ridge itself has a total length X and a position-dependent width W (x) measured from the left (say) vertex. We can immediately infer, as a geometrical constraint, that W (x) W (X2 ) \u2192 0 as x X \u2192 0 (43) in the limit h W x X (See Fig. 8). We now ask how the left side goes to zero in this limit. We assume that W (x) \u223c xpX q in this limit with both p; q\u00bf 0 so that (43) is satis/ed. From earlier calculation we know that W (x)|x\u2248X \u223c h 1 3X 2 3 \u223c XpX q (44) and hence that p + q = 2=3. If we take W (x) to have the strongest x behaviour possible then the inequalities imposed on q imply that we can take q = 0, so that W (x) \u223c x2=3. Under this assumption of strong x dependence we can look at the behaviour this implies for various energetic quantities associated with the ridge" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003798_acs.4480030106-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003798_acs.4480030106-Figure1-1.png", "caption": "Figure 1 . Parametrization of the plant for combined MRAC", "texts": [ " The plant transfer function Wp(s) given in (17) is expressed in terms of the parameters ai and b, for i = 0, 1, ..., n - 1 and j = 0, 1 , ..., m. While this parametrization is adequate for the case n* = 1 , for reasons that will be made clear towards the end of this section, a different parametrization of the plant (and hence the identifier) is needed when n* 2 2 to make the problem analytically tractable. The latter uses the reference model transfer function in the parametrization6 as shown in Figure 1 . and a ( t ) 4 [ w i ( t ) , o ? ( t ) , ..., w : - ~ ( t ) ] T~ R\"-', E with w / ( t ) , w f ( t ) E R for i = 0,1, ..., n - 2, will be referred to as the control sensitivity vectors T ~ n - 1 U l ( t ) 4 I w b ( t ) , w t ( t ) , ..., w ~ - 2 ( t ) l 60 MODEL REFERENCE ADAPTIVE CONTROL and are generated using the differential equations & i ( t ) = A w l ( t ) + lu(t) &(t) = A w ( ~ ) + lyp(t ) where A is a stable (n - 1) x (n - 1) matrix, I is an (n - 1)-vector and the pair (A, I ) is controllable", " Since our ultimate objective is to define closed-loop estimation errors, as in the first-order case, we need to relate the desired control parameters 8* to the plant and reference model parameters. To make this relationship simple, we choose (A, I ) to be in controllable canonical form such that where X i ? [ & , X 1 , ..., X n - 2 ] T E I R n - 1 , X i E I R for i = O , l , ..., n-2, and I ( n - 2 ) is the (n - 2) x (n - 2) identity matrix. With this choice we have that BT(sI - A)-'l = P(s)/A(s) and + P , , - ~ s \" - ~ + - - - + PO and A(s) e sn- l + X n - z ~ \" - ~ + + XO is the characteristic polynomial of the matrix A. From Figure 1 it follows that Qi and bj in equation (17) and the parameters a, P and a n - 1 are related by the Bezout identity. aT(sI - A)-'I = a(s)/A(s), where a(s) !l a , , - 2 ~ ~ - ~ + a n - 3 s n - 3 + * * * + ao,P(s) i? @n-2Sn-2 Rp(s) + a (~ ) l + k m Z p ( s ) I P 6 ) + a n - lA(s)l = Zp(s)Al@)Rrn(s) (18) A l ( s ) in equation (18) is any monic, stable polynomial of degree n - m - 1, with the property that A(s) = Zfn(s)Al(s) . An equivalent representation of the plant is shown in Figure 2, where the transfer function W,,,(s) is included both in the forward path as well as in the feedback path", ", 2* 2* MODEL REFERENCE ADAPTIVE CONTROL 63 plant parameters a, 0, an-l and kp as follows: e : + p = o kpe: + kman- 1 = 0 kpe; + kma = 0 k*kp - kIn = 0 From equations (22) the closed-loop estimation errors are defined as &el ( t ) = e m + P ( t ) &eo(t) = kp(t)eo(t) + km&- I ( t ) &e, ( t ) = fi ,( t)ez(t) + km&(t) ek( t ) = k(t)&(t) - k, These equations can also be written as 3.3. Parameter updating The basic adaptive controller used in the direct approach for controlling an nth-order plant shown in Figure 1 has to be conveniently modified in order to include an augmentation network as indicated in Figure 5 . This modification is necessary only when the relative degree of the plant is greater than unity. In what follows, we will consider only the general case. The filtered version of the control sensitivity vector is obtained as G ( t ) 4 Wm(s)Izno(t), where 3(t) P [?( t ) , 3T(t) ,Yp(t) , G $ ( t ) ] 6 R2\", &(t) [&(t), Ci:(t), ..., S;-2(t)] and &(t) [GB(t), G!(t), ..., Gi-2(t) lT, with wj( t ) , G f ( t ) , " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001005_tasc.2020.2990774-Figure11-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001005_tasc.2020.2990774-Figure11-1.png", "caption": "Fig. 11. Magnetic flux tube division of air gap between stator and mover at aligned position. (a) Part I. (b) Part II.", "texts": [ " \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 R11 4Rsp1 4Rsp1 4Rsp2 4Rsp2 4Rsp1 R22 4Rsp1 4Rsp2 0 4Rsp1 4Rsp1 R33 0 \u22124Rg1 4Rsp2 4Rsp2 0 R44 4Rsp2 4Rsp2 0 \u22124Rg1 4Rsp2 R55 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 \u00b7 \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 \u03c61 \u03c62 \u03c63 \u03c64 \u03c65 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 = \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 4(F1 + F2 + F3) 4F1 4F1 4F2 4F2 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 (31) In this formula: R11 = 4 ( Rsp1 +Rsp2 +Rsp3 +Rg3 + 1 2 \u00b7Rmp + 1 2 \u00b7Rsy2 +Rsy1 ) (32) R22 = 4(Rsp1 +Rg1) (33) R33 = 4(Rsp1 +Rg1) (34) R44 = 4(Rg1 +Rsp2 +Rg2) (35) R55 = 4(Rg1 +Rsp2 +Rg2) (36) Next, the reluctance of each part of the air gap is specifically determined. In the aligned position, the division of the stator tooth is basically the same as that in the unaligned position, except that the lengths of h1 and h2 are different. In Fig. 10, h1 = Lp/5, h2 = 7Lp/10. Rg1 = \u03c0 \u00b7 Cs 2 \u00b7 \u03bc0 \u00b7 Ls \u00b7 h1 (37) Rg2 = Cs \u03bc0 \u00b7 Ls \u00b7 h2 (38) At the aligned position, the reluctance of the air gap is composed of Rg3a, left-right symmetrical Rg3b, and front and back symmetrical Rg3c. In Fig. 11, h3 = Lp/20. Rg3a = \u03b4 \u03bc0 \u00b7 ((Bs +Bm)/2) \u00b7 (Ls + Lm)/2 (39) Rg3b = \u03c0 \u03bc0 \u00b7 ((Ls + Lm)/2) \u00b7 ln((\u03b4/2)/(\u03b4/2 + h3)) (40) Rg3c = \u03c0 \u03bc0 \u00b7 ((Bs +Bm)/2) \u00b7 ln((\u03b4/2)/(\u03b4/2 + h3)) (41) Then the expression of Rg3 is: Rg3 = 1 1/Rg3a + 2/Rg3b + 2/Rg3c (42) In the division of the flux tube in the stator tooth part, the calculation method and expression of the reluctance of the aligned position and the unaligned position are the same, except that the length of h1 and h2 changes. The mover part changes and its reluctance expression is: Rmp = Lst \u03bcmp \u00b7 Lm \u00b7Bm (43) where \u03bcmp is the permeability of the mover tooth" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001449_j.mechmachtheory.2021.104396-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001449_j.mechmachtheory.2021.104396-Figure9-1.png", "caption": "Fig. 9. Teeth profiles on planes with different z of f .", "texts": [ " Rather, the profile changes like a negative-shifted gear tooth profile. Consequently, referring to Fig. 8 (a), if no rake-surface-offset is provided along the tool axis (i.e., z of f = 0 ), the generating surface and clearance surface will interfere. In other words, the clearance surface interferes with the internal gear profile. Accordingly, referring to Fig. 8 (b), an appropriate rake-surface-offset, z of f , must be assigned. The cutting-edge of a skiving tool is the intersection curve between the generating surface and the rake surface. Referring to Fig. 9 , s 0 represents the intersection of the plane with z of f = 0 and the generating surface, and s 1 is the intersection of any plane with z of f > 0 and the generating surface. Obviously, s 1 lies inside s 0 and does not intersect it at any point. Since the generating surface is barrel-shaped, curve s 0 is similar to the tooth profile of a gear with a zero-shifted coefficient, while curve s 1 is similar to the tooth profile of a gear with a negative-shifted coefficient. From the gear principle, it can be seen that the tooth profile of s 1 is thinner than that of s 0 , lies within s 0 , and does not intersect with s 0 at any point" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003388_978-3-662-04831-3-Figure401-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003388_978-3-662-04831-3-Figure401-1.png", "caption": "Figo 401: Vector diagram used in the definitions of linear momentum and angular momentum", "texts": [ "1) 130 40 Dynamics of planar and spatial rigid-body systems Then the expression P~ :=I RrRdm (402) is called linear momentum of the rigid body with respect to the origin 0 of frame R, represented in R, and L~ := IrR 0 R7-R dm (403) is called angular momentum of the rigid body with respect to 0 of R and represented in R, where the velocity vector RrR in ( 402) and ( 403) is measured in R and represented in Ro Consider a second frame L with origin 0 L = P, and fixed on the bodyo Then the vector r can be written as (Figure 401) rR := r~o + XR = r~o + A RL 0 XL 0 The velocity vector RrR is RrR = Rr~o + Rx_R or ( 4.4a) (4o4b) 4.1 Linear momentum and angular momentum of a rigid body 131 Due to the rigid-body property (4.5) and to the relation A. RL- ARL -L - \u00b7WLR' the resulting velocity vector is (4.6) Then the linear momentum P~ of the rigid body can be written as or as (4.7a) with C as the center of mass of the body, with L 1 I L rcp := m. X dm (4.8) as the vector from the origin P of L to C, and with m :=I dm (4.9) as the mass ofthe body", " Using the relation xL 0 xL = - [ (xL) T 0 xL 0 13 - xL 0 (xL) T] = (xL 0 xL) T im plies, together wi th ( 4 01 7) J~ = f [ (xL) T 0 XL 013- XL 0 (xL) T] dm, or written in components with respect to frame L, with ( 4023) (4o24a) (4o24b) J~xx := J [ (x~ f + (x~ f] dm, etco, as the moments of inertia and (4o24c) J~xy := J X~ 0 X~ dm, etco, as the products of inertia 401 Linear momentum and angular momentum of a rigid body 135 of the rigid body with respect to a body-fixed point P, and with L ( L L L)T X = Xx, Xy, Xz as the vector from point P to the mass element dm located at the point Q (Figure 401)0 4.1.3.2 Time dependence of Jf; and Jf!. For rigid bodies of constant mass m, the inertia matrix J~ is a constant matrix when represented in frame L, whereas the matrix (4025) represented in frame R, is in general a time-dependent matrix, due to A RL = A RL ( 7](t) )o 4.1.3.3 Steiner-Huygens relation. Changing the reference point of J from point C ( origin of frame K) to point P ( origin of frame L) provides the following transformation of J: J L ALK JK AKL (( L )T L I L ( L )T) P = 0 e 0 + m 0 Tep 0 Tep 0 3- Tep 0 Tep 0 Or, written in components, ( Jf5xx ' J~ = -J~xy' -Jexz ' -oJL -o e +mo with L ( L L L )T Tep = Xep' YeP' Zep L 2 L 2 'Xep +zep ' L L -ZepYeP (4o26a) (4o26b) (4o26c) Planar case (moment ofinertia): In the planar case only rotations about the z-axis perpendicular to the x-y plane occuro Then J}J = J~ = hzz =: Jp E lR1 , (4o27a) and the Steiner-Huygens relation is L L ( L 2 L 2) L Jp =Je+ m 0 Xep + YeP =Je+ m 0 (4o27b) 136 40 Dynamics of planar and spatial rigid-body systems Proof of the Steiner-Huygens relation (4.26): Inserting the relation X= rcp + p (Figure 401) into ( 4017) provides the relation J~=- jxLoxLdm=- j(r~p+PL)o(r~p+PL)dm, and, together with (a + b) = a + b, the relation J L f -L - L d - L - L p=- p op m-r0 porcpom - r~p 0 (/ pL dm) - (/ pL dm) 0 r~po Together with j PL dm = 0 , pL := r~0 , and J pL dm = 0 ( due to the definition of C), this yields the transformation relation J L JL -L -L P = c- rcp 0 rcp 0 m with J~ := - f PL 0 PL dm = f ( (pL)T 0 PL 0 13- PL 0 (pL)T) dmo Due to J~ =ALK 0 J{\u00a7 0 AKL and to r~p 0 r~p =- ( (r~p)T 0 r~p 0 13 - r~p 0 (r~p)T) , the following relation holds J L ALK JK AKL (( L )T L I L ( L )T) p= 0 co + rcp orcpo 3-rcpo rcp omo This proves (4o26a)o ( 4028) ( 4029) (4030) (4031) ( 4032) (4033) (4034) D 402 Newton-Euler equations of an unconstrained rigid body 137 4" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003405_j.1460-2687.2002.00093.x-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003405_j.1460-2687.2002.00093.x-Figure2-1.png", "caption": "Figure 2 Definitions of clubface loft (A), open/closed (B), and tilt (C) orientation angles. For (A) and (B), a black arrow (fi) represents the vector perpendicular to the clubface and a gray arrow (fi) represents the velocity vector of the clubface. Different values for \u00d8, the angle between the two vectors, will affect the ball launch condition and subsequent flight pattern.", "texts": [ " A linear interpolation using this impact ratio was used to estimate the position of the four clubface markers at the instant of impact based on their preimpact and postimpact coordinates. The positions of the four markers at impact were then used to calculate orientation of the clubface and impact position relative to the centre of the ball. Clubface marker coordinate data was used to determine three angles describing clubface orientation at impact: Loft, open/closed, and Tilt angles. These measures were obtained as follows: Loft (Fig. 2a): The angle a line perpendicular to the clubface made relative to a horizontal reference at impact with the ball where the greater the positive angle, the greater the loft. The change in loft angle (Dloft) was defined as the difference between the loft angle predicted for impact and the second frame after impact. Open/closed (Fig. 2b): The angle between the direction the clubface was moving at impact and a line perpendicular to the clubface projected onto the x-y plane. An open clubface was positive, and would tend to cause the ball to fade or slice. A negative angle would tend to make a ball draw or hook. The change in open/closed angle (DOp/Clo) was defined as the difference between the loft angle predicted for impact and the second frame after impact. 2002 Blackwell Science Ltd \u2022 Sports Engineering (2002) 5, 65\u201380 67 Tilt (Fig. 2c): The angle that a line along the bottom of the clubface made with a horizontal line. The location of the ball on the clubface was measured relative to a reference mark for each club, which was the centre of the driver clubface and the central manufacturer\u2019s mark on the 5-iron. As shown in Fig. 3, the origin of the clubface coordinate system was at this reference mark, and the impact location was measured using a horizontal (Dx) and vertical (Dz) coordinate. These were defined as follows: Horizontal distance (Dx): Distance in centimetres from the centre reference point to the centre of the predicted ball impact point", " A positive value is toward the toe of the club, and a negative value is toward the heel of the club. Vertical distance (Dz): Distance in centimetres from the centre reference point to the centre of the predicted ball impact point. A positive value is above the reference point, and a negative value is below the reference point. \u00d8 Tilt Down: \u00d8 = negative angleTilt Up: \u00d8 = positive angle \u00d8 C Figure 3 The location of the ball impact position relative to the club face centre was referenced using a coordinate system where the x-axis was parallel to a line between F3 and F4 (Fig. 2) and the z-axis was perpendicular to the x-axis in the plane of the clubface. 68 Sports Engineering (2002) 5, 65\u201380 \u2022 2002 Blackwell Science Ltd The swing plane angle was calculated by determining the centre marker on the clubface for each frame of data during the swing and finding the plane that best fit the data using a least-squares fit. Zero degrees was vertical and the greater the angle, the flatter the swing, as indicated in Fig. 4(A). The velocity of the clubhead was calculated from the raw (unfiltered) 3-D coordinates" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003951_tia.2005.863907-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003951_tia.2005.863907-Figure4-1.png", "caption": "Fig. 4. Effect of the application of the vectors u1, u3, and u5 in the first sector.", "texts": [ " Actually, when the stator flux linkage lies in the kth sector, the application of the kth voltage vector produces an increase in the flux amplitude and a slight decrease of the electromagnetic torque (since the stator flux linkage lies in the upper subsector), the application of the (k + 2)th voltage vector produces a slight decrease in the flux amplitude and an increase in the electromagnetic torque, while the application of the (k \u2212 2)th voltage vector produces a slight decrease in the flux amplitude and a decrease in the electromagnetic torque. As an example, Fig. 4 shows that, when the stator flux vector \u03c8s(t) lies in the first sector and one of the voltage vectors u1, u3, and u5 is applied, the flux vector resulting after a sampling time of the control system Tc becomes, respectively, \u03c81 s (t+ Tc), \u03c83 s (t+ Tc) or \u03c85 s (t+ Tc). In particular, the application of u1 causes a strong increase of the flux amplitude and a slight decrease of the torque, the application of u3 causes a slight decrease of the flux amplitude and a strong increase of the torque and, finally, the application of u5 causes a strong decrease of the flux amplitude and a strong decrease of the torque", " With specific regard to the classic DTC, the time domain waveform of the common-mode voltage is a repetition of pulses of amplitude \u00b1Udc/6, duration equal to the sampling time of the control system Tc and distance between each pulse T . T depends on the control law, in general is not predictable, and is a multiple of Tc. To have an approximate idea of the harmonic content of this voltage, the series expansion of a generic trapezoidal pulse waveform with amplitude Udc/6 = 93.3 V, rise time tr = 6 \u00b5s (equal to the fall time), duration Tc = 83 \u00b5s, and distance between pulses T = 2 Tc = 166 \u00b5s can be adopted (Fig. 4). In this case, the Fourier series expansion complex coefficients Cn are the following [22]: Cn = Udc 6 Tc T sin ( 1 2n\u03c90Tc ) 1 2n\u03c90Tc sin ( 1 2n\u03c90tr ) 1 2n\u03c90tr e \u2212jn\u03c90(Tc+T ) 2 (4) where \u03c90 = 2\u03c0/T . This formulation shows that, under the hypotesis that the rise time is equal to the fall time, the amplitude of the harmonics results from the product of two terms of the type sin(x)/x; each of these terms defines a set of harmonic clusters in a definite region of the frequency domain. To predict the limit values of the harmonic content with frequency, the envelope of the amplitude plot can be deduced [22]" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003706_j.mechmachtheory.2004.02.011-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003706_j.mechmachtheory.2004.02.011-Figure1-1.png", "caption": "Fig. 1. Open-loop kinematic chain mechanism.", "texts": [ " The article develops this technique for two-degree-of-freedom planar articulated open-loop mechanisms. Through a performed simulation, a comparison between a mechanism using the proposed method, an unbalanced one and one only statically balanced is also provided. 2004 Elsevier Ltd. All rights reserved. Keywords: Mechanism; Robot manipulator; Balancing; Decoupling Almost every robot manipulator presents its structural topology based on mechanisms with open-loop kinematic chains for controlling the position and orientation of its end-effector in three-dimensional space (Fig. 1). According to Asada and Slotine [1], dynamic equations for this category of mechanisms can be written in the following form, * Co E-m 0094-1 doi:10 si \u00bc Xn j\u00bc1 Dij\u20acqj \u00fe Xn j\u00bc1 Xn k\u00bc1 Dijk _qj _qk \u00fe Di; i \u00bc 1; . . . ; n \u00f01\u00de rresponding author. Tel.: +55-11-3091-5760; fax: +55-11-3814-2424x217. ail address: tarcisio.coelho@poli.usp.br (T.A.H. Coelho). 14X/$ - see front matter 2004 Elsevier Ltd. All rights reserved. .1016/j.mechmachtheory.2004.02.011 where si is the driving torque (or force) acting upon ith joint; qi is the relative displacement of the ith link; _qi; \u20acqi are, respectively, relative velocity and acceleration of the ith link; the first term on the right-hand side of Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000936_j.mechmachtheory.2019.103607-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000936_j.mechmachtheory.2019.103607-Figure4-1.png", "caption": "Fig. 4. The step-by-step process of model order reduction for a single helical gear: (a) the FE model of a helical gear, (b) two sets of mode shapes adopted in the Craig\u2013Bampton method, (c) the plot of normalized amplitude (magnification factor) of a helical gear in terms of frequency ratio and the low-frequency approximation (LFA) where only the static modes are kept while the contribution of vibration modes is ignored, (d) the ALE formulation in which only the static modes of three meshing tooth-faces are considered.", "texts": [ "1 and Section 2.2 , respectively. Then, we study the interaction between the helical gear pair in Section 2.3 . Finally, the governing equations of the whole system and the integration algorithm are given in Section 2.4 . To improve computational efficiency, it is fundamental to reduce the system DOFs, which are determined by the way that generalized coordinates are selected. In this section, the selection of generalized coordinates for a single helical gear is illustrated step by step, as shown in Fig. 4 . First, under the framework of FFRF, the generalized coordinates of a helical gear are selected as q = [ r T \u03d5 T u T ]T = [ r T \u03d5 T u T 1 . . . u T n ]T , (1) where r and \u03d5 refer to the position and orientation of the floating frame, respectively. u = [ u T 1 . . . u T n ] T is the nodal displacement vector where n is the total number of FE nodes. The DOFs of this gear are 6 + 3 n, which is on the order of 10 6 due to the large number of FE nodes used to discretize the gear, as shown in Fig. 4 (a). To reduce the system DOFs, the nodal displacement vector u can be approximated by using the Component Mode Syn- thesis (CMS) method, i.e., u = \u03b7, where = [ 1 . . . m ] \u2208 R 3 n \u00d7m is the mode matrix and \u03b7 = [ \u03b71 . . . \u03b7m ] T is the modal coordinate vector with m \u2248 10 4 3 n . The columns of the mode matrix span a subspace which determines the i rate of convergence and influences the computational efficiency of the simulation. In particular, using the Craig\u2013Bampton method [26] , two sets of mode shapes are employed to represent the flexibility of gears, see Fig. 4 (b). One set is the constraint modes C (static modes), which can be obtained by giving each boundary DOF a unit displacement while holding all the other boundary DOFs fixed. The other set is the fixed-boundary normal modes N (vibration modes), which are determined by solving the eigenvalue problem with all the boundary DOFs fixed. By partitioning the system DOFs u into boundary DOFs u B and interior DOFs u I , the displacement transformation can be expressed as u = [ u B u I ] \u2248 [ C N ][\u03b7C \u03b7N ] = [ I 0 IC IN ][ \u03b7C \u03b7N ] , (2) where \u03b7C and \u03b7N are the modal coordinates of constraint modes and fixed-boundary normal modes, respectively, and IC and IN are the interior partition of constraint-mode and fixed-boundary matrices. Considering the fact that most gears in engineering machinery are very stiff, the dynamic response of the gears can be assumed as quasi-static due to the fact that the dynamic loads from gear-shaft system fall into the lower end of the spectrum and can be approximated rather accurately with low frequency approximation. Therefore, as shown in Fig. 4 (c), the DOFs of a single helical gear can be further reduced from m i + 6 zn b to 6 zn b by ignoring the contribution of vibration modes, where m i is the number of vibration modes, z the teeth number, n b the number of boundary nodes for each tooth face, and 6 zn b = z \u00b7 2 \u00b7 3 n b the number of static modes. It is noted that there are two tooth faces for each gear tooth and three DOFs for each 3D boundary node. Therefore, the total DOFs of a single helical gear are reduced to 6 + 6 zn b , and Eq", " Additionally, for a meshing gear pair, the excitation load arises from the meshing forces between the gear and pinion, and the excitation frequency is equal to the meshing frequency \u03c9 mesh . The meshing frequency is the product of the number of gear teeth z and the corresponding rotational velocity of the gear \u03c9, i.e., \u03c9 mesh = \u03c9 gear \u00b7 z gear = \u03c9 pinion \u00b7 z pinion . To avoid resonance in the system, the angular velocity of the gear pair is usually set within the sub-critical range in the design process, resulting in a meshing frequency which is much lower than the natural frequency of gears, see Fig. 4 (c). As a result, the dynamic response of the gear can be approximately regarded as quasi-static, i.e., magnification factor \u2248 1, which means it transmits the load from one gear to the other with time-variant static deformation. Therefore, in this condition, the low-frequency approximation (LFA) technique is employed to obtain sufficiently accurate results by only considering static modes, while ignoring the contribution of fixed-boundary normal modes. For example, using the gear parameters in Supplementary Materials, the upper limit of rotation speed for the helical gear can be calculated as high as 3140r/min when the requirement of LFA is satisfied, i", " In this table, the index on the left and right side of the dash (e.g. 3B and 3A in the tooth-face pair 3B-3A) refer to the tooth faces of the I-gear and J-gear, respectively, and A and B refer to the anterior and posterior faces of a gear tooth, respectively. As shown in Table 1 , at most three pairs of tooth faces may come into contact simultaneously. As a result, the FE nodes of the three tooth faces are sufficient to describe the dynamic behavior of the whole gear in all situations using the ALE formulation, see Fig. 4 (d). Hence, the vector of boundary DOFs for the ALE-like helical gear is u = [ u T I u T II u T I I I ]T , (4) where u I , u II , and u III are the elastic displacement vectors (modal coordinates) of the three meshing tooth-faces, respectively. It is worth noting that u I , u II , and u III are not associated with any specific material points, and can be tied to different material points at different times. For example, for the I-gear, u I , u II , and u III are tied to the material points of tooth-faces 3B, 2B, and 1B when 0 < t\u0304 < 0 " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003277_s004220050495-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003277_s004220050495-Figure1-1.png", "caption": "Fig. 1a,b. A manipulator consisting of three segments described by vectors L1, L2, and L3, which are connected by the three joints. The joint angles are a, b, and c. The position of the ende ector is described by vector R. Furthermore, two additional vectors D1 and D2, describing the diagonals, are shown. a The nonvectorial version as has been used in an earlier model (Cruse and Steinku\u00c8 hler 1993): b The vectorial version on which the new network is based", "texts": [ " In the feedback loop, the joint space values will therefore be transformed to workspace coordinates. This is called direct transformation. In the feedforward loop, the workspace coordinates have to be transformed into joint space coordinates, which is called inverse transformation. Here, we will concentrate only on kinematic systems. In this case, the transformations are called direct kinematics and inverse kinematics, respectively. If we deal with a redundant system, for example, when we consider a three-joint manipulator which moves in a two-dimensional plane (see Fig. 1), the direct kinematics are easy to calculate, but for the inverse kinematics there is an in\u00aenite number of solutions. Therefore, in the case of a redundant system, additional constraints are necessary to permit a unique solution. The classical servosystem has the disadvantage that it is quite slow due to the temporal delays which might be caused by computation time and, in particular in biological systems, limited signal velocity. One solution to improve the situation is to introduce an internal model of the process including inverse kinematics and use this internal model parallel to the servocontroller (e", " In an extreme case, the direct kinematic could also be solved by this model by providing as input values only the joint angles. The model consists of a recurrent network which relaxes to adopt a stable state corresponding to a geometrically correct solution, even when the input does not fully constrain the solution. The underlying idea is that several geometrical relationships are used to calculate the same value (e.g. angle b) several times in parallel. The \u00aenal output is then obtained by calculation of the mean value of these multiple computations (MMC). This is then fed back for the next iteration. As an example, Fig. 1a shows a planar, three-joint arm. In this case the value of angle b, for example, can be calculated by the following six equations: b p\u00ff arccos L2 1 L2 2 \u00ff D2 1 2L1L2 b p\u00ff b1 \u00ff b2 b e1 c1 b e\u00ff e2 c\u00ff c2 b e1 c\u00ff c2 b e\u00ff e2 c1 As these equations show, several nonlinearities occur in these calculations. In the complete set of equations, additional square root functions, recti\u00aeers, sine and cosine functions were necessary. The whole system functions as an autoassociator which completes an only partly speci\u00aeed input vector", " Second, we will expand this system by some nonlinear control structures. In this version, the system can be used to describe manipulators with \u00aexed segment lengths, and the joints may be constrained to being simple hinge joints (a short version of this is given by Steinku\u00c8 hler et al. 1995). Finally, we will give an example of the MMC net representing the geometry of a six degrees of freedom (DoF) human arm. To introduce a simple linear MMC model, we will use the manipulator with three joints in a 2D space (Fig. 1b) as an example. The net could, however, be directly extended to the 3D case and an arbitrary number of segments. The coordinates of the joints can be described in a Cartesian coordinate system x, y, the origin of which is situated in the ``shoulder'' of the manipulator. We describe the segments as vectors L1, L2, L3. For later use, we will also introduce the three angles a, b, and c which describe the relative position of the segments, as shown in Fig. 1b. Note that these are de\u00aened di erently to those used by Cruse and Steinku\u00c8 hler (1993). As in the earlier version, the vector R pointing to the ende ector, and the vectors D1, D2 describing the diagonals, are additionally introduced (Fig. 1b). For these vectors, the following seven equations hold: L3 L2 L1 \u00ff R 0 L2 R \u00ff D2 \u00ff D1 0 \u00ffL3 L1 D2 \u00ff D1 0 L2 L1 \u00ff D1 0 L3 L2 \u00ff D2 0 L3 \u00ff R D1 0 L1 \u00ff R D2 0 1 In this system, each value L1, L2, L3, R, D1, and D2 appears four times. Therefore, for each value, four of these equations can be used to calculate this value. For example, L3 could be determined by L3 \u00ffL2 \u00ff L1 R L1 D2 \u00ff D1 \u00ffL2 D2 R \u00ff D1 According to the MMC principle, all four values L3 can be summed, and this sum divided by four to obtain the mean value L3 m", " For this purpose, the desired ende ector coordinates Rx, Ry have to be given as input values for the net. The system always \u00aends a solution for the inverse problem but, as the segment lengths are not \u00aexed, they might change during relaxation. In Fig. 3a this is obvious for the basal segment L1. As an example, Fig. 3c,d shows, in the same format, the application to a two-joint, and therefore non redundant, system. Application of a graph theoretical approach leads to a more general mathematical description of a multisegment manipulator: set E {L1, L2, L3, R, D1, D2} in Fig. 1 can be viewed as the set of edges of an asymmetric, complete directed graph G (V, E) with four vertices. According to this terminology, the manipulator can, however, be identi\u00aeed with a spanning tree of G and the seven equations (1) correspond to the circuits in G. Moreover, the whole linear iterative relaxation process can be described in terms of the circuit matrix of the directed graph G. It could be shown for this system (and the general 3D version) that, from any given starting position, it always converges to a stable and geometrically correct \u00aenal state (Appendix; see also Steinku\u00c8 hler 1994)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001278_j.mechmachtheory.2020.103865-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001278_j.mechmachtheory.2020.103865-Figure7-1.png", "caption": "Fig. 7. The forces on the junctions of limbs and moving platform, and the series structure: (a) three main forces, (b) torque generated in the translation of forces.", "texts": [ " In order to ensure the reliability of the connecting pair, it is necessary to restrain the force of the bearing and the ball joint within the permissive load by constraining the relevant dimensional parameters of the series joint. To simplify the restraint process, the position where the ball joint is most stressed is selected as the assessment position. Since the robot structure is symmetrical about the coordinate plane uA 0 w , only the force projected onto the coordinate plane uA 0 w is considered. As shown in the following Fig. 7 a, the moving platform, the series joint and the spindle are regarded as a whole, the center of gravity of which is recorded as C G mp _ s _ ee . The whole body is subject to three forces: supporting force F N 12 of limb1 and limb2, supporting force F N 3 of limb3 and gravity m CG g of its own. Distance d CG represents the vertical distance from gravity center C G mp _ s _ ee to the line C 2 C 3 ; distance d S denotes the distance from point C 1 to the line along the direction of F N 3 . Distances d CG and d S are not shown in the figure below. Assume that the permissive static load of the bearing is [ C 0 ] 12 , and the permissive static load of the ball joint is [ C 0 ] 3 . The following load constraint C 3 can be obtained by the transfer of the force and the torque as shown in Fig. 7 b. s.t. \u23a7 \u23aa \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23aa \u23a9 F N12 cos \u03b11 + F \u2032 N3 sin \u03b12 = m CG g F N12 sin \u03b11 = F \u2032 N3 cos \u03b12 F N12 2 \u2264 [ C 0 ] 12 F \u2032 N3 \u2264 [ C 0 ] 3 \u03c4c 3 = \u03c4S = m CG g \u2032 d = F N3 d S = m CG g ( d \u2212 d CG ) min d = F N3 d S / m CG g \u2032 (33) where F \u2032 N3 equals to F N 3 ; m CG g \u2032 and m CG g \u2032\u2032 represent the components of m CG g at point A 1 (or A 2 ) and C 3 respectively; the torque \u03c4c 3 is produced by the translation of m CG g \u2032 from the point C 3 to A 1 (or A 2 ); the torque \u03c4 S is produced by the translation of F N 3 from point C 3 to A 1 (or A 2 )" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000302_tsmc.2016.2641926-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000302_tsmc.2016.2641926-Figure7-1.png", "caption": "Fig. 7. Estimation of unknown hysteresis density function p (t, r).", "texts": [ " 3 illustrates that the system output y = x1 (solid line) follows the desired trajectory yr (dashed line) precisely when the ASPI hysteresis compensation items are considered and the system output failed to follow the desired trajectory when the ASPI hysteresis compensation items are ignored. Fig. 4 shows the tracking errors with and without considering the ASPI hysteresis compensation items. From Fig. 4, it is obvious that the ASPI hysteresis compensation items effectively mitigate the ASPI hysteresis existing in the control system. Figs. 5 and 6 illustrate the control signal u(t) and the hysteresis output w(t) with and without considering ASPI hysteresis compensation items. Fig. 7 shows the 3-D map of the estimation of the density function p (r) defined in (8). Fig. 8 is the estimation of the norm of the ideal fuzzy vector \u03b8\u2217 := max{(1/gm)\u2016\u03d1\u2217 i \u20162 i = 1, 2} and Fig. 9 is the estimation of Rp defined in (52). B. Example 2: Adjustable Metal Cutting System In this example, a mechanical system, i.e., the adjustable metal cutting system [29] shown in Fig. 10 is considered to show the validity of the proposed controller in (63). Based on the above schematic model in Fig. 10, the mathematical model of the adjustable metal cutting system can be described explicitly by a differential equation as mx\u0308 + cx\u0307 + kx = F + kau + d(t) (82) where x represents the fluctuating part of the depth of cut m, c, and k are the equivalent mass, damping coefficient, and spring stiffness for the metal cutting machine, respectively, ka is the equivalent spring for the magnetostrictive actuator, u is the magnetostrictive actuator output, F represents the cutting force variation of the machine tool and is proved to be a nonlinear function with respect to the chip thickness variation, and d(t) denotes the disturbance from external environment" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000281_s12206-016-0823-0-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000281_s12206-016-0823-0-Figure7-1.png", "caption": "Fig. 7. The stationary coordinate system and the moving coordinate system.", "texts": [ " Similarly, the reference coordinate system of each planet gear also rotates with the planet carrier but the origin of this reference coordinate system is the center of each planet gear (refer to Fig. 5). The coordinate system of the bearing of each planet gear ( mb x , mb y ) is consistent with the coordinate system of the planet gear, which revolving around the sun gear at a rotational speed of c w with the planet carrier. Therefore, a time varying angle existed between the moving coordinate system ( mb x , mb y ) of the bearing in the coupling system and the stationary coordinate system ( sb x , sb y ) described in Sec. 2, as shown in Fig. 7. For the convenience of calculation, the expression of the supporting force of a bearing in the stationary coordinate system can be obtained and subsequently transformed to the expression of the supporting force of the bearing in a moving coordinate system. The angle between the dynamic and stationary coordinate systems at time t is c w t . Therefore, the supporting force of a bearing in a moving coordinate system can be expressed as ( ) ( ) ( ) ( ) Bx Bx Byi i i By Bx Byi i i M S c S c M S c S c F F cos w t F sin w t F F sin w t F cos w t = + = \u2212 + (30) where Bxi S F and Byi S F (See Eqs" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000084_icacci.2017.8125901-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000084_icacci.2017.8125901-Figure1-1.png", "caption": "Fig. 1. Quanser 2-DOF Helicopter [10]", "texts": [ " The paper is organized as follows: Section II presents the modeling of 2- DOF helicopter dynamics. Section III and IV present integral backstepping controller and adaptive integral backstepping controller respectively. Section V presents an interface of 2- DOF helicopter hardware system with MATLAB/Simulink and the simulation and experimental results. The conclusion and future works are available in the last Section. 2-DOF Quanser helicopter model (fixed base) with two propellers driven by DC motors, is shown in Fig. 1. The elevation of the nose over the pitch axis is controlled by the front propeller and the rotational motion around the yaw axis is controlled by the back propeller. The voltages across the pitch and yaw motors are \u00b124V and \u00b115V respectively. The pitch angle \u03b8 and the yaw angle \u03c8 represent two degrees of freedom. When the nose of helicopter goes up, we get \u03b8 > 0, and the yaw axis becomes positive when the rotation of helicopter is in the clockwise direction [12]. The helicopter model dynamics is shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000346_j.mechmachtheory.2017.09.013-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000346_j.mechmachtheory.2017.09.013-Figure3-1.png", "caption": "Fig. 3. Kinematic chain ABCDE in motion.", "texts": [ " As the screw motion equation is independent with reference coordinate system, we substitute Eq. (5) into Eq. (6) , elimi- nate $ C \u2032 , $ F and $ F \u2032 , then we have, m I l I $ A \u2212 $ B + ( m II l II \u2212 m I l I ) $ C + $ D \u2212 m II l II $ E = 0 (7) When the coincident joint F is fixed, we have, \u03b8F \u2212 \u03b8F \u2032 = K (8) where K is a constant value. When the linkage I or II is moving, as K is a constant value, the revolute variables of linkage I and II are ganged. The kinematic chain ABCDE in motion is shown as Fig. 3 . In Fig. 3 , K is a constant value, so the geometric parameters of link AE keeps constant. The geometric parameters of other links keep constant, too. When the linkages I and II move, only the lengths of m I , l I , m II , l II change, Eq. (6) always exists. For the new kinematic chain ABCDE, Eq. (7) always exists, only the coefficients changes in motion. Eq. (7) is the motion screw equation of kinematic chain ABCDE. We analyze the case when the coefficients of Eq. (7) equal zero firstly, in which case the kinematic chain ABCDE is in singular configuration, then we analyze the general case with none of coefficients equals zero" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003084_6.1998-4357-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003084_6.1998-4357-Figure2-1.png", "caption": "Fig. 2 The top view of the helicopter. The lift distribution on the rotor disk when a forward cyclic (pitch forward) input is applied. The precession effect will pitch the helicopter forward.", "texts": [ " This curve is traditionally obtained via trial and error. The yaw command controls the pitch of the tail rotor blade. The tail rotor on a helicopter is used to counteract the yaw moment created by the main rotor blade; thus, altering the amount of pitch on the tail rotor can create more or less total yaw moment for the helicopter. The pitch and roll commands influence the cyclic control, varying the cyclic pitch (8cyc} of the rotor blades around each cycle of rotation, creating different amounts of lift in different regions (as shown in Figure 2). These differing amounts of thrust create a moment around the rotor hub, and can thus create pitch and roll moments on the helicopter. Before developing the dynamic equations, we introduce some basic aerodynamic terms that will be required. The advance ratio, /z, and the descent ratio, v, represent the airspeed components parallel to and perpendicular to the rotor disk respectively.17 They are close to zero when the helicopter is hovering. Both quantities are non-dimensionalized by R\u00a3lJ To define these quantities, we first need to find the velocity of the hub point with respect to the inertial coordinate frame represented in body coordinates", ") of the flybar and the position and angular velocity (\u00a3, Q) of the main rotor blade. As mentioned before, the flybar plays a major role in augmenting the stability of the helicopter. This system is often called as a Bell-Hiller mixer, because it takes advantage of two different cyclic control systems, as shown in Figure 5. Cyclic control is the mechanism by which the rotor blade's pitch is changed in a rotation so that an unequal distribution of the lift applies a moment around the rotor hub. This moment then provides pitch and roll attitude control as depicted in Figure 2. The Bellmixer allows the blade pitch to be changed directly from the cyclic servo actuator. It is fast in response, but lacks stability. Meanwhile, the Hiller-mixer allows the pitch of the flybar to be changed instead of the pitch of the blade. The flybar then flaps, and this flapping motion causes the pitch of the main blade to change. There is a direct relationship between the cyclic input applied to the main blades 6cyc (which is .the function of stick commands 6s and 6$) and the cyclic angle of the rotor blades 8cyc", " acts to apply an appropriate compensation input to the main blade cyclic control system to stabilize the helicopter. Actuator dynamics Once the flybar dynamics have been found, the rest of the actuator dynamics can be derived. The thrust generated by the rotor blade is T, and the moments represent the moments created by the rotor blade around the roll and the pitch axes are M^ and Me respectively. The moment created by a roll cyclic input is derived by summing the forces around a revolution and along a rotor blade. As per Figure 2, a positive pitch input 5g produces roll moment M$, but acts as pitch moment Me due to the precession effect.16 2ir i-R = 5/7m Jo Jo r sin \u00a3 dL We assume that the rotor angular velocity is constant; thus \u00a3 = Qi. The lift element equation is similar to the flybar lift used in equation (10). dLm = -f ecyc - cdr - sin^ - - cost (13) The induced air velocity V{ must be derived empirically.16 However, it is usually of similar magnitude around the rotor disk, especially in hover or lowvelocity motions" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003607_978-1-4020-2249-4_29-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003607_978-1-4020-2249-4_29-Figure3-1.png", "caption": "Figure 3. Kinematic structure of a fully-isotropic parallel manipulator with different structural solutions for Al and A2", "texts": [ " The elementary kinematic chains A3 and A4 composing D2 have the following arrangements of joints: A3 ~-Rz-Rz) and A4 ~-Pz-Rz-Rz-Rz-Rz). The complex kinematic chain D2 is obtained by connecting A3 and A4 by the three revolute joints R2, R3 and R4 which axes are parallel with the rotation axis of the moving platform (z axis). The two examples presented in Figs.2 and 3 have: AI(J:O-2-3-4-5), A2(1:0-6-7-8-5), A3(1:0-9-10-11) and A4(1:0-12-13-14-15-16-17). The moving platform is n:17. The example presented in Fig. 2 has identical structural solutions for Al ~-Rx-Rx-Rx) and A2 (Ey-Ry-Ry-Ry). The example presented in Fig. 3 has other two distinct solutions for Al ~-Rx Pyz-Rx) and A2 (Ey-pz-Ry-Ry). An approach has been proposed for structural synthesis of a family of fully-isotropic T3Rl-type parallel manipulators. Special legs were conceived to achieve fully-isotropic conditions. As far as we are aware this paper presents for the first time fully-isotropic parallel manipulators with four degrees of mobility and a method for their structural synthesis. This work was sustained by CNRS (The French National Council of Scientific Research) in the frame of the project ROBEA-MAX (Complex Architecture Machines) 2002-2003" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000716_j.mechmachtheory.2019.07.013-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000716_j.mechmachtheory.2019.07.013-Figure3-1.png", "caption": "Fig. 3. Generation of the conical spur involute gear.", "texts": [ " The upper sign in matrix M ba corresponds to left tooth surface of the rack, and the lower to the right. \u03b1n represents the pressure angle measured on the normal plane of the rack cutter. Dimension L d is calculated as: L d = \u03bb\u03c0m n 2 ( 1 + \u03bb) cos \u03b1n (4) where, \u03bb = s 0 w 0 (5) m n is the module of the rack cutter. Parameter \u03bb represents the ratio between the blank and tooth thickness of the rack cutter measured on the pitch line, and typically \u03bb= 1. Generation of tooth surfaces of the conical spur involute shaper is implemented by a rack cutter in a conical blank. Fig. 3 shows the profile crowned rack cutter meshing with the being-generated conical spur involute shaper. It also provides the coordinate systems applied for the determination of tooth geometries of the conical spur involute shaper. Coordinate systems S s and S r are attached to the conical spur involute shaper and the rack cutter, respectively. A fixed coordinate system S e is rigidly connected to the spatial frame and used as a reference system. S d is an auxiliary coordinate system. Tooth surfaces s of the conical spur involute shaper are conjugated as an envelope set of tooth surfaces r of the rack cutter, and can be defined in the coordinate system S s as: { r s ( u s , l s , \u03c8 s ) = M se ( \u03c8 s ) M ed M dr r r ( u s , l s ) f rs ( u s , l s , \u03c8 s ) = n r ( u s ) \u00b7 v rs r ( u s , l s , \u03c8 s ) = 0 (6) where, M se ( \u03c8 s ) = \u23a1 \u23a2 \u23a3 cos \u03c8 s sin \u03c8 s 0 0 \u2212 sin \u03c8 s cos \u03c8 s 0 0 0 0 1 0 0 0 0 1 \u23a4 \u23a5 \u23a6 (7) M ed = \u23a1 \u23a2 \u23a3 1 0 0 s c 0 1 0 \u2212r ps 0 0 1 0 0 0 0 1 \u23a4 \u23a5 \u23a6 (8) M dr = \u23a1 \u23a2 \u23a3 1 0 0 0 0 cos \u03b4 sin \u03b4 0 0 \u2212 sin \u03b4 cos \u03b4 0 0 0 0 1 \u23a4 \u23a5 \u23a6 (9) Here, s c is the displacement of the rack cutter along the axis z r of coordinate system S r during meshing with the conical spur involute shaper" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000346_j.mechmachtheory.2017.09.013-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000346_j.mechmachtheory.2017.09.013-Figure7-1.png", "caption": "Fig. 7. Configuration III for the combination of two Bennett linkages.", "texts": [ " Fix the coincident joints F and F \u2032 , eliminate the coincident links CF and C \u2032 F \u2032 , then in the obtained kinematic chain, the offsets of joints A and E are both zero, the link length is d = b + b , the twist of link AE is \u03b1 = \u03b2 + \u03b2 . AE I II AE I II (III) In this configuration, we have K = 0 and b I = b II . According to the properties of Bennett linkages, if the two linkages are not coincident, we have \u03b2I + \u03b2II = \u03c0 . The links AF and EF \u2032 are coincident now. After the similar construction we have that the length of link AE equals zero, the joints A and E becomes to a U joint, the angle from joints A to E equals \u03b2I \u2212 \u03b2II . In Fig. 7 , thick dash line indicates the coincident links AF and EF \u2032 . (IV) In this configuration, we have K = 0 and b I = b II , then links AF and EF \u2032 are in a straight line but their length are not equal. After the similar construction, we have that, the length between joints A and E is not zero but equals d AE = | b I \u2212 b II | , the offsets of joints A and E equal zero, the twist of new link EA is \u03b1EA = \u03b2II \u2212 \u03b2I . In Fig. 8 , the thick dash line indicates the coincident part of links AF and EF \u2032 . From the above analysis we conclude that the angle K has no effect on the DOF of the linkage" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001089_tia.2020.3046195-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001089_tia.2020.3046195-Figure3-1.png", "caption": "Fig. 3. Meshes of cooling water jacket concept.", "texts": [ " Applying (7), the momentum equation for the MRF in terms of the absolute velocity is \u2202 (\u03c1u) \u2202t +\u2207 \u00b7 (\u03c1umu) + \u03c9m \u00d7 u = \u2212\u2207p+\u2207 \u00b7 \u03c4 + \u03c1s. (8) Polyhedral mesh is used for all domains with cell sizes varying from 0.8 to 2 mm. The wall Y+ in the turbulent flow domain has significant effect on the pressure drop and heat transfer calculation. The y+ is kept to less than 1 in the 90% of the total surface of the wall of interest to get consistent solution by setting near wall cell height to 0.01 mm with the body-fitted prism layer mesh. Fig 3 shows the volume mesh of the steady-state cooling jacket thermal flow simulation of the spiral concept, containing 1.7 million cells approximately. 50%\u201350% water ethylene glycol is used as coolant, with inlet mass flow rates of 3 and 10 LPM (liter per minute) and temperature of 75 \u00b0C at the jacket inlet, and atmospheric pressure and temperature of 80 \u00b0C at the jacket outlet. The jacket wall temperature is set to 100 \u00b0C in the steady-state cooling jacket thermal simulations indicated in Fig. 3. Fig. 4 shows the volume mesh of the transient state full motor thermal simulation, including the outer and inner shells, cooling jacket, stator, slot liners, windings, rotor, magnets, shaft, and air volume inside the motor, with 23 million cells approximately. Modeling of the surrounding air effect is simplified to convection boundary condition on the motor surfaces exposed to the air, as Authorized licensed use limited to: Central Michigan University. Downloaded on May 14,2021 at 13:37:14 UTC from IEEE Xplore" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001059_j.mechmachtheory.2020.104101-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001059_j.mechmachtheory.2020.104101-Figure8-1.png", "caption": "Fig. 8. Modified mechanism with translational drives (named as the linearly adjustable 4-bar mechanism).", "texts": [ " 7 was chosen as the most appropriate and useful for adaptation to the complex knee movement. This solution is the 4-bar mechanism ( Fig. 2 ), which has already been applied for knee joint modelling. However, in this case it is further enhanced by introducing additional DOFs. The exploration process and the whole variety of achieved solutions were presented in previous work [32] . The chosen solution (that relates to Fig. 7 ) was first modified by adding prismatic joints to bars (2, 3) in order to introduce the two additional DOFs ( Fig. 8 ). However, the same motion can be achieved by applying 2-link modules that are driven by rotational motors, thus obtaining the new solution that is presented in ( Fig. 9 ). This paper is focused on the rotationally adjustable 4-bar mechanism from Fig. 9 . It has two additional DOFs (total of 3 DOFs calculated using the Kutzbach-Gr\u00fcbler equation) with rotational motors (R 1 , R 2 ) instead of cylinders (S 1 , S 2 ), which were previously used in paper [33] . Each 2-link module is composed of 2 rotationally connected elements, which can be seen in Fig", " IC R Z = W Z W m = \u2212P B v YC + P C v Y B v ZB v YC \u2212 v ZC v Y B IC R Y = W Y W m = \u2212P C v ZB + P B v ZC v ZB v YC \u2212 v ZC v Y B (7) where: P B = \u2212 ( v ZB Z B + v Y B Y B ) P C = \u2212 ( v ZC Z C + v YC Y C ) and: The results of the four performed types of simulations are listed in Table 1 together with the acquired numerical values that are further shown in the plots of Figs. 16 to 19 . In order to obtain the driving forces of the mechanisms\u2019 motors, a vertical force V = 1 kN ( Fig. 11 ) is assumed on the femoral link, simulating human body weight. For both mechanisms (the rotationally adjustable 4-bar mechanism in Fig. 11 and the linearly adjustable 4-bar mechanism in Fig. 8 ), and in all simulations, the calculations are performed to find the ICR trajectory according to the previously described procedure ( Fig. 15 and Eq. (7) ). Fig. 16 shows the Walker et al. trajectory (I) and the two example trajectories (II, III \u2013 the named boundary trajectories) in order to cover a range of possible paths. This is due to the fact that the knee joint\u2019s ICR trajectory is different for each individual person. The performed simulations can be summarised as follows: \u2022 Ex.1 \u2013 the Walker et al", " 7 that is identified to model approximately the kinematic mobility of knee. Moreover, even if the ICR trajectory could be achieved more accurately by using a mechanism with other dimensions, e.g. as shown in [24] with a mean error of 0.2 mm, the trajectory could still not be fully reproduced. Even more important is that such a mechanism would only be useful in the case of this one particular knee joint\u2019s ICR trajectory. For these reasons, by applying 2 additional DOFs, as the prismatic joints in the crossing bars, a linearly adjustable 4-bar mechanism is obtained in Fig. 8 . It is a compromise solution with structure simplified to planar motion, but it has the ability to reproduce the knee movement with a satisfying accuracy. Nevertheless, the prosthesis solution in Fig. 8 cannot be considered feasible from biomechanical viewpoint both for the sliders and the overall size. Thus, the solution is converted in the linkage design to the rotationally adjustable 4-bar mechanism in Fig. 9 made of revolute joints only (except for the main linear motor). Therefore its mechanical design with reduced sizes can be more convenient for rehabilitation or orthopaedic implementation. Moreover, the new mechanism\u2019s main advantage is the possibility of real-time control, as well as being able to alter the dimensions of a 4-bar mechanism during motion" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000346_j.mechmachtheory.2017.09.013-Figure12-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000346_j.mechmachtheory.2017.09.013-Figure12-1.png", "caption": "Fig. 12. Constructing process of 6R-L SLOL.", "texts": [ " The configuration in Table 6 is the case when b III < b II . When b III > b II , we have d CE = b III \u2212 b II . For 6R-B-F SLOL, the configuration in Table 6 is the case b I < b II , b III < b II . 3.2.3. Three Bennett linkages arranged in L shape Take three Bennett linkages ABCH,C \u2032 H \u2032 FG \u2032 , EGC \u2032\u2032 D with the parameter as below: { a I = a II , b II = b III \u03b1I = \u03b1II , \u03b2II = \u03b2III (35) Where I, II, III indicate the linkages ABCH, C \u2032 H \u2032 FG \u2032 , EGC \u2032\u2032 D. Arrange the three linkages in L shape, as in Fig. 12 , eliminate the overlapped links CH, C \u2032 H \u2032 , C \u2032 G \u2032 , C \u2032\u2032 G, fix the coincident joints H, H \u2032 , G \u2032 , G, translate the coincident joints C, C \u2032 , C \u2032\u2032 to a single joint C, then we obtain a new single loop kinematic Table 4 ( continued ) In Fig. 12 , we apply configuration I to both parts 1 \u00a9 and 2 \u00a9. In this case, the offsets for joints A, E, and F are all not equal to zero, it is also the general form of L shaped 6R Goldberg linkage [4,13] . Similar to Sections 3.2.1 and 3.2.2 , we can apply other configurations to parts 1 \u00a9 and 2 \u00a9 to obtain linkages with zero joint offsets. The detail is shown as below. For the linkages in Table 8 , the 6R-L-B is a 6R 5-bar linkage, joints A and F are translated to a U joint. The 6R-L-D is a 6R 4-bar linkage, joints A, E and F are merged to a spherical joint" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003511_s0094-114x(00)00024-0-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003511_s0094-114x(00)00024-0-Figure2-1.png", "caption": "Fig. 2. Geometry of the straight-edged cutting blade.", "texts": [ " The proposed analysis procedures and the developed computer programs are most helpful in designing and analyzing worm gear sets, as well as in designing oversize hob cutters. The ZN-type worm is cut by a straight-edged cutting blade, and the cutting blade is placed on the groove normal section of the produced worm, as shown Fig. 1. Parameter b1 is the lead angle of the worm. The surface equations of the straight-edged cutting blade, represented in the blade coordinate system Sc Xc; Yc; Zc , as shown in Fig. 2(b), can be expressed by: xc rt l1 cos a1; yc 0; 1 zc l1 sin a1; where l1 is the surface parameter of the straight-edged cutting blade and lmin6 l16 lmax. Design parameter a1 is the half-apex blade angle formed by the straight-edged cutting blade and Xc-axis, as shown in Fig. 2(a) and (b). The plus sign of zc expressed in Eq. (1) is associated with the righthand cutter blade and the minus sign of zc is associated with the left-hand cutter blade. The cutting blade width must equal the normal groove width of the produced worm, design parameter rt can be obtained from Fig. 2(c) and (d), which can be represented as follows rt r2 1 \u00ff s2 n 4 sin2 b1 r \u00ff sn 2 tan a1 ; 2 where r1 is the pitch radius and sn the normal groove width of the produced worm. The ZN-type worm is cut by a straight-edged cutting blade placed on its groove normal plane. Therefore, the ZN-type worm surface is the locus of the cutting blade, and the worm surface geometry depends on the design parameters of the cutting blade and on machine-tool settings. The ZN-type worm cutting mechanism can be simpli\u00aeed by considering the relative motion of a straight-edged cutting blade performing a screw motion along the worm rotation axis" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003052_s101890050039-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003052_s101890050039-Figure3-1.png", "caption": "Fig. 3. Law of corresponding cones (2D view in the plane of the ellipses).", "texts": [ " If two FCDs are in contact at two points like M and P (to simplify matters, the reader may visualize C1 and C2 as two ellipses, and C \u2032 1 and C \u2032 2 as two hyperbolae, see Figures 3 and 4, but the result does not depend on such a specialization), then indeed the cones of revolution with the common vertex M and resting, respectively, on C \u2032 1 and C \u2032 2 are identical, because they have the same axis (the tangent to C1 and C2 at M), and a point in common, point P . Since they coincide, C \u2032 1 and C \u2032 2, being on the same cone, have two intersections, P and Q. In other words, two FCDs that have one common generatrix and two contacts on their generating conics, obey l.c.c. The law of corresponding cones leads to the geometrical construction of Figure 3. If two conics are coplanar, the triples F1, M , F \u2032 2, and F \u2032 1, M , F2, are aligned; F1, F2, F \u2032 1, F \u2032 2, are the foci of C1 and C2. Point A is the common projection of the two intersections P and Q of C \u2032 1 and C \u2032 2. Figure 1 of reference [7] illustrates l.c.c. in the coplanar case for a photograph by C. Williams. Figure 4 restitutes in 3D the continuity of cyclides along the generatrices of contact in the case of two incomplete FCDs obeying l.c.c. The points of contactM and P are the centers of curvature of the Dupin cyclides passing through all the points \u00b5 on the segment MP , whether they are considered to belong to one FCD or to the other" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003068_jsvi.1997.1298-Figure12-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003068_jsvi.1997.1298-Figure12-1.png", "caption": "Figure 12. Schematic of experiment used for the forced response study.", "texts": [ " This is obvious from a large change in natural frequencies of individual ring gears when they are meshed with each other. Once the eigensolutions have been obtained for a disk-shaft sub-assembly, the modal superposition method can be used to calculate forced response characteristics such as sinusoidal transfer functions. Dynamic compliance HP/Q and accelerance AP/Q between points P(rP , uP ) and Q(rQ , uQ ) on a disk-shaft subassembly are given as follows where yr (rP , uP ) and yr (rQ , uQ ) are the deformation of the rth mode at points P and Q (see Figure 12), vr and jr are the rth natural frequency and modal damping ratio, respectively, and v is the excitation frequency: HP/Q (v)= rP FQ (v) = s NS r=1 yr (rP , uP )yr (rQ , uQ ) (v2 r \u2212v2)+2jjr vvr , AP/Q (v)= aP FQ (v) = s NS r=1 \u2212yr (rP , uP )yr (rQ , uQ ) v2((v2 r \u2212v2)+2jjr vvr ) . (46a, b) Here, rP and aP are dynamic displacement and acceleration respectively at point P due to a sinusoidal force FQ applied at point Q. The series can be truncated to NS modes depending on the frequency range of interest", " T 8 Natural frequencies of single mesh gear assembly VI as obtained from FEM and MBD formulation; see Table 1 for gear specifications Natural frequencies vnr (Hz) Mode ZXXXXXXXXXCXXXXXXXXXV r MBD FEM e%\u2020 1 0 0 0\u00b70 2 159 155 2\u00b75 3 198 190 0\u00b70 4 284 275 3\u00b72 5 429 416 3\u00b70 6 479 466 2\u00b77 7 526 510 3\u00b70 8 526 510 3\u00b70 9 604 608 0\u00b77 10 617 610 1\u00b71 11 673 704 6\u00b70 12 677 707 4\u00b70 13 834 855 2\u00b75 14 893 904 1\u00b72 15 893 904 1\u00b72 16 894 904 1\u00b71 17 894 904 1\u00b71 18 963 928 3\u00b76 19 968 953 1\u00b75 20 981 968 1\u00b73 21 1008 997 1\u00b71 22 1118 1073 0\u00b70 23 1264 1264 0\u00b70 24 1264 1264 0\u00b70 25 1265 1264 0\u00b71 26 1265 1264 0\u00b71 27 1290 1334 3\u00b74 28 1291 1334 3\u00b73 29 1647 1692 2\u00b77 30 1648 1692 2\u00b77 \u2020 e%= =vn,FEM \u2212vn,MBD = vn,FEM \u00d7100. An experimental clamp was built to simulate the gear-shaft interface at the inner edge (ri ) of annular gear-like disks as shown in Figure 12. The characteristics of this clamp-disk assembly is described by the authors in reference [23]. An electrodynamic shaker (5-lb force) was attached at point Q and an accelerometer at P to obtain the cross-point and driving point accelerances. The dimensions and other relevant data of several annular-like disks used in this study are given in Table 10. Figures 13\u201315 show the measured accelerances. In particular, Figure 13(a) compares the experimental with the analytical driving point accelerance (AQ/Q ) obtained by using equation (31b) for the annular-like disk no. 1. This resembles an annular plate. Experimental values of damping ratios were used in the analytical formulation. Predicted and experimental accelerance transfer functions compare well. Next, the accelerometer was located at point P (Figure 12) to obtain the cross-point accelerance which is shown in Figure 13(b). Again, the overall characteristics of two accelerance plots are similar except between 1000 and 1700 Hz where the experimental data has several resonance peaks that are not predicted by the modal superposition method. In reference [23], it has been shown that this clamp, like any other real life clamping condition, does not act as a perfectly rigid support, but has some dynamic characteristics of its own which couple with those of the disk" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000343_ec-03-2017-0086-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000343_ec-03-2017-0086-Figure2-1.png", "caption": "Figure 2. Relationship between the rack cutter and generated FS", "texts": [ " Hence, the unit normal vector n i\u00f0 \u00de a of the two regions of the rack cutter can be derived as follows: n i\u00f0 \u00de a \u00bc N i\u00f0 \u00de a N i\u00f0 \u00de a (5) Substituting equations (2) and (3) into equation (4) yields the unit normal vector n 1\u00f0 \u00de a and n 2\u00f0 \u00de a represented in coordinate system Sa (Xa, Ya) as follows: Straight-edge region: n 1\u00f0 \u00de a \u00bc n 1\u00f0 \u00de ax n 1\u00f0 \u00de ay 8< : 9= ; \u00bc 7sina1 cosa1 ( ) (6) where the upper sign and lower sign in \u201c7\u201d represent the left and right sides of the rack cutter, respectively. Rounded-tip region: n 2\u00f0 \u00de a \u00bc n 2\u00f0 \u00de ax n 2\u00f0 \u00de ay 8< : 9= ; \u00bc 6sin d S cos d S ( ) (7) where the upper sign and lower sign in \u201c6\u201d represent the left and right sides of the rack cutter, respectively. Figure 2 illustrates the relative movement between the rack cutter and the generated FS. The coordinate systems S0 (X0, Y0) and Sa (Xa, Ya) are rigidly connected to the rack cuter and the center of generated FS, respectively. Symbol r1 denotes the pitch radius of the generated FS. During the generating process, the axode p of the rack cutter translates r1f 1, whereas the FS rotates counterclockwise with an angle of f 1. Accordingly, the loci of the rack cutter can be transformed to the coordinate system S0 (X0, Y0) by the following homogeneous coordinate system transformation matrix: R i\u00f0 \u00de 0 \u00bc M0a\u00bd R i\u00f0 \u00de a (8) Study of a harmonic drive 2111 D ow nl oa de d by S ou th er n C ro ss U ni ve rs ity A t 0 6: 17 2 0 O ct ob er 2 01 7 (P T ) where M0a\u00bd \u00bc cos\u00f0f 1\u00de sin\u00f0f 1\u00de r1\u00f0cos f 1 \u00fe f 1 sin f 1\u00de sin\u00f0f 1\u00de cos\u00f0f 1\u00de r1\u00f0sin f 1 f 1 cos f 1\u00de 0 0 1 2 4 3 5" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003451_robot.2001.933226-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003451_robot.2001.933226-Figure5-1.png", "caption": "Figure 5: Photo of a piezoleg and sketch of its cross section", "texts": [ " The required bend direction m of each, piezoleg is calculated by transferring the coordinates of all three ball axes into the coordinate system of the piezoleg (e,,e,,eJ. The absolute values of these vectors are the desired turning velocities around these axes. The resulting bending vectors of the leg can be summed up, since the rotation axes are perpendicular to each other [7]. 391 0 2.1.1. Compensation of the anisotropic bending The legs are tube-shaped piezoelectric actuators. The outer electrode of these tubes is divided into four parts (see Figure 5) . Thus, the legs can be bent in all directions by applying voltages (+150 V) between one or more of the outer electrodes and the inner one. In Figure 5 , an example for such a bending situation is shown in the cross section of a leg. For a desired bending direction the necessary voltage of the electrodes can easily be calculated from the corresponding components of this vector. However, in diagonal directions, four electrodes (two contracting and two expanding) cause the bending while in horizontal and vertical direction only two electrodes are involved. Therefore, the diagonal component of the cal- behavior of the piezolegs culated vector must be weakened by the factor 40.5 . Otherwise, the bending is distorted towards the diagonal causing e.g. a tilting of the turning axes of the manipulator ball. The vector addition for this compensation is shown in Figure 5 resulting in a corrected vector. Using its components for driving the electrodes results in a leg bending in the desired direction. 2.1.2. \u201cGear change\u201d Some manipulating experiments as shown in Figure 3 with relatively large microobjects have been performed with open-loop control. In this object range above 100 pm, the fast slip-stick moving principle is employed that is also used for driving the robot over long distances across the microscope stage. In this mode, the force (and torque, respectively) applied on the knob of the 6Dmouse, which is a measure for the desired speed of the robot\u2019s movement in the corresponding axes, determines the frequency of microsteps" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001393_j.conengprac.2020.104721-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001393_j.conengprac.2020.104721-Figure1-1.png", "caption": "Fig. 1. Quadrotor with coordinate systems.", "texts": [ " Section 3 presents the proposed MUDE attitude control law, and the stability analysis is given in . The experimental setup and obtained results are given in Section 5. Finally, Section 6 concludes this paper. In this section, the quadrotor attitude and actuator models used for the controller design are presented. First, the attitude dynamic model is built and linearized using feedback linearization techniques. Second, the actuator model is introduced, and the identification results are presented. r B t d \ud835\udc3d \ud835\udc85 i a \ud835\udf49 b As shown in Fig. 1, the quadrotor platform with an X airframe configuration is used in this work, and it is controlled by four motors that are mounted on the end of the arm. Euler angles \u0398 = [\ud835\udf19, \ud835\udf03, \ud835\udf13] are used to express the orientation of the quadrotor, where \ud835\udf19 is the oll angle, \ud835\udf03 is the pitch angle, and \ud835\udf13 is the yaw angle, respectively. y applying the so-called small angle approximation (Lu et al., 2018), he attitude dynamics of the quadrotor in the inertial frame can be escribed as ?\u0308? = 1 \ud835\udc3d\ud835\udc65\ud835\udc65 [ ( \ud835\udc3d\ud835\udc66\ud835\udc66 \u2212 \ud835\udc3d\ud835\udc67\ud835\udc67 ) " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000775_tro.2019.2906475-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000775_tro.2019.2906475-Figure1-1.png", "caption": "Fig. 1. General CDPR geometry.", "texts": [ " Section III proposes the idea of adding two pendulum actuators to the mobile platform for regulating out-of-plane vibrations. Section IV describes the test setup used for obtaining experimental results and the developed prototype reaction system. Section V presents a summary of the observed experimental performance of the proposed reaction system. This section briefly presents a general CDPR kinematic and dynamic model. For a more in-depth analysis on CDPR modeling, the reader is referred to [21]. Considering the rigid platform presented in Fig. 1, the length of the ith cable li is obtained as li = \u221a (ai \u2212 bi) T (ai \u2212 bi) (1) where vectors ai and bi, respectively, correspond to the fixed-frame and platform cable attachment points in the global frame. For a given robot pose p = [x, y, z]T , bi can be found as bi = p+Rg pri (2) where ri is the offset from the platform center to the platform cable attachment point in the platform-fixed frame andRg p is a rotation matrix (defined by the Euler angles {\u03b8x, \u03b8y, \u03b8z}) that transforms ri from the 1552-3098 \u00a9 2019 IEEE" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001427_j.mechmachtheory.2021.104300-Figure13-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001427_j.mechmachtheory.2021.104300-Figure13-1.png", "caption": "Fig. 13. Joint constraints for workspace analysis.", "texts": [ " The mechanism\u2019s constraints determine the shape and dimensions of the workspaces. We can specify the following ones for the considered manipulator: 1) Constraints on the generalized coordinates: q i min < q i < q i max , (43) where q i min and q i max are the lower and the upper bounds for q i . 2) Constraints on the angles in spherical joints B j , C j , and S i : \u2223\u2223\u03b2Si \u2223\u2223 < \u03b2Si max , \u2223\u2223\u03b2Cj \u2223\u2223 < \u03b2Cj max , \u2223\u2223\u03b2Bj \u2223\u2223 < \u03b2Bj max , (44) where \u03b2Si is the angle between link S i A j and unit vector n Si , parallel to axis O i Y i ( Fig. 13 ); \u03b2Cj is the angle between link A j B j and unit vector n Cj , perpendicular to the base plane; \u03b2Bj is the angle between link A j B j and unit vector n Bj , perpendicular to the platform; \u03b2Si max , \u03b2Cj max , and \u03b2Bj max are the maximum allowed values of the angles above. 3) Constraints on the angles between links S i A j and A j B j : \u2223\u2223\u03b2Ai \u2223\u2223 > \u03b2Ai min , (45) where \u03b2Ai is the angle between links S i A j and A j B j , and \u03b2Ai min is its minimum allowed value. Angle constraints (44) and (45) can be represented graphically by the cones ( Fig. 13 ): links S i A j and A j B j should stay inside the cones with vertices at points S i , C j , and B j , and link S i A j should be outside the cone in A j . One can easily find angles \u03b2Si , \u03b2Cj , \u03b2Bj , and \u03b2Ai from the following expressions ( Fig. 13 ): \u03b2Si = arccos ( \u2212n T ASi n Si ) , \u03b2Cj = arccos ( \u2212n T ABj n Cj ) , \u03b2Bj = arccos ( \u2212n T ABj n Bj ) , \u03b2Ai = arccos ( n T ASi n ABj ) , (46) where n ASi = ( p Si \u2212 p Aj ) /L ASi , n ABj = ( p Bj \u2212 p Aj ) /L ABj , (47) n Si = n Cj = [ 0 0 1 ]T , n Bj = R pl [ 1 \u22123 , 3 ] . Notation R pl [1\u20133, 3] in (47) represents the third column of the platform rotation matrix R pl . 4) Previously, during the velocity analysis, we have found that there is a singular configuration when intermediate link S i A j is perpendicular to the slider guide (see (37) ), in other words: SA T i z i = 0 " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001756_j.mechmachtheory.2021.104345-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001756_j.mechmachtheory.2021.104345-Figure5-1.png", "caption": "Fig. 5. The coordinate system.", "texts": [ " For straight edge profile, position vector r p and normal vector n p of cutting cone are expressed as follows: 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 \u03b8p 1 \u23a4 \u23a5 \u23a6 (4) n p ( \u03b8p ) = [ cos \u03b11 cos \u03b8p cos \u03b11 sin \u03b8p \u2212 sin \u03b8p ] (5) where s p and \u03b8p represent cutter-head parameters, R p represents cutter radius, and \u03b11 represents profile angle. For tool tip fillet, position vector r p and normal vector n p of cutting cone are expressed as follows: r p (\u03b8, \u03b8p ) = \u23a1 \u23a2 \u23a3 ( C x + \u03c1p sin \u03b8 ) cos \u03b8p ( C x + \u03c1p sin \u03b8 ) sin \u03b8p \u2212( C y \u2212 \u03c1p cos \u03b8 ) 1 \u23a4 \u23a5 \u23a6 (6) n p (\u03b8, \u03b8p ) = [ sin \u03b8 cos \u03b8p sin \u03b8 sin \u03b8p cos \u03b8p ] (7) where C x and C y represent center coordinates of tool tip fillet, and \u03c1p represents fillet radius. Fig. 5 shows the coordinate system between cutter-head and pinion, where S p and S 1 are connected with pinion and cutter-head, respectively. What should be mentioned here in detail is that \u03d5p represents cradle rotation angle, \u03d51 represents pinion rotation angle, S r 1 represents cutter radial setting, q 1 represents initial cradle angle setting, E m 1 represents vertical offset, X represents sliding base feed setting, X represents increment of machine center to back and \u03b3 represents b 1 G 1 1 machine root angle" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000036_iecon.2016.7793436-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000036_iecon.2016.7793436-Figure1-1.png", "caption": "Figure 1. STA\u0308UBLI TX90L on linear axis at its final configuration along the given path.", "texts": [ " Therein, a nullspace basis of the velocity Jacobian is computed. A linear combination of its basis vectors is then added to the IK equation to fully exploit possible internal motion. The balance of the elements in the linear combination is subjected to a trajectory optimization scheme such that time-optimal trajectories are obtained. The effectiveness of both methods will be shown in the example of a STA\u0308UBLI TX90L industrial robot with 6 DOF that is mounted on a 1 DOF linear axis as depicted in Fig. 1. The manipulator\u2019s task is to track a given path where the EE position and orientation is specified, except for the rotation about one axis yielding a task-redundant system of degree 2. With the IK problem treated by the aforementioned approaches, the overlying trajectory optimization problem is formulated by means of direct multiple shooting and solved using an interior-point method. In the next section, the problem of kinematic redundancy and time-optimal trajectory planning for given EE paths will be described in detail", " deviations from the given task space path. The aforementioned joint quantities are required to compute the constrained joint torques (33). Equation (34) is required to close the state integration gaps between adjacent shooting intervals. As this NLP is non-convex, globally optimal solutions cannot be guaranteed. Solutions obtained from this problem depend on the initial guess. The manipulator considered in this example is a STA\u0308UBLI TX90L industrial robot with 6 DOF that is mounted on a 1 DOF linear axis, as depicted in Fig. 1. In total, the manipulator consists of n= 7 actuated joints. Limitations apply to its joint positions q and velocities q\u0307 as well as to its motor torques Q. A model for the dynamics of the robot is given as its equations of motion, derived using the Projection Equation [16]. As shown in Fig. 1, in this example, the robot is set to track part of an elliptic curve with semi-axes 0.4 m and 0.5 m with its EE whose orientation such that the Ex axis is perpendicular to the plane with the path. Note that the rotation about this axis is free, thus a 5 DOF task is created. The described task space is of dimension l = 5, the degree of task redundancy is (n\u2212 l) = 2. The robot\u2019s initial configuration is chosen as q0, its final pose qN is not specified and thus result of the optimization. The motion is required to be performed as a rest-to-rest maneuver, i" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000716_j.mechmachtheory.2019.07.013-Figure17-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000716_j.mechmachtheory.2019.07.013-Figure17-1.png", "caption": "Fig. 17. Simulation model of the ground face gear of case 1.", "texts": [ " Only slight difference in the number of the grinding tracks is discovered for the face gears in case 1 \u223c case 4. A simulation platform of face gear grinding based on QMK50A five-axis CNC machine tool is developed by using Vericut software ( Fig. 16 ). The relative motion coordinates between the face gear and the grinding disk wheel for the grid nodes grinding of the tooth surface of the face gear for case 1 \u223c case 4 have been obtained from the calculation of the envelope residuals of the gear tooth surfaces. Fig. 17 shows the model of the ground face gear of case 1. The partial enlargement of one ground space of the gear tooth is exhibited at the left side. The overlapping surfaces of the ground gear tooth and the theoretical gear tooth, which is generated by the geometry theory of the face gear drive, are given at the right side of Fig. 17 . The working surfaces of the ground face gear are in good agreement with the tooth surfaces of the theoretical face gear. However, the residual materials are discovered at the fillet surfaces and the root of the ground face gear tooth. The deviations between the ground tooth surfaces and the theoretical tooth surfaces of the face gear for case 1 \u223c case 4 are shown in Figs. 18\u201321 . The gouge check and the excess check are performed by the auto-diff function of the Vericut software. The results indicate that, for all numerical cases in Table 1 , only deviations of excess exist on the ground tooth surfaces of the face gear" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001780_tro.2021.3082020-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001780_tro.2021.3082020-Figure7-1.png", "caption": "Fig. 7. Closed-loop response (black) to step and sinusoidal input (yellow) for isolated segment (distal) and direction (sensor 1) of a serpentine continuum manipulator with tubular ionic liquid stretch sensor feedback. Gray lines mark standard deviation for 40 acquisitions, ranging from a maximum 1.4% to a minimum 0.6% of the continuum segment length.", "texts": [ " This warm-up time (measured to be 10\u201312 min regardless of sensor length or degree of degassing) was attributed to a relaxation effect as described in [55], where the potential difference across the sensor creates a field that Authorized licensed use limited to: BOURNEMOUTH UNIVERSITY. Downloaded on July 03,2021 at 07:42:14 UTC from IEEE Xplore. Restrictions apply. forces the long anion molecules into alignment with the smaller cations. A proportional-integral-derivative (PID) control scheme was implemented to drive each of the four bending degrees of freedom. Each sensor axis was tuned and tested in isolation with a planar target trajectory (a number of \u03c0 6 steps and a 0.6 rad amplitude sine curve) along the sensor direction of bend. Fig. 7 shows the results of one of the distal segment sensors, with the target shown in yellow, an example acquisition shown in black and a range of plus\u2013minus one standard deviation from the mean of 40 acquisitions shown in gray, ranging from a maximum 1.4% to a minimum 0.6% of the segment continuum length (with minimal variability for all four sensors). The PID controller with resistive stretch sensor feedback achieved accurate tracking with various inputs (maximum tip deviation was 1.8% of the segment continuum length) with all four sensors showing similar results in isolation (1" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000027_s00170-016-9596-y-Figure10-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000027_s00170-016-9596-y-Figure10-1.png", "caption": "Fig. 10 Calibration models for dimension compensation in Zdirection. a CAD model. b SLMprocessed parts", "texts": [ " The principle of dimensional compensation method is that: CADmodel DCZ\u00f0 \u00de \u00bc Target dimension DTZ\u00f0 \u00de \u00fe Systemic error \u0394ZZ\u00f0 \u00de \u00fe Shrinkage error \u03b4ZZ\u00f0 \u00de \u00f010\u00de Namely, all the errors (including the systemic and random error) that occur during the SLM process are added to the dimensions of CADmodel as compensations during the CAD model design stage. The systemic error was determined by a trial and error testing conducted by Wang [32], and it was fixed at +30 \u03bcm in the current study. The shrinkage error can be calculated as follows: \u03b4ZZ \u00bc DTZ\u2212\u0394ZZ\u00f0 \u00de\u22c5FZ \u00f011\u00de A contrast testing was conducted to verify the dimension compensation. As shown in Fig. 10a, two step models were designed. The designed height of each layer was 5 mm. One of the models did not compensate the shrinkage while the other one did. The shrinkage error of each layer is 0.12 mm, namely, the height of each layer of CAD model is 5.15 mm. Both the two-step models were manufactured with the optimized process parameters obtained in Section 3.4; the asprocessed models are shown in Fig. 10b. The measuring points were arranged at the four corners of each layer, as shown in Fig. 10a. Eachmeasuring point was measured thrice, and the average value of four points was considered as the actual dimension of Z1\u2013Z5, the result is shown in Table 6. It is evident that the error rates of the samples without dimension compensation range from 2.4 to 3.2 %, while those with dimension compensation are less than 0.8 %. It is demonstrated that the dimension compensation is beneficial for improving the dimensional accuracy of SLM-processed parts. One of the shortcomings of SLM-processed parts lies in the surface roughness, which generally requires surface treatments such as grinding, sanding, and polishing" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003876_978-1-4612-4990-0-Figure23-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003876_978-1-4612-4990-0-Figure23-1.png", "caption": "Figure 23. Spool valve with no solenoids activated.: All four lines are isolated from one another.", "texts": [ " The limits of motion for the foot as defined by the hip joint and actuators. ................................ 29 Figure 17. The natural motions of the machine. ........................ 30 Figure 18. Single ended cylinder. ................................... 32 Figure 19. Double ended cylinder. .................................. 32 Figure 20. Parts of a spool valve. ................................... 33 Figure 2I. Spool valve with left solenoid activated. ..................... 34 Figure 22. Spool valve with right solenoid activated. .................... 34 Figure 23. Spool valve with no solenoids activated. ..................... 35 Figure 24. A spool valve with thin lands in the center position. ............ 35 Figure 25. Standard symbols for spool valves. ......................... 36 Figure 26. Flow of inhibition in the walking program. ................... 39 List of Illustrations xiii Figure 27. Figure 28. Figure 29. Figure 30. Figure 31. Figure 32. Figure 33. Figure 34. Figure 35. Figure 36. Figure 37. Figure 38. Figure 39. Figure 40. Figure 41. Figure 42", " The two solenoids are mounted on opposite ends of the body so that when one has current flowing in it the spool moves to that end of the body. When no solenoid is turned on a spring returns the spool to a central position. There are four connections to the valve, labeled A, B, P, and T. Figure 21 shows the configuration when the left solenoid is activated. In this configuration the line labeled A is connected to T and the one labeled B is connected to P. Figure 22 Section 4.4 Hydraulic system 33 shows the configuration when the right solenoid is activated, connecting lines Band T together and lines A and P. Finally, Figure 23 shows the spool valve when neither solenoid is activated and the spring has returned the spool to the middle position, blocking all lines. Other configurations of spool valves may be achieved by altering the width of the lands. Figure 24 shows a spool valve with narrower lands in the center position with both solenoids off. In this configuration all four of the lines are connected together. The other two configurations of this valve have the same properties as the valve shown in Figure 21 and Figure 22" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003388_978-3-662-04831-3-Figure1.10-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003388_978-3-662-04831-3-Figure1.10-1.png", "caption": "Fig. 1.10: Roller rig and bogie", "texts": [ "7 that includes three rigid-bodies subject to large spatial motion (ram, pitman, and eccentric drive), additional16 rigid bodies that model small spatial deflections of the frame, and several revolute and universaljoints as well as various springs and dampers ([14], [15], [16]); or 2. the model of a loaded roller rig of Figures 1.8, and 1.9, 1.10, 1.11 and 1.12 that includes more than 60 rigid bodies (most subject to small spatial motion), connected by various revolute, prismatic, and universal joints, and driven by several servo-hydraulic actuators (compare the technical drawing of the roller stand of Figure 1.10), and that includes models of the rolling contact of elastic bodies in the presence of dry friction; ([17], [18], [19]); 8 1. Introduction 1.4 Prototype applications of rigid-body mechanisms 9 10 1. Introduction (a ) F ro nt v ie w fr on ta l w he el ( r) (c ) H or iz on ta l pr oj ec ti on (d ) E ng in ee ri n g m o d el f or v ib ra ti on a na ly si s F ig . 1. 6: S te er in g m ec ha ni sm o f an a ut om ob il e ..... . ;... '\"0 ..... 0 '\"\"'\" 0 '\"\"'\" '< : \"0 ct> \"' \"0 '2 . ('; ' ~ c;\u00b7 1:1 [/ ) 0 " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000310_icrom.2016.7886777-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000310_icrom.2016.7886777-Figure4-1.png", "caption": "Figure 4. Situations in which using stepping strategy is not possible.", "texts": [ " However the contact between the foot and floor is a unilateral constraint and if the ankle torque will become too large, the ZMP will be move beyond the edge of the foot and the foot will start to rotate. In case of a larger disturbance the capture point will be left the support polygon. Angular momentum of the upper body can be generated in the direction of the disturbance by applying a torque on the hip joint or arm joint as shown in Fig. 3(b). This strategy also called CMP Balancing. With increasing the disturbance the useful strategy will be steeping Fig. 3(c), however there are several situations might occur where stepping is not possible as shown in Fig. 4. In this situation the balance recovery by Hip-Ankle strategy is necessary [11]. Moreover in the situations that contact surface is small such as right side of Fig. 4, generating upper body angular momentum for balance recovery is unavoidable. In this paper the Hip-Ankle strategy is combined in single MPC scheme that will be presented in the following section. III. PUSH RECOVERY CONTROLLER Let us discretize (6), the dynamic equation of LIPM+flywheel. Considering as the look ahead time interval. Because of LIPM dynamics is decoupled in sagittal and frontal plane. Here we discretize the sagittal plane and it can be repeated for frontal plane similarly. Therefore we obtain: = (1 \u2212 ) + (10) = (1 + ) + \u2212 ( , + , ) + , = , + , , = , + , This system can be re-written in discrete state-space form: = + (11) Where = , , , , are states variable and = , are control inputs, the last state variable will be activated in a step-time that push is exerted by defining \u03bc, therefore when push is exerted we have \u03bc = 1 and in the other step-times is zero, therefore we have: = (1 \u2212 ) 0 0 00 (1 + ) \u22120 0 1 0 00 0 0 1 00 0 0 0 \u03bc = 0 00 0000 0 (12) Given a sequence of control inputs , the linear model in (11) can be converted into a sequence of states, , for the whole prediction horizon, = + = \u2026 = \u2026 (13) Where And are defined recursively from (12)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003451_robot.2001.933226-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003451_robot.2001.933226-Figure4-1.png", "caption": "Figure 4: 6D-mouse [6] (left) and sketch of the piezolegs and the manipulator ball (right)", "texts": [ " It is desirable that the tweezers have a kind of intelligence to be able to avoid obstacles and perform difficult tasks as the releasing of objects automatically. This can be achieved by using the sensor system described in chapter 2.2. The flexibility of the microrobots is also advantageous in the assembly of hybrid microsystems, especially at development stages when single parts have to be handled and the final tolerances are not yet determined. As an example, Figure 3 shows the teleoperated microassembly of a micro gear with the help of a 6D-mouse (Figure 4) and an additional lateral miniature camera. The 6D-mouse is a very intuitive and sensitive user interface. Besides the transition data, it directly provides the desired turning angles of the manipulator. To move the manipulation unit accordingly, the bend direction of each piezoleg must be calculated from these turning angles. This is shown in Figure 4 (right) for the rear leg and the yaw axis (b), exemplarily. The required bend direction m of each, piezoleg is calculated by transferring the coordinates of all three ball axes into the coordinate system of the piezoleg (e,,e,,eJ. The absolute values of these vectors are the desired turning velocities around these axes. The resulting bending vectors of the leg can be summed up, since the rotation axes are perpendicular to each other [7]. 391 0 2.1.1. Compensation of the anisotropic bending The legs are tube-shaped piezoelectric actuators" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000913_j.mechmachtheory.2019.06.026-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000913_j.mechmachtheory.2019.06.026-Figure8-1.png", "caption": "Fig. 8. Dynamic model of the wind turbine drivetrain.", "texts": [], "surrounding_texts": [ "Similarly, based upon Eqs. (1) , (10) , and (13) , the kinetic energy of components, including parallel stage gears ( g = u ),\nimpeller ( g = 20 ), and generator rotor ( g = 21 ), is obtained as\nT kin _ 2 =\n1\n2\n\u2211\ng = u\n[ ( v I g )T M g ( v I g ) + ( w I g )T J g ( w I g )] + 1\n2\n21 \u2211\ng =20\n[ ( v I g )T M g ( v I g ) + ( w I g )T J g ( w I g )] (43)\nBased upon Eq. (37) , the kinetic energy of flexible shafts is\nT kin _ 3 =\n\u2211\nT kin _ \u05d2 (44)\nwhere \u05d2 ( \u05d2 = 7, 8, 10, 11, 12, 14, 15, 16, 18, 19) denotes the serial number of the shaft element referring to Fig. 5 .\nThe total kinetic energy of the system is\nT kin = T kin _ 1 + T kin _ 2 + T kin _ 3 (45)\n3.5.2. Potential energy\nThe elastic potential energy of gear mesh deformations is\nU m\n=\n1 ( k G 1 G 2 2 G 1 G 2 + k G 3 G 4 2 G 3 G 4 ) + 1 \u2211 N\ni =1\n( k spi 2 spi + k rpi 2 rpi ) (46)\n2 2", "The elastic potential energy of bearing deformations is\nU b =\n1\n2\n\u2211 l= s,r,c ( X T l K b l X l ) + 1\n2\n\u2211 N\ni =1\n( T\ncpi K b i cpi\n) + 1\n2\n\u2211 [ ( X\ns H ) T K b H X s H\n] (47)\nwhere cpi denotes the bearing deformation vector between the carrier and the i th planet [22] . H = 7, 9, 10, 13, 14, 16, 19.\nBased upon the Eq. (38) , the elastic potential energy of flexible shafts is\nU s =\n\u2211\nU b _ \u05d2 (48)\nThe elastic potential energy of the connection between components q and p is [22]\nU link =\n1\n2\n\u2211 ( T\nqp K qp qp\n) (49)\nwhere K qp represents the connecting stiffness matrix, and qp denotes the deformation vector between components q (18, s , and 17) and p ( c , 8, and 21).\nAccording to Eqs. (20) and (39) , the gravitational potential energy of CMCs is\nU g _ CMC =\n\u2211\ng = l, i,u\nU g _ g +\n21 \u2211\ng =20\nU g _ g (50)\nin addition, the gravitational potential energy of flexible shafts is\nU g _ sha f t =\n\u2211\nU g _ \u05d2 (51)\nThen, the total potential energy of the system is\nU = U m + U b + U s + U link + U g _ CMC + U g _ sha f t (52)\n3.5.3. Equations of motion\nThe generalized displacement vector X of the system is defined as\nX = ( X\nT s , X T r , X T c , X T 1 , . . . , X T N , X T 7 , . . . , X T 17 , X T 18 , . . . , X T 20 , X T 21\n)T (53)", "Substituting Eqs. (45) , (52) and (53) into the Lagrange\u2019s equation in Eq. (54) [28,32,33] , the equations of motion of the\nsystem are obtained as shown in Eq. (55) .\nd\nd t\n( \u2202 T kin\n\u2202 \u02d9 X\n) \u2212 \u2202 T kin\n\u2202X\n+\n\u2202U\n\u2202X\n= F (54)\n( M G + M s ) \u0308X + [ C m + C s + C t + C b + ( \u02d9 \u03b8 z I \u2212II C G _ I \u2212II + \u02d9 \u03b8 z III C G _ III ) + ( C tr F _ I \u2212II + C tr F _ III )] \u02d9 X\n+ [ K m + K s + K t + K b + ( \u02d9 \u03b8 z c )2 K + \u03b8\u0308 z c K A + ( K tr F _ I \u2212II + K tr F _ III )] X = F + F tr F _ I \u2212II + F tr F _ III (55)\nwhere\nF = ( 0 , . . . , 0 , M x , 0 , . . . , 0 , T m , 0 , . . . , 0 , . . . , T em ) T (56)\nin which M G is the mass matrix of CMCs, and M s denotes the mass matrix of flexible shafts. K m ( C m ) is the mesh stiffness (damping) matrix, K s ( C s ) is the stiffness (damping) matrix of flexible shafts, K t ( C t ) is the connecting stiffness (damping) matrix, K b ( C b ) is the bearing stiffness (damping) matrix, K is the centripetal stiffness matrix, and K A is the tangential stiffness matrix. C G _ I\u2212II is the gyroscopic matrix of CMCs, and \u02d9 \u03b8 z I\u2212II denotes the corresponding rotational speed matrix. \u02d9 \u03b8 z III and C G _ III are the rotational speed and gyroscopic matrices of flexible shafts, respectively. M x is the non-torque load, T m is the aerodynamic torque, and T em is the electromagnetic torque. C m is obtained by the empirical formula [25] . C s , C t , and C b are derived by the proportional damping [25] . Owing to the platform motions, there occur the additional matrices, including\nstiffness matrices K tr F _ I\u2212II and K tr F _ III , damping matrices C tr F _ I\u2212II and C tr F _ III , and force excitation matrices F tr F _ I\u2212II and F tr F _ III , which are detailed in Appendixes A and B . The total number of DOFs of the wind turbine drivetrain is 6( N + 3) + 6 P + 1, where N\nand P are numbers of planets and flexible shaft nodes, respectively.\nWhen the platform is fixed and the frame F t b is parallel to F o , C tr F _ I\u2212II , C tr F _ III , K tr F _ I\u2212II , K tr F _ III , F tr F _ I\u2212II , F tr F _ III are vanished.\nM G , M s , C m , C s , C t , C b , K m , K s , K t , K b , and F are similar to Refs. [22,23] . K , K A , and C G _ II (the gyroscopic matrix of CMCs in the planetary gear stage) are similar to the Ref. [24] , and C G _ III and C G _ I (the gyroscopic matrix of CMCs in the parallel gear stage) are similar to Refs. [32,33] .\n4. Dynamic analysis\nWind turbine drivetrain is a typical transmission system with the large mass and mass moment of inertia for each\ncomponent [22] . The external excitations, including wind and wave, are in low-frequency range for an offshore wind turbine\n[27] . Therefore, the low-order vibration modes attract more attention. Table 2 [22] lists the first four modes of the system,\nignoring the damping terms, force excitation terms, and platform motions in Eq. (55) . The corresponding mode shapes of\nthe main shaft are presented in Fig. 9 . The first one ( f 0 ) is the rigid body mode where the natural frequency is zero due to rotating freely. The natural frequency corresponding to the second mode ( f 1 ) is 1.94 Hz, where the mode shape is the rotation of the system. The third mode ( f 2 ) contains the lateral and rocking motions of the main shaft along X L and Y L axes (defined in the Ref. [11] ), respectively. The fourth mode ( f 3 ) is comprised of the lateral and bending motions of the main shaft along Y L and X L axes, respectively." ] }, { "image_filename": "designv10_11_0000034_s12206-016-1103-8-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000034_s12206-016-1103-8-Figure2-1.png", "caption": "Fig. 2. Meshing process of a gear pair.", "texts": [ " For simplicity, the rectangular wave function is used to approximate the mesh stiffness in this paper, where it represents the transition between single tooth contact and double tooth contact. The mesh damping ( ) jc t is related to mesh stiffness jk by a timeinvariant damping ratio jx as follows: 2 ( )j j j eqc k t Iz= , 1,2j n= L , (15) where ( )2 2/eq p g p bg g bpI I I I R I R= + is the equivalent mass. 2.5 Time-varying friction force ( )j fF t The meshing process of a spur gear pair is determined by the rigid gear geometry. Fig. 2 shows the meshing process of a gear pair at the beginning of the mesh cycle where tooth pair 2 just enters the mesh zone at point A and tooth pair 1 simultaneously contacts at point C . When tooth pair 2 accesses to point B , tooth pair 1 is about to exit the meshing zone at point D . P is the pitch point where the relative sliding velocity between the pinion and gear reverses, resulting in a reversal of the friction force. And the friction forces with a periodically varying coefficient of friction in the meshing tooth pairs are derived as follows: ( ) ( ) ( )sign( )j j j f w sF t t F t um= , 1,2j n= L , (16) where ( )j tm is the time-varying coefficient of friction due to varying mesh properties and lubricant film thickness as the gears roll through a full cycle" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001563_s00170-021-07221-0-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001563_s00170-021-07221-0-Figure7-1.png", "caption": "Fig. 7 Position of ball, inner, and outer rings before and after loading: (a) part of the bearing structure and (b) schematic of position", "texts": [ " The rotor eddy current loss of the permanent magnet synchronous motor is expressed as Hr \u00bc \u03c1rl\u222cJ 2ds \u00f024\u00de whereHr denotes the eddy current loss of rotor; \u03c1r and l are the resistivity of the rotor material and the axial length of the rotor, respectively; J denotes the induced eddy current density; and s represents the cross-sectional area of the rotor. As a crucial parameter in the thermal network model, the frictional heat generated by the bearing should be considered and calculated accurately. The definition of the position angle for the bearing balls is shown in Fig. 6, and the position of ball and the inner and outer rings before and after loading is illustrated in Fig. 7.Without loss of generality, the curvature center of the bearing outer raceway is assumed to be fixed in this work. Under the action of force F = [Fx, Fy, Fz, Mx, My], the relative displacement \u03b4 (\u03b4 = [\u03b4x, \u03b4y, \u03b4z, \u03b8x, \u03b8y]) in the bearing occurs. In consideration of frictional heat, the thermal displacement u (u = [ua, ur]) in the bearing is generated. At high speed, the centrifugal displacement uc is produced by the bearing. As shown in Fig. 7, at the position angle \u03a8j, the relative axial distance A1j and radial distance A2j between the bearing inner and outer raceways can be expressed as follows: where parameter B is written as B = fi + fo \u2212 1; fi and fo represent the curvature radius coefficients of the inner and outer raceways, respectively; Db is the diameter of the ball; \u03b10 is the initial contact angle of the bearing; \u0394a and \u0394r denote the total relative axial and radial displacements in the bearing, respectively; and uc represents the centrifugal displacement of the inner raceway, which has been calculated in Jorgensen and Shin [8]", "5); and ur represents the radial thermal displacement in the bearing and is expressed as ur \u00bc \u03b3i\u0394Tidi \u00fe \u03b3s\u0394Ts 1\u00fe \u03bcs\u00f0 \u00de\u2212\u03b3i\u0394Ti\u00bd d 2 di \u2212\u03b3h\u0394Th 1\u00fe \u03bch\u00f0 \u00deDo\u2212\u03b3b\u0394TbDb cos\u03b1i \u00fe cos\u03b1o\u00f0 \u00de \u00f031\u00de where \u03b3i, \u03b3s, and \u03b3h denote the thermal expansion coefficient of the inner ring, spindle, and bearing housing, respectively;\u0394Ti, \u0394Ts, and \u0394Th represent the temperature variation of the inner ring, spindle, and bearing housing, respectively; \u03bcs and \u03bch are the Poisson\u2019s ratios of the spindle and bearing housing, respectively; d denotes the bearing inner diameter; and di and Do are the diameters of the bearing inner and outer raceways, respectively. From Fig. 7, the geometrical compatibility equation in the bearing can be written as A1 j\u2212X 1 j 2 \u00fe A2 j\u2212X 2 j 2\u2212 f i\u22120:5\u00f0 \u00deDb \u00fe \u03b4ij 2 \u00bc 0; \u00f032\u00de X 1 j 2 \u00fe X 2 j 2\u2212 f o\u22120:5\u00f0 \u00deDb \u00fe \u03b4oj 2 \u00bc 0; \u00f033\u00de where X1j and X2j denote the axial and radial distances between the ball and curvature centers of the outer raceway, respectively, and \u03b4ij and \u03b4oj are the contact deformation values of the inner and outer raceways contacting with the ball, respectively. As shown in Fig. 9, force is loaded on the ball. On the basis of outer raceway control theory, the gyroscopic moment on the ball is prevented by the contact friction between the ball and the outer raceway at high speed; otherwise, it is equally shared by the friction in the contact area" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003519_robot.1997.619323-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003519_robot.1997.619323-Figure1-1.png", "caption": "Fig. 1: Three axis robot model", "texts": [ " The numerical calculation is accomplished using the steepest gradient method, and it can be formulated as where: K is a vector which is chosen sf as to allow the convergence of updating process. a + i l ( 2 5 i 5 N - 2) is the control point of the B-Spline. The weight parameter p ( t ) is renewed by (28), only if (25) is not satisfied. By this algorithm, (25) is maintained and (15) is minimized. I t is clear that the inverse matrix calculation is not needed, which consequently, makes the calculation very simple. 241 7 4 4.1 Model and Assumptions The described method is applied to a three-axis manipulator with redundant degree-of-freedom as shown in Fig. 1. The parameters of the motor drivers and the robot manipulator are listed in the table I. Simulations and Experiments on a redundant manipulator L [ml r iml M 1x01 U1 #2 #3 0.40 0.30 0.30 0.15 0.10 0.70 5.0 2.0 1 .o 4.2 Simulation Results The first trajectory (# 1 line) is a straight line from point \"A\" to point \"B\" as shown in Fig. 2. The initial position (A) in the joint space is (30\", 30\u00b0, 30\") that means end-effector position (0.76,0.50)(m), and the final position (B) is selected as (0.10,0" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003540_0005-1098(92)90158-c-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003540_0005-1098(92)90158-c-Figure4-1.png", "caption": "FIG. 4. Convergence of function to its desired form as the number k of steps of the algorithm increases. Algorithm AL, target function 4.14 (dashed-line), memory responses f (solid lines), cyclic training s o = 12,", "texts": [ " The desired responses used in the learning algorithms are either directly the target function values, i.e. rj = f(sj) , (4.17) which is the undisturbed case, or they are disturbed by adding to the target function values some white noise with a Gaussian distribution, zero mean and standard deviation o so that rj = / ( s j ) + n(j) . (4.18) The disturbances in general introduce inconsistencies in the equations (3.2). The equations always start with all weights x i set equal to zero. In all experiments p = N + p - 1. Figure 4 gives an example of how a memory response looks typically in different stages of the learning process. The accuracy of the memory response after k training steps is expressed by the root mean square error erms(k): 1 N-- I \"1 t/2 erms(k ) . . . . - i n _ , },/2 xlO0% (4.19) s~o (f(s))2 Learning in the CMAC or AMS has the properties that (i) in general the reproduction error e,m~(k) does not necessarily decrease monotonically with k and (ii) variations of minor experiment parameters such as So or 40 may result in substantial deviations in the learning process" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001319_tec.2020.3007802-Figure13-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001319_tec.2020.3007802-Figure13-1.png", "caption": "Fig. 13. The zeroth mode vibration caused by: (a) Zeroth order force, (b) 36th slot order force, (c) 72th slot order force, (d) All force.", "texts": [ " Integer slot PM motors Using the same method and process as the 10p/12s PM motor above, the vibration accelerations of the 6p/36s PM motor can be obtained. The radial force density varying with time and space is shown in Fig.11. Fig.12 indicates the spatial harmonic distribution of the force density at slot frequency (900Hz), and the amplitudes of 0-, 36-, 72-, and 108-order components are 968, 23895, 5441 and 4899N/m2 respectively. It can be seen that the amplitude of the slot-order force is larger than that of the 0-order force. Fig.13 presents radial vibrations of the stator when different forces are loaded. Authorized licensed use limited to: University of Exeter. Downloaded on July 16,2020 at 00:15:50 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. It can be concluded from Fig.13 that both the 0-, 36-, and 72-order force densities can cause the zeroth mode vibration. The maximum values of the surface vibration of the stator caused by the 0-, 36-, and 72-order force densities are 0.027, 0.1692, and 0.016m/s2 respectively, and the zeroth mode vibration caused by the 36-order force density is more than 6 times of that by the 0-order force density, which matches with the analysis in Fig.5. When all the force are loaded, the vibration acceleration is 0.172m/s2, which indicates that the zeroth mode vibration at slot frequency is mainly contributed by the 36-order force", "17, the measured and simulated vibration acceleration of the integer slot PM motor is presented as the speed is 1500r/min. The rotation frequency fr is 25Hz, and the 1st slot frequency (Zfr) is 900Hz. The measured and simulated vibration acceleration of the motor at 900Hz are 0.172m/s2 and 0.187m/s2 respectively, which is consistent with each other. The vibration mode shape which is extracted from the relative phase of the vibrations of fifteen accelerometers is drawn in Fig.18, and it shows a zeroth mode when the frequency is 900Hz. This is consistent with the simulation result in Fig. 13. Authorized licensed use limited to: University of Exeter. Downloaded on July 16,2020 at 00:15:50 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. VII. CONCLUSION In this paper, the mechanical pivot role that the tooth plays in force transmission and vibration analysis is introduced and illustrated" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001406_tmag.2021.3057391-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001406_tmag.2021.3057391-Figure7-1.png", "caption": "Fig. 7. Selection of design variables.", "texts": [ " The conventional GA is a search method that cannot consider the mutual influence between the design variables and is easy to fall into the local optimal situation [8]. While the MOGA is a multi-objective optimization method adopting the concept of Pareto ranking, which can generate a series of Pareto optimal solutions for selection according to the specific requirements. Compared with GA, the MOGA is more efficient and readily available globally optimal solution. The optimal design process by MOGA is shown in Fig. 6. The design variables are selected as shown in Fig. 7, which optimization ranges are determined as shown in (5). The optimization objective functions are established as shown in (6), and the design constraints are set to avoid magnetic flux leakage between magnetic poles as shown in (7). 1) Design Variables: 2.5 mm \u2264 hPM (Thickness of PMs) \u2264 4 mm 10\u25e6 \u2264 \u03b8Alnico (Radian of Alnico) \u2264 40\u25e6 0\u25e6 \u2264 \u03b8Air (Radian of Air) \u2264 10\u25e6 10\u25e6 \u2264 \u03b8NdFeB (Radian of NdFeB) \u2264 30\u25e6 \u221220\u25e6 \u2264 \u03b1 (Current phase angular) \u2264 20\u25e6. (5) 2) Optimization Objective Functions: Maximize the average torque (T ) Minimize the torque pulsation (Tr ) Minimize the torque cost (Tc)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000674_s1560354718070122-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000674_s1560354718070122-Figure4-1.png", "caption": "Fig. 4. Typical dependences of the angular velocity \u03c9 on time for \u03d5(t) = \u03b1 sin\u03a9t+ \u03b2 and for the fixed parameters J1 = 30, J2 = 3,M = 3, c1 = 2, c2 = 1, \u03b5 = 1, \u03b4 = 2, \u03b1 = 1 3 , \u03a9 = 1, \u03b2 = 0 and initial conditions t = 0, v2 = 0.", "texts": [ "2), we rewrite the absolute angular velocity of the first platform in the form \u03c9(t) = G1(t)t+ F1(t), G1(t) = k sin\u03d5(t)e\u03b4\u0394(\u03d5(t)) ( J1 sin 2 \u03d5(t) +M(c1 cos\u03d5(t) + c2)2 ) 1 2 , F1(t) = \u2212f(t) sin\u03d5(t) + c2\u03d5\u0307(t) c1 cos\u03d5(t) + c2 . Depending on the average value of the function G1(t) for period T \u3008G1\u3009 = 1 T T\u222b 0 G1(t)dt, we can single out two cases: REGULAR AND CHAOTIC DYNAMICS Vol. 23 Nos. 7\u20138 2018 \u2014 \u3008G1\u3009 = 0, then, as t \u2192 +\u221e, the angular velocity \u03c9(t) has infinitely many zeros, the distance between which is equal to T (see Fig. 4a); \u2014 \u3008G1\u3009 = 0, then the average value of the angular velocity \u03c9(t) increases linearly for period T (see Fig. 4b). The expression which determines the angle of rotation of the first platform \u03c8 is represented as \u03c8(t) = 1 2 \u3008G1\u3009t2 +G2(t)t+ F2(t), G2(t+ T ) = G2(t), F2(t+ T ) = F2(t). For a complete description of the motion of the Roller Racer in the inertial coordinate system, it is necessary to analyze quadratures for the coordinates x and y of the attachment point of the platforms. This problem remains open. Numerical experiments show that in the case \u3008G1\u3009 = 0 and at a small amplitude of oscillations of \u03d5(t), the Roller Racer starts from rest and performs for some time directed motion with an REGULAR AND CHAOTIC DYNAMICS Vol" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000356_j.ifacol.2017.08.1823-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000356_j.ifacol.2017.08.1823-Figure4-1.png", "caption": "Fig. 4. Hexrotor with Tilted Fixed-Pitch Propellers", "texts": [ " Based on this intuition, the following repulsion term is proposed \u03c1c(v) = \u2212 max { \u03b6\u2212\u03c7(v) \u03b6\u2212\u03b4 , 0 } max {\u221a v2\u03c6 + v2\u03b8 , \u03b7c } 03\u00d71 v\u03c6 v\u03b8 0 , (32) 12 [B\u22121]i is defined as the i-th row vector of matrix B\u22121. 13Since \u03c7(v) is not a class C1, one would have to define its gradient using non-smooth analysis. Proceedings of the 20th IFAC World Congress Toulouse, France, July 9-14, 2017 Bryan Convens et al. / IFAC PapersOnLine 50-1 (2017) 12715\u201312720 12719 where \u03b7c > 0 is a smoothing parameter and where \u03b6 > \u03b4 is an influence margin such that \u03c7(v) \u2265 \u03b6 implies \u03c1c(v) = 0. 6. SIMULATIONS The fully actuated UAV used in the following simulations is illustrated in Fig. 4. The control inputs are generated by six motors (Antigravity MN2214 T-MOTOR), all equipped with 10inch fixed-pitch propellers. These actuator modules are characterized by the lift and drag coefficients: cLi = 8.996\u00d710\u22126Ns2 and cDi = 1.799\u00d710\u22127Nms2. The lower and upper saturation limit are umin = 0(rad/s)2 and umax = 7.555\u00d7 105(rad/s)2, respectively. The centers of pressure are positioned coplanar, with angles of 60\u25e6 between the radii of the adjacent propellers and with \u2016pAi M \u2016 = 0.254m. The propellers are tilted about two different axes such that the combined thrust vectors span the space of the cartesian forces and torques and full controllability of the 6 degrees of freedom is guaranteed" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000009_ijius-10-2015-0012-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000009_ijius-10-2015-0012-Figure5-1.png", "caption": "Fig. 5. Take-off motion Fig. 6. Landing Motion", "texts": [ " If the speeds of all rotors are the same then no moment about the yaw axis is created. By altering the rpms of the sets of counter rotating rotors, a moment will be created and the copter will yaw. Quadcopter has four inputs, and essentially the thrust is generated by the propellers attached to the rotors. The speed of each motor is controlled independently, and the motion or direction of quadcopter is controlled by varying the speed and direction of each motor. Take-off motion is the motion that lifts the quadcopter from ground to hover position. As shown in Fig. 5 there are total four motors, two rotating in the clockwise direction and two rotating in counter clockwise direction. To fly the quadcopter in hover position, increase the speed of each rotor simultaneously. For landing the quadcopter to ground decrease the speed of each rotor simultaneously as shown in Fig. 6. D ow nl oa de d by U ni ve rs ite L av al A t 0 4: 49 1 3 M ay 2 01 6 (P T ) Forward motion of the quadcopter is controlled by increasing the speed of the rear rotor and decreasing the speed of the front rotor simultaneously as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001292_00207721.2020.1746436-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001292_00207721.2020.1746436-Figure1-1.png", "caption": "Figure 1. Quadrotor UAV scheme.", "texts": [ " (5) Owing to the theoretical analysis, the design policy is investigated and made clear. The PPC technique is adopted to ensuremoderate constraints without very small prescribed ultimate error bounds which may make some internal signals sensitive, whereas the DOBs are used to achieve sufficiently small ultimate control errors. (6) Finally, extensive simulation results are provided to verify the theoretical results. Let B = {XB,YB,ZB} be the body-fixed frame, and E = {Xe,Ye,Ze} be the earth-fixed frame as shown in Figure 1. Define p = [px, py, pz]T and v = [vx, vy, vz]T as the position and velocity vectors of the origin of the body-fixed frame related to that of the earth-fixed frame, q = [\u03c6, \u03b8 ,\u03c8]T as the Euler angle vector in the earth-fixed frame, and = [\u03c9x,\u03c9y,\u03c9z]T as the attitude angular velocity vector in the body-fixed frame. The mathematical model is established as the following (Carrillo et al., 2013; Nonami et al., 2010). p\u0307 = v, mv\u0307 = \u2212mgsI + FT + d, (1) q\u0307 = W(q) , J\u0307 = \u2212 \u00d7 J + \u03c4 + \u03c4 d, (2) where, sI = [0, 0, 1]T , m is the total mass of the quadrotor, g is the gravity acceleration, FT \u2208 R 3 is the translational driving force vector, J(q) = diag(Jx, Jy, Jz) is the inertial matrix, \u03c4 = [\u03c4x, \u03c4y, \u03c4z]T is the driving torque vector" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000469_j.matlet.2019.05.027-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000469_j.matlet.2019.05.027-Figure2-1.png", "caption": "Fig. 2. Simulated gra", "texts": [ " To ensure simulation efficiency, some small details in DED solidification which are not critical will be ignored according to Wei, Elmer, and DebRoy\u2019s research [15]. The critical simulation parameters were referred from the journal [7] published by Rodgers, Madison, and Tikare. These parameters are listed include 2 kW laser power, 4 mm spot size, 600 mm/ min transverse speed, and two scanning patterns. A simulation domain in this study is shown in Fig. 1. A rectangular coating patch (24.5 mm X 24.5 mm X 3 mm) was deposited through DED with two different scanning patterns. The powder material is stainless steel 304L. Three observation views (shown in Fig. 2) were chosen to entirely observe the grain morphology. In top view, most of columnar elongated grains formed between adjacent scanning paths, while fine equiaxed grains appeared near the center line of scanning path. The primary reason for these morphologies is the varying melted pool movement in DED process. DED\u2019s fundamentals are local and mobile melting/solidification thanks to the highly energy-concentrated laser beam\u2019s transverse movements and continuous powder input. As the melted pool moves forward, the trailing area solidifies, then steep temperature gradient causes grains to grow quickly", " The columnar grains formed under bidirectional scanning pattern did not have obvious crescentic shapes, but had morphologies close to linear segments. The front view is the coating\u2019s cross section. In the front view, a faint melt pool profile is visible. Small equiaxed grains are shown in the center region of the melt pool. Larger elongated columnar grains surround the melt pool profile, and almost all point to the melt pool center. In side view, all the columnar grains orientate toward the laser scanning, which moves along the negative Y axis shown in Fig. 2. Near the laser beam, the primary grain morphologies have a fine and equiaxed shapes. Different laser scanning patterns can cause diversified grain morphologies, which further affects grain boundary distribution. The grain boundary acts as a barrier to the continued slip under external force [16]. Therefore, the grain morphologies generated in DED process will result in distinctive properties in DED manufactured part. atterns in DED coating process. in morphologies. Table 1 The comparison of grain sizes" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000775_tro.2019.2906475-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000775_tro.2019.2906475-Figure4-1.png", "caption": "Fig. 4. Equivalent linearized system.", "texts": [ " Similarly, suppose that the torque of each pendulum is controlled by a PD controller such that \u03c4a,i = \u2212kp\u03b8p,i \u2212 kd\u03b8\u0307p,i where kp and kd denote the pendulum controller gains. Under such conditions, an equivalent system of the CDPR can be considered as illustrated in Fig. 3 where each cable is replaced with a spring damper with kcp and kcd coefficients and the pendulums motors are replaced with a rotational spring damper with kp and kd coefficients. The system illustrated in Fig. 3 is a nonlinear system where its equivalent linearized system is shown in Fig. 4. The spring-damper in each direction is formed by projecting the spring-damping effects of the cables in those directions. Accordingly, it can be shown that kx = kcp n\u2211 i=1 c\u0302i,x ky = kcp n\u2211 i=1 c\u0302i,y k\u03b8z = kcp n\u2211 i=1 (ri,xc\u0302i,y \u2212 ri,y c\u0302i,x) (15) and kd,x = kcd n\u2211 i=1 c\u0302i,x kd,y = kcd n\u2211 i=1 c\u0302i,y kd,\u03b8z = kcd n\u2211 i=1 (ri,xc\u0302i,y \u2212 ri,y c\u0302i,x) (16) are obtained as the equivalent stiffness and damping coefficients in the planar directions of x, y, and \u03b8z , which means the CDPR is benefiting from an equivalent linear damper in any planar direction, as illustrated in Fig. 4. Having an equivalent damper in each planar direction dissipates the system energy in each planar direction and guarantees the systems asymptotic stability in the case of planar vibrations. Projections of the damping effects in out-of-plane directions are zero. Accordingly, it cannot be guaranteed that the cables damping effects can necessarily dissipate system energy in those directions. If the moving platform vibrations in all out-of-plane directions are coupled with those in the planar directions, exciting the system in the out-of-plane directions will excite the CDPR in the planar directions as well, which results in the asymptotic stability of the whole system", " Considering the out-of-plane DOFs, using the Taylor expansion technique, the decoupled linearized model of the system in out-of-plane direction is obtained as Mrq\u0308r +Crq\u0307r +Krqr = 0 (17) where qr = [z, \u03b8x, \u03b8y, \u03b8p,1, \u03b8p,2] T and Mr , Kr , and Cr are defined in (18) as shown at the bottom of this page. kz , k\u03b8x, and k\u03b8y denote the equivalent stiffness of the moving platform in the out-of-plane directions, the inertia of the pendulums are considered negligible and each pendulum is considered as a concentric mass where its connection point is located in the xy plane, which is denoted by ra,i, as illustrated in Fig. 4. Lemma 1: The system (17) is stable if each pendulum is controlled with a PD controller with the positive gains kp and kd and we have kz = k\u03b8xmp(lra,y + lp)/Ip,xx all over the CDPR workspace. Proof: Consider the energy of system (17) as the Lyapunov function V = 1 2 [ q\u0307T r q T r ] [Mr 0 0 Kr ][ q\u0307r qr ] (19) with the time derivative V\u0307 = q\u0307T r (Mrq\u0308r +Krqr) (20) where substituting (17) in (20) gives V\u0307 = \u2212kd(\u03b8\u0307 2 p,1 + \u03b8\u03072p,2) \u2264 0 (21) which is negative unless \u03b8\u0307p,1 = 0, \u03b8\u0307p,2 = 0 (22) which implies \u03b8\u0308p,1 = 0, \u03b8\u0308p,2 = 0, \u03b8p,1 = c1, \u03b8p,2 = c2", " By violating the condition of (33), we have ci = 0, i = 7, 8, 9, 10, 12, which indicates the equilibrium conditions z = \u03b8x = \u03b8y = 0 for the system. Accordingly, by violation of (33), the system (17) is stable all over the workspace. Regarding consideration of the most severe case for the coupling conditions between the system planar and nonplanar vibrations in the provided analysis and also having the equivalent damping effects in all planar directions, we can conclude that for any vibration in any direction of the system, the energy of the whole linearized system, as illustrated in Fig. 4, will be dissipated to reach the static conditions, which, based on Theorem 1, means the asymptotic stability conditions for the whole nonlinear system, as illustrated in Fig. 2, are satisfied. It is worth mentioning that (33) shows a specific condition of the systems parameters where an uncoupled vibrational mode shape can happen in out-of-plane directions of z and \u03b8x without stimulating the pendulum mechanism to suppress the system energy. However, the condition of (33) can be easily violated in the CDPR design for all points of the workspace" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000851_tia.2019.2961878-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000851_tia.2019.2961878-Figure6-1.png", "caption": "Fig. 6. FEM result of variation in the magnetic flux density distribution of an IPMSM with increasing severity of ITSF.", "texts": [ " The analysis is carried out assuming zero contact resistance (Rf=0 \u03a9) to find out the post-fault behavior of the machine. The analysis is carried out using a 2D-FEM model of the machine with a 25436 number of meshes. 1) Magnetic Flux Density characteristics: Fig. 5 shows the comparison of phase-A current and the circulating current obtained at rated speed and load. Both the circulating and phase currents have opposite phase; thus, their linkage fluxes are opposing each other. The contour plot of the magnetic flux density distribution at healthy and various intensities of ITSF is shown in Fig. 6. At time t=t0, the machine is healthy, and the magnetic flux density distribution is uniform. However, as the intensity of ITSF is increases the flux density of faulty slot (A2) decreases while the remaining healthy slots of phase-A (A1 and A3) got saturated at t=t5. Fig. 7 illustrates the same phenomenon in a rectangular plot which confirms the phenomena presented in Fig. 2(b). This asymmetry of machines leads to higher power loss, vibration, and torque ripple. 0093-9994 (c) 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003110_s0093-6413(03)00088-0-Figure10-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003110_s0093-6413(03)00088-0-Figure10-1.png", "caption": "Fig. 10. Slack cable assumption for the McKibben FE model.", "texts": [ " Furthermore when increasing the inclination angle, that is with an increase in the contraction ratio, the rubber tube and the braided cords appear to be physically separated. This kinematics was found very hard to be modeled with precision. However, its effect was accurately simulated by taking advantage of a simple analytical statement as the one that follows. It is considered the cylindrical FEM model of an equivalent wire evolved on the plane either in the preload condition, when its length is LR or in the rest condition, with length of LN , as shown in Fig. 10, where H0, D0 and H , D are the dimensions of the rubber tube under the pre-load and at the rest conditions, respectively. The numerical model may not simulate the position of the unloaded braided cords spaced very much from the inner rubber tube in the rest condition as in the reality but in any case it models cords and rubber when connected. Therefore a numerical slack length of the equivalent cable is computed as follows: d \u00bc LN LR LN \u00f07\u00de An accurate modeling of the McKibben kinematics is made possible by using this assumption, since the braided cords begin to pull only once their maximum length is reached" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000560_s00170-016-8857-0-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000560_s00170-016-8857-0-Figure2-1.png", "caption": "Fig. 2 Head-cutter blade profiles: (a) Straight lined, (b) consisting of two circular arcs", "texts": [ " The machine tool settings are the radial machine tool setting (e), the tilt angle of the cutter spindle with respect to the cradle rotation axis (\u03ba), the swivel angle of cutter tilt (\u03bc), and the tilt distance from tilt centre to reference plane of head-cutter (hd). The tooth surface of the imaginary generating crown gear is obtained by coordinate transformations from the coordinate system Ke(xe,ye,ze) (attached to the head-cutter) to coordinate system Kc(xc,yc,zc) (attached to the imaginary generating crown gear) by applying the following equation (based on Fig. 1): r!c \u00bc M c4\u22c5M c3 e; ig1 \u22c5M c2 \u03bc;\u03ba; hd\u00f0 \u00de\u22c5M c1 rt0\u00f0 \u00de\u22c5 r!e \u00bc M ec\u22c5 r!e \u00f01\u00de Matrices Mc1, Mc2, Mc3, and Mc4 are presented in Ref. [32]; r!e is the radius vector of the blade profile points (Fig. 2). In the tooth surface generating process, the work gears are rolled with the imaginary generating gear (Figs. 1 and 3). The coordinate system Kc(xc,yc,zc) is attached to the generating crown gear; the coordinate systems K1(x1,y1,z1) and K2(x2,y2,z2) are attached to the pinion and gear, respectively. The teeth surfaces of the pinion and of the gear are defined by the following system of equations: r! i\u00f0 \u00de i \u00bc Mi3\u22c5Mi2\u22c5Mi1\u22c5 r! i\u00f0 \u00de c \u00bc Mi3\u22c5Mi2\u22c5Mi1\u22c5Mec\u22c5 r! i\u00f0 \u00de e \u00f02a\u00de v! i;c\u00f0 \u00de c0 \u22c5 e! i\u00f0 \u00de c0 \u00bc 0 \u00f02b\u00de where i =1 and i =2 for the pinion and the gear, respectively", " 0 @ 1 A it ;iz\u00f0 \u00de : \u00f012\u00de An optimization method is applied to systematically define optimal head-cutter geometry and machine tool settings to simultaneously minimize maximum tooth contact pressure and angular displacement error of the driven gear. The proper manufacture variables, objective function, and constraints needed to be defined. The following manufacture parameters are taken as the basis of the proposed optimization formulation: the radii of the head-cutter blade profile (rprof1 and rprof2, Fig. 2), the difference in head-cutter radii for the manufacture of the contacting tooth flanks of the pinion and the gear (\u0394rt0), tilt (\u03ba) and swivel (\u03bc) angles of the cutter spindle with respect to the cradle rotation axis (Fig. 1), tilt distance (hd), variation in the radial machine tool setting (\u0394e, Fig. 1), and variation in the ratio of roll in the generation of pinion tooth-surface (\u0394ig1). The variations of the tilt and swivel angles, tilt distance, radial machine tool setting, and the ratio of roll are conducted by polynomial functions of fifth-order: \u03ba \u00bc c10 \u00fe c11\u22c5 \u03c8c1\u2212\u03c8c10\u00f0 \u00de \u00fe c12\u22c5 \u03c8c1\u2212\u03c8c10\u00f0 \u00de2::::\u00fe c15\u22c5 \u03c8c1\u2212\u03c8c10\u00f0 \u00de5 \u03bc \u00bc c20 \u00fe c21\u22c5 \u03c8c1\u2212\u03c8c10\u00f0 \u00de \u00fe c22\u22c5 \u03c8c1\u2212\u03c8c10\u00f0 \u00de2::::\u00fe c25\u22c5 \u03c8c1\u2212\u03c8c10\u00f0 \u00de5 hd \u00bc c30 \u00fe c31\u22c5 \u03c8cl\u2212\u03c8c10\u00f0 \u00de \u00fe c32\u22c5 \u03c8cl\u2212\u03c8c10\u00f0 \u00de2::::\u00fe c35\u22c5 \u03c8cl\u2212\u03c8c10\u00f0 \u00de5 \u0394e \u00bc c40 \u00fe c41\u22c5 \u03c8c1\u2212\u03c8c10\u00f0 \u00de \u00fe c42\u22c5 \u03c8c1\u2212\u03c8c10\u00f0 \u00de2::::\u00fe c45\u22c5 \u03c8c1\u2212\u03c8c10\u00f0 \u00de5 \u0394ig1 \u00bc c50 \u00fe c51\u22c5 \u03c8c1\u2212\u03c8c10\u00f0 \u00de \u00fe c52\u22c5 \u03c8c1\u2212\u03c8c10\u00f0 \u00de2::::\u00fe c55\u22c5 \u03c8c1\u2212\u03c8c10\u00f0 \u00de5 \u00f013\u00de where \u03c8c1 is the angle of rotation of the imaginary generating crown gear in pinion tooth surface generation" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000621_j.matpr.2018.03.039-Figure13-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000621_j.matpr.2018.03.039-Figure13-1.png", "caption": "Figure 13 Carbon/Glass Leaf Spring Deformation during Acceleration", "texts": [], "surrounding_texts": [ "Assume the vehicle is slowing down from 60 km/h to 30 km/h. Distance covered by vehicle during deceleration is assumed as 20 m. Load acting on a leaf spring:Vf 2 = Vi 2 + 2\u00d7a\u00d7d Where,Vf = Final Velocity = 30 km/h = 8.335 m/s, Vi= Initial Velocity = 60 km/h = 16.67 m/s,a = acceleration,d = distance travelled by vehicle = 20m.(8.335)2 = (16.67)2 + 2\u00d7a\u00d720,208.42 = 40a,a = 5.208 m/s2. Decelerating Force, Fd = ma,Where,m = mass of the vehicle= 2900 kg, a = acceleration= 5.208 m/s2, Fd= 2900\u00d75.208, Fd= 15110.21 N (For all four-leaf springs),For one leaf spring, Fd = 15102.32/4, Fd= 3775.58 N. Total load acting on the leaf spring is Ft = F+ Fd, Ft= 7112.25+3775.58,Ft=10887.83N. The results obtained for transient structural analysis for deceleration are shown in Figures 16-20 and listed in table 6. Table 6 Results during Deceleration Parameter Steel EN45A Carbon/Glass Composite Max Stress 415.79 MPa 545.53 MPa Max Deformation 8.9656 mm 15.005 mm Figure 16 Load during deceleration 14518 Jenarthanan M.P et al/ Materials Today: Proceedings 5 (2018) 14512\u201314519 3.4 Inference From this result, we can understand that even though deformation and equivalent stress values of Carbon/Glass Epoxy Hybrid Composite Leaf Spring increases, they are well within the safety limits." ] }, { "image_filename": "designv10_11_0000970_j.mechmachtheory.2019.103747-Figure11-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000970_j.mechmachtheory.2019.103747-Figure11-1.png", "caption": "Fig. 11. Combined singularities and special situations: (a) combined FI-1, II-2, and IF singularity for \u03bb = \u03c0/ 2 , (b) combined FI-2 and FF singularity for \u03b3 = \u03be = \u03c0/ 2 , (c) combined FI-1 and FF singularity for \u03b3 = \u03be = \u03c0/ 2 , (d) combined FI-1, FI-2, and FF singularity for \u03bb = \u03b3 = \u03be = \u03c0/ 2 , (e) special FF singularity for \u03bb = \u03b3 = \u03be = \u03c0/ 2 where second motor becomes locked.", "texts": [ " It also has an interesting property: If and only if \u03bb = \u03c0/ 2 , all three singularities can occur simultaneously. From Section 4.1.1 , the Inverse I singularity always happens at Z = \u00b1[0 1 0] T . Also, using Eq. (A.2) and EE assuming C 3 = C 4 = 0 , S 3 = \u00b11 and S 4 = \u00b11 , we have Z EE = \u00b1[ \u2212C \u03bbC 2 S \u03bbC 2 S 2 ] T for the combined Inverse II and Forward singularities. For all three singularities to happen simultaneously, both expressions for Z EE should become equal, which leads to \u03bb = \u03c0/ 2 and S 2 = 0 . Fig 11 (a) shows a configuration where all these three singularities are present. In such configuration, the first motor becomes locked and only the second motor can move the mechanism away from this combined singularity. For \u03b3 = \u03be = \u03c0/ 2 , an special case of symmetric structure occurs in which all three singularities become finite (type 1 from Table 5 ). Previous studies on orthogonal 5R-SPM shows that all singularities of the orthogonal structure are finite [21] . However, based on our geometrical analysis, the condition \u03b3 = \u03be = \u03c0/ 2 is sufficient for all singularities to be finite with no limitation for the value of \u03bb. As a result, the corresponding X EE for the forward singularity becomes \u00b1 [0 0 1] T , which is perpendicular to the corresponding Z EE of both inverse singularities (refer to Table 5 ), causing combined FI-2 and FF or combined FI-1 and FF simultaneously ( Fig. 11 (b and c)). In combined FI-2 and FF singularity, the mechanism can move by moving either links 2 and 3 around Y EE or links 3 and the end-effector around X EE . For \u03bb = \u03c0 /2, the two inverse singularities cannot occur simultaneously. The last case to investigate is when \u03bb = \u03b3 = \u03be = \u03c0/ 2 , which is equivalent to the orthogonal structure. This is the com- bination of the previous two cases, so that all three singularities are finite and can occur simultaneously. In this combined singular configuration, ( Fig. 11 (d)), the first motor becomes locked, two different free motions exist (similar to Fig. 11 (b)). Nevertheless, this case has also another configuration for forward singularity, happening when Y EE and Y 0 become aligned, where the second motor becomes locked ( Fig. 11 (e)). In this paper, we introduced a new non-symmetric 5R-SPM, which benefits from a compact and light design and collision-free workspace when used as the head of a surgical robot [15] . This non-symmetric structure is also interesting from analytical point of view since it contains the challenges of both orthogonal and non-orthogonal kinematic chains and the results of which may be compared with the previous studies. The singularities and configurations of the designed mechanism were investigated by developing a geometrical method which transforms the configuration and singularity analysis of a 5R-SPM into finding the intersection of two cones and/or planes with a common vertex (the mechanism\u2019s center)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000886_j.mechmachtheory.2019.03.044-Figure10-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000886_j.mechmachtheory.2019.03.044-Figure10-1.png", "caption": "Fig. 10. Schematic of transmission error acquisition.", "texts": [ " n p \u03b8p ] (7) \u03d5 g = [ 0 \u03b8g \u2212 \u03b8g1 2 \u03b8g \u2212 \u03b8g1 \u2212 \u03b8g2 3 \u03b8g \u2212 3 \u2211 i =1 \u03b8gi . . . n p \u03b8g \u2212 n p \u2211 i =1 \u03b8gi ] (8) where n p is the total number of rotations of the pinion. Finally, based on Eq. (1) , the NLSTE can be expressed as: e = r b2 ( | \u03d5 g \u2212 \u03d5 g (1) | \u2212 z p z g | \u03d5 p \u2212 \u03d5 p (1) | ) \u00d7 \u03c0 180 (9) To validate the numerical analysis, a power closed gears test rig was designed to measure the no-load static transmission error of the spur gear directly, as shown in Fig. 9 . The schematic of transmission error acquisition is presented in Fig. 10 . The gear pair analyzed in this study is assembled in the test gearbox and the driving side and driven side are installed in the same way as numerical analysis. Two LM13 magnetic ring encoder systems (number of pulses per revolution is 3200, resolution is 101.25 arc seconds and divisional error is \u00b130 arc seconds) have been fixed to the test gearbox to determine the angular position of each gear shaft. The signals from the encoders were transmitted into LMS SCADA. Based on the Eq. (1) , a transmission error measurement system was designed to process the LMS SCADA signals to compute the transmission error" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003471_027836499601500204-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003471_027836499601500204-Figure1-1.png", "caption": "Fig. 1. The Ambler.", "texts": [ " This article presents results of our investigation of perception, planning, real-time and task-level control for the Ambler, a six-legged walking robot. The result is a robot system that can autonomously traverse rugged terrain for extended periods of time. The Ambler (Fig. L) is built for mobility and efficiency. A related article (Bares and Whittaker 1994) describes in detail the configuration and physical form of the robot. The Ambler\u2019s novel features include stacked, orthogonal legs (as in Fig. 1) and the ability to walk with a circulating gait. The three-degree-of-freedom orthogonal legs decouple horizontal and vertical motions, leading to simplified planning and control. Further, the design increases mobility by allowing legs to be placed adjacent to steep terrain features, such as sheer faces of rocks. The stacked arrangement of legs enables the Ambler to exhibit a unique circulating gait. To move forward, one rear leg circulates through the body cavity, moving ahead of the other two legs on its stack (see Fig", " In this way, the Ambler can turn in place by having the legs on one stack move retrograde with respect to the legs on the other stack. The gait planner utilizes two constraints to determine the extent of the body move. The first constraint is based on the kinematic limits of the legs. Given that the feet1. We have also developed a planner for a crab gait, one that enables the Ambler to walk from side to side. at MICHIGAN STATE UNIV LIBRARIES on June 12, 2015ijr.sagepub.comDownloaded from 166 at MICHIGAN STATE UNIV LIBRARIES on June 12, 2015ijr.sagepub.comDownloaded from 167 Fig. 1l. Stack reachability constraint. are fixed, the planner determines how far each stack can move along the arc before reaching a kinematic limit (Figure 11A). The second constraint is based on stability. To be statically stable, the rover\u2019s center of mass must lie within the support polygon formed by the convex hull of the feet. For added safety, we insist that the Ambler always lie within the conservative support polygon (CSP), which is defined as the intersection of all five-legged support polygons (see Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003129_iecon.2000.973184-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003129_iecon.2000.973184-Figure4-1.png", "caption": "Figure 4: The function for the basic motion and navigation", "texts": [ " the alarm is sent to the monitoring station. 3.1 Outline Figure::; shows the appearance of the guard robot and explains each part. This robot consists of the top and the bottom parts. The top part is for the guard functions, and the bottom part is devoted to the autonomous robot and navigation function. Except the leak sensor to detect the water-flow is exceptionally installed at the side of the wheel in bottom. 3.2 Basic functions The functions for the basic motion and navigation are shown in Figure 4. The guard robot has two driving wheels at left and right of body center, and four casters in front and back to support the body. Encoders are mounted at thc motors for driving wheels to realize odometery system. An exclusi ve controller which is called vehicle control module, estimates the robot current position based on odmetry and optical fiber gyro sensor. and controls the driving wheels to move to given position. . The vehicle control command language \"Spur\" [ I] and execution system is used" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000621_j.matpr.2018.03.039-Figure14-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000621_j.matpr.2018.03.039-Figure14-1.png", "caption": "Figure 14 Steel Leaf Spring Von-Mises Stress during Acceleration", "texts": [], "surrounding_texts": [ "Assume the vehicle is slowing down from 60 km/h to 30 km/h. Distance covered by vehicle during deceleration is assumed as 20 m. Load acting on a leaf spring:Vf 2 = Vi 2 + 2\u00d7a\u00d7d Where,Vf = Final Velocity = 30 km/h = 8.335 m/s, Vi= Initial Velocity = 60 km/h = 16.67 m/s,a = acceleration,d = distance travelled by vehicle = 20m.(8.335)2 = (16.67)2 + 2\u00d7a\u00d720,208.42 = 40a,a = 5.208 m/s2. Decelerating Force, Fd = ma,Where,m = mass of the vehicle= 2900 kg, a = acceleration= 5.208 m/s2, Fd= 2900\u00d75.208, Fd= 15110.21 N (For all four-leaf springs),For one leaf spring, Fd = 15102.32/4, Fd= 3775.58 N. Total load acting on the leaf spring is Ft = F+ Fd, Ft= 7112.25+3775.58,Ft=10887.83N. The results obtained for transient structural analysis for deceleration are shown in Figures 16-20 and listed in table 6. Table 6 Results during Deceleration Parameter Steel EN45A Carbon/Glass Composite Max Stress 415.79 MPa 545.53 MPa Max Deformation 8.9656 mm 15.005 mm Figure 16 Load during deceleration 14518 Jenarthanan M.P et al/ Materials Today: Proceedings 5 (2018) 14512\u201314519 3.4 Inference From this result, we can understand that even though deformation and equivalent stress values of Carbon/Glass Epoxy Hybrid Composite Leaf Spring increases, they are well within the safety limits." ] }, { "image_filename": "designv10_11_0001013_fitee.1900455-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001013_fitee.1900455-Figure2-1.png", "caption": "Fig. 2 Force and movement analysis of the ankle motion in the sagittal plane with the exoskeleton on: (a) plantarflexion; (b) dorsiflexion Fh: tension force on the heel cable; Lh: length between the heel connection point and the center of the rotation; \u03b8h: application angle of Fh; Th: heel moment; Ff: tension force on the forefoot cable; Lf: length between the forefoot connection point and the center of the rotation; \u03b8f: application angle of Ff; Tf: forefoot moment. The moment arm of Th can be described as Lh\u00b7sin \u03b8h and that of Tf is Lf\u00b7sin \u03b8f", "texts": [ " The gait cycle of the human is detected in real time using the foot pressure sensor and the inertial measurement unit (IMU). Combined with the force sensor to achieve force feedback control, the exoskeleton can provide real-time power matching the corresponding human biological data (ankle torque) during walking, while achieving ankle plantarflexion-dorsiflexion bidirectional movement through four cables at the heel and forefoot respectively. 2.1 Mechanical design 2.1.1 End-effector The end-effector is the part of the exoskeleton interacting directly with the human foot as shown in Fig. 2. For the human foot during walking, the rotation and translation motion of the ankle joint in the sagittal plane is dominant (Sawicki and Khan, 2016). Therefore, the design of the end-effector is focused mainly on assisting movement of the ankle joint. It is a design principle of the end-effector that it does not interfere with movements of other planes (coronal plane, transverse plane) or other joints (knee, hip) of the body. Based on the design requirements above, we completed the end-effector structure as shown in Fig. 2. A special shoe was made with four cables (Dyneema cable, maximum load weight of 140 kg). Fig. 2 shows only two of the cables. To balance the torque generated by the end-effector in the coronal plane, another two cables were set on the other side of In (a), the power of the motor can be transferred to the end-effector by cables and the transmission system, and the plantarflexion-dorsiflexion bidirectional motion of the ankle is achieved by clockwise or counterclockwise rotation of the motor (seen from the encoder to the motor). In (b), the motor shaft drives four bobbins to rotate, wherein the first and fourth bobbins are wound counterclockwise and connected to the forefoot, and the second and third bobbins are wound clockwise and connected to the heel. In (c), four cables wind through the pulley assembly, and a joint limit is designed to ensure safety the shoe, parallel to the two cables shown in Fig. 2. Thus, there were four cables in total acting on the endeffector. One pair was fastened at the heel of the shoe and the other pair was fixed at the forefoot of the shoe close to the metatarsophalangeal joint of the foot. To realize cable pre-tensioning, a pair of cable endconnectors was used to connect the cable segments between the shoe and the shank mounting. In addition, a pair of support tubes was designed to support shank mounting, and a spring was placed in the tube to make the tube length adjustable. In order not to restrict movement in the coronal plane or transverse plane, ball bearings were provided at both ends of the support tube. For the plantarflexion assistance of the ankle, as shown in Fig. 2a, the cable at the heel is tensioned by the motor to provide the assistance force, and the metatarsophalangeal joint acts as the center of rotation. The tension force on the heel cable Fh can be measured by the force sensor I (ZZ210-013, Zhizhan Measurement & Control, Shanghai, China) connected in the cable, and the length between the heel connection point and the center of the rotation is Lh; thus, the heel moment Th provided by the exoskeleton can be expressed as Th=FhLhsin \u03b8h, (1) where \u03b8h is the application angle of Fh, the value of which will change along with the ankle plantarflexion. For the dorsiflexion assistance of the ankle, as shown in Fig. 2b, the forefoot cable is tensioned by the motor, and the ankle rotation center acts as the center of rotation. The tension force on the forefoot cable Ff can be measured by the force sensor II connected in the forefoot cable, and the length between the forefoot connection point and the center of the rotation is Lf. Therefore, the forefoot moment Tf can be expressed as Tf=FfLfsin \u03b8f, (2) where \u03b8f is the application angle of Ff, the value of which will change along with the ankle dorsiflexion movement" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000946_rpj-02-2019-0035-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000946_rpj-02-2019-0035-Figure3-1.png", "caption": "Figure 3 Intersection points between cylinder and triangle", "texts": [ " The intersection exists only when this equation has one or two solutions: x1 x0\u00f0 \u00de2 1 y1 y0\u00f0 \u00de2 h i t2 1 2 x0 x1 x0\u00f0 \u00de 1 2 y0 y1 y0\u00f0 \u00de t1 x02 1 y02 r2 \u00bc 0; 0 t 1 (3) As we mentioned before, there exist 0, 1 or 2 intersections on edge. As there is no vertex of model on the cylinder surface after modification, a triangle intersects with cylinder only has 2, 4 or 6 intersections. Using N1-N2-N3 to indicate intersection state, e.g. 1-1-2 means two edges of the triangle have one intersection and the third edge has two intersections. Generally, states 1-2-1 and 2-1-1 are same as 1-1-2. As shown in Figure 3, there are five intersection states: two intersections. The intersection states are 2-0-0 and 1- 1-0; four intersections. The intersection states are 2-2-0 and 2- 1-1; and six intersections. The intersection state is 2-2-2, i.e. each edge has two intersections. After finishing the calculating of intersection points, the slicing contours are constructed by two steps: link the intersections of a triangle to form line segments. Through the mesh topology, find and connect any two adjacent segments sharing a common intersection" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001272_1464420720909486-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001272_1464420720909486-Figure3-1.png", "caption": "Figure 3. Finite element model of gear pair: (a) boundary conditions of model, (b) element mesh in the contact region, and (c) element mesh in the fillet region.", "texts": [ " In a contact analysis, the use of a three-dimensional, full-gear model is computationally intensive for simulations entailing large deformation. The computational efficiency can be improved by conducting a planar analysis on the gear models with a reduced number of teeth. For static analysis, a twodimensional (2D), three-tooth model is apposite for determining the bending stress with less than 1% error as compared to a full-gear model.7 Hence, a 2D multipair contact model (MPCM) with three teeth and a full rim was developed (Figure 3). The following assumptions were applied to the model: . The involute profile was ideal and devoid of any imperfections. . The material behavior was linear elastic and isotropic. . It had a plane strain condition. . The contact surfaces were frictionless. Many works have utilized the linear elastic model for calculating the bending stress of polymer gears.9,10 Also, in the low load regions, the linear elastic model agrees with the viscoelastic model. Frictionless contact was assumed to calculate a conservative value of the bending stress" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000048_tmag.2017.2698004-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000048_tmag.2017.2698004-Figure4-1.png", "caption": "Fig. 4. Rotor mechanical stress analysis.", "texts": [ " Due to the self-shielding effect of the Halbach-array magnets [10], the rotor back-iron is not essential for Machine I. The inner stator, reluctance rotor and the outer stator compose the double-stator VPM machine (Machine II). The 3D rotor structure is shown in Fig. 3. There is a magnetic bridge behind the Halbach-array PMs, and the thickness of the magnetic bridge is chosen as 0.5mm in this paper. Also, several mounting holes are punched in the rotor iron, and the rotor is supported at both ends. Then, the rotor stress analysis is also conducted. It can be seen in Fig. 4 that the maximum mechanical stress of rotor support is 0.81 MPa, which is smaller than the yield strength of the carbon steel. So the mechanical structure of the rotor is feasible. In order to make both of the magnetic fields excited by the two machines induce back-EMF in the same outer stator windings, the number of outer stator slot Zs, winding pole pair Ps, rotor PM pole pair Pr and inner stator PM pole pair Pis should satisfy: Pr \u00b1 (Pr \u2212 Pis)= Zs (1) Ps = min(Pr, Pr \u2212Pis) (2) The explanation is as follows" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003710_0957-4158(92)90043-n-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003710_0957-4158(92)90043-n-Figure4-1.png", "caption": "Fig. 4. Safety conditions.", "texts": [ " The rotational slipping is a combined motion of simple slipping and rotation which are produced by the force and rotational moment , respectively. It has a very complicated friction mechanism. When the force is acting inside the cup radius, //r < 1, then the motion is close to a pure slipping, and w h e n / / r > 2, it can be seen as a pure rotation with the m o m e n t / W . In Fig. 3, an experimental result of rotational slipping is presented. The total safety conditions are summarized by the following equations and they are shown in Fig. 4. The upper side of each curve gives a safety zone. (a) Pure slipping on a vertical wall; (b) Pure falling on a vertical wall; (c) Rotational slipping on a vertical wall; (d) Falling off on the floor; (e) Falling off from the ceiling; l~F/W > 1 (1) F/W > h/r (2) ItF/W> 1 f o r / / r < 1 (3) ItF/W > 1/r f o r / / r > 2 F/W > l/r - 1 (4) F/W > 1/r + i. (5) most severe condition is falling off from the ceiling, so the pace of walking on the ceiling should be taken as being lower. Rotational slipping on a vertical wall is the next most severe condition", " When the model is moving on a vertical wall or is in transition to another wall, the coordinates of the center of gravity must be known to examine the safety conditions at any time. This can be done by using the coordinates on the wall and model geometry as shown in Fig. 5. The angles of or, /3, 7 and 6 are measured by the sensors and h and ! are calculated from these angles. If the frictional coefficient /~ is assumed, the required negative pressure in the sucker can be estimated by combining Figs 4 and 5, i.e. F/W or I~F/W in Fig. 4 can be determined by h and ! in Fig. 5, which gives the minimum required sucking force. The minimum required pressure Po(Po = F/S, where S is the base area of the sucker) can be given on the blower performance map, shown in Fig. 6 as an example. On the other hand, just after a cup is fixed on the wall, the negative pressure is measured, which is P in Fig. 6 for example. It gives a little larger value than P0. The input voltage of the blower, V, must be increased to V = V1 to get a certain pressure margin", " They are connected to the I /O ports of the computer. To build up a control program, the walking motion was simulated by a computer . Two cases are presented as an example. One is walking on a vertical wall, and the other is a transition motion f rom the vertical wall to the ceiling. In Fig, 8 the analysed motion on a vertical wall is presented and for each station the force acting on the fixed sucker is shown in Fig. 9 by using the corresponding letters. The abscissa is the distance h and / is given in Fig. 4. The transition motion from a vertical wall to ceiling is shown in Fig. 10. It can be seen that the most severe condition is given by point i or j in this figure and this is verified from Fig. 9, i.e. the largest value of F/W is assumed for a point of i or j. The required negative pressure in the cup is given in Fig. 11 on the curves of blower performance. Assumed curves of A and B correspond to lesser and larger leakages, respectively. The amount of leaked air depends on the wall surface roughness and the shape and material of the peripheral lip" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001230_tec.2020.3044917-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001230_tec.2020.3044917-Figure5-1.png", "caption": "Fig. 5. 2D Geometry of magnetic FE at aligned position for phase A (left) and 3D Cross-section (right) of structural FE simulation model of 12/10 SSRM.", "texts": [ " In the first stage, during turn-off, the phase voltage changes from Vdc to 0 by utilizing the freewheeling loop (zero voltage), and the first vibration occurs then. A free decay vibration will oscillate corresponding to the resonant frequency. Then, after a half period of a resonant cycle Tr/2, the negative voltage \u2212Vdc is applied to the phase winding, which generates the second vibration against the first vibration. Tr denotes a resonant cycle. Fig. 4 (bottom) shows the implementation of the twostep commutation control. Fig. 5 shows the geometry details of 12/10 SSRM for 2D magnetic FE and 3D structural FE simulation model including all mechanical parts of the motor. The mechanical material properties of the structural model are obtained from [23]. The simulation of AVC control has been performed under the current chopping control. The conditions of the current control are the same, with speed = 500 r/min, desired average torque = 30 Nm, turn-on = 0 mechanical degrees at the unaligned rotor position, turn-off = 16 mechanical degrees before the aligned rotor position at 18 mechanical degrees, and a 580 Vdc link voltage" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003912_1.2118687-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003912_1.2118687-Figure9-1.png", "caption": "Fig. 9 Parallel manipulator Gough-Stewart", "texts": [ " Further, the absolute closure algebra is the three-dimensional algebra of spatial translations Aa m/f = j=1 3 Aj m/f = t 3 . Thus, this parallel manipulator satisfies the assumptions of Proposition 2, in Sec. 4.1 and the mobility of the parallel manipulator is given by Eq. 8 F = i=1 r f i \u2212 j=1 k dim Aj m/f + dim Aa m/f = 12 \u2212 j=1 3 4 + 3 = 3. Furthermore, for the passive degrees of freedom, see Eq. 32 , Fp = i=1 r f i \u2212 j=1 k dim Aj m/f = 12 \u2212 j=1 3 4 = 0. 6.7 Gough-Stewart Parallel Manipulator. Consider a Gough-Stewart parallel manipulator, shown in Fig. 9. The manipulator is formed by six serial connecting chains. Each serial connecting chain is formed by a pair of spherical pairs located at the ends of the serial connecting chains and a prismatic pair. The kinematic pairs of each serial connecting chain generate the Lie algebra, e 3 ; i.e., Vj m/f = Aj m/f = e 3 \u2200 j = 1,2,\u2026,6. It should be noted that the Lie algebra has dimension six and i=1 7 f ji = 7 dim Vj m/f = dim Aj m/f = 6, \u2200 j = 1,2,3,4,5,6. Furthermore Aa m/f = j=1 6 Aj m/f = e 3 . Thus, the parallel manipulator is a trivial one, this class of platforms was analyzed in Proposition 3 in Sec" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001551_j.triboint.2021.106901-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001551_j.triboint.2021.106901-Figure1-1.png", "caption": "Fig. 1. A selection of common tribometer configurations (a) ball-on-disc, (b) linear reciprocating, (c) block-on-ring and (d) four-ball [35].", "texts": [ " Contents lists available at ScienceDirect Tribology International journal homepage: http://www.elsevier.com/locate/triboint https://doi.org/10.1016/j.triboint.2021.106901 Received 1 August 2020; Received in revised form 17 December 2020; Accepted 25 January 2021 Tribology International 157 (2021) 106901 application. Therefore, a universal ultrahigh-speed tribometer is essential to promote the study of friction and wear mechanisms in a very high sliding speed. Some of the common tribometer configurations with high versatility are shown in Fig. 1, including the ball-on-disc, linear reciprocating, block-on-ring and four-ball. The four-ball test configuration was originally designed to investigate the anti-wear properties of a lubricant under boundary lubrication [26\u201328]. Ball-on-disc, linear reciprocating, and block-on-ring are usually used to evaluate the friction and wear properties [29\u201331]. However, there is no clear evidence depicts that specific in-service conditions must be simulated by specific tribometer configurations. For example, the ball-on-disc and block-on-ring are also often used to test the performance of lubricants [32\u201334]" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001041_j.ijmecsci.2020.106020-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001041_j.ijmecsci.2020.106020-Figure1-1.png", "caption": "Fig. 1. Three-dimensional model of a spur face gear drive.", "texts": [ " The paper is organized as follows: the feasible analysis and theoretial derivation of spur face gear shaving are presented in Sections 2 and , the investigation of LTCA and experiments with spur face gear shaving re presented in Sections 4 and 5 , and Section 6 gives the conclusions. . Principle of spur face gear shaving .1. Formation mechanism for tooth surfaces A spur face gear drive\u2019s left flank and right flank are symmetric along he radial direction of the face gears, and the drive can transmit moion and torque between orthogonal and non-orthogonal axes [1] . A 3D odel of a spur face gear drive is shown in Fig. 1 . \ud835\udefe is the included an- le between the face gear and pinion along their rotational axes. A spur ace gear drive with axes at right angles ( \ud835\udefe = 90 \u25e6) is the research object f this paper. The tooth surface of spur face gears is generated by an involute haper cutter simulating the pinion motion in Fig. 2 . The formation moion consists of a rotational motion of the shaper cutter around its central xis Z c with an angular velocity \ud835\udf14 c and a rotational motion of the face ear around its central axis Z f with angular velocity \ud835\udf14 f " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000839_j.mechmachtheory.2019.103678-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000839_j.mechmachtheory.2019.103678-Figure4-1.png", "caption": "Fig. 4. (a) Geared linkage KG, (b) Its tricolor topological graph.", "texts": [ " The solid vertex, hollow vertex, solid edge, and dashed edge represent the link, multiple joint, revolute pair, and geared pair, respectively. 2.6. Multicolor graph A multicolor graph is often used to represent the topological graph of PGT, gear linkage, gear cam, and cam linkage mechanism. In this study, the solid vertex (\u201c\u25cf\u201d) denotes a link and an edge denotes a joint, the hollow vertex (\u201c\u25e6\u201d) denotes a multiple joints, and the double circle hollow vertex (\u201c\u25e6ledcirc \u201d) denotes gear pairs or cam pairs. For example, in Fig. 4 (b), vertices c and d are multiple joints, whereas vertices e and f are gear pairs. 2.7. Contracted graph A contracted graph is obtained by replacing every binary string in a graph with a single edge. Therefore, a contracted graph has no binary vertices, whereas it may contain parallel edges. Fig. 1 (c) shows the contracted graph of the Stephen chain in Fig. 1 (b). 3. Similarity recognition 3.1. Basis of similarity recognition In 1988, T. Lv [42] verified the necessary and adequate conditions for similar vertices, including two lemmas" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000970_j.mechmachtheory.2019.103747-Figure10-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000970_j.mechmachtheory.2019.103747-Figure10-1.png", "caption": "Fig. 10. Geometric representation of (a) inverse singularity of first kinematic chain and (b) forward singularity.", "texts": [ " This is particularly important for avoiding forward singularities as they occur inside the workspace. As discussed before, the orthogonal chain of a 5R-SPM covers the whole S 2 workspace. Hence, the workspace limitations of the designed non-symmetric 5R-SPM comes from the second kinematic chain, which always contains inverse singularity at the boundary of the workspace. Now, as shown previously, the inverse singularity of the first kinematic chain occurs when Z EE and Y 0 become aligned, making Y EE perpendicular to Y 0 ( Fig. 10 (a)). There are three links between Y 0 and Y EE with link lengths \u03bb, \u03b3 and \u03be ; so the maximum possible angle between Y 0 and Y EE is \u03bb + \u03b3 + \u03be . Therefore, the necessary and sufficient condition for the existence of inverse singularity in the first kinematic chain is \u03bb + \u03b3 + \u03be \u2265 \u03c0/ 2 . Interestingly, unlike symmetric and orthogonal structures that always possess forward singularity [18,20] , the proposed non-symmetric 5R-SPM may have no such singularity. To geometrically describe the existence condition of the forward singularity, one can first consider a plane that includes the mechanism center and is normal to X EE . Both Y 0 and Y EE are perpendicular to X EE and therefore lie on this plane. Since X EE , Y EE and Z 3 become coplanar in forward singularity, the angle between Z 3 and the plane is \u03be ( Fig. 10 (b)). Moving from Y 0 , the maximum possible angle between the plane and Z 3 is \u03bb + \u03b3 . Thus, the necessary and sufficient condition for the existence of forward singularity is \u03bb + \u03b3 \u2265 \u03be . An overview of the different link length combinations and their associated singularity types are provided in Table 5 . Since the first chain is orthogonal, its inverse singularity, if exists ( \u03bb + \u03b3 + \u03be \u2265 \u03c0/ 2 ), is always finite (FI-1). The inverse singularity of the second chain always exists and, depending on the values of \u03b3 and \u03be , is either instantaneous (II-2) or finite (FI-2)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001162_s00170-020-05514-4-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001162_s00170-020-05514-4-Figure2-1.png", "caption": "Fig. 2 Schematics of the end milling process", "texts": [ " 1b) was adopted to reduce the residual stress and deformation of the sample during SLM [28]. The scanning angle between the adjacent layers (nth and (n + 1)th) was 90\u00b0. Table 2 shows the process parameters used in the SLM process. The as-SLM-produced samples were fabricated with the optimized SLM process parameters. The counterparts were annealed at 650 \u00b0C for 4 h [29] to eliminate the residual stress induced by SLM. Milling tests were conducted on the asSLM-produced samples and as-annealed samples, as illustrated in Fig. 2. The samples were milled with different axial cutting depths using a flat carbide end milling tool of a diameter of 6 mm. The end milling process parameters used in this study are listed in Table 3. The relative density of the samples was measured using an electronic balance (ME204E, Mettler Toledo, Switzerland). With the relative density measurements, a set of the optimized SLM parameters was determined. The volume energy density (VED) was defined to correlate the process parameters with the relative density [30]: VED \u00bc P v h t ; \u00f01\u00de where P is the laser power (W), v is the laser scanning speed (mm/s), h is the hatch distance (mm), and t is the layer thickness (mm)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000650_tia.2018.2880143-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000650_tia.2018.2880143-Figure8-1.png", "caption": "Fig. 8. Copper shield.", "texts": [ " RESULTS In order to validate the characteristics of the modified winding shape and the cylindrical copper shield, the experimental setup is composed including oscilloscope, test motor, SVPWM inverter, and dynamo set, as shown in Fig. 5. Fig. 6 (a) shows the appearance of the six-pole nine-slot test motor (IPMSM) used in experiment and Fig. 6 (b) shows the plastic end plate, which is used to electrically separate the bearing and the stator. Moreover, the brush is contacted to measure the shaft-to-frame voltage. Fig. 7 shows the test models with and without modified winding shape. Moreover, Fig. 8 shows the cylindrical copper shield construction. Due to the end plated is the plastic material, separate wire is used to connect the copper shield with the ground (housing). 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. methods The simulation is performed using the equivalent circuit model, as shown in Fig. 2. TABLE IV represents the variation of the calculated parasitic capacitances, according to different mitigation methods" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001537_tcst.2021.3051716-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001537_tcst.2021.3051716-Figure2-1.png", "caption": "Fig. 2. 1-DOF VSA exoskeleton [4]. (a) Overview of the MeRIA. (b) Stiffness actuation. (c) Test bench.", "texts": [ " Section III presents the design and validation of a gain-scheduled torque controller and the stability test of the impedance control system. Section IV investigates the stability of the human exoskeleton system and presents the estimation of the knee stiffness and the exoskeleton experiments with the subject. Section V concludes this brief with the discussion of the main results and the limitations of Case II. The plant in this brief refers to our independent-setup VSA, the so-called mechanical-rotary variable impedance actuator (MeRIA). The overview of this actuator is shown in Fig. 2(a). The actuator output torque is provided by the combination of the joint motor Motor 1 (brushless dc motor, EC90, Maxon Motor AG) and a Harmonic Drive (HFUC-20-100-2UH, Harmonic Drive AG). The output flange of that motor gearbox unit installs two symmetric bending bars (leaf springs). The compliance generated from the bending bars can be transmitted to the actuator\u2019s output shaft via the cam followers. The cam followers are part of the stiffness actuation that is highlighted with the black dashed line in Fig. 2(a). The details of the stiffness actuation are shown in Fig. 2(b). The power source of this actuation is the combination of Authorized licensed use limited to: Rutgers University. Downloaded on May 15,2021 at 01:09:42 UTC from IEEE Xplore. Restrictions apply. the stiffness motor Motor 2 (brushless dc motor, BX4 2232, Dr. Fritz Faulhaber GmbH & Co. KG) and a planetary gearhead (22F, Dr. Fritz Faulhaber GmbH & Co. KG). This motor gearbox unit drives a slide screw (via the belt drives) to achieve the linear motion of the cam followers. The position variation of the cam followers, i", " Remark 1: Following the analysis of a cantilever beam [22], the stiffness variation is dependent on the effective length if the elastic deflection of the bending bar is small (see [13]). In our application, the deflection of the bending bar could always be relatively small since the large torque operates at high stiffness (see the high-impedance task). This discussion is related to the LPV VSA model presented in Section III-A. The load of the actuator is a leg-swing platform designed for the knee joint motion experiment, as shown in Fig. 2(c). This combination establishes a test bench for the 1-DOF knee exoskeleton. On this test bench, the experiment of torque and impedance control can be conducted with the torque sensor (DR-2477, Lorenz GmbH) and the encoder (MHAD50, Baumer). Real-time control of the test bench in practice was achieved by the dSPACE DS1103 system (the sampling frequency was set at 1 kHz). All experiments in this brief were performed on this test bench. III. IMPEDANCE CONTROL SYSTEM A. Inner Torque Loop of the MeRIA-Based 1-DOF Exoskeleton The independent-setup VSA can be modeled as a compliant joint model [23], [24] with a variable stiffness parameter [1], [8], [12] (i" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000909_02678292.2019.1609109-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000909_02678292.2019.1609109-Figure2-1.png", "caption": "Figure 2. Conceivable particle morphologies derived by deforming a spherical shape.", "texts": [ " In liquid crystalline polymers (LCPs) the mesogens can either be part of the polymer chain (main-chain LCPs) or they are attached to the polymer backbone via alkyl spacer (side-chain LCPs) as illustrated in Figure 1 [3\u20135]. Various shapes are conceivable for such LCP particles that differ from the perfect sphere. By stretching of a sphere, prolate (elongated) ellipsoids are obtained, shaped like a rugby ball. Further stretching leads to rod-like or pillar-like structures and finally to fibres having a very large aspect ratio. In contrast, compressing of a sphere results in oblate (flattened) ellipsoids, shaped like a lentil. Proceeding this, disk-like structures are obtained (Figure 2). Beside solid particles, also hollow morphologies like hollow spheres or tubings CONTACT Rudolf Zentel zentel@uni-mainz.de \u00a9 2019 Informa UK Limited, trading as Taylor & Francis Group are imaginable. And by adding a second immiscible polymer, Janus-like structures can be adopted. In order to produce LCP samples which exhibit these morphologies, four different general approaches were performed. The first one is based on a more or less individual, unstructured process. LCP fibres can, for example, simply be drawn from a molten LCpolymer" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003735_41.281604-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003735_41.281604-Figure2-1.png", "caption": "Fig. 2. 'bo-degree-of-freedom manipulator.", "texts": [ " The admissible region of s, [smin, imax] for the whole manipulator is obtained as a product of admissible regions for each joint torque limit: n [gmin, imax] = nrqin, q n x ] i=l Note that the range of the region [smin, smax] depends on the path velocity i. If the velocity is too large, the admissible region of s cannot exist and the motion along the path is impossible. It determines the admissible velocity. The minimum-time trajectory is composed by connecting maximudminimum acceleration trajectory segments so as to obtain maximum velocity without exceeding the admissible velocity. An example of the trajectory planning for a two DOF horizontally articulated manipulator (Fig. 2) is shown. The joint torque limit is -2 5 7 1 5 2, -1 5 7 2 5 1 ( N . m). The desired path is a circle (Fig. 3; center: [0.4, 01, radius: 0.1 m). In this case, the path coordinate system is a polar coordinate system whose origin is at the center of the path. The s component along the path is angle a, and the 2 component normal to the path is radius T. In the planned trajectory, the velocity d! along the path (Fig. 4(a), bold line) is obtained by switching maximum acceleratioddeceleration without exceeding the admissible velocity (Fig", " Therefore, this control system can stretch or shrink the time axis in order to achieve path tracking. As the time to complete the path tracking may be different from that of the nominal trajectory, the end of the tracking should be watched: X = -. The value of X is monitored during the path tracking. If the manipulator is on the path, 0 5 X 5 1. The path tracking control is terminated when X = 1. s - so Sf - s o (25) V. SIMULATIONS Path tracking simulations were carried out with a two DOF horizontally articulated manipulator (Fig. 2). A minimum-time trajectory (Fig. 4) was planned as the nominal trajectory for a desired path of Fig. 3. Viscosity friction and coulomb friction (b) Conventional Method [Joint 1: 0.2 sgn(4) + 0.48 ( N . m), Joint 2: 0.1 sgn(8) + 0.24 (N.m)] were applied to the joints as disturbances. Friction was not considered in the dynamic model used for the trajectory planning algorithm and the controllers. Fig. 7 shows the simulation results. Although the manipulator deviates from the desired path in the case of the conventional method [(b), the computed torque method in operational space], tracking error in the case of the proposed method (a) is small" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003023_s0168-874x(97)81968-3-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003023_s0168-874x(97)81968-3-Figure1-1.png", "caption": "Fig. 1. Choice of contact positions for analysis.", "texts": [ " In this paper, the analyses include two configurations, steel/plastic gear pairs and plastic/plastic gear pairs. The steel gear is considered as a rigid body, and the plastic gear is a deformable body with the quadrilateral plane strain elements. Both gear models have 4 or 5 teeth to reflect the influence of the adjacent teeth of the contacting gear pairs. To begin with the analysis, some positions, where one or two pairs of teeth mesh, are chosen along the path of contact in one base pitch as shown in Fig. 1. Then, the driving gear rotates about its axis with a small angle in every increment, and the driven gear is fixed. The mesh and boundary condition of a steel/plastic gear pair are shown in Fig. 2. The total force obtained from the contact nodes will be the normal load transmitted by the contacting pair of teeth, and the total rotation angle of the driving gear multiplied by the radius of the base circle will be the static transmission error. This method is called multi-tooth contact analysis. The results obtained by using the Houser's method and the multi-tooth contact analysis will be compared in this :section" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000740_tcst.2019.2950399-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000740_tcst.2019.2950399-Figure1-1.png", "caption": "Fig. 1. Reference frames.", "texts": [ " Suppose that the pursuer and target spacecraft are both rigid bodies. Three reference frames, i.e., the earth-inertial frame FI = {O, xi , yi , zi }, the pursuer body-fixed frame Fp = {P, xp, yp, z p}, and the target body-fixed frame Ft = {T, xt , yt , zt }, are available to construct the system dynamics. More specifically, frame FI is identical with the one introduced in [2], and frames Fp and Ft are centered at the mass centers of the pursuer and target spacecraft and are constrained by right-hand rule (RHR), respectively (see Fig. 1 for an illustrative example). 1) Relative Attitude Dynamics: The attitude of each spacecraft is expressed by a rotation matrix R \u2208 SO(3) = {R \u2208 R 3\u00d73 | det R = 1, R RT = RT R = I3}, where SO(3) stands for a Lie group of special orthogonal matrices. This attitude representation is unique and global and effectively avoids the singular and ambiguous issues in the Euler angle and unit quaternion representations [24], [29]. Moreover, according to Euler\u2019s formula [29], the rotation matrix R can be formulated by R = R(\u03c6, n\u0302) = cos\u03c6 I3 + (1 \u2212 cos\u03c6)n\u0302n\u0302T \u2212 sin \u03c6n\u0302\u00d7 (6) where \u03c6 \u2208 (\u2212\u03c0, \u03c0] and n\u0302 \u2208 S2 are the corresponding Euler angle and axis, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000775_tro.2019.2906475-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000775_tro.2019.2906475-Figure7-1.png", "caption": "Fig. 7. Mobile platform with integrated pendulum actuators.", "texts": [ " Each actuator consisted of a direct drive Beckhoff AM8131 dc motor with absolute encoders, a mount plate, a pendulum shaped load mass, and a coupler to fix the load mass to the motor shaft. The dimensions and spacing present in the actuator design were chosen based on the constraints imposed by the size of the platform and available motors. The actuators were placed beneath the platform to ensure the pendulums can swing fully without any chance of collision with the mobile platform or cables. Fig. 7 provides a close up view of the mobile platform after fabrication and integration. The relevant actuator parameters are provided in Table I. Experimental validation was performed using the setup described in Section IV. The test procedure was used to give the mobile platform a nonzero initial condition and allow the platform to oscillate freely thereafter. In the open-loop case, the pendulums were held at a constant zero-degree position. For the closed-loop case, the pendulums were enabled to actively suppress platform vibrations using a nonlinear, multi-input, multioutput, sliding mode controller, presented in [24]" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001760_tie.2021.3076715-Figure10-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001760_tie.2021.3076715-Figure10-1.png", "caption": "Fig. 10. Geometrical projection of lumped element-3 (Scale 1:2).", "texts": [], "surrounding_texts": [ "Geometrical parameters of PMSM and DC generator of experimental setup is given in Table III, which is used for natural frequency and mode shape calculations [30]. Geometrical projections of lumped elements 2, 3 & 4 are shown in Figs. 9, 10 & 11 which is required for inertia and stiffness matrix calculations. Further, damping and excitation torque is required for time response of torsional vibration of system. Authorized licensed use limited to: Carleton University. Downloaded on May 30,2021 at 21:54:56 UTC from IEEE Xplore. Restrictions apply. 0278-0046 (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. 7 Stiffness of any shaft under torsion is given by GiJi/Li, where Gi is Shear modulus of shaft and coupler (for stainless steel (Grade-304), Gi is 77\u00d7103 MN/m2). The material of shaft and coupler is steel having density of 7780 kg/m3 [31]. Ji is an area polar moment of inertia given by \u03c0di 4/32, where di is diameter of shaft and Li is the length of element. By using spring series addition and geometrical properties, equivalent mass polar moment of inertia and equivalent torsional stiffness for elements 2, 3 & 4 are calculated and given in Table IV, respectively." ] }, { "image_filename": "designv10_11_0001616_j.eswa.2021.115395-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001616_j.eswa.2021.115395-Figure1-1.png", "caption": "Fig. 1. Overall structure diagram of the SbW system.", "texts": [ " The effectiveness of the proposed control approach is validated by different simulations and experiments. The remainder of the paper is arranged as follows: Section 2 introduces the modeling of SbW system and some necessary problem formulation. The discrete-time HANN controller with DOs is introduced in Section 3. Different numerical simulations and experimental results are presented in Section 4. Finally, conclusions are presented in Section 5. The basic structure of an SbW system is shown in Fig. 1. It is clearly observed that the traditional mechanical linkage between the handwheel and the steering actuator is removed. Instead, two separate motors are installed on the SbW system: the steering motor generates the driving torque for the steering responses of front wheels and the feedback motor provides the feedback torque for drivers to feel the interaction between wheels and road surface. For a safe driving, the steering motor needs to drive the front-wheel steering angle to closely follow the reference angle generated by the handwheel" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000238_1.4033045-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000238_1.4033045-Figure9-1.png", "caption": "Fig. 9 A model of six-axis CNC bevel gear generating machine", "texts": [ " (30) with respect to time, the relative velocity can be derived as follows: v02 u0; l; h\u00f0 \u00de \u00bc dr0 u0; l; h\u00f0 \u00de dt \u00bc dr0 u0; l; h\u00f0 \u00de du0 du0 dt \u00bc x1 dr0 u0;l; h\u00f0 \u00de du0 \u00bc x1 dM02 du0 r2 l; h\u00f0 \u00de (32) where x1, the relative velocity between coordinate system S1 and coordinate system S0, remains constant and can be considered as 1 rad/s. Hence, the equation of meshing can be represented as f \u00f0u0;l; h\u00de \u00bc n0\u00f0u0;l; h\u00de v02\u00f0u0;l; h\u00de \u00bc 0 (33) Finally, the tooth surfaces of the generated noncircular spiral bevel gear can be represented by n0\u00f0u0; l; h\u00de v02\u00f0u0;l; h\u00de \u00bc 0 r0\u00f0u0;l; h\u00de \u00bcM02\u00f0u0\u00der2\u00f0l; h\u00de (34) Figure 9 shows a model of six-axis CNC bevel gear generating machine [30], which is configured with six kinematical components. In comparison with the traditional cradle style generating machines, the cradle motion is replaced by a vertical slider (Yaxis) and a horizontal slider (X-axis). The machine center is set at the pitch apex of generated gear. The relative motion of each axis is defined by UA for A-axis, RB for B-axis, Dx for x-axis, Dy for yaxis, and Dz for z-axis, respectively. In order to implement the generation of noncircular spiral bevel gears, we need to define the kinematics of the machine model" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000913_j.mechmachtheory.2019.06.026-Figure10-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000913_j.mechmachtheory.2019.06.026-Figure10-1.png", "caption": "Fig. 10. Three kinds of platform motions.", "texts": [ " The first one ( f 0 ) is the rigid body mode where the natural frequency is zero due to rotating freely. The natural frequency corresponding to the second mode ( f 1 ) is 1.94 Hz, where the mode shape is the rotation of the system. The third mode ( f 2 ) contains the lateral and rocking motions of the main shaft along X L and Y L axes (defined in the Ref. [11] ), respectively. The fourth mode ( f 3 ) is comprised of the lateral and bending motions of the main shaft along Y L and X L axes, respectively. For the case study, three kinds of platform motions are given in Table 3 and plotted in Fig. 10 , in which the corre- sponding descriptions are in the Ref. [2] . The platform motion is assumed to be a sinusoidal motion and expressed as M b = A b sin ( 2 \u03c0 f b t ) , where A b and f b are the amplitude and frequency of platform motions, respectively. The equations of motion of the system are built in Matlab/Simulink and solved by numerical integration under the rated condition [34] . 4.1. Case 1 For a CMC in the planetary gear stage, some specific parameters in the additional matrices, which are introduced by platform motions, are summarized in Eq", " Moreover, the resonant peaks corresponding to f 2 and f 3 are predominant in the planetary gear stage but not in the parallel gear stage, which is consistent with the results in Fig. 11 . The 3-D spectra of gear mesh deformations are described in Fig. 16 . As shown in Figs. 14\u201316 , the platform motion strongly influences the planetary gear meshes, and the modulation frequency ( f b \u00b1 f c ) significantly appear in Figs. 15 and 16 , such as f m 1 \u00b1 f b \u00b1 f c , compared with the results in Figs. 11\u201313 . These differences are ascribed to two reasons. First, the plane of platform motion (PPM) ( Y 0 O 0 Z 0 in Fig. 10 ) is perpendicular to the gear mesh plane (GMP) ( XOY and x u o u y u in Fig. 7 ) in case 1, while the PPM ( X 0 O 0 Y 0 in Fig. 10 ) is parallel to the GMP ( XOY and x u o u y u in Fig. 7 ) in case 2. The majority of the additional load excitations are applied to all components along the axial direction in case 1, but these excitations are changed to be along the direction of translations in case 2. Second, the mode shapes corresponding to f 1 contain the tangential translations of planets, and the mode shapes corresponding to f 2 ( f 3 ) include the lateral and rocking (bending) motions of the main shaft. These mode shapes are sensitive to the translational loads" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003701_e2005-00038-5-Figure10-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003701_e2005-00038-5-Figure10-1.png", "caption": "Fig. 10. Notation of the indentation lengths H1 and H2 in the isotropic buckling regime. The total indentation length is given by H = H1 + H2. R is the radius of the undeformed spherical shell. r is the radius of the circular bending strip whose width is denoted by w.", "texts": [ " By contrast, the continuous buckling takes place when Cs/\u03b5 = 100 for which the data deviate from others. Figure 9 is a similar plot of the adhesion energy W/\u03b5 as a function of Cb/\u03b5. When Cs/\u03b5 is larger than 300, W/\u03b5 is almost independent of Cb/\u03b5 in the unbuckled region, but starts to decreases as the buckling takes place. For Cs/\u03b5 = 100, however, W/\u03b5 decreases continuously as Cb/\u03b5 is reduced. To investigate the nature of the buckling transition in more detail, we have measured the indentation lengths H1 and H2 as defined in Figure 10. In Figure 11, we plot H1/R as a function of Cb/\u03b5 for various Cs/\u03b5 ranging from 100 to 900. Here the radius of the undeformed spherical shell is R = 0.75\u03c3 when N = 812 (see Sect. 4.6 or Tab. 1). In accordance with the aforementioned discussion, H1 changes discontinuously at the transition point for larger Cs/\u03b5, revealing the first-order nature of the buckling transition. This discontinuous buckling transition takes place between the disk formation regime and the isotropic buckling regime (Figs. 2b and c)", " Analogous to the liquid-gas coexistence region of van der Waals fluids, the region of discontinuous transition has been shaded in Figure 13. In the present model, the parameter Cs/\u03b5 plays a role similar to the temperature of van der Waals fluids. Another similar phenomenon is the volume transition of gels which is induced either by changing the temperature or the ionic strength. Here we analyze the geometry of the buckled shell from a different aspect. In Figure 14, we have plotted the relation between the scaled ring radius r/R and the total indentation length H/R (see Fig. 10 and Eq. (38)) for various combinations of Cb/\u03b5 and Cs/\u03b5 when N = 812. Different points represented by the same symbol correspond to different Cb/\u03b5 values having the same Cs/\u03b5 values. Interestingly, most of the data collapse onto a single line, and we find that a scaling relation r/R \u223c (H/R)1/2 holds in this regime. This scaling relation results from a simple geometrical consideration. As we will discuss in the next section, the buckled region is almost a mirror image of the original undeformed shell. The data deviate from a straight line when H/R is small because the deformation of the shell cannot be described by the geometry in Figure 10. Moreover, the above scaling relation does not hold in the anisotropic buckling regime in which the polygonal ridges are formed (see Figs. 3e or f). So far, we have discussed only the results when N = 812. Even the shell size N is varied, the qualitative properties of the deformation are unchanged from the case of N = 812. For example, the total indentation length H behaves similarly to Figure 13 although the location of the critical point shifts systematically. Table 1 summarizes the values of the critical point for four different sizes N = 92, 272, 812 and 2432", " (51) The minimized total elastic energy Ee = Es + Eb scales as E(I) e \u223c Y h2H2/R \u223c (CbCs/L2 0) 1/2H2/R. (52) Varying this with respect to H gives the force: f (I) \u223c (CbCs/L2 0) 1/2H/R, (53) which is proportional to H . This result indicates the linear Hooke\u2019s law of the deformation. In the isotropic buckling regime (case II), on the other hand, the adhesion is strong enough for the shell to undergo the buckling as in Figure 2c. Then most of the elastic energy is concentrated over a narrow bending strip of width w and radius r as defined in Figure 10. The buckled region is assumed to be a spherical cap which is a mirror image of its original shape. We remind that the assumption of vanishing spontaneous curvature plays an important role here. Then the following relation holds according to the simple geometrical reason [18]: r \u223c H1/2R1/2, (54) where H is the total indentation length. This explains the scaling relation which we found in our simulation (see Fig. 14). Since the order of magnitude of the displacement of a point within the bending strip is \u03b6 \u223c wr/R, the strain is given by \u03b6/R \u223c wr/R2, and the curvature is \u03b6/w2 \u223c r/Rw" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001379_tec.2020.3030042-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001379_tec.2020.3030042-Figure2-1.png", "caption": "Fig. 2. Simplified model of stator core.", "texts": [ " For the stator core inserting piriform slot, the stator teeth can be simplified into a combination of three simple structures, as shown in Fig. 1. The tooth foot and tooth shoulder are respectively simplified to structure b and structure c, the density of the simplified structures are reasonably adjusted to ensure that their mass are equal to the actual ones. Accordingly, the stator core can be regarded as a cylindrical shell with additional axial combined ribs on the inner surface, as shown in Fig. 2. Actually, the stator core is fixed on the enclosure by interference fit, thus the influence of the enclosure on the natural frequencies of the stator must be considered. The structures of the stator with enclosure are complicated, and it is necessary to simplify them reasonably. As shown in Fig. 3, the enclosure can be regarded as an elastic cylindrical shell that is coaxial but unequal length to the stator core. The terminal box, cooling ribs and other structures attached to the outer surface of the frame are equivalent to cooling ribs A with uniform distribution, and the density of the equivalent cooling ribs A are reasonably adjusted to ensure that their mass are equal to the actual ones" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001456_s10846-021-01411-4-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001456_s10846-021-01411-4-Figure2-1.png", "caption": "Fig. 2 Representative angles (roll \u03c6, pitch \u03b8 and yaw \u03c8) between Fv and Fb frames", "texts": [ " Typically, UAVs use the following state variables in North-East-Down (NED) nomenclature: the vector \u03b71 = [pn, pe, h]T represents the inertial North, East and Altitude (facing down) coordinates of the aircraft center of gravity along axis i\u0302I , j\u0302 I and k\u0302I in the inertial frame; the vector \u03b72 = [\u03c6, \u03b8, \u03c8]T represents roll, pitch and yaw angles in the vehicle frame (i\u0302v, j\u0302 v, k\u0302v). The vectors \u03bd1 = [u, \u03c5, \u03c9]T and \u03bd2 = [p, q, r]T represent the three dimensional linear and angular velocities over the axes (i\u0302b, j\u0302 b, k\u0302b) in the body frame. Figure 2 illustrates the reference frames (Fv and Fb) and the respective roll, pitch and yaw angles. For better explain, the vehicle frame is set at the QTR center of gravity, strictly aliened with the Inertial Frame F I . Summarizing, the vehicle position is defined by the vector \u03b71 \u2208 R 3 in the inertial frame F I , while its angles are defined by \u03b72 \u2208 R 3 in the vehicle frame Fv . Moreover, \u03bd1 \u2208 R 3 and \u03bd2 \u2208 R 3 are the linear and the angular velocities, measured in the frame Fb. According to [29], (1) presents the default nomenclature: \u03b71 = [pn pe h]T \u03b72 = [\u03c6 \u03b8 \u03c8]T \u03b7 = [\u03b71 \u03b72]T (1) Regarding the velocities, (2) presents them: \u03bd1 = [vb] = [u v w]T \u03bd2 = [\u03c9b] = [p q r]T \u03bd = [\u03bd1 \u03bd2]T (2) where \u03bd \u2208 R 6 is the generalized velocity vector, \u03bd1 \u2208 R 3 is the linear velocity vector, \u03bd2 \u2208 R 3 is the angular velocity vector, both in Fb" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003608_9783527618811-Figure1.5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003608_9783527618811-Figure1.5-1.png", "caption": "Fig. 1.5 A sequence of finite rotations of a cube: 180\u25e6 about n = [0 1/2 \u221a 3/2] followed by 180\u25e6 about k = [0 0 1]. The composite rotation is about i = [1 0 0] by 60\u25e6 as the shown by the Rodrigues spherical triangle displayed in the last panel.", "texts": [ " With \u03b3 in hand, the axis of the composite rotation is simply n = V(qp)/ sin 1 2 \u03b3 The Rodrigues triangle construction may also be given by the following equivalent description. Refer to the spherical triangle constructed in Fig. 1.4. Given a spherical triangle with vertices p, q, and r and vertex angles \u03b1/2, \u03b2/2 and \u03b3/2 successive rotations about p by angle \u03b1, q by \u03b2, and r by \u03b3 yield the identity transformation. Rr(\u03b3)Rq(\u03b2)Rp(\u03b1) = Mq\u2032Mp\u2032Mp\u2032Mr\u2032Mr\u2032Mq\u2032 = I Example 1.2 An illustration of the composition of rotations of a cube and the associated Rodrigues spherical triangle is shown in Fig. 1.5. The analytic expression of that composition is Rk(\u03c0)Rn(\u03c0) = R\u2212i(2\u03c0\u2212 \u03c0/3) = Ri(\u03c0/3) Note the orientation of the Rodrigues triangle. \u2666 We close this section with an application of the Rodrigues triangle. Let a, b, and b\u2032 = Ra(\u03b1)b be points on the unit sphere. Construct the spherical triangles shown in Fig. 1.6. If each triangle is interpreted as a Rodrigues triangle for composition of rotations, we obtain the relation Ra(\u03b1)Rb(\u03b2) = Rb\u2032(\u03b2)Ra(\u03b1) = Rc(\u03b3) This is referred to as Rodrigues\u2019 transposition of rotations [3, 12] or rotation reversal [13]" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003370_j.1460-2687.1999.00028.x-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003370_j.1460-2687.1999.00028.x-Figure1-1.png", "caption": "Figure 1 The double pendulum model.", "texts": [ "eywords: golf swing, ball position, contact, energy Most golfers, if asked, will claim that they try to swing the club with the aim of achieving maximum clubhead speed at impact and the degree of success, or otherwise, is dependent on the skill of the player. Several authors have studied the dynamics of the golf swing and, in particular, the downswing has received detailed attention. For example, Daish (1972) modelled the downswing as the motion of a double pendulum with the upper pivot located at a point in the player's spine a few centimetres below the base of the neck and the second pivot at the player's wrist joint, as illustrated in Fig. 1. The turning motion of a player's body was modelled by the application of a torque to the upper lever (upper torso and arms), and any wrist action imparted by the player by a second couple which was applied to the lower lever (the club). The downswing was modelled in two phases. In the \u00aerst, the wrists are fully cocked (a p/2, see Fig. 1) and the upper body rotates as a rigid body under the turning action of the player. In the second, the player allows the wrist joint to turn freely, commonly referred to as the release of the club, or wrist `uncocking.' The correct anatomical term is wrist adduction; see, for example, McLaughlin & Best (1994). It is, of course, the player's decision at what point in the swing to allow this second phase to begin and this affects the clubhead velocity (and various other parameters) at the instant of contact of the clubhead with the ball", " 2), the ball is placed at the point in the downswing where the clubhead 162 Sports Engineering (1999) 2, 161\u00b1172 \u00b7 \u00d3 1999 Blackwell Science Ltd achieves its maximum horizontal component of velocity. This position is unknown in advance and has to be determined during the course of the computations. It might be regarded as preferable to choose the point A as the point in the downswing where the clubhead achieves its maximum resultant velocity but, as noted by Milne (1990), there is also a dif\u00aeculty in deciding the form of torque input to use in a computational model, and of particular relevance here is the torque G1 applied to the upper lever (Fig. 1). Jorgensen (1970) assumed that G1 is constant throughout the swing, Lampsa's (1975) calculations suggested that, optimally, G1 should be linearly increasing with time and Milne (1990) used a linearly increasing torque up to a maximum value which is maintained until impact, although precise details are not given. All such torque models lead to continuously increasing computed resultant clubhead velocities as the downswing proceeds and consequently the maximum resultant clubhead velocity occurs well past any possible point of contact with the ball and well into the `followthrough' or upswing", " \u00d3 1999 Blackwell Science Ltd \u00b7 Sports Engineering (1999) 2, 161\u00b1172 163 It should be noted that I1 + m1h1 2 (the moment of inertia of the upper lever about the upper pivot) is given as data by Lampsa (1975) (Lampsa's parameter Ia) and thus explicit values for m1 and h1 are not required in Eq. (1). Furthermore, an explicit value for I1 is not given by Lampsa (1975). Thus from Eqs (1), (2) and (3) we \u00aend that A 1.30, B 0.18 and D 0.30, all being in units of kg m\u00b12. These values are very similar to those given by Daish (1972). If b is the angle through which the upper body rotates and a is the angle between the line of the upper arm and the line of the club (as indicated in Fig. 1), then the kinetic energy of the system is T, where T 1 2 A _b 2 1 2 D _a _b 2 \u00ff B _b _a _b cos a: 4 This expression is that given by Daish (1972; eqn (6)) where Daish's angles h and / are related to a and b by a / \u00b1 h + p, b h + p. When gravity is neglected, the Lagrangian equations of motion for the upper arm and club are, respectively, d dt @T @ _a @T @a G2 and 5 d dt @T @ _b @T @b G1; 6 where G1 and G2 are the couples exerted by the golfer on the upper body and the club, as shown in Fig. 1. It follows from Eqs (4), (5) and (6) that d dt A _b D _a _b \u00ff B _a 2 _b cos a h i G1 7 and dT dt G1 _b G2 _a: 8 If G1 and G2 are given as functions of time then these equations may be integrated numerically to give a and b as functions of time. It is perhaps worth mentioning here that eqs (8) and (9) of Daish (1972; p. 113) [or eqs (5) and (6) of Jorgensen 1970] may be obtained from our Eqs (7) and (8) by carrying out the differentiation with respect to t followed by some algebraic manipulation", " Thus, for bs > 0, the same value of _bR will be achieved as for the case bs 0 but at some later stage (larger value of bR) in the swing. The subsequent motion for the case bs > 0 is thus identical with that for bs 0 but offset by bs, as also noted by Jorgensen (1970). In all calculations presented here it is assumed that bs 0. Impact criterion, computed parameters at impact, scaling As indicated in the Introduction, in addition to solving Eq. (18), the horizontal component of \u00d3 1999 Blackwell Science Ltd \u00b7 Sports Engineering (1999) 2, 161\u00b1172 165 clubhead velocity, vh, is calculated as the computation proceeds. From Fig. 1 it follows that vh is given by vh \u00ffl1 _b cos b l2 _a _b cos a b ; 22 and hence, by differentiating Eq. (22) with respect to t, it follows that vh will be a maximum when \u00ff l1 b cos b l1 _b2 sin b l2 a b cos a b \u00ff l2 _a _b 2 sin a b 0: 23 Eq. (18) was solved by the fourth-order Runge\u00b1 Kutta method subject to the initial conditions described above and the expression on the lefthand side of Eq. (23) was evaluated at each timestep. The computation was halted a few steps beyond the stage where Eq. (23) changed from a positive to a negative value and the time for which Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001319_tec.2020.3007802-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001319_tec.2020.3007802-Figure9-1.png", "caption": "Fig. 9. The radial force densities exerted on the stator: (a) Second order force density, (b) Tenth order force density.", "texts": [ " In order to separate the radial force density, a 2-D fast Fourier transform (FFT) analysis can be performed in space and time domains. Fig.8 shows the waveform at one instant and its spatial harmonic spectrum of radial magnetic force density with twice the fundamental frequency. From Fig.8 (b), it can be seen that the amplitudes of decomposed 2-order and 10-order components are 785.6 N/m2 and 15280 N/m2 respectively, and their waveforms are shown in Fig.8 (a). Then, these forces will exert on the stator, as shown in Fig.9. Fig.10 presents the vibration caused by these forces. 0 60 120 180 240 300 360 -30000 -20000 -10000 0 10000 20000 30000 F o rc e d e n s it y ( N /m 2 ) Rotor position (Mech.degree) All order 2 order 10 order 14 (a) Authorized licensed use limited to: University of Exeter. Downloaded on July 16,2020 at 00:15:50 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" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001379_tec.2020.3030042-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001379_tec.2020.3030042-Figure5-1.png", "caption": "Fig. 5. Equivalent structure of stator core.", "texts": [ " The potential energy and kinetic energy of the simple-supported elastic beam can be expressed as 2 2 20 2 2 2 20 , 2 sin 2 L L EI x y x t PE dx x t y x EI x dx x (2) 2 0 2 2 2 0 , 2 cos 2 L L x y x t KE dx t t x y x dx (3) Ignoring the damping of the elastic beam, Umax=Tmax can be obtained from the energy conservation of the system, thus the Rayleigh quotient expression of the simply-supported elastic beam can be described as discrete orthogonal functions, scilicet 1 1 2 2 1 tN Nt Nt i i i y x c x c x c x x c \u03c7 (5) where Nt is the number of functions in the orthogonal function cluster, the orthogonal function cluster \u03c7 and the weighting coefficient c are 1 2, , , , ,i Ntc c c cc (6) T 1 2, , , , ,i Nt \u03c7 (7) Substituting (5) into (4), the simplified Rayleigh quotient expression can be obtained as T 2 T cKc cMc (8) The Rayleigh quotient takes the extreme value of the weighting coefficient c, then T T T T 2 T cMc cKc cKc cMc c c 0 c cMc (9) where the specific elements of the stiffness matrix K and the mass matrix M are 22 2 20 L ji ij xx k EI x dx x x \u03c7\u03c7 (10) 0 L ij i jm x x x dx \u03c7 \u03c7 (11) Simplifying (9) according to the related theory of matrix calculation, the characteristic equation of natural frequencies of the elastic beam can be expressed as 2 0K M c (12) Consequently, the vibration displacement of continuous systems can be discretized based on Galerkin discretization, and the characteristic equation of natural frequencies of elastic beams can be obtained by energy conservation. The energy method is used to calculate the natural frequencies of the system, which avoids the simulation of various complex boundary conditions. The equivalent structure of the stator core is shown in Fig. 5. u, v and w represent the axial, circumferential and radial displacements of the mid-surface in the cylindrical shell, respectively. R, h and L are the average radius, thickness and axial length. The eccentricity of the axial ribs to the mid-surface of the cylindrical shell is eti, and the angle between adjacent ribs is \u03b8s. Authorized licensed use limited to: Carleton University. Downloaded on November 07,2020 at 09:19:17 UTC from IEEE Xplore. Restrictions apply. 0885-8969 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000096_s0373463318000024-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000096_s0373463318000024-Figure3-1.png", "caption": "Figure 3. The Earth-fixed frame and the body-fixed frame.", "texts": [ "02 m long intelligent equipment platform owned by Dalian Maritime University, which has the functions of water sampling, marine monitoring, maritime rescue, etc. (Fan et al., 2015). The Lanxin USV is shown in Figure 1. It can be seen from Figure 2 that when the propeller changes its propulsion angle, the vectored thrust produced by the propeller can be decomposed into two directions: forward thrust component which propels the vessel forward and a lateral thrust component which achieves steering. 2.2. Planar motion model. Conventionally, the Earth-fixed frame and the body-fixed frame are adopted to study the USV model. As shown in Figure 3, O \u2212 X0Y0Z0 is the available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0373463318000024 Downloaded from https://www.cambridge.org/core. University of New England, on 12 Mar 2018 at 03:31:19, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0373463318000024 Downloaded from https://www.cambridge.org/core. University of New England, on 12 Mar 2018 at 03:31:19, subject to the Cambridge Core terms of use, inertial coordinate system and o \u2212 xyz is the attached body coordinate system" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000970_j.mechmachtheory.2019.103747-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000970_j.mechmachtheory.2019.103747-Figure6-1.png", "caption": "Fig. 6. Finite inverse singularity of the second kinematic chain corresponding to geometrical configurations (h), (i), and (j) from Fig. 3 at (a) \u03b3 = \u03be = \u03c0/ 2 and Y EE = X 2 , (b) \u03b3 = \u03be = \u03c0/ 2 and Y EE = X 2 , and (c) \u03b3 = \u03be = \u03c0/ 2 and Y EE = \u2212X 2 .", "texts": [ " \u03c3 = | \u03b3 \u00b1 \u03be | yields inverse singularity of the second chain, in which the axes X 2 , Z 3 , Y EE are coplanar. In this situation, according to Fig. 2 , link 3 is completely folded or unfolded with respect to link 2, corresponding to C 3 = 0 . \u03b3 = \u03be yields instantaneous inverse singularity of the second chain (corresponding to geometrical configurations (d) to (g) in Fig. 3 and refereed to as II-2 in the rest of this paper) and \u03b3 = \u03be results in finite inverse singularity (refereed to as FI-2 in the rest of this paper). As shown in Fig. 6 , for \u03b3 = \u03be = \u03c0/ 2 geometrical configuration (h) and for \u03b3 = \u03be = \u03c0/ 2 geometrical configurations (i) and (j) occur. Finally, for \u03c3 < | \u03b3 \u2212 \u03be | or \u03c3 > \u03b3 + \u03be , there is no solution for the inverse kinematics problem and the given end-effector position is out of workspace. Since the inverse singularities occur at C 3 = 0 and C 5 = 0 , the proposed 5R-SPM has four solutions for inverse kinematic in regular configuration (four working modes), based on the sign of C 5 and C 3 ( Fig. 7 ). The former indicates the solution of the first chain and the latter corresponds to the solution of the second chain", " For S 3 = \u22121 , L and N become S \u03b3 \u2212\u03be and C 5 \u2212 C \u03bb(C \u03b3 \u2212\u03be ) , respectively. L = 0 leads to \u03b3 = \u03be which, knowing also that C 3 = 0 , corresponds to finite inverse singularity of the second kinematic chain (FI-2) ( Figs. 6 (a)). N = P = 0 leads to C 5 = C \u03bb and C 1 = 0 which indicates the orientation of the end-effector vector, which is Z EE = \u00b1[ C \u03bb \u2212 S \u03bb 0] T . For S 3 = 1 , L and N become S \u03b3 + \u03be and C 5 \u2212 C \u03bb(C \u03b3 + \u03be ) and L = N = P = 0 yields \u03b3 = \u03be = \u03c0/ 2 , 5 = \u2212C \u03bb, and C 1 = 0 . This also corresponds to FI-2 ( Fig. 6 (b-c)). Therefore, as long as we avoid FI-2, the determinant of the coefficient matrix is nonzero and and \u03b82 can be obtained from Eq. (A.28) . To summarize the exhausting analysis provided above, L = M = 0 occurs at one of the following situations: either folded links with link lengths \u03b3 = \u03be or folded or unfolded links with link lengths \u03b3 = \u03be = \u03c0/ 2 . These situations yields infinite number of solutions for \u03b82 , corresponding to a finite inverse singularity of the second chain (FI-2). Again, all these possibilities for FI-2, were simply found using the proposed geometrical approach, by investigating the sign of the denominator and radicand of Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000716_j.mechmachtheory.2019.07.013-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000716_j.mechmachtheory.2019.07.013-Figure8-1.png", "caption": "Fig. 8. Coordinate systems of the generating surfaces of the grinding disk wheel.", "texts": [ " Matrix M ts is considered to transfer the coordinates of the section geometry of the reference shaper from coordinate system S s of the reference shaper to coordinate system S t . The upper and lower signs in Eq. (20) correspond to the left and right section profiles of the reference shaper, respectively. The vector [( t s - t l )/2 0 0 1] T makes the top thickness t g of the grinding disk the same with the top width t l of the reference shaper at the heel end. t s denotes the top width of the reference conical spur involute shaper at the toe end. Fig. 8 shows a new coordinate system S g , having origin O g coincides with O t of coordinate system S t . The coordinate system S g is established in order to form the complete generating surfaces of the disk wheel. The radius of the grinding disk \u03c1g can be determined indirectly by the given distance E gs and the radius of the section profiles of the reference shaper at the toe end. The generating profiles defined in coordinate system S t can be expressed in coordinate system S g by rotating around the axis z g with an angle \u03b8 g " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003224_0921-8890(95)00019-c-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003224_0921-8890(95)00019-c-Figure2-1.png", "caption": "Fig. 2. Biomorph computational structure.", "texts": [ " They smoothly morph through several stages: sensors that deliver modification information to a heuristic neural net \"brain,\" which influences an independent neuron machine core that ,contains a highly abstract and condensed representation of the external world. Outwards the mechanical body, also computing continuously, can interact with the external world, but has no knowledge that it even belongs to an integrated creature: a sum of components, all with soft demarcation boundaries, blending to form survival adequacy. Fig. 2 gives a typical design representation for a quadruped creature, which can be quickly extended to 6, 8, or 2n legged devices (odd number legged devices are possible but ineffective as the odd leg induces a drag on the structure that the control core can make little use of). Biomorphic survival traits and behaviors can be emphasized, not set, by the careful matching of the variables among layered components. To represent this, we chose to equip biomorphic machines with an expandable internal landscape that self-assembles an internal abstract world" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003471_027836499601500204-Figure12-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003471_027836499601500204-Figure12-1.png", "caption": "Fig. 12. Constraints on geometrically feasible footfalls.", "texts": [ " In most situations, the planner considers the rearmost legs on each stack; however, for tight turns (arc radii less than the distance between the body and stack centers, or about 2 m), one of the stacks moves in retrograde motion (Fig. 11B), so that the planner must alternate moving the legs on one stack from rear to front, and the legs on the other stack from front to rear. There are a number of geometric constraints that come into play in determining where to place the feet. The kinematic limits of the leg define a torus outside which the leg cannot reach. In addition, the leg must be placed so that it does not collide with the current frontmost leg, nor should it be placed within the current path of the body (Fig. 12). Finally, there are constraints needed to ensure the feasibility of subsequent movements: the leg must be placed far enough forward so that a subsequent leg move on the opposite stack keeps the body within the CSP, and the leg must not be placed so far forward that subsequent leg moves on the same stack become kinematically infeasible. These kinematic constraints define an area within which all footfalls are geometrically feasible. If the area for a leg is insignificant, the planner tries moving the leg on the other stack" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000048_tmag.2017.2698004-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000048_tmag.2017.2698004-Figure2-1.png", "caption": "Fig. 2. Decomposition of the proposed VPM machine: (a) Machine I. (b) Machine II.", "texts": [ " The proposed dual-stator VPM machine can be regarded as a superposition of two machines: a I Manuscript received March 19, 2017. Corresponding author: Dawei Li (email: daweili@hust.edu.cn). Digital Object Identifier inserted by IEEE 0018-9464 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. single-stator PM machine (Machine I) and a double-stator VPM machine (Machine II), shown in Fig. 2. The consequent-pole PM rotor and the outer stator compose the single-stator PM machine (Machine I). Due to the self-shielding effect of the Halbach-array magnets [10], the rotor back-iron is not essential for Machine I. The inner stator, reluctance rotor and the outer stator compose the double-stator VPM machine (Machine II). The 3D rotor structure is shown in Fig. 3. There is a magnetic bridge behind the Halbach-array PMs, and the thickness of the magnetic bridge is chosen as 0.5mm in this paper" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003891_s0003-2670(00)82081-4-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003891_s0003-2670(00)82081-4-Figure1-1.png", "caption": "Fig . 1 . Schematic representation of the fibre-optic biosensor for analysis by flow injection .", "texts": [], "surrounding_texts": [ "Apparatus A schematic diagram of the fibre-optic sensor associated with a flow cell is shown in Fig . 1 . Reagents were delivered by a one-channel peri- S.M. GAUTIER ET AL ." ] }, { "image_filename": "designv10_11_0001449_j.mechmachtheory.2021.104396-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001449_j.mechmachtheory.2021.104396-Figure8-1.png", "caption": "Fig. 8. Interference situation between clearance surface and generating surface of two cylindrical type power-skiving tools: (a) no rake-surface-offset ( z of f = 0 mm ) along tool axis, and (b) rake-surface-offset z of f = 10 mm along tool axis.", "texts": [ " In other words, the shape of the re-sharpened tool is basically the same as that of a brand-new tool (albeit, the length of the tool is shorter). Consequently, the cutting situation between the tool and the gear workpiece also remains unchanged after the tool is resharpened. Recalling the discussions in the previous section, the generating surface produced by the internal gear no longer has a constant cross-sectional profile along its axis (see Fig. 5 ). Rather, the profile changes like a negative-shifted gear tooth profile. Consequently, referring to Fig. 8 (a), if no rake-surface-offset is provided along the tool axis (i.e., z of f = 0 ), the generating surface and clearance surface will interfere. In other words, the clearance surface interferes with the internal gear profile. Accordingly, referring to Fig. 8 (b), an appropriate rake-surface-offset, z of f , must be assigned. The cutting-edge of a skiving tool is the intersection curve between the generating surface and the rake surface. Referring to Fig. 9 , s 0 represents the intersection of the plane with z of f = 0 and the generating surface, and s 1 is the intersection of any plane with z of f > 0 and the generating surface. Obviously, s 1 lies inside s 0 and does not intersect it at any point. Since the generating surface is barrel-shaped, curve s 0 is similar to the tooth profile of a gear with a zero-shifted coefficient, while curve s 1 is similar to the tooth profile of a gear with a negative-shifted coefficient", " As a result, the cutting speed distribution range is quite wide, and hence it is insufficient to consider the cutting speed only at the pitch point. As described in Section 4 . (iv), the cross-sectional profile of the skiving-tool is assumed to be constant along the helical protrusion direction of the teeth, and is thus suitable for re-sharpening. For comparison purposes, two rake-surface-offsets are considered, namely Case 1: z of f = 0 mm and Case 2: z of f = 10 mm . Figs. 8 (a) and 8(b) present schematic illustrations of the resulting power-skiving tool designs. In the Case 1 design ( Fig. 8 (a)), the generation surface and clearance surface interfere. In other words, the clearance surface interferes with the internal gear profile, and the tool design is thus unacceptable. However, as shown in Fig. 7 (b) for the Case 2 design, interference is avoided, and hence the design is feasible. Figs. 14 (a) and (b) present the full-view analysis results for the working clearance angles of the cutting-edge (including right, left, root, and top regions) in the Case 1 and Case 2 designs, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001296_s10846-019-01143-6-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001296_s10846-019-01143-6-Figure1-1.png", "caption": "Fig. 1 Schematics of a moving manipulator with R-S joints", "texts": [ " The kinematic controller of the examined system is analytically developed in Section 3 through an optimization process, and the asymptotical stability of the closed-loop system is verified. Then in the same section, the dynamic controller of this system is obtained using a similar procedure. Computer simulation is performed in Section 4 to evaluate the efficacy of the suggested control approach in the face of existing uncertainties. Eventually, the summary and the conclusion of this work are presented in Section 5. This paragraph presents the kinematics of a multi-rigid-link robotic manipulator with R-S joints which is installed on a moving base (Fig. 1). Each link\u2019s coordinate system (xiyizi) is oriented based on the laws proposed by Denavit & Hartenberg (D-H). The frame attached to the moving platform is x0y0z0, whose origin is fixed at Point P; the x0 axis is along the axis of symmetry of the moving base, y0 is along the rolling wheels\u2019 axis of rotation (toward the left rolling wheel), and the z0 axis completes the orthogonal coordinate system. Also, the ground-fixed XGYGZG frame can be taken as the global reference frame. To accomplish the mathematical modeling of the above robotic system, the succeeding assumptions are adopted: 1) the wheels roll on an even surface without slipping, 2) The moving base is confined to travel in the XGOGYG plane, and 3) In order to uphold the no-slipping condition, Point P\u2019s velocity is assumed to be co-linear with the platform\u2019s axis of symmetry", " Finally, by equating the obtained result to the generalized forces associated with the quasi-velocities, the governing motion equations are derived. It can be easily proved that the Gibbs function for a rigid body has the following form S \u00bc 1 2 m a!G T \u22c5 a!G \u00fe 1 2 \u03c9!\u0307T \u22c5IG \u03c9!\u0307\u00fe \u03c9!\u0307T \u22c5e\u03c9IG \u03c9! \u00f015\u00de m and IG respectively denote the mass and moment of inertia about the centroid, a!G is the centroid\u2019s acceleration, \u03c9! and \u03c9!\u0307 respectively represent the rigid body\u2019s angular velocity and acceleration, and e\u03c9 indicates the skew symmetric matrix associated with vector \u03c9!. The robotic system shown in Fig. 1 is constructed of n + 3 rigid bodies (one moving base, two rolling wheels and n rigid links). Since wheel masses are integrated with base mass, G0 represents the centroid of platform and wheels. So, using Eq. (15), the Gibbs function of the moving robotic manipulator can be written as S \u00bc \u2211 n i\u00bc0 h 1 2 mi i a!Gi T \u22c5 i a!Gi \u00fe 1 2 i \u03c9!\u0307i T \u22c5IGi i \u03c9!\u0307i \u00fe i \u03c9!\u0307i T \u22c5 ie\u03c9iIGi i \u03c9!i i \u00fe 1 2 Iw \u03b8 ::2 R \u00fe \u03b8 ::2 L\u00de \u00f016\u00de where m0 and IG0 respectively indicate the total mass of the moving base and wheels and their mass moment of inertia about the vertical axis passing through the centroid G0, mi is the ith link\u2019s mass, IGi is the i th link\u2019s mass moment of inertia about the vertical axis passing through the centroid Gi, and Iw is the mass moment of inertia of the left/right rolling wheel about its axis of rotation" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003277_s004220050495-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003277_s004220050495-Figure7-1.png", "caption": "Fig. 7. The coordinate systems describing the con\u00aeguration of the three-segmented, six DoF manipulator which can move in 3D space", "texts": [ " For the smaller rectangle on average of 13.4 iterations were necessary for the inverse kinematic tasks and 11.5 iterations for the direct kinematic tasks. For the larger rectangle the corresponding \u00aegures were 10.8 and 11.5, respectively (a damping parameter of d 3 has been applied for these tests). The MMC principle can be used to solve any underconstrained or mixed problem. To show this in two examples, the net will now be expanded for a threesegment, six DoF manipulator acting in 3D space (Fig. 7). The shoulder joint has three DoF which are described by angle a1 (movement around the vertical axis), angle b1 (movement around a horizontal axis), and a2. The last describes the rotation of the upper manipulator, L1, around its long axis. The elbow contains a simple hinge joint, angle b2. The wrist has two DoF, described by the angles a3 and b3. To represent this manipulator, the linear part of the net has to be expanded by a third subnet for the z coordinate, as mentioned earlier. The rotation of the elbow coordinate system (Fig. 7) is now described by the two transformations L00x L0x cos b L0z sin b L00y L0y L00z \u00ffL0x sin b L0z cos b Ty and L0x Lx cos a\u00ff Ly sin a L0y Lx sin a Ly cos a L0z Lz Tz The angles are determined by a atan2 y; x b atan2 x cos a y sin a; z which corresponds to the transformation P of the 2D case. After these angles are fed back, the following equations correspond to the transformation Q of the 2D case: L0x L cos a sin b L0y L sin a sin b L0z L cos b The values have then be transformed by Ty \u00aerst and Tz second" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000245_lra.2016.2527065-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000245_lra.2016.2527065-Figure2-1.png", "caption": "Fig. 2. 2 DOF needle insertion robot. A motor provides the linear motion to insert the needle into the phantom tissue. A second motor attached to the needle rotates it around its shaft. The axial force (along Z) at the needle base is measured by a force sensor. Images of the needle inside tissue are recorded by a camera in the (Y,Z) plane by an ultrasound probe in the (X ,Y ) plane. The ultrasound probe is mounted on a second linear stage (not visible) that is controlled such that the ultrasound imaging plane always contains the needle tip.", "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. expressions with only n unknown parameters. Therefore, one can solve for the tip force using the extended system of equations when image feedback is available. The description of how the needle deflection is measured in ultrasound images can be found in [14]. Note that position feedback of the needle could be obtained from another imaging or sensing modality. Fig. 2 shows the two-degrees-of-freedom robotic system used for conducting needle insertion experiments in soft tissue. A 6-DOF force/torque sensor (JR3, Inc. Woodland, USA) is connected to the needle base and measures the axial insertion force (the other 5-DOF of force/torque sensing are not used). A RE-25 Maxon motor can rotate the needle around its shaft. The assembly can translate thanks to a linear stage actuated by a RE-40 Maxon motor through a belt and pulley mechanism. Validation of the proposed method in this paper is performed using camera and ultrasound images to measure the needle deflection in semitransparent and biological phantoms respectively. A camera records at 30 Hz images of the needle inside a semitransparent tissue from the side of the tissue container (in the (Y,Z) plane defined in the upper left corner of Fig. 2). The needle is steered such that its deflection plane is parallel to the camera imaging plane. The images are processed to output the needle shape in the form of a polynomial, from which the position of the needle tip is calculated given the needle insertion depth. The image processing algorithm used to measure the needle deflection in camera images can be found in [10]. For validation of the model in biological tissue, a 4DL145/38 Linear 4D ultrasound transducer connected to a SonixTouch ultrasound machine (Ultrasonix, Richmond, Canada) is placed above the tissue to acquire 2D images of the needle in the (X ,Y ) plane shown in Fig. 2. The ultrasound probe is connected to a second motorized linear stage so that the position of the probe can be independently controlled (not visible in Fig. 2). The horizontal position of the probe is recorded by a linear potentiometer (Midori Precisions, Tokyo, Japan) and it is controlled such that the imaging plane always contains the needle tip. We use the method proposed in [14] to measure the needle deflection in ultrasound images. The needle appears as a bright spot along with extraneous background objects. To remove the majority of these objects we first define a region of interest (ROI) that limits the search for the needle to a small section of the image" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003566_0094-114x(94)90031-0-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003566_0094-114x(94)90031-0-Figure4-1.png", "caption": "Fig. 4. Screw triangle associated with the displacement of a point.", "texts": [ " As long as the c, satisfy this equation, ~s, obtained from equation (16), is one of the possible screws for displacing the specified line. Note that equation (21) gives a constraint only on the ratios among the cs. This allows us to normalize c, in order to make ~s a unit screw. Since (21) is not linear in the c~, the screws represented by equation (16), with constraint (21), do not form a linear space. From the above analysis, we know that, using the new definition for pitch, the screw system can be represented as a nonlinear subset of a a-system. 3.3. A point As shown in Fig. 4, R~ and R s are the initial and final positions of the point of interest. Let r~ ~= (a, b, c) and r~ = (d, e , f ) be the position vectors of Rs and R s, respectively. The free parameters xs xl X2 x3 X4 g 0.5 (log P -> - 0 . 3 0 1 ) (Fig. 6a). The o ther branch of the b = 1 con tour is the line of all perfect circular folds, and it represents a max imum possible bluntness for acute perfect folds (q~/2 < 90 \u00b0) (Fig. 6b) and a min imum possible bluntness for obtuse perfect folds (~/2 > 90 \u00b0) (Fig. 6c). This relat ionship results in the negative slope of lines of constant ~ for < 180 \u00b0, and the positive slope of these lines for ~ > 180 \u00b0 (Fig. 5). The point where the two branches of the b = 1 con tour join, i.e. (P, ~ , b) = (0.5, 180 \u00b0, 1), represents an isoclinal perfect circular fold (Fig. 6a). Obtuse perfect folds are limited by ano ther geometr i - cal constra int if the folds occur as par t of a periodic train of identical folds (Fig. 7). F r o m the relat ions shown at the top of Fig. 7(a), it is clear that re = M (7) and f rom the relat ions shown along the median line, we see that equa t ion (4) holds for r0. Substituting equat ions (4) and (7) into (2) shows that the bluntness ratio is independen t of the aspect ratio B = 2 sin ~/2. (8) Thus f rom equat ions (8) and (6), the limiting geome t ry of such folds is comple te ly de te rmined by only a single pa ramete r , which for these equat ions we can choose to be the folding angle ~" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000740_tcst.2019.2950399-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000740_tcst.2019.2950399-Figure2-1.png", "caption": "Fig. 2. Distribution of thrusters.", "texts": [ " Moreover, according to [32], the dynamics of vt and vp , respectively, satisfy mt v\u0307t + mt\u03c9 \u00d7 t vt = 0 (18) m p v\u0307p + m p\u03c9 \u00d7 p vp = At f + fd (19) where mt \u2208 R and m p \u2208 R are the masses, At \u2208 R 3\u00d7N is the distribution matrix of the orbit control thrusters satisfying rank(At ) = 3, f \u2208 R N is the control force, and fd \u2208 R 3 is the disturbance force. By considering (18) and (19), taking the derivative of (14) yields m p \u02d9\u0303v = \u2212m pCt v\u0303 \u2212 m pnt + At f + fd (20) where nt = (R\u0303T\u03c9t ) \u00d7 R\u0303T vt + R\u0303T v\u0307t + \u03c9\u0303\u00d7 R\u0303T \u03b4\u00d7t \u03c9t \u2212 R\u0303T \u03b4\u00d7t \u03c9\u0307t . 1) Thruster Faults: In practice, the pursuer carries N pairs of attitude-driven thrusters and N pairs of orbit-driven thrusters. Each pair of thrusters generates the torque component \u03c4i or the force component fi in the opposite directions (see Fig. 2 for example, where Pi and Qi constitute a pair of attitude-driven thrusters, while Ti and Hi constitute a pair of orbit-driven thrusters). Suppose that the generating force and torque are subjected to faults, which have been diagnosed as multiplicative and additive ones. In particular \u03c4 = \u03d2r\u03ber + \u03c6r (21) f = \u03d2t\u03bet + \u03c6t (22) where \u03bei \u2208 R N , i = r, t , denote the command controls, \u03d2i = diag(\u03b3i,1, \u03b3i,2, . . . , \u03b3i,N ) with \u03b3i, j \u2208 [0, 1], i = r, t and j = 1, 2, . . . , N denote the multiplicative faults, and \u03c6i \u2208 R N , i = r, t , denote the additive faults" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001464_j.jsv.2021.116360-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001464_j.jsv.2021.116360-Figure9-1.png", "caption": "Fig. 9. Two-stage parallel shaft gearbox test rig.", "texts": [ " It can be seen that the amplitude of these six characteristic frequencies all increase significantly, which shows the strong evidence of gear fault. The above simulation example demonstrates a good potential for the proposed method in gearbox fault diagnosis. X. Yu et al. Journal of Sound and Vibration 511 (2021) 116360 In this section, we performed experiments on a two-stage parallel shaft gearbox test rig to verify the effectiveness of the proposed method in the practical gear fault diagnosis. Fig. 9 shows the gearbox test rig in which the replacement of fault gear can be achieved by simple sliding. Two triaxial accelerometers are attached on the gearbox housing to acquire vibration signals. Gear parameters of the two-stage parallel shaft gearbox and frequency information under the experimental condition are listed in Table 2. In the following paragraphs, fm indicates the meshing frequency of the fault gear pair, fc1, fc2, and fc3 indicate the rotating frequency of the driven shaft, immediate shaft and driving shaft, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000164_hri.2016.7451840-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000164_hri.2016.7451840-Figure2-1.png", "caption": "Figure 2: Schematic overview of tactile transducer setup.", "texts": [ " This pressure sensitive sensor system has to cover the entire area (4.0 by 6.0 meters) of the shared workspace. For this we developed single tactile transducer modules with a size of 0.50 by 0.50 meters. Each tactile transducer module has been composed of piezo-resistive composite material, sandwiched between two electrodes and arranged as sensor array of 16 individual taxels 3 . The outer shell of the tactile transducer modules is made from robust PVC that has been approved in industrial flooring applications (see Figure 2). The size of 0.125 by 0.125 meters of a single taxel is sufficient to robustly detect the footprint of humans. The entire floor comprises 1536 taxels whose sensor signals are acquired by a single central sensor controller. This sensor controller features a high-performance Analog-to-Digital converter theoretically capable of conversion rates up to 2 million samples per second (MSPS) with a resolution of 12 bits. At the actual stage of development we reach a sampling frequency for the overall flooring of about 50 Hz provided by an industrial RS485 bus" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000594_tia.2018.2799178-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000594_tia.2018.2799178-Figure3-1.png", "caption": "Fig. 3. Relative permeability distribution of stator and equal potential line distribution for armature field. (a) All ETW S3p. (b) All ETW D3p. (c) Alternate ETW S3p. (d) Alternate UETW S3p.", "texts": [ " The All ETW D3p machine shows the best performance for both FCS and FOS machines, while the Alternate UETW S3p machine has the highest fluctuation, especially for the machine with FOSs. Comparing the torque ripple of the All ETW S3p and Alternate ETW S3p machines, the latter one is larger and this is more obvious for FOS machines. The reason for torque ripple difference between these electrical machines is the different saturation level of magnetic circuit between each other. This can be seen from the stator core relative permeability distribution and the equal potential line distribution due to armature field only, as shown in Fig. 3 for FCS machines. From Fig. 3, it can be seen that the influence of the 1 st harmonic becomes increasingly high in the sequence of the All ETW D3p, All ETW S3p, Alternate ETW S3p and Alternate UETW S3p machines. The saturation of the stator yoke is accordingly affected, which leads to different output torque and torque ripple. (4) There are 6 ripples over one electrical period for electrical machines adopting single 3-phase winding, whilst it is 12 for dual 3-phase winding. This will be explained from a more essential point of view, viz", " It clearly shows that the average value of on-load torque is the addition of PM and armature componenta, while the on-load cogging torque has no contribution. This coincides with eq. (3)-(6). For the high order harmonics, the magnitudes of PM and armature components are much higher than the corresponding on-load torque, which is owing to those obvious spikes shown in Fig. 5. Since the on-load cogging torque does not have these spikes, each higher order harmonic just has a bit larger magnitude compared with resultant on-load torque harmonics. The local saturation of tooth bridge area shown in Fig. 3 is the source for on-load cogging torque. When the rotor operates under on-load condition, the local saturation due to armature reaction will lead to the sharp variation of tooth bridge permeance, which has the equivalent effect of slotting. Thus, when the PM inter-region approaches the tooth bridge, the total stored energy will vary and on-load cogging torque is generated. The most important harmonic is 6, which is the major content of on-load torque ripple. The All ETW D3p machine does not have this 0 2 4 6 8 0 6 12 18 24 30 36 M a g n it u d e ( N m ) Orders OL PM Arm Cog Average 0093-9994 (c) 2018 IEEE" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003441_s0094-114x(02)00042-3-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003441_s0094-114x(02)00042-3-Figure1-1.png", "caption": "Fig. 1. The special case of parallel input and output shafts.", "texts": [ " One of the earliest known 6R linkages, the double-Hooke\u2019s-joint chain, is a hybrid of two spherical four-bars. It is a commonly applied mechanism and has significant simplifying features. Yet, to my knowledge, there is no published analysis of the loop as a 6R chain, although Ref. [14] includes a set of mobility criteria and a sample of numerically produced relationships. Instead, one encounters special-purpose analyses, founded upon the component spherical linkages, for the two particular cases of parallel (Fig. 1) and symmetrically intersecting (Fig. 2) input and output shafts. Our intention here is to provide a full six-bar formulation for this important linkage and, subsequently, to generalise it further to a less constrained loop. Our exposition will reveal the difficulties presented by displacement\u2013closure equations for loops of relatively high connectivity-sum. The analytical tools adopted here have been employed many times and appear among the cited references (for example, in Refs. [1\u20134]). We are concerned with delineating a linkage known to be mobile rather than searching for mobile solutions, so that certain simplifications can be introduced to the usual strategy", " Although we have had to place no conditions on angles of skew, the analyses to follow are greatly eased if we represent the standard industrial practice of setting clevis-pins at rightangles to shafts and to each other in Hooke\u2019s joints. That is, we adopt the values a56 \u00bc a61 \u00bc p 2 \u00bc a23 \u00bc a34: We now turn to the two special cases mentioned above. As well as the dimensional conditions specified in the previous section, we impose here the requirement a45 \u00bc 0; whence the result (3.i) is reduced to a212 \u00bc a245 \u00fe \u00f0T4 \u00fe T5\u00de2; \u00f04:i\u00de a property which can be observed from Fig. 1. We direct our primary attention to the determination of input\u2013output relationships. Equations involving clevis angles are obtained incidentally through the solution procedure but are of little interest in the present context. We show that a judicious selection from the three translational closure equations and their variants is sufficient for our purposes. That is, there is no need to call upon the body of rotational equations. Let us choose Eq. (B.10); (B.10) with indices advanced by 2, (B.11); (B", "8) leads to sT5 sa12\u00f0T4 \u00fe T5\u00de a12 sh5 \u00fe ca12ch5 \u00bda212 \u00f0a45sh5\u00de2 1=2 \u00bc rf\u00f0T4 \u00fe T5\u00dech4 T4ch4g\u00bda212 \u00f0a45sh4\u00de2 1=2; or sfsa12\u00f0T4 \u00fe T5\u00desh5 \u00fe a12ca12ch5g\u00bda212 \u00f0a45sh5\u00de2 1=2 \u00bc ra12ch4\u00bda212 \u00f0a45sh4\u00de2 1=2 : \u00f04:10\u00de By division between Eqs. (4.9) and (4.10), which introduces no non-trivial singularities, we have a12fca12\u00f0T4 \u00fe T5\u00deth5 a12sa12g \u00bc \u00f0T4 \u00fe T5\u00deth4fsa12\u00f0T4 \u00fe T5\u00deth5 \u00fe a12ca12g; or \u00f0T4 \u00fe T5\u00de2sa12th4th5 \u00fe a12\u00f0T4 \u00fe T5\u00deca12\u00bdth4 \u00fe th5 a212sa12 \u00bc 0: \u00f04:11\u00de This is the general input\u2013output relationship for the present case. Clearly, linearity between the trigonometric variables requires parallelism of the clevis-pins on the connecting-rod. Such is the situation for the usual industrial mechanism, as indicated by Fig. 1. Then Eq. (4.11) is reduced to th4 \u00fe th5 \u00bc 0: We note, from Eqs. (4.4) and (4.7), that the linkage is partially locked when T4 \u00fe T5 \u00bc 0; under the prescribed constraints on angles of skew, by virtue of part-chain mobility about the connecting-rod. This circumstance obtains when the connecting-rod is directed perpendicular to the shafts. Besides the dimensional constraints specified in Section 3 above, we have the conditions a45 \u00bc 0 \u00bc T4 T5; which reduce Eq. (3.i) to a212 \u00bc 2T 2 4 \u00f01\u00fe ca45\u00de; or a12 \u00bc 2T4c a45 2 ; \u00f05:i\u00de (where we may set T4 > 0, p > a45 > 0\u00de, as is clear from Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003106_s0165-0114(02)00105-7-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003106_s0165-0114(02)00105-7-Figure3-1.png", "caption": "Fig. 3. The inverted pendulum system.", "texts": [ " The plant is assumed to contain unknown parameters, but its structure is known. The fuzzy controller is constructed from fuzzy systems whose parameters are adjusted indirectly from the estimates. The adaptation law adjusts the plant parameters a\u0302i; b\u0302i on-line such that the state x of plant tracks the state xm of reference model, which allows plant output to follow the reference model output. The design concept of FFLC is illustrated through an example in this subsection. The example is the problem of balancing and swing-up of an inverted pendulum on a cart shown in Fig. 3. The dynamic equations of motion for the pendulum are given as follows [14,16]: x\u03071 = x2; (5.1a) x\u03072 = g sin(x1) \u2212 amlx2 2 sin(2x1)=2 \u2212 a cos(x1) u 4l=3 \u2212 aml cos2(x1) ; (5.1b) where x1 denotes the angle (in radian) of the pendulum from the vertical, and x2 is the angular velocity (Fig 3). g= 9:8 m=s2 is the gravity constants, m is the mass of the pendulum, and u is the force applied to the cart (in newtons). a= 1=(m+M). The control objective in this example is to balance the inverted pendulum for the approximate range x1 \u2208 (\u2212)=2; )=2). To apply the FFLC design approach, we use the TS fuzzy model representing the dynamics of the inverted pendulum (5.1). We use the TS fuzzy model derived in [16] as a representation of the system (5.1). In [16], the dynamic equations are approximated by the following two-rule TS fuzzy model" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003388_978-3-662-04831-3-Figure2.7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003388_978-3-662-04831-3-Figure2.7-1.png", "caption": "Fig. 2.7: Vector representations", "texts": [ "1 also hold in the spatial case, with slight modifica tionso As in the planar case, the spatial vectors and matrices will also be written in bold faced letterso Consider a reference frame R with origin 0 = 0 R and with the orthogonal basis BR = { exR' eyR' ezR} ' eiR E OC3 ' defined by the relation ( R )T R { 1 , i = j eiR 0 ejR = 0 ' i -1- j i,j=x,y,z, (2.42a) with efk as the basis vector eiR represented in Ro Consider a second frame L with origin OL and with orthogonal basis BL = {exL, eyL, ezL} fixed to a rigid body (Figure 207a)o Let roLoR be the (geometrical) displacement vector from 0 to OLo Then roLoR = roLo can be represented with respect to Ras (2.42b) or in algebraic form (2.42c) with x~Lo, y~Lo, z{5L 0 as Cartesian coordinates of roLo with respect to frame Ro Consider an arbitrary point P on a rigid body (Figure 207a) and the displacement vectors r POL from 0 L to P and r PO from 0 to P 0 Then the following translation relation holds: rpo = rpoL + roLo, or, representing r PO in the frame R, (2.43) Consider the vector r PO in Figure 20 7b and two orthogonal frames R and L with a common origin 0 and with basis vectors { e\"R, eyR, ezR} and {exL, eyL, ezL}, respectivelyo Then rpo can be written as 2.2 Spatial vectors and matrices 55 56 20 Planar and spatial vectors, matrices, and vector functions R R R Tpo = Xpo 0 exR + YPO 0 eyR + Zpo 0 ezR, (2.44a) or L L L rpo = Xpo 0 exL + YPo 0 eyL + Zpo 0 ezL, (2.44b) or abbreviated in algebraic form R ( R R R )T Tpo = Xpo' YPO' Zpo (representation of r PO in R) (2.44c) and L ( L L L )T Tpo = Xpo' YPO' Zpo ( representation of r PO in L) 0 (2.44d) 2.2.1.1 Basis transformation. Given two frames R and L (Figure 207b) with orthogonal basis vectors {exR, eyR, ezR} of Rand {exL, eyL, ezL} of Lo Then exR = 1 o exR + 0 o eyR + 0 o ezR, eyR = 0 \u00b0 exR + 1 \u00b0 eyR + 0 \u00b0 ezR, (2.45a) ezR = 0 o exR + 0 o eyR + 1 o ezR, or e~R~ 0). e:n~ G} and R -ezR - 0). and exL = 1 o exL + 0 o eyL + 0 o ezL, eyL = 0 \u00b0 exL + 1 \u00b0 eyL + 0 \u00b0 ezL, ezL = 0 o exL + 0 o eyL + 1 o ezL, or e~L~ 0). e~L~ 0} and L ezL = (D (2.45b) Consider the projections of exL, eyL and ezL onto the basis vectors of R; ioeo, the expressions (e:Rf 0 (e~L) =: fx , (e:R)T 0 (e~L) =: fy , (e:R)T 0 (e~L) =: fz (e:Rf 0 (e~L) =: mx, (e:R) T 0 (e~L) =: my, (e:R) T 0 (e~L) =: mz (e~)To (e~L)=:nx, (e~)To (e~L)=:ny, (e~)To (e~L)=:nz (2", "y , fz ) mx 'my 'mz nx ' ny ' nz the relations ( 2 .48b) and ( 2 .48c) prove the orthogonality relations ARL 0 (ARL) T = ARL 0 ALR = 13 or ( RL)T ( RL)-l LR A = A =A 0 Then, due, to (2.46b) and (2.46c), R (~) =ARL 0 0) = ARL 0 eL exL = xL' R - (~) =ARL 0 (D = ARL 0 eL eyL - yL' R -ezL - (::) = A\"' G) = A\"' e~L' and L ALR R exR = 0 exR' L ALR R eyR = 0 eYR' eL = ALR 0 eR zR zR with ALR = (ARL)T 0 (2.48d) (2o49a) (2o49b) (2050) 2.2.1.2 Coordinate transformation. Given two orthogonal frames Rand L with a common origin 0 (Figure 207b) and a vector rpo from 0 toP with representations in R and L, R R R rpo = Xpo 0 exR + Ypo 0 eyR + Zpo 0 ezR (2o5la) and L L L rpo = Xpo 0 exL + Ypo 0 eyL + Zpo 0 ezL, (2o5lb) or 60 20 Planar and spatial vectors, matrices, and vector functions ( R) Xpo R _ rpo- Y~o Zpo and ( L ) Xpo L _ rpo- Y~o 0 Zpo Inserting the basis transformation relations (2o47a) into (2o5la) yields rpo= x~0 \u00b0 (fxoexL+fyoeyL+fzoezL) =: exR + Y~o o (mx o exL + my o eyL + mz o ezL) =: eyR + Z~o o (nx o exL + ny o eyL + nz o ezL), =: \u20aczR r PO = ( x~o 0 Rx + Y~o 0 mx + z~o 0 nx) 0 exL + ( x~0 \u00b0 Cy + y~0 \u00b0 my + z~0 \u00b0 ny) 0 eyL + ( X~o 0 Rz + Y~o 0 mz + z};o 0 nz) 0 \u20aczL or ( :t~) z~o ", "43) R R R rpo = roLo + rpoL (2o58a) and a rotation R ARL L TpoL = 0 TpoL 0 (2o58b) This yields the combined ( translation-rotation) transformation R R ARL L rpo=roLo+ orpoL (2o59a) and its inverse r L - ALR ( R R ) POL - 0 r PO - r 0 L 0 ' 202 Spatial vectors and matrices 65 with the special cases pure rotation pure translation and (2o59c) These latter two relations are the basis for deriving kinematic relations of rigid-body systems (vector loops and orientation loops) under spatial motion (see Beetions 3 and 5)0 2.2.2 Time derivatives of displacement vectors and orientation matrices In this section, time derivatives of spatial displacement vectors and orien tation matrices will be considered together with the kinematic differential equation that relates angular velocities to the time derivatives of angleso 2.2.2.1 Velocities and angular velocities. Consider a vector from the point 0 offrame R to a point OL (Figure 207a), where roLoL is assumed to move smoothly in time, Represented in frame R, the vector roLo(t) is written as roLo(t) = x~Lo(t) 0 exR + Y~Lo(t) 0 eyR + z{!;Lo(t) 0 ezRo (2o60a) (2o60b) Taking the time derivative of r~L0 (t) with respect to frame R yields RoR Rd Rd ( R ) roLo(t) := dt (roLo(t)) := dt x0 L0 (t) 0 exR (2o60c) Rd Rd +dt (yf5Lo(t) 0 eyR) + dt (zf5Lo(t) 0 ezR) 0 Rd By the definition of the operator \"-\" (see Equations 2028a to 2028f), the dt basis vectors eiR (i = x, y, z) of frame R do not depend on to This yields, together with eiR := 0, the relation or (2o60e) with unambiguous time derivatives x~L 0 (t), y{" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000576_1.4960094-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000576_1.4960094-Figure3-1.png", "caption": "FIG. 3. Acquisition image and the tracking spot.", "texts": [ " Test preparation can be divided into four steps: first, assemble the mandrel to the top of the aerostatic spindle and adjust the error motion of the spindle with the mandrel under 0.1 \u00b5m; second, cleaning the bearing with aviation kerosene, especially the cage, and making a white spot on the cage surface to capture cage motion by the Motion; third, according to the working condition, filling grease quantity and running-in several hours to make the distribution of grease uniform; and finally, adjust the high-speed camera and lighting, including focal length of lens, resolution and exposure of the camera. Fig. 3 shows a frame image of the test bearing. A white spot is marked on the cage surface for capturing the cage motion by software, then the Motion tracks the spot to obtain the trajectory of the cage. B. Image acquisition and processing A Phantom Miro M310 high-speed camera is used to capture cage images at different speeds. The camera is 1 megapixel with a 3.2 gigapixels/second (Gpx/s) throughput. This translates to over 3200 frames-per-second (fps) at full 1280 \u00d7 800 resolution. Frame rates up to 650 000 fps are available at reduced resolution" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000088_j.jsv.2017.12.022-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000088_j.jsv.2017.12.022-Figure3-1.png", "caption": "Fig. 3. Illustration of effective gear mesh coupling; (a) Spring-damper element generated from TCA (b) Quasi-static tooth contact analysis (QTCA).", "texts": [ " The modeling and analysis above shows that TE functions generated from specific gear mesh analysis can describe distinct characteristics of surface geometry which indicates that TE with different orders will have significant influence on the dynamic performance of gearmesh. Therefore, in this session, traditional parabolic, fourth order and sixth order TE functions are selected and compared to study the dynamic behavior of a hypoid gear rotor system. System sensitivity is also evaluated in both frequency and time domain. Based on tooth contact analysis (TCA), the coupling between engaging gear teeth can be simplified as a spring-damper element shown in Fig. 3(a) which is comprised of several major mesh parameters including mesh stiffness km, mesh point om, LOA Lm and unloaded TE (denoted as eu in Fig. 3). The expression for different types of unloaded TE functions can be written as: eiUa \u00bc Xn i\u00bc0 ai 41 40 1 i \u00bc Xn i\u00bc0 aix i \u00f0i \u00bc 2;4;6\u00de (12) By specifying different values of i, the TE function can be parabolic (i \u00bc 2), fourth order (i \u00bc 4) or sixth order (i \u00bc 6) type. The other major mesh parameters are generated from quasi-static tooth contact analysis (QTCA) [33] and mean values for these parameters are used so that the effect of TE on dynamics can be studied separately. The contact area illustrated in Fig. 3(b) is firstly divided into n contact cells. For each cell, contact stress fi, position Ri and normal vectors Ni can be specified [34]. The combined contact force vector in three directions are expressed as: Fl \u00bc Xn i\u00bc1 \u00f0Nilfi\u00de; l \u00bc x; y; z (13) The total mesh force amplitude is written as: Fm \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi F2x \u00fe F2y \u00fe F2z q (14) Accordingly, effective mesh stiffness that describes the contact elasticity between meshing gear pair is derived frommesh force, loaded and unloaded TE: km \u00bc Fm=\u00f0eL eU\u00de (15) where the translational loaded eL and unloaded eU TE are calculated from angular TE: eL \u00bc eLa,ly; eU \u00bc eUa,ly (16) The directional rotation radius around the rotation axis ly is derived from effective mesh point (xm; ym; zm) and LOA (Nx;Ny;Nz): ly \u00bc zmNx xmNz (17) More modeling details can be found in related studies [29,37] which is beyond the scope of this work", " Ml and Ilm; \u00f0l \u00bc p; g;m \u00bc x; y; z\u00de are the body mass and moment of inertia of pinion and gear. Accordingly, the displacement vector is expressed as: fxg \u00bc n qD; xp; yp; zp; qpx; qpy; qpz; xg ; yg ; zg; qgx; qgy; qgz; qL oT (20) Based on the theory of coupled multibody dynamics [28], the torsional coordinates of pinion/gear body, engine and load are used to describe large rotational displacement which is different from pure vibration analysis. Notice that the coordinate system of the complete geared rotor system is different from that of TCA illustrated in Fig. 3, so that coordinate transformation is performed when mesh parameters are applied for dynamic analysis. The effective stiffness consists of input kD and output kL shaft torsional stiffness and lumped shaft-bearing support stiffness on pinion \u00bdKp and gear \u00bdKg shaft. The system damping matrix \u00bdC is derived from component support damping model. The combined stiffness matrix can be written as: \u00bdK \u00bc 2 664 kD Kp Kg kL 3 775 (21) The force vector is comprised of internal and external excitations which can be defined as: fFg \u00bc TD;hp,Fm; hg,Fm; TL T \u00fe fFextg (22) where TD and TL are torque at driving and load end" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003060_s0020-7683(99)00178-x-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003060_s0020-7683(99)00178-x-Figure2-1.png", "caption": "Fig. 2. (a) Plane reticulated system with two ``end to end'' members in its reference state. (b) Plane reticulated system with two ``end to end'' members in its deformed state, in mechanism's vicinity.", "texts": [ " Finally, this is a \u00aenite mechanism, since all the length variation coe cients {e } may be cancelled for every order with u 1\u00ff m2 p \u00ff 1: The connection matrix of selfstress coe cients is evaluated in order to obtain strain energy value at second order in the mechanism vicinity: D0 q01 q02 0 0 q01 q02 ) W 1 O2 1 2 d K t D0 d K \u00ffq01 q02 m2 2 a\u00ff a m 2 2 0 53 Strain energy is always equal to zero until order two, independently of applied selfstress states. Mechanism {dK} is a higher order mechanism. Let us consider now, a plane reticulated system comprising two members of identical length, assembled end to end (Fig. 2(a)). Analysis of equilibrium matrix A 1 \u00ff1 0 0 leads to the determination of a mechanism basis fd Kg mf0, 1gt, orthogonal displacements fd Ig uf0, 1gt, and selfstress states fq0g af1, 1gt: Which is the order of a non zero mechanism {dK} (i.e. m 6 0)? Is it a \u00aerst-order mechanism? Vector {e } is calculated until second order, in the vicinity of mechanism {dK} (Fig. 2(b)). According to relationship (29), we get:8>>><>>>: e1 1 O2 u m2 2 e2 1 O2 \u00ff u m2 2 since DAd K 0 0 m m 54 The length variation coe cients e1 and e2 are not equal to zero, independently of the value u. None displacement {d I} cancels {e } at second order. Mechanism {dK} is associated with length variations of second order, therefore, it is a \u00aerst-order mechanism. D0 q01 q02 0 0 q01 q02 ) W 1 O2 1 2 d K t D0 d K \u00ffq01 q02 m2 2 am2 55 Strain energy W can be equal to zero, for at least one selfstress state (corresponding to any a 6 0)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003133_tec.2002.801731-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003133_tec.2002.801731-Figure2-1.png", "caption": "Fig. 2. Two-axis model in the rotor reference frame.", "texts": [ "00 \u00a9 2002 IEEE II. MODELING The cross\u2013section of the stator and rotor structure of the studied synchronous reluctance machine is shown in Fig. 1. The stator is made with symmetrical three-phase windings and the rotor contains a squirrel cage. For the modeling, magnetic hysteresis, the skin effect (in the rotor bars) and iron losses are neglected. The air-gap magnetomotive forces are assumed to be sinusoidally distributed. The two-axis representation of the electrical equivalent machine is given in Fig. 2. The voltage equations of the two-axis representation written in the rotor reference frame are (1) (2) (3) (4) The stator and rotor flux linkage in equations (1)\u2013(4) are related to the currents as follows: (5) (6) (7) (8) Introducing magnetizing currents and in the two\u2013axis, stator flux linkages become with (9) with (10) Usually, total inductances are split up into a leakage and magnetizing component. Magnetizing inductance changes with the saturation level and the leakage one are supposed to remain constant" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003448_1.1539514-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003448_1.1539514-Figure7-1.png", "caption": "Fig. 7 Line and flat pencil singularities of the Jacobian", "texts": [ " For planar robots, when more than two lines of ]A/]xj intersect at one point it causes flat pencil singularity of the Jacobian derivatives. Figure 6 shows a flat pencil singularity @Fig. Journal of Mechanical Design rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 08/23/20 6~a!# and point singularity @Fig. 6~b!# of ]A/]xj for a planar 3 DOF non-redundant manipulator. In both configurations the matrix J\u0303 has a rank of 2, which means that Eq. ~43! has no exact solution for an arbitrary Kj. Figure 7~a! and 7~b! show flat pencil and point singularities of the matrix A ~and J!. Figure 8 illustrates a redundant planar parallel manipulator with six linear actuators. The dimension of the nullspace of the Jacobian of this planar robot is 3 or higher. This means that we can control the stiffness elements in the j th column of the stiffness matrix provided that rank of the matrix J\u0303 associated with this column is no less than 3. The manipulator in the configuration of Fig. 8 illustrates a singularity of J\u0303 ~rank( J\u0303),3) caused by flat pencil singularity of ]A/]xj since the lines of ]A/]xj intersect in one point as shown in the figure" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001273_0278364920903785-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001273_0278364920903785-Figure4-1.png", "caption": "Fig. 4. Coordinate frame motion due to respiration: CT , catheter tip; BB, base of distal bending section; Instr, working instrument pose; and World, EM tracker transmitter. Green dotted lines demonstrate typical motion trajectories. EM sensors are mounted at BB, BT , and Instr. The cyan rectangle at the CT frame is the US imaging transducer.", "texts": [ " We use EM sensors to measure the effects of respiratory motion on the US catheter by deactivating the motors and measuring catheter tip and bending section motion due to breathing disturbance only. Then during active steering, we compare the current pose measurements to model-based breathing estimates. The difference represents the motion due to robot actuation. We accomplish this by measuring the catheter tip (CT , the location of the US transducer), the base of the distal bending section (BB), and the working instrument pose (Instr), across multiple breathing cycles while the robot is not actuating the controls. Coordinate frames are shown in Figure 4. The World frame refers to the EM tracker transmitter and BT refers to the tip of the bending section. One EM sensor is mounted between the CT and BT frames (no bending occurs between CT and BT, so their relationship is constant). A second EM sensor is mounted just proximal to the BB frame. A third EM sensor is mounted to the Instr frame on the catheter being tracked. Green dotted lines demonstrate typical CT , BB, and Instr motion trajectories. Breathing models of CT , BB, and Instr are calculated initially and then used throughout navigation to estimate the amount of motion from respiratory effects versus robot actuation", " The mean of cycles is shown in black with 95% confidence intervals shaded gray. The maximum standard deviation of 0.11 mm was small enough to neglect amplitude variations, meaning that respiration disturbs the catheter tip repeatedly enough that we can represent the average breath by a model. We define periodic models for the low-pass-filtered CT, BB, and Instr disturbance motions due to respiration as described and bench top tested in Loschak et al. (2017). All coordinate frame breathing motion trajectories in Figure 4 are cyclical but different from each other. An example model on in vivo breathing data is shown in Figure 7. The blue line represents the raw EM measurements of the CT ycoordinate. The black line represents the low-pass-filtered CT y-coordinate. The red line represents the initialized Fourier series model estimate. The mean absolute error between the y-coordinate model values and the low-passfiltered measurements is 0.057 mm (s = 0:041 mm). The mean absolute model error for the x-axis is 0.037 mm (s = 0:027 mm) and for the z-axis is 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000863_aieepas.1957.4499555-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000863_aieepas.1957.4499555-Figure1-1.png", "caption": "Fig. 1. Schematic cros section of canned motor", "texts": [ " by using a canned motor to drive the pump and allowing the primary coolant Nomenclature to completely fill the rotor cavity of the A =cross-sectional area of can, inches motor. Any leakage of primary fluid to B -peak flux density in the air gap, lines per the atmosphere is then prevented by the square inch thin can in the air gap. A schematic D =diameter at gap, inches cross-sectional view of a typical canned E= induced voltage, volts K,=Carter's coefficient for the stator slots motor is shown in Fig.1 . K Rp =pitch factor These motors are of the squirrel-cage Kd distribution factor induction type and have been built in K,d KvXK4 sizes from fractional horsepower up to Kr = reduction factor for rotor can ripple about 1,500 horsepower. Most units loss; see Fig. 4 are wound*for eit'hertwoorfourpoles, K, = reduction factor for stator can loss; are wound for ther two four poles see Fig. 3 but a considerable number of 2-speed N=series turns, per phase P =number of poles R =resistance, ohms V = volts per phase W= watts b = width of stator tooth at air gap, inches b==width of stator slot at air gap, inches f-=frequency, cycle per second I= length of core, inches n =speed of rotating field, revolutions per second =thickness of can, inches v = velocity of flux cutting the can, inches per second r =pole pitch, inches rb =rotor bar pitch, inches ,-=stator slot pitch, inches p =resistivity of can, ohm-inches ,O =flux per pole, lines (maxwells) X= leakage reactance of rotor bars at slot ripple frequency X" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001190_tmag.2020.3009479-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001190_tmag.2020.3009479-Figure5-1.png", "caption": "Fig. 5. 3-D model of the studied coupling.", "texts": [ " Similarly, the traction forces generated by other loops can be obtained by formula (18), and the total electromagnetic torque of the coupling is T = 8\u2211 n=1 Fnrm (20) where n = 1, 2, . . . , 8, and Fn is the traction force corresponding to loops 1\u20138. Both FEM and experiment are used to verify the validity of the 2-D model established. The results obtained by the two methods are compared with those obtained by the analytical calculation. The parameters of the finite element model are consistent with Table I. Fig. 5 shows the structure of the 3-D model. In addition, the meshing of PMs, air gap, and the conductor is refined to ensure the accuracy of simulation results. The FE model meshed is shown in Fig. 6. Fig. 7(a) and (b) shows the density distribution and trends of eddy current in conductor disk, respectively. Fig. 7(a) shows that the magnitudes of eddy current in iron teeth and back iron are negligible compared with that in the conductor. Fig. 7(b) shows that the paths of eddy current in each fan conductor of conductor disk are different" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003912_1.2118687-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003912_1.2118687-Figure5-1.png", "caption": "Fig. 5 The Cartesian parallel manipulator proposed by Kim and Tsai", "texts": [ " Furthermore, since the first two serial connecting chains i=1 3 f ji = 3 = dim Vj m/f = dim Aj m/f j = 1,2, while for the third serial connecting chain i=1 4 f3i = 4 dim V3 m/f = dim A3 m/f = 3. It follows that Fp = f ji \u2212 j=1 3 Vj m/f = 1. Hence, there is a passive degree of freedom; i.e., there is a selfmotion associated with the third serial connecting chain, and the motion has one degree of freedom. 6.3 The Kim and Tsai\u2019 Cartesian Parallel Manipulator. Consider the cartesian parallel manipulator proposed by Kim and Tsai 5 , shown in Fig. 5.4 The manipulator is formed by three similar serial connector chains. Each chain is formed by a prismatic pair and three revolute pairs, the direction of the prismatic pair and the axes of the revo- 4The same architecture has been also proposed by Carricato and Parenti-Castelli 18,19 and Kong and Gosselin 20,21 . Journal of Mechanical Design rom: http://mechanicaldesign.asmedigitalcollection.asme.org/pdfaccess.as lute pairs are parallel and generates the Lie subalgebra associated with the Sch\u00f6nflies group RP 4 e\u0302 j , moreover the unit vectors e\u03021 , e\u03022 , e\u03023 are linearly independent; i" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003923_j.jtbi.2005.10.015-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003923_j.jtbi.2005.10.015-Figure1-1.png", "caption": "Fig. 1. Generic jumper model: The parameters of the generic jumper model are the mass of the trunk, upper legs and lower legs (m1, m2 and m3 respectively), and the length of the leg segments (s). The knee angle is defined as 2y (see Appendix A for detailed description of the model).", "texts": [ " In a futuristic discussion on interplanetary Olympics, it has been argued that equal jumpers achieve equal take-off velocities on all planets because mass-specific work stays the same (Stewart, 1992); it will now be clear that this claim is congruent with Borelli\u2019s law and thus cannot be true. As soon as a jumper encounters a planet where the gravitational torque equals the maximal muscle torque, it becomes impossible to accelerate and build up velocity at all. To quantify the effect of size on jumping performance in a slightly more realistic model and to assess how the relationship between size and jumping performance contributes to our understanding of real jumping animals, numerical simulations were conducted using a more realistic generic jumper model (Alexander, 1995) (Fig. 1), details of which are given in the Appendix A. One hundred perfectly isometric bipedal jumpers ranging from 7 10 6 to 70 kg were modelled. Jumpers were actuated by constant knee extensor torques that scaled with mass, allowing all jumpers to produce similar amounts of mass-specific work during the push-off. Take-off velocity was determined for each jumper. As expected, small jumpers achieved higher take-off velocities than large jumpers (Fig. 2). As a quantitative example, scaling a jumper from 70 to 0", " A small jumper needs relatively less muscle mass than a large jumper to achieve a certain take-off velocity. Muscle tissue is energetically expensive for an animal because of its high (resting) metabolism (Alexander, 2000). If the benefits of high take-off velocity (i.e. fast escape from predators) are combined with the challenge to sustain as little muscle tissue as possible, being small might be the best compromise. The generic jumper model To investigate the effect of geometric scaling on jumping performance, a generic jumper model was used (Fig. 1) (Alexander, 1995). This symmetric model has two segments per leg and a trunk segment, the movement of which is constrained to vertical translation. During push-off, this one degree-of-freedom model is actuated by equal knee joint torques. The masses of the trunk (m1), both thighs (m2) and both shanks (m3) were 0.7mB, 0.2 mB and 0.1 mB, respectively, where mB was the total body mass. The thigh and shank were modelled as uniform rods of equal length s and mass m2=2 and m3=2, respectively. In the static starting position, the knee angle (2y) was set to 601" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003060_s0020-7683(99)00178-x-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003060_s0020-7683(99)00178-x-Figure4-1.png", "caption": "Fig. 4. Deformed reticulated system without length variations at orders one, two and three.", "texts": [ " We apply the algorithm to determine the order of the internal mechanism fd Kg m 1 : Length variation coe cients vector fe 2 g is evaluated at order two. e 2 A t d I 2 1 2 DAd K 1 t d K 1 u1, \u00ff u1, u2 \u00ff u3 1 2 m21, u3 1 2 m21 t 79 In this example and following ones, notations may be simpli\u00aeed: order of scalars m1, u1, u2 and u3) is not indicated, since there is no possible confusion. The system fe 2 g f0g admits one solution: u1 0, u2 \u00ffm21 and u3 \u00ff1 2 m21 80 Consequently, order of mechanism fd Kg fd K 1 g is higher than one, since there exists a displacement fd I 2 g (Fig. 4) which cancels at order two, the length variation coe cients for every member of the system. Is this mechanism of order two ? Answer is given by the second step of algorithm. Vector fe 3 g is calculated at order three, taking into account the following displacements: d K d K 1 \u00ff since DK f0g in case of m 1 81 d I d I 2 DI with kDIk 0O3 82 where fd K 1 g f0, 0, m1, 0gt, fd I 2 g f0, \u00ffm21, 0, \u00ff 1=2 m21gt and fDIg fU1, U2, 0, U3gt: Then: e 3 A t DI DAd K 1 t d I 2 fU1, \u00ffU1, U2 \u00ffU3, U3gt 83 It is obvious that system fe 3 g f0g admits only the zero solution: U1 U2 U3 0 or DI d I 3 f0g 84 There exists a displacement fDIg fd I 3 g which cancels {e } at order three", " We evaluate fe 4 g, with the following displacements: d K d K 1 85 and d I d I 2 d I 3 DI with kDIk 0O4 86 Since (according to the expression (73)) e 4 A t DI 1 2 DAd I 2 t d I 2 87 then e 4 U1 1 2 m41, \u00ffU1 1 2 m41, U2 \u00ffU3 1 8 m41, U3 1 8 m41 t 88 It does not exist value of U1 solution of the system fe 4 g f0g: Therefore, there is no displacement fd Ig cancelling at order four length variation generated by mechanism fd Kg: So, fd Kg f0, 0, m1, 0gt is an in\u00aenitesimal mechanism of order three, which is in accordance with results from Tarnai (1989) and Kuznetsov (1991a) and displacements expressions that were given by the \u00aerst author. It is interesting to notice that this method gives simultaneously the order of mechanism and values of node displacements fd Kg and fd Ig which cancel length variations until the order of the mechanism (Fig. 4). We notice that another T assembly, comprising \u00aeve members (Fig. 5). which is considered by Kuznetsov (1988) as an order two mechanism, and by Salerno (1992) as a mechanism at least of order three, is also a mechanism of order three. Application of our algorithm leads to a system fe 4 g f0g, which has no U1 solution. Let us search mechanisms of order higher than one for a plane reticulated system submitted by Kuznetsov (1991a, 1991b, 1991c). Length of member 6 (Fig. 6) is parametered by ``a'' a 6 0)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003454_s0957-4158(03)00064-3-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003454_s0957-4158(03)00064-3-Figure1-1.png", "caption": "Fig. 1. Ship coordinate frames.", "texts": [ " Section 2 describes the mathematical model for the dynamically positioned ship system along with its corresponding properties. The adaptive output feedback controller, error system development, and stability analysis are presented in Section 3. Simulation results illustrating the performance of the proposed control law are given in Section 4. Conclusion remarks are made in Section 5. The mathematical model for the dynamically positioned ship controlled exclusively by means of thrusters, shown in Fig. 1, is assumed to have the following form [6,11] 1 N M _m \u00fe Dm \u00bc s \u00f01\u00de _g \u00bc R\u00f0w\u00dem \u00f02\u00de where g\u00f0t\u00de, \u00bdx\u00f0t\u00de; y\u00f0t\u00de;w\u00f0t\u00de T 2 R3 contains the ship translational position denoted by the variables x\u00f0t\u00de, y\u00f0t\u00de and yaw angle denoted by the variable w\u00f0t\u00de relative to an Earthfixed coordinate frame fXe; Yeg, m\u00f0t\u00de 2 R3 represents the ship velocity relative to the body-fixed coordinate frame fXb; Ybg, s\u00f0t\u00de 2 R3 represents the control force/torque input vector provided by the thruster system, M 2 R3 3 is the constant, positivedefinite, symmetric, mass\u2013inertia matrix, D 2 R3 3 is the constant damping matrix, and R\u00f0w\u00de 2 R3 3 is the rotation matrix 1 between the Earth and body-fixed coordinate frames" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000417_s00170-018-2799-7-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000417_s00170-018-2799-7-Figure9-1.png", "caption": "Fig. 9 Skiving process analysis: (a) working condition in static work coordinate frame; (b) working condition in dynamic work coordinate frame; (c) spatial cutting condition of cutter 1; (d) swept condition of cutter 1; (e) spatial cutting condition of cutter 2; (f) swept condition of cutter 2", "texts": [ " Both the intermedia status and the final machined gear slots were demonstrated as shown in Fig. 8, and the maximum residual error of these two tasks was no more than 0.01 mm. The aforementioned manifested that the calculated cutting edge can machine the desired profile, and this proofed the correctness of the proposed method. On the basis of cutting edge curve calculation, skiving process simulation and the contact analysis can be exhibited in both intuitional perspective and swept forming perspective. As shown in Fig. 9(a), with respect to their own kinematic parameters, a pair of cutting edge and workpiece underwent the process that includes engaging contact, keeping contact, and exiting contact with following the spatial contact curve. The detailed working conditions for cutter 1 and cutter 2 were respectively illustrated in Fig. 9(c, e). In both of them, left cutting edge began continuous cutting at Ps; in sequence, the contact point followed the spatial contact curve and went through point Pm; and the generating cutting was terminated at point Pewhere the cutting edge separatedwith the workpiece. Concurrently, the right cutting edge followed the spatial contact curve, and began cutting at Ps, then kept continuous cutting went through Pm, and exited cutting at Pe till cutting edge separated with workpiece. For both cutter 1 and cutter 2, owing to diverse rake flanks, the cutting action conditions were different, and the detailed cutting between cutting edges and desired machining surface was demonstrated in Fig. 9(d, f) for cutter 1 and cutter 2, respectively. On the one hand, the swept surfaces of cutting edge in these two cases obviously took different shapes. On the other hand, the contact curves that were placed on both the swept surface of cutting edges and the desired machining surface were different, and it can be deduced directly in Fig. 9(c, e) based on the divergence between the two spatial contact curves. Naturally, different rake flank performs different cutting condition at every moment, and abovementioned simulation will helpful in figuring out the detailed instantaneous contact condition. The proposed cutting edge calculation method and the simulation were significant in the geometrical optimization of skiving cutter. Focus on the skiving for general profiles, this paper proposed a universal cutting edge identification method based on discrete surfaces enveloping, and have given the corresponding simulation of skiving motion in further" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003519_robot.1997.619323-Figure10-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003519_robot.1997.619323-Figure10-1.png", "caption": "Fig. 10: four-axis robot", "texts": [ " The total consumed energy is compared with and without optimization for #2 line, and the result is shown in Fig. 7. Fig. 8 shows the third trajectory which is a circle (# 3 circle) with the center (-0.050,0.756)(m) in workspace, and the radius is 0.150(m). The total consumed energy is compared with and without optimization, and the result is shown in Fig. 9. 4.3 Experimental results The trajectory references generated by the proposed method are tested on a four-axis manipulator using the upper three-links. The experimental robot manipulator is shown in Fig. 10. Each joint of the manipulator is driven by a DC servo motor with a 1/100 reduction gear. The characteristics of each motor and each arm are shown in Table I. The manipulator is controlled by the CP(Continuous Path) control strategy, based on a combination of disturbance observer and sliding mode control. One DSP (NEC-pPD77230) accomplishes all computation from reference data acquisition to voltage control of each motor. The sampling time for CP and servo control is 200psec. The mieasurement of the consumed energy from the robot system is realized by measuring the terminal voltage and the current that flow from the DC power source to robot system" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000716_j.mechmachtheory.2019.07.013-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000716_j.mechmachtheory.2019.07.013-Figure4-1.png", "caption": "Fig. 4. Illustration of the varying tooth thickness of the conical spur involute shaper.", "texts": [ " The normal to the tooth surfaces of the rack cutter can be expressed as: N r ( u s ) = L rb L ba N a ( u s ) , N a ( u s ) = [ \u22121 2 a s u s 0 ] (11) and the unit normal, n r ( u s ) = N r ( u s ) | N r ( u s ) | (12) The unit normal of the conical spur involute shaper can be determined by transferring the unit normal n r of the rack cutter from coordinate system S r to coordinate system S s . n s ( u s , \u03c8 s ) = L se ( \u03c8 s ) L ed L dr n r ( u s ) (13) Here, Matrices L in Eqs. (11) and (13) are 3 \u00d7 3 submatrices of the corresponding matrices M after removing the last column and last row. This is because the projections of the normal on each coordinate axis have no relationship with the origin of the coordinate system. Fig. 4 shows a generated conical spur involute shaper. It is visible that the tooth thickness of the conical spur involute shaper is varying from the heel end to the toe end. This makes a feasibility for the backlash modification of the face gear drive by axially moving the pinion. Fig. 5 shows a face gear which is meshing with the generating conical spur involute shaper with a shaft angle of \u03b3 m . The coordinate systems used for tooth surfaces generation of the face gear are displayed. Coordinate systems S m and S 2 belong to the being-generated face gear" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003912_1.2118687-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003912_1.2118687-Figure6-1.png", "caption": "Fig. 6 Kim and Tsai\u2019s modified cartesian manipulator", "texts": [ " 8 F = i=1 r f i \u2212 j=1 k dim Aj m/f + dim Aa m/f = 12 \u2212 j=1 3 4 + 3 = 3. Furthermore, there is no passive degrees of freedom since Fp = f i \u2212 j=1 k dim Aj m/f = 12 \u2212 j=1 3 4 = 0. It should be noted that Kim and Tsai 5 , after applying the mobility criterion based on the Kutzbach-Gr\u00fcbler criterion, Eq. 1 , found that this parallel manipulator has zero degrees of freedom. 6.4 Kim and Tsai\u2019s Modified Cartesian Manipulador. Consider the cartesian parallel manipulator, similar to that proposed by Kim and Tsai 5 , shown in Fig. 6. The manipulator is composed of three serial connecting chains. The first two serial connecting chains are formed by a prismatic pair and three revolute pairs, the direction of the prismatic pair and the axes of the three revolute pairs are parallel and the kinematic pairs generate the subalgebra associated with the Sch\u00f6nflies group RP 4 e\u0302 j , the third chain is formed by a prismatic pair and only two revolute pairs, the direction of the prismatic pair and the axes of the revolute JANUARY 2006, Vol" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000697_s00339-019-2652-3-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000697_s00339-019-2652-3-Figure1-1.png", "caption": "Fig. 1 Representation of the NCNPs@CuO nanoarchitectures formation on ITO", "texts": [ "0%), urea (U, reagent grade, 98%), sodium chloride (NaCl, \u2265 99%, AR) etc., were of analytical grades from Sigma Aldrich. Indium Tin Oxide (ITO) substrates [dimension: 2\u00a0 cm \u00d7 1\u00a0 cm (length \u00d7 width), thickness: 1.1\u00a0mm, and sheet resistance: 378\u00a0\u2126\u00a0sq\u22121] purchased in KINTEC was rinsed with acetone and 10% NaOH, finally washed with de-ionized water and dried. The soot deposition on the surface of pre-cleaned ITO was accomplished by directly burning pyrrole under air atmosphere with a flame temperature of ~ 1000\u00a0\u00b0C (Fig.\u00a01), which is optimal for the generation of NCNPs [23\u201326]. The pre-cleaned ITO was placed above the pyrrole-air combustion flame source at a height of 3\u00a0cm. The growth process was lasted for 3\u00a0min and the obtained NCNPs/ ITO was used for further analysis without any further purification. The obtained NCNPs/ITO was immersed in 0.05\u00a0 M Cu(NO3)2\u00b73H2O for 3\u00a0h, followed with an inclusion of 1\u00a0M NH4OH and its hydrothermal treatment at 160\u00a0\u00b0C for 6\u00a0h (Fig.\u00a01). The mass ratio of NCNPs and Cu2+ ions was persevered as 1:2 and consequential product is termed as NCNPs@CuO(1:2)/ITO. Similarly, the NCNPs@CuO/ ITOs were prepared with different mass ratios of 1:1 and 1:3 between NCNPs and Cu2+ ions and the resultant products are termed, respectively, as NCNPs@CuO(1:1)/ITO and NCNPs@CuO(1:3)/ITO. The direct growth of nanostructures on ITO plate was achieved in the active area of \u201c1\u00a0cm \u00d7 1\u00a0cm\u201d by covering \u201c1\u00a0cm \u00d7 1\u00a0cm\u201d of \u201c2\u00a0cm \u00d7 1\u00a0cm\u201d sized ITO with the transparent insulating tape. The scheme 1 3 involved in the synthesis of NCNPs and NCNPs@CuO as detailed in Fig.\u00a01. The directly grown NCNPs and NCNPs@CuO nanostructures on ITOs were scratched from the substrates for the scrutiny of their morphological and structural characterizations. The transmission electron microscope (TEM) images of prepared nanostructures were scrutinized with a JEOL JEM-2010 TEM operated at 200\u00a0kV. Powder X-ray diffraction (XRD) patterns were recorded on a Rigaku Miniflex Goniometer operated at an acceleration voltage of 30\u00a0kV and a current of 15\u00a0mA. Fourier transform infrared (FT-IR) spectroscopy was performed with SHIMADZU-EQUINOX" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003894_mcs.2005.1499390-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003894_mcs.2005.1499390-Figure3-1.png", "caption": "Figure 3. Geometry and free-body diagram of a pendulum with a bob of mass m attached to a fixed support by a massless rope of length l(t). mg is the gravitational force on the bob, is the tension in the rope, and the angle of the rope with respect to the vertical is \u03b8(t).", "texts": [ " A look around the neighborhood playground reveals that children playing on swings generally follow the same strategy. In this article, we show that if the transitions to standing and squatting occur instantaneously, then this pumping strategy is time optimal (Figure 2). The rider-and-swing system is modeled as a pendulum with a bob of mass m attached to a fixed support by a rope of variable length l(t). The rope is taken to be massless, and the angle of the rope with respect to the vertical is denoted by \u03b8(t) (Figure 3). Let l+ and l\u2212, satisfying 0 < l\u2212 < l+, denote the maximum and minimum lengths of the pendulum corresponding to squatting and standing, respectively. Let L (1/2)(l+ + l\u2212) be the mean length of the pendulum. Dissipative forces such as bearing friction and wind drag are ignored. The length of the pendulum is the control input for the system. Conservation of angular momentum for the pendulum gives dH dt = \u03c4, where H ml 2\u03b8\u0307 is the angular momentum of the pendulum about the fixed support, and \u03c4 is the net torque about the fixed support due to all of the forces acting on the pendulum bob" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001267_j.jclepro.2020.120491-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001267_j.jclepro.2020.120491-Figure8-1.png", "caption": "Fig. 8. Distribution of single-link linkage structure coordinate system.", "texts": [ " The human foot is equivalent to the moving platform, and the human lower leg is equivalent to the stationary platform. The three active variables of the moving platform are taken as input values, and the angle between each active rod and the static platform is used as the output value to perform the inverse kinematic solution of the ankle joint structure. Since the mechanism moving platform is connected with the mechanical static platform through three sets of the same structure link chains, one set of connecting rods is selected as an example for kinematics analysis. As shown in Fig. 8, the dynamic and static platforms are equivalent to an equilateral triangle and the two are equal, the x-axis and x\u2019-axis passes through the regular triangle end C1, A1, the size parameters of the regular triangle are known. Set in the static coordinate system o xyz, the o point coordinates are (0, 0, 0), o\u2019 Point coordinates are (X, Y, Z), following closed-loop vector equation (He et al., 2015c) could be constructed: oo\u2019 ! \u00feo\u2019Ai ! \u00bc oAi !\u00bc oCi !\u00feCiBi !\u00feBiAi ! i\u00bc1;2;3 (9) Based on the geometry of the regular triangle itself, the vector o\u2019Ci " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003194_s0956-5663(03)00007-1-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003194_s0956-5663(03)00007-1-Figure1-1.png", "caption": "Fig. 1. Cross-section of an amperometric biosensor installed in a flow cell.", "texts": [ " Thus the weight of glucose oxidase used for this immobilized enzyme membrane was 0.1 mg, and it corresponded to 17 U. The weight of glucose oxidase was decided in order to obtain 100 nA of detecting current even the immobilization efficiency was several percent or less. This enzyme electrode, counter electrode, which was a coil of a platinum wire of diameter 4 mm (BAS Inc., USA), and reference electrode (RE-1C, Ag /AgCl, BAS Inc., USA) were attached to a flow cell, to fabricate an amperometric biosensor (Fig. 1). The inner volume of the flow cell was 340 ml, and the salivary sample volume need for analysis was 100 ml. A flow-injection-type device was used as an analytical system of salivary amylase activity (amylase activity analytical system, Fig. 2). The pH optimum of a- glucosidase and glucose oxidase were 7.2 and 5.6, respectively. So phosphoric acid buffer solution (pH 7.3) was used into which maltopentaose as a substrate was dissolved. A mixing coil was shaped using a tube of 630 mm length, and it was attached in order to reduce the pulsation of the buffer solution caused by a rotary pump (U4-XV, Alitea, Sweden)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001773_tte.2021.3085367-Figure16-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001773_tte.2021.3085367-Figure16-1.png", "caption": "Fig. 16. Subdomain model.", "texts": [ " Finally, the AGFD of the investigated machine is calculated by combining the results of the slotless stator model and the relative permeance function, which can be given by: ( ) ( ) r r r r B r B B B B B \u03b8 \u03b8 \u03b8 \u03b8 \u03bb \u03bb \u03b8 \u03bb \u03bb = + = \u2212 (35) where Br and B\u03b8 are the radial and tangential distributions of the AGFD of the slotless model. To provide a computationally efficient initial design guideline for VFMMs, the subdomain method [36], [38]-[39] is employed in this paper for the on-load performance prediction of the investigated machine, and the corresponding analytical model is shown in Fig. 16. The model can be separated and represented by three regions, namely, Region 1 (air-gap), Region 2i (slot openings), and Region 3i (winding slot). The general solutions of the magnetic vector potentials for the three regions can be respectively formulated as ( ) ( ) ( ) ( ) ( ) ( )1 1 1 , , cos sin , ,k k r k r z k k s r k s rk D r R D r R A A k C k D R R D R R \u03b8 \u03b8 = + (36) ( ) ( ) ( ) ( ) ( )/ , / ,2 2 2 2/ , / , 2 2 0 0 cos ln t t a t a t k r R k r R ii i z k k k R R k R Rk i i E E k A A B E E A A r \u03c0 \u03b2 \u03c0 \u03b2 \u03c0 \u03b2 \u03c0 \u03b2 \u03c0 \u03b8 \u03b8 \u03b2 \u2212 = \u2212 \u22c5 + + (37) ( ) ( ) ( )2 2 3 2 2 3 0 0 / ,3 1 2 1 1/ , 1 1ln 2 2 1cos 2 s t s i z j s k r Ri s k i k R Rk A A J R r r FR kA k E \u03c0 \u03b2 \u03c0 \u03b2 \u03bc \u03b2 \u03c0 \u03b8 \u03b8 \u03b2 \u03b2 \u03c0 \u03b2 = + \u2212 + \u22c5 \u2212 \u2212 \u2212 (38) where \u03b21 and \u03b22 represente the angles of the slot width and slot opening width respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000374_tie.2018.2795525-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000374_tie.2018.2795525-Figure1-1.png", "caption": "Fig. 1. The structure of SLIM (a) the ladder-slit secondary (b) the flat-solid secondary", "texts": [ " The flux density and eddy current are obtained through the 3-D FEM model with the edge and end effects. Variations of the transverse force are calculated and analyzed with different transverse displacements. The influence on the lateral stability and safety of the train is analyzed and compared when the ladder-slit and flat-solid secondary are applied respectively. II. THE MODEL OF THE SLIMS WITH THE LADDER-SLIT SECONDARY The structure of the SLIMs with the ladder-slit secondary is shown in the Fig.1. The primary consists of the iron core and the three-phase windings. The secondary consists of the aluminum and back-iron plate. The width of the secondary is larger than that of the primary core, and the overhang of the winding oversteps the width of the secondary. The parameters of primary are shown in the Table I. In Fig.1, only the aluminum plate is slit, the back-iron plate remains unchanged. Therefore, the ladder-slit secondary is also simple. When the vehicle is running in the turning of the rail shown in the Fig.2 (a), the primary installed under the bogie will be at a displaced position, the paths of the eddy current in different secondaries with the lateral displacements will be shown in the Fig.2 (b)-(c). In the Fig.2 (b)-(c), the regions I and III are the overhangs of the secondary and the region II is the active zone between the primary and secondary", "2 (c), the region I ' is the coupled zone of the secondary conductor and the overhang of the windings, the region I '' is the coupled zone of the secondary side bar and the overhang of the windings, as well as the region III ' and III '' .It can be seen that the current in ladder-slit secondary is more inerratic than it in flat-solid secondary, and the x-component of the eddy current in the region I is much smaller, the edge effect is much smaller consequently. In order to stabilize the vehicle in the curve rails, the ladder-slit type secondary shown in the Fig.1 can be helpful in achieving neutral equilibrium, since, for the displacements, this structure can largely reduce the edge effect. 0278-0046 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. III. THE NUMERICAL ANALYSIS METHOD In order to obtain the air-gap density and the eddy current density in the secondary, the T-\u03a9 Method has been presented [25]" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001456_s10846-021-01411-4-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001456_s10846-021-01411-4-Figure1-1.png", "caption": "Fig. 1 Exploded view of servomotor, propulsion motor assembly and tilting angle reference (\u03b3 ), where \u03b3 = 0 is the upward servomotor direction", "texts": [ " This paper is divided as follows: Section 2 presents the prototype designed in this work, showing the QTR UAV kinematics and dynamics nonlinear modelling, such as the necessary knowledge to apply the FCA; Section 3 describes the new methodology proposed, the FCA with all characteristics in a generic formulation; Afterwards, Section 4 does the explanation about the FCA applied to the QTR UAV, showing the respective formulations; Section 5 depicts some simulation and experimental results where the whole system is tested through open field tests and test bench giroscopic platform; at the end, Section 6 concludes this work, presenting the most important remarks and, also the novelties. This section will describe the aircraft kinematics and dynamics modelilng, taking the servomotor tilting angles into consideration for future formulations. After the main modeling, Section 2.1 presents a particular consideration of the propulsion forces and torques on the aircraft. First, Fig. 1 shows details of the servomotors mounting design: As seen above, it was chosen the H quadrotor topology considering the possibility to tilt the servomotors only in one axis direction, permitting to increase considerably the forward/backward velocity. By consequence, yawing maneuverability will also be increased. Furthermore, the aircraft modelling is extremely necessary once it directly affects the FCA design, as shown in Section 3. Some UAV physical properties are measured in the Vehicle Frame Fv , while others are measured in the BodyFixed Frame Fb and Inertial Frame F I " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000101_j.mechmachtheory.2018.01.008-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000101_j.mechmachtheory.2018.01.008-Figure1-1.png", "caption": "Fig. 1. Coordinate system of misalignments of spiral bevel and hypoid gears.", "texts": [ " The wheel machine settings are obtained from this design. The ease-off surface of the pinion is obtained by generating the conjugate pinion surface first as a reference surface, then modifying the reference surface with the control parameters [17] . Because this process is beyond the scope of this paper, it is described in Appendix A . In the actual gear meshing process, misalignments, including those in the direction of the shaft offset ( E ), pinion axis ( P ), wheel axis ( W ) and shaft angle ( ), must be considered. Fig. 1 shows the coordinate system of misalignments used in this paper. A typical ease-off surface is shown in Fig. 2 (a), and (b) shows the contact path on the pinion projection plane. To simplify the description, the range of horizontal and vertical coordinates of the grid points on the projection plane is \u22121 to 1 in both the lengthwise and profile directions. The numbers of grid points on the ease-off surface in the lengthwise direction and profile direction are 9 and 7, respectively. The ease-off surface can be described by three control parameters, namely, the slope of the contact line k s , the semi-axis of the contact ellipse b , and the coefficient controlling unloaded transmission error (UTE) a ", " Given a grid point ( i, j ) based on L and R values, the theoretical coordinates and unit normal vectors can be calculated as r i j 2 and n i j 2 according to Eqs. (A-14) and (A-15) , where i \u2208 [1, m ] and j \u2208 [1, n ] are the indices in the lengthwise and profile directions of the surface point. \u23a7 \u23a8 \u23a9 x 2 (\u03b8 i j 2 , \u03c6i j 2 ) = L \u221a y 2 (\u03b8 i j 2 , \u03c6i j 2 ) 2 + z 2 (\u03b8 i j 2 , \u03c6i j 2 ) 2 = R (A-15) In the actual gear meshing process, misalignments, including those in the direction of the shaft offset ( E ), the pinion axis ( P ), the wheel axis ( W ) and the shaft angle ( ), must be considered. Fig. 1 (in Section 2.1 ) shows the coordinate system of misalignments. The position vector r 2mis and the unit normal vector n 2mis of the wheel surface, considering misalignments, are obtained as follows: { r i j 2 mis = M 2 M 1 r i j 2 n i j 2 mis = M 2 M 1 n i j 2 , (A-16) where M 1 represents the translation matrix and M 2 represents the rotation matrix, and M 1 = \u23a1 \u23a2 \u23a3 1 0 0 P 0 1 0 W 0 0 1 E \u23a4 \u23a5 \u23a6 , M 2 = \u23a1 \u23a2 \u23a3 cos sin 0 0 \u2212 sin cos 0 0 0 0 1 0 \u23a4 \u23a5 \u23a6 . 0 0 0 1 0 0 0 1 A.2. Calculating the ease-off surface The ease-off surface can be described by three control parameters, namely, the slope of the contact line k s , the semi-axis of the contact ellipse b , and the coefficient controlling unloaded transmission error (UTE) a " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001773_tte.2021.3085367-Figure17-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001773_tte.2021.3085367-Figure17-1.png", "caption": "Fig. 17. The FE mesh of the investigated VFMM.", "texts": [ " 2 2 1 1 2 2 1 2 2 2 3 2 2 3 , , 2 2 0 others , , 2 2 , , 2 2 0 others , i i a a r r i i a a i i t t r r t t H r RH r R B Br R r R H r RH r R B Br R r R \u03b8 \u03b8 \u03b8 \u03b8 \u03b2 \u03b2\u03b8 \u03b8 \u03b8 \u03b2 \u03b2\u03b8 \u03b8 \u03b8 \u03b2 \u03b2\u03b8 \u03b8 \u03b8 \u03b8 \u2208 \u2212 + == = = \u2208 \u2212 + = = \u2208 \u2212 + == = = \u2208= = 2 2, 2 2i i \u03b2 \u03b2\u03b8 \u03b8 \u2212 + (39) By substituting the general solutions (38) into the boundary conditions (39), the corresponding radial and tangential flux density components can be obtained, which can be expressed as 1 r t AB r AB r \u03b8 \u2202 = \u2202 \u2202 = \u2212 \u2202 (40) In the on-load condition, the flux densities PMB and AB generated by the PMs and armature reactions can be superimposed [36] to obtain the AGFD, which can be expressed as load PM AB B B= + (41) Therefore, the air-gap flux densities of the investigated VFMM under different MSs can be derived based on the no-load air-gap flux densities and the armature reactions. Furthermore, the cogging torque and the on-load torque can be obtained, which can be expressed as ( ) ( ) 2 2 00 r t LrT B r, B r, d \u03c0 \u03b8 \u03b8 \u03b8 \u03bc = \u22c5 (42) where L is the axial length. IV. EXPERIMENTAL VALIDATION The JMAG Designer 18.1 package is employed as the FE software to perform the magnetic field simulation of the investigated machine. The FE mesh is plotted in Fig. 17, which has 37,507 elements and 20,762 nodes. The no-load AGFDs predicted by the proposed hybrid field analytical method are in comparison with the FE solutions in Fig. 18, both of which are in acceptable agreement. Besides, it can be seen that the investigated HMC-VFMM demonstrates a flux regulation range with more than twice times. To confirm the validity of the SC transformation for considering the stator slotting effect, the air-gap flux densities of the investigated machine by the proposed method, MEC model, and FE method are shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001581_j.matchar.2021.111074-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001581_j.matchar.2021.111074-Figure2-1.png", "caption": "Fig. 2. Schematic illustration of the SLM-fabricated samples and the dimensions of the tensile test specimens.", "texts": [ " The processing conditions provided by the manufacturer for conventional Ti-6Al-4V alloy were used. The powder layer thickness was set as 20 \u03bcm, and randomly island scanning strategy was used to minimize thermal and residual stress build-up in the part. Under a highpurity argon atmosphere, rectangular samples of 70 \u00d7 12 \u00d7 2 mm3 (Y \u00d7 Z \u00d7 X) were prepared without preheating the substrate, and the schematic illustration of the SLM-fabricated samples and the dimensions of the tensile test specimens are shown in Fig. 2. Q. Wang et al. Materials Characterization 176 (2021) 111074 The concentration of interstitial elements in CP-Ti powder and SLMfabricated samples were determined by oxygen, nitrogen and hydrogen analyzer (G8 GALILEO, Germany) and carbon sulfur analyzer (LECO TC500, USA). The metal elements content was determined by inductively coupled plasma massspectrometry (ICP-MS, Aglient 7800, USA). All samples were sliced parallel to the BD, phase constitutions were examined by X-ray diffractometer (XRD, Bruker D8 Advance, Germany) with Cu K\u03b1 radiation source, at 40 kV and 40 mA with a step size of 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000453_j.apm.2019.03.008-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000453_j.apm.2019.03.008-Figure1-1.png", "caption": "Fig. 1. Geometric model of an involute spur gear and EHL model.", "texts": [ " A robust numerical algorithm for high speed and heavy-load operating conditions considering surface roughness is successfully achieved. Using alumina nanoparticles as an example, influences of nanoparticle shape and concentration on tribology performance of lubricating films are investigated; the normal and tangential stiffness of oil films from engaging into recesses are computed. Finally, the dynamic film velocity field evolution in rough contact is discussed. The geometric parameters of an involute gear pair are shown in Fig. 1 , where O a N 1 = R ba and O b N 2 = R bb are pinion and gear base circle radius, respectively; \u03c9 a and \u03c9 b are pinion and gear angle speed, respectively; \u03d5 is pitch circle pressure angle; the line segment N 1 N 2 is the ideal line of action (LOA); K is engaging point and P is pitch point, and the length between K and P is KP = s ; and N 1 K = R a and N 2 K = R b are the curvature of pinion and gear teeth at engaging point K , respectively. The contact between two gear teeth is approximated by two cylinders of different radii" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000970_j.mechmachtheory.2019.103747-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000970_j.mechmachtheory.2019.103747-Figure1-1.png", "caption": "Fig. 1. The proposed non-symmetric 5R-SPM as the head of a surgical robot (a) surgical robot (b) robot\u2019s head .", "texts": [ " In Section 5 , a dimensional synthesis for the designed mechanism, based on the existence and type of the singularities, is provided. Finally, Section 6 summarizes this paper. In spite of the widespread use of orthogonal and symmetric 5R-SPMs, there are special applications for which a non- symmetric structure is preferred, to reduce the size and weight and avoid internal and external collisions. One such appli- cation is in robotic surgery, for manipulation of wristed laparoscopic instruments [15] ( Fig. 1 ). This application requires fast motion of the whole system; thus, apart from rigidity and kinematic performance, the weight and size of the mechanism should be minimized. Moreover, the collisions between the links, instrument and the base robotic arm should be avoided. The proposed non-symmetric 5R-SPM for this application ( Fig. 1 (b)) consists of orthogonal links in one kinematic chain and arbitrary links in the other. The Y-shaped design of the first link yields high link stiffness and joint rigidity in the first kine- matic chain [9] . Besides, the arbitrary links of the second kinematic chain allow for minimizing the size of the mechanism, avoiding collisions, and maximizing the stiffness of the second kinematic chain. The kinematic chains of the non-symmetric 2DOF 5R-SPM is illustrated in Fig. 2 . The end-effector is connected to the base via two kinematic chains" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001009_s0263574720000284-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001009_s0263574720000284-Figure5-1.png", "caption": "Fig. 5. Comparison of different material combination modules. (a) Bending deformation of previous design. (b) Bending deformation of new design.", "texts": [ " Uppsala Universitetsbibliotek, on 15 May 2020 at 00:12:18, subject to the Cambridge Core terms of use, available at The structure of soft manipulator or soft crawling robot is shown in Fig. 4. The upper chamber is mainly composed of corrugated shapes, with low hardness and high elongation material. On the contrary, the material in bottom is high hardness and low elongation.16, 17 In the air inflating processes, a larger deformation can be produced in the upper chamber due to the difference in hardness of the upper and lower chamber. The bottom deformation is smaller, so the whole cavity is curved upward. Bending deformation is shown in Fig. 5(a). However, it was found in the experiment that due to the low hardness of the upper chamber and the large deformation in the process of inflation, the corrugation of the upper chamber would become a flat arc surface. It would affect the force of friction during crawling. On the contrary, the new design of the earthworm-like soft robot with an upper chamber made of high hardness silicone and a bottom made of lower hardness. During the inflating process, the entire cavity is bent toward the bottom. Bending deformation is shown in Fig. 5(b). This design (b) first deforms downward when the modules are combined, but the modules cannot be deformed downward too much due to the extrusion inside the respective cavities when the air pressure increases, thereby deforming upward. So the deformation is significantly smaller than the design (a), and the upper surface can still be corrugated. 2.2.2. Elongation function. The angle of the single module is 120\u25e6. As shown in Fig. 6, a link of the earthworm-like robot is combined with three modules" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000327_j.mechmachtheory.2017.05.014-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000327_j.mechmachtheory.2017.05.014-Figure8-1.png", "caption": "Fig. 8. Force of helical curve face gear.", "texts": [ " Loaded tooth contact analysis The face gear pair always cover a certain load in practical application, so the tooth contact analysis (TCA) is not enough, and further loaded tooth contact analysis (LTCA) is needed to evaluate the characteristics of helical curve face gear. According to Hertz\u2019s theory on the contact between two surface elastomers, the contact ellipse, maximum contact stresses and surface stress distribution on the surface of curve face gear are obtained. For those results, the force on the surface of tooth should be available at first. During the meshing process of helical curve face gear pair, the Force on meshing point P have been shown in Fig. 8 . So the force on the surface could be calculated as follows: \u23a7 \u23a8 \u23a9 F t ( \u03b81 ) = T 1 R F n ( \u03b81 ) = F t ( \u03b81 ) cos ( \u03b1n ) F a ( \u03b81 ) = F t ( \u03b81 ) tan ( \u03b1n ) (21) Where, \u03b1n is the changeable pressure angle of curve face gear and \u03b1n = \u03b10 + \u03c0/ 2 \u2212 arctan ( r( \u03b81 ) / r \u2032 ( \u03b81 ) ) . In the meshing process, the contact ratio \u025b of this helical curve face gear pair changes from 1.3 to 2.5, so the curve face gear will have 2 or 3 teeth meshing with non-circular gear simultaneously at some rotating angle in the half cycle" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000417_s00170-018-2799-7-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000417_s00170-018-2799-7-Figure8-1.png", "caption": "Fig. 8 Simulations of skiving by VERICUT", "texts": [ " These were reasonable because AB and EF segments were confronted to the main involute profile, while the root segments included a serial of minimum serrated profile and there was no high precision requirement. Furthermore, simulations by these two kinds of rake angle were performed by VERICUT, which is a widely used commercial machining simulation software, according to the parameters in Table 1 and the calculated cutting edge curves. Both the intermedia status and the final machined gear slots were demonstrated as shown in Fig. 8, and the maximum residual error of these two tasks was no more than 0.01 mm. The aforementioned manifested that the calculated cutting edge can machine the desired profile, and this proofed the correctness of the proposed method. On the basis of cutting edge curve calculation, skiving process simulation and the contact analysis can be exhibited in both intuitional perspective and swept forming perspective. As shown in Fig. 9(a), with respect to their own kinematic parameters, a pair of cutting edge and workpiece underwent the process that includes engaging contact, keeping contact, and exiting contact with following the spatial contact curve" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000261_1464419315615451-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000261_1464419315615451-Figure2-1.png", "caption": "Figure 2. Schematic of the meshed 2D finite element model for the cylindrical roller bearing.", "texts": [ " Two-dimensional shell elements having two degrees-of-freedom at each node (translations along the X- and Y-directions) are used to model the roller bearing as a solid structure. The 2D shell elements are defined as plane strain elements.40 The finite element model is meshed with a mixture of quadrilateral and triangular elements. The ratio of the triangular elements is less than 3%. Moreover, all contact areas of the components of the roller bearing are meshed using the quadrilateral elements. The whole finite element model has 180,246 elements and 183,585 nodes. The meshed finite element model is shown in Figure 2. The isotropic elastic material model is chosen for the proposed finite element model. The shaft, the outer race, the inner race, the cage, the rollers, and the adapter are modeled using the material properties of steel. The Young\u2019s modulus is equal to 200 GPa, the density is 7850 kg/m3, and the Poisson\u2019s ratio is 0.3. To simulate the real-time operation of a roller bearing in a typical application, the boundary conditions of the finite element model are as follows. (i) A radial load of 6 kN on the top edge of the adapter along the negative global Y-direction is applied to formulate the radial load of the roller bearing" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001448_j.cirp.2021.04.052-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001448_j.cirp.2021.04.052-Figure3-1.png", "caption": "Fig. 3. Inter-layer ultrasonic peening during PBF.", "texts": [ " The parameter set with laser power, scanning speed, and hatch spacing of 135W, 700mm/s, and 0.12mm yielded the highest density of 99.89% (Archimedes) and 98% (X-ray CT) (Fig. 2d). The corresponding energy density was 32.1 J/mm3. All subsequent samples for this research were printed with the optimized parameter set described above. Interlayer peening was accomplished using an ultrasonic probe with 110W output power and 20 kHz frequency mounted to a linear stage. The probe had four ultrasonically vibrating needles that redistributed stress and caused surface hardening, as shown in (Fig. 3). The needles were 3mm in diameter and evenly spaced from each other by 2mm. All hybrid-AM samples were 100 layers tall (i.e., 5mm) and ultrasonically peened on the 80th (i.e., 4mm from the bottom) and 100th layers. Using hybrid terminology, the layer treatment frequency was L20 for two cycles starting from layer 100 (i.e., top surface). Twenty layers was chosen because prior experiments revealed that higher layer treatment frequencies induced cracking and lower frequencies failed to produce sufficient compressive residual stress to measure by hole-drilling" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003279_s0092-8240(05)80070-9-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003279_s0092-8240(05)80070-9-Figure4-1.png", "caption": "Figure 4. The angle ~ between the translational velocity V and the rotational velocity ~ affects the handedness of the helix and the direction of the axis of the helix K. (a) ~ < ~ / 2 : ~ is parallel to K, and the helix is right-handed. (b) ~>7c/2: m is antiparallel to K, and the helix is left-handed. (c) ~ = ~/2: the trajectory is a circle. (d)", "texts": [ " There is an exception to this rule. Define 0 as the angle between V b and o~ b . If V b changes direction such that 0 changes from an angle less than to one greater than re/2, or vice versa, then K changes from parallel (or antiparallel) to \u00a2o to antiparallel (or parallel) to ~ with a concomitant change in the handedness of the helix (Crenshaw, 1993a). Consider an organism that moves such that < re/2. This organism moves along a right-hand helix for which \u00a2o is parallel to handedness, and K reverses direction (Fig. 4b). Note that if ~ = re/2 then the = 0: the trajectory is a straight line with ~ parallel to the direction of motion. (If = ~, the trajectory is a straight line with ~ antiparallel to the direction of motion.) trajectory is a circle (Fig. 4c), and if 0 = 0 or rc then the trajectory is a line (Fig. 4d). Motion in which Yb changes direction can also be simulated with the program presented in Appendix B. Now, ~J0 b is constant. Figure 5a presents a trajectory for which the direction of Yb changes at three discrete points (marked by dots). The changes in the direction ofV b are visible as kinks in the trajectory, demonstrating how the assumption of smoothness in the previous section has been violated. Nevertheless, as expected, the axes of the helical trajectories between the kinks are all straight and parallel" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003160_cdc.1999.830084-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003160_cdc.1999.830084-Figure1-1.png", "caption": "FIGURE 1.", "texts": [], "surrounding_texts": [ "First suppose that (6) is (qdyn, +&,)-reducible to (8). Let c : [O,T] -+ Q be a geodesic so that (c',O) is a (%dyn,T)solution of (6). If we ask that c'(0) E &in then part (i) of Definition 4.1 implies that there exists ii : [0, T] -+ IR\" so that (c,ii) is a (%j,,,T)-solution of (8). Indeed, ii is defined by\nc'(t) = P ( t ) X a ( c ( t ) )\nand so is smooth. Further, this implies that &in is geodesically invariant. The remainder of this part of the proof will be directed towards showing that Dkin = Ddyn.\nLet e, be the uth standard basis vector for IR'\" and let U,: [O,T] -+ Rm be the control defined by ULL(t) = e,. If 0: [O,T] -+ T Q is an integral curve for the vector field Z+ verlift(Y,,), then (o,U,) is a (%dyn,T)-solution for (6). By part (i) of Definition 4.1, (r must be tangent to Dkin. Since &in is geodesically invariant, is tangent to &in, therefore verlift(Y,) must be tangent to &in. This implies that Ddyn C Dkin.\nTo show that &in C Ddyn we employ the following lemma.\nLEMMA: If a distribution D is geodesically invariant for an afine connection V , then for each q E Q and each X E Dy there exists T > 0 and a smooth curve c : [0, T ] -+ Q with the following properties\n(i) c'(t) E for t \u20ac10, T ] and (ii) V'J(O)C'(O) = x.\nProof Let (U,$) be a normal coordinate chart [7, Proposition 8.41 with $(q) = 0. In such a chart the Christoffel symbols for V satisfy r;k(0) + ri,i(0) = 0, i, j , k = 1,. . . ,n. Let P > 0 be small if necessary and let E : [O,T] -+ Q be the geodesic satisfying E'(0) = X . Let us denote the local representative of E in our normal coordinate chart by t H (q ' ( t ) , . . . ,q\"(t)) . We must then have ?(O) = 0, i = 1,. . . , n since E is a geodesic and we are using normal coordinates. Since D is geodesically invariant, E ' ( t ) E Dc(f) for t E]O,P]. Now define 7: [O,T] -+ [0 ,$T2] by 7 ( t ) = i t 2 . Let T = iT2, define c: [O,T] -+ Q by c = E O T , and denote by t H (q ' ( t ) , .. . ,q\"(t)) the local representative of c. Then we have\n, 2t$(t) . q'( t ) = - T L = l \" \" l n ~ ' ( 0 ) =#(o), i = 1,. . . ,n.\nSince E'(0) = X the result follows. v\nNow let q E Q and X E Dkin+,. Choose a curve c : [0, T ] -+ Q as in the Lemma. Define a smooth map ii: [0, T ] -+ IRfi by asking that it satisfy\n~ ' ( t ) = i ia ( t )Xa(c( t ) ) .\nThen (c,ii) is a (%k,n,T)-solution of (8) and so, by part (ii) of Definition 4.1, there exists a map U : [O,T] -+ IR'\" so that\n( c ' , ~ ) is a (%dy,,T)-solution of (6). Indeed, since c' is smooth, U will also be smooth. Furthermore we have\nx = vcyo)c'(0) = uU(0)Y,(c(O))\nThis shows that &in C Ddyn which completes the proof of the \"only if\" part of the Theorem.\nNow suppose that (i) and (ii) hold (and so h = m). First, (ii) implies that (6) leaves Ddyn invariant since verlift(Y,), a = 1,. . . ,m , is tangent to Ddyn. If (0, U) is a (%&,n,T)-solution of (6), then 0: [0, T ] -+ TQ is absolutely continuous, and so c L? T Q W is also absolutely continuous. In fact, CT = c' and so not only is c absolutely continuous, but c' is absolutely continuous. If we further suppose that c'(0) E D,(o), then c'(t) E Dc(t) for t E [O,T]. We may then define ii: [O,T] -+ Et\" by\nwhich uniquely defines ii since (6) leaves Ddyn, and hence &in, invariant. It remains to show that is absolutely continuous. To prove this, we work locally around qo = c(0) and extend the vector fields {XI,. . ,Xf i} to a local basis {XI,. . ,X,,} for vector fields. Thus the matrix X j ( q ) , i , j = 1,. . . , n is invertible for q sufficiently near qo, and we denote the inverse matrix by V j ( q ) , i , j = 1 , . . . ,n. We also extend ii to take values in IR\" by asking that the last n - f i entries be zero, and we denote the corresponding map by 9: [0, TI -+ IR\". For t sufficiently near zero we have\nc'(t) = i i a ( t ) X a ( c ( t ) )\ncj'(t) = ~ i ( t ) ~ j ( q ( t ) ) , i = 1,. . . , n\nd ( t ) = Vj(q(t))Qj(t), i = I , . . . ,n . a\nNote that the terms in the right-hand side of the second equation are absolutely continuous. This implies that 17 is absolutely continuous, and so ii is absolutely continuous. Thus part (i) of Definition 4.1 holds.\nFinally, let (c,ii) be a (%jln,T)-solution of (8). Thus c is absolutely continuous, and c' is integrable. Since Ddyn, and therefore is geodesically invariant, V,J(,)c'(t) E Ddyn,,(t) for t E [0, TI. Thus we may write\nV,J(f)C'(t) = Yu (c ( t )\nwhich defines U : [0, T ] -+ R'\". It remains to show that U is integrable. Again, we work locally around qo = c(0). We extend {Yl , . . . , Ym} to a local basis {YI, . . . , Y,} of vector fields near 40. We denote by W;(q) , i , j = 1,. . . ,n, the components of the inverse of the matrix with components Y;(q) , i , j = l , ..., n. W e t h e n e x t e n d u t o a m a p w : [O ,T]+IRm by asking that w be zero in its last n - m components. We have\ni i ' ( t ) + l-;k(s(r))4'(t)qk(t> = w J W j ( 4 ( t ) ) *\ni = 1,. . . ,n. Using properties of integrable functions, we assert that U is integrable. This shows that part (ii) of Defi-\nw'(t) = w;(ii/(t) +r~e (q ( t ) )qk ( t )qe ( t ) ) ,\nnition 4.1 holds, which completes the proof.", "4.3 REMARKS: 1 . By not asking that &in = Ddvn a priori, we have ensured that we have captured all possible ways a system (6) may be (%dyn,%kin)\u2018 reducible to (8).\nWe have chosen to use a fairly rich class of inputs %dyn for our mechanical control problem. One could certainly formulate Theorem 4.2 for other classes of inputs, but the conditions (i) and (ii) would remain in any such result.\nGiven an affine connection, a generic distribution will not be geodesically invariant. Thus, a generic system of the form (6) will not be (%dyn,%kin)-reducible to a system of the form (8). However, as is often the case with such genericity statements, it is not hard to find physical examples where conditions (i) and (ii) of Theorem 4.2 hold. 0\n5 Examples\nA few simple examples will help clarify Theorem 4.2. We shall only sketch certain of the details involved in the computation of the Christoffel symbols, and refer the reader to the cited references for details. As we shall see, the first two examples we consider are (%dyn, %ki,)-reducible to kinematic systems, and the last example is not. However, as asserted by Remark 4.3-3, such odds are not to be generally expected.\n5.1 Robotic leg We consider a rigid body with inertia J and pinned at its centre of mass. Affixed to the body is a massless, extensible leg with a point mass rn at its tip (Figure 5.1). The inputs we\nconsider for the system are an internal torque which moves the leg relative to the body and a force which extends the mass on the end of the leg. This example is studied in [8] and [9] as a kinematic (i.e., \u201cnonholonomic\u201d) control system, and in [ I ] as a simple mechanical control system. Thus one can expect it to be (%&,%&)-reducible. However, let us go through the machinations of verifying the hypotheses of Theorem 4.2. We refer to [l] for details on the system\ndata, i.e., the Riemannian metric and the input vector fields. Let us merely write down, in the coordinates (r,O,t+f) indicated in Figure 5.1, the non-zero Christoffel symbols for the Levi-Civita affine connection, using (4):\nand the input vector fields:\nWith this data one readily computes\n2 a (Y, : Y l ) = (Y, : Y2) = 0, (Y2 : Y2) = 0.\nm2r3 ar \u2019 Since the first order symmetric products for the basis of Ddyn remain in Ddyn, the condition (ii) of Theorem 4.2 is satisfied, and so the mechanical control problem for the robotic leg is (%&, %ki,)-reducible to the kinematic system\n(9)\nThis is essentially the system studied in [8] and [9]. One readily shows, for example, that the system is locally controllable. We can say a little bit more as well. Note that the distribution spanned by { Y2) is also geodesically invariant. Thus, if we consider the system as having only the input Y2, it is (%dyn, %ki,)-reducible to\n1 m r = 0 = 0 , \\ir = 0.\nHowever, this system is obviously not locally controllable. It is also clear that with just the input vector field Y1, the robotic leg is not (%&, %ki,)-reducible to a kinematic system.\n5.2 Upright rolling disk Here we consider a uniform disk rolling upright without slipping on a flat surface orthogonal to the direction of gravity (Figure 2). We use coordinates (n,y ,O,$) as indicated in\nthe figure. We denote by m the mass of the disk, r the radius of the disk, J the moment of inertia about the z-axis, and I the moment of inertia about its centre of mass in the direction of a line orthogonal to its face. For this example, we must use an affine connection which is not Levi-Civita, but", "which is computed using the methodology of Lewis [ 2 ] , to which we refer for the details. Here we merely record that the non-zero Christoffel symbols are given by\nand the input vector fields by\nl a y2 = -- .I ae\u2018\nOne then readily computes the symmetric products\n(Y1 : Yl) = 0, (Y1 : Y2) = 0, (Y2 : Y2) = 0.\nClearly then Ddyn is geodesically invariant for this example, and so the mechanical control system corresponding to the rolling disk is (%dynr %ki,)-reducible to the kinematic system\nrcose y - rsine I + mr2 I+mr2u x=-\ne = \u2018i i2 J \u2019 \u2018 7 s \u2018 6\u2019 .\nOne also readily verifies that the distribution Ddyn is maximally involutive and so the system is locally configuration controllable.\n5.3 Planar rigid body The system we consider here is a planar rigid body of mass rn and moment of inertia J about its centre of mass. We use coordinates ( x , y , 0 ) as indicated in Figure 3. The forces we\nconsider are applied to the body some distance h from the centre of mass. Without loss of generality, we assume that this point of application is situated along the body x\u2019-axis through the centre of mass (again, see Figure 3). This system was investigated first by Lewis and Murray [ 11 and then\nby Bullo and Lewis [lo], in the latter case as a left-invariant system on the Lie group SE(2) . The Christoffel symbols for the Levi-Civita affine connection in the coordinates (x , y , 0) are all zero (the Riemannian metric is constant in these coordinates), and the input vector fields are\nyl = - cose - a + - sine - a m ax m ay\u2019\nsine a case a h a y2 = -- m ax m ay J a 8 \u2018\nWe compute the following symmetric products:\n2hcos8 a 2hsin8 a (Yl : Yl) = 0, (Y2 : Y2) = --\nml a x + T & * hsin8 a hcose a\n(YI : Y2) = -- - -- ml ax mJ ay\u2018\nFrom these computations we see that Ddyn is not geodesically invariant, and so the planar rigid body is not (%dyn, @kin)-redUCibk to any driftless system. That is to say, when considering this system, the dynamics must be taken into account.\nReferences [I] A. D. Lewis and R. M. Murray, \u201cControllability of simple mechanical control systems,\u201d SIAM Journal on Control and Optimization, vol. 35, pp. 766-790, May 1997. [2] A. D. Lewis, \u201cSimple mechanical control systems with constraints.\u201d To appear in IEEE Transactions on Automatic Control, Mar. 1997.\n[3] A. D. Lewis and R. M. Murray, \u201cControllability of simple mechanical control systems.\u201d To appear in SIAM Review, 1999. [4] E. D. Sontag, Mathematical Control Theory: Deterministic Finite Dimensional Systems. No. 6 in Texts in Applied Mathematics, New York-Heidelberg-Berlin: Springer-Verlag, second ed., 1998. [5] R. Abraham and J. E. Marsden, Foundations of Mechanics. Reading, MA: Addison Wesley, second ed., 1978. [6] A. D. Lewis, \u201cAffine connections and distributions with applications to nonholonomic mechanics,\u201d Reports on Mathematical Physics, vol. 42, no. 112, pp. 135-164, 1998. [7] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, vol. I of Interscience Tracts in Pure and Applied Mathematics. New York: Interscience Publishers, 1963. [8] Z. Li, R. Montgomery, and M. Raibert, \u201cDynamics and control of a legged robot in flight phase,\u201d in Proceedings of the IEEE International Conference on Robotics and Automation, IEEE, May 1989. [9] R. M. Murray and S. S. Sastry, \u201cNonholonomic motion planning: Steering using sinusoids,\u201d Institute of Electrical and Electronics Engineers. Transactions on Automatic Control, vol. 38, no. 5, pp. 700-71 6, 1993. [IO] E Bullo and A. D. Lewis, \u201cConfiguration controllability of mechanical systems on Lie groups.\u201d Proceedings of MTNS \u201996, June 1996." ] }, { "image_filename": "designv10_11_0001272_1464420720909486-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001272_1464420720909486-Figure1-1.png", "caption": "Figure 1. Master and test gears.", "texts": [ " The test gears were prepared by injection molding using the DGP Windsor (model: ST-50) machine. Prior to molding, the moisture trapped in the pellets was expelled by pre-heating at 353K for 2 h. The injection molding pressure was 7MPa. The temperatures in the barrel heating zones were 558, 563, 568, and 573K. After molding, the test gears were preserved in a desiccator for stabilization and the prevention of moisture infiltration before testing. The master gear material was AISI SS 316. The wire cut electric discharge machining process was used for the fabrication of the master gear. Figure 1 depicts the master and test gears. An in-house developed gear test rig was used to conduct constant frequency bending fatigue tests. The test rig is shown in Figure 2. The test rig included a servo motor-based loading system, a control system, and a data acquisition system (DAQ). The test gear was mounted as the driven gear. In the bending fatigue fixture recommended by SAE J1619, the gear tooth is loaded by an upper anvil insert connected to a loading arm. The gear rotation is prevented by placing the lower adjacent tooth on the lower anvil insert" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003539_robot.1996.506835-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003539_robot.1996.506835-Figure2-1.png", "caption": "Fig. 2: The different transformations used", "texts": [ " In this section we present the procedures used to identify the three offsets eloff, 020g, 830E of the three first joints, the position m o r s d,, dy, d, and the orientation errors &, $, & of the robot base with respect to the environment. These errors are assumed to be small. Two procedures allsw one to identify two sets of parameters: (1) &, &, d,, eloff, 820ff, 830ff and (2) dx, d,, &. Note that the offsets can also be identified with the second set of parameters. The offset on the fourth joint Obff is not identified since it has no influence on the end effector position and a negligible influence on its orientation along 24 axis. The frames defined to present the procedures are (figure 2): R,: the reference frame associated to the work cell, %: the base plate frame tied to its center Ob, \u20ac&: the mobile plate frame tied to its center Ot, R: the sensor frame associated to the point 0,, the zc axis is on the sensor optical axis. Using homogeneous transformations matrix 'Tj [2] to describe in the frame Ri the coordinates of a vector given in the frame Rj we can define wTb, bTt, 'T,: -6, 6, X,+d, l o o x , 0 1 0 y 0 0 0 1 BO YO &IT are the nominal coordinates of Ob in R,. The coordinates of [x, Y, 2;lT are computed using the direct kinematic equations (DKE) taking into account the offsets 6 l O f f 7 %ff, [ x, I: 2, IT = DIE( e, +q,,e, +e,, ,e3 +e,, e,) 8, is the i\" joint variable" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001034_tie.2020.3009578-Figure10-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001034_tie.2020.3009578-Figure10-1.png", "caption": "Fig. 10. Contour maps of magnetic flux density and magnetic field distributions of 24s/17p-F2A6-SWFFSM-I with identical stator slots. (a)Jf=7A/mm2, Ja=0A/mm2. (b) Jf=0A/mm2, Ja=7A/mm2.", "texts": [ "6 (b), it can be found that the 24s/17p-F2A6SWFFSM exhibits the smallest cogging torque, which is proportional to the GCD (Ns/2, Nr) and inversely proportional to the least common multiple of Ns/2 and Nr. As shown in Table \u2163, when these topologies with long end-windings and high extra copper losses are not considered, the SWFFSM which possess the maximum IDC, best harmonic performance, lowest cogging torque and feasible slot/pole combination is 24s/17p-F2A6-SWFFSM. Theoretically, the topology with larger IDC, which corresponds to larger back EMFs, can output higher torque. However, as shown in Fig.10, a much longer magnetic flux path produced by overlapping armature windings may facilely cause the saturation of the magnetic circuit at the stator yoke, which will restrict the torque capability, while the short magnetic flux path caused by field winding possesses the relatively lower magnetic flux density. Therefore, the crux to improve the torque output capacity of OW-SWFFSMs is to reduce the magnetic saturation at stator yoke. In addition to optimizing the stator yoke height appropriately, the most effective approach to improving this problem is to optimize the ratio of excitation ampere turns and armature ampere turns" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003735_41.281604-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003735_41.281604-Figure3-1.png", "caption": "Fig. 3. Desired path.", "texts": [ " If the velocity is too large, the admissible region of s cannot exist and the motion along the path is impossible. It determines the admissible velocity. The minimum-time trajectory is composed by connecting maximudminimum acceleration trajectory segments so as to obtain maximum velocity without exceeding the admissible velocity. An example of the trajectory planning for a two DOF horizontally articulated manipulator (Fig. 2) is shown. The joint torque limit is -2 5 7 1 5 2, -1 5 7 2 5 1 ( N . m). The desired path is a circle (Fig. 3; center: [0.4, 01, radius: 0.1 m). In this case, the path coordinate system is a polar coordinate system whose origin is at the center of the path. The s component along the path is angle a, and the 2 component normal to the path is radius T. In the planned trajectory, the velocity d! along the path (Fig. 4(a), bold line) is obtained by switching maximum acceleratioddeceleration without exceeding the admissible velocity (Fig. 4(a), thin line). One of the joint torques is always saturated [Fig. 4(b), (c)]", " As the time to complete the path tracking may be different from that of the nominal trajectory, the end of the tracking should be watched: X = -. The value of X is monitored during the path tracking. If the manipulator is on the path, 0 5 X 5 1. The path tracking control is terminated when X = 1. s - so Sf - s o (25) V. SIMULATIONS Path tracking simulations were carried out with a two DOF horizontally articulated manipulator (Fig. 2). A minimum-time trajectory (Fig. 4) was planned as the nominal trajectory for a desired path of Fig. 3. Viscosity friction and coulomb friction (b) Conventional Method [Joint 1: 0.2 sgn(4) + 0.48 ( N . m), Joint 2: 0.1 sgn(8) + 0.24 (N.m)] were applied to the joints as disturbances. Friction was not considered in the dynamic model used for the trajectory planning algorithm and the controllers. Fig. 7 shows the simulation results. Although the manipulator deviates from the desired path in the case of the conventional method [(b), the computed torque method in operational space], tracking error in the case of the proposed method (a) is small" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003876_978-1-4612-4990-0-Figure66-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003876_978-1-4612-4990-0-Figure66-1.png", "caption": "Figure 66. Natural and unnatural motions of an arm.: The left figure illustrates a natural motion for the two link, two joint manipulator. The right figure illustrates a straight line motion that is not natural for this mechanism and suggests the manipulator motions that are required to produce it.", "texts": [ " Plot of the positions taken by the center of support for the machine during a walk. ............................ 95 Figure 62. Table of experiments with wave number associated. ........... 94 Figure 63. Time trace of leg recoveries for 160 seconds of walking without excitation. ............................... 96 Figure 64. Time trace of leg recoveries for 160 seconds of walking with excitation. ............................... 96 Figure 65. Time tradeoffs for dynamic balance. ....................... 101 Figure 66. Natural and unnatural motions of an arm. .................. 103 Figure 67. Natural motions for a task. .............................. 103 Figure 68. Sample plot of recovery values estimated from inhibition data taken during experiment run July 28,1983. . ........ 126 Figure 69. Sample of progress estimates for the two sides of the machine. ., 126 Figure 70. Sample of all six load traces. ............................. 127 List of Illustrations xv Welcome back my friends To the show that never ends", "2 Scaling constraints on walking strategies 101 hence permitting the animal to get by with fewer than six legs. An open question is whether the capabilities required to make a large six legged machine walk with static gaits wouldn't also be adequate to make a similar machine walk dynamically. If so, there would be no point in building a large statically stable machine. A natural motion of a manipulator is one that can be achieved by varying only one of the mechanism's degrees of freedom, as illustrated in Figure 66. No complex behavior is required involving coordinated motions by several actuators. A natural motion for a task is a path that some part of the mechanism must take if the task is to be performed correctly. A great deal of work in robotics has been concentrated on kinematic solutions of mechanisms and path planning because the natural motions of manipulators and the natural motions imposed by tasks are usually not the same. The kinematic solutions and path planning are done in an effort to use the natural motions of the mechanism to achieve the natural motions of tasks" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003410_s0039-9140(01)00532-x-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003410_s0039-9140(01)00532-x-Figure1-1.png", "caption": "Fig. 1. Voltammetric behaviour of a Dupont printed electrode (a) and of an amphiphilic modified Dupont printed electrode (b). Both electrodes were immersed in a deoxygenated solution of anthraquinone sulfonate (1 mM) phosphate buffer solution (0.1 M, pH 7) and the potential was cycled at scan rates of 20, 50 and 100 mV s\u22121.", "texts": [ " This was confirmed by estimating the enzymatic activity of the electrolyte after polymerisation of the polymer, which showed, for Acheson and Dupont printed electrodes, the quantity of enzyme that leached from the electrode surface was 34.3 and 27.2%, respectively, of the total amount of enzyme preabsorbed. In comparison to Acheson and Dupont printed electrodes, the quantity of enzyme that leached from Gwent electrodes was only 18.8% of the total pre-absorbed. As a direct consequence, there will be a large variation in sensor sensitivity between each electrode. The voltammetric behaviour of amphiphilic modified SPCEs were studied using the redox analyte anthraquinone-2-sulphonate. Fig. 1(a) and (b) illustrate the voltammetric behaviour of this redox analyte for an unmodified and amphiphilic modified Dupont graphite-based printed electrode, respectively. For the three unmodified printed electrodes different quasi-reversible voltammograms were obtained, with Gwent electrodes exhibiting the most favourable reversible behaviour. For Gwent electrodes, the difference in peak potential, E, (140 mV) was considerably lower compared to Acheson and Dupont printed electrodes, 500 and 400 mV, respectively. The observed difference in peak potential is directly related to the variation in charge-transfer kinetics between the printed electrodes. When printed electrodes were modified with tyrosinase-based amphiphilic polymers, the voltammetric behaviour of the electrodes towards anthraquinone-2-sulphonate changed dramatically, Fig. 1(b). Apart from an increase in peak potential separation (Gwent 400 mV, Acheson 800 mV and Dupont 880 mV), which can be attributed to an increase in electrode impedance, an increase in the cathodic and anodic currents was also observed. As anthraquinone-2sulphonate is an electroactive anion it will therefore be incorporated into the polymer film as the counter-ion when the electrode is immersed in a solution of the analyte [23,24]. Consequently, the currents flowing in oxidation and reduction will be larger for amphiphilic modified electrodes, due to the incorporation of anthraquinone-2sulphonate, compared to unmodified electrodes", " Modelling of the impedance data using the equivalent circuit described above indicated that the charge-transfer resistances for unmodified Gwent, Acheson and Dupont electrodes had increased from 100, 200 and 500 [18], respectively, to 4.2, 3.6 and 6.5 k , respectively, for polymer modified electrodes. This increase in charge-transfer resistance could be due to the resistance of the surface polymer. Moreover, the observed increase in charge-transfer resistance correlated well with cyclic voltammographs of modified and unmodified SPCEs in anthraquinone-2-sulphonate solution which showed the reduction and oxidation potentials for this redox analyte increasing upon modification of the electrode surface with amphiphilic polymers, Fig. 1. For Gwent electrodes modified with amphiphilic polymers a distortion in the \u2018depressed\u2019 semi-circle arc was observed at high frequencies ( 10 Hz). It is generally accepted that such distortions of the semi-circle arc at high frequencies are dominated by surface effects, e.g. surface roughness [25]. Thus, for amphiphilic Gwent electrodes, the presence of the polymer has altered the bulk surface properties of the electrode compared to unmodified Gwent printed electrodes. Modified Acheson and Dupont printed electrodes, however, did not exhibit a distortion of the semi-circle arc at the high frequency domain" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001009_s0263574720000284-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001009_s0263574720000284-Figure6-1.png", "caption": "Fig. 6. Model diagram of the one-link earthworm-like robot.", "texts": [ " During the inflating process, the entire cavity is bent toward the bottom. Bending deformation is shown in Fig. 5(b). This design (b) first deforms downward when the modules are combined, but the modules cannot be deformed downward too much due to the extrusion inside the respective cavities when the air pressure increases, thereby deforming upward. So the deformation is significantly smaller than the design (a), and the upper surface can still be corrugated. 2.2.2. Elongation function. The angle of the single module is 120\u25e6. As shown in Fig. 6, a link of the earthworm-like robot is combined with three modules. When the internal pressure increases, because radial cross-sectional area is far greater than axial cross-sectional area, the expansion of the interior of the cavity is mainly axial direction. Under the action of axial force, the axial elongation can be produced. https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0263574720000284 Downloaded from https://www.cambridge.org/core. Uppsala Universitetsbibliotek, on 15 May 2020 at 00:12:18, subject to the Cambridge Core terms of use, available at The forward motion can be achieved through successive elongation of the earthworm-like robot" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001427_j.mechmachtheory.2021.104300-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001427_j.mechmachtheory.2021.104300-Figure6-1.png", "caption": "Fig. 6. Location of the reference frames: a) on the base; b) on the platform.", "texts": [ " Generalized coordinate q i , i = 1\u20266, can now be found from the following formula: q i = z Oi Aj \u00b1 \u221a L 2 ASi \u2212 ( x Oi Aj )2 \u2212 ( y Oi Aj )2 , (9) where x Oi Aj , y Oi Aj , and z Oi Aj are the components of vector p Oi Aj ; L ASi is the length of link A j S i . The choice of the sign in the expression above depends on the mechanism design. Notice that each number j corresponds to a couple of numbers i . We will use j = 1 for i = 1 and i = 2, j = 2 for i = 3 and i = 4, and j = 3 for i = 5 and i = 6. Consider an example of the inverse kinematics problem solution. The mechanism parameters correspond to the CAD model in Fig. 2 , Fig. 6 , and Table 1 . We assume the symmetry in the manipulator geometry: points C j , B j , and O i are distributed uniformly around the circles with radii r C , r B , and r O , respectively; all the rods have the same length L AB ; all the intermediate links have the same length L AS . Points O gl , O i , S i , and C j share a common plane. Points B j and O pl also lie in one plane. The axes of the coordinate frames have directions according to Fig. 6 . Let, for example, output link trajectory X ( t ), where t is the time, be the following (a spiral along axis Z gl with a constant zero orientation): x = 10 cos ( 8 \u03c0t ) mm , y = 10 sin ( 8 \u03c0t ) mm , z = \u2212300 \u2212 50 t mm , \u03d5 = \u03b8 = \u03c8 = 0 , (10) where t is in seconds. Expressions (6) \u2013(10) have been modeled in MATLAB for the time interval of one second. Fig. 7 presents the obtained results as q i ( t ) plots. One can see the effect of periodic and linear motions (10) on the generalized coordinates", " To find solutions, we have used Bertini software [51] together with the MATLAB package BertiniLab [52] . This software uses homotopy continuation techniques [53] to solve systems of polynomial equations. First, we have performed several general tests with arbitrarily chosen values of the manipulator geometrical parameters and generalized coordinates q . All the tests have led to 1968 distinct solutions, however, all of them were complex. At the next step, we have considered the particular geometry of the manipulator ( Fig. 6 and Table 1 ) and used the value of q according to the previous example of the inverse kinematics for X ( t ) at t = 0: X = [ 10 0 \u2212300 0 0 0 ]T ( position in mm ) , (22) q = [ 170 . 1 133 . 3 125 . 9 141 . 8 160 . 1 182 . 5 ]T mm . (23) With these parameters, we have found 1968 solutions again, but this time 20 were the real ones. These real solutions correspond to the different assembly modes of the manipulator possible for the given combination of the parameters. Fig. 9 presents all these modes, and #14 on Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000956_02670836.2019.1685770-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000956_02670836.2019.1685770-Figure2-1.png", "caption": "Figure 2. Finite-element model.", "texts": [ " Point 1 Point 2 Point 3 Point 4 Point 5 Direction X Y X Y X Y X Y X Y Residual stress (MPa) 121 8 66 4 17 9 30 9 101 10 Error\u00b1 (MPa) 7 4 8 1 3 4 1 4 3 5 During the simulation, the three-dimensional mathematical model is set up in Creo at first, pour into DEFORM after meshing. In DEFORM, according to the sample physical parameters and tensile stress and strain data in Table 3, Table 4 and Figure 3 to establish new material AlSi10Mg, in addition, the residual stress of SLM sample measured by X-ray is imported into the 3D model as the initial stress of the workpiece. The mesh model of the workpiece is shown in Figure 2, the right side of Figure 2 is the simulation schematic diagram, where Q is the total heat transferred to the sample by the resistance furnace during heating. In this work, a method for evaluating stress, strain and microstructure changes during heat treatment of SLM AlSi10Mg alloy is proposed. Its accuracy is verified through the comparison of heat-treatment experiments and simulations. Based on the proposed method, the stress and strain changes in the course of heat treatment are discussed in four parts. Then, the process is optimised from three aspects: microstructure, residual stress and residual strain" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003156_ias.2000.881127-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003156_ias.2000.881127-Figure2-1.png", "caption": "Fig. 2.Cross section of the three phases machine", "texts": [ " 1 Machine presentation In this paper, we present a new structure for a synchronous polyphased (three-phase) machine with a stator concentrated flux and permanent magnets. This particular structure uses the principles of both flux switching and flux concentration [1,2,3]. As shown in Fig. 1, an elementary magnetic cell serves to explain the operating principle of this machine. According to the position of the mobile part, the magnetic flux-linkage in the armature winding can be counted as either positive or negative, and is then alternative. From the elementary cell, we developed a prototype (see Fig. 2), in accordance with applicable design rules [lo]. i a I! of v1 4- Armature Winding i a .- Fig.l.Elementary cell of the machine This machine is composed of a stator that includes armature coils and permanent inductor magnets. The salient rotor is simply made of stacked soft-iron sheets. The prototype is a three-phase machine containing twelve magnets, with each phase thus comprising 4 magnets and 4 concentric coils. The rotor contains Nr teeth (with Nr = lo), and the relation between the mechanical rotation frequency F and the electrical frequency f can be expressed as: f = N, F" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003551_0094-114x(95)00101-4-FigureI-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003551_0094-114x(95)00101-4-FigureI-1.png", "caption": "Fig. I. Scheme of a serial manipulator.", "texts": [], "surrounding_texts": [ "~ Pergamon Mech. Mach. Theory Vol. 31, No. 5, pp. 589~05, 1996 Copyright \u00a9 1996 Elsevier Science Ltd\n0094-114X(95)00101-8 Printed in Great Britain. All rights reserved 0094-114X/96 $15.00 + 0.00\nA H O M O G E N E O U S M A T R I X A P P R O A C H T O\n3D K I N E M A T I C S A N D D Y N A M I C S - - I I .\nA P P L I C A T I O N S T O C H A I N S O F R I G I D B O D I E S A N D\nS E R I A L M A N I P U L A T O R S\nGIOVANNI LEGNANI\nDip. di Ins. Meccanica, Universita' di Brescia, Via Branze 38, 25123 Brescia, Italy\nFEDERICO CASALO, PAOLO RIGHETTINI and BRUNO ZAPPA\nDip. Trasporti e Movimentazione, Politecnico di Milano, Pz.a L. Da Vinci 32, 20133 Milano, Italy\n(Received for publication 16 November 1995)\nAbstract--In this paper we present applications of the new approach to the kinematic and dynamic analysis of systems of rigid bodies presented in Part I. An extension of the method to the Lagrangian formulation of the dynamics of chains of rigid bodies is also presented. The kinematic and dynamic analysis is preformed for a generic serial manipulator either in open and closed loop. Two numerical examples concerning an open loop and a closed loop are presented too. Two software packages based on our approach are also briefly introduced. Copyright \u00a9 1996 Elsevier Science Ltd.\n1. I N T R O D U C T I O N\nThis part of the paper is devoted to the presentation of the application of the matrix approach described in Part I of the paper to open and closed chains of rigid bodies; moreover the dynamics are extended to the Lagrangian formulation. We present an analytical example that shows how to write the kinematic and dynamic matrices of the well known Standford Arm. A second example concerning a closed loop system is also developed. A further example refers to a numeric solution for the direct kinematics and the inverse dynamics of any serial manipulator using two standard libraries written in C and in C + + language. These software packages outline the good correspondence between the theoretical approach of the problem and its implementation in simulation programs. The notation used in the following paragraphs is explained in Part I of the paper which is assumed known to the reader. Since, in the study of chains of rigid bodies, subscripts often assume standard values, it is possible to use an abbreviated notation which makes the notation more compact. In other wordst some subscripts can be omitted and we assume that Li_ ld = L~_ ,.i<, ~),\nW i - l.i = W i - I,i(i- i), Hi- J,i = Hi_ L,~- o'\n2. C H A I N S O F R I G I D B O D I E S\n2.1. General considerations\nIn agreement with the Denavit and Hartenberg approach, we suppose that all links of the system are coupled to each other by one degree of freedom lower pairs (prismatic, revolute or screw pairs). Then if the system has joints with more than one degree of freedom we should simulate it by introducing dummy bodies with one degree of freedom. In relation to the serial manipulator of", "590 Giovanni Legnani et al.\ncan be expressed as a function of matrix L, which in this case is a sort o f generalized velocities ratio matr ix\nW , _ I.h = L ,_ I.hqh\"\nBy remembering the relation between matrix H and L revealed in Part I we can write\n= L 2 ,42 H , _ I.* h- l.h~* + L , _ J.*~/h\nL has similar properties (base reference transformation rule) to the correspondent matrix W and takes, for prismatic and screw pairs respectively, the two forms:\n0 u y b\no 0 0 o 0- O- 0 0 where u (unit vector) contains the direction cosines in (k) of the axis of the joint between the two bodies i and j, b = - ut + pu, p is pitch of the pair, and t is the position in (k) of an arbitrary point of the axis. u and t can be immediately obtained from the appropriate position matrix. A revolute joint is a screw joint having a null pitch (p = 0). I f the reference frame of two subsequent bodies (h - 1 and h) are placed according to Denavit and Hartenberg notation, vector u assumes the simple form u t = [0, 0, 1]' and matrix L is simply:\n0 0 0 0\n0 0 0 0 SL = PLh-l.h= 0 0 0~ 1 h-l.h\no---6--b-,,-o\n0 - 1 0 0\n1 0 0 0 _o___o____o_ o 0 0 0 0\n(l)\nThe position, speed and acceleration matrices of each body i can be found starting from the base of the manipulator and moving towards the end effector applying the motion composition rule\nM0., = M0.h_ i Mh_ I.h\nW0.h = W0.h- I + Wh- ~.h(0)\nHo.h = H0.,_ I + H,_ I.u0)+ 2W0.h iWh-I.h~0)", "3D kinematics and dynamics--ll 591\nwhere Mo.o = [1] (identity matrix) and Wo. o = Ho.o = [0] (null matrix). These equations can be generalized, for i >/2 as follows:\ni\nMo., = I-I M(q,)j_ ,.j j = t\ni i\nWo,, = E W/-L/,o) = X L/_t,g REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 4 length determines the cable tension, and the cable tension and external load determine the joint moment of the CMRJ. Third, if the statically calculated joint moment is not minimized at first, the calculation is repeated until it is. When the moment is minimized, the equilibrium position is derived (Fig. 4). We constructed a kinematic model to calculate the forward kinematics of the CMRJ. As shown in Fig. 5(a), we set two frames {\ud835\udc56\ud835\udc56} and {\ud835\udc57\ud835\udc57}, which are the centers of the rolling surfaces in the \ud835\udc56\ud835\udc56 th segment. Frame {\ud835\udc56\ud835\udc56} is located at the center of the upper rolling surface, and frame {\ud835\udc57\ud835\udc57} is at the center of the lower rolling surface in the segment. \ud835\udc5f\ud835\udc5f is the radius of the rolling surface, and \ud835\udc51\ud835\udc51 is the distance between the centers of the rolling surfaces [Fig. 5(a)]. We created two steps to represent frame {\ud835\udc56\ud835\udc56 + 1} of the (\ud835\udc56\ud835\udc56 + 1)th segment in frame {\ud835\udc56\ud835\udc56}. Step 1: Describe frame {\ud835\udc57\ud835\udc57 + 1} of the (\ud835\udc56\ud835\udc56 + 1)th segment in frame {\ud835\udc56\ud835\udc56}. As shown in Fig. 5(b), frames {\ud835\udc56\ud835\udc56} and {\ud835\udc57\ud835\udc57 + 1} have three constraints. First, the distance between the frames is a constant at 2\ud835\udc5f\ud835\udc5f. Second, frame {\ud835\udc57\ud835\udc57 + 1} is located at the position rotated by \ud835\udf03\ud835\udf03\ud835\udc56\ud835\udc56 2 at a distance of 2\ud835\udc5f\ud835\udc5f from the origin of frame {\ud835\udc56\ud835\udc56}. Third, frame {\ud835\udc57\ud835\udc57 + 1} is rotated to \ud835\udf03\ud835\udf03\ud835\udc51\ud835\udc51 relative to frame {\ud835\udc56\ud835\udc56}. With these constraints, we assumed two revolute joints to illustrate frame {\ud835\udc57\ud835\udc57 + 1} in frame {\ud835\udc56\ud835\udc56} [Fig. 5(c)]. The first revolute joint has a link with a length of 2\ud835\udc5f\ud835\udc5f and rotates by \ud835\udf03\ud835\udf03\ud835\udc56\ud835\udc56 2 . The second revolute joint only rotates by \ud835\udf03\ud835\udf03\ud835\udc56\ud835\udc56 2 at that location. Step 2: Describe frame {\ud835\udc56\ud835\udc56 + 1} in frame {\ud835\udc57\ud835\udc57 + 1}. Frame {\ud835\udc56\ud835\udc56 + 1} has the same orientation and is located at a distance \ud835\udc51\ud835\udc51 in the -z-direction in {\ud835\udc57\ud835\udc57 + 1}. Thus, we assumed the prismatic joint to illustrate frame {\ud835\udc56\ud835\udc56 + 1} in frame {\ud835\udc57\ud835\udc57 + 1} [Fig. 5(d)]. As a result, frame {\ud835\udc56\ud835\udc56 + 1} is derived from frame {\ud835\udc56\ud835\udc56} by using two revolute joints and one prismatic joint. We derived the product of exponential (PoE) formula to illustrate the reference frames of the segments in fixed frame {\ud835\udc60\ud835\udc60} . \ud835\udc40\ud835\udc40\ud835\udc51\ud835\udc51 \u2208 \ud835\udc46\ud835\udc46\ud835\udc46\ud835\udc46(3) denotes the configuration of link frame {\ud835\udc56\ud835\udc56} relative to fixed frame {\ud835\udc60\ud835\udc60} when the mechanism is at zero position. \ud835\udc40\ud835\udc40\ud835\udc51\ud835\udc51 were given the same orientation as fixed frame {\ud835\udc60\ud835\udc60}. The orientation \ud835\udc45\ud835\udc45\ud835\udc51\ud835\udc51\ud835\udc36\ud835\udc36 of \ud835\udc40\ud835\udc40\ud835\udc51\ud835\udc51 was derived to be \ud835\udc45\ud835\udc45\ud835\udc51\ud835\udc51\ud835\udc36\ud835\udc36 = \ud835\udc51\ud835\udc51\ud835\udc56\ud835\udc56\ud835\udc51\ud835\udc51\ud835\udc51\ud835\udc51(1,1,1) \u2208 \ud835\udc60\ud835\udc60\ud835\udc60\ud835\udc60(3)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001395_s12206-020-1240-y-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001395_s12206-020-1240-y-Figure8-1.png", "caption": "Fig. 8. Circumferential temperature distributions of stator: (a) crown part (x = -53 mm); (b) cross-section (x = 0 mm); (c) welded part (x = 53 mm).", "texts": [ " As can be seen from the circumferential temperature distribution, the temperature is approximately 4 % lower in the crown part than it in the welded part; this is due to the influence of the insulating paper, welding, and epoxy. This implies that heat transfer is more efficient at the crown part than at the welded part. Therefore, hot spot in the longitudinal direction appears to be biased toward the welded part. The temperature distribution of the stator is analyzed in the circumferential and longitudinal directions. Fig. 8 depicts the temperature distributions in the circumferential direction of the stator. There are three flow paths in the stator, and oil flows through the two inlets per flow path at the top. The sprayed oil flows along the outer diameter of the stator. The upper part of the stator is the spot that the cooled oil first touches after spraying. Therefore, the top of stator has the lowest temperature. The bottom of the stator is immersed in oil flowing to the outlet. Therefore, the temperature is higher at the 4:30 and 7:30 positions than at the bottom of the stator, with a difference of approximately 10 %. In comparing the crown part with the welded part, it is seen that the welded part has a higher temperature than the crown part, with a difference of approximately 5-8 %. This is because heat that cannot escape from the welded part of the coil is conducted to the stator. However, the temperature distribution in the middle section of the stator, as depicted in Fig. 8(b), has a temperature distribution different from that at both ends. In the middle section of the stator, the yoke is cooled through direct contact with the oil flowing in the stator flow path. The teeth of the stator are not well cooled due to the hot spot in the coil. For this reason, the rate of temperature change in the circumferential direction of the stator middle section is large. Fig. 9 depicts the temperature distribution in the longitudinal direction of the stator. The upper part of the stator is the part that the cooled oil first touches after spraying" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001393_j.conengprac.2020.104721-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001393_j.conengprac.2020.104721-Figure7-1.png", "caption": "Fig. 7. The rotary test platform for quadrotor attitude control.", "texts": [], "surrounding_texts": [ "The tracking error dynamics are \u23a1 \u23a2 \u23a2 \u23a3 \u0303\u0307\ud835\udf03 \u0303\u0308\ud835\udf03 \u0303\u0307\ud835\udf02 \u23a4 \u23a5 \u23a5 \u23a6 = \ud835\udc68 \u23a1 \u23a2 \u23a2 \u23a3 \ud835\udf03 \u0303\u0307\ud835\udf03 ?\u0303? \u23a4 \u23a5 \u23a5 \u23a6 \u23df \u23df \u2212\ud835\udc69 [ ( \ud835\udc58\ud835\udf02 + 1 ) \ud835\udc531 + \ud835\udefc ( \u0303\u0307\ud835\udc531 + \ud835\udc532 )] , (31) ?\u0303? \ud835\udc50 where \ud835\udc68 = \u23a1 \u23a2 \u23a2 \u23a2 \u23a3 0 1 0 0 0 1 \ud835\udc3d\ud835\udc66\ud835\udc66 \u2212 \ud835\udc58\ud835\udc5d \ud835\udefc \u2212 \ud835\udc58\ud835\udc51 \ud835\udefc \u2212 ( \ud835\udc58\ud835\udf02+1 ) \ud835\udefc \u23a4 \u23a5 \u23a5 \u23a5 \u23a6 , \ud835\udc69 = \u23a1 \u23a2 \u23a2 \u23a3 0 0 1 \ud835\udefc \u23a4 \u23a5 \u23a5 \u23a6 , (32) 1\u0303 = \ud835\udc531 \u2212 \ud835\udc531, \u0303\u0307\ud835\udc531 = \ud835\udc531 \u2212 \u0302\u0307\ud835\udc531, \ud835\udc532 = \ud835\udc532 \u2212 \ud835\udc532. (33) The characteristic polynomial of \ud835\udc68 is |\ud835\udc60\ud835\udc703 \u2212\ud835\udc68| = \ud835\udc603 + \ud835\udc58\ud835\udf02 + 1 \ud835\udefc \ud835\udc602 + \ud835\udc58\ud835\udc51 \ud835\udc3d\ud835\udc66\ud835\udc66\ud835\udefc \ud835\udc60 + \ud835\udc58\ud835\udc5d \ud835\udc3d\ud835\udc66\ud835\udc66\ud835\udefc . (34) By Routh criterion, the stability conditions are \ud835\udc58\ud835\udc5d > 0, \ud835\udc58\ud835\udc51 > 0, \ud835\udc58\ud835\udf02 > \u22121, ( \ud835\udc58\ud835\udf02 + 1 ) \ud835\udc58\ud835\udc51 \u2212 \ud835\udefc\ud835\udc58\ud835\udc5d > 0. (35) Under the stability conditions, the tracking accuracy relies on the estimation residual error \ud835\udc53\ud835\udc5f\ud835\udc52\ud835\udc60 = ( \ud835\udc58\ud835\udf02 + 1 ) \ud835\udc531 + \ud835\udefc ( \u0303\u0307\ud835\udc531 + \ud835\udc532 ) . (36) It is seen that \ud835\udefc ( \u0303\u0307\ud835\udc531 + \ud835\udc532 ) has little impact on the tracking accuracy since the time constant of the motor \ud835\udefc \u2248 0.04 is small. Therefore the bandwidths of estimators (which determines the noise sensitivity as well) for \u0307\ud835\udc531 and \ud835\udc532 are not necessarily to be too large. The estimation errors satisfy \ud835\udc391(\ud835\udc60) = [ 1 \u2212 \ud835\udc3a\ud835\udc531 (\ud835\udc60) ] \ud835\udc391(\ud835\udc60) = \ud835\udc47 \ud835\udc531\ud835\udc60 \ud835\udc47 \ud835\udc531\ud835\udc60 + 1 \ud835\udc391(\ud835\udc60), (37) \u0303\u0307 1(\ud835\udc60) = [ 1 \u2212 \ud835\udc3a \u0307\ud835\udc531 (\ud835\udc60) ] ?\u0307?1(\ud835\udc60) = \ud835\udc47 \u0307\ud835\udc531 1 \ud835\udc602 + \ud835\udc47 \u0307\ud835\udc531 2 \ud835\udc60 \ud835\udc47 \u0307\ud835\udc531 1 \ud835\udc602 + \ud835\udc47 \u0307\ud835\udc531 2 \ud835\udc60 + 1 ?\u0307?1(\ud835\udc60), (38) \ud835\udc392(\ud835\udc60) = [ 1 \u2212 \ud835\udc3a\ud835\udc532 (\ud835\udc60) ] \ud835\udc392(\ud835\udc60) = \ud835\udc47 \ud835\udc532\ud835\udc60 \ud835\udc47 \ud835\udc532\ud835\udc60 + 1 \ud835\udc392(\ud835\udc60). (39) o show how the estimation errors are related to the filter parameters, he following parameter mapping is applied = \ud835\udf00\ud835\udefc , \ud835\udc50 = \ud835\udf00\ud835\udefc ,\u2026 , \ud835\udc50 = \ud835\udf00\ud835\udefc , (40) 0 1 1 2 \ud835\udc58 \ud835\udc58 f \ud835\udc39 c \ud835\udc39 r r T f \ud835\udc47 i ( b to the general form of stable low-pass filters: \ud835\udc3a(\ud835\udc60) = 1 \ud835\udc500\ud835\udc60\ud835\udc58+1 +\u22ef + \ud835\udc50\ud835\udc58\ud835\udc60 + 1 , (41) where \ud835\udefc1,\u2026 \ud835\udefc\ud835\udc58+2 and \ud835\udf00 are positive parameters. Then the following results can be obtained. Lemma 1. For all stable filters in the form of (41) with parameters replaced by (40), letting \ud835\udf00 \u2192 0 leads to sufficiently small \ud835\udc39 (\ud835\udc60) = [1 \u2212 \ud835\udc3a(\ud835\udc60)]\ud835\udc39 (\ud835\udc60) provided that \ud835\udc39 (\ud835\udc60) is bounded. Proof. By (40) and (41), it readily has \ud835\udc39 (\ud835\udc60) = \ud835\udf00 \u22c5 \ud835\udefc1\ud835\udc60\ud835\udc58+1 +\u22ef + \ud835\udefc\ud835\udc58+1\ud835\udc60 \ud835\udf00\ud835\udefc1\ud835\udc60\ud835\udc58+1 +\u22ef + \ud835\udf00\ud835\udefc\ud835\udc58+1\ud835\udc60 + 1 \ud835\udc39 (\ud835\udc60). (42) Note that mapping (40) will not change the poles of filter \ud835\udc3a(\ud835\udc60). Thereore \ud835\udefc1\ud835\udc60\ud835\udc58+1+\u22ef+\ud835\udefc\ud835\udc58+1\ud835\udc60 is bounded-input-bounded-output stable since its \ud835\udf00\ud835\udefc1\ud835\udc60\ud835\udc58+1+\u22ef+\ud835\udf00\ud835\udefc\ud835\udc58+1\ud835\udc60+1 \ud835\udc53 denominator is identical to that of \ud835\udc3a(\ud835\udc60). Then by the boundedness of (\ud835\udc60), it is clear that \ud835\udf00 \u2192 0 renders \ud835\udc39 (\ud835\udc60) arbitrarily small. The proof is omplete. Lemma 1 concludes that the estimation errors of the proposed UDEs \u03021, \u0302\u0307\ud835\udc391 and \ud835\udc392, can be reduced by tuning the filter parameters. This esult will be used to show the ultimate bounds of the estimation esidual error (36) and tracking error. heorem 1. Under Assumption 1 and stability conditions (35), when the ollowing parameter mapping \ud835\udc531 = \ud835\udf00\ud835\udefc1, \ud835\udc47 \u0307\ud835\udc531 1 = \ud835\udf00\ud835\udefc2, \ud835\udc47 \u0307\ud835\udc531 2 = \ud835\udf00\ud835\udefc3, \ud835\udc47 \ud835\udc532 = \ud835\udf00\ud835\udefc4, \ud835\udefc1, \ud835\udefc2, \ud835\udefc3, \ud835\udefc4, \ud835\udf00 > 0, (43) s applied to filters \ud835\udc3a\ud835\udc531 (\ud835\udc60), \ud835\udc3a \u0307\ud835\udc531 (\ud835\udc60) and \ud835\udc3a\ud835\udc532 (\ud835\udc60), the estimation residual error 36) is bounded by \ud835\udc53\ud835\udc4f(\ud835\udf00), and the tracking error \u2016?\u0303?(\ud835\udc61)\u20162 is ultimately ounded by \ud835\udc53\ud835\udc4f(\ud835\udf00) as \ud835\udc61 \u2192 \u221e, where the bounds satisfies \ud835\udc53\ud835\udc4f(\ud835\udf00) \u2192 0 and \u0304 \ud835\udc4f(\ud835\udf00) \u2192 0 as \ud835\udf00\u2192 0. i \ud835\udc53 w t \u2016 \u2016 e t m s 5 5 2 2 F i t t s e t 5 c c b P d \ud835\udc62 Proof. Assumption 1 guarantees the boundedness of \ud835\udc391(\ud835\udc60), ?\u0307?1(\ud835\udc60) and \ud835\udc392(\ud835\udc60). Applying the result of Lemma 1 to estimation error dynamics (37)\u2013(39) straightforwardly yields \ud835\udc39\ud835\udc5f\ud835\udc52\ud835\udc60(\ud835\udc60) = \ud835\udf00\ud835\udc3b(\ud835\udc60), where \ud835\udc3b(\ud835\udc60) = \ud835\udefc1\ud835\udc60 \ud835\udf00\ud835\udefc1\ud835\udc60 + 1 \ud835\udc391(\ud835\udc60) + \ud835\udefc2\ud835\udc602 + \ud835\udefc3\ud835\udc60 \ud835\udf00\ud835\udefc2\ud835\udc602 + \ud835\udf00\ud835\udefc3\ud835\udc60 + 1 ?\u0307?1(\ud835\udc60) + \ud835\udefc4\ud835\udc60 \ud835\udf00\ud835\udefc4\ud835\udc60 + 1 \ud835\udc392(\ud835\udc60) (44) s a bounded signal. Therefore in the time domain it can conclude that ?\u0303?\ud835\udc52\ud835\udc60(\ud835\udc61) \u2264 \ud835\udf00\u2016\u210e(\ud835\udc61)\u2016\u221e \ud835\udee5 = \ud835\udc53\ud835\udc4f(\ud835\udf00), (45) here \ud835\udc53\ud835\udc4f(\ud835\udf00) \u2192 0 as \ud835\udf00\u2192 0. Under stability conditions (35), it is clear that he zero-input response of (31) converges to the origin, i.e. \u2016?\u0303?\ud835\udc67\ud835\udc56\ud835\udc5f(\ud835\udc61)\u20162 = \ud835\udc52\ud835\udc68\ud835\udc61?\u0303?(0)\u20162 \u2192 0 as \ud835\udc61 \u2192 \u221e. The 2-norm of the zero-state response satisfies ?\u0303?\ud835\udc67\ud835\udc60\ud835\udc5f(\ud835\udc61)\u20162 = \u2016\u222b \ud835\udc610 \ud835\udc52 \ud835\udc68(\ud835\udc61\u2212\ud835\udc61\ud835\udc60)\ud835\udc69\ud835\udc53\ud835\udc5f\ud835\udc52\ud835\udc60(\ud835\udc61\ud835\udc60)\ud835\udc51\ud835\udc61\ud835\udc60\u20162 \u2264 \u2016\u222b \ud835\udc610 \ud835\udc52 \ud835\udc68(\ud835\udc61\u2212\ud835\udc61\ud835\udc60)\ud835\udc51\ud835\udc61\ud835\udc60\u20162\u2016\ud835\udc69\u20162\u2016\ud835\udc53\ud835\udc5f\ud835\udc52\ud835\udc60(\ud835\udc61)\u2016\u221e \u2264 \u2016(\ud835\udc52\ud835\udc68\ud835\udc61 \u2212 \ud835\udc703)\u20162\u2016\ud835\udc68\u22121 \u20162\u2016\ud835\udc69\u20162\u2016\ud835\udc53\ud835\udc5f\ud835\udc52\ud835\udc60(\ud835\udc61)\u2016\u221e (46) By (45) and (46), as \ud835\udc61\u2192 \u221e results \u2016?\u0303?(\ud835\udc61)\u20162 \u2264 \u2016?\u0303?\ud835\udc67\ud835\udc56\ud835\udc5f(\ud835\udc61)\u20162 + \u2016?\u0303?\ud835\udc67\ud835\udc60\ud835\udc5f(\ud835\udc61)\u20162 \u2264 \u2016\ud835\udc68\u22121 \u20162\u2016\ud835\udc69\u20162\ud835\udc53\ud835\udc4f(\ud835\udf00) \ud835\udee5 = \ud835\udc53\ud835\udc4f(\ud835\udf00). (47) This ends the proof. Theorem 1 shows that decreasing \ud835\udf00 (which, correspondingly, reduces filter parameters \ud835\udc47 \ud835\udc531 , \ud835\udc47 \u0307\ud835\udc531 1 , \ud835\udc47 \u0307\ud835\udc531 2 and \ud835\udc47 \ud835\udc532 ) renders the steady-state estimation errors and closed-loop tracking error arbitrarily small. This result provides a clear relationship between the filter parameters and tracking accuracy, making the parameter tuning easier. Remark 4. In practice, however, there is a contradiction between rejecting disturbances and reducing the sensitivity of MUDE to measurement noises (Zhu, Zhu, Liu, & Qin, 2020). The measurement noises in \ud835\udf03 and ?\u0307? due to the low-cost onboard sensors, and the \ud835\udf0f estimation \ud835\udc66 rror caused by the actuator modeling and identification error, may ogether limit the smallest feasible \ud835\udf00. Therefore, a trade-off needs to be ade between improving the tracking performance and reducing the ensitivity to measurement noise and actuator model uncertainties. . Experimental results .1. Experimental setup A quadrotor prototype composed of an F330 DJI frame, PropDrive 826 1200Kv motors, LitteBee 20A ESCs, 8045 propellers, and a 3S 200 mAh 25C LIPO battery is used for the experiments. The experiments are conducted on the rotary test platform shown in ig. 7. The platform\u2019s base is mounted on the table, and the quadrotor is nstalled on the rotatable end of the platform. The \ud835\udc66-axis of the quadroors body-frame is aligned with the rotation axis of the platform, such hat only the pitch motion of the quadrotors is activated. A bamboo tick with a payload hood is attached to the quadrotor, and during the xperiments, a payload can be hung on the hook to simulate a possibly ime-varying external disturbance torque on the pitch motion. .2. Tested controllers In the experiments, three controllers are tested, including the casade PID (CPID) controller (Dronecode, 2020), the classic UDE-based ontroller (Lu et al., 2018) given by (30), and the proposed MUDEased controller (19). The cascade PID controller is embedded inside X4 firmware and is widely used in most commercial autopilots. It is esigned in a cascade form as follows CPID \ud835\udf03 = \ud835\udc58\ud835\udc5d \u0303\u0307\ud835\udf03 + \ud835\udc58\ud835\udc56\u222b \ud835\udc61 0 \u0303\u0307\ud835\udf03\ud835\udc51\ud835\udc61 + \ud835\udc58\ud835\udc51 \u0303\u0308\ud835\udf03, (48) where the reference for the attitude angular rate ?\u0307?\ud835\udc51 is generated by a proportional controller ?\u0307?\ud835\udc51 = \ud835\udc58\ud835\udf03. R a d o t p t a h p i a g f a s 5 T r \ud835\udf03 w q i o d v w 1 emark 5. In the proposed MUDE-based controller, the uncertainty nd disturbance estimators (23)(26)(29) are designed in the frequency omain. To program it in C language and implement the whole solution n a Pixhawk flight controller running PX4 firmware 1.8.2, they need o be translated into the discrete-time form. The computational comlexity of the proposed solution is considered to be low in the sense hat the Pixhawk only equips with an STM32F427 processor running t 168 MHz. The codes are published in Github and can be found at ttps://github.com/potato77/Firmware_MUDE. For the aforementioned feedback controllers investigated in the exeriments, the pitch angle is obtained from the embedded EKF module n PX4 firmware, while the pitch rate is measured by the gyroscope nd is processed by a low-pass filter. The default controller feedback ains are shown in Table 2. It is noteworthy that the same control eedback gains \ud835\udc58\ud835\udc5d and \ud835\udc58\ud835\udc51 are chosen for classic UDE and MUDE to give n equitable comparison result. The flight-proven feedback gains are elected for CPID. p .3. Experimental results The case studies considered in the experiments are summarized in able 3. Three typical references are considered, and the sinusoidal eference satisfies \ud835\udc51 = 0.5236 \u22c5 sin(4\ud835\udc61) rad, (49) here 0.5236 rad = 30\u25e6 is almost the maximum tilt angle of the uadrotor during a real flight for safety considerations. The disturbance s added to the quadrotor pitch motion by hanging a payload (150 g) n the hook, which, in the steady-state when \ud835\udf03 = 0, is an equivalent isturbance torque of approximately 0.6 N m. When the pitch angle aries, the payload acts as a time-varying disturbance (0.6 cos \ud835\udf03 N m, hen neglecting the swinging of the payload) to the system. In Cases \u20134, the CPID controller (48), the UDE-based control (30) and the roposed MUDE-based control (19) are tested and compared. In Cases 5 d I e c c 5 o t s t \u20136, the parameters \ud835\udc47 \ud835\udc531 and \ud835\udc47 \ud835\udc532 are respectively tuned for MUDE, emonstrating the effectiveness of the proposed tuning guidelines. n Case 7, the quadrotor is manually controlled to fly in an indoor nvironment, and the real flight test results are presented. The videos of the experiments can be found at https://www.bilibili. om/video/av60962814/ (for Cases 1\u20136) and https://www.bilibili. om/video/BV1v54y1q7X7 (for Case 7). .3.1. Case 1 The results are shown in Fig. 8. It is noticed that the tracking errors f three controllers are close, but MUDE-based control delivers smallest racking error when the quadrotor is tracking a constant reference ignal, as shown in Fig. 8(a). Since the quadrotor is in the steady-state, he torque command \ud835\udc62\ud835\udf03 converges to a small neighborhood of zero, and thus the motors are spinning at a nearly constant speed shown in Fig. 8(b). Under this particular circumstance, the dynamics of the actuators can be ignored. As for the sinusoidal trajectory tracking results shown in Fig. 8(c)\u2013 (e), however, there is a remarkable improvement in the tracking accuracy by the MUDE-based controller, while the results of its rival controllers exhibit some residual errors of an amplitude of around 0.05 \u223c 0.08 rad. This is because the actuator-generated torque is not in agreement with the torque command due to the dynamics of the actuator and the time delay, when the quadrotor is doing maneuvers. Compared with CPID and classic UDE-based control, the term \ud835\udc532 in the MUDE actively compensates for this torque difference, and the additional torque error feedback term \ud835\udc58\ud835\udf02\ud835\udf0f in the proposed controller (19) helps to enlarge the system stability margin and improve the convergence speed of attitude tracking, thus overall steady-state and transient tracking performance is simultaneously enhanced. This point is verified by the torque commands generated by these controllers, as shown in Fig. 8(e). CPID lacks feedforward control, and thus the torque command has an obvious phase delay, whereas the feedforward term in the classic UDE-based control helps to correct this phase delay to some extent. The MUDE additionally compensates for the dynamic delay and time delay of the actuator, which further corrects the phase delay in the torque command. Based on the above analysis, with regard to accurate attitude tracking problems, especially when the quadrotor maneuvers aggressively, the control design considering actuator dynamics are of practical importance. Similar conclusions can be found in Castillo et al. (2019), in which the considered actuator model is a first-order system. It will be showed in Case 6 that the time delay of the actuator considered in this paper has a significant impact on the tracking performance, and thus the proposed approach has certain advantages over the DOBC proposed in Castillo et al. (2019) in the sense that the actuator delay is well-address by the MUDE-based control." ] }, { "image_filename": "designv10_11_0001070_j.mechmachtheory.2020.104127-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001070_j.mechmachtheory.2020.104127-Figure2-1.png", "caption": "Fig. 2. Co-simulation of DWAS-K&C test rig.", "texts": [ " The DWAS nonlinear multi-body dynamic model is built in ADAMS/VIEW and the subroutines are written by FORTRAN. Experiments for the testing characteristic of the bushing and air spring are conducted with the MTS hydraulic tester. The sub-models (air spring model, bushing model and contact clearance model) are generated by using customized FORTRAN subroutines. The suspension model outputs the penetration depth of clearance joints and the deformations of bushings and air springs to the sub-models, and then the sub-models outputs the calculated forces to the suspension model (see Fig. 2 ). Air spring assemblies consist of the cover plate, piston, bellow and air hole (see Fig. 3 ). The total force of the air spring is the combined results of the thermodynamic force and the Berg\u2019s friction force. Note that the viscoelastic forces of the elastic parts are assumed to be zero due to the K&C test is consider as a quasi-static test. The air spring elastic force F e defined as follows [58] : P c = P \u2212 P atm (2) where P b is the gauge pressure, P is the absolute pressure in the air spring and P atm is the pressure of the atmosphere, and A e is the effective cross section area" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001614_j.ndteint.2021.102491-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001614_j.ndteint.2021.102491-Figure1-1.png", "caption": "Fig. 1. Schematic configuration of a transient thermoreflectance (TTR) measurement system.", "texts": [ " The test results and feasibility for in-situ porosity monitoring are presented in Section 5, and the conclusions are finally provided in Section 6. TTR has been widely used to investigate thermal transport in thin and bulk materials, across material interfaces, and liquids [28,29]. TTR measurements can be gathered using time-domain and frequency-domain methods [30]. The time-domain method is often utilized in a pump-probe setup, in which a pump laser pulse excites a target sample, and a time-delayed probe laser pulse indicates variations of the optical properties induced by the pump pulse [28]. As shown in Fig. 1, a single laser pulse is divided into the intense pump and weak probe pulses through a beam splitter. These pulses are focused on one location on the target sample (i.e., a newly deposited layer in this study). As the pump pulse is exerted on the deposited layer, its electromagnetic energy is partially absorbed by the layer and converted into heat. In a cylindrical coordinate system, the resulting thermal conduction in the isotropic material can be expressed as follows [31]: \u03c1Cp \u2202T(r, z, t) \u2202t =\u2207(\u03bb\u2207T(r, z, t)) + Q (1) where T(r, z, t) is the temperature distribution; t, r and z are time, and the distance from the origin along the radial and depth directions, respectively; z = 0 is at the top surface", " \u03b5 = (n + i\u03ba)2 is the complex dielectric constant, where n and \u03ba indicate the real and imaginary parts of the optical index, respectively. k = k0(n + i\u03ba), and k0 is the wave vector in air. A is the amplitude of the optical field in the deposited layer, and A0 and B0 correspond to the amplitudes of the falling and reflected optical fields, respectively. Eq. (4) shows that the surface displacement u0(r, t), which can be observed using the interferometric technique, contributes only to the imaginary part of \u0394R/R. The relative reflectivity change observable in the reflectometric technique (Fig. 1) can be then simplified as follows: \u0394R R = \u0394RT R + \u0394R\u03b7 R (5) where the photothermal reflectivity change, \u0394RT, and photoelastic reflectivity change, \u0394R\u03b7, are the real parts of the relative reflectivity change in Eq. (4) caused by temperature and strain, respectively. This study focuses on the measurement of \u0394RT in the deposited layer for porosity inspection. A femtosecond laser (with a pulse duration of 350 fs) is chosen as the laser source for TTR measurement. The femtosecond laser pulse induces a transient temperature rise in the deposited layer, with temperature variations lasting around 1\u20132 ns", "2 m between the split pump and probe pulses with 8 \u03bcm incremental movements. This delay allows the measurement of the reflectivity change up to 4 ns ( 1.2 m 3\u00d7108 m/s, 3 \u00d7 108 m/s is the speed of light) with the finest time resolution of 26.7 fs ( 8 \u03bcm 3\u00d7108 m/s). This time resolution corresponds to a maximum sampling rate of 37.5 THz ( 1 26.7 fs) [32]. For improving the measurement efficiency and signal quality, the pump pulses are modulated by an acousto-optic modulator (AOM) with a reference sinusoidal wave, as shown in Fig. 1. The duration of the pump pulse induced heating (in a nanosecond scale) is much shorter than the set time interval (1 \u03bcs in this study) between two successive pump pulses; therefore, each pump pulse can be treated as an independent event with a modulated amplitude. Because the temperature rise due to a single pump pulse is in the order of a few kelvins or less under typical experimental conditions, the response of the deposited layer to the pump pulse input may be assumed to be linear and timeinvariant [28]" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001773_tte.2021.3085367-Figure20-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001773_tte.2021.3085367-Figure20-1.png", "caption": "Fig. 20. Stress distributions under different speeds. (a) 1500 rpm. (b) 10000 rpm", "texts": [ " (b) The reluctances are automatically imported into MATLAB to create a hybrid model. (c) The hybrid model is solved for both the no-load and on-load conditions. It can be seen that the proposed method only takes a total of 139 seconds, while the 2D and 3D FE counterparts take 29 minutes and 2 days 1 hour, respectively, which confirms the high computational efficiency of the proposed hybrid analytical method. Due to the investigated machine features a triangle flux barrier design in the rotor core, a stress analysis of the rotor structure is necessary. Fig. 20 illustrates the stress distributions of the machine at the speeds of 1500rpm and 10000rpm. It can be seen that the maximum stress occurs at the sharp corner of the triangle flux barrier, and the maximum stresses at 1500rpm and 10000 rpm are 0.38Mpa and 19.42Mpa respectively, which is much lower than the threshold value of 440 MPa. The stator/rotor assemblies of the manufactured prototype are depicted in Fig. 21. Furthermore, in no-load condition, the analytically predicted and experimentally measured back-EMF waveforms are compared in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000828_j.mechmachtheory.2019.103658-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000828_j.mechmachtheory.2019.103658-Figure5-1.png", "caption": "Fig. 5. Definition of assembly errors.", "texts": [ " 4: Then, the form deviations of the tooth surfaces can be obtained as a linear combination of basis functions, expressed as: S m = M\u00d7N \u2211 i =1 \u03bbi B i (2) where S m is the coordinate deviations of sampling points on the tooth surfaces with machining errors, B i represents the basis functions of the geometric features and \u03bbi represents the weighting coefficients of the basis functions. In the case of parallel shaft gears, such as spur gears, assembly errors typically include center distance errors and shaft misalignments, as shown in Fig. 5 . In Fig. 5 , the shafts of a pair of spur gears without assembly errors are represented as AB and CD . When an assembly errors occur, CD will deviate from the ideal position to C \u2032 D \u2032 with respect to AB . The deviations in the gear shafts can be divided into translations T x along the X axis, translations T z along the Z axis, rotations R x around the X axis, and rotations R z around the Z axis. T x and T z are regarded as the center distance errors and R x and R z are regarded as the shaft misalignments" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000346_j.mechmachtheory.2017.09.013-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000346_j.mechmachtheory.2017.09.013-Figure5-1.png", "caption": "Fig. 5. Configuration I for the combination of two Bennett linkages.", "texts": [ " 4 , the revolute joints expressed by dotted line are the fixed joints. In the constructing process, there are four geometric configurations between link AF and EF \u2032 . The four configurations are also the configurations when two Bennett linkages are combined, they are shown as below. (I) This configuration is the most general configuration, there is no special geometric relation between the two Bennett linkages. In the obtained single loop kinematic chain, there is an offset between the axes of joints A and E, as shown below. In Fig. 5 , double dot dash lines indicates the links before eliminating, they are then eliminated. (II) In this configuration, K = \u03c0 , link AF and EF \u2032 are in a straight line. Fix the coincident joints F and F \u2032 , eliminate the coincident links CF and C \u2032 F \u2032 , then in the obtained kinematic chain, the offsets of joints A and E are both zero, the link length is d = b + b , the twist of link AE is \u03b1 = \u03b2 + \u03b2 . AE I II AE I II (III) In this configuration, we have K = 0 and b I = b II . According to the properties of Bennett linkages, if the two linkages are not coincident, we have \u03b2I + \u03b2II = \u03c0 " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001278_j.mechmachtheory.2020.103865-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001278_j.mechmachtheory.2020.103865-Figure2-1.png", "caption": "Fig. 2. Schematic diagrams of parallel structure in three kinds of robots: (a) hybrid robot studied in this paper, (b) Tricept, (c) Exechon.", "texts": [ " Point C 3 is the intersection of two lines, one is the line of the first joint rotating axis, the other is parallel to the moving platform and passing the point C 2 . The distance from C 3 to C 1 is denoted as d , and the distance between C 2 and C 3 is denoted as p . The distance from the end point C 4 of the spindle to the other points has been fixed and presented in the Fig. 1 b below. The differences between the robot in this paper and the well-known Tricept and Exechon in parallel structure are illustrated by the schematic diagrams ( Fig. 2 ). There are fewer passive pairs in the proposed robot than those in Tricept, which can effectively reduce the motion error produced by pair clearance. Compared to Exechon, the kinematic pairs which connect limb3 to the fixed platform and to the moving platform are interchanged in this hybrid robot, which makes it possible to use one-piece precision ball pair instead of three rotating pairs and thus avoid the assembly error. Since the hybrid robot is composed of series and parallel structure, the forward kinematics can be solved through two steps by the intermediate variable method" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001059_j.mechmachtheory.2020.104101-Figure11-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001059_j.mechmachtheory.2020.104101-Figure11-1.png", "caption": "Fig. 11. The rotationally adjustable 4-bar mechanism with optimised dimensions - as in the ADAMS model.", "texts": [ " The optimisation\u2019s target is to minimise the deviation of the obtained ICR trajectory from the reference one (the solid violet line and dotted line in Fig. 10 ). The minimum average value of the objective function ( Eq. (1) ) is searched for by changing the parameters\u2019 values. An optimal mechanism is obtained with the following parameters: l 1 = 38.8, l 2 = 48.6, l 3 = 43, l 4 = 37.3, Z A = 13.9, Y A = 49.7 [mm], \u03b1o = 120 \u00b0, \u03b2 = 162 \u00b0. A model was built in ADAMS using its basic rigid elements such as links and cylinders, as shown in Fig. 11 . In order to connect elements into a movable mechanism, rotational and translational joints are applied. The optimized 4-bar mechanism is improved in accordance to the selected kinematic scheme in Fig. 9 by incorporating 2 additional DOFs with 2-link modules. Their dimensions have to be chosen in order to achieve suitable distances between joints A and B, as well as C and D. At first, revolute eccentric pins are applied as the upper elements BE and CF of the 2-link modules (navy blue elements in Fig. 11 ). These are rotationally connected with bushings at the ends of lower elements AE and DF, which are presented in Figs. 9 and 11 .The data obtained from the optimization process, and the results of simulations for the linearly adjustable 4-bar mechanism, are used as a basis for selecting the dimensions of the 2-link modules. The optimal lengths of the anterior and posterior elements are 43 mm (l 2 between C and D) and 48.6 mm (l 3 between A and B), respectively, whereas the global minimum / maximum required anterior and posterior lengths obtained during the simulations of the linearly adjustable 4-bar mechanism are equal to 42", " Solving the system of these two equations using determinants enabled the ICR point as the intersection point of the two straight lines to be found. IC R Z = W Z W m = \u2212P B v YC + P C v Y B v ZB v YC \u2212 v ZC v Y B IC R Y = W Y W m = \u2212P C v ZB + P B v ZC v ZB v YC \u2212 v ZC v Y B (7) where: P B = \u2212 ( v ZB Z B + v Y B Y B ) P C = \u2212 ( v ZC Z C + v YC Y C ) and: The results of the four performed types of simulations are listed in Table 1 together with the acquired numerical values that are further shown in the plots of Figs. 16 to 19 . In order to obtain the driving forces of the mechanisms\u2019 motors, a vertical force V = 1 kN ( Fig. 11 ) is assumed on the femoral link, simulating human body weight. For both mechanisms (the rotationally adjustable 4-bar mechanism in Fig. 11 and the linearly adjustable 4-bar mechanism in Fig. 8 ), and in all simulations, the calculations are performed to find the ICR trajectory according to the previously described procedure ( Fig. 15 and Eq. (7) ). Fig. 16 shows the Walker et al. trajectory (I) and the two example trajectories (II, III \u2013 the named boundary trajectories) in order to cover a range of possible paths. This is due to the fact that the knee joint\u2019s ICR trajectory is different for each individual person. The performed simulations can be summarised as follows: \u2022 Ex", " Similarly to the case of the rotationally adjustable 4-bar mechanism, for the linearly adjustable 4- bar mechanism with additional DOFs the reference trajectories are exactly achieved (the acquired plots correspond to those in Fig. 16 ) and the calculated relative error of the obtained ICR trajectories with respect to the reference ones is lower than 0.07% ( Table 1 ). During the simulations, other kinematic and dynamic aspects were also investigated. The motor\u2019s angular displacement ( Figs. 17 and 18 ) and torque ratios ( Figs. 17 and 19 ), i.e. the measured motor torque M T in relation to the length of eccentricities (BE and CF) and external load V ( Fig. 11 ), were determined. The maximum values of the angle changes of the anterior and posterior motors reach about 1.27 rad and 1.15 rad, respectively, while the motors\u2019 maximum torque ratios are equal to 0.9 and 1.83, respectively. Furthermore, the global maximum values of angle changes are calculated as the difference between the global maximum and the global minimum of the motors\u2019 positions from all the simulations. These values are equal to 1.32 rad and 1.20 rad respectively for the anterior and posterior motors" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000302_tsmc.2016.2641926-Figure10-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000302_tsmc.2016.2641926-Figure10-1.png", "caption": "Fig. 10. Schematic of the adjustable metal cutting system.", "texts": [ " 5 and 6 illustrate the control signal u(t) and the hysteresis output w(t) with and without considering ASPI hysteresis compensation items. Fig. 7 shows the 3-D map of the estimation of the density function p (r) defined in (8). Fig. 8 is the estimation of the norm of the ideal fuzzy vector \u03b8\u2217 := max{(1/gm)\u2016\u03d1\u2217 i \u20162 i = 1, 2} and Fig. 9 is the estimation of Rp defined in (52). B. Example 2: Adjustable Metal Cutting System In this example, a mechanical system, i.e., the adjustable metal cutting system [29] shown in Fig. 10 is considered to show the validity of the proposed controller in (63). Based on the above schematic model in Fig. 10, the mathematical model of the adjustable metal cutting system can be described explicitly by a differential equation as mx\u0308 + cx\u0307 + kx = F + kau + d(t) (82) where x represents the fluctuating part of the depth of cut m, c, and k are the equivalent mass, damping coefficient, and spring stiffness for the metal cutting machine, respectively, ka is the equivalent spring for the magnetostrictive actuator, u is the magnetostrictive actuator output, F represents the cutting force variation of the machine tool and is proved to be a nonlinear function with respect to the chip thickness variation, and d(t) denotes the disturbance from external environment" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003160_cdc.1999.830084-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003160_cdc.1999.830084-Figure3-1.png", "caption": "FIGURE 3.", "texts": [ " Clearly then Ddyn is geodesically invariant for this example, and so the mechanical control system corresponding to the rolling disk is (%dynr %ki,)-reducible to the kinematic system rcose y - rsine I + mr2 I+mr2u x=- e = \u2018i i2 J \u2019 \u2018 7 s \u2018 6\u2019 . One also readily verifies that the distribution Ddyn is maximally involutive and so the system is locally configuration controllable. 5.3 Planar rigid body The system we consider here is a planar rigid body of mass rn and moment of inertia J about its centre of mass. We use coordinates ( x , y , 0 ) as indicated in Figure 3. The forces we consider are applied to the body some distance h from the centre of mass. Without loss of generality, we assume that this point of application is situated along the body x\u2019-axis through the centre of mass (again, see Figure 3). This system was investigated first by Lewis and Murray [ 11 and then by Bullo and Lewis [lo], in the latter case as a left-invariant system on the Lie group SE(2) . The Christoffel symbols for the Levi-Civita affine connection in the coordinates (x , y , 0) are all zero (the Riemannian metric is constant in these coordinates), and the input vector fields are yl = - cose - a + - sine - a m ax m ay\u2019 sine a case a h a y2 = -- m ax m ay J a 8 \u2018 We compute the following symmetric products: 2hcos8 a 2hsin8 a (Yl : Yl) = 0, (Y2 : Y2) = -- ml a x + T & * hsin8 a hcose a (YI : Y2) = -- - -- ml ax mJ ay\u2018 From these computations we see that Ddyn is not geodesically invariant, and so the planar rigid body is not (%dyn, @kin)-redUCibk to any driftless system" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000591_icstcc.2016.7790668-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000591_icstcc.2016.7790668-Figure1-1.png", "caption": "Figure 1 \u2013 Illustrative figure of the quadcopter with its state variables.", "texts": [ " Controllers will be tuned by the technique called Saturation Constraints and Performance Technique (SCPT). It will also be showed that PID controllers can perform a safe flight, without the need to embed a complex control technique. In the study of unmanned vehicle systems, it is important to understand how different mobile bodies are and how are they related to each other [14]. To better understand the kinematics modeling equations and quadrotor dynamics, it is necessary to know their state variables. Fig. 1 illustrates the quadcopter with its state variables. The variables , , and , are related to roll, pitch, and yaw angles, respectively. The variables , and are related to quadcopter speeds measured along the axis of its fixed rigid frame. The rates of roll, pitch and yaw, are defined through variables , and . N Thus, the kinematics and dynamics modeling equations for six degrees of freedom are shown in (1), (2), (3) and (4): \u210e = \u2212 ++ \u2212\u2212 \u2212 (1) = \u2212\u2212\u2212 + \u2212 sc sc c + 00\u2212 (2) = 1 s t s t0 c \u2212 s0 s sec c sec (3) = + (4) where = cos ; = ; t = tan ; , , \u210e are the inertial positions North, East and Altitude, respectively; is the propulsion generated by all 4 quadcopter motors; is the quadcopter total mass; , and are the moment of inertia in axis , and , respectively; , and are the roll, pitch and yaw torque, respectively applied to the vehicle; g is the standard gravity constant (9" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001041_j.ijmecsci.2020.106020-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001041_j.ijmecsci.2020.106020-Figure7-1.png", "caption": "Fig. 7. Coupling coordinate systems of the shaving cutter and shaper cutter based on the simultaneous meshing in Fig. 3.", "texts": [ " \u20d7 \ud835\udc50 = \ud835\udf15\ud835\udc5f \ud835\udc50 \ud835\udf15\ud835\udf03\ud835\udc50 \u00d7 \ud835\udf15\ud835\udc5f \ud835\udc50 \ud835\udf07\ud835\udc50 | \ud835\udf15\ud835\udc5f \ud835\udc50 \ud835\udf15\ud835\udf03\ud835\udc50 \u00d7 \ud835\udf15\ud835\udc5f \ud835\udc50 \ud835\udf15\ud835\udf07\ud835\udc50 | = \u23a1 \u23a2 \u23a2 \u23a3 \u2212 cos ( \ud835\udf03\ud835\udc500 + \ud835\udf03\ud835\udc50 ) \u2213 sin ( \ud835\udf03\ud835\udc500 + \ud835\udf03\ud835\udc50 ) 0 \u23a4 \u23a5 \u23a5 \u23a6 (3) here \u2018 \u00b1 \u2019 corresponds to \u2018 1 \u2212 1 \u2019 and \u2018 2 \u2212 2 \u2019 corresponds to the involute rofile. The following calculations take the involute profile \u2018 2 \u2212 2 \u2019 as the bject. Notes: The \u20191\u2019 is added to the last row in Eq. (2) to maintain the same umber of conversion matrix rows as below, and this is convenient for the atrix calculations. The coordinate systems are established according to the relative poitions of the shaving cutter and the shaper cutter in Fig. 7 . Five coorinate systems are defined: two fixed coordinate systems at the initial osition of the shaper cutter S c 0 ( O c 0 , X c 0 , Y c 0 , Z c 0 ) and the shaving cutter s 0 ( O s 0 , X s 0 , Y s 0 , Z s 0 ), two movement coordinate systems for the shaper utter S c ( O c , X c , Y c , Z c ) and the shaving cutter S s ( O s , X s , Y s , Z s ), and one ccasional coordinate system S k ( O k , X k , Y k , Z k ) at a distance of E s along he Y s 0 axis direction from the coordinate system S c 0 ", " \ud835\udc1c\ud835\udfce , \ud835\udc1c = \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 cos \ud835\udf19\ud835\udc50 \u2212 sin \ud835\udf19\ud835\udc50 0 0 sin \ud835\udf19\ud835\udc50 cos \ud835\udf19\ud835\udc50 0 0 0 0 1 0 0 0 0 1 \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 (5) The transformation matrix from the coordinate system S c 0 to S k can e expressed as: \ud835\udc24 , \ud835\udc1c\ud835\udfce = \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 1 0 0 0 0 1 0 \u2212 \ud835\udc38 \ud835\udc60 0 0 1 0 0 0 0 1 \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 (6) The transformation matrix from the coordinate system S k to S s 0 can e expressed as: \ud835\udc2c\ud835\udfce , \ud835\udc24 = \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 cos \ud835\udefd 0 \u2212 sin \ud835\udefd 0 0 1 0 0 sin \ud835\udefd 0 cos \ud835\udefd 0 0 0 0 1 \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 (7) The transformation matrix from the coordinate system S s 0 to S s can e expressed as: \ud835\udc2c , \ud835\udc2c\ud835\udfce = \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 1 0 0 0 0 cos \ud835\udf19\ud835\udc60 \u2212 sin \ud835\udf19\ud835\udc60 0 0 sin \ud835\udf19\ud835\udc60 cos \ud835\udf19\ud835\udc60 0 0 0 0 1 \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 (8) Then, the transformation matrix from the coordinate system S c to S s \ud835\udc2c , \ud835\udc1c = \ud835\udc0c \ud835\udc2c , \ud835\udc2c\ud835\udfce \ud835\udc0c \ud835\udc2c\ud835\udfce , \ud835\udc24 \ud835\udc0c \ud835\udc24 , \ud835\udc1c\ud835\udfce \ud835\udc0c \ud835\udc1c\ud835\udfce , \ud835\udc1c = \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 cos \ud835\udefd cos \ud835\udf19\ud835\udc50 \u2212 cos \ud835\udefd sin \ud835\udf19\ud835\udc50 sin \ud835\udf19\ud835\udc50 cos \ud835\udf19\ud835\udc60 \u2212 cos \ud835\udf19\ud835\udc50 sin \ud835\udefd sin \ud835\udf19\ud835\udc60 cos \ud835\udf19\ud835\udc60 cos \ud835\udf19\ud835\udc50 + sin \ud835\udefd sin \ud835\udf19\ud835\udc50 sin sin \ud835\udf19\ud835\udc50 sin \ud835\udf19\ud835\udc60 + cos \ud835\udf19\ud835\udc50 sin \ud835\udefd cos \ud835\udf19\ud835\udc60 sin \ud835\udf19\ud835\udc60 cos \ud835\udf19\ud835\udc50 \u2212 sin \ud835\udefd sin \ud835\udf19\ud835\udc50 cos 0 0 The radial vector and unit normal vector of the shaving cutter can b \u20d7 \ud835\udc60 ( \ud835\udf07\ud835\udc50 , \ud835\udf03\ud835\udc50 , \ud835\udf19\ud835\udc50 ) = \ud835\udc0c \ud835\udc2c , \ud835\udc1c \u20d7\ud835\udc5f \ud835\udc50 ( \ud835\udf07\ud835\udc50 , \ud835\udf03\ud835\udc50 ) \u20d7 \ud835\udc60 ( \ud835\udf03\ud835\udc50 , \ud835\udf19\ud835\udc50 ) = \ud835\udc0b \ud835\udc2c , \ud835\udc1c \u20d7\ud835\udc5b \ud835\udc50 ( \ud835\udf03\ud835\udc50 ) here L s,c is the upper left 3 \u00d7 3 submatrix of M s,c and \u20d7\ud835\udc5f \ud835\udc60 ( \ud835\udf07\ud835\udc50 , \ud835\udf03\ud835\udc50 , \ud835\udf19\ud835\udc50 ) is t \u20d7 \ud835\udc60 ( \ud835\udf07\ud835\udc50 , \ud835\udf03\ud835\udc50 , \ud835\udf19\ud835\udc50 ) = \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 \ud835\udc5f \ud835\udc4f\ud835\udc50 cos \ud835\udefd cos \ud835\udf19\ud835\udc50 \ud835\udc58 \u2212 \ud835\udf07\ud835\udc50 sin \ud835\udefd + \ud835\udc5f \ud835\udc4f\ud835\udc50 ( sin \ud835\udf19\ud835\udc50 cos \ud835\udf19\ud835\udc60 \u2212 cos \ud835\udf19\ud835\udc50 sin \ud835\udefd sin \ud835\udf19\ud835\udc60 ) \ud835\udc58 \u2212 \ud835\udc5f \ud835\udc4f\ud835\udc50 ( cos \ud835\udf19\ud835\udc50 cos \ud835\udf19\ud835\udc60 + \ud835\udc5f \ud835\udc4f\ud835\udc50 ( sin \ud835\udf19\ud835\udc50 sin \ud835\udf19\ud835\udc60 + cos \ud835\udf19\ud835\udc50 sin \ud835\udefd cos \ud835\udf19\ud835\udc60 ) \ud835\udc59 \u2212 \ud835\udc38 \ud835\udc60 sin \ud835\udf19\ud835\udc60 \u2212 \ud835\udc5f \ud835\udc4f\ud835\udc50 ( cos 1 here k = sin ( \ud835\udf03\ud835\udc500 + \ud835\udf03\ud835\udc50 ) \u2212 \ud835\udf03\ud835\udc50 cos ( \ud835\udf03\ud835\udc500 + \ud835\udf03\ud835\udc50 ) and l = cos ( \ud835\udf03\ud835\udc500 + \ud835\udf03\ud835\udc50 ) + \ud835\udf03\ud835\udc50 sin ( \ud835\udf03\ud835\udc500 + The unit normal vector of the shaving cutter is \u20d7 \ud835\udc60 ( \ud835\udf03\ud835\udc50 , \ud835\udf19\ud835\udc50 ) = \u23a1 \u23a2 \u23a2 \u23a3 cos \ud835\udefd sin \ud835\udf19\ud835\udc50 sin ( \ud835\udf03\ud835\udc500 + \ud835\udf03\ud835\udc50 ) \u2212 cos \ud835\udefd cos \ud835\udf19\ud835\udc50 c \u2212 cos ( \ud835\udf03\ud835\udc500 + \ud835\udf03\ud835\udc50 )( sin \ud835\udf19\ud835\udc50 sin \ud835\udf19\ud835\udc60 + cos \ud835\udf19\ud835\udc50 sin \ud835\udefd cos \ud835\udf19\ud835\udc60 ) \u2212 \ud835\udc60\ud835\udc56\ud835\udc5b ( \ud835\udf03\ud835\udc500 + \ud835\udf03\ud835\udc50 \u2212 cos ( \ud835\udf03\ud835\udc500 + \ud835\udf03\ud835\udc50 )( sin \ud835\udf19\ud835\udc50 cos \ud835\udf19\ud835\udc60 \u2212 cos \ud835\udf19\ud835\udc50 sin \ud835\udefd sin \ud835\udf19\ud835\udc60 ) \u2212 \ud835\udc60\ud835\udc56\ud835\udc5b ( \ud835\udf03\ud835\udc500 + \ud835\udf03\ud835\udc50 .2. Theoretical derivation of the spur face gears The machining coordinate systems of spur face gear shaving are estab re shown in Fig. 8 . The coordinate system S f 0 ( O f 0 , X f 0 , Y f 0 , Z f 0 ) is the oordinate system. S p ( O p , X p , Y p , Z p ) is the occasional coordinate system xis direction. \ud835\udf19f is the rotation angle of the spur face gear, which has t ine with the definition in Fig. 7 . \ud835\udf19\ud835\udc60 \ud835\udf19\ud835\udc53 = \ud835\udc41 \ud835\udc53 \ud835\udc41 \ud835\udc60 = \ud835\udc5a \ud835\udc60\ud835\udc53 r and w e rat can b M \ud835\udc0c \u2212 c \ud835\udc5f . (17 A \ud835\udc63 w ) , \ud835\udc50 = \ud835\udc53 he re o f the m toot T havin \ud835\udc5f w n [18 T . here N f is the number of teeth of the spur face gear and m sf is the driv Then, the transformation matrix from the coordinate system S s to S f k,s0 , M s0,s are given in the Appendix. \ud835\udc1f , \ud835\udc2c = \ud835\udc0c \ud835\udc1f , \ud835\udc1f \ud835\udfce \ud835\udc0c \ud835\udc1f\ud835\udfce , \ud835\udc29 \ud835\udc0c \ud835\udc29 , \ud835\udc24 \ud835\udc0c \ud835\udc24 , \ud835\udc2c\ud835\udfce \ud835\udc0c \ud835\udc2c\ud835\udfce , \ud835\udc2c = \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 sin \ud835\udefd sin \ud835\udf19\ud835\udc53 + cos \ud835\udefd cos \ud835\udf19\ud835\udc53 sin \ud835\udf19\ud835\udc60 ( cos \ud835\udefd sin \ud835\udf19\ud835\udc53 \u2212 sin \ud835\udefd cos \ud835\udf19\ud835\udc53 ) 0 cos \ud835\udf19\ud835\udc60 cos \ud835\udefd sin \ud835\udf19\ud835\udc53 \u2212 cos \ud835\udf19\ud835\udc53 sin \ud835\udefd \u2212 sin \ud835\udf19\ud835\udc60 ( sin \ud835\udefd sin \ud835\udf19\ud835\udc53 + cos \ud835\udefd cos \ud835\udf19\ud835\udc53 ) 0 0 The radial vector of the spur face gear can be obtained as Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003889_tmag.1987.1065384-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003889_tmag.1987.1065384-Figure3-1.png", "caption": "Fig . 3 Radial Flux Machine ( s e c t i o n ) .", "texts": [ " It c o n s i s t s of a magneta:ootive force (MMF) i n s e r i e s w i t h a re luc tance [ 5 ] . For magnet thickness h,, the MMF Fm i s given as: F, = Brhm/prpo = - H c m h (1) Reluctance R, is given as: R, = hm/prpoAm (2) w h e r e E, i s t h e r e s i d u a l f l u x d e n s i t y , l to i s t h e p e r m e a b i l i t y of f r e e s p a c e and A,, is cross -sec t iona l a r e a of the magnet. Dual inductance Lm can be e a s i l y found as inverse ly p ropor t iona l tohe r luc tance [ 5 1 . 0018-9464/87/0900-3625$01.00@1987 IEEE 3626 Radial Flux - Fig. 3 conta ins a s e c t i o n of a 3-phase permanent magnet motor wi th rad ia l ly or ien ted ?id B Fe magnets. The magnets may be custon made t o \u20ac i t the curved rotor shape as shown i n F i g . 3 o r w i t h l i t t l e l o s s of e f f e c t i v e n e s s a s e t of f l a t magnets m y be placed s ide by s i d e t o make up the po le s t ruc tu re . A non-magnetic f i l l e r may be placed between poles to reduce losses . Usually the magnets ae f i rmly f ixed t o t h e r o t o r s u r f a c e and i f n e c e s s a r y a th in g lass banding maybe wound under tension over the rotor surface", " I n deve lop ing t he equ iva len t c i r cu i t s , i t has been assumed tha t t he ro to r and s t a to r i rons have h igh permeabi l i ty and these have negl igible r luctance. T h e s t a t o r MMF fo r phase a is denoted by Fa. Making u s e o f t h e s y m m e t r y , Fm i s e a s i l y r e p r e s e n t e d by c u r r e n t s o u r c e T m [ 51. Figs . 4(a) and 4(b) show t h e magnet ic equiva len t c i rcu i t s \u20acor the d i rec t (d) ax is and quadrature (9) axis, respectively for phase a. Figs. 5(a) and 5(b) show the dua l e l ec t r i c equivalent c i r c u i t s f o r t h e d and q-axis, respeci:tvely. The I I Fig. 4 Magnetic Equivalent Circuit for Fig. 3 ( a ) D-axis, (b ) Q-axis. a i r g a p r e l u c t a n c e R and s t a to r l eakage r e luc t ance Rls c an be a s sumed l inea r wh i l e t he main magnet and a s s o c i a t e d l e a k a g e r e l u c t a n c e s Rm and Rlm a re bo th non- l inear [3] . This fac t is represented by t h e equiva len t on- l inear reac tances in F igs . 5 (a) and 5 (b ) . The d and q-axis ta tor per phase res is tances a r e e q u a l t o Rs. g e q u i v a l e n t c i r c u i t s f o r t h e d a n d q - a x i s , respec t ive ly " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000088_j.jsv.2017.12.022-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000088_j.jsv.2017.12.022-Figure8-1.png", "caption": "Fig. 8. TCA result based on semi-analytical and FE method; (a) Instantaneous contact stress (b)Projection of contact pattern and contact path.", "texts": [ " The unloaded TCA result is plotted in Fig. 6(b). Here, The length a of long axis of ellipse is 10 mm, and the angle G is 32 deg. The parabolic, fourth and sixth order TE values at different contact points are listed in Table 3. The corresponding TE curve and surface ease-off values are illustrated in Fig. 7. Table 4 shows the coefficients in Equation (12). For loaded TCA, 80 Nm is applied as input torque acting at the driving end of the model illustrated in Fig. 4. The generated contact pattern and contact path are illustrated in Fig. 8 which is similar to unloaded TCA results in Fig. 6. Under such torque level, other mesh parameters including mesh stiffness, LOA and mesh point are mainly dominated by external load [30], and unloaded TE is the major profile dependent parameter inmesh coupling according to Equation (24). Therefore, the difference in gear dynamic response can accurately reflect system sensitivity to TE variation. Detailed system parameters are listed in Table 5. The following dynamic analysis consists of several steps: Firstly, different orders of TE curves within one mesh cycle are plotted to evaluate their peak to peak amplitude and fluctuation period" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003905_1.2033899-Figure10-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003905_1.2033899-Figure10-1.png", "caption": "Fig. 10 Modified Poincare maps at cage speed with taper ball", "texts": [ " The widening of the vibration peaks indicates a longer period of vibration rotational angle of the shaft due to the increase in areas of surface damage. Note the existence of the two 180-deg-apart peaks in the modified Poincare map as compared to the single-peak pattern in the radial bearing that characterizes the passage of the damage location through the vibration sensor in each revolution as shown in Fig. 6. The results from the two-times effects when the damage passes through the vibration sensor as well as when the damage passes through the opposite side of the sensor due to the tapered geometry of the bearing . Figure 10 shows the modified Poincare map of the damaged bearing using the relative carrier speed. Note that all 11 peaks generated from the contact of the ball elements with the inner race damage location during one revolution of the carrier with respect to the shaft can be clearly identified. As the damaged area and magnitude increases, the width of the peak increases and the definite shape of the peaks become somewhat unclear. One can see that although the amplitude in the modified Poincare maps increases significantly from Figs. 10 a through 10 e , the shape Fig. 7 Modified Poincare maps at cage speed with good and damaged ball bearings of the peaks becomes unrecognizable the 11 peaks cannot be Transactions of the ASME of Use: http://asme.org/terms Downloaded F recognized clearly . On the other hand, the 300% increase in vibration amplitude from no damage in Fig. 10 a to maximum damage in Fig. 10 e does provide important information in identification and quantification applications. Figure 11 depicts the relationships between the vibration amplitude and the level of inner race surface damage in terms of the volume of the pitting. Figure 11 a shows both the maximum and average vibration amplitudes in the modified Poincare map based on the shaft speed. The relationships between the volume of damage and the vibration amplitude vary somewhat nonlinearly and can be fitted using a third order least square algorithm as given in Table 2" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001089_tia.2020.3046195-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001089_tia.2020.3046195-Figure4-1.png", "caption": "Fig. 4. Mesh of transient state full motor thermal flow simulation.", "texts": [ " Fig 3 shows the volume mesh of the steady-state cooling jacket thermal flow simulation of the spiral concept, containing 1.7 million cells approximately. 50%\u201350% water ethylene glycol is used as coolant, with inlet mass flow rates of 3 and 10 LPM (liter per minute) and temperature of 75 \u00b0C at the jacket inlet, and atmospheric pressure and temperature of 80 \u00b0C at the jacket outlet. The jacket wall temperature is set to 100 \u00b0C in the steady-state cooling jacket thermal simulations indicated in Fig. 3. Fig. 4 shows the volume mesh of the transient state full motor thermal simulation, including the outer and inner shells, cooling jacket, stator, slot liners, windings, rotor, magnets, shaft, and air volume inside the motor, with 23 million cells approximately. Modeling of the surrounding air effect is simplified to convection boundary condition on the motor surfaces exposed to the air, as Authorized licensed use limited to: Central Michigan University. Downloaded on May 14,2021 at 13:37:14 UTC from IEEE Xplore. Restrictions apply. majority of the heat (>90%) is absorbed by the coolant via the cooling jacket [20]. The MRF domain is outlined in Fig. 4 around the rotor to consider the rotor rotation using the MRF defined in (8). Table I lists the transient operation conditions of full motor simulation. Operation 1 has the power of 8.5 kW, torque of 17 N\u00b7m with speed of 4800 r/min. Operation 2 has the power of 19 kW, torque of \u201355 N\u00b7m with speed of 3300 r/min. The motor surfaces exposed to air are treated as convection boundary condition with ambient temperature of 65 \u00b0C and fixed heat transfer efficient (HTC) of 5 W/m2K based on internal calibration and best practice" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000088_j.jsv.2017.12.022-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000088_j.jsv.2017.12.022-Figure4-1.png", "caption": "Fig. 4. Lumped parameter model of hypoid geared rotor system.", "texts": [ " The combined contact force vector in three directions are expressed as: Fl \u00bc Xn i\u00bc1 \u00f0Nilfi\u00de; l \u00bc x; y; z (13) The total mesh force amplitude is written as: Fm \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi F2x \u00fe F2y \u00fe F2z q (14) Accordingly, effective mesh stiffness that describes the contact elasticity between meshing gear pair is derived frommesh force, loaded and unloaded TE: km \u00bc Fm=\u00f0eL eU\u00de (15) where the translational loaded eL and unloaded eU TE are calculated from angular TE: eL \u00bc eLa,ly; eU \u00bc eUa,ly (16) The directional rotation radius around the rotation axis ly is derived from effective mesh point (xm; ym; zm) and LOA (Nx;Ny;Nz): ly \u00bc zmNx xmNz (17) More modeling details can be found in related studies [29,37] which is beyond the scope of this work. The dynamic system shown in Fig. 4 is a 14-DOF lumped parameter model. The complete equation of motion can be written in matrix form as: \u00bdM f\u20acxg \u00fe \u00bdC f _xg \u00fe \u00bdK fxg \u00fe \u00bdG f _xg \u00fe \u00bdGa fxg \u00bc fFg (18) \u00bdM \u00bc diag ID;Mp;Mp;Mp; Ipx; Ipy; Ipz;Mg;Mg;Mg; Igx; Igy; Igz; IL (19) where ID and IL denote the mass moment of inertia of engine and load respectively. Ml and Ilm; \u00f0l \u00bc p; g;m \u00bc x; y; z\u00de are the body mass and moment of inertia of pinion and gear. Accordingly, the displacement vector is expressed as: fxg \u00bc n qD; xp; yp; zp; qpx; qpy; qpz; xg ; yg ; zg; qgx; qgy; qgz; qL oT (20) Based on the theory of coupled multibody dynamics [28], the torsional coordinates of pinion/gear body, engine and load are used to describe large rotational displacement which is different from pure vibration analysis", " The effective stiffness consists of input kD and output kL shaft torsional stiffness and lumped shaft-bearing support stiffness on pinion \u00bdKp and gear \u00bdKg shaft. The system damping matrix \u00bdC is derived from component support damping model. The combined stiffness matrix can be written as: \u00bdK \u00bc 2 664 kD Kp Kg kL 3 775 (21) The force vector is comprised of internal and external excitations which can be defined as: fFg \u00bc TD;hp,Fm; hg,Fm; TL T \u00fe fFextg (22) where TD and TL are torque at driving and load end. Coordinate transition vector hl\u00f0l \u00bc p; g\u00de is used for projecting mesh force along LOA onto pinion or gear local coordinate system illustrated in Fig. 4. It consists of normal vector and rotational radii of effective mesh point which can be expressed as: hl \u00bc n Nlx;Nly;Nlz; llx; lly; llz o (23) The mesh force Fm along LOA is calculated from translational dynamic transmission error (d) and unloaded transmission error (eu): Fm \u00bc km,f \u00f0d eu\u00de cm, _d _eu (24) in which km denotes the mesh stiffness derived from loaded and unloaded TE expressed in Equation (15) and cm is the empirical mesh damping ratio. Dynamic transmission error d describes the difference between ideal and real position at certain rotation speed which can be written as: d \u00bc hTp, n xp; yp; zp; qpx; qpy; qpz o hTg, n xg; yg; zg; qgx; qgy; qgz o : (25) The clearance type nonlinear function f \u00f0d eU\u00de has three stages depending on the relationship between (d eu) and backlash bc as shown in Fig", " Based on the correction approach described in session 2, the ease-off gear surface Q is built and shown in Fig. 6(a). The unloaded TCA result is plotted in Fig. 6(b). Here, The length a of long axis of ellipse is 10 mm, and the angle G is 32 deg. The parabolic, fourth and sixth order TE values at different contact points are listed in Table 3. The corresponding TE curve and surface ease-off values are illustrated in Fig. 7. Table 4 shows the coefficients in Equation (12). For loaded TCA, 80 Nm is applied as input torque acting at the driving end of the model illustrated in Fig. 4. The generated contact pattern and contact path are illustrated in Fig. 8 which is similar to unloaded TCA results in Fig. 6. Under such torque level, other mesh parameters including mesh stiffness, LOA and mesh point are mainly dominated by external load [30], and unloaded TE is the major profile dependent parameter inmesh coupling according to Equation (24). Therefore, the difference in gear dynamic response can accurately reflect system sensitivity to TE variation. Detailed system parameters are listed in Table 5" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003179_(sici)1099-1239(19991215)9:14<1013::aid-rnc450>3.0.co;2-4-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003179_(sici)1099-1239(19991215)9:14<1013::aid-rnc450>3.0.co;2-4-Figure1-1.png", "caption": "Figure 1. LMTAS tailless \"ghter aircraft con\"guration", "texts": [ " Simulation results, which include illustrations of the adverse interactions, mitigation approaches, and recon\"guration capability for the RESTORE con\"guration are given in this section. The LMTAS RESTORE programme uses one of the tailless \"ghter con\"gurations developed under Internal Research and Development funding and matured under the Air Force Research Laboratories (AFRL) sponsored Innovative Control E!ectors (ICE) program.2 Under this program, four con\"gurations were investigated and matured for the Air Force. The con\"guration selected for the RESTORE program is shown in Figure 1. This con\"guration is referred to in this paper as the RESTORE con\"guration. The RESTORE tailless \"ghter aircraft con\"guration is a single engine, 653 sweep #ying wing design in the 38 000 pound (take-o! gross weight) class. This con\"guration employs aggressive, all-aspect low observable technologies and was sized for a 1100 nautical mile high}low}low}high air-to-ground mission. The aircraft features two internal weapon bays each capable of carrying (2) GBU-27 laser guided bombs or (2) AIM-9 plus (2) AIM-120 air-to-air missiles" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001773_tte.2021.3085367-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001773_tte.2021.3085367-Figure8-1.png", "caption": "Fig. 8. Relative permeability distributions under two magnetization operations. (a) Remagnetization. (b) Demagnetization.", "texts": [], "surrounding_texts": [ "The conventional MEC model can predict the no-load AGFD in a computationally efficient way, in which the magnetic reluctance of the stator core is generally ignored. However, it should be noted that a significant magnetic saturation in the stator core will happen when a quite high-level d-axis current is employed to realize different magnetization operations in VFMM. Therefore, the nonlinearity of the stator core should be considered in the MEC solution for a magnetization operation. The magnetic flux density distributions and the relative permeability distributions under two magnetization operations are illustrated in Figs. 7 and 8. Obviously, the stator teeth and yoke show seriously saturated. Based on the nonlinear FE analysis, the stator reluctances Rs1 and Rs2 can be obtained respectively. Furthermore, the MEC models for remagnetization and demagnetization operations are shown in Fig. 9. The magnetomotive force engendered by the d-axis current can be expressed as: m dF NI= (26) where N denotes the number of turns per phase. Authorized licensed use limited to: BOURNEMOUTH UNIVERSITY. Downloaded on July 05,2021 at 00:17:07 UTC from IEEE Xplore. Restrictions apply. 2332-7782 (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. According to the MEC model and piecewise-linear hysteresis model, the remanence predictions of the LCF PMs under different magnetization currents are obtained and compared with FE predictions as indicated in Fig. 10, which exhibits satisfactory agreements. It should be noted that the magnetic reluctances of the stator core under different magnetizing current levels should be changed according to the FE results when the magnetic saturation occurs due to the excessive d-axis current." ] }, { "image_filename": "designv10_11_0000913_j.mechmachtheory.2019.06.026-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000913_j.mechmachtheory.2019.06.026-Figure6-1.png", "caption": "Fig. 6. Shaft beam element and coordinate systems.", "texts": [ " 5 , the main shaft and parallel stage shafts are modeled by using the Timoshenko beam element. Only the bearing and gear nodes are retained (Type B), where the diameter variation of the shaft is ignored. The \u05d2 th shaft element contains two nodes, i.e., nodes \u05d2 and \u05d2 + 1. Each node considers six DOFs. The generalized coordinate of the \u05d2 th shaft element is defined as [22] X s \u05d2 , \u05d2 +1 = [ ( X s \u05d2 ) T , ( X s \u05d2 +1 )T ] T = ( x \u05d2 , y \u05d2 , z \u05d2 , \u03b8 x \u05d2 , \u03b8 y \u05d2 , \u03b8 z \u05d2 , x \u05d2 +1 , y \u05d2 +1 , z \u05d2 +1 , \u03b8 x \u05d2 +1 , \u03b8 y \u05d2 +1 , \u03b8 z \u05d2 +1 )T (21) As described in Fig. 6 , the deformation vector of an arbitrary cross-section o z in the \u05d2 th shaft element expressed in the frame F L is u \u05d2 ,z = ( v \u05d2 ,z , w \u05d2 ,z , z \u05d2 ,z , \u03b1\u05d2 ,z , \u03b2\u05d2 ,z , \u03b3\u05d2 ,z ) T . Setting the point A as a starting point of the \u05d2 th shaft element, the position vector of the cross-section o z in the frame F t b is given by O t b O s = O t b A + A O z (22) in which AO z denotes the distance from the point A to o z and is expressed as A O z = ( v \u05d2 ,z , w \u05d2 ,z , z \u05d2 ,z ) T + ( 0 , 0 , L A _ oz ) T (23) where L A _ oz is the distance from the point A to o z with the undeformed shaft" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000108_tec.2018.2820083-Figure17-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000108_tec.2018.2820083-Figure17-1.png", "caption": "Fig. 17. Deformation when applying 1200Hz radial force only", "texts": [ " For the frequency of force, two typical frequencies are used, 1200Hz and 2500Hz, which are close to the two modal natural frequencies of pulsating modal and bending modal shape obtained from modal test in the section V. Fig. 16, 17 and 18 show the deformation response of the stator caused by radial force and bending moment together, radial force only, and bending moment only, respectively, where the frequencies of radial force and bending moment are 1200Hz. Fig. 19, 20 and 21 show the corresponding results when the frequencies of radial force and bending moment are 2500Hz. In these figures, the situation is 1=9 , and only the two instants are shown when the deformation are maximum. From Fig. 17 and Fig. 18, it can be seen that the maximum deformation of the bending mode is nearly 10 times higher than that of the pulsating mode. While in Fig. 20 and Fig. 21, the maximum deformation of the pulsating mode is nearly 10 times higher than that of the bending mode. The reason of this phenomenon is that when 1200Hz is close to the modal frequency 1496 Hz of bending modal obtained from modal test in section V, the bending modal dominates the vibration deformation. When 2500Hz is close to the modal frequency 2498 Hz of pulsating modal obtained from modal test in section V, the pulsating modal dominates the deformation", " 23 shows the FRF measured at two points: Point A at the center of the pole and Point B at the midpoint between the poles. Fig. 24 presents five experimentally extracted mode shapes, and the natural frequencies corresponding to the circumferential modes 1 to 5 are identified to be 474 Hz, 1496 Hz, 2498 Hz, 4185 Hz, and 5241 Hz, respectively. In addition, it should be paid more attentions that Mode 2 in Fig. 24(b) is the bending modal shape, and its frequency is 1496Hz nearing to the 1200Hz in section IV. Mode 3 in Fig. 17(c) is the pulsating modal shape, and its frequency is 2498Hz being near to the 2500Hz and far from the 1200Hz in section IV. In order to verify the analysis in this paper, the vibration and Operational Deflection Shapes (ODS) experiment are performed. The test DC motor with 1 =9 is hanged on the bracket by elastic rope. To pay more attention to the vibration mode, the multi-probe mode-included test method of vibration acceleration is proposed, and fifteen accelerometers produced by PCB PIEZOTRONICS Company are evenly attached to the surface of stator in the circumferential direction as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001061_j.measurement.2020.108492-Figure12-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001061_j.measurement.2020.108492-Figure12-1.png", "caption": "Fig. 12. Dismantle Gearbox.", "texts": [ " With further increase in load to 75 N m, the dominance of 2nd and 3rd harmonics of GMF and increase in amplitude of vibration at 2nd harmonic of GMF by 100 folds indicate further increase in misalignment which overstresses the mating gears and increases wear of gears. It is observed that the increase in load increases the misalignment and leads the wear P. Kumar and H. Hirani Measurement 169 (2021) 108492 of mating gears from run-in to scuffing. Different gearbox related faults (gear mesh, taper roller bearing etc.) as predicted by vibration analysis are also confirmed by visual and microscopic examinations of dismantle gearbox and its components as shown in Fig. 12. As hypothesized that the misalignment in gearbox (drive end) should severely affect the right-side taper roller bearing (32206) and gear contact; experimental findings observe similar type of failure behaviour. On visual inspection of gearbox, the right-side taper roller bearing (32206) is severely damage and severe wear marks are observed on almost all the mating gears teeth surfaces. Dismantle front rotor sub-assembly and the zoom pictures of rightside bearing are shown in Fig. 13. Several pits are observed on all the roller surfaces and inner cone" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000594_tia.2018.2799178-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000594_tia.2018.2799178-Figure1-1.png", "caption": "Fig. 1. Cross-sections of prototype PM machines with 12S/10P combination. (a) All ETW S. (b) All ETW D3p. (c) Alternate ETW S3p. (d) Alternate UETW S3p.", "texts": [ " The reason for torque ripple difference between these electrical machines is addressed as well, together with the analysis of current value influence on torque performance. Moreover, the results of electrical machines with the complementary slot/pole number combination (12S/14P) are also shown to further verify the conclusion. Finally, some experimental results are presented to validate the correctness of the analysis. The cross-sections of 12S/10P prototype machines analyzed in the paper are shown in Fig. 1, together with the winding layouts. For simplicity, they are named by the abbreviation form which shows the winding arrangement, stator core structure and current supply pattern, viz. All ETW S3p, All ETW D3p, Alternate ETW S3p and Alternate UETW S3p machine, respectively. In order to make the comparison as reasonable as possible, all of the machines have been optimized with the same rotor, stator inner/outer diameter, total coil turns and peak current value. As can also be seen in Fig. 1, the FCSs are adopted, which will ideally eliminate the open-circuit cogging torque. Some different phenomena are expected to be observed in these machines compared with those having slot openings. It is worth noting that two sets of windings have 30 electrical degree phase shift between each other for the All ETW D3p machine. The stator yoke thickness of the Alternate UETW S3p machine was increased in accordance with the thick teeth to ensure the machine not oversaturated. The major parameters of these PM machines are listed in TABLE I", " Since all of the electrical machines are surface-mounted type, the difference between d- and q-axis is pretty small, viz. negligible reluctance torque [1]. Therefore, zero d-axis current control strategy is adopted. When all of them are supplied with rated current, the corresponding torque is shown in Fig. 2 and the major information about torque performances are summarized in TABLE II. Since the FCS machines have strong local saturation compared with the fully open slot (abbreviated as \u201cFOS\u201d) counterparts shown in Fig.1, the on-load torque of FOS machines are also given to illustrate this effect. The winding factors of working harmonic (kw), viz. rotor pole pair number, predicted by the methods in [3] and [12] are given to show the inherent property of each kind of winding. It consists 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. of winding pitch factor (kp) and distribution factor (kd)", " To show the influence of armature field and stator core structure on torque ripple, the relative permeability of adjacent stator teeth under open-circuit, armature and on-load conditions are all investigated. The teeth are grouped into two categories and the teeth within each group have the same saturation variation except the fixed phase shift between each other over one electrical period. The teeth having odd number belong to group 1, while the group 2 contains the teeth with even numbers, as shown in Fig. 1. The influence of the 1 st harmonic on torque ripple difference will be reflected on these two groups and only tooth 1, 2 and 3 (T1, T2 and T3) are chosen for simplicity. The corresponding tooth relative permeability variation picked at the center of each tooth is shown in Fig. 8 for open-circuit and armature field. (a) (b) (c) 0 2 4 6 8 10 0 90 180 270 360 R e la ti v e p e rm e a b il it y Rotor position (electrical degree) T1 T2 T3 Open-circuit Armature X1e3 Position 1 Position 2 0 2 4 6 8 10 0 90 180 270 360 R e la ti v e p e rm e a b il it y Rotor position (electrical degree) T1 T2 T3 ArmatureOpen-circuit X1e3 Position 1 Position 2 0 2 4 6 8 10 0 90 180 270 360 R e la ti v e p e rm e a b il it y Rotor position (electrical degree) T1 T2 T3ArmatureOpen-circuit X1e3 Position 1 Position 2 0093-9994 (c) 2018 IEEE", " For other three electrical machines, they show the similar phenomenon as shown in Fig. 11(b). E. Influence of slot and pole number combinations For the sake of further illustration, the complementary slot/pole number combination (12S/14P) is also analyzed. The same four prototype machines are compared and their cross-sections of FCS machines are shown in Fig. 12. (a) (b) (c) (d) Fig. 12. Cross-sections of FCS machines with 12S/14P combination. (a) All ETW S. (b) All ETW D3p. (c) Alternate ETW S3p. (d) Alternate UETW S3p. Comparing Fig. 12 and Fig.1, the major difference is the rotor pole number and the winding layout, while other structure parameters are kept the same for easy comparison. For all of the S3p machines, simply exchanging the phase B and C layouts of 12S/10P machines will lead to 12S/14P machine windings. If two sets of windings are changed in the same time, D3p for 12S/14P machine can be obtained as well. There is another obvious difference being observed for UETW machine. For the electrical machines with higher slot number than pole number, the coils will be wound on thicker teeth to capture more effective flux, while it is the thinner teeth that should be wound if the slot number is smaller than pole number [24]" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003539_robot.1996.506835-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003539_robot.1996.506835-Figure3-1.png", "caption": "Fig. 3: Identification of &, ti, d,, eloff, Bzoff, &f", "texts": [ " The coordinates of [x, Y, 2;lT are computed using the direct kinematic equations (DKE) taking into account the offsets 6 l O f f 7 %ff, [ x, I: 2, IT = DIE( e, +q,,e, +e,, ,e3 +e,, e,) 8, is the i\" joint variable. If [x, Y, Z,lT are the 0, coordinates in R, then: 10 0 0 1 J &=O, Y,=O, Z, are the nominal coordinates of 0,; the sensor optical axis is aligned with the zt axis of Rt. 4.1 Identification of &, & d, OlON, OhN, Os, P is an horizontal support plane accurately positioned in the work area. Its altitude in R, is hp. The robot is driven to reach the knots Ni of a virtual horizontal pattern grid whose altitude in R, is h, (figure 3). For each knot Ni the distance di between the sensor head 0, and the plane P is recorded 976 1 -6, 6, X o + X , + S y . ( Z ~ + Z c ) - 6 g . . I : + d r -6, 6, 1 %,+Z,+Z,+6* . . -6 , .X ,+d , \"T = 4 1 -6= r,+I:-s,.(z~+~~!,)cs,.x,+d, 0 0 0 1 -6, 6, x.1 0 I =[+, i -: If the sensor optical axis is aligned with the z, axis of & frame, one can calculate the theoretical distance di between 0, [X Y' ZIT and the plane P along the z, direction whose components in R, are [6,. -& 1IT. d,' = (2' - hp) . J(6:m' neglecting the second order terms leads to: din = (Z' - hp) The vector of parameters PI=[& S, d, 62oe 6 3 , ~ l ~ that has to be identified is the one that minimizes for all the number M of measurement points Ni: CI i" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000970_j.mechmachtheory.2019.103747-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000970_j.mechmachtheory.2019.103747-Figure4-1.png", "caption": "Fig. 4. Geometric representation of different angle sets, from Table 2 , corresponding to (a) inverse kinematics of the first chain, (b) inverse kinematics of the second chain, and (c) forward kinematics .", "texts": [ " Kinematic u v w \u03b21 \u03b22 \u03b4 Inverse 1 Z EE Y 0 X EE \u03c0 /2 \u03c0 /2 \u03bc Inverse 2 Y EE X 2 Z 3 \u03be \u03b3 \u03c3 Forward X EE Z 3 Y EE \u03c0 /2 \u03be \u03b7 Fig. 3. Geometrical configurations based on angles \u03b21 and \u03b22 and the orientations of u and v in Eq. (1) . In this section, the proposed geometrical approach, described in section 3 , is used to analyze the configurations and sin- gularities of the designed non-symmetric 5R-SPM and the results were compared with those obtained from the conventional method of calculating the Jacobian matrix and inverse and forward kinematics. Fig. 4 shows the equivalent axes u, v , and w , equivalent link lengths \u03b21 and \u03b22 , and equivalent angle \u03b4 for each of the two chains of inverse and also forward kinematics, respectively, with their summary presented in Table 2 . Based on these parameters, we derived the equivalents of Eq. (1) for each kinematics. Later, in the Appendix, these equations are used to solve the inverse and forward kinematics. However, for the geometrical analysis of different configurations and singularities, the equivalent values for \u03b21 , \u03b22 , and \u03b4 from Table 2 suffice", " (1) and substituting equivalent parameters for the first chain (see Table 2 , row 1), one obtains X EE = 1 S 2 \u03bc { (Z EE \u00d7 Y 0 ) \u00d7 (C \u03c0/ 2 Z EE \u2212 C \u03c0/ 2 Y 0 ) \u00b1 \u221a (C \u03c0 \u2212 C \u03bc)(C \u03bc \u2212 C 0 ) (Z EE \u00d7 Y 0 ) } (3) = 1 S 2 \u03bc { \u00b1 \u221a 1 \u2212 C 2 \u03bc(Z EE \u00d7 Y 0 ) } = \u00b1Z EE \u00d7 Y 0 S \u03bc where \u03bc is the angle between the axis of first joint, Y 0 = [0 1 0] T , and the given end-effector position Z EE . Since both links of the first kinematic chain are orthogonal, only configurations 1 and 3 from Table 1 may occur, meaning that, with respect to the first chain, any arbitrary end-effector position is either regular or in finite singularity. Referring to Fig. 4 , finite singularity occurs when Z EE becomes aligned with Y 0 ( Z EE = [0 \u00b1 1 0] T , \u03bc = 0 or \u03c0 ), corresponding to geometrical configurations (i) and (j) in Fig. 3 . In this situation, as shown in Fig. 5 , while Z EE is fixed, X EE can rotate around Y 0 . In other words, for the given end-effector vector Z , there are infinite number of solutions for \u03b8 and \u03b8 . Since \u03bc = \u03b8 + \u03c0/ 2 (see EE 1 2 5 Fig. 2 ), the denominator of Eq. (3) , S \u03bc, becomes zero at C 5 = 0 . Therefore, the finite inverse singularity of the first chain (refereed to as FI-1 in the rest of this paper) occurs at C 5 = 0 " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001777_j.mechatronics.2021.102595-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001777_j.mechatronics.2021.102595-Figure1-1.png", "caption": "Fig. 1. Illustration of the error sources in the geometric parameters of CDPRs.", "texts": [ " The verification experiment results are provided in Section 5. Finally, conclusions are presented in Section 6. Calibration by external measurement devices is a typical practice. Owing to the effect of sensor measurement noise, the calibration precision of geometric parameters (GPs) is reduced. Therefore, the EKF algorithm was adopted in this study to improve the accuracy of calibration results, and the detailed calibration processes of GPs were designed. A CDPR comprises drive units, cables, a mobile platform, and a structure platform, as shown in Fig. 1. The mobile platform has \ud835\udc5b-DOFs and is driven by \ud835\udc5a cables. The {\ud835\udc42} denotes the base frame of CDPRs, and the {\ud835\udc40} denotes the mobile platform frame which located at the geometric center of the mobile platform. The pose of the mobile platform frame in the base frame can be defined as \ud835\udc42 \ud835\udc40\ud835\udc7f = [\ud835\udc42\ud835\udc40\ud835\udc91,\ud835\udc42\ud835\udc40 \ud835\udf53]\ud835\udc47 , and it can be computed precisely by direct kinematics when the drive unit angles are known. The vector \ud835\udc42 \ud835\udc40\ud835\udc91 denotes the position, and \ud835\udc42 \ud835\udc40\ud835\udf53 denotes the mobile platform\u2019s orientation. The vector \ud835\udc82\ud835\udc56 denotes the theoretical position of drive unit \ud835\udc34\ud835\udc56, and vector \ud835\udc83\ud835\udc56 denotes the theoretical position c \ud835\udc8d \ud835\udc59 C \ud835\udc68 i T \ud835\udf16 2 o m u c o t s i \ud835\udc71 w o s c u w c r \ud835\udc99 H a c T \ud835\udc77 T a b \ud835\udc9b w \ud835\udc58 c l T o \ud835\udc97 t a f \ud835\udc99 [ t of cable attachment point \ud835\udc4f\ud835\udc56 at the mobile platform" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001377_012102-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001377_012102-Figure2-1.png", "caption": "Figure 2. Scheme of GLDITM with a fourlink single-circuit chain: 0 - frame;1, 2, 3 - levers; 4, 5, 6, 7 - gear wheels", "texts": [ " In this roller pair, one of the working shafts (1) rotates on the axis (O1) forming a rotational pair with the frame (0), and the second working shaft (2) rotates on the axis (O2), which is pivotally connected to the frame by means of a lever (3) along the O3 axis. In the roller machines built according to this scheme, at the moment of change in interaxle distance (O1O2), the center of rotation of the movable working shaft (O2) moves in an arc-like manner relative to the center of O3 along an arc of a circle with a radius equal to the lever length (3). Figure 2 shows a diagram of a GLDITM with a four-link lever chain 0ABS0. The mechanism consists of a frame (0), levers (1, 2, 3) and gears wheels (4, 5, 6, 7). The axis of rotation of the gear wheel 4 is installed on the frame, the axis of rotation of the gear wheel 5 is mounted on the lever 1, and the axes of rotation of the gear wheels 6 and 7 are mounted on the lever units 1, 2, and 3. In the mechanism, all the gear wheels have the ability to rotate around their own axes O1 , A, B and C, in addition, the axes of rotation of the gears 5 and 6 have the ability to move circularly around the axis O1, and the axis of rotation of the gear 7 is able to move around the axis O3", " 1, 2, 3, 4, 5 - levers; 6, 7, 8, 9 - gear wheels Considering that in most roller machines the diameters of the working shafts are equal to each other, considera special case of the transmission mechanisms for such a roller machine. In roller machines with similar diameters of the working shafts, the gear ratio of the working shafts is a unity, with a ICECAE 2020 IOP Conf. Series: Earth and Environmental Science 614 (2020) 012102 IOP Publishing doi:10.1088/1755-1315/614/1/012102 constant interaxle distance of the working shafts; it is provided under the same reference diameter of all gear wheels (gears 4, 5, 6, 7 in Fig. 2 and gears 6, 7 , 8, 9 in Fig. 3) or, in pairs, under the same reference diameter of the driving gears (gear 4 in Fig. 2, and gear 6 in Fig. 3) with the driven one (gear 7 in Fig. 2 and gear 9, in Fig. 3) and idle gears (gears 5 and 6 in Fig. 2 and gears 7 and 8 in Fig. 3). Therefore, in a comparative analysis, we take all the corresponding geometrical parameters of the mechanisms to be equal and the positions of the mechanisms to be the same. That is, d4 = d5 = d6 = d7 = d- for the mechanism in Figure 2, d6 = d7 = d8 = d9 = d - - for the mechanism in Figure 3, whered4, d5, d6, d7, d8, d9 - are the reference diameters of the corresponding gear wheels. The initial values of \u03b1 and \u03c6 in two mechanisms under consideration are the same. \u03b1 is the angle of the mechanism position, \u03c6 is the angle of the position of the levers CO3 and CO5. \u0421O3 = \u0421O5, Figure 4 shows the design diagram of the GLDITM lever circuit with a four-link single-circuit lever chain, and Figure 5 shows the design diagram of the GLDITM lever circuit with a six-link doublecircuit lever chain" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003808_pat.590-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003808_pat.590-Figure1-1.png", "caption": "Figure 1. Structure and dimensions (in mm) of the integrated microelectrode composed of a carbon rod as a working electrode (A\u00bc 0.006 cm2) which was laterally coated with insulating cellulose and placed in a stainless steel 18G needle as an auxiliary electrode.", "texts": [ " is catalytically oxidized at the surface of the modified electrode. In this paper the first all synthetic electrochemical sensor for O2 . using the electrodeposited film of the iron porphyrin complex, especially in the presence of 1-methylimidazole as an axial ligand to enhance the selectivity for O2 . is reported. A needle-type coaxially integrated microelectrode composed of a laterally coated carbon rod as the working electrode was fabricated, which was inserted in a stainless steel 18 G needle as the auxiliary electrode (Fig. 1). Then the focus is placed on the detection of O2 . by a two-electrode method Copyright # 2005 John Wiley & Sons, Ltd. *Correspondence to: M. Yuasa, Department of Pure & Applied Chemistry, Faculty of Science and Technology, Tokyo University of Science, Noda 278-8510, Japan. E-mail: yuasa@rs.noda.tus.ac.jp using the microelectrode; detailed studies on the detection of O2 . at definite electrode potentials versus a reference electrode are outside the scope of the present report. SOD (EC 1.15.1.1 from bovine erythrocytes) and xanthine oxidase (XOD) (from buttermilk suspended in 10 mmol/l sodium phosphate buffer (pH 7", " The formation of the iron complex was followed by UV-vis spectra, which revealed reduction of the Q-bands upon replacement of the inner protons with the iron(III) center as a result of the increase in molecular symmetry, accompanied by the hypsochromic shift of the Soret band. 1H-NMR spectra were recorded on a JEOL JNM-AL300 spectrometer with chemical shifts downfield from tetramethylsilane (TMS) as the internal standard. UV-vis spectra were recorded on a Shimadzu UV-2100 spectrometer. Fast atom bombardment mass spectrometry (FAB-MS) spectra were recorded on a JEOL JMS-SX102A spectrometer using nitrobenzyl alcohol as a matrix. Electrochemical measurements were carried out in a one-compartment cell. An integrated microelectrode shown in Fig. 1 was used as the working electrode and the auxiliary electrode. The surface of the working electrode was polished before each experiment with No. 800 sandpaper for 30 min, followed by wet polishing with No. 2000 sandpaper for 5 min, which was then carefully rinsed with CH2Cl2 with ultrasonic irradiation for 2 min. The reference electrode was a commercial Ag/Ag\u00fe immersed in a solution of 0.1 mol/l tetrabutylammonium perchlorate (TBAP) in CH3CN, which was placed in the cell compartment. The formal potential of the ferrocene/ferrocenium couple in CH2Cl2 was 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001184_j.measurement.2020.108198-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001184_j.measurement.2020.108198-Figure6-1.png", "caption": "Fig. 6. A defect on the outer race of the rolling element bearing and size of the defects.", "texts": [ " To this, in this study, a comparison of the three different types of sensors is made to define the capability of different sensors in acquiring data and calculating conventional timedomain parameters for diagnosing the defects. Fig. 4 shows the different acoustic emission sensor types used in this study. The rolling element bearings in this experiment are angular contact ball bearing manufactured by SKF type 7202BEP with inner and outer diameters of 15 and 35 mm. In this study, four states of bearings, normal, small defect, medium defect, and large defect bearings are used. Fig. 6 shows the bearing\u2019s defect which is an artificial defect and is linearly aligned with the bearing axis and generated on the outer race of the bearing by the help of EDM machine. The esperiments tested in four rotational speeds of 600, 900, 1200 and 1500 rpm which were loaded with four different low to high loadings using four screws. The data transducers are connected to the bearings cage by grease. Fig. 7 shows the sensors and preamplifiers connected to them. The general purpose of acoustic emission sensors, R6a, wideband sensor, WSa, and miniature sensor, pico, with a piezoelectric operational frequency range of 35\u2013100 kHz, 100\u20131000 kHz, and 200\u2013750 kHz are used" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003665_iecon.2005.1569239-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003665_iecon.2005.1569239-Figure4-1.png", "caption": "Fig. 4.The robot structure.", "texts": [ " To interface the card with the motors a very simple MOSFET based driver circuit was developed to make the interface between the PWM output of the card and the circuit that powers the motors through the batteries. When using battery operated variable speed drills, we could use the power circuit inside the drill to drive the motors. Hence, we used a USB card to interface the laptop with the motors. There are plenty of free I/O ports in the acquisition card that might be used to cope with analog or digital sensors that may increase the ability of the robot to sense the environment. Figure 4 presents a general view of the built robot. The first prototype was named \u201cRasteirinho\u201d The processing unit is a normal laptop that is placed on the top of the robot. The advantage of using a normal laptop is that it is easy in a group of two or three students to find one with a laptop. Using their own laptops and interfacing it to the robot (which is lent to them), students may work with it at any place and hours independently of the availability of the laboratory. The laptop is fixed to the robot by easily removable Velcro bands (in fig. 4, four Velcro bands are visible on the top robot corners). To sense the environment, students might use sensors that are widely available in the market, and could interface them to the USB card free I/O ports. However, keeping it simple and challenging, we decide to guide the robot through normal webcams, widely available at a low cost (less than 20 USD). The USB camera acts as a general purposed sensor to guide the robot through the environment. A low-cost, flexible link, web camera for guiding the robot is presented in fig 5" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000108_tec.2018.2820083-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000108_tec.2018.2820083-Figure6-1.png", "caption": "Fig. 6. Equivalent pulsating force and bending moment on one pole", "texts": [ " Electromagnetic force density distribution on one pole at one instant The stator is divided into same shape sectors of pole number because of PM poles, and the radial force density distribution on one pole is derived from (4). If the pole is considered as a rigid body, the radial force on any point of the pole can be moved parallel to the center of the pole by adding one additional equivalent bending moment on the pole. As said before, here only the third term in (4) is of interest for vibration analysis. By integrating the radial force density based on the third term in (4), the pulsating radial force ( )npp t and bending moment ( )npm t on the pole can be obtained, which are shown in Fig. 6. The pulsating radial force ( )npp t on the center causes pulsating type vibration, and the additional bending moment ( )npm t causes bending type vibration. The electromagnetic exciting force distribution on the surface of the PM pole varies with the rotation of the rotor. The equivalent pulsating radial force on the center of every pole can be obtained by parallel moving or integrating the force densities on one pole, i.e., the third term in (4). For simplicity, only 1 among k is considered hereinafter" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000936_j.mechmachtheory.2019.103607-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000936_j.mechmachtheory.2019.103607-Figure7-1.png", "caption": "Fig. 7. Detailed \u201ctooth-change\u201d process: the change of (a) generalized coordinates and (b) modal basis matrix of the I-gear. Notice that each nodal displacement column i is partitioned according to the tooth index.", "texts": [ " For example, the tooth-face pairs in contact are changed from (3B-3A, 2B-2A, 1B-1A) to (2B-2A, 1B1A, 20B-30A) at the first \u201ctooth-change\u201d instant as illustrated in Fig. 5 (c) and further changed to (1B-1A , 20B-30A , 19B-29A) at the second \u201ctooth-change\u201d instant in Fig. 5 (f). 2. Generalized coordinates/velocities The vectors of generalized coordinates and velocities are updated. The position and rotation vector of gear remain unchanged, while the modal coordinates are updated from the boundary DOFs of current tooth-face pairs to those of the subsequent ones. For example, as shown in Fig. 7 (a), [ u T 3 B u T 2 B u T 1 B ] is updated to [ u T 2 B u T 1 B u T 20 B ] for I-gear, and [ u T 3 A u T 2 A u T 1 A ] is updated to [ u T 2 A u T 1 A u T 30 A ] for J-gear, which also applies to the update of generalized velocities. Additionally, it is worth mentioning that the initial value of updated generalized coordinates can be predicted using the displacements of corresponding boundary nodes in the time steps prior to the tooth-change instants, which can effectively reduce the number of iterations and numerical oscillations in our time integration algorithm \u00e2 backward differentiation formula (BDF). This technique and the aforementioned careful selection of \u201ctooth-change\u201d instants are both used to make the \u201ctooth-change\u201d process smooth and accurate. 3. Modal basis matrix As illustrated in Fig. 7 (b), the modal basis matrix = [ 1 . . . 9 n b ] is transformed to a , and to b in two steps, where i (i = 1 \u223c 9 n b ) is the i th-order mode and there are 9 n b = 3 \u00b7 3 n b boundary DOFs for three tooth-faces in contact. In the first step, i has to be transferred from the position of the current tooth to the subsequent one, which corresponds to the successive change of generalized coordinates. It can be expressed in the following matrix form, a = T , (18) where T is the transfer matrix, T z\u00d7z = \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 0 I n t 0 \u00b7 \u00b7 \u00b7 0 0 0 I n t \u00b7 \u00b7 \u00b7 0 . . . . . . . . . . . . . . . 0 0 0 \u00b7 \u00b7 \u00b7 I n t I n t 0 0 \u00b7 \u00b7 \u00b7 0 \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 , (19) which consists of z \u00d7 z sub-matrices and I n t = diag ( I 3 \u00d73 . . . I 3 \u00d73 ) has n t \u00d7 n t unit matrices. n t is the number of nodes for a single tooth. In the second step, considering the relative rotation \u03b4\u03b8 between the floating reference frame O \u2212 xy and the area of boundary DOFs in Fig. 7 (a), a rotation transformation is performed to obtain b by using b = R T zn t a R 3 n b , (20) where R T zn t = diag ( R T . . . R T ) and R 3 n b = diag ( R . . . R ) consist of zn t \u00d7 zn t and 3 n b \u00d7 3 n b rotational sub-matrices, respectively, with R = [ cos ( \u03b4\u03b8 ) sin ( \u03b4\u03b8 ) 0 \u2212 sin ( \u03b4\u03b8 ) cos ( \u03b4\u03b8 ) 0 0 0 1 ] . (21) \u03b4\u03b8 = 2 \u03c0/z is the rotational angle. zn t and 3 n b denote the total number of nodes of helical gear and those in the \u201cpotential contact area\u201d. 4. Stiffness matrix Due to the relative rotation between the floating reference frame O \u2212 xy and the area of boundary DOFs, stiffness matrix K should be updated in a similar way as modal basis matrix, which can be expressed as K a = R T 3 n b KR 3 n b " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000518_012145-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000518_012145-Figure2-1.png", "caption": "Figure 2. The movement of the rolling body in the nest.", "texts": [ " The overload scheme is shown by curve 2, according to which [1]: - at the initial value of the friction coefficient, the beginning of curve 2 is at the point belonging to straight line 1 and corresponding to the specified value of the friction coefficient; - the magnitude of the overload, with an increase in the friction coefficient of the value, depends on the current value of the friction coefficient, and increases with the growth of the latter; - after moving the rolling body relative to the forming wall of the socket to the position corresponding to the friction coefficient reached, the safety clutch will transmit the nominal torque, as the pressure angle and the gain factor increase, this process is reflected in Figure 1 line segments 3; - at the initial value of the friction coefficient, different from, the process of the action of overloads in the safety coupling is shown in Figure 1 by curves 4 and straight lines 5. Consider the scheme shown in Figure 2. The diagram shows the process of moving the rolling element during automatic regulation. Position I of the rolling element corresponds to the operation of the safety clutch with the minimum value of the friction coefficient. The abscissa axis passes through the center of the rolling body, the ordinate axis through the point of contact of the side wall of the nest and the rolling body. In the specified position of the rolling element, the initial ordinate of the contact point is equal to. XII International Scientific Conference on Agricultural Machinery Industry IOP Conf" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001377_012102-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001377_012102-Figure5-1.png", "caption": "Figure 5. Design diagram of the GLDITM lever circuit with a six-link double-circuit lever chain: 0 - frame; 1, 2, 3, 4, 5 - levers", "texts": [ " That is, d4 = d5 = d6 = d7 = d- for the mechanism in Figure 2, d6 = d7 = d8 = d9 = d - - for the mechanism in Figure 3, whered4, d5, d6, d7, d8, d9 - are the reference diameters of the corresponding gear wheels. The initial values of \u03b1 and \u03c6 in two mechanisms under consideration are the same. \u03b1 is the angle of the mechanism position, \u03c6 is the angle of the position of the levers CO3 and CO5. \u0421O3 = \u0421O5, Figure 4 shows the design diagram of the GLDITM lever circuit with a four-link single-circuit lever chain, and Figure 5 shows the design diagram of the GLDITM lever circuit with a six-link doublecircuit lever chain. We willdetermine the lever circuits and the kinematic parameters of the mechanisms depending on the velocity of the centers of rotation of the driven gear wheels (VC). The kinematic parameters were determined by the centroid method. Having determined sequentially the instantaneous centers of rotation of all lever links of the mechanisms, we obtain the angular and linear velocities of the characteristic points of the mechanism links", " Series: Earth and Environmental Science 614 (2020) 012102 IOP Publishing doi:10.1088/1755-1315/614/1/012102 ,11 APVA (5) whereCP3, CP2, BP2, BP1are determined by ;33 LCP (6) where L3 \u2013 is the length of the lever CO3 (link 3) ; 2 cos 2 sin arcsin 2 sin 1 2 d BP d CP (7) cos1 sin2 1 arccos 3L d ; 2 cos 2 sin arcsincos 1 2 d BP d BP ; (8) )cos1(21 dBP ; (9) According to the scheme shown in Fig. 5, we can write: ; 5 5 CP VC (10) ; 4 4 CP VC (11) ;44 BPVB (12) ; 1 4 41 AP BP (13) ,11 APVA (14) where - CP4, CP5, BP4, AP1 are determined by 55 LCP ; (15) ICECAE 2020 IOP Conf. Series: Earth and Environmental Science 614 (2020) 012102 IOP Publishing doi:10.1088/1755-1315/614/1/012102 whereL5 \u2013 is the length of the lever\u0421\u041e5 (link 5) \u0421P4= ; )4sin( 2sin d (16) ; )sin( cossin2 4 d d BP (17) dAP 1 ; (18) The gear circuits of the GLDITM are solved after solving the lever circuits of the GLDITM, using the obtained formulas" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000405_s12540-018-0142-3-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000405_s12540-018-0142-3-Figure2-1.png", "caption": "Fig. 2 a Sample extraction locations for cross section samples, phase characterizations (XRD) and tensile samples, b schematic showing the locations of microhardness, c dimensions of tensile specimens in mm", "texts": [ " During solution heat treatment, the wall components were heated from room temperature to 350, 450 and 550\u00a0\u00b0C in 50\u00a0min and were maintained at this temperature for 7\u00a0h. At last, wall components were quenched by 100\u00a0\u00b0C water and cooled to room temperature. The wall components at different heated treatment temperature were marked as T350 (wall components heated treatment at 350\u00a0\u00b0C), T450 (wall components heated treatment at 450\u00a0\u00b0C) and T550 (wall components heated treatment at 550\u00a0\u00b0C), respectively. Four different conditions of wall components were used for specimens testing. Figure\u00a02a shows the extraction location for various material samples. The cross sections (X\u2013Z plane) of specimens were wire-cut from the middle part 1 3 of the additively manufactured wall for the microstructure analysis and hardness test. In order to investigate hardness at different location within the deposited component, the measurement was performed along the centerline from fusion line to the top surface of cross section. Figure\u00a02b indicates microhardness test lines. There are three transverse lines (near the top surface, middle surface and bottom surface) and a centerline along the normal direction. Tensile properties of wall component were measured in both deposition direction (Z) and welding direction (Y). Figure\u00a02c shows the size of tensile specimens. Three specimens of each direction were extracted and measured for mean value. The microstructures were observed by optical microscope and scanning electron microscope (SEM) after polishing with 2\u00a0\u03bcm diamond polishing fluid and etching with Keller\u2019s reagent solution. Vickers microhardness were performed at a 100\u00a0g load for a dwell time of 15\u00a0s along the vertical centerline of the cross sections. The interval was 0.5\u00a0mm. Tensile measurements were performed at room temperature with instron at test speed of 2\u00a0mm/min" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003068_jsvi.1997.1298-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003068_jsvi.1997.1298-Figure8-1.png", "caption": "Figure 8. Mode shapes of geared assembly II. (a) Mode 13, (0, 2) flexible body mode of the driver; and (b) mode 17, (0, 4) flexible mode of the driver.", "texts": [], "surrounding_texts": [ "Assembly V describes a reverse-idler reducer configuration of Table 1 with three helical gears and two meshes as shown in Figure 1(c). Both FEM and MBD predictions of natural frequencies of this assembly are given in Table 7 together with the predicted error which is less than 3% for all of the modes studied. Figures 9(a) and (b) show two selected mode shapes of this dual mesh system. The first mode shape illustrates some coupling between the rigid and flexible d.o.f. The driver and the driven gears exhibit (0, 0) flexible body modes while the idler undergoes a rigid body rotation. Due to the relatively high mesh stiffness (Km =108 N/m2), the dynamic deformations in all the gears are such that the relative motion at the mesh points on the gears is very small. This shows a strong interaction between the mesh and the structural deformation modes. The second mode shape is an example of the case where all the gears exhibit different flexible body modes. The driver and the driven gears are undergoing (0, 2) modes while the idler gear exhibits a (0, 0) mode. Notice again that the nodal diameters in the two outer gears are located such that there is a minimum possible deformation at either gear mesh interfaces." ] }, { "image_filename": "designv10_11_0001773_tte.2021.3085367-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001773_tte.2021.3085367-Figure1-1.png", "caption": "Fig. 1. Configuration of the investigated HMC-VFMM. (a) Topology. (b) 3-D view.", "texts": [ " In Section IV, the air-gap flux densities (AGFDs) of the HMC-VFMM are analytically predicted by combining the MEC solution and the SC transformation. In addition, a subdomain model with consideration of the armature reaction is adopted to predict the output torque of the machine. Finally, the effectiveness of the hybrid field analytical method is confirmed by both the FE solutions and measured results. II. MACHINE TOPOLOGY AND FLUX REGULATION PRINCIPLE The configuration of the investigated HMC-VFMM is illustrated in Fig. 1, which is geometrically characterized by a 21-slot/4-pole structure. Besides, the key parameters of the machine are tabulated in Table I. As shown in Fig. 1(a), the machine has a dual-layer PM structure, i.e., \u201cU\u201d-shaped and \u201cspoke\u201d-shaped hybrid PM arrangements. The HCF PMs located on the q-axis form a \u201cspoke\u201d-shaped PM structure, while the LCF and HCF PMs close to the inner side of the triangle flux barrier are designed as a U-shaped PM structure. The \u201cU\u201d-shaped and \u201cspoke\u201d-shaped hybrid PM arrangements are employed to maintain an extended flux regulation range and a stable withstand capability for accidental demagnetization simultaneously [9]. In addition, triangular q-axis magnetic barriers are embedded in the middle of the two adjacent LCF PMs to reduce the risk of accidental on-load demagnetization" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003511_s0094-114x(00)00024-0-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003511_s0094-114x(00)00024-0-Figure8-1.png", "caption": "Fig. 8. Bearing contacts and contact paths of the ZN-type worm gear set under di erent center-distance o set assemblies.", "texts": [ " In this example, the separation value of the bearing contours is chosen as 0.00635 mm which is the size of coating particles used in the rolling-test experiments. Fig. 7 shows kinematical errors of the worm gear set, with pitch diameters of oversize hob cutter 85.00 and 80.00 mm, are 2.76 and 0.27 arc-s, respectively. The in\u00afuences of assembly errors on the ZN-type worm gear set are investigated when the worm gear is cut by an oversize hob cutter with pitch diameter of 85.00 mm and pitch diameter of the matting worm is 79.50 mm. Fig. 8(a) and (b) show the bearing contacts of the worm gear set with 0.42 mm (0.233% center-distance) and \u00ff0:42 mm (\u00ff0:233% center-distance) center-distance o sets, respectively. The kinematical errors of 0.233% and \u00ff0:233% center-distance o sets are 2.95 and 2.50 arc-s, respectively, as shown in Fig. 9. Fig. 10(a) and (b) show the bearing contacts of the worm gear set with axes misalignments of 0:25\u00b0 and \u00ff0:49\u00b0, respectively. Fig. 11 shows the kinematical errors are 2.91 and 2.97 arc-s for the worm gear set with axes misalignments of 0:25\u00b0 and \u00ff0:49\u00b0, respectively", " Meanwhile, if the pitch diameter of oversize hob cutter is smaller than 80.00 mm, edge contact will be occur, and edge failure may happen. For these reasons, the working life of the hob cutter can be ranged oversize from 6.92% to 0.63% pitch diameter. If the worm gear set has 0.233% center-distance o set, bearing contacts will be located near the upper worm gear surface. On the contrary, if the worm gear set has \u00ff0:233% center-distance o set, bearing contacts will be located near the bottom worm gear surface, as shown Fig. 8. In order to avoid the edge contact on worm gear surface, an admissible assembly center-distance o set can be limited in the range of 0.233% and \u00ff0:233% center-distance variation. If the worm gear set has 0:25\u00b0 rotation axes misalignment, bearing contacts will be located near the right side of worm gear surface and spread over a longer contact area. If the worm gear set has \u00ff0:49\u00b0 rotation axes misalignment, bearing contacts will be located near the left side of worm gear surface, as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001452_tro.2021.3076563-Figure17-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001452_tro.2021.3076563-Figure17-1.png", "caption": "Fig. 17. Linkage model of the finger. \u03bbj is the tilt angle of segment j with respect to ground. Lj is the length of segment j. mj is the mass of segment j. Cj is the distance between the center of mass of segment j to vertex j. \u03c1 is the angle between the two sides of fingers (\u03c1 = 120\u25e6). \u03be is the orientation of the UR3e arm\u2019s end-effector with respect to ground. s1 and s2 are base dimensions. g is the gravitational constant (j = 0, 1, 2, 3).", "texts": [ " We calculated the strain energy component \u0394Vi,s by measuring the stiffness at each vertex (see Fig. 11) and integrating to calculate the potential energy (see Fig. 12) Vi,t = \u0394Vi,s +\u0394Vi,g (10) Vi,s(\u03d5) = \u222b \u03d5 0 \u03c4(x)dx (11) \u0394Vi,s = Vi,s(\u03d5u)\u2212 Vi,s(\u03d50). (12) The model for the gravitational energy component \u0394Vi,g differs slightly because it depends on the weight of all facets connected to the distal side of the vertex, so we present separate sets of equations for each vertex. We first calculated the tilt of each segment relative to the ground (see Fig. 17) \u03bb0 = \u03be \u2212 \u03c1 2 + \u03c0 2 (13) \u03bb1,0 = \u03bb0 \u2212 \u03d51,0 (14) \u03bb1,u = \u03bb0 \u2212 \u03d51,u (15) \u03bb2,0 = \u03bb1,0 \u2212 \u03d52,0 (16) \u03bb2,u = \u03bb1,u \u2212 \u03d52,u (17) \u03bb3,0 = \u03bb2,0 \u2212 \u03d53,0 (18) \u03bb3,u = \u03bb2,u \u2212 \u03d53,u (19) where \u03d5x is the displacement of vertex x, \u03bbj is the tilt angle of segment j with respect to ground, \u03bbj,0 and \u03bbj,u are the tilt angles Authorized licensed use limited to: University of Prince Edward Island. Downloaded on July 03,2021 at 12:01:06 UTC from IEEE Xplore. Restrictions apply. at the initial position and transformation threshold, \u03c1 is the angle deflection at the base of the gripper (in our device, \u03c1 = 120\u25e6), and \u03be is the acute angle between the gripper\u2019s central axis and the horizontal plane, which can be calculated from the end-effector speed vee = [vx, vy, vz] \u03be = arctan \u221a v2x + v2y vz ", " 4) Kinetic Energy: For each segment j Tj = 1 2 mjv 2 j = 1 2 mj(\u03c9Dj) 2 = 1 2 mj\u03c9 2(x2 j + y2j ) (37) bx = s1 cos \u03be \u2212 s2 sin \u03be (38) by = s1 sin \u03be + s2 cos \u03be (39) x1 = bx + L0 cos \u03bb0 + C1 cos \u03bb1,0 (40) y1 = by + L0 sin \u03bb0 + C1 sin \u03bb1,0 (41) x2 = bx + L0 cos \u03bb0 + L1 cos \u03bb1,0 + C2 cos \u03bb2,0 (42) y2 = by + L0 sin \u03bb0 + L1 sin \u03bb1,0 + C2 sin \u03bb2,0 (43) x3 = bx+ L0cos \u03bb0+ L1 cos \u03bb1,0+ L2 cos \u03bb2,0+ C3 cos \u03bb3,0 (44) y3 = by+ L0sin \u03bb0+ L1 sin \u03bb1,0+ L2 sin \u03bb2,0+ C3 sin \u03bb3,0 (45) where mj is the weight of each segment, vj is the linear velocity at the center of gravity, \u03c9 is the angular velocity of the segment, Dj is the distance between the center of mass and the rotational center, xj and yj are local coordinates of the center of mass, and s1 and s2 are base dimensions (see Fig. 17). To predict the transformation of vertex 1, we include the kinetic energy of all three segments T = T1 + T2 + T3. (46) To predict the transformation of vertex 2, we include the kinetic energy of segments 2 and 3 T = T2 + T3. (47) Authorized licensed use limited to: University of Prince Edward Island. Downloaded on July 03,2021 at 12:01:06 UTC from IEEE Xplore. Restrictions apply. 5) Pinch to Wrap Mode: In the pinch mode, the configurations of vertices 1\u20133 were parallel, antiparallel, and antiparallel, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003374_rsta.2003.1186-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003374_rsta.2003.1186-Figure3-1.png", "caption": "Figure 3. A hypothetical molecular autonomous agent. For clarity, the reaction of the two DNA trimers to form the hexamer without coupling to pyrophosphate breakdown is not shown. See text for description.", "texts": [], "surrounding_texts": [ "Our next task is to exhibit a conceptual example of a molecular autonomous agent. The example is not meant to be realistic in the detailed chemistry among the molecular components that it proposes. Rather it is meant to make concrete the concepts involved. Figure 2 shows a hypothetical molecular autonomous agent. It consists of a selfreproducing molecular system comprised of a single-stranded DNA hexamer and two trimers, which are its Watson{Crick complements, coupled to a molecular motor that drives excess replication of the DNA hexamer. The entire system is a new class of open thermodynamic chemical reaction networks. This system takes in matter and energy in the forms of the two DNA trimers and a photon stream. As a preamble, I would note that self-reproducing molecular systems have been achieved experimentally, as have molecular motors. It remains to put the two together in a single system. First, some familiar points should be made. The system I exhibit is a chemical reaction network some of the components of which are enzymes. Enzymes do not change the equilibrium of a chemical reaction, they merely speed the approach to equilibrium. As will be familiar to most readers, a chemical reaction can approach equilibrium from either an initial excess of substrates or products. As a simple example, suppose A converts to B, and B converts to A. If one starts with pure A, A is Phil. Trans. R. Soc. Lond. A (2003) converted to B. As B builds up, B is converted to A. Equilibrium is achieved when the net rate of conversion of A to B equals the net rate of conversion of B to A. Physical chemists draw this as an energy diagram, with the reaction coordinate on the X -axis and free energy on the Y -axis ( gure 3). A spontaneous chemical reaction always proceeds `exergonically\u2019 in the direction of losing free energy until the minimum free energy is reached at equilibrium. If the reaction system is to be driven beyond equilibrium, say in order to synthesize more B than would be achievable by the undriven system, energy must be added to the system to drive it beyond equilibrium in an endergonic process. Returning to the hypothetical autonomous agent, the DNA hexamer is capable of acting as an enzyme linking the two trimers into a hexamer that is a second copy of the initial hexamer, hence autocatalysis, or self-replication, is achieved. (This physical system, without coupling to pyrophosphate (PP), has actually been realized experimentally (von Kiedrowski 1986).) In the example, the synthesis of hexamer by linking the two trimers is coupled to the exergonic breakdown of PP to two monophosphates, P+P. This exergonic breakdown is used to drive endergonic excess Phil. Trans. R. Soc. Lond. A (2003) synthesis of the hexamer compared with the equilibrium ratio of hexamer and trimers that would characterize the equilibrium of that subsystem. So, just as I pushed on the piston, the exergonic breakdown of PP is used to push excess replication of hexamer compared with equilibrium. Once the PP has been used to drive the endergonic synthesis of excess hexamer, it is necessary to restore the PP concentration to its former level by driving the endergonic synthesis of PP from the two monophosphates. To supply the energy for this endergonic synthesis, I imagine an electron which absorbs a photon, is driven to an excited state, and, when it spontaneously and thus exergonically falls back to its ground state, uses that loss of free energy in a coupled reaction which drives the endergonic synthesis of PP. I invoke one of the trimers as the catalyst that speeds up this coupled reaction. Just as gears and escapements coordinate the \u00aeow of processes in the real Carnot engine, I invoke their analogues in the hypothetical autonomous agent. Speci cally, I want the forward reaction synthesizing excess hexamer to happen rapidly, then I want the reverse reaction resynthesizing PP to occur. Accordingly, I assume that monophosphate (P) feeds back as an allosteric activator of the hexamer enzyme. Thus, the forward reaction proceeds slowly until the concentration of P rises su\u00af - ciently, then, thanks to the feedback activation of the hexamer enzyme, the forward reaction `\u00aeushes through\u2019, yielding excess synthesis of the new copies of the hexamer. Simultaneously, to stop the reaction resynthesizing PP from P + P, I invoke PP itself as an allosteric inhibitor of the enzyme catalyzing the resynthesis of PP from monophosphate. Thus, the forward reaction synthesizing hexamer occurs, then, after the concentration of PP falls, the resynthesis of PP occurs. My colleagues and I have written down the appropriate di\u00acerential equations for this system and it behaves as described. This system has a self-reproducing subsystem, the trimers and hexamer. And it has a chemical motor, the PP \u00c1! P + P reaction cycle. The engine\u2019s running can be seen by the fact that there is a net rotation of P counterclockwise around this reaction cycle. Thus, this hypothetical system exhibits a molecular autonomous agent. Several points need to be made. (i) This is a perfectly legitimate, if unstudied and new, class of open thermodynamic chemical reaction networks. (ii) The system does not cheat the second law. The system eats trimers and photons, and, via the work cycle, pumps that energy into the excess synthesis of hexamer. (iii) The system only works if displaced from chemical equilibrium in the `right\u2019 direction, towards an excess of trimers and photons. Agency only exists in systems displaced from equilibrium. (iv) As pointed out to me by Phil Anderson, there is energy stored in the excess concentration of hexamer compared with its equilibrium concentration. That energy could later be used to correct errors, as happens in contemporary cells. (v) Like the Carnot cycle, the autonomous agent contains a reciprocal and cyclic linking of spontaneous and non-spontaneous processes. Phil. Trans. R. Soc. Lond. A (2003) (vi) Like the gears of a real Carnot engine, the allosteric couplings achieve the organization of the processes that is integral to the autonomous agent. I should point out that we are likely to construct autonomous agents in the coming decades. Such systems actually do work and reproduce. They promise a technological revolution. Moreover, if I have stumbled onto an adequate de nition of life, they will constitute novel life forms. Sometime or another we will nd or make novel life forms, and the way will be open to the creation of a general biology, freed from the constraints on our imagination of the only biology we know." ] }, { "image_filename": "designv10_11_0000020_s1052618816040026-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000020_s1052618816040026-Figure3-1.png", "caption": "Fig. 3.", "texts": [ " The screws orthogonal to the obtained gradient screw belong to the five-member screw group. The scalar product of each of the five screws by the gradient screw equals zero. From this condition, we identify five kinematic screws that lead to the neighboring singular positions, viz., \u03a91(1, 0, 0, 0, 0, 0), \u03a92(0, 1, 0, 0, 0, 0), \u03a93(0, 0, 1, 0, 0, 0), \u03a94(0, 0, 0, 1, 0, 0), and \u03a95(0, 0, 0, 0, 1, 0). The positional relationship between the forcing screws Ei, the five obtained kinematic screws \u03a9, and the gradient screw \u03a9* is shown in Fig. 3. il \u0394 \u2212 \u2212 \u0394 = = \u2212 \u2212 \u2212 \u2212 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 ( ) 0. 0 0 1 1 1 0 0 0 1 1 1 0 1 0 1 1 0 1 U 294 JOURNAL OF MACHINERY MANUFACTURE AND RELIABILITY Vol. 45 No. 4 2016 ALESHIN et al. We should note that for the robot in question, the form of the singularity zones is easy to represent. In this case, the singular position zone is on the same plane as screws E1, E2, and E3 positioned between points B1, B2, and B3 and point A1. In this case, the five screws that lead to the neighboring singular positions are two translation displacements on the plane of screws E1, E2, and E3 and three rotations around point A1" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003331_msf.414-415.385-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003331_msf.414-415.385-Figure1-1.png", "caption": "Figure 1 a) Schematic view of laser cladding by powder injection and b) cross section of a laser clad coating.", "texts": [ "aser cladding by powder injection is a method of producing good quality, metallurgically bonded coatings with minimal heat input into the work piece (Fig. 1). Frequently, the aim of laser cladding is to improve the wear and corrosion resistance of surfaces, by generating a protective layer of a different material [1, 2, 3]. The laser cladding operating window is defined in terms of laser beam power (P) and spot diameter (D), scanning speed (S) and powder feed rate (F). However, not all combinations of the processing parameters will produce good quality coatings. Only values within limited ranges can be applied to generate tracks meeting the geometrical requirements to produce adherent and pore free coatings by overlapping single tracks [2, 4, 5]" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000886_j.mechmachtheory.2019.03.044-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000886_j.mechmachtheory.2019.03.044-Figure7-1.png", "caption": "Fig. 7. Assembly of gear pair: (b) is the magnified view in the green rectangular area of (a).", "texts": [ " The coordinate system S 1 ( x 1 , y 1 , z 1 ) and S 2 ( x 2 , y 2 , z 2 ) are attached to the pinion and the gear, respectively. The y 1 -axis and y 2 -axis are the rotational axes of the pinion and the gear, respectively. The axial misalignment can be simulated by the coupling of \u03b1 and \u03b2 , where are the deflection angles of coordinate system S 1 ( x 1 , y 1 , z 1 ) with respect to x f -axis and z f -axis, respectively. Symbols \u03b4 and a are the position misalignment of tooth width direction and center distance direction, respectively. The assembly of measured discrete tooth surfaces is illustrated in Fig. 7 . To determine the angular position of the pinion and the gear, the simulation of gear meshing is carried out, as shown in Fig. 8 . The handling of double-tooth-engagement situation is based on the assumption that two pairs of tooth surfaces are simultaneously meshing. Firstly, by adjusting the angular position of the gear pair, a pair of tooth surfaces just start to mesh. Symbols tf p and tf g are the tooth surfaces of the pinion and the gear, respectively. The pinion rotates counterclockwise at an angle of \u03b8p and the gear rotates clockwise at an angle of \u03b8 g to separate tf p and tf g " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000913_j.mechmachtheory.2019.06.026-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000913_j.mechmachtheory.2019.06.026-Figure3-1.png", "caption": "Fig. 3. Derivation of the angular velocity of a CMC.", "texts": [ " Thus, the absolute position vector of a CMC center relative to the frame F o is O o O L = O o O t b + O t b O L (9) Differentiating the O o O L with respect to t , the absolute translational velocity v I d can be obtained as v I d = [ \u02d9 xb \u02d9 yb \u02d9 zb ] + R T ob [ \u02d9 xd \u02d9 yd \u02d9 zd ] + R T ob \u02dc w b [ x lb + x d y lb + y d z lb + z AL + z d ] (10) where \u02dc w b is associated with w b of Eq. (6) [38] . At the right-hand side of Eq. (10) , the first term is due to platform motions. The second term is due to translational deformations of a CMC relative to the platform. The third term is induced by the coupling between the rotations of the platform and the translational deformations of a CMC. As described in Fig. 3 , the rotation of a CMC relative to the platform is described by the orientation of F 3 L with respect to F t b . Initially the frame F L is parallel to F t b . The rotational deformations of a CMC are described by Euler angles ( \u03b8 x d , \u03b8 y d , \u03b8 z d ) that are used as follows. The frame F L is rotated about Y L by \u03b8 y d , then about X 1 L by \u03b8 x d , finally about Z 2 L by \u03b8 z d , the new frame F 3 L is obtained. After that, similar to Eq. (4) , the angular velocity vector of a CMC in the frame F 3 L is obtained as w L 3 = ( w L 3 x , w L 3 y , w L 3 z )T (11) where w L 3 x , w L 3 y , and w L 3 z are components of w L 3 in the X 3 L , Y 3 L , and Z 3 L axes, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003581_0141-0229(91)90115-q-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003581_0141-0229(91)90115-q-Figure2-1.png", "caption": "Figure 2 Construction of a fermenter probe for in situ glucose monitoring and control of Bakers' yeast production", "texts": [ " A further development included an on-line flow dilution system which was used to extend the effective linear range and to improve the response and recovery time) 47'148 The use of mediator-modified electrodes circumvents the problem of oxygen supply. Such sensors are often oxygen-insensitive and suitable for in situ appli52 53 cation. A basic design of glucose biosensor ' has been developed in our laboratories into an in situ probe, capable of sterile operation and on-line calibration, that satisfies most of the above requirements for process monitoring and control.6-8 Figure 2 illustrates the probe design. The outer housing was made of stainless steel with a 0.22-~m polycarbonate membrane across the base. This housing was designed for installation in the fermenter top plate. After steam sterilization, the Perspex insert (containing the sensors and supporting elec- trodes) was placed in the housing. The bulk glucose concentration in Escherichia coli cultures was monitored by equilibrium diffusion across the membrane. The unit could also act as a flow cell for calibration" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003083_1.1285943-Figure12-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003083_1.1285943-Figure12-1.png", "caption": "Fig. 12 Finite element model of the modified outer ring", "texts": [ " Taking advantage of this feature, the FE model was constructed using four-node quadrilateral plane strain elements. A diagram of this type of element is shown in Fig. 11. The shape functions are: u5 1 4 @ul~12s !~12t !1uJ~11s !~12t !1uK~11s !~11t ! 1uL~12s !~11t !#1u1~12s2!1u2~12t2! (23) and v5 1 4 @v l~12s !~12t !1vJ~11s !~12t !1vK~11s !~11t ! 1vL~12s !~11t !#1v1~12s2!1v2~12t2! (24) where u and v are the displacements along the z and y directions, rom: http://vibrationacoustics.asmedigitalcollection.asme.org/ on 01/28/2 respectively. Shown in Fig. 12 is the mesh of plane-strain elements used to model the bearing. For the steel outer ring, structural elements were used. Considering the electro-mechanical interaction associated with the piezoelectric sensor, coupled-field elements were used for sensor output analysis. The constitutive equations for the piezoceramic material are: H $T% $D%J 5F @C# @e# @e#T 2@\u00ab# G H $S% 2$E%J (25) where $T% is a stress vector, $D% is an electric flux density vector, @C# is an elasticity matrix, @e# is the piezoelectric matrix, @\u00ab# is the dielectric matrix, $S% is a strain vector, and $E% is an electric field vector" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000087_60008-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000087_60008-Figure4-1.png", "caption": "Fig. 4: Phase trajectories of the system (6) in projection on the (p, q)-plane for the cases a) when there is no moving internal mass, \u03bc = 0, b) when self-acceleration takes place at \u03bc = 0.3, s = \u22120.1, \u03b5 = 0.2, and c) when the motion occurs bounded in the momentum space at \u03bc = 0.3, s = 0.2, \u03b5 = 0.2. The remaining parameters are I0 = 1, a = 1.", "texts": [ " The solid lines are plotted using data from the straightforward numerical integration of eqs. (6) with initial conditions p = 0, q = 0 for respective values of s and \u03bc, and the dots are plotted as obtained from (18). Let us discuss the arrangement of the phase space of the system. Without the moving internal mass, the dynamics of the Chaplygin sleigh in continuous time, as known [3,19,22], generate a family of orbits of elliptic form on the (p, q)-plane, which arrive asymptotically in time to a set of fixed points located on the positive semi-axis p (fig. 4(a)). For the sleigh with vibrating internal mass, the initial parts of the trajectories in the projection onto the (p, q)plane are similar to those shown in diagram (a), but when approaching the positive semi-axis p they do not stop and behave in a different manner (see panels (b), (c)). In the region of acceleration, the representative points in the (p, q)-plane approaching the positive semi-axis p gradually move along this axis further and further, that is accompanied by transversal oscillations (fig. 4(b)). Increase of the speed continues unlimitedly, following the power law u \u221d t1/3. In regions of bounded dynamics as the trajectories approach the positive semi-axis p, they begin to go back in the direction opposite to the previous case, towards the origin, performing transversal oscillations (fig. 4(c)), so they do not leave the bounded region of the generalized momenta. Coexistence of regular and chaotic regimes at large amplitudes of oscillations of the internal mass. \u2013 Let us turn now to discussion of the phase portraits on the plane (p, q) obtained from numerical iterations of the two-dimensional map (9), concentrating the attention on the parameter regions of bounded dynamics. In the absence of the oscillating internal mass (\u03bc = 0), the same situation as in fig. 4(a) takes place, with the only difference that interpreted in terms of the stroboscopic map, the representative points do not travel along the continuous trajectories, but make jumps along the curves drawn in the diagram. 60008-p4 As the amplitude of the oscillations of the vibrating mass increases, the dynamics become more complicated as seen from the illustrations in fig. 5. As the amplitude parameter grows, the transformation of the situation corresponding to fig. 4(a) leads to such a picture that the region on the phase plane occupied by the closed invariant curves (arisen with the initial conditions in certain domains) is surrounded by a region of chaotic motions (fig. 5(a)). The closed invariant curves correspond to quasi-conservative dynamics; indeed, the calculation of the Lyapunov exponents by standard methods [23\u201325] gives for the stroboscopic map (9) two values equal to zero (within numerical errors). On the other hand, trajectories located in the chaotic region have Lyapunov exponents, one of which appears to be positive, and the second is negative, exceeding the first one in absolute value" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001781_s12046-021-01650-z-Figure14-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001781_s12046-021-01650-z-Figure14-1.png", "caption": "Figure 14. Various cooling strategies for rotor cooling model, [77].", "texts": [ " A 22% drop in temperature near slots and a 51% temperature drop near teeth are significant because otherwise, they are always under high thermal stresses. A finite volume CFD was used to predict the coolant fluid flow velocity, pressure drop, and volume flow rate. ANSYS was used to predict the thermal performance of the model [76]. Various cooling strategies such as the inclusion of heat pipes, phase change materials, lamination cooling, air gap cooling, winding head cooling, and shaft cooling are investigated for the cooling enhancement, figure 14 [77]. Stator winding losses are considerable when PMSMs are operated under less speed conditions. Hence maximum stator temperature is the controlling point over here. In the case of PMSMs operating under high rotational speed conditions the majority part of losses is in the rotor and stator lamination. Hence, the high temperature in the permanent magnets is the controlling point. Direct rotor lamination cooling and direct end winding cooling approaches are investigated to enhance the operational range of the PMSM [77]" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003007_s0142-1123(98)00077-2-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003007_s0142-1123(98)00077-2-Figure8-1.png", "caption": "Fig. 8. Rings used for testing.", "texts": [ " Before reaching the test cell the lubricant in this study passed through a hydraulic-oil filter rated to \u03b23=200. \u03b23=200 rating means that one in two hundred particles of 3 \u00b5m will pass through the filter. The lubricant flow is approximately 0.3\u20130.6 l/min from the nozzle when performing a test. The lubricant used for this study is gearwheel oil, Shell Spirax 80W/90. The temperature of the oil during the testing was 80\u00b0C. Oil and filter changes were made at regular intervals. Exact dimensions of the rings are given in Fig. 8. The rings used in this project have been manufactured from a rolling bearing steel, SS 14 2258. This steel is also known as SAE 52 100 and DIN 100Cr6. The chemical composition of this material is shown in Table 2. The rings were turned to the right dimension, heat treated and then ground to reach a average surface roughness (Ra) of approximately 0.2 \u00b5m. The heat treatment was a quench and temper operation with a final surface hardness of approximately HRC 65 ( < > : 1 \ufffd R b sin \ufffd 1 2 \u03b3 \ufffd\ufffd2 1 R2 9 > = > ; (5) The situation of the flow pattern is more complex for a spiral bevel gear. For being convenient to study, the force exerted by the flow on any elemental helical gear (see Fig. 4) is represented in differential form. Some assumptions come from Akin and Ville [10,40]\u2014namely, the air flow impinging on a tooth is deflected by the previous tooth along the direction of rotation, which approximately limits the active tooth surface by a line from the leading edge of the next tooth to the tip corner on the trailing edge of the previous tooth (Fig. 5). The following assumptions are retained: \ufffd Permanent flow; \ufffd Friction forces between fluid and tooth flanks are negligible; \ufffd Inertia forces are ignored; \ufffd Homogeneous pressure in the environment. On the basis of the Newton equation, the differential force is expressed as: dF\u00bc \u03c1UdQ (6) with: \ufffd \u03c1: density of the fluid [kg/m3]; \ufffd dQ: differential of fluid flow [m3/s]; \ufffd U: fluid flow rate [m/s]. The projections on the axis (OX and OY) in the OXY coordinate system (Fig. 4) is given as follows, respectively. dFx\u00bc \u03c1U0dQ0 \u00fe \u03c1U1 sin \u03b2 0 dQ1 \u03c1U2 sin \u03b2 0 dQ2 (7) dFy\u00bc \u03c1U0 sin \u03b2 0 dQ0 \u03c1U1 cos \u03b2 0 dQ1 \u00fe \u03c1U2 cos \u03b2 0 dQ2 (8) And: sin \u03b2 0 \u00bc 1 D0 \ufffd R 0 e\u00fe Rem R0e \u00f0D0 sin\u03b2m Rem\u00de \ufffd R0e\u00bcRe b r 0 \u00bc \u00f0Re b\u00desin \u03b4 where Q1and Q2 are the volume flow rate in the direction of tooth trace, Q0 is in the direction of the radius (see Fig. 4). dFy does not involve in windage loss since this direction of force is parallel to the axial direction of the gear. The friction forces are negligible and the ambient pressure is homogeneous, the equation of velocities is presented: U0 \u00bcU1 \u00bc U2 (9) The projection on the axis (O\u2019t) in the reference system (O\u2019nt) is put forward: \u03c1U0 sin \u03b2 0 dQ0 \u00fe \u03c1U1dQ1 \u03c1U2dQ2 \u00bc 0 (10) And: dQ0 \u00bc dQ1 \u00fe dQ2 (11) So: dQ1 \u00bc 1 2 \u00f01 sin \u03b2 0 \u00dedQ0 (12) dQ2 \u00bc 1 2 \u00f01\u00fe sin \u03b2 0 \u00dedQ0 (13) Substitute Eq. (12) and Eq. (13) into Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001089_tia.2020.3046195-Figure22-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001089_tia.2020.3046195-Figure22-1.png", "caption": "Fig. 22. IR thermal image and predicted temperature distribution across the motor components at 600 s after power turning ON for coolant flow rates of 1 LPM.", "texts": [ " Parameter study of the contact resistance and effective windings density was carried out to achieve these results. Fig. 20 shows the IR and CFD images across the motor components at 600 s after power turning ON, and Fig. 21 shows measured (with error bar) and predicted temperature histories on stator end turn and lamination, both for the flow rates of 10 LPM. As expected, the temperatures of 10 LPM are lower than that of 3 LPM because more heat removed at high flow rate. The predicted temperatures match the measured data. Fig. 22 shows the IR and CFD images across the motor components at 600 s after power turning ON, and Fig. 23 shows the measured and predicted temperature histories on stator end turn and lamination, both for the flow rates of 1 LPM. The temperatures of 1 LPM are higher than that of 3 LPM because of less heat removed at low flow rate. The predicted temperatures on the windings end turn and lamination are slightly higher than the measurement. Overall, the predicted temperatures can match the measured data reasonably for different coolant flow rate by calibrating the thermal resistances and windings effective density for the motor thermal analysis procedure" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003807_j.euromechsol.2005.11.001-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003807_j.euromechsol.2005.11.001-Figure2-1.png", "caption": "Fig. 2. Member (and limb) of the second one-rotational and two-translational DOFs asymmetrical PKM family.", "texts": [ " G(x) is generated by any array of three pairs among R and P pairs, provided that the R axes are parallel to x and the P pair are perpendicular to x and eliminating the combination PPP that generates T2(\u22a5x) \u2282 G(x). The enumeration of limbs that generate G(z)G(y) without passive mobility between the distal bodies is now available online (Lee and Herv\u00e9, 2005). One can readily verify that any serial arrangement of a 2-DOF planar chain and a 3-DOF planar chain generates a doubly planar 5-DOF kinematic bond. Fig. 2(a) shows a member of another family that also provides one-rotational and two-translational DOFs. Two limbs generate G(x)R(O,y); a third limb generates T (y)G(y) = X(y) (if the axes of the R pairs are not in a plane). Again, using Lie group theory one can demonstrate the full-cycle mobility of that mechanism. The set of allowed displacements of the moving platform is G(x)R(O,y) \u2229 X(y). G(x) = T2(\u22a5x)R(A,x), \u2200A, X(y) = T R(B,y), \u2200B \u21d2 X(y) = T R(O,y), G(x)R(O,y) \u2229 X(y) = T2(\u22a5x)R(A,x)R(O,y) \u2229 T R(O,y) = T2(\u22a5x) [ R(A,x) \u2229 T (x) ] R(O,y) = T2(\u22a5x)R(O,y). This set is a product of a subgroup of planar translations and a subgroup of rotations. However, three fixed motors cannot actuate the platform motion. As a matter of fact, if the fixed joints are locked, then a 1-DOF motion can always happen because we have a planar 4R sub-chain explained by R(O,y) \u2229 G(y) = R(O,y). See Fig. 2(b) for a better view of that limb. This problem can be overcome by using another generator of X(y) without an unactuated planar subchain. Alternatively, one can exchange the location/order of the P and R joints or use a cylindrical joint. The other members of the family are obtained by replacing the generator RRR of G(x) by equivalent chains producing also G(x) and by replacing the generator PRRR of X(y) by other generators of the same Schoenflies motion. Fig. 3(a) shows a representative of a family of PKMs that can provide the platform with one-translational-tworotational DOFs" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001780_tro.2021.3082020-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001780_tro.2021.3082020-Figure6-1.png", "caption": "Fig. 6. Two-segment, four-axis, tendon-driven continuum robot with tubular ionic liquid stretch sensor proprioception. Details show (I) distal segment tendons, (II) proximal segment tendons, (III) distal segment sensors, (IV ) proximal segment sensors, (V ) flexible backbone, (V I) retro-reflective tracking markers, (V II) motor drivers, (V III) linear actuators, and (IX) continuum robot base component.", "texts": [ "7) was applied over the length of the electrode and overlapped with the start of the electric cable. 4) Sensor end preparation: The needle was pulled out of the sensor while injecting a small amount of additional liquid. At this point, the sensor was threaded through any holes too narrow to fit the electrodes (e.g., vertebral holes). 5) Second electrode attachment: The second electrode was inserted into the silicone tube as in first electrode attachment. The low cost, two-segment, dual backbone serpentine manipulator (Fig. 6) consists of 16 resin (Clear V2.0, FormLabs, Somerville, MA, USA) vertebrae of diameter 13mm and thickness 5.0mm, with the lower eight vertebrae forming the first (proximal) segment and the upper eight forming the second (distal) segment. Alternating bend directions at each vertebra give each manipulator segment two directions of flex. Each vertebra has a top and bottom bending planes and corresponding tapers to allow a wider range of motion. One set of three 0.45-mm Authorized licensed use limited to: BOURNEMOUTH UNIVERSITY. Downloaded on July 03,2021 at 07:42:14 UTC from IEEE Xplore. Restrictions apply. diameter, 7-core braided stainless steel tendons (Fig. 6.I) terminates after the 16th vertebra and drives the distal segment of the manipulator, while a second set of three tendons (Fig. 6.II) terminates at the eighth vertebra and drives the proximal segment. For this construction, the tendon offset angles are \u03c8P = 75\u25e6 and \u03c8D = 15\u25e6 (for proximal and distal segments, respectively). This common type of series continuum construction presents an additional control challenge from coupling between segments due to parasitic tendon forces. One pair of orthogonal through holes in each vertebra houses the distal TILSS (Fig. 6.III) while a second pair of orthogonal through holes houses the proximal TILSS (Fig. 6.IV). The proximal sensors run from the 0th vertebra (the manipulator base plate seen in Fig. 6.IX) to the 8th vertebra, and the distal sensors run from the 8th vertebra to the 16th vertebra. Dual super-elastic Nitinol backbone rods (Fig. 6.V) alternate bend direction after each vertebra, with a flexible length of 3.125mm each, giving each segment a length of 65mm and a total manipulator length of 130mm. A central passage allows for routing of sensor cables from the distal electrodes and power supply for end effectors. For this construction, the sensor offset angles are \u03c6P = 205\u25e6 and \u03c6D = 25\u25e6. Tendons are driven by six 100N-ELA (RS Pro, Corby, U.K.) linear actuators (Fig. 6.VIII) with LP3575S unipolar stepper motor drivers (Fig. 6.VII). The linear actuators\u2019 maximum torque limits the bend angle to a maximum of 50\u25e6 per segment. Six pulleys redirect the tendons by 90\u25e6 from the linear actuators to the vertebrae holes. The stepper motor drivers are connected to the digital output ports of a BNC-2110 breakout board (National Instruments, Austin, TX, USA) and PCI-6229 IO board and the robot is controlled from a EMP373 portable computer (ACME Portable, Azusa, CA, USA) at a frequency of 250Hz. Retro-reflective passive markers were positioned on surfaces attached to the 8th and 16th vertebrae (Fig. 6.VI) and an optical motion capture system (Vicon Motion Systems Ltd, Yarnton, The sensors are vacuum degassed tubular resistive stretch sensors which were prestretched to allow measurement in both bend directions (i.e., the sensor is under tension through the entire continuum segment stroke). U- and S-shaped electrodes were fitted to the center and end vertebrae with bends on the gold wire immediately after the silicone tubing to allow full range of motion for adjacent vertebrae. The sensor cables were connected to four isolated voltage dividers and subsequently to the analog input ports of the BNC-2110 breakout board (National Instruments, Austin, TX, USA) and PCI-6229 IO board (16 b, 250 kS/s). Table II shows the manipulator sensor constants, obtained using second-order polynomial regression of \u03be with data from 50 strain cycles (bends from \u03b5 = 0.15 to \u03b5 = 0.25). The marked difference between the value of \u03b2 for proximal and distal sensors was attributed to the difference in length and prestretch caused by a thick robot base component (IX in Fig. 6), although the exact reason for the causation is outside the scope of this work. It was observed that sensor resistance increases independently of elongation in the minutes following application of current before settling to a steady value. This warm-up time (measured to be 10\u201312 min regardless of sensor length or degree of degassing) was attributed to a relaxation effect as described in [55], where the potential difference across the sensor creates a field that Authorized licensed use limited to: BOURNEMOUTH UNIVERSITY" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001406_tmag.2021.3057391-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001406_tmag.2021.3057391-Figure3-1.png", "caption": "Fig. 3. Comparison of three proposed models. (a) Different stators with the same rotor and (b) the distribution of stator MMFs.", "texts": [ ", NdFeB, to overcome the risk of irreversible demagnetization because its magnetizing direction is opposite to the stator MMF direction. Therefore, the SPMM adopting hybrid NdFeB-Alnico magnets with a proper design can not only reduce the magnet cost but also maintain better torque performance. To reduce the torque pulsation, three proposed models are configured with 6-slot stator, 24-slot stator, and 27-slot stator, respectively, and the same 4-pole rotor with hybrid NdFeBAlnico magnets is all adopted, as shown in Fig. 3(a). Based on the analysis of the stator MMF in Section II, it can be known that the stator MMF is the key factor affecting the torque performance. The distribution of the stator MMF is depicted in Fig. 3(b). The fast Fourier transform (FFT) is performed and the Fourier series of the stator MMF of the three proposed models can be described as follows: F6s = \u221e\u2211 n=1 3Ni n\u03c0 ( sin n\u03c0 3 \u2212 sin 2n\u03c0 3 ) cos(n\u03b8) (1) F24s = \u221e\u2211 n=2,4\u00b7\u00b7\u00b7 4Ni n\u03c0 [ cos n\u03c0 8 \u2212cos 5n\u03c0 8 +2 ( cos n\u03c0 24 \u2212cos 11n\u03c0 24 ) +cos 5n\u03c0 24 \u2212 cos 7n\u03c0 24 ] sin(n\u03b8) (2) F27s = \u221e\u2211 n=1 Ni n\u03c0 [ 2 ( sin 4n\u03c0 9 +sin 8n\u03c0 9 \u2212sin 2n\u03c0 27 +sin 10n\u03c0 27 \u2212 sin 16n\u03c0 27 \u2212sin 26n\u03c0 27 ) \u2212 3 ( sin 22n\u03c0 27 + sin 2n\u03c0 3 ) +4 ( sin 2n\u03c0 9 + sin 8n\u03c0 27 \u2212sin 20n\u03c0 27 )] cos(n\u03b8) (3) where N is the number of turns per phase per slot winding, i is the rms value of stator phase current, and \u03b8 is the rotor angular position" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000977_j.triboint.2020.106258-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000977_j.triboint.2020.106258-Figure3-1.png", "caption": "Fig. 3. Turbulent and laminar flow zones.", "texts": [ " 2) is presented as: dF\u00bc 1 2 Cx\u03c1\u03c92r2ds \u00bc \u03c0Cx\u03c1\u03c92r3dr (1) with: \u03c1 is the fluid density, Cx\u00bc n \ufffd \u03c1\u03c9r2 \u03bc \ufffdm according to Ref. [10] (see Table 1), where n and m are coefficients up to the nature of the fluid flow surrounding the element annulus. Integrating the elemental friction force over the total surface (S), the dimensionless moment coefficient Cf is expressed as: Cf \u00bcM \ufffd 1 2 \u03c1\u03c92R5\u00bc n \ufffd \u03c1\u03c9 \u03bc \ufffdm 2\u03c0 R5 Z \u00f0S\u00de r4 2mdr (2) which, after dividing into laminar and turbulent flow zones, the dimensionless moment coefficient Cf transforms into (Fig. 3). Cf \u00bc 2n2\u03c0 5 2m2 \ufffd 1 Rem2 1 Re*m2 \ufffd R* R \ufffd5\ufffd \u00fe 2n1\u03c0 5 2m1 1 Re*m1 \ufffd R* R \ufffd5 (3) X. Zhu et al. Tribology International 146 (2020) 106258 with: ni, mi is coefficients for fluid flows, (i \u00bc 1, 2. 1 denotes laminar flows and 2 is turbulent flow); Re*is the critical Reynolds number approximately equal to 3x10\u2075; R is the outside radius for a disk or pitch radius for a gear; R*is the critical radius turning from laminar to turbulent zones, and expressed as R* \u00bc ffiffiffiffiffiffiffi \u03bcRe* \u03c1\u03c9 q ; Without the turbulent flow zone, Equation (3) would be simplified by setting R* \u00bc R and Re* \u00bc Re" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000371_j.isatra.2017.12.023-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000371_j.isatra.2017.12.023-Figure4-1.png", "caption": "Fig. 4. Tensions and weight of the infinitesimal element of a mooring line.", "texts": [ ", Reliability-based robust and offloading vessel with unknown time-varying disturbances and j.isatra.2017.12.023 the seabed by anchors as shown in Fig. 2. Due to the influence of buoys, the mooring lines are no longer catenary as shown in Fig. 3. However, the model of tension exerted on the FPSO vessel from the mooring lines can still be established based on the classic catenary's theory. For a mooring line, the weight is far greater than the buoyancy and fluid forces exerted on the mooring line, so the influence of buoyancy and fluid forces are ignored. Then, Fig. 4 shows the forces on a mooring line's infinitesimal elementds: In Fig. 4, uj is the mass per unit length of mooring line's sectionj;4 is the angle between the mooring line microelement and the horizontal plane, and Tis the mooring line tension. The tensions \u00f0T \u00fe dT and T\u00de and the weight \u00f0ujds\u00de keep the infinitesimal element in balance. Resolving T \u00fe dTand ujdsalong the tangential and normal directions ofds; the following equilibrium equations can be obtained: T sin d4 \u00bc uj cos 4ds; (7) \u00f0T \u00fe dT\u00decos d4 T \u00bc uj sin 4ds: (8) Since sin d4 \u00bc d4 and cos d4 \u00bc 1 when the angle d4 approaches dynamic positioning for a turret-moored floating production storage input saturation, ISA Transactions (2018), https://doi" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003901_ip-b.1984.0010-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003901_ip-b.1984.0010-Figure4-1.png", "caption": "Fig. 4 Schematic diagram of a doubly-fed machine with the primary winding on the rotor", "texts": [ "2 Doubly-fed machine as a generator A steady-state analysis may be based on the torque equations of Prescott and Raju [7]. Assuming the two applied voltages to be sinusoidal, these equations can be modified to form the two-axis equations of eqn. 3. Vd! % Vd2 rt+ Lyp COyLy Mp sco, M t + Mp COyM r2 + L SCOy L2 (3) where p is the derivative operator and s is the slip defined as and L1, L2, rlt r2 and M have the usual meanings, and coy = IOOTT. Eqn. 3 is derived from the equivalent circuit of Fig. 3 with the machine represented in quadrature dq-axes with the rotor as the primary as shown in Fig. 4. The load angle a can be considered as the leading or lagging phase displacement shown in Figs. 5A and 5B, and the voltages on the three axes are: - 0 0 ! Mp \u2014 SCO r2 + M L2 2 P idl' id2 iq2 S = CO, \u2014 CO2 CO, a is positive 1EE PROCEEDINGS, Vol. 131, Pt. B, No. 2, MARCH 1984 63 The torque is now a is negative where the suffixes 1 and 2 in the voltage terms correspond to the magnetic axes of the primary and the secondary, respectively. The transformation co-ordinate system, defined in Appendix 7.1, results in the following expressions for the dand q-voltages: (6) Inverting the matrix of eqn" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001176_j.mechmachtheory.2020.103969-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001176_j.mechmachtheory.2020.103969-Figure2-1.png", "caption": "Fig. 2. Geometric relationship between the actuation space and the configuration space.", "texts": [ " Unlike the multi-backbone robots [ 7 , 13 , 14 ] as well as the concentric tube robots [8] , the shape and the actuation forces of the cable actuated continuum manipulators can be approximately measured by sensing the effective length and the pull forces of the cables, and the relevant sensors can be mounted on the external of the manipulators [ 11 , 25 ]. This special structure makes it possible to realize impedance control in the configuration space, the operation space, as well as the actuation space. In this section, the kinematics and dynamics modeling method will be concisely reviewed since they will be used in this paper. In order to parameterize the CDCM, the coordinate frames are illustrated in Fig. 2 for the segment o i \u22121 \u2212 o i , i = 1 , 2 , . . . .N, where the base frame \u2211 i \u22121 is o i \u22121 \u2212 x i \u22121 y i \u22121 z i \u22121 , which is fixed to the center of the base disk, while the body frame i is o i \u2212 x i y i z i , which is fixed to the end disk, and the radius of all disks is the same R . Both the axes z i \u22121 and z i are tangential to the arc of the backbone i \u22121 . The torsion angle of the body with respect to the axis z i \u22121 is defined to be \u03d5 i \u22121 , while the dihedral angle \u03b8i \u22121 is defined to be the angle between the top and bottom disks, and the radius of the dihedral fan o i \u22121 \u2212 o i \u2212 A is r i \u22121 ", " This work is supported by the National Key R&D Program of China under Grant No. 2019YFB1309603 , the Natural Science Foundation of China under Grant 51775002 , the Natural Science Foundation of Beijing under Grants L172001 , 4204097 , 3172009 and 3194047 , and Beijing Municipal Education Commission under Grant KZ202010 0 09015 . The forward kinematics from the actuation space to the configuration space In order to obtain the kinematics relationships between the actuation space and the configuration space, referring to Fig. 2 and Fig. 3 , it is not difficult to get the following relationships r i \u22121 , j = r i \u22121 \u2212 R cos \u03d5 i \u22121 , j for j = 1 , 2 , 3 (A.1) Since the passing through points of the cables are distributed uniformly around the base cross section, without loss of generality, we can write down the following geometric relationships \u03d5 i \u22121 , 1 = \u03c0 2 \u2212 \u03d5 i \u22121 , \u03d5 i \u22121 , 2 = 7 \u03c0 6 \u2212 \u03d5 i \u22121 , and \u03d5 i \u22121 , 3 = 11 \u03c0 6 \u2212 \u03d5 i \u22121 (A.2) Under the assumption of piecewise constant curvatures, it can also be shown that \u03bai \u22121 = 1 / r i \u22121 , r i \u22121 , j \u03b8i \u22121 = i \u22121 , j and r i \u22121 \u03b8i \u22121 = i \u22121 (A" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000004_1.4033611-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000004_1.4033611-Figure9-1.png", "caption": "Fig. 9 Watt chains with seven prismatic joints", "texts": [], "surrounding_texts": [ "082301-6 / Vol. 138, AUGUST 2016 Transactions of the ASME Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jmdedb/935363/ on 01/27/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use" ] }, { "image_filename": "designv10_11_0003561_s0302-4598(01)00099-x-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003561_s0302-4598(01)00099-x-Figure1-1.png", "caption": "Fig. 1. Schematic representation of the spectroelectrochemical cell based on a gold capillary and optical fibres. Horizontal cross-section. For important dimensions, see Section 2.2 in the text.", "texts": [ "acid were purchased from Aldrich Dorset, England . \u017d .Buffer chemicals were from Merck Darmstadt, Germany . Piranha solution was prepared by mixing in a ratio of 3 to \u017d .1 concentrated sulphuric acid Merck and 30% hydrogen \u017d .peroxide Merck . All aqueous solutions were prepared \u017dusing water purified with a Milli-Q system Millipore, .Bedford, USA . A specially designed spectroelectrochemical cell with a volume of less than 1 ml and an optical path length of about 1 cm was constructed for the spectroelectrochemical \u017d .measurements see Fig. 1 . The cell was made of a 1-cmlong gold capillary with an inner diameter of 0.2 mm \u017d .Goodfellow, Cambridge, UK that served as the working electrode. The capillary was inserted into PEEK tubing and \u017d .glued within a Teflon housing see Fig. 1 , which served also as a basis for entire spectroelectrochemical cell. Opti\u017d .cal fibres diameter 50 mm were directed into the gold capillary by sliding them inside PEEK tubings with inner diameter of 100 mm. These PEEK tubings were mounted into plastic holders sliding on stainless steel rails to facilitate centering of the fibres and gold capillary of the cell \u017d .Fig. 1 . The inlet for loading the cell, the outlet, and the \u017d .fittings to connect the compartments not shown of a counter and reference electrodes were made from flexible \u017dsilicone tubing inner and outer diameters about 0.5 and 2 .mm, respectively to allow free moving of the mentioned < < \u017dparts. An Ag AgCl KCl reference electrode q197 mVsat .vs. NHE with diameter of about 0.3 cm was from Cypress \u017d .Systems Inc Lawrence, KS, USA . A platinum wire \u017d .Goodfellow served as a counter electrode. The potential was applied and controlled with a LC-3E Petit Ampere` \u017d ", " For this, the capillary was thoroughly cleaned by filling it with Piranha solution for a few minutes, followed by rinsing it with water. It was then electrochemically cycled eight times in 0.2 M NaOH be REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 9 The 3D finite element model of the stator with enclosure are shown in Fig. 16. The mechanical performance parameters of the enclosure are: density \u03c12=6821kg/m3, elastic modulus E2=110GPa and Poisson\u2019s ratio \u03bc2=0.25. The equivalent model of the enclosure is established based on the actual structure of the prototype. The outer diameter, inner diameter and axial length of the frame in the equivalent model are 260mm, 274mm and 270mm, respectively. 44 cooling ribs with the same length as the frame are uniformly attached to the outer surface of the frame, and the width and height of the cross section of the cooling rib are 3" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000625_j.jmatprotec.2018.06.027-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000625_j.jmatprotec.2018.06.027-Figure5-1.png", "caption": "Fig. 5. Schematic of the pin-on-disc rig and the dimensions of the samples.", "texts": [ " Six indentations tests were performed on the surface of each sample. Material phase identification was performed using the X-ray diffraction (XRD). The surface topography and metallographic * \u201cMeander\u201d is a scanning strategy defined in the Renishaw system. It scans the whole area successively using a zigzag pattern (Segura-Cardenas et al., 2017). examinations of the etched samples were carried out using a confocal laser scanning microscopy (CLSM) and scanning electron microscope (SEM). A pin-on-disc machine (Fig. 5) was used to study the influence of pores on lubricating behaviors of the SLMed pins. The diameter of round head pins is 6 mm. Disks were made of 38CrMoAl by conventional process. All discs were hardened to a depth of 0.5mm using ionnitriding technology. The measured hardness was approximately 1000 HV. The contacting surfaces of the disks were finished by polishing to a root mean square (RMS) value Ra=0.05 \u03bcm. SLM components are known to have a relatively rough surface finish (approximately Ra =5 \u03bcm, which is the best it can achieve)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003349_1464419001544124-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003349_1464419001544124-Figure1-1.png", "caption": "Fig. 1 (a) Time-dependent EHL contact problem and (b) equivalent spring damper model", "texts": [ " Owing to the high pressure in the lubricated rolling contacts, a strong interaction exists between the fluid film formation and the deformations of the contacting surfaces. This tribological phenomenon is called elastohydrodynamic lubrication (EHL). The transfer of vibrations through a rolling bearing is affected by the stiffness and damping behaviour of EHL contacts between rolling elements and raceways. To estimate the damping within a lubricated rolling contact, the time dependent behaviour of a single EHL contact is studied (see Fig. 1). The equations of motion for both the lubricant film and the contacting structural elements have to be solved. Greatly simplified analytical models as presented in the literature do not lead to satisfactory results (see the literature review in reference [3]). Hence, appropriate solutions of the contact problem can only be obtained numerically. Nowadays, with the help of advanced multigrid techniques [8, 9], the time dependent solution can be obtained within reasonable time. In the present work, damping values are calculated with a fast multigrid algorithm developed at the SKF Engineering and Research Centre BV", " It has been found that, for the considered parameter range (sufficiently high contact preloads and frequencies below 1000 Hz), the EHL contact behaviour can be taken to be linear viscoelastic (however, it is indicated in reference [2] that for certain parameter combinations, e.g. low speeds and high frequencies, EHL damping shows some frequency dependence). With the EHL algorithm, the vibration response (decaying vibration) of the rolling element to an initial velocity imposed on the rolling element can be calculated. From the decay rate of the vibration response, equivalent viscous damping coefficients, c, can be estimated as indicated in Fig. 1. It should be noted that the calculated EHL damping coefficients are dependent on the choice of the length of the \u2018inlet zone\u2019 of the EHL contact. The \u2018inlet zone\u2019 is the lubricated zone in front of the high-pressure area of the EHL contact (see Fig. 1). For different values of the inlet zone length, more or less oil is drawn into the EHL contact. This influences the calculated damping values. A more thorough investigation of the influence of the amount of lubricant in the contact and the effects of starved lubrication is a topic of current research. Although today\u2019s EHL solvers are quite fast, full numerical solutions for a complete bearing are still time consuming. For this reason, a simple power law for the equivalent oil-film damping coefficient of a single EHL contact was derived from the EHL calculations by performing a least squares curve fit on the numerical data", " The lubricant used (standard mineral oil) has a nominal viscosity of 68 mm2/s at a temperature of 40\u00b0C. The dash\u2013dotted lines indicate the amount of damping computed for damping sources other than the lubricant film (see Section 2.2). For these other damping sources a loss factor of 2 per cent was assumed. The two dashed lines indicate the range of EHL damping values obtained from calculations. A full range of damping values is obtained since the calculated values are dependent on the choice of the length of the inlet zone of the EHL contact (see Fig. 1). The two dashed lines are obtained for very small and very large values of the inlet zone length (values of between 1.5 and 4 times the length of the semi-major axis of the Hertzian contact ellipse). Further investigations of the influence of the inlet zone are being carried out. As can be seen from the presented results, measured and calculated damping values are of the same order of magnitude. The agreement reached in the present work is better than that reported in other relevant publications known to the author (see the review in reference [3])" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000346_j.mechmachtheory.2017.09.013-Figure10-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000346_j.mechmachtheory.2017.09.013-Figure10-1.png", "caption": "Fig. 10. 3D model of a 6R-U SLOL.", "texts": [ " Then for the rank of the motion screw system $ of kinematic chain ABCDEF, we have d = rank ($) \u2264 5 (29) where $ = [ $ A $ B $ C $ D $ E $ F ] According to Theorem 2 of thesis [25] , for the five screws $ A , $ B , $ C , $ D , $ E , no two of them lie in the same plane and no four of them lie on the same regular quadric surface, so they are linearly independent. On the basis of Eq. (29) , we have d = 5 (30) The mobility of ABCDEF is calculated as, M = d(n \u2212 g \u2212 1) + g \u2211 i =1 f i + v = 5 \u00d7 (6 \u2212 6 \u2212 1) + 6 + 0 = 1 (31) In the motion of kinematic chain ABCDEF, the above equations remain unchanged, so it is a 6R SLOL, which is defined as 6R-U SLOL, this kind of constructing method is feasible. This 6R SLOL is also the general form of the 6R Goldberg linkage [4,13] . A 3D model of a 6R-U SLOL is shown in Fig. 10 . The singular state analysis of 6R-U SLOL is similar to the 5R SLOL, we would take it in another study. In the synthesis process of 6R-U SLOL in Fig. 9 , we apply the configuration I to the combining parts 1 \u00a9 and 2 \u00a9, so there exist offsets for the joints A and F. In order to obtain the linkages with excellent deployability, we apply other configurations to the construction process and get several configurations for the 6R-U SLOL with zero joint offset. The added constraints of the 6R-U SLOL are shown in Table 3 , the construction process of 6R-U SLOL is shown in Table 4 " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003879_j.wear.2004.11.018-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003879_j.wear.2004.11.018-Figure8-1.png", "caption": "Fig. 8. Set-up consisting of two V-grooved guideways between which two balls roll. One guideway is fixed, while the other is actuated with a linear actuator.", "texts": [ " 6 and their quantitative values are of minor importance for the presented analysis. 4.3. Set-up with commercial guideway First, the results from the commercial guideway are detailed. Fig. 10 shows several hysteresis loops with different amplitudes for the commercial set-up at one position X. The figure also shows the identified virgin curve of the form represented by Eq. (14) for these loops. This virgin curve fits the F w han 0.1 m (Bently type 3300). Note that both force is aplied and displacement is measured at the centerline of the olling balls. As Fig. 8 shows, there is also a possibility to ary the preload on the guideway. Rails of different geometry V-angle) can be mounted and different balls (size and mateial) can be inserted in the set-up. In this way, the influence f these variables on the hysteretic friction can be measured nd classified. .2. Experimental results In all experiments, the steady-state response of the system o very low frequency sinusoidal input forces with a certain mplitude is measured. These steady-state responses are peridic and are called \u2018hysteresis loops\u2019", " Based on these initial experiments, the equivalent damping ratio at resonance \u03b6r seems to be a good global characteristic parameter to describe the guideway as it is positionindependent, in contrast to a detailed identification of the virg 4 l e g b d b o b 4 g t S s h T D ig. 11. Experimental results for four different positions of the commercial uideway. (a) Hysteresis loops for different positions (solid, dashed, dotted nd dashed-dotted line). (b) \u03b6r-curves for different positions. d P M L G B in curve, and describes the dynamics in one lumped quantity. .4. Set-up with roller guideway The specially designed set-up of Fig. 8 is used to anayze the dependency of the hysteresis characteristics and the quivalent damping ratio at resonance on material, load and eometric parameters of the guideway (see Table 1). The results on this set-up are expressed in terms of a single all, so that global results of a guideway system can be deuced in function of the number, size, orientation, etc. of the alls. Multiple balls can be handled as a parallel connection f single balls. (Note that \u03b6r is independent of the number of alls). .4", " An examination of the Maxwell-slip model will reveal this fact, which is consistent with the experimental results obtained, namely that the harder (therefore stiffer) materials show smaller pre-rolling distance [9]. The corresponding \u03b6r-curves are shown in Fig. 12b. From this figure, it can be concluded that the (small) difference in the hysteresis loops for the diamond coated steel balls and the Si3N4 balls are hardly detectable in the \u03b6r-curves for these two ball materials. The \u03b6r values of the guideway with the steel balls are approximately 22% lower than those of the two other ball materials. 4.4.2. Various loads o with different weights on the cantilever beam of Fig. 8. The load for one ball is derived as: (equivalent mass of the cantilever + added mass) \u00d7 5 \u00d7 9.81/2, with 2 being the number of balls. Fig. 13a shows hysteresis loops for several loads of the configuration with steel balls with a diameter of 6 mm and a groove angle of 90\u25e6. Although a large number of load increments has been used only a set is displayed to improve the clarity of the figure. Increasing the normal load leads to increasing the contact area (real and apparent) and therefore the tangential stiffness of the contact" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000852_01691864.2019.1707708-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000852_01691864.2019.1707708-Figure1-1.png", "caption": "Figure 1. Lifting forces and restorative torque.", "texts": [ " The statics model of body bending has been used to analyze the stress situation in bendingwork. The Chaffin and Anderson back force model [22] was adopted in this paper, which treats the human body as a rigid body and evaluates the fatigue of backmuscles by analyzing the torque at the hip joint. The objective of this is to examine the feasibility and effectiveness of the implementation of a control algorithm to minimize the erector spinae muscle force at L5/S1 using a trunk-supporting exoskeleton. Considering Figure 1 as a simple model (one degree-of-freedom) of the human torso, the erector spinae muscle force and FM , can be represented by Equation (1) [23]: FM = (Fmlm + Fnln) g d sin\u03b2 \u2212 \u03b2\u0308 I d (1) where Fm and Fn represent the mass of the upper body and the part to be lifted, respectively. Body and part lengths from L5/S1, lm and ln are shown in Figure 1, and d is the distance between the Erector spinae muscle force and the spine center. To reduce themoment at L5/S1, we intend to impose a torque at the exoskeleton torso to help the operator during a lifting task. When the worker wears an exoskeleton, the exoskeleton system imposes a force F on the worker\u2019s upper body. Rewriting equations (1) while incorporating F results in equations (2) for FM : FM = (Fmlm + Fnln) g d sin\u03b2 \u2212 \u03b2\u0308 I d \u2212 FL d (2) In theory, if F is chosen as Equation (3), then FM reduces to zero (Equation 4): F = 1 L (g(Fmlm + Fnln) sin\u03b2 \u2212 \u03b2\u0308I) (3) FM = 0 (4) This means, in theory, it is possible to reduce the erector spinae muscle force FM , to zero by controlling the force acting on the person F" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000020_s1052618816040026-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000020_s1052618816040026-Figure1-1.png", "caption": "Fig. 1.", "texts": [ " To develop the subject, in [13], the problem of searching for close neighboring singular positions is solved by identification of the components of the gradient screw and \u201corthogonally\u201d positioned kinematic screws that transfer robots into these positions. The purpose of this work is to ascertain how the mount point coordinates of kinematic chains of a parallel-structure robot affect the kinematic gradient screw that withdraws the robot from singular positions most quickly. The method is set forth in [13\u201315]. It consists in identifying the fastest change in the matrix determinant of the Plucker coordinates of single forcing screws. Let us consider a spatial parallel-structure robot (Fig. 1) with six degrees of freedom, where Ai and Bi are the points of the output link and the base and ri(rxi, ryi, rzi) and \u03c1i(\u03c1xi, \u03c1yi, \u03c1zi) are the vectors that connect the origin of the fixed coordinate system to the points (i = 1, 2, \u2026, 6). The output link of the robot is subjected to the action Ei of the forcing screws located on the linear actu- ator axes Ei = ei + , (i = 1, 2, \u2026, 6), where k2 = 0 and ei \u00b7 = 0. The coordinates of vector ei are expressed through the coordinates of the corresponding points (xAi \u2013 xBi)/li, (yAi \u2013 yBi)/li, and (zAi \u2013 zBi)/li, where " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001005_tasc.2020.2990774-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001005_tasc.2020.2990774-Figure4-1.png", "caption": "Fig. 4. 1/4 MEC diagram of DSRLM and 3D amplification of the end part at unaligned position.", "texts": [ " Due to the end-effect, the inductance of the unaligned position increases by 20%\u201330% [18], [19], and the inductance of the motor is directly related to the reluctance of the air gap. Since the magnetic field line at the air gap is divergent than the magnetic field line at the silicon steel sheet, it is not suitable to utilize the simple two-dimensional MEC method for DSRLM. Therefore, this paper performs three-dimensional decomposition of the air gap reluctance at unaligned positions. In the unaligned position, the 1/4 of the motor\u2019s MEC diagram and the 3D amplification effect of the end portion are shown in Fig. 4. Then according to the symmetry of DSRLM, the MEC diagram of the whole motor is simplified to Fig. 5. In Fig. 5, \u03c61, \u03c62, \u03c63, \u03c64 and \u03c65 are magnetic fluxes of several loops respectively. Referring to the loop current analysis method in the circuit theorem, this paper lists five loop equations for the equivalent magnetic circuit: R11\u03c61 +R12\u03c62 +R13\u03c63 +R14\u03c64 +R15\u03c65 = 4 (F1 + F2 + F3) (1) R21\u03c61 +R22\u03c62 +R23\u03c63 +R24\u03c64 +R25\u03c65 = 4F1 (2) R31\u03c61 +R32\u03c62 +R33\u03c63 +R34\u03c64 +R35\u03c65 = 4F1 (3) R41\u03c61 +R42\u03c62 +R43\u03c63 +R44\u03c64 +R45\u03c65 = 4F2 (4) R51\u03c61 +R52\u03c62 +R53\u03c63 +R54\u03c64 +R55\u03c65 = 4F2 (5) And they are simplified as following: \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 R11 4Rsp1 4Rsp1 4Rsp2 4Rsp2 4Rsp1 R22 4Rsp1 4Rsp2 0 4Rsp1 4Rsp1 R33 0 \u22124Rg1 4Rsp2 4Rsp2 0 R44 4Rsp2 4Rsp2 0 \u22124Rg1 4Rsp2 R55 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 \u00b7 \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 \u03c61 \u03c62 \u03c63 \u03c64 \u03c65 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 = \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 4(F1 + F2 + F3) 4F1 4F1 4F2 4F2 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 (6) In this formula: R11 = 4 ( Rsp1 +Rsp2 +Rsp3 + 1 2 Rg3 + 1 4 Rmp + 1 2 Rsy2 +Rsy1 ) (7) R22 = 4(Rsp1 +Rg1) (8) R33 = 4(Rsp1 +Rg1) (9) R44 = 4(Rg1 +Rsp2 +Rg2) (10) R55 = 4(Rg1 +Rsp2 +Rg2) (11) Next, the reluctance of each part of the air gap is specifically determined" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000530_978-3-319-45340-8-Figure5.2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000530_978-3-319-45340-8-Figure5.2-1.png", "caption": "Fig. 5.2 Top view a and cross-sectional view b of the high-temperature and high-pressure cell for optical microscopy. 1 Optical window, 2 reactor body, 3 stopper, 4 Belleville spring, 5 compression nut, 6 thermocouple. Adapted with permission from (Deguchi and Tsujii 2002)", "texts": [ " Deguchi (&) Research and Development Center for Marine Biosciences, Japan Agency for Marine-Earth Science and Technology (JAMSTEC), 2-15 Natsushima-Cho, Yokosuka 237-0061, Japan e-mail: shigeru.deguchi@jamstec.go.jp \u00a9 Springer International Publishing AG 2017 H. Ehrlich (ed.), Extreme Biomimetics, DOI 10.1007/978-3-319-45340-8_5 119 We have developed high-temperature and high-pressure cells that can be used with optical microscope so that direct observation of behaviors of polysaccharides can be performed in hydrothermal conditions with high optical resolution (Deguchi and Tsujii 2002; Mukai et al. 2006). Figure 5.2a, b show a top view and a cross-sectional side view of a cell body. The cell was designed to operate above the critical point of water up to 400 \u00b0C and 35 MPa. Unlike water at ambient conditions, corrosion is a severe problem in supercritical water (SCW) (Shaw et al. 1991). Thus, the cell body was machined from a block of corrosion-resistant Ni-based superalloy, Inconel 600. The outer dimension of the cell body was 80 \u00d7 40 \u00d7 35 mm, and a sample chamber of 3.18 mm \u00d7 1/8 in. ID was bored. The volume inside the chamber was 0", "3 mm thick) and fixed by a compression nut. Initially flat titanium gasket deformed as the compression nut was driven to 25 Nm and made effective seal between the window and the cell body. Two Belleville washers (10 mm ID, 20 mm OD, 9 mm thick) were placed between the window and the compression nut to accommodate the thermal expansion mismatch among Inconel 600, titanium, and diamond. Temperature of the sample inside the reactor was monitored by a chromel\u2013alumel thermocouple (1.59 mm \u00d7 1/16 in. OD, 6 in Fig. 5.2), inserted in the cell body and located 10 mm away from the sample. Tubes of 3.18 mm \u00d7 1/8 in. ID, also made of Hastelloy C22, were welded at both ends of the sample chamber and served as an inlet and outlet of the reactor. The cell body was placed between two heater blocks made of brass. Two 250 W electric cartridge heaters were embedded in each block. The sample was heated indirectly by the heat transfer from the heater blocks to the reactor body. The cell body and the heater blocks were contained in a cooling jacket (150 \u00d7 150 \u00d7 62" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001584_tmech.2021.3068622-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001584_tmech.2021.3068622-Figure5-1.png", "caption": "Fig. 5. Preliminary experiment testbench", "texts": [ " Although previous studies have modeled this type of nylon fiber rope [19], modelling the fibers of this rope is difficult because several strands are twisted spirally with each other; consequently, when subjected to a force, the physical properties of nylon as well as its geometrical characteristics are altered. Therefore, assuming that the nylon fiber rope does not change with respect to time, the rope can be expressed as a simple model where the spring and damper are connected in parallel, as shown in Fig. 4. This model was analyzed using preliminary experiments and analyses. The test bench in Fig. 5 can be divided into two parts. First, a measurement structure consisting of a load cell and linear encoder was used to measure the tension and vertical position of the rope, respectively. Additionally, weights (initial mass) can be attached to create a spring-damper system of the rope in order to account for the robot's mass. Second, the test bench involves an electromagnet and a transport structure. The electromagnet can generate a tensile force (additional weight) of up to 250 kgf. The transport structure is driven by a motor at the bottom of the test bench, which can generate a tensile force of up to 90 kgf" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003280_0731-7085(95)01040-r-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003280_0731-7085(95)01040-r-Figure3-1.png", "caption": "Figure 3 J o b ' s c u r v e s o f e q u i m o l a r so lu t ions . CKPL -~- CR = 2 .5 X l0 4 M; p H 4 .03; p. = 0.5 M.", "texts": [ "3 analyte is necessary for maximum complex formation; the absorbance did not increase when a further excess of palladium(II) chloride o.2 was used. Little influence of ionic strength (0.05-1.00 M) on the course of the reaction was observed. 0.~ Under these conditions the complex was completely formed after 5 min and was unchanged up to 24 h. Composition of the captopril-palladium(I1) complex The composition of the complex was established by the continuous - - variation method [15, 16]. The plot reached a maixmum at a fraction Xmax 0.33 which indicates the formation of 2:1 captopril-palladium(II) complex (Fig. 3). The curves obtained by the molar ratio method [17] show a break point at a captopril: Pd(II) molar ratio of 2:1 (Fig. 4). The results were confirmed by means of Nash's graphical method [18]. A linear dependence was found for y2 = f ( -x) (Fig. 5), where: 38Ohm 370 nm i 0.5 1.0 115 2.0 tool R molKPL F i g u r e 4 M o l a r r a t i o m e t h o d . CKPL = 1.5 X 10 -4 M; p H 4.03; p~ = 0.5 M. % 3 2 I 0 -1 -2 /; 380nm 370nm 0.2 0.3 0.4 - x F i g u r e 5 N a s h ' s m e t h o d . CKPU = 6 X 10-5--1" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003235_1.1332398-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003235_1.1332398-Figure4-1.png", "caption": "Fig. 4 The spindle model", "texts": [ " Values below 2ms result in unacceptably long computation, whilst for values in excess of 10 ms computational inaccuracies may result. A fixed step size of 5 ms is employed and the percentage error is set at eq50.05 percent. The results presented below further examines the response characteristics of the grinding spindle reported by Aini et al. @10#, this time under lubricated contact conditions in the support bearings. The following are the particulars of the model employed. This arrangement of the precision grinding spindle as shown in Fig. 4 is used unless otherwise stated. Oil film viscosity, ho : 0.37 Ns/m2. Pressure-Viscosity coefficient, a: 15.1029 m2/N. Modulus of elasticity, E: 206.109 N/m2. Poisson ratio, y: 0.33 Inner race bore, 0.04 m Inner race diameter, 0.046 m Outer race diameter, 0.062 m Ball diameter, D: 0.00794 m Unloaded contact angle, ao : 15\u00b0 Number of balls per bearing, 16 Pitch diameter of the ball set, 0.054 m Length of the shaft, (a1a11b1): 0.421 m Mass of the shaft, M: 5.5 kg Distance between the support bearings, 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000716_j.mechmachtheory.2019.07.013-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000716_j.mechmachtheory.2019.07.013-Figure2-1.png", "caption": "Fig. 2. Definition of the rack cutter with parabolic profiles and applied coordinate systems.", "texts": [ " Generation of tooth surfaces of the conical spur involute shaper and the mating face gear is explained in this section. Tooth geometries of the conical spur involute shaper are determined by a rack cutter with slightly tilt installation and simultaneous consideration of meshing equation. Tooth surfaces of the face gear are determined by the conjugate motion of the conical spur involute shaper. A straight rack cutter with parabolic profiles is defined aiming to obtain a profile crowned conical spur involute shaper. The shaper will be then used to generate a profile crowned face gear. Fig. 2 shows the generating surfaces of the rack cutter and the applied coordinate systems. A point P located on the profile is considered as a generating point of the tooth surface of the rack cutter. Two auxiliary coordinate systems S a , S b are established for coordinate transformation. The equation of the generating surfaces r of the rack cutter is represented in the coordinate system S r as: r r ( u s , l s ) = M rb ( l s ) M ba r a ( u s ) , r a ( u s ) = \u23a1 \u23a2 \u23a3 a s u 2 s \u2212u s 0 1 \u23a4 \u23a5 \u23a6 (1) where, M rb ( l s ) = \u23a1 \u23a2 \u23a3 1 0 0 0 0 1 0 0 0 0 1 l s 0 0 0 1 \u23a4 \u23a5 \u23a6 (2) M ba = \u23a1 \u23a2 \u23a3 \u00b1 cos \u03b1n \u00b1 sin \u03b1n 0 \u00b1( L d cos \u03b1n + u 0 sin \u03b1n ) \u2212 sin \u03b1n cos \u03b1n 0 u 0 cos \u03b1n \u2212 L d sin \u03b1n 0 0 1 0 0 0 0 1 \u23a4 \u23a5 \u23a6 (3) r a ( u s ) is the position vector of generating point P represented in coordinate system S a . u s and l s ( Fig. 2 ) stand for the two parametric coordinates of tooth surfaces of the rack cutter. a s is the parabolic coefficient for the modified profile of the rack cutter. Parameter u 0 controls the shift distance of the tangent point O a of the parabolic profile from the origin O b of the coordinate system S b along the positive part of axis y a . Matrices M rb ( l s ) and M ba describe the coordinate transformation from the coordinate system S a to the coordinate system S r . The upper sign in matrix M ba corresponds to left tooth surface of the rack, and the lower to the right" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001190_tmag.2020.3009479-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001190_tmag.2020.3009479-Figure7-1.png", "caption": "Fig. 7. Eddy current in the conductor disk. (a) Density distribution. (b) Real paths.", "texts": [ " , 8, and Fn is the traction force corresponding to loops 1\u20138. Both FEM and experiment are used to verify the validity of the 2-D model established. The results obtained by the two methods are compared with those obtained by the analytical calculation. The parameters of the finite element model are consistent with Table I. Fig. 5 shows the structure of the 3-D model. In addition, the meshing of PMs, air gap, and the conductor is refined to ensure the accuracy of simulation results. The FE model meshed is shown in Fig. 6. Fig. 7(a) and (b) shows the density distribution and trends of eddy current in conductor disk, respectively. Fig. 7(a) shows that the magnitudes of eddy current in iron teeth and back iron are negligible compared with that in the conductor. Fig. 7(b) shows that the paths of eddy current in each fan conductor of conductor disk are different. The distributions of eddy current are mainly shown as an elliptical shape in a single fan conductor or an elliptical ring shape in the adjacent fan conductors (the specific shape is determined by the geometry of the conductor disk). These distributions are caused by the variation of the areas of conductor and iron teeth facing PMs during movement. Fig. 8 shows the experimental measurement system, including a prime motor, two torque sensors, and a magnetic particle brake, which is used to provide load" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000971_1077546319896124-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000971_1077546319896124-Figure1-1.png", "caption": "Figure 1. Meshing process of standard helical gears.", "texts": [ " The meshing process in the course of dynamic modeling of a helical gear pair has not been fully considered. Compared with spur gear, the theoretical meshing process of a helical gear pair can be described as follows. Take the driven gear as an example, first, driven gear meshes-in from the tooth top in the front end (B1 point). Second, the contact line changes from short to long. Then, the contact line changes from long to short. Finally, driven gear meshes-out from the tooth root in the back end (E0 point). Obviously, the meshing line \u0394L is longer than that of the spur gear (Figure 1). The change of contact line on tooth surface is shown in Figure 2. In aforementioned description, it is an ideal contact condition without considering the machining error, installation error, and modification of gear. Actually, it is improper to ignore them. According to Fang (1997a, 1997b) and Litvin et al. (1999), the path of contact on the tooth surface is shown in Figure 3. From Figure 3, it can be found that the meshing process considering errors and modification of helical gears can be described as follows" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003448_1.1539514-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003448_1.1539514-Figure3-1.png", "caption": "Fig. 3 Lines of the Jacobian in W \u201eworld coordinate system\u2026", "texts": [ " yield: JT5B21A (9) Where B21 is given by: B215F I 0 @2p3# IG (10) Contrary to wRpui , which is a varying vector in W, the vector bi is constant in W. This simplifies the expression of the derivative of JT. In this formulation, the lines of A pass through fixed points, bi , in W and therefore their derivatives are easily shown to be lines as will be shown later. The physical interpretation of multiplying a Plu\u0308cker line\u2019s coordinates by the matrix B21 is a translation the line while maintaining its direction. Figure 3 shows a 6-6 Stewart-Gough platform manipulator with the lines of the Jacobian in W indicated by thin arrows. Another important feature of B21 is that its determinant is equal to 1, which means that the above multiplication, Eq. ~9!, does not add to the singularities of J. 3 Formulation of the Derivative of the Jacobian Matrix The derivatives of Jt with respect to the moving platform\u2019s position variables is obtained from Eq. ~9! as: dJT dx 5 dB21 dx A1B21 dA dx (11) The matrices dJT/dx, dB21/dx, dA/dx are three-dimensional 63636 matrices for non-redundant six degrees-of-freedom manipulators" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003796_j.conengprac.2004.07.004-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003796_j.conengprac.2004.07.004-Figure1-1.png", "caption": "Fig. 1. Actuator\u2019s position in CS2.", "texts": [ " CS2 is a scale model (scale 1 70 th approx.) of an oil platform supply ship, which has been developed at the Department of Engineering Cybernetics at NTNU. The testing of the optimised controllers in the real model has been performed in the MCLab at NTNU. The MCLab is an experimental laboratory for testing of ships and underwater vehicles. The length of CS2 is 1.255m and its mass is 23.8 kg. It is actuated by means of a tunnel-thruster placed at the bow and two main propellers with rudders situated at the stern as shown in Fig. 1. For position measurement purposes, CS2 is fitted with three three-dimensional emitters. The signals emitted are detected by four PC/cameras that provide the measurements of the (x, y) coordinates plus the heading angle to the user. CS2 is also equipped with an onboard PC running QNX real-time operating system. The control calculations are performed in real-time by an onshore PC. The connection between both PCs is made through a wireless Ethernet link and an automatic C-code generator. Matlab Simulink and Real Time Workshop are coupled with a graphical user interface in LabView to provide a real-time presentation of the results", " / Control Engineering Practice 13 (2005) 739\u2013748 741 produced (assuming M to be invertible): _m _g \u00bc M 1\u00f0C\u00f0m\u00de \u00fe D\u00de 0 J\u00f0g\u00de 0 \" # m g \u00fe M 1 0 \" # s: (1) Here M is the mass/inertia matrix, C is the Coriolis matrix, D is the damping matrix and J is the Euler matrix. Also, m \u00bc u; n; r\u00bd T is the body-fixed linear and angular velocity vector, g \u00bc \u00bdx; y;c T denotes the position and orientation vector with coordinates in the earth-fixed frame and s \u00bc \u00bdt1; t2; t3 T is the input force vector, given that t1; t2 and t3 are the forces along the body-fixed X- and Y-axes, and the torque about the body-fixed Z-axis, respectively (see Fig. 1). This expression corresponds to a non-linear statespace equation in the form: _x \u00bc A\u00f0x\u00de x \u00fe B s: (2) In order to evaluate the robustness against environmental disturbances of the controllers obtained through the GA optimisation, simulations of manoeuvres in the presence of environmental disturbances have been carried out. There are three main types of environmental disturbances: wind-generated waves, ocean currents and wind. However, in this research the analysis has been restricted to the disturbance considered to be the most relevant for surface vessels, i" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003710_0957-4158(92)90043-n-Figure10-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003710_0957-4158(92)90043-n-Figure10-1.png", "caption": "Fig. 10. Transfer mot ion from the wall to ceiling.", "texts": [ " To build up a control program, the walking motion was simulated by a computer . Two cases are presented as an example. One is walking on a vertical wall, and the other is a transition motion f rom the vertical wall to the ceiling. In Fig, 8 the analysed motion on a vertical wall is presented and for each station the force acting on the fixed sucker is shown in Fig. 9 by using the corresponding letters. The abscissa is the distance h and / is given in Fig. 4. The transition motion from a vertical wall to ceiling is shown in Fig. 10. It can be seen that the most severe condition is given by point i or j in this figure and this is verified from Fig. 9, i.e. the largest value of F/W is assumed for a point of i or j. The required negative pressure in the cup is given in Fig. 11 on the curves of blower performance. Assumed curves of A and B correspond to lesser and larger leakages, respectively. The amount of leaked air depends on the wall surface roughness and the shape and material of the peripheral lip. If the surface is fiat and smooth, the leaked air is small and higher pressure can be obtained for the same motor input voltage" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001779_s10999-021-09548-8-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001779_s10999-021-09548-8-Figure1-1.png", "caption": "Fig. 1 Virtual prototype of the parallel manipulator. (Color figure online)", "texts": [ " 3 that discusses the mobility and singularities of the translational manipulator. Its dynamic formula and several important indices are separately presented in Sects. 4 and 5. The parallel manipulator is consisted of three identical branches. Each branch contains an active prismatic joint connected to the fixed platform, a parallelogram module (4R links) in the middle, and a passive prismatic joint attached to the moving platform. The conceptual design of a vertical milling parallel machine based on this mechanism is shown in Fig. 1. The whole architecture will be upside down for operation. The schematic design of this manipulator is represented in Fig. 2. The global coordinate system attached to the base is also established as shown in Fig. 2. All inclined links (red rods in Fig. 1) have the same length. The driving joints in limb A and B, and the passive prismatic joint of limb C are parallel to axis X. Two passive prismatic pairs of limb A and B, and the active joint of limb C are parallel to axis Y. The revolute joints axes of two parallelogram modules in limb A and B are parallel to axis Y, while the other rotational joints axes are parallel to axis X. Since two passive prismatic joints of limb A and B own the same kinematic condition, these two joints coincide to promise a compact design", "1 Reachable workspace The reachable workspace generally denotes all the feasible poses (positions and orientations) the moving platform can reach. It is an essential step to analyze and evaluate the performance of a parallel architecture. For this parallel manipulator, it has a constant orientation workspace since the mobile platform only translates in 3D space. The dimensions of the proposed parallel structure are given here, L1 = 100 mm, L2 = 30 mm and L3 is 5 mm. Considering current configuration of the physical model shown in Fig. 1, the moving platform only moves above the base to avoid singularity. Thereby, the center of the moving platform is constrained in a cuboid above the fixed platform. The physical constraints are expressed as L3 x L1 L3 L3 y L1 L3 L3 z L2 L3 8>< >: \u00f025\u00de The strokes of three active sliders are constrained as 2\u00f0x x1\u00dek1 \u00fe 2\u00f0x x2\u00dek2 \u00bc \u00f0m3 \u00fe m5\u00de\u20acx\u00fe m2\u00f04\u20acx\u00fe \u20acx1 \u00fe \u20acx2\u00de \u00fe m2L 2 2 _z 2 2\u00f0x x1\u00de3 FE;1 2\u00f0y y1\u00dek3 \u00bc \u00f0m4 \u00fe m5\u00de\u20acy\u00fe m2\u00f02\u20acy\u00fe \u20acy1\u00de FE;2 2z\u00f0k1 \u00fe k2 \u00fe k3\u00de \u00bc m3 \u00fe m4 \u00fe 3 2 m2 \u20acz\u00fe m2L 2 2 2 \u20acz\u00f0x x1\u00de2 2 _z\u00f0x x1\u00de\u00f0 _x _x1\u00de \u00f0x x1\u00de4 \" # \u00fe \u00f03m2 \u00fe m3 \u00fe m4 \u00fe m5\u00deg FE;3 FA;1 \u00bc m1 \u20acx1 \u00fe m2 1 2 \u20acx1 \u00fe \u20acx \u00fe m2L 2 2 _z 2 2\u00f0x x1\u00de3 2\u00f0x1 x\u00dek1 FA;2 \u00bc m1 \u20acx2 \u00fe m2 1 2 \u20acx2 \u00fe \u20acx 2\u00f0x2 x\u00dek2 FA;3 \u00bc m1 \u20acy1 \u00fe m2 1 2 \u20acy1 \u00fe \u20acy 2\u00f0y1 y\u00dek3 8>>>>>>>>>>>>>>< >>>>>>>>>>>>>>>: \u00f024\u00de L3 x1 L1 2L3 2L3 x2 L1 L3 2L3 y1 L1 L3 8>< >: \u00f026\u00de Based on the inverse kinematic solution Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001760_tie.2021.3076715-Figure11-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001760_tie.2021.3076715-Figure11-1.png", "caption": "Fig. 11. Geometrical projection of lumped element-4 (Scale 1:1).", "texts": [], "surrounding_texts": [ "Geometrical parameters of PMSM and DC generator of experimental setup is given in Table III, which is used for natural frequency and mode shape calculations [30]. Geometrical projections of lumped elements 2, 3 & 4 are shown in Figs. 9, 10 & 11 which is required for inertia and stiffness matrix calculations. Further, damping and excitation torque is required for time response of torsional vibration of system. Authorized licensed use limited to: Carleton University. Downloaded on May 30,2021 at 21:54:56 UTC from IEEE Xplore. Restrictions apply. 0278-0046 (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. 7 Stiffness of any shaft under torsion is given by GiJi/Li, where Gi is Shear modulus of shaft and coupler (for stainless steel (Grade-304), Gi is 77\u00d7103 MN/m2). The material of shaft and coupler is steel having density of 7780 kg/m3 [31]. Ji is an area polar moment of inertia given by \u03c0di 4/32, where di is diameter of shaft and Li is the length of element. By using spring series addition and geometrical properties, equivalent mass polar moment of inertia and equivalent torsional stiffness for elements 2, 3 & 4 are calculated and given in Table IV, respectively." ] }, { "image_filename": "designv10_11_0003242_s0094-114x(00)00003-3-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003242_s0094-114x(00)00003-3-Figure1-1.png", "caption": "Fig. 1. Three-degree-of-freedom planar parallel manipulator.", "texts": [ " The closed-form dynamic equations of motion for the respective manipulators have been obtained with the help of Newton\u00b1Euler formulation [6]. All the numerical results were obtained by using the software package Matlab and the singular and non-STLC regions have been enumerated by checking the ``condition number'' of the H and C matrices respectively. The condition number and subsequently the rank de\u00aeciency of the C matrix has been calculated for low velocities of the output variables. The three-degree-of-freedom planar parallel manipulator, shown in Fig. 1, has three P. Choudhury, A. Ghosal /Mechanism and Machine Theory 35 (2000) 1455\u00b114791462 prismatic actuated joints and six passive revolute joints. The equations of motion of this planar manipulator are given by M \u00c8t a Z Hf 11 where the block elements of the mass matrix M are M11 MpE2 X3 i 1 Qi M12 MT 21 \u00ff MpR? X3 i 1 Qiqi? ! M22 Ip Mp \u00ff R2E2 \u00ff RRT X3 i 1 qT i?Qiqi? and Z 2666664 Mp \u00ff o2R\u00ff g X3 i 1 Ui \u00ffMpR g X3 i 1 qi Ui 3777775 P. Choudhury, A. Ghosal /Mechanism and Machine Theory 35 (2000) 1455\u00b11479 1463 H s1 s2 s3 q1 s1 q2 s2 q3 s3 f f1 f2 f3 T In the above equation, Z is the column vector containing the centripetal, Coriolis and other non-linear terms, H is the force transformation matrix and vector f denote the input actuations", " The workspace boundary has been evaluated based on the joint limits of all six prismatic joints. The controllability matrix for this manipulator has dimension 12 12. The regions where the STLC condition is violated along with the workspace boundary are shown on the right-hand side of Fig. 4. It can be seen that the non-STLC regions are surrounding the singular zones. P. Choudhury, A. Ghosal /Mechanism and Machine Theory 35 (2000) 1455\u00b114791468 If an additional actuated leg is added to the 3-DOF planar manipulator shown in Fig. 1, then we have the case of a redundant parallel manipulator with m> n. The equations of motion for the planar redundant manipulator shown in Fig. 5 are M \u00c8t a Z HF 14 where the block elements of the mass matrix M are M11 MpE2 X4 i 1 Qi M12 MT 21 \u00ff MpR? X4 i 1 Qiqi? ! M22 Ip Mp \u00ff R2E2 \u00ff RRT X4 i 1 qT i?Qiqi? and P. Choudhury, A. Ghosal /Mechanism and Machine Theory 35 (2000) 1455\u00b11479 1469 Z 2666664 Mp \u00ff o2R\u00ff g X4 i 1 Ui \u00ffMpR g X4 i 1 qi Ui 3777775 H s1 s2 s3 s4 q1 s1 q2 s2 q3 s3 q4 s4 f f1 f2 f3 f4 T In the above equation, Z is the column vector containing the centripetal, Coriolis and other non-linear terms, H is the force transformation matrix and vector f denotes the input actuations", " 9 where we plot the singular and non-STLC regions on the left- and right-hand side, respectively. The workspace boundary is calculated based on the leg-length limits satisfying the constraint equations. The non-STLC regions along with the positions at which the Lagrange multipliers become in\u00aenite (marked by ) are shown in the right-hand column. It can be observed that the Lagrange multipliers become in\u00aenite at some of the regions where the system does not meet the STLC requirement. If we use two actuators for the 3-DOF manipulator as shown in Fig. 1, then the manipulator is under-actuated. For this speci\u00aec case the H matrix will be rectangular of dimension 3 2. The manipulator will encounter force singularities when the rank of H matrix becomes less than 2. The numerical simulation for case is shown in Fig. 10. The singular and non-STLA regions are shown side by side. The numerical results were obtained by not actuating one of the legs in the 3-DOF manipulator shown in Fig. 1. P. Choudhury, A. Ghosal /Mechanism and Machine Theory 35 (2000) 1455\u00b114791474 In this paper, we have analyzed the singularities, non-STLA and non-STLC regions in parallel manipulators and closed-loop mechanisms. The singularities associated with a gain of degree of freedom were obtained by considering the rank de\u00aeciency of the force transformation matrix. The non-STLC and non-STLA regions of a parallel manipulator or a closed loop mechanism were obtained by considering the rank de\u00aeciency of the controllability matrix after deriving the equations of motion in terms of Cartesian space variables" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000238_1.4033045-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000238_1.4033045-Figure5-1.png", "caption": "Fig. 5 Cradle location of the cutter head for a left-hand gear (a) and right-hand gear (b)", "texts": [ "org/about-asme/terms-of-use zv l\u00f0 \u00de \u00bc 1 tan ai W 2 l l < W 2 Wi2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2 pi l\u00feW 2 Wi1 2 s \u00fe rpi W 2 Wi2 l < W 2 \u00feWi1 0 W 2 \u00feWi1 l < W 2 Wo1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2 pi l W 2 \u00feWo1 2 s \u00fe rpi W 2 Wo2 l < W 2 \u00feWo2 1 tan ap l W 2 l W 2 \u00feWo2 8>>>>>>>>>>>>< >>>>>>>>>>>>: xv l\u00f0 \u00de \u00bc l\u00fe rv 8>>>>>>>>>>>>>>< >>>>>>>>>>>>>: (1) where W is the point width of the cutter blade; rv is the radius of the cutter head; l is a variable of the tooth profile: the distance between the cutter blade and the radius of the cutter head; rpi and rpo are the fillet radius of inner blades and outer blades, respectively; other parameters Wi1, Wi2, Wo1, and Wo2 are all illustrated in Fig. 4 and can be calculated as follows: Wi1 \u00bc rpi= tan ai 2 \u00fe p 4 Wo1 \u00bc rpo= tan ao 2 \u00fe p 4 Wi2 \u00bc Wi1 sin ai\u00f0 \u00de Wo2 \u00bc Wio sin ao\u00f0 \u00de 8>>>>>< >>>>>: The surfaces of the cutter can thus be obtained by rotating the plane curve presented in Eq. (1) at an angle h rC\u00f0l; h\u00de \u00bc \u00bd xv\u00f0l\u00decos\u00f0h\u00de xv\u00f0l\u00desin\u00f0h\u00de zv\u00f0l\u00de 1 T (2) Figure 5 shows the cradle location with the cutter head and the coordinate system S2\u00f0O2 x2y2z2\u00de that is connected to the cradle. The radial distance of the cutter head can be calculated using the following equation: re \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2 f \u00fe r2 v 2rf rv sin\u00f0bf \u00de q (3) where rf is the mean cone distance, and bf is the mean spiral angle of the generated gear. The initial cradle angle of cutter /0 can be calculated as /0 \u00bc 6a cos r2 f \u00fe re 2 r2 v 2rf re ! (4) Positive cradle angle corresponds to a left-hand gear (Fig. 5(a)), and negative cradle angle corresponds to a right-hand gear (Fig. 5(b)). When generating a pair of noncircular bevel gears in contact, we assume that the cradle angle of the pinion is /0i, the cradle angle of the gear can be obtained Journal of Manufacturing Science and Engineering AUGUST 2016, Vol. 138 / 081013-3 Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/ on 01/07/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use /0o \u00bc 7/0i \u00fe /f 2 (5) where the index angle of the cradle is calculated by /f \u00bc 6 Lp zrf where Lp is the arc-length of mean pitch curve for the generated gear and whose calculation will be presented in Sec" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001406_tmag.2021.3057391-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001406_tmag.2021.3057391-Figure1-1.png", "caption": "Fig. 1. Topology of the basic SPMM model.", "texts": [ " The multi-objective genetic algorithm (MOGA) is adopted to optimize the quantities and proportion of Alnico and NdFeB magnets to improve torque performance and reduce the cost. To verify the effectiveness of the optimization, the optimized model with hybrid NdFeB-Alnico magnets is compared with other models with only NdFeB magnets at the same operating conditions, with the aid of the finite element method (FEM). Furthermore, the demagnetization analysis within five times of the rated current excitation is performed to verify the ability of the optimized model to resist irreversible demagnetization. A basic SPMM model with 6-slot/4-pole is investigated as shown in Fig. 1, in which each magnetic pole adopts a radially magnetized NdFeB magnet (span by 65 mechanical degrees). The main specifications of the motor are shown in Table I. For the SPMM operating at maximum torque per ampere, its stator MMF leads the rotor magnet by 90 electrical degrees (\u03b3 = 90\u25e6), as shown in Fig. 2. In this case, assuming that 0018-9464 \u00a9 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See https://www.ieee.org/publications/rights/index.html for more information" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003007_s0142-1123(98)00077-2-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003007_s0142-1123(98)00077-2-Figure7-1.png", "caption": "Fig. 7. The connection between slip ratio and tooth force on the probability of pitting on a gearwheel tooth, after [15].", "texts": [ " Slip is an important parameter in rolling/sliding contact fatigue. Studies [4,15] have shown that contact fatigue lives in contact fatigue model testing can be compared to data from gearwheel testing if the slip in the model test have the same slip ratio as that experienced on the surface of the gear where the maximum frequency of pitting is observed. The slip ratio on a gearwheel changes as the contact moves along the gear tooth. An example of how the slip and amount of pitting varies on a gear tooth is seen in Fig. 7. It should be noted that the author in [4] found that the maximum amount of pits are found at different positions depending on the material used for the gear. The example in Fig. 7 shows a situation where the maximum amounts of pits are found at 28 to 210% slip ratio. Examples from [4] show another example where the maximum amounts of pits are found at 225 to 230% slip. The maximum numbers of pits are found below the rolling circle where the slip is negative. The frequency of pits found is also dependent on the tooth force when the gearwheels are in contact. A gear tooth on a gearwheel in contact with another gearwheel experiences three different loads at the different stages of contact" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000884_s40997-019-00290-3-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000884_s40997-019-00290-3-Figure9-1.png", "caption": "Fig. 9 Stress and deformation distribution of the tooth surface of the internal ring gear", "texts": [ " The dynamic deformation varies periodically. The maximum deformation for both the pitch line and the tooth top appear at the ends of the internal ring gear tooth along the width direction. The deformation of the tooth top is larger than the deformation of the pitch line. The dynamic deformation of the pitch line and the tooth top is symmetric about the midpoint and gradually increases to both ends along the tooth width direction. The stress and deformation distribution of the tooth surface at the time T/2 is shown in Fig.\u00a09. The results show that the stress gradually increases from tooth top edge to tooth root edge. The stress distribution is symmetric around the centerline of the tooth surface and the maximum value on the midpoint of the tooth root (at B/2) is 485\u00a0MPa, which is 25% larger than the value for the midpoint of the pitch line. The stress mainly appears in the middle of the tooth width. The deformation gradually increases from tooth root edge to tooth top edge. The deformation distribution is symmetric around the centerline of the tooth surface, and the maximum deformation at both ends of the tooth top is 316\u00a0\u03bcm" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001379_tec.2020.3030042-Figure17-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001379_tec.2020.3030042-Figure17-1.png", "caption": "Fig. 17. Finite element model of end cover.", "texts": [ " Therefore, in an electrical machine with an unequal length of the stator core and the enclosure, the axial modal of the stator with enclosure becomes more complicated, and the cantilever shell is no longer free vibration limited by the shorter stator core. The natural frequencies corresponding to the composite modals of stator core and enclosure that are not deformed synchronously cannot be directly calculated by this method. D. Calculation of Natural Frequencies of Entire Motor As an essential part of the motor, it is necessary to analyze the vibration characteristics of the end cover before analyzing the modal of the entire motor. The finite element model of end cover is shown in Fig. 17, the asymmetry of the end cover of the motor in both the axial and radial directions is large, and its natural frequencies are difficult to obtain by the analytical calculation. The modal shapes and corresponding natural frequencies obtained by the FEM are shown in Tab. VIII, respectively. It can be seen that the each order modal frequency of the end cover under free vibration is greater than that of other parts of the motor. Therefore, the end cover cannot be easily ignored in the modal analysis of the motor" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001395_s12206-020-1240-y-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001395_s12206-020-1240-y-Figure1-1.png", "caption": "Fig. 1. Motor geometry: (a) model; (b) welded part inlet; (c) crown part inlet; (d) stator inlet; (e) outlet.", "texts": [ " First, the numerical model was validated with experiment, and then it was analyzed how the oil flowed through the coil and stator. Subsequently, the circumferential and longitudinal heat distributions of the coil and stator were analyzed. The total heat distribution was also analyzed to understand the effect of the insulating paper and insulator of the coil welded part. Finally, a parametric study was conducted to understand the effect of the oil inlet temperature and flow rate on the temperature distribution of the motor. The results show the cooling effect of the motor with oil cooling. Fig. 1 illustrates a hairpin winding motor with an oil cooling system, similar to that currently used in electric vehicles. Figs. 1(b) and (c) are each the welded part and the crown part of coil. Considering the flow of oil, an oblique shape similar to the actual shape is reflected on the outer surface of the coil. Endwinding in Fig. 1(b) protrudes in the positive x-axis owing to the use of epoxy, insulating paper, and welding. This part is called welded part. Unlike the welded part, the end-winding in Fig. 1(c) has no protruding parts because it does not involve the use of epoxy, insulating paper, or welding. This part is referred to as the crown part. Coil is layered between the slots of the stator, with an insulating paper on the outside of the coil in the slots. Oil enters the inlet located at the top. There are ten inlets in the coil; five in each of the welded and crown sections. The injected oil flows along the outer side of the coil. The stator has three flow paths and a total of six inlets, with two inlets per flow path" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001563_s00170-021-07221-0-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001563_s00170-021-07221-0-Figure1-1.png", "caption": "Fig. 1 Geometric model of motorized spindle", "texts": [ " In Section 2, the thermal network model for motorized spindle is established, and a new method for solving bearing heat is provided. In Section 3, the computation flowchart is given to acquire the steady temperature field of the motorized spindle, and a comparison analysis with the experimental results is performed. Thermal displacement, contact angle, contact load, friction heat, and temperature for bearings are investigated in Section 4 to interpret the change law of temperature with speeds. Lastly, the conclusions are indicated in Section 5. A three-dimensional geometry model of a motorized spindle is shown in Fig. 1. Bolts, bolt holes, cooling pipes, and lubrication pipes are omitted, and some small chamfers and rounded corners are simplified. The rotor is connected with the rotating shaft by pressure matching, and the helical cooling jacket is fitted on the stator surface. Angular contact ball bearings are utilized to support the rotating shaft. Herein, three B7018C bearings are installed at the front of the shaft, and one B7011C bearing is installed at the rear of the shaft, as shown in Fig. 1. The heat generated by the stator is carried away by the coolant in the helical cooling jacket, and part of the friction heat in the bearing raceway is taken away by grease. The motorized spindle is axisymmetric; hence, its thermal characteristics can be analyzed by establishing a twodimensional heat transfer structure. In Fig. 2, the red lines with arrows represent heat transfer paths, and the heat diffuses outward to the environment in the arrow direction. Points A and B represent test points 1 and 2 near the outer ring of the bearing presented in Section 3", " (28b). In Eq. (28), \u03b2b represents the thermal conductivity of the balls; \u0394Tb denotes the temperature rise of the balls; \u03b1i is the contact angle between the ball and the inner raceway; \u03b1o is the contact angle between the ball and the outer raceway under operation; and uh and us denote the thermal displacement of the bearing housing and spindle, respectively. Notably, bearings 1, 2, and 3 form an O-type configuration, and bearings 3 and 4 constitute an X-shaped configuration in this work, as shown in Fig. 1. For the bearing housing and spindle without internal heat source, uh and us can be expressed as follows: 1 2 Housing Spindle Fx Fz Fy O Mx My Housing Spindle Fx Fz Fy O Mx My 3 4 (a) (b) Fig. 8 Install types of bearings: a O-type and b X-type u x\u00f0 \u00de \u00bc c3\u03b3 2 x2 \u00fe c4\u03b3x\u00fe c1x\u00fe c2; \u00f029\u00de where \u03b3 denotes the thermal expansion coefficient of the components; and c1, c2, c3, and c4 are the integral constants. c3 and c4 are determined using temperature boundary conditions, whereas c1 and c2 can be obtained using displacement boundary conditions" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001272_1464420720909486-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001272_1464420720909486-Figure6-1.png", "caption": "Figure 6. Critical section parameters of symmetric and asymmetric configurations based on ISO and FEM: (a,b) 20 /20 , (c,d) 20 /34 , and (e,f) 34 /20 (all dimensions are in mm).", "texts": [ " In the analytical method, to determine the critical section thickness, the tangent line method was used to identify the maximum stress point on the fillet. The angle of tangent on the drive side ( d) was assigned a value of 30 . The angle of tangent on the coast side ( c) was determined using equation (1) c \u00bc 30\u00fe d c \u00f01\u00de The relations used for calculating rHPSTC, HPSTC, and Load,HPSTC have been reported in detail elsewhere.14 Based on the determined values of the aforementioned parameters, hf and sf were estimated graphically (Figure 6(a), (c), and (e)). In the bending stress calculation, the exclusion of the compressive stress caused by the radial component can induce significant errors for gears with high pressure angles.7 Hence, the compressive stress component was included in the form factor expression. The form factor (YF) and the stress correction factor (YS) were estimated using equations (2) to (6) YF,ISO \u00bc 6\u00f0hfm\u00de cos Load,HPSTC \u00f0sf\u00de 2 Tensile \u00f0I\u00de m sin Load,HPSTC sf Compressive \u00f0II\u00de \u00f02\u00de YS,ISO \u00bc \u00f01:2\u00fe 0:13L\u00deqas \u00f03\u00de where L \u00bc sf hf \u00f04\u00de qs \u00bc sf 2 f \u00f05\u00de a \u00bc 1:21\u00fe 2:3 L 1 \u00f06\u00de The maximum tensile stress at the drive side fillet is calculated by the ISO 6336 Method B (7) as follows ISO, max \u00bc Fn bm YF,ISOYS,ISO \u00f07\u00de where Fn is the normal force, b is the face width, and m is the module", " From this relation, a normalized, nondimensional factor called the fillet stress factor ( F,ISO) was defined (8) to compare the stresses of the different configurations14 F,ISO \u00bc ISO,max Fn bm \u00bc YF,ISOYS,ISO \u00f08\u00de In the FEM, the torque was selected so that equal normal forces were applied on the symmetric and asymmetric gears. The normal force acting on the 20 /20 configuration for a torque of 1Nm was selected as a baseline, and the torque on the 34 /20 configuration was calculated according to the following expression: T \u00bc Fn rb. The critical stress locations on the drive and coast side fillets were extracted from the nodal coordinates during post-processing. The hf, sf, and Load,HPSTC values corresponding to the steel\u2013polymer gear pairs are depicted in Figure 6(b), (d), and (f). The form factor (YF,FEM) was calculated by substituting hf and sf in the expression for YF,ISO(2). The stress correction factor (YS,FEM) was calculated using the inverse relation (9) as follows YS,FEM \u00bc F,FEM YF,FEM \u00f09\u00de where F,FEM is the fillet stress factor calculated using the FEM given by (10) F,FEM \u00bc FEM, max Fn bm \u00f010\u00de Analytical method vs. finite element method A comparison of the bending stresses of the steel\u2013steel and steel\u2013polymer pairs calculated using the ISO method and FEM is shown in Figure 7", " Thus, if the radial component was discounted, the fillet stress factor calculated by the ISO method would be higher than the FEM result. As evident from Figure 7, the inclusion of compressive stress in ISO method B resulted in an underestimation of the bending stress. From a design perspective, underestimating the bending stress leads to a lower tooth strength. Hence, for a conservative tooth design, excluding the compressive stress when determining the bending stress is desirable. In comparison to the symmetric configuration, the bending moment arm and critical section thickness were higher in asymmetric configurations (Figure 6). Asymmetric configurations exhibited lower YF and higher YS values. The high critical section thicknesses in asymmetric gears reduced the form factor. On the other hand, the reduced fillet length amplified the stress concentration in asymmetric gears. These results are in agreement with the findings of Sekar and Muthuveerappan.14 As evident from Figure 8, fillet stress factors (YFYS) of the 34 /20 and 20 /34 configurations are lower than that of the 20 /20 configuration. The fillet stress factors (YFYS) and bending stress results are concurrent", " Contrary to our results, Mertens and Senthilvelan26 reported that the fatigue life of asymmetric gear (34 /20 ) was lower than that of the symmetric gear (20 /20 ). The inferior performance was attributed to the domination of contact fatigue over bending fatigue. This was confirmed by the presence of excessive tooth wear and the absence of root crack. In this study, the 34 /20 configuration exhibited a higher bending fatigue life than the 20 /34 configuration. The average fatigue life reduction for the 20 / 34 configuration compared to the 34 /20 configuration was 20%. In the 34 /20 configuration, the combination of a lower bending moment arm (Figure 6(f)) and higher compressive stress reduced the bending stress and enhanced the fatigue life. The trend lines displayed convergence at the top, indicating an improved bending fatigue life for the 20 /34 configuration at high loads. This improvement could be attributed to the bending stress alleviation caused by the deflection-induced load sharing. In general, the load sharing in gears depends on the contact ratio. Because the contact ratio of 20 /34 configuration (\"d\u00bc 1.53) was greater than that of the 34 /20 configuration (\"d\u00bc 1" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000690_s11012-019-00973-w-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000690_s11012-019-00973-w-Figure5-1.png", "caption": "Fig. 5 Gear pair model with detail of the mesh", "texts": [ " (Color figure online) f \u00f0kh eh\u00de \u00bc kh eh 1 kh eh [ 1 0 1 kh eh 1 kh eh \u00fe 1 kh eh\\ 1 8 < : \u00f04c\u00de k00h \u00fe 2f\u00f0k0h e0h\u00de \u00fe Km\u00f0s\u00def \u00f0kh eh\u00de \u00bc Tg \u00f04d\u00de Equation (4d) presents a description of a nonlinear differential equation with time-varying coefficient which causes chaos in the system. Based on the fourth order Runge\u2013Kutta, the dynamic behavior of the system is computed by a numerical integration. To make sure about the output, a validation is done. What is compared with the numerical results of the dynamic solver is the experimental data of Kahraman and Blankenship [23]. The test is conducted on a spur gear utilizing data from Table 1. Details of the mesh on gear pair model is shown in Fig. 5. In order to evaluate the mesh stiffness of gear pair (Fig. 6), the \u2018\u2018Helicalpair\u2019\u2019 software and MSC Marc commercial finite element code are used. \u2018\u2018Helicalpair\u2019\u2019 software has been developed by Vibration and Powertrain laboratory in the University of Modena and Reggio Emilia. The finite element model with all boundary conditions and other details are prepared by \u2018\u2018Helicalpair\u2019\u2019 software. The model, which possesses nonlinearity due to contact, send toMSCMarc finite element solver to obtain the solution" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001449_j.mechmachtheory.2021.104396-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001449_j.mechmachtheory.2021.104396-Figure7-1.png", "caption": "Fig. 7. Determination of rake plane.", "texts": [ " (29) , and transforming r r to frame (xyz) t via the relation t r gen ( u 1 , \u03b8gen ) = t A g g A r r r . (39) ii) Determination of cutting-edge During power-skiving (see Fig. 6 ), only the tool cutting-edge meshes with the gear tooth surface. Therefore, the tool cutting-edge can be considered as an arbitrary curve on the generation surface, t r gen . In the present study, the cutting-edge (i is assumed to be constructed by the intersection of a plane rake surface t R rk , which tilts with a specific direction, with t r gen . Referring to Fig. 7 , t R rk can be obtained mathematically as t R rk ( u rx , u ry ) = Tran (0 , 0 , z of f ) Rot (x, \u03b7x ) Tran (0 , u ry , 0) \u23a1 \u23a2 \u23a2 \u23a3 u rx 0 ( u rx \u2212 r out ) T an\u03c4 1 \u23a4 \u23a5 \u23a5 \u23a6 , (40) where z of f (referred to henceforth as the rake-surface-offset) is the offset of the rake surface from the xy -plane of the tool frame (xyz) t , \u03c4 and \u03b7x determine the rake angle relative to the rake surface, u rx and u ry are the arguments of the rake surface, and r out is the tool outer radius. Substituting Eqs. (39) and (40) into the equation t r gen ( u 1 , \u03b8t ) = t R rk ( u rx , u ry ) , parameters \u03b8t , u rx and u ry can all be solved relative to the argument u 1 ", " (iv), the cross-sectional profile of the skiving-tool is assumed to be constant along the helical protrusion direction of the teeth, and is thus suitable for re-sharpening. For comparison purposes, two rake-surface-offsets are considered, namely Case 1: z of f = 0 mm and Case 2: z of f = 10 mm . Figs. 8 (a) and 8(b) present schematic illustrations of the resulting power-skiving tool designs. In the Case 1 design ( Fig. 8 (a)), the generation surface and clearance surface interfere. In other words, the clearance surface interferes with the internal gear profile, and the tool design is thus unacceptable. However, as shown in Fig. 7 (b) for the Case 2 design, interference is avoided, and hence the design is feasible. Figs. 14 (a) and (b) present the full-view analysis results for the working clearance angles of the cutting-edge (including right, left, root, and top regions) in the Case 1 and Case 2 designs, respectively. For the Case 1 design ( Fig. 14 (a)), the working clearance angles are negative in some parts of the top and root regions of the tool, and are thus unacceptable. However, for the Case 2 design ( Fig. 14 (b)), the minimum clearance angle is around 3" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001585_lra.2021.3068905-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001585_lra.2021.3068905-Figure6-1.png", "caption": "Fig. 6. Results of joint angle prediction using the LSTM model when applied sinusoidal input powers at the frequency of 0.01hz with various amplitudes (corresponding to duty cycle from 0.1 to 0.35). When the applied power is positive, only actuator 2 is heated, and when the applied power is negative, only actuator 1 is heated.", "texts": [], "surrounding_texts": [ "To verify the control design, experiments have been carried out. The prediction horizon is chosen as Np = 5." ] }, { "image_filename": "designv10_11_0003836_bf02844015-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003836_bf02844015-Figure8-1.png", "caption": "Figure 8 Combined images of ball at a time t = 3 ms from the start of impact, for the normal and oblique impacts. This initial velocity vectors of the two impacts are also shown.", "texts": [ " However, it also shows that the volume decreases by an extra 10% for the oblique impact, compared to the normal impact. Fig. 7(d) confirms that the vertical rebound velocity (of the ball) is 5% higher for the oblique impact, compared to the normal impact. This represents a difference in vertical COR of 0.04, which is very similar to the difference found experimentally. It has been shown that the ball COM displaces more and the volume enclosed by the rubber shell decreases more, for the oblique impact. In Fig. 8, images of the deformed balls, for the normal and oblique impacts, are combined. This snapshot was taken at a time t = 3 ms from the start of impact (a typical contact time is 4 ms). For the oblique impact, it can be seen that the ball appears to lean forward during the impact, owing to the unbalanced horizontal inertia forces in the rubber core. These forces, in addition to the reaction force, act to compress the air inside the core, resulting in a higher \u00a9 2005 isea Sports Engineering (2005) 8, 145\u2013158 153 pressure than would have been achieved in a normal impact", " In the second case the horizontal rebound velocity of the ball V x equals the surface tangential velocity \u03c9 rB. Using this theory, the value of can only be less than or equal to unity, where unity signifies rolling. However, previous research (Dignall, 2004; Cross, 2002; Goodwill & Haake, 2004) has published experimental data that has measured spin ratios ( ) of greater than unity. This signifies that the ball is spinning faster than rolling and the friction force would reverse direction at some point during the impact, i.e. the friction force on the ball would act towards the right in Fig. 8 and therefore accelerate the horizontal velocity of the ball. Cross (2002b) hypothesised that the high spin ratios were due to the normal reaction force acting behind the ball centre of mass. This would increase the torque acting on the ball, and thus also increase the spin attained during the impact. For low speed impacts (V < 4 m s\u20131), offset distances of approximately 3 mm were calculated for the model to correlate with the experimental data. Although this model is well presented and justified theoretically, the calculated distances were not verified experimentally in that paper" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003704_j.msea.2004.02.053-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003704_j.msea.2004.02.053-Figure1-1.png", "caption": "Fig. 1. Scheme of the laser interaction region and cross-section of the multi-layer.", "texts": [ " The problem can be described by the energy conservation and mass balance equations \u2202T \u2202t = \u2207(\u03ba \u2207T) + Q \u03c1C \u2212 (\u03bdsc\u2207)T, (1) \u2202\u03c1 \u2202t + \u2207(\u03c1\u03bdsc) = 0, (2) where Q is the heat generated per unit volume, \u03bdsc stands for the surface scanning velocity, and C, \u03c1 and \u03ba are the material dependent coefficients: specific heat, density, and heat conductivity, respectively. By introducing the thermal conductivity of the material, \u03bb = \u03ba\u03c1C, and taking into account that the laser beam represents the only heat source, i.e. the term (vsc\u2207)T equals 0, Eq. (1) can be rewritten in the form \u03c1C \u2202T \u2202t = \u2207(\u03bb\u2207T) + Q. (3) A similar approach was extensively discussed in [8] for the case of a single layer laser cladding. The interaction region under consideration and the laser beam position relative to the multi-layer are shown schematically in Fig. 1. Numbers in circles denote the base (0) and consecutive layers (1\u20133). Eq. (3) should be supplemented with an appropriate boundary condition for the component of the laser power flux in a direction normal to the upper surface of the molten pool \u2212\u03bb \u2202T \u2202n = ql \u2212 \u03c7(TS \u2212 T0), (4) \u03bbs \u2202Ts \u2202n \u2212 \u03bbl \u2202Tl \u2202n = Vm\u03c1L for T = Tm, (5) where ql is the laser intensity absorbed by the irradiated surface or interface, \u03c7 represents the surface-related heat transfer coefficient, \u2202T/\u2202n are the temperature gradients normal to the solid\u2013liquid interface, T0, TS, Tm are the ambient, irradiated surface and melting point temperature values, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001264_tsmc.2020.2967433-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001264_tsmc.2020.2967433-Figure2-1.png", "caption": "Fig. 2. Coordinate system of a coupled 2-D ballbot.", "texts": [ " Notations: \u03c3min(\u2022) and \u03c3max(\u2022) denote the minimum and maximum eigenvalues of the matrix (\u2022), respectively. \u2016\u2022\u2016 and \u2016 \u2022 \u20162 represent the L1 norm and the Euclidian norm of the vector (\u2022), respectively. diag(\u2022) denotes the diagonal matrix constructed by the vector (\u2022). | \u2022 | is the absolute value of the function (\u2022). C\u03c6 = cos(\u03c6) and S\u03c6 = sin(\u03c6). For coupled 2DBD, the BTS describes the balance and transfer of the robot in vertical planes. Its GCs can be written in vector form as q = [ px py \u03b8 \u03d5 ]T . The subsystem governs the robot\u2019s heading motion around the z-axis, where the GC is the yaw angle \u03c8 . Fig. 2 describes the coordinate system of the BTS, where {I} is the inertial world frame; {S} is the ball frame, which has the same orientation as {I} and is attached to the center of the ball; and {B} is the body-fixed frame, which is attached to the mass center of the body. The relationships among these coordinate frames can be described as follows: {I} Tpx x \u00b7Tpy y\u2212\u2192 {S} R\u03b8y \u00b7R\u2212\u03d5 x \u00b7Tl z\u2212\u2192 {B}. Here, T \u2208 SE(3) \u2282 4\u00d74 and R \u2208 SO(3) \u2282 4\u00d74, respectively, are the translational and rotational matrices, where the superscripts and subscripts indicate the amounts and axes of the transformation, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003608_9783527618811-Figure6.6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003608_9783527618811-Figure6.6-1.png", "caption": "Fig. 6.6 Geometry of the wobblestone modeled as a semi-ellipsoid rolling without slipping on a horizontal plane \u03a0. The vector r goes from the center of mass, c.m., to the point of contact.", "texts": [ " The rocking of the stone caused by the tap is quickly converted into a spin. The source of the quote also describes several of the stones many of which are shaped like a tri-axial ellipsoid sliced in half in the plane containing the two longest semi-axes. Our first step is to construct a mathematical model. The body will be the semi-ellipsoid described in the last paragraph with mass distributed such that the principal axes of inertia are skewed to the axes of the ellipsoid. We shall also assume that all the ellipsoid axes are unequal. The geometry is shown in Fig. 6.6. 184 6 Numerical Methods To derive the equations of motion we need to be able to relate the orientation of the body to the contact point. The normal to body surface at the contact point is \u2212e\u03043. Let the normal be \u03b3 = {\u03b31, \u03b32, \u03b33} in body fixed coordinates with origin at the center of mass and oriented along the ellipsoid axes (not the principal axes. Let the equation of the ellipsoid be E : g(x, y, z) = x2/a2 + y2/b2 + (z + z\u0304)2/c2 \u2212 1 = 0 The distance from the origin to the tangent plane is \u03a0 : f (x, y, z) = rt\u03b3 = x\u03b31 + y\u03b32 + z\u03b33 The contact point can be found by finding the minimum of f subject to the constraint E which is solved by Lagrange multipliers" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003773_1.2164465-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003773_1.2164465-Figure1-1.png", "caption": "Fig. 1 Schematic diagram of a staved EHL line contact", "texts": [ " When the velocity gradient in the x direction has been obtained from Eq. 7 , the velocity u can be calculated simply by integrating the gradient: u = ua + 0 z u z dz , and then the velocity w can be calculated from the equation of continuity. The mass flux in a steady-state line contact is a constant and can be expressed for the thermal and non-Newtonian problem by 9 : mx = \u2212 1 12 / eh 3dp dx + *hue, 8a which reduces into the familiar form for the isothermal and Newtonian problem: mx = \u2212 h3 12 dp dx + hue. 8b As shown in Fig. 1, it is assumed that both surfaces a and b bring a thin layer of lubricant into the contact, and the thicknesses of the oil layers are ha and hb, respectively. The mass continuity condition for the available lubricant and that passing the contact is: 0 haua + hbub = mx. 9 In order to simplify the mathematical model and facilitate the discussion, in this paper the two layers of lubricant moving respectively with velocities ua and ub are replaced by a single layer of lubricant moving with the entrainment velocity ue" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001333_tsmc.2020.3018756-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001333_tsmc.2020.3018756-Figure7-1.png", "caption": "Fig. 7. Experimental setup.", "texts": [ " To ensure the integrality of each module in motion, the central braided sleeve and three outer braided sleeves are connected with plastic connectors spaced 25 mm apart. By inflation and deflation in different contractile PMAs, each module of the continuum manipulator can be bent in different directions. In the experiment, we are committed to studying the tracking control of the angular position, and the loading operations (e.g., grasping) are not involved. Hence, the extensor PMA aimed at increasing the stiffness is not used during the entire process of this experiment. The experimental setup illustrated in Fig. 7 is employed to achieve angular position tracking by the selective activation of different contractile PMAs. The setup is as follows: the control method is executed in a 64-bit Windows-7-based host computer with an Intel Core i7 processor @ 3.40 GHz as well as 16-GB RAM, which has the ability to operate at an execution rate of 1000 Hz using the Simulink platform (Mathworks, Natick, MA, USA). Then, the data of the obtained control signals are transmitted through USB serial communication at 100 Hz to the microcontroller (Arduino Mega2560, Hesai Technology Inc" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000971_1077546319896124-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000971_1077546319896124-Figure5-1.png", "caption": "Figure 5. Physical model of tooth contact analysis for a helical gear pair.", "texts": [ " The dynamic meshing force/speed/ displacement is calculated, which offers the data for the calculation of sliding friction coefficient on tooth surface and arm of friction force. The sliding friction coefficient on tooth surface, arm of friction force, and dynamic formulas of a helical gear pair form a coupled system. By decoupling the calculation, the equations are solved. An example is demonstrated finally. Figure 4 shows the flow diagram for the dynamic model of a helical gear pair considering tooth surface friction. The TCA technology is a method to simulate the gear meshing process under the condition of error and modification; the physical model is shown in Figure 5. Detailed solution of TCA of a helical gear pair can be found in Fang (1997a, 1997b) and Litvin et al. (1999). In the common coordinate system ofxfyfzf, the coordinates of meshing point of the driving gear and driven gear are same, they can be represented as 8< : r~\u00f01\u00de f \u00f0u1;f1; \u03c61\u00de \u00bc r~\u00f02\u00de f \u00f0u2;f2; \u03c62\u00de n~\u00f01\u00de f \u00f0u1;f1; \u03c61\u00de \u00bc n~\u00f02\u00de f \u00f0u2;f2; \u03c62\u00de (1) 8< : r~\u00f01\u00de f \u00f0u1; \u00f0f1\u00de;f1; \u03c61\u00de \u00bc r~\u00f02\u00de f \u00f0u2;f2; \u03c62\u00de \u2202r~\u00f01\u00de f \u2202\u03b81 n~\u00f02\u00de f \u00f0u2;f2; \u03c62\u00de \u00bc 0 (2) In equations (1) and (2), the angle of rotation \u03c61 of the driving gear is taken as a given quantity" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003701_e2005-00038-5-Figure17-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003701_e2005-00038-5-Figure17-1.png", "caption": "Fig. 17. Notation of the indentation lengths H in the disk formation regime. R is the radius of the undeformed spherical shell. d is the radius of the circular disk.", "texts": [ " (45) Combining these three relations, h and Y are given by h = (8CbL 2 0/Cs)1/2, (46) Y = 1\u221a 6 C 3/2 s C 1/2 b L3 0 \u00b7 (47) In the disk formation regime (case I), the effect of adhesion is weak so that the shell deforms only slightly at the bottom as we have seen in Figure 2b. This situation is analogous to the case of a shell subjected to a small localized force [18]. Let d be the dimension of the deformed region which is caused by the contact between the shell and the substrate as depicted in Figure 17. The out-ofplane displacement \u03b6 (see Eq. (11)) in the deformed region can be identified as the indentation length H , i.e., \u03b6 \u223c H . Following the continuum treatment, the strain tensor is of the order of \u03b6/R \u223c H/R. Hence the total stretching energy is Es \u223c Y hH2d2/R2, (48) where we have multiplied the area of the deformed region d2. The fact that \u03b6 varies considerably over a distance d gives the curvature \u03b6/d2 \u223c H/d2. Then the total bending energy behaves as Eb \u223c Y h3H2/d2. (49) Note that the stretching energy increases and bending energy decreases with increasing d" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000663_s10846-018-0965-7-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000663_s10846-018-0965-7-Figure2-1.png", "caption": "Fig. 2 The three mass inverted pendulum model depicted in 3D space. xc is the CM of the robot, x1 is the position of the mass attached on the right knee, and x2 is the position of the mass attached on the left knee", "texts": [ " The inverse kinematics are solved by an iterative method using Jacobian transpose matrices with roll-pitch-yaw (RPY) conventions as follows: x\u0307COG 1 = JCOG 1 \u03b8\u03076\u00d71, x\u0307 end 1 = Jend 1 \u03b8\u030712\u00d71 (2) where xCOG 1 is a 6x1 matrix, \u03b86\u00d71 is a 6\u00d71 matrix and \u03b812\u00d71 is a 12\u00d71 matrix composed of joint angles, JCOG 1 is a 6\u00d76 matrix and J end 1 is a 6\u00d712 matrix. Inverse kinematics are easily analyzed by using the transpose of Eq. 2, which is the pseudo-inverse iterative approach to solving inverse kinematics. 2.2Walking Pattern Generation with a ThreeMass Model A walking pattern is generated with the three mass inverted pendulum model as shown in Fig. 2. Unlike widely used walking pattern generation based on multiple mass models, we used the original LIPM dynamics which is single mass model to represent dynamics of the robot and adopted a compensated ZMP that is derived from two masses attached on the right and left knees as it can be used in realtime pattern generation due to computational simplicity. The dynamics of the LIPM are derived by using the ZMP equation as follows [2, 3]: x\u0308c = g Zc (xc \u2212 p) (3) where xc is the position of the CM with respect to support origin, p is the ZMP vector with respect to the support polygon\u2019s origin, Zc is the height of the CM, and g is the gravity constant" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000931_j.mechmachtheory.2019.103595-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000931_j.mechmachtheory.2019.103595-Figure2-1.png", "caption": "Fig. 2. Solid model of the rotatable-axis revolute joint.", "texts": [ " The centre points of the three spherical joints form an equilateral triangle. The position and attitude transformation of the mobile platform is achievable by co-controlling the expansion or contraction of the three actuators. The reconfigurability of this mechanism stems from the configuration change of the rR joint. The axis of a traditional revolute joint can no longer rotate after installed. The direction of the rotation axis of the rR joint in this metamorphic parallel mechanism can be altered yet. As shown in Fig. 2 , the rR joint is mainly composed of an inner support body, a rotating shaft and an outer mount. One side of the inner support body is connected with the output end of the P pair, that is, the output shaft of the linear actuator, by a bearing. The other side of the inner support body is U-shaped and has a through hole that the rotating shaft passes through to coupled with the master link. The outer mount that two grooves is inside, is seated outside of on the inner support body. Every groove has two straight sections and one helix section (see Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000401_s12206-018-0611-0-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000401_s12206-018-0611-0-Figure3-1.png", "caption": "Fig. 3. (a) Perfect tooth model and tooth cross-section; (b) cantilever beam model.", "texts": [ " However, they focused on a fixed spur gear pair and provided no analytical equations to quantify the TVMS reduction with chipping growth. In addition, they only considered a single chipped tooth. The chipping defects usually occur on multiple teeth simultaneously in practice. Therefore, it is necessary to evaluate the effects of multi-tooth chipping on the TVMS and dynamic responses of the gear set. In this study, we will propose an improved TVMS evaluation method to address the above shortcomings. The tooth model, the tooth cross-section xs , and the cantilever beam model for a perfect tooth are shown in Fig. 3. The gear tooth is treated as a cantilever beam on the root circle, and the tooth fillet curve is approximated using a straight line for the convenience of equation derivation [26]. The improved potential energy method is used to evaluate the TVMS. Four stiffness components are considered here: Hertzian, bending, shear, and axial compressive stiffness. The expressions are given as [26]: ( )24 11 hk Ew u p - = (8) ( ) 2 1 1 0 cos sin1 d b x d x h dx k EI a a\u00e9 \u00f9- -\u00eb \u00fb= \u00f2 (9) 2 1 0 1 1.2cosd s x dx k GA a = \u00f2 (10) 2 1 0 1 sind a x dx k EA a = \u00f2 (11) where w is the tooth width, E , G and u denote the Young\u2019s modulus, shear modulus and Poisson\u2019 ratio, respectively, 1a refers to the gear contact point, d is the distance between the gear contact point and the tooth root, h is the distance between the gear contact point and the central line, and xA and xI denote the area and area moment of inertia of the cross-section from which the distance to the tooth root is x , respectively. As Fig. 3(a) shows, the shape of the cross-section xs is a rectangle, denoted by A B C D- - - , thus, the area xA and area moment of inertia xI of the cross-section xs are expressed as [26]: 2x xA h w= (12) 32 3x xI h w= (13) where xh is half the length of the cross-section xs . Based on the properties of the involute curve (see Fig. 3(b)), h , xh , d and x are expressed as [26]: 1 2 1 1( )cos sinbh r a a a a= + -\u00e9 \u00f9\u00eb \u00fb (14) ( ) 2 1 2 1 sin 0 cos sin b x b r x d h r d x d a a a a a \u00a3 \u00a3\u00ec\u00ef= \u00ed \u00e9 \u00f9- + \u00a3 \u00a3\u00ef \u00eb \u00fb\u00ee (15) ( )1 2 1 1 3sin cos cosb fd r ra a a a a\u00e9 \u00f9= + + -\u00eb \u00fb (16) ( ) 1 2 3 1 0 cos sin cosb f x x d x r r d x da a a a a \u00a3 \u00a3\u00ec\u00ef= \u00ed \u00e9 \u00f9- - - < \u00a3\u00ef \u00eb \u00fb\u00ee (17) where br and fr are the radius of the basic circle and the root circle, respectively, 2a represents the half tooth angle on the base circle, and 3a is the approximated half tooth angle on the root circle" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001267_j.jclepro.2020.120491-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001267_j.jclepro.2020.120491-Figure6-1.png", "caption": "Fig. 6. Exoskeleton high compliance ankle joint and its structural diagram.", "texts": [ " Based on the ANSYS software, the human foot exerts a certain force on the bone ankle joint component in the direction perpendicular to the vertical axis of the human lower limb. At its extreme position, the strength analysis results are shown in Fig. 5. It could be seen from the analysis results that the exoskeleton ankle joint component also uses 6061 aluminum alloy as the main material satisfies the requirement under the ultimate stress condition, that is, the design is reasonable. The underactuated robotic ankle exoskeleton described herein is a highly compliant structure based on an underactuated 3-RRS spherical parallel mechanism. As shown in Fig. 6, the structure body is connected by three dynamic and static platforms through three identical branches. Each branch contains two rotating pairs (R) and one spherical pair (S). The static platform end is connected with the rotating pair, and the dynamic platform end connects with the spherical side. The mechanical diagram could be obtained by simplifying each structure, and the dynamic and static platforms are equivalent to two congruent equilateral triangles, and the branch is equivalent to a chain structure composed of a rod member, a spherical pair and a rotating pair" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001715_j.jallcom.2020.158319-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001715_j.jallcom.2020.158319-Figure4-1.png", "caption": "Fig. 4. (a) The dimensional drawing of the deposited bulk; (b) The schematic of the scanning strategy; (c) the tensile specimens.", "texts": [ " LMD was conducted with an LSF-I LMD fabrication platform (with a 4-kW TRUMPF disk laser) developed by SWAI (LSF-I, SWAI, Mianyang, SC, China). The set-up comprised a laser source, a powder-feeding system, a mechanical arm with a coaxial nozzle, and a gas protection chamber, as depicted in Fig. 3. The deposition path was mainly determined by the displacement of the coaxial nozzle. In addition, the powder-feeding system comprised a multi-chamber container to facilitate the successive deposition of different materials. Fig. 4a and b show the schematic of the scanning strategy, (BD: building direction, SD: scanning direction, TD: transverse direction). The rotation of the scan direction between each successive layer was 90\u00b0, to ensure the uniformity of heat transfer as well to avoid porosity. The deposition substrate used in this experiment was an 8 mmthick rolled TC4 plate, the top surface of which was ground with 600-grit sandpaper and cleaned with alcohol before deposition. Thereafter, TC4 powder, intermediate materials, and 30CrNi2MoVA steel powder were deposited successively on the Ti substrate", " The testing was conducted with a DHV-1000Z hardness tester (DHV-1000Z, SCTMC, Shanghai, China) with a loading force of 500 g and a loading time of 15 s. More than three points were tested to ensure accuracy at every testing interval, with various spacings between the intervals. Calculations were performed using ThermoCalc software with the Fe-alloy TCFE6 database in order to determine an appropriate composite transition interlayer. Tensile specimens of each fabricated bulk were machined with dimensions of 42 mm \u00d7 6 mm \u00d7 2 mm (Fig. 4c) parallel to the SD, and the tensile tests were conducted using an Instron 5569 testing machine (Instron 5569, Instron, Norwood, MA, USA) at room temperature and a strain rate of 0.033 mm/s. Each test was performed with at least three identical specimens to ensure the accuracy of the mechanical characteristics. Furthermore, the fracture morphologies were analyzed in detail. Fig. 6 shows the microstructure acquired by OM and the EDS line scan results obtained for the 2 V and 4 V specimens. The EDS line scans were performed with SEM in the backscatter mode" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003681_37.229559-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003681_37.229559-Figure2-1.png", "caption": "Fig. 2. Inverted pendulum setup.", "texts": [ " By defining y such that the demand with respect to one or more design goals increases when y increases, we may define the H, control design problem as finding the largest y such that there exists a controller K(s) for which An important consequence of (2) for the sequel of this article is that the inifinity norm of the uncertainty must be bounded. Otherwise, no solution can be found. If no uncertainty block is present, a direct computational solution is available, based on the solution of two algebraic Ricatti equations. This solution has been implemented in the software package MATLAB386 [ 1 I ] using a small adaption of the algorithm given by Glover and Doyle 161 (see also [3]). Experimental Setup Description The inverted pendulum setup (see Fig. 2). can be split into four parts, which will be considered consecutively: mechanical part, sensors with accompaning electronics, digital control sys- ings have a considerable amount of friction (the drivetrain also contributes to this) and will have to be taken into account at the control design stage. The drivetrain consists of a toothed belt, actuated by an electrical servomotor. The belt is attached to the cart, and combined with a toothed wheel on the motor it provides slip-free traction. Motor, drivetrain, and cart have an equivalent mass of 2 kg", " A rotary variable differential transformer (RVDT) at the rotation point of the pendulum, measuring the angle. 3. A tacho generator on the servomotor, measuring the angular velocity of the motor, which is approximately linear dependent on the cart velocity. All sensors are sufficiently accurate (less than 1% deviation) and have a high bandwidth (well exceeding 100 Hz). Digital Corztrol System. The digital control system is a DSPbased system of dSPACE GmbH [4], with an IBM-AT compatible host (see Fig. 2). Accompaning software provides discretization, scaling (see, for instance, [SI) and assembly source code generation almost automatically. The use of fast A/D and D/A converters in combination with a Texas Instruments TMS320C25 DSP provided adequate computational speed under all circumstances. Actuator with Power Amplifei: The actuator is a 400-W DC electromotor connected to a voltage driven power amplifier. Under normal circumstances, the motor with amplifier has a linear behavior, with a high bandwidth (well above the eigenfrequencies of the mechanical part)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001452_tro.2021.3076563-Figure15-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001452_tro.2021.3076563-Figure15-1.png", "caption": "Fig. 15. Finger stops. (a) Red figure design when flat. (b) Back view of the red finger, showing the location of stops (circled). (c) Blue finger design when flat. (d) Back view of the blue finger, showing the location of stops (circled).", "texts": [ " This ensured that the fingers had the appropriate kinetic energy during each transformation step. Six extension springs were included in the design to preload the motor-driven linkages and stabilize the system (see Fig. 14). They were 31.75 mm long with ak-value of 49 N/m. Two springs were installed between opposing fingers to pretension the lower vertices, and four were connected between the middle vertices of each finger and the gripper base. Mechanical stops were included on two hinges of each finger (see Fig. 15). Some potential finger configurations result in nonfunctional grasp modes, and it was simpler to physically prevent these configurations than design our transformation process around avoiding them. 1) Multivertex Transformation: When multiple vertices are transforming simultaneously, the criteria for transformation can change. If one vertex transforms and it shares a spinal crease with another vertex, the transformation criteria for the Authorized licensed use limited to: University of Prince Edward Island", " In the fingers, we observed this pass-through transformation (or lack of transformation) whenever a lower vertex transformed. Therefore, when considering finger transformation, it may be easier, conceptually, to consider the fold directions of the segments (see Fig. 16). Here, we refer to a segment with the convex side pointing toward the gripper palm as a valley (V) fold, and a segment with the convex side pointing away from the palm as a mountain (M) fold. 2) Finger Stops: The mechanical stops prevented their corresponding hinges from folding in one direction (see Fig. 15). One stop was located on the spinal crease of the fourth segment. This kept the fourth segment folded in the mountain direction, which forced the third vertex to be parallel when the third segment was in the mountain direction and antiparallel when the third segment was in the valley direction. The second stop was on one of the peripheral creases connected to the second vertex. This kept that crease in the mountain direction. When the second segment was in the valley direction, the second vertex was forced into the parallel configuration", " (47) Authorized licensed use limited to: University of Prince Edward Island. Downloaded on July 03,2021 at 12:01:06 UTC from IEEE Xplore. Restrictions apply. 5) Pinch to Wrap Mode: In the pinch mode, the configurations of vertices 1\u20133 were parallel, antiparallel, and antiparallel, respectively. The fold direction of the segments were, in order, M-M-V-M. In wrap mode, the vertices were antiparallel, parallel, antiparallel, and the segment fold directions were M-V-V-M. In each finger, the stops (see Fig. 15) forced the third and fourth segments to maintain their fold direction, so only the second segment (the upper segment of the first vertex) needs to be considered (see Fig. 16). 6) Wrap to Neutral Mode: In the wrap mode, the vertex configurations were antiparallel, parallel, antiparallel, and the segment fold directions were M\u2013V\u2013V\u2013M. In the neutral configuration, the vertex configurations were all parallel, and the segment fold directions all mountain. Therefore, the second and third segments had to change direction, while the stop on the fourth segment forced it to maintain the mountain direction" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000939_j.advengsoft.2019.102722-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000939_j.advengsoft.2019.102722-Figure9-1.png", "caption": "Fig. 9. Simplified structure of hydro-pneumatic suspension.", "texts": [ " = + +m m m m m t( )/2 [( )sin( )]/2b U F U F (5) In the above formula, mU represents the empty mass and mF represents the full load mass. The hydro pneumatic suspension integrates the spring unit and the shock absorber in one. Furthermore, unlike the traditional suspensions, the stiffness and damping characteristics of hydro pneumatic suspension are nonlinear which are conducive to improving the vehicle ride comfort. In this study, a kind of common passive hydro pneumatic suspension is selected, and its structure is shown in Fig. 9. This hydro pneumatic suspension consists of the cylinder, valve system, air chamber, and piston rod. In the reciprocating movement of the piston rod, the volume of air chamber alters constantly and the elastic force changes accordingly. Only during the compression stroke, the check valve is open. Thus, the damping in the compression stroke and recovery stroke is different. On the basic of the working principle of hydro pneumatic suspension, the mathematical formulas of elastic force and damping force are derived as follow: = =F PA m g x h(1 / )e g s n 0 (6) = + + F A v C A A v v 2 { [1 sgn( )]} sgn( )d d n d 0 3 2 2 1 2 2 (7) where P is the pressure in air chamber, h0 is the initial height of air chamber, ms is the static load, A0 is the cross-sectional area of ring oil cavity, An is the cross-sectional area of damping hole, Ad is the crosssectional area of check valve, \u03c1 is the oil density, Cd is the flow coefficient" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001327_s00170-020-05927-1-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001327_s00170-020-05927-1-Figure4-1.png", "caption": "Fig. 4 Structural diagram of face gear CNC processing machine. 1, radial slide (X); 2, axial slide (Y); 3, tangential slide (Z); 4, pitch angle (B); 5, rolling angle (A); 6, cutter spindle (C)", "texts": [ " rd represents the radius of the grinding wheel, \u03d5d is the tooth profile parameter of the grinding wheel, and Ed represents the distance between the center of the grinding wheel and the central axis of the pinion, Ed = rd \u2212 rps. The tooth profile equation of the grinding wheel is as follows: Mds \u03d5s\u00f0 \u00de \u00bc rd ut;\u03d5c\u00f0 \u00de \u00bc Mst \u03c6s\u00f0 \u00dert \u03bct;\u03d1t\u00f0 \u00de nd \u03d5d;\u03c6s ut\u00f0 \u00de\u00f0 \u00de \u00bc Lds \u03d5s\u00f0 \u00dens 1 0 0 0 0 cos\u03d5d sin\u03d5d \u2212Edcos\u03d5d 0 \u2212sin\u03d5d cos\u03d5d Edsin\u03d5d 0 0 0 1 2 64 3 75 \u00f07\u00de where \u03c6s \u00bc ut rpssin\u03b3t . The calculation method of the computer numerical control (CNC) grinding tool-path for face gear is completed on the special five-axis grinding machine, and the structure of machine tool is shown in Fig. 4. It can be seen that the face gear grinding machine has five numerically closed-loop controlled axes: three rectilinear axes (X, Y, Z) and three rotational axes (A, B, C). In the process of face gear grinding, the X-axis, Y-axis, and Z-axis are used to realize the radial feed motion when grinding, the axial feed motion, and the auxiliary feed motion of the disk CBN wheel relative to the face gear. The rotational motion in the A, B, and C directions realizes the rotation of the face gear about its own axis, the swinging of the face gear about the virtual axis, and the rotating of the wheel around its own axis" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000606_j.triboint.2018.02.028-Figure8-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000606_j.triboint.2018.02.028-Figure8-1.png", "caption": "Fig. 8. The TRB with a outer-raceway defect.", "texts": [ " 8>>>>< >>>>: XZ j\u00bc1 Qj cos \u03b1cos \u03c6j \u00fe Fc cos \u03c6j \u00fe Fx \u00bc 0 XZ j\u00bc1 Qj cos \u03b1sin \u03c6j \u00fe Fc sin \u03c6j \u00fe Fy \u00bc 0 XZ j\u00bc1 Qj sin \u03b1\u00fe Fz \u00bc 0 (5) Where Qj is the contact load betweenjth roller and raceway; Fc is the centrifugal force of roller; \u03b1 is the contact angle between roller and raceway; \u03c6j is the angular position of jth roller; Fx; Fy ; Fz are the external loads of outer ring in different direction. WhereK; n is the stiffness coefficient and stiffness index between roller and raceway, respectively; \u03b4 is the elastic approach between roller and raceway; Q is the contact load between roller and raceway. The defect region is determined by angular position and angular distance of defects as shown in Fig. 8. The defect width can be considered as the arc length of angular distance of defect. As the roller enters defect region, the roller-raceway contact stiffness changes. Taking the defect on outer-raceway for example, the contact stiffness of j th roller is represented as Kj; nj \u00bc \u00f0Kd; nd\u00de j\u03b8j \u03d5d j < \u0394\u03d5d=2 \u00f0Kn; nn\u00de non defect area (7) Where \u03b8j is the angular position of jth roller; \u03d5d is the angular position of defect; \u0394\u03c6d is the angular distance of defect; Kd; nd are the stiffness coefficient and index under defect condition; Kn; nn are the stiffness coefficient and index under non-defect condition", " The quasi-static model of defected roller bearing is simultaneous nonlinear equations, which can be solved by the Newton-Raphson iteration algorithm. The detailed solution process of defected roller bearing model is illustrated in Fig. 9. The modeling of defected roller bearing is carried out on TRB 32008J with the presented defect modeling method. The parameters of TRB 32008J are shown in Table 1. The defect is positioned to have its axis (Fig. 7) on the center of roller-raceway contact area, and the angular position of defect (Fig. 8) is 0 rad. The processing of roller passing over a defect is simulated to demonstrate the effects of defect on contact pressure and contact stiffness. As shown in Fig. 10, the relative displacement between defect and contact area Dx increases from negative to positive, as the roller passes over defect. When the sum of half contact width bc/2 and half defect width bd/2 is larger than jDxj, the roller will enter the defect area. According to the effect of defect on roller-raceway contact area, the contact state can be divided into the following stages: In state 1or 5, the roller is not located in defect region, and the contact area remains constant; In state 2 or 4, the roller is in contact with both axial and radial edge of defect, and the contact area gradually changes with the changing of Dx; In state 3, the roller is only in contact with axial edge of defect, and the contact area remains constant" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0002454_piae_proc_1925_020_032_02-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0002454_piae_proc_1925_020_032_02-Figure7-1.png", "caption": "FIG. 7 .", "texts": [ " If D E receive displacement through a small angle only, the end D d l vibrate harmonically in a direction perpendicular to AD. If D E be displaced parallel to at UNIV NEBRASKA LIBRARIES on May 27, 2016pau.sagepub.comDownloaded from itself to HG, the end D will move harmonically in the line DG, also perpendicular to AD, but in a different period. If both motions occur simultaneously, the end D will vibrate in a line perpendicular to AD, but in a manner which is the superposition of thc two separate motions. This movement of the end D can be displayed by a displacement-time curve, and Fig. 7a is drawn for the simple case in which the period and amplitude of one motion arc each tmice those of the other, and both vibrations start in the same place. The broken lines give the component simple sine curves and the full line the summation. I t will be seen that the motion as a whole is irregular, a wide excursion alternating with a nearly equal period of comparative rest. The phase affects tho motion considerably, and in Fig. 7b is shown the result of a quarter of the shorter period alteration in the phase. If the periods are nearly but not exactly in this simple ratio, the motion will gradually change as the phase alters. By giving a motion t ( J tho rod in the direction of its length, the nature of the motion of D can be rendered visible, a spot being marked a t D azld observed in plan, when it appears to trace out the curve upon a harmonic-time base. Actually the bar will have three more degrees of freedom, being a rigid body elastically supported, and so three more modes of vibration and periods, but thme are of lesser interest", " of the accelerations-important quantities-will be in the ratio of the amplitudes of the movements divided by the squares of the periodic times, since periodic times are inversely as w. I f the motion of P be given by u sin (a l t + a ) and that of Q by If , z = u sin (u) t+a) at UNIV NEBRASKA LIBRARIES on May 27, 2016pau.sagepub.comDownloaded from 520 THE INSTITUTLON OF AUTOMOBILE ENGINEERS. \u2018 ~ 1 sin (03,t + fi), the motion of any point U, Fig. 13, is expreEsed by z =UV =uw +vw- = UQ.u.sin(o,t + a ) + vUP.sin(co,t + fi) PQ ancl is the type of motion possessed by the point D in Fig. 7 and represented by the curves in Fig3. 7a and 7b. The acceleration of the point U will be so that the coipponent sine curves nil1 be in tlic same phases as originally but \\+ill have different amplitudes. The acceleration curves corresponding to Fig. 7a are of a siiiiilar nature. Aa the object of this paper is the presentation of a mode of analysis of the vibrations, elucidating the fundamentals of the fnotioii and affording a basis of design, the author does not propose to cliseues details of arrangement or mhether it mould be advisable t o place a seat a t a position which proffers a motion and acceleration such as represented in Fig. 7b, xliicli vould possibly enhance I -[( UQ/PQ).uw,z sin (colt + a ) + (UP/PQ).vc9,2 sin (wzt f i s ) ] , the ecstacy of a joy ride, or at a position such as P, which offers a motion to which most persons are accustomed early in life. The author considers that, as whatever the brain easily apprelicnds or quickly becomes accustomed to, causes least distraction, for mcrc conveyance or ease, the use of the points of simple harmonic motion presents advantages. If a seat be arranged at some definite position in the car, the springing can be adjusted-by the aid of the hyperbolic curves or Equations--so that a point at the seat has siinpl1e harmonic motion Into this adjustment only the position,s of G and C and the values of h and k will enter" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000998_j.jsv.2020.115374-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000998_j.jsv.2020.115374-Figure1-1.png", "caption": "Fig. 1. Schematic of an ACCBB.", "texts": [ " In order to obtain more accurate calculation results, the dynamic characteristics of bearings are analyzed from the view of conservation of energy considering nonlinear contact stiffness and damping, and then the radiation noise of an ACCBB is calculated. This study has a high calculation accuracy. The total RN of an ACCBB and its frequency spectrum are studied by the analysis of the vibrational response of the bearing components. Then the distribution characteristics and directivity of the sound field of an ACCBB are discussed. Fig. 1 illustrates the schematic of an ACCBB. In this study, the external forces acting on the ceramic bearing are analyzed only in the axial directionwith the preload. A bearing system is simplified as a massespringedamping model, as presented in Fig. 2. In Figs. 1 and 2, the generalized coordinate system {O; X, Y, Z} is fixed in the bearing plane. Subscript i, o and b mean inner ring, outer ring and ceramic ball, respectively. The j denotes the order number of the ceramic ball. Oi is the geometric center of the inner ring" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001773_tte.2021.3085367-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001773_tte.2021.3085367-Figure6-1.png", "caption": "Fig. 6. The slotless stator MEC model. (a) MEC model. (b) Fluxes distribution.", "texts": [ " Since the rotor shape forms an uneven air-gap, the reluctances of the air-gaps with distinctly different lengths should be analyzed separately. The AGFDs of the slotless stator model under different MSs are calculated by the FE method and shown in Fig. 5. It can be seen that the Bg1 can be considered as the contribution of the \u201cspoke\u201d-shaped PM, while the Bg2 as the contribution of both the \u201cU\u201d- and \u201cspoke\u201d-shaped hybrid PMs. To accurately calculate Bg1 and Bg2, a slotless stator MEC model is established in Fig. 6(a). Furthermore, Fig. 6(b) illustrates the corresponding flux distribution of the model. \u03d5L1, \u03d5h1 and \u03d5h2 are the fluxes over LCF and HCF PMs. \u03d5b11, \u03d5b12, \u03d5b21 and \u03d5bL2 are the leakage fluxes via the core bridges. \u03d5b22 and \u03d5bL1 are the leakage fluxes via the magnetic barriers. \u03d5g1 and \u03d5g2 are the fluxes passing via the air-gap, in which \u03d5b22 and \u03d5bL1 can be neglected. The corresponding fluxes and reluctances of LCF, HCF1 and HCF2 magnets can be respectively expressed as: 2L rL LB w L\u03c6 = (12) 2 2bL sat LB w L\u03c6 = (13) 02 L mL r L hR w L\u03bc \u03bc = (14) 1 12h rh HB w L\u03c6 = (15) 11 11b sat HB w L\u03c6 = (16) 12 13b sat HB w L\u03c6 = (17) 1 1 0 12 H mh r H hR w L\u03bc \u03bc = (18) 2 22h rh HB w L\u03c6 = (19) 21 21b sat HB w L\u03c6 = (20) 2 2 0 22 H mh r H hR w L\u03bc \u03bc = (21) where BrL and Brh are the magnet remanences of the LCF and HCF PM respectively, Bsat is calculated from the B-H curve of core material which assumes the full saturation of the iron bridges" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000716_j.mechmachtheory.2019.07.013-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000716_j.mechmachtheory.2019.07.013-Figure1-1.png", "caption": "Fig. 1. Rotorcraft transmission system with concentric split-torque face gear drives.", "texts": [ " However, this has no influence on the meshing of the face gear drive. The processing efficiency of the face gear grinding is sufficiently affected by the prescribed processing precision. \u00a9 2019 Elsevier Ltd. All rights reserved. Face gear drive including a conical involute pinion has been considered as a replacement of the conventional one in advanced rotorcraft transmission design [1\u20133] . The aim is to improve the load sharing between the multiple pinions and idlers in the concentric split-torque face gear transmission system ( Fig. 1 ). This type of face gear drive regards a conical involute gear as the pinion member [4,5] , whereas the conventional face gear drives take the cylindrical involute gear [6\u201310] . Consequently, the tooth backlash of the face gear drive including a conical involute pinion can be modified by means of axially moving of the pinion. In this way, the property of the load sharing of the concentric split-torque face gear transmission system is expected to be improved. The key factor in applying the face gear drive is to improve its precision of finishing operations" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003725_ip-b.1993.0027-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003725_ip-b.1993.0027-Figure3-1.png", "caption": "Fig. 3 Flux distribution on a studied domain for one position", "texts": [ " Only a numerical local field calculation, such as by the method of finite elements, can be used for such a determination. We have developed a calculation code based on finite elements. This code permits a simulation of the motor rotation. One pole pitch of the machine is considered as a calculation domain. A triangular mesh is used for both of the stator and rotor while a macro element is used in the airgap to permit rotation simulation. The flux distribution in the motor calculated for each position (Fig. 3). The EMF and inductance values are deduced from flux values. Three MPSMs have been modelled. Both EMF and inductance variations for each machine have been determined [9, 10]. The cross sections of the machines (called a, p and y) and the different results are shown in Figs. 4, 5 and 6, respectively. We see that, for machine a which belongs to the surface mounted magnet family, only the third harmonic can be observed fo the obtained EMF. The other harmonics are negligible. Moreover, the inductances variations are very small, the rotor saliency is negligible and the consideration of the fundamental variations of self and mutual inductances is sufficient" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000546_s00170-016-8533-4-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000546_s00170-016-8533-4-Figure4-1.png", "caption": "Fig. 4 Schematic of laser setup", "texts": [ " This particular software converts the STL geometry in to thin slices of 70 \u03bcm and writes the output as machine specific ABF file. The ABF file instructed the machine control on how to proceed with the actual part production. Figure 3 shows one of the resulting EBM part. Lasertec-40 from DMG\u2122 was used for laser experiments. This machine was equipped with the Q-switched Nd:YAG laser operating at a wavelength of 1064 nm and an average power of 100 W. The laser spot size and pulse duration were kept constant at 20 \u03bcm and 10 \u03bcs, respectively. Figure 4 gives schematic of the laser setup. Laser ablation was done on vertical surfaces of the EBM samples. The experiments were carried out based on the factorial design methodology with four factors at two levels. Table 2 shows the selected factors and their respective levels. Laser ablation for each setting was carried out within 11\u00d711-mm sectors. Fifty scan cycles were run in each sector. The depth of material removed was measured using the probe attached to the machine itself. Table 2 Selected experimental factors and their respective levels Factors Levels Low High Lamp intensity (%) 75 95 Pulse frequency (kHz) 15 45 Scan speed (mm/s) 200 700 Track displacement (\u03bcm) 6 14 Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001267_j.jclepro.2020.120491-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001267_j.jclepro.2020.120491-Figure4-1.png", "caption": "Fig. 4. 3-RRS spherical parallel exoskeleton ankle joint structure.", "texts": [ " Through the above formula, it is not difficult to find that there are three DOFs in the 3-RRS spherical parallel mechanism. The analysis shows that mainly motion is the pitching and flipping in the space, and themoving platform is moving up and down relative to the static platform. The motion model is consistent with the exoskeleton. The requirements of the joints could adapt to various daily activities of the human body ankle joints and have high institutional compliance. The 3-RRS spherical parallel exoskeleton ankle joint structure is shown in Fig. 4. The 3-RRS spherical parallel ankle joint structure includes 1-calf telescopic component, 2-foot ankle brace, 3-foot strap, 4-foot bottom pad, 5-foot pedal, 6-articular platform lower end, 7-articular platform upper end, 8-ball joint, 9-branch lower link, 10- branched upper link, 11-Joint static platform, and 12-platform support rod. The ankle joint component formed by the components 2e11 is directly fixed to the bottom of the calf telescopic component, and the platform support bar strengthens the connection stability between the static platform and the telescopic component and the rigidity of the overall structure" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0002454_piae_proc_1925_020_032_02-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0002454_piae_proc_1925_020_032_02-Figure6-1.png", "caption": "FIG. 6.", "texts": [ " 5 , be attached to the top of a vertical rod, fixed at its lower end and capable of acting as a cantilever spring so that the movement of the mass A can be regarded ayy being in a horizontal plane, the mass will have two degrees of freedom. If the section of the rod be circular m d the mass A displaced to any point P, it will vibrate in the straight line PA&. and whatever be the direction of this line the periodic time will be the Bame, so that it can be regarded as having one single period. If, however, the rod be of other section, such as rectangular, as indicated in Fig. 6 , the period when the mass at UNIV NEBRASKA LIBRARIES on May 27, 2016pau.sagepub.comDownloaded from 510 THE INSTITUTION OF AUTQ~MOBILE ENGINEERS. is set in vibration along Ox parallel to one edge of the rectangle will be different from that in which it will vibrate parallel to the other edge. In either of these directions it will execute simple Q .-a. - , #\u2019 F I G . 5 . harmonic vibrations, but i f it be displaced in another direction to P and released, i t will not vibrate along O P but will vibrate in a manner compounded of its simple vibration along Ox with amplitude OM (where PM is drawn perpendicular to Ox) and of its simple vibration along Oy with amplitude PM. If the periods along Ox and Oy have a simple ratio, the path repeats at UNIV NEBRASKA LIBRARIES on May 27, 2016pau.sagepub.comDownloaded from THE MAIN FREE VIBRATlONS O F AN AUTOCAR. 51 1 after one type of oscillation has gained a complete vibration on the other. Thus the curve in Fig. 6 shows the complete path for a ratio of 2 : 3. Usually no simple relationship exists and the shape of the path alters continuously. ~vitli its length in the direction 02, it may still be considered as confined to the horizontal plane in its vibrations, and as an additional degree of freedom (angular) has been introduced, there will be three periodic times. If D E receive displacement through a small angle only, the end D d l vibrate harmonically in a direction perpendicular to AD. If D E be displaced parallel to at UNIV NEBRASKA LIBRARIES on May 27, 2016pau", " While the poink P and Q have simple harmonic motion only, that of a point such as R, Fig. 16, is now comprised of the superposed vibrations about P and Q. Thus, it may he RW, the vector summation of RU perpendicular to PR, due to the motion about P and RV perpendicular to QR, due to the motion about Q, GUEST. 34 at UNIV NEBRASKA LIBRARIES on May 27, 2016pau.sagepub.comDownloaded from 530 THE INSTITUTLON OF AUTOMOBILE ENGINEERS. when either the displacement or the velocity of R is under consideration. The type of motion is that of which a simpler example is given in Fig. 6. If viscous friction exist at any point R, it will be of the amount 6.WR where WR is the total velocity of the point. Accord,Xngly i t can be analysed into 6.UR opposing the motion about P, and G.VR opposing the motion about Q. Taking the summation of the viscous resistances a t all points, it is evident that each of the oscillations about P and Q is damped without affecting the motion about the other, and thus the damped oscillations are independent as before. The rolling motion presents no points of interest here, the effects of a raised centre of gravity ,having no effect on Equation (4), the quantities being as there described" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003239_s0022-0728(02)01447-x-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003239_s0022-0728(02)01447-x-Figure4-1.png", "caption": "Fig. 4. Cyclic voltammograms of a CCE modified in 0.1 M acetate buffer (pH 5) at a scan rate of 5 mV s 1 in the absence (c) and presence of 60 mM insulin solution (d). (a and b) Same for a bare CCE.", "texts": [ " The results show that the formal potentials and response currents are almost constant. This modified electrode can be used as a stable sensor at physiological pH values. One of the objectives of this work was to fabricate a modified electrode capable of the electrocatalytic oxidation of insulin. In order to test the electrocatalytic activity of the Ru-complex doped carbon composite ceramic electrode, the cyclic voltammograms were obtained in the absence and presence of 60 mM insulin in buffer solution (pH 5). In the absence of insulin (Fig. 4 curve c) a well-defined cyclic voltammogram was observed for the carbon ceramic electrode modified with the Ru(II)/Ru(III) couple. The anodic peak potential for insulin oxidation at this modified CCE is about 700 mV versus the reference electrode (Fig. 4 curve d), while insulin is not oxidized until 1.2 V at the bare CCE (Fig. 4 curve b). Thus, a decrease in overpotential and an enhancement of the peak current for insulin oxidation is achieved with the modified electrode. One of the advantages of this modified electrode in comparison with similar modified electrodes [35], is that the cyclic voltammogram of the Ru(II)/Ru(III) redox couple shows clearly defined anodic and cathodic peaks, and the oxidation peak of the Ru(II) complex and insulin (700 mV) do not overlap with the oxidation of water (1100 mV). The responses of the Ru-complex doped carbon ceramic electrode in 30 mM insulin solutions at different pH values (3 /8) are presented in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003608_9783527618811-Figure4.3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003608_9783527618811-Figure4.3-1.png", "caption": "Fig. 4.3 Local trivialization of a fiber bundle.", "texts": [ " The relevance of this example is that the M\u00f6bius strip is built from a base circle with line segments and a twist and these are 124 4 Constrained Systems precisely the ingredients of a fiber bundle. Namely, a fiber bundle consists of the elements {E,M, F, \u03c0,G} where E is a manifold (the total space), M is a manifold (the base space), \u03c0 : E \u2192 M is a projection of E onto M, F is a manifold (the fiber) and G is a group acting on F. The elements satisfy the following conditions: \u2022 There is an open covering {Ui} of M such that E is locally trivial, that is, \u03c0\u22121(Ui) \u223c= Ui \u00d7 F. In other words, there are diffeomorphisms \u03c6i : \u03c0\u22121(Ui) \u2192 Ui \u00d7 F : \u03c6i(u) \u2192 (p, f ) such that \u03c0[\u03c6\u22121 i (p, f )] = p (Fig. 4.3). \u2022 If Ui and Uj are not disjoint, then the transition functions cij = \u03c6j \u25e6 \u03c6\u22121 i are elements of the group G (Fig. 4.4). A notation sometimes used to describe a fiber bundle {E,M, F, \u03c0,G} is F \u21aa\u2192 E \u03c0\u2192M The M\u00f6bius strip is a fiber bundle in which E is the surface,M is the circle, F is a line segment and G is the two element group {1, a|a2 = 1}. There is an open cover of the circle with two open sets: say \u2212\u03c0 < u < 1 2 \u03c0 and 0 < u < 3 2 \u03c0. These intervals intersect on two subsets (0, 1 2 \u03c0) and (\u03c0, 3 2 \u03c0)" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000594_tia.2018.2799178-Figure10-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000594_tia.2018.2799178-Figure10-1.png", "caption": "Fig. 10. Illustration of subharmonic influence. (a) All ETW S3p. (b) All ETW D3p. (c) Alternate ETW S3p. (d) Alternate UETW S3p.", "texts": [ " Therefore, this kind of asymmetric saturation of adjacent stator teeth can be regarded as the major reason for torque ripple difference. In order to further explain this adjacent stator teeth asymmetric saturation phenomenon, the virtual harmonic fields due to armature field at two specific positions are shown. Although the armature field contains abundant harmonics, only the three most important components, viz. 1, 5 and 7, are used to approximate. For the two specific positions, rotor d-axis coincides with the center of teeth 1 and 2, the magnetic circuit path for three representative harmonics are shown in Fig. 10. The solid, dotted and point lines are used to represent the 1 st , 5 th and 7 th fields, respectively. 0 2 4 6 8 10 0 90 180 270 360 R e la ti v e p e rm e a b il it y Rotor position (electrical degree) T1 T2 T3 X1e3 Position 1 Position 2 0 2 4 6 8 10 0 90 180 270 360 R e la ti v e p e rm e a b il it y Rotor position (electrical degree) T1 T2 T3 X1e3 Position 1 Position 2 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. When the 1 st harmonic does not exist, there will not be difference between teeth 1 and 2, as shown in Fig. 10(b) for the All ETW D3p machine. This means that all of the teeth have the same saturation level over one electrical period and the torque ripple should be minimal compared with other electrical machines. With the increase of the 1 st harmonic, the All ETW S3p machine shows some differences between teeth 1 and 2, as shown in Fig. 10(a). However, due to the small portion compared with the working harmonic, the influence is small and the torque ripple does not evidently increase. When the alternate teeth wound winding is adopted, the amplitude of the 1 st harmonic is beyond the working harmonic and its influence on torque ripple is obvious. Thus, the difference between teeth 1 and 2 is obvious for the Alternate ETW S3p machine, as shown in Fig. 10(c). For the Alternate UETW S3p one, the asymmetry due to UETW stator core structure will further aggravate such side effect, as shown in Fig. 10(d). Overall, the higher level of adjacent stator teeth asymmetric saturation leads to the higher torque ripple. The subharmonic coming from winding topology and the stator asymmetric core structure like UETW are the two major factors. D. Influence of current value Since the armature field is affected by current value, the torque-current, PP torque-current and torque ripple-current characteristics are shown in Fig. 11 within three times of rated current. It can be found that the saturation phenomenon appears for torque-current characteristic if the current is larger than rated value" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000346_j.mechmachtheory.2017.09.013-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000346_j.mechmachtheory.2017.09.013-Figure4-1.png", "caption": "Fig. 4. 3D model of the 5R Goldberg.", "texts": [ " (23) , we have d = 4 (24) The mobility of the kinematic chain ABCDE is calculated as, M = d(n \u2212 g \u2212 1) + g \u2211 i =1 f i + v = 4 \u00d7 (5 \u2212 5 \u2212 1 ) + 5 + 0 = 1 (24) where M indicates the mobility of kinematic chain, n indicates the number of links, g is the number of kinematic joint, f i is the DOFs of the i th joint, v is the parallel-redundant-constraint factor and in the single-loop mechanism, \u03bd = 0. So kinematic chain ABCDE is a 5R SLOL, this kind of construction method is feasible. This 5R SLOL is also the general form of the 5R Goldberg linkage [4] . A 3D model of the 5R Goldberg linkage is given in Fig. 4 , two configurations in its motion are also given in this figure. In Fig. 4 , the revolute joints expressed by dotted line are the fixed joints. In the constructing process, there are four geometric configurations between link AF and EF \u2032 . The four configurations are also the configurations when two Bennett linkages are combined, they are shown as below. (I) This configuration is the most general configuration, there is no special geometric relation between the two Bennett linkages. In the obtained single loop kinematic chain, there is an offset between the axes of joints A and E, as shown below" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001449_j.mechmachtheory.2021.104396-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001449_j.mechmachtheory.2021.104396-Figure1-1.png", "caption": "Fig. 1. Coordinate definition of power-skiving machining system.", "texts": [ " The literature contains many methods for avoiding such interference issues, including designing the tool tooth profile with a conical shape [2-6] , or adding a tilt angle to the tool movement mode [7] . However, these methods further increase the complexity of the tool design process and / or machining conditions. Accordingly, the present study proposes a new power-skiving tool design method and associated full-view angle analysis method for designing simple cylindrical power-skiving tools capable of preventing both interference scenarios. Fig. 1 shows the general power-skiving scenario for the machining of an involute internal gear. The world frame (i.e., (xyz) world ) is located at the workpiece (or internal gear) center and does not move with the workpiece. By contrast, the workpiece frame (i.e., (xyz) w ) is fixed at the workpiece center and moves with the workpiece. In other words, the pose of frame (xyz) world with respect to frame (xyz) w is given as w A world = Rot (z, \u2212\u03b8w ) , (1) where \u03b8w is the rotation angle of the workpiece. The tool frame (i" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003122_s0094-114x(96)00033-x-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003122_s0094-114x(96)00033-x-Figure7-1.png", "caption": "Fig. 7. Singularity corresponding to case 3 for $2 and $3.", "texts": [ " For this singular configuration, the line S~$2 intersects the axis o f R~ and the line S~$3 intersects the axis o f R3. This is equivalent to Condi t ion (1) applied to two different loops and two different ro tary joints. Mathematical ly, the partial derivatives o f the first and third loop-closure functions with respect to 0~ and 02, respectively, are equal to zero. This singularity also occurs along a curve, but the mechanism gains two degrees o f freedom in this case. This is the curve where the singularity surfaces of the spherical joints $2 and $3 intersect. Figure 7 shows the singular configuration. 4,1.4. A special case. Lastly, the singularity caused by all three spherical joints together is worth mentioning. In this case, the three common tangents are parallel to each other and all are perpendicular to the platform. Therefore, the platform is in the same plane as the base. In this case, the mechanism gains three degrees of freedom and this singularity can happen at a finite number of points. All the elements of the Jacobian matrix are zero in this case. Figure 8 shows the four possible ways the mechanism can be assembled with the platform in the same plane as the base" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000628_tie.2018.2849970-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000628_tie.2018.2849970-Figure9-1.png", "caption": "Fig. 9. Flux line and flux density distribution of the proposed BFMPM machine.", "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. Based on the optimization results, the slot number of the prototype is 24, the conductor number per slot of the power winding 1 is 45 and the conductor number per slot of the power winding 2 is 55. The parameters of the prototype are shown in Table I. Using the FEM, the no-load flux line and flux density distribution of the proposed BFMPM machine are shown in Fig. 9. It is obvious that there is a two pole pair component in the stator core due to the bi-directional flux modulation effect. The outer rotor PMs also result in a significant 13 pole-pair harmonic component in the airgap. The FFT analysis result of the flux density in the airgap between the outer rotor and the stator is shown in Fig. 10. The FFT result shows the 13rd and 2nd order harmonics are much larger than other magnetic field harmonics in the airgap. Therefore, the FEM simulation results agree with the analytical model very well" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003068_jsvi.1997.1298-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003068_jsvi.1997.1298-Figure9-1.png", "caption": "Figure 9. Mode shapes of multi-mesh geared assembly V. (a) Mode 15, coupled flexible and rigid body modes, (0, 0) flexible body mode of driver and driven gears, rotational rigid body mode of the idler; and (b) mode 20, coupled flexible body modes of the gears, (0, 2) mode of the driver and the driven gear, (0, 0) mode of the idler.", "texts": [], "surrounding_texts": [ "stiffness (Km =108 N/m2), the dynamic deformations in all the gears are such that the relative motion at the mesh points on the gears is very small. This shows a strong interaction between the mesh and the structural deformation modes. The second mode shape is an example of the case where all the gears exhibit different flexible body modes. The driver and the driven gears are undergoing (0, 2) modes while the idler gear exhibits a (0, 0) mode. Notice again that the nodal diameters in the two outer gears are located such that there is a minimum possible deformation at either gear mesh interfaces.\nNow we consider a dual mesh system consisting of four spur gears in two planes, as designated by assembly IV in Figure 1, and Table 1. Table 8 compares the natural frequencies yielded by our theoretical (MBD) model with those predicted by FEM. An excellent agreement is again observed since the error is less than 3%. Mode shapes are similar to the example discussed earlier in section 7.5. Two selected bending and rocking mode shapes are shown in Figure 10.\nThe next example is a gear assembly consisting of two dissimilar spur gears which resemble rings. Relevant dimensions of this assembly (VII) are given in Table 1. The transverse deformations have been artificially suppressed since this case is used to illustrate\nT 7\nNatural frequencies of single mesh gear assembly V as obtained from FEM and MBD formulation; see Table 1 for gear specifications\nNatural frequencies vnr (Hz) Mode ZXXXXXXXXXCXXXXXXXXXV\nr MBD FEM e%\u2020\n1 0 0 0\u00b70 2 245 241 1\u00b76 3 419 408 2\u00b76 4 464 451 2\u00b78 5 464 451 2\u00b78 6 480 467 2\u00b77 7 525 510 2\u00b79 8 634 632 0\u00b73 9 645 640 0\u00b78 10 681 675 0\u00b79 11 681 675 0\u00b79 12 772 772 0\u00b70 13 864 854 1\u00b72 14 895 904 1\u00b70 15 966 957 0\u00b79 16 1025 1018 0\u00b77 17 1113 1101 1\u00b71 18 1285 1264 1\u00b76 19 1290 1264 2\u00b70 20 1291 1287 0\u00b73 21 1373 1345 2\u00b70 22 1392 1410 1\u00b73 23 1668 1692 1\u00b74 24 1791 1798 0\u00b74\n\u2020 e%= =vn,FEM \u2212vn,MBD = vn,FEM \u00d7100.", "the coupling between the radial deformation motion in thin compliant gears and the gear mesh regime. Also, for the same reason, gears are free-floating, i.e., not connected to any shaft or bearings. Table 9 lists natural frequencies of individual ring gears together with those of the coupled assembly. Again, the error between the analytical (MBD) and finite element model predictions is below 3% for the first 22 modes. Figures 11(a\u2013d) show a few mode shapes of this assembly. Unlike the previous examples, where the spur gear mesh did not result in strong coupling between the rigid body and the transverse flexural deformation modes, the radial deformation modes of the ring gears are very strongly effected by the mesh stiffness. This is obvious from a large change in natural frequencies of individual ring gears when they are meshed with each other.\nOnce the eigensolutions have been obtained for a disk-shaft sub-assembly, the modal superposition method can be used to calculate forced response characteristics such as", "sinusoidal transfer functions. Dynamic compliance HP/Q and accelerance AP/Q between points P(rP , uP ) and Q(rQ , uQ ) on a disk-shaft subassembly are given as follows where yr (rP , uP ) and yr (rQ , uQ ) are the deformation of the rth mode at points P and Q (see Figure 12), vr and jr are the rth natural frequency and modal damping ratio, respectively, and v is the excitation frequency:\nHP/Q (v)= rP\nFQ (v) = s\nNS\nr=1\nyr (rP , uP )yr (rQ , uQ ) (v2 r \u2212v2)+2jjr vvr ,\nAP/Q (v)= aP\nFQ (v) = s\nNS\nr=1\n\u2212yr (rP , uP )yr (rQ , uQ ) v2((v2 r \u2212v2)+2jjr vvr ) . (46a, b)\nHere, rP and aP are dynamic displacement and acceleration respectively at point P due to a sinusoidal force FQ applied at point Q. The series can be truncated to NS modes depending on the frequency range of interest.\nT 8\nNatural frequencies of single mesh gear assembly VI as obtained from FEM and MBD formulation; see Table 1 for gear specifications\nNatural frequencies vnr (Hz) Mode ZXXXXXXXXXCXXXXXXXXXV\nr MBD FEM e%\u2020\n1 0 0 0\u00b70 2 159 155 2\u00b75 3 198 190 0\u00b70 4 284 275 3\u00b72 5 429 416 3\u00b70 6 479 466 2\u00b77 7 526 510 3\u00b70 8 526 510 3\u00b70 9 604 608 0\u00b77 10 617 610 1\u00b71 11 673 704 6\u00b70 12 677 707 4\u00b70 13 834 855 2\u00b75 14 893 904 1\u00b72 15 893 904 1\u00b72 16 894 904 1\u00b71 17 894 904 1\u00b71 18 963 928 3\u00b76 19 968 953 1\u00b75 20 981 968 1\u00b73 21 1008 997 1\u00b71 22 1118 1073 0\u00b70 23 1264 1264 0\u00b70 24 1264 1264 0\u00b70 25 1265 1264 0\u00b71 26 1265 1264 0\u00b71 27 1290 1334 3\u00b74 28 1291 1334 3\u00b73 29 1647 1692 2\u00b77 30 1648 1692 2\u00b77\n\u2020 e%= =vn,FEM \u2212vn,MBD = vn,FEM \u00d7100." ] }, { "image_filename": "designv10_11_0003551_0094-114x(95)00101-4-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003551_0094-114x(95)00101-4-Figure3-1.png", "caption": "Fig. 3. Slider crank mechanism.", "texts": [ "i on each link can be found starting from the end effector, the only link on which the external force acts (known), calculating the inertial action matrix, summing the total action matrix of the successive link and summing the weight action matrix \u00a2'i = ~ i + \u00a2'i+l + ~i It is very hard to write the dynamic relation of the manipulator in Fig. 2 in symbolic form, so this part is presented only in numeric form in Section 6 which outlines the easy implementation of the presented formulation. 5. C L O S E D L O O P E X A M P L E In this section we present an application of the methodology applied to the closed loop system in Fig. 3, writing the kinematic and dynamic equations. We describe the joint space coordinate by 598 Giovanni Legnani et al. the vector Q = [~tt, a2, ~3, a]. Using the local flame of the fourth link shown in Fig. 3 and letting ci = cos(zti) and si = sin(~J the relative position matrices are: ] V l o , I = cl - s ~ 0 l llc, I sl cj 0 l l js l 1 0 0 1 , 0 . . . . . . . . . . L _ 0 0 0 ~ , 1 c2 -s2 0 i 12c2 s2 c2 0 ',12s2 ] M L 2 = I O 0 1 0 I i-o-- C - - S 3 0 0 s3 c3 0 0 Mz3= 0 0 1 0 -d---O---6----(- I 1 0 0 - a 0 i 0 0 M3'4= 0 0 1 0 0 0 0 l Applying the position equation (4) yields: COS(Oq+ctz+~t3)--sin(cq+~2+~t3) 0 llcos(~q)+12cos(~q+ot2)--a sin(cq + ch + at3) cos(al + ~z + ~t3) 0 llsin(~l)+12sin(al+72) 0 0 1 0 ", "L___I lo 0 0101 0 0 0~0 Matrices L can be referred in the absolute frame (0) using the following relation Applying equation (7) to this closed loop system we have LO,,(O,& + L ,,2~0,~2 + L2.3(0,~3 + L,,O(O,b = lOI from which, remembering that L matrices have six independent elements, the system Ag = 101 of Section 2.2 reduces to 0 0 0 0 0 0 0 0 1 1 1 0 0 I, sin(a,) I, sin(a,) + 1, sin(a, + az) 1 0 -1, cos(a,) -I, cos(a, ) - 1, cos(a, + a2) 0 0 0 0 0 aI a2 = a3 ci is equivalent to three equations with four unknowns. Note that the position system equations outline the geometrical relations (see Fig. 3) I, sin(a,) + I2 sin(a, + a2) = 0 I, cos(a,) + 1, cos(a, + a2) = a that can be used to simplify matrix A. The accelerations of the bodies of the mechanism can be obtained by equations (6) and (3). For the mechanism of Fig. 3 we have Lo. I(O)4 + L2(0@2 + L *.x0$3 + L3.00, ii + f: CLi- l.i(Oj4i)2 + 2 i '2' Lo - I.s(O)L k.r(0)4.~4, = lOI i=l r=2 s=J 600 Giovanni Legnani et al. and the acceleration equations system, A# = b becomes 0 0 0 0 0 0 1 1 1 0 /, sin(a, ) Ii sin(~ ) +/2 sin(~l + ~2) 0 - l , cos(a,) --ll COS(~l)--/2cos(~l + ~2) 0 0 0 0 ~l 0 ~2 1 ~3 0 // 0 0 0 0 -211 cos(a, )o~l o~2 - 2a(o~, + ~2)0~ 3 -21j sin(oq )0~ I ~2 - 2a(o~, + ~2 + 0\u00a23) 0 where the matrix coefficient is equal to the matrix the first time derivatives of the free coordinates equations system" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000716_j.mechmachtheory.2019.07.013-Figure9-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000716_j.mechmachtheory.2019.07.013-Figure9-1.png", "caption": "Fig. 9. Coordinate systems for face gear grinding by the disk wheel.", "texts": [ " The grinding method for the tooth surfaces of the face gear is based on the application of the grinding disk, which has been explained in the previous subsection. The disk wheel moves across the tooth width of the face gear along grinding tracks (theoretical contact lines) on the tooth surfaces of the face gear. The relative motions between the disk wheel and the face gear are controlled to imitate the generating motion between the face gear and the virtual reference conical spur involute shaper. As shown in Fig. 9 , five coordinate systems are established in order to describe the proposed technique. The layout of the coordinate systems is considered as a simplified model of the QMK50A five-axis CNC machine tool (QCMT&T). Point O f is a fixed point in space. d x , d y and d z represent the linear movement of the machine components along x -axis, y -axis and z -axis of the machine tool, respectively. The fixed coordinate system S m is rigidly connected to the frame of the face gear. The moveable coordinate system S 2 is rigidly connected to the face gear" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000101_j.mechmachtheory.2018.01.008-Figure10-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000101_j.mechmachtheory.2018.01.008-Figure10-1.png", "caption": "Fig. 10. (a) Loaded contact pattern of the optimized design. (b) Contour plot of the contact pressure of the optimized design (MPa). (c) Loaded transmission error curve of both the optimized design and original design. (d) Contour plot of the maximum tooth bending stress of the wheel (MPa). (e) Contour plot of the maximum tooth bending stress of the pinion (MPa).", "texts": [ " Item S 2 (mm 2 ) S 1 (mm 2 ) \u03c3 c (MPa) LTE ( \u03bcrad) \u03c3 pstress (MPa) \u03c3 gstress (MPa) Original design 65.06 10.15 1583.6 (edge contact) 28.67 321.5 291.9 Optimized design 53.95 0.076 1412.96 19.99 283.5 285.2 Improvement 17.1% 99.3% 10.8% 30.3% 11.8% 2.3% of S 1 is slightly large, the absolute value is 0.011 mm 2 , which is very small. Therefore, the accuracy of the surrogate model is satisfied. The results of the optimized design are shown in Table 5 together with the improvements relative to the original design. The loaded contact pattern of the optimal design is shown in Fig. 10 (a) together with the original design. The contour plot of the contact pressure is shown in Fig. 10 (b). Other constraints are shown in Fig. 10 (c)\u2013(e). The following conclusions can be drawn from the optimization results: (1) The non-coincident area inside the ideal contact area S 2 (the objective function) is 53.95 mm 2 , which is a reduction of 17.1% relative to the original case (65.06 mm 2 ). The loaded contact zone falls within the ideal contact zone. The non-coincident area outside the ideal loaded contact zone S 1 is reduced from 10.15 mm 2 to almost 0. (2) The maximum contact pressure does not appear at the tips of the pinion and wheel. The load distribution is improved compared with the original design, as Fig. 10 (b) shows. (3) None of the constraints are beyond the limits. The maximum contact pressure is reduced by 10.8%, the LTE is reduced by 30.3%, and the maximum root bending stresses of the pinion and wheel are reduced by 11.8% and 2.3%, respectively. The abovementioned results indicate that the methodology proposed in this paper provides an ideal result with respect to the objective function and constraints. This work proposes a methodology for obtaining an optimized tooth flank considering the loaded contact area, LTE, maximum contact pressure and root bending stress" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000979_j.jmapro.2020.02.003-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000979_j.jmapro.2020.02.003-Figure1-1.png", "caption": "Fig. 1. The geometry meaning of characteristic parameters in (a) circle route and (b) triangle route.", "texts": [ " = \u2212x xl xi (9) = \u2212y yl yj (10) Where xi and yj are the index components along the x- and y-directions, respectively, xl and yl presented the heat source location at x- and ydirection, respectively. The heat source location moved with the arc heat source route. In the circle route, the heat source location is expressed as: = + \u2212 \u00d7xl xs r r cos \u03b8( ) (11) = + \u00d7yl ys r sin \u03b8( ) (12) = =\u03b8 \u03c9t \u03c0 T t2 a (13) Where xs and ys is the heat source start location at x- and y- direction, respectively, r is the circle route, \u03b8 is rotation angle, \u03c9 is angle velocity, Ta is total time, t is time. The geometry meaning of major parameters of circle route are shown in Fig. 1(a). In equilateral triangle route, the heat source location is expressed as: \u23a7 \u23a8\u23a9 = + \u00d7 \u00d7 < \u2264 = + \u00d7 \u00d7 < \u2264 xl xs V cos \u03b8 t t lt yl ys V sin \u03b8 t t lt ( ) (0 ) ( ) (0 ) (14) \u23a7 \u23a8\u23a9 = + \u00d7 \u00d7 < \u2264 = + \u2212 \u00d7 \u00d7 \u2212 < \u2264 xl xs V cos \u03b8 t lt t lt yl ys h V sin \u03b8 t lt lt t lt ( ) ( 2 ) ( ) ( )( 2 ) (15) \u23a7 \u23a8\u23a9 = + \u2212 \u00d7 \u2212 < \u2264 = < \u2264 xl xs l V t lt lt t T yl ys lt t T ( 2 )(2 ) (2 ) a a (16) In Eqs. (14)\u2013(16), V is travel speed at each edge, \u03b8 is each angle, t is time, lt is the time at each edge, h is the height of triangle, l is the edge length of triangle. The geometry meaning of major parameters of triangle route are shown in Fig. 1(b). On the curved top surface, Marangoni stress, \u03c4, drives the convective flow of molten metal inside the pool. It depends on the temperature gradient (G) along the 3D curved surface, liquid fraction and temperature coefficient of surface tension [17] in x, y and z directions, respectively. The three components of Marangoni stress are expressed as: = =\u03c4 \u03bc du dz f d\u03b3 dT Gx l x (17) = =\u03c4 \u03bc dv dz f d\u03b3 dT Gy l y (18) = =\u03c4 \u03bc dw dr f d\u03b3 dT Gz l z (19) whereT is the temperature, \u03b3 is the surface tension, \u03bc is the viscosity of the liquid metal, r is the radial distance from the central axis of the heat source, and u, v, and w are the velocities of the liquid metal along the x, y and z directions, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003490_j.optlastec.2003.12.003-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003490_j.optlastec.2003.12.003-Figure4-1.png", "caption": "Fig. 4. Laser approaches perpendicularly to the contour.", "texts": [ " Assuming that the angle is equivalent to 45\u25e6, the powder concentration on an inclined side of the existing clad layer was calculated with Eq. (1) as shown in Fig. 3. It is seen that the position of the peak concentration varies. As a result, the position of the peak of the clad pro(le moves upwards. The side surface would be more declining in the succeeding cladding. Propagation of declining of side surfaces can be avoided by adjusting the approach orientation of the laser head to the part as illustrated in Fig. 4, where the approach of laser is maintained perpendicular to the contour along which material is being deposited. The peak of the distribution concentration and the clad pro(le would move downwards, and the trend of declining of the side surface is held back. Appropriate orientation can be achieved by moving either the work-piece or the laser head. If the work-piece is moved for the laser beam to remain perpendicular to the existing layer, then there is the added advantage that gravity drives the liquid metal in the molten pool towards the supporting layer, assisting surface tension in holding the molten pool on the existing layer" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001756_j.mechmachtheory.2021.104345-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001756_j.mechmachtheory.2021.104345-Figure4-1.png", "caption": "Fig. 4. Cutter head parameters.", "texts": [ " The concave TE curve is defined as follows: { \u03c62 = \u03c62 M + Z 1 Z 2 \u03d5 1 M + \u03b4\u03c62 \u03b4\u03c62 = c 0 + c 1 \u03d5 1 M + c 2 \u03d5 2 1 M + c 3 \u03d5 3 1 M + c 4 \u03d5 4 1 M + c 5 \u03d5 5 1 M + c 6 \u03d5 6 1 M + c 7 \u03d5 7 1 M (1) where c i (i = 1 , 2 , ..., 7) represent polynomial coefficients. Z 1 and Z 2 represent tooth numbers. \u03d5 1 M = \u03c61 \u2212 \u03c61 M (2) Based on the ease-off technology, position vectors p \u2217 of discrete point i ( i = 1, 2,\u2026, q ) on pinion target surface can be achieved with the following equation [26] : p \u2217 i = p \u2032 i + n \u2032 i \u03b4yi (3) where p \u2032 and n \u2032 represent position vector and unit normal vector of discrete points on pinion auxiliary surface. \u03b4y represent flank modification value. As is shown in Fig. 4 , the straight edge of cutter head is used to process pinion working surface, and the arc segment of cutter head is used to process pinion transition surface. For straight edge profile, position vector r p and normal vector n p of cutting cone are expressed as follows: 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 \u03b8p 1 \u23a4 \u23a5 \u23a6 (4) n p ( \u03b8p ) = [ cos \u03b11 cos \u03b8p cos \u03b11 sin \u03b8p \u2212 sin \u03b8p ] (5) where s p and \u03b8p represent cutter-head parameters, R p represents cutter radius, and \u03b11 represents profile angle" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000238_1.4033045-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000238_1.4033045-Figure3-1.png", "caption": "Fig. 3 Tooth surfaces with circular tooth line formed by flattop generator", "texts": [ " Such a difference forms mismatch between the tooth surfaces of the pinion and the gear. In Gleason face-milling method [30,31], a flat-top generator is used, as shown in Fig. 2. In order to generate tapered teeth, the axis of the generator is perpendicular to the root cone of the generated gear. In this case, the face cone of the generator is a disk, and the pitch cone angle of the generator is less than 90 deg. In the generating process, the pitch cones of the generator and generated gear perform a pure relative rolling rotation. Figure 3 illustrates the formation of the circular lengthwise teeth of the flat-top generator. According to the conjugate generation condition described previously, since both pinion and gear are generated by the same flat-top generator with the generating axis perpendicular to the root cone of each gear member, mismatched tooth surfaces (tooth surfaces with deviation from conjugacy) are naturally formed as a result [24]. 3.1 Formation of Tooth Surfaces of the Generator. As shown in Fig. 4(a), coordinate system Sv\u00f0Ov xvyvzv\u00de is attached on the cutter, the zg -axis is along the direction of the rotating axis of the cutter and xvyv -plane is located at the tips of the cutter" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001756_j.mechmachtheory.2021.104345-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001756_j.mechmachtheory.2021.104345-Figure7-1.png", "caption": "Fig. 7. Meshing impact principle.", "texts": [ " , x 2 n ] T (28) By solving equations shown above, the normal displacement of gear under load can be obtained. By converting normal displacement into angular displacement, the LTE of gear under given load can be obtained. The LTE is one of the main vibration excitation of spiral bevel gear transmission. Then the second objective is to minimize the LTE amplitude of spiral bevel gear transmission under given working con- ditions: min f 2 ( a i , b i ) = max ( T e ) \u2212 min ( T e ) (29) where T e represents the LTE of spiral bevel gear transmission under given working conditions. As shown in Fig. 7 , during gear transmission, the base pitch difference generated from loaded deformation causes mesh- ing impact. The detailed calculation method of meshing impact of spiral bevel gear transmission is provided in [28] . As shown in Fig. 8 , impact velocity v s is as follows: v s = ( v 1 \u2212 v 2 ) n h (30) The gear elastic deformation is caused by meshing impact, and the corresponding impact force is the maximum impact force. According to Timoshenko\u2019s elastic theory, it is assumed that the equation established in the static state is also valid in the process of impact [35] " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001212_tmrb.2020.3027871-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001212_tmrb.2020.3027871-Figure6-1.png", "caption": "Fig. 6. Capsule-endoscope-size soft-robot experiments in synthetic bowels. (A) Single robot. (B) Two-component assembled robot. (C) Test setup with rotating actuator magnet mounted on a gantry system for linear translation of the actuator magnet parallel to the lumen. When the robot moves to the right the actuator-magnet rotation is clockwise, and vice versa. (D) Box-whisker plot of single robot and two-component robot velocities distribution over 30 trials. Notches indicate the 95% confidence intervals on the medians.", "texts": [ " 5(C), the robot\u2019s velocity is symmetric with respect to rotation direction, with the speed decreasing as the lumen deviates from the plane of the rotating dipole. We find that the locomotion is quite robust to deviations up to 45\u25e6. These results demonstrate that locomotion can still be achieved when the orientation of the lumen at the robot\u2019s current location is not well known. In this section, we explore the application of the magnetic gait for capsule-endoscope-size robots applicable to the GI tract. The capsule-endoscope-size robot shown in Fig. 6(A) has corresponding dimensions in the \u201cCapsule\u201d column of Table I. It was modeled after existing clinical capsule devices [38], which at 12 mm in diameter and 25 mm in length is small enough to avoid getting stuck in the pylorus (rigid objects up to 20 mm in diameter) but still short enough to make the sharp turns of the intestines (rigid objects up to 50 mm in length) [39]. A single robot has the potential to be coupled with a second robot to form a longer two-component robot as shown in Fig. 6(B), potentially via directed self-assembly (more on this below). The two-component robot is 50 mm in length, and since it is not rigid, it should still be able to make the sharp bends of the intestine. To connect two robots they need to have alternating polarities, i.e., one needs to have magnet polarities pointing outward and the other needs to have polarities pointing inward, as shown in Fig. 6(B). Once connected, this robot will travel with an undulatory gait using the same principle of actuation as a single robot. Both the single robot and the two-component robot are tested in a synthetic bowel. The experimental setup is shown in Fig. 6(C), with parameters shown in the \u201cCapsule\u201d column of Table I. The rotation of the actuator magnet is controls by a stepper motor. The actuator magnet and stepper-motor assembly are attached to a gantry system to enable translation parallel to the lumen as the robot moves. The lumen environment used is a 305-mmlong synthetic intestine (SynDaver, Double-Layer Bowel). To create an internal cavity, the intestine is placed in a plastic support to keep it propped open. For this experiment, the actuator magnet is rotating at 2 Hz while translating at 8 mm/s", "org/publications_standards/publications/rights/index.html for more information. magnet directly overhead. At the start of the trial, the actuator magnetic would start rotating and translating. The time it took the robot to travel to the other end was used to compute a mean velocity. For the single robot, the mean velocity was 8.7 mm/s with a standard deviation of 0.90 mm/s. For the two-component robot, the mean velocity was 9.5 mm/s with a standard deviation of 0.51 mm/s. The distribution of the trials is shown in Fig. 6(D). We observed a significantly faster speed (p < 0.05) with the two-component robot. The two-component robot would enable larger, more complex robotic systems than would be feasible in a single-capsule paradigm, with the individual components swallowed and selfassembled inside the stomach (in addition to the improvement in locomotion efficiency discovered above). For example, each component could have a single dedicated function (e.g., imaging, localization). Nagy et al. [40] proposed magnetic selfassembly for such an application, in which each component had a permanent magnet on each end (as in our concept), but their magnets were diametrically magnetized (as opposed to the axial magnetization in our concept)", " As the catheter is inserted from the proximal end, the distal end could actively advance to reduce buckling or help guide and steer the catheter through more complex environments. It is almost certain that such an application of the concept would lead to improved insertion based on the results herein, but the degree of improvement is left as an open question. Going further, distributing many such elements along the length of a continuum device may lead to further improvement. The locomotion efficiency of the two-component robot compared to the single robot (Fig. 6) suggests that this may be the case. For continuum devices, our concept\u2019s optional internal lumen could potentially be used as a passageway for tools or fluids once the device has reached its desired location. Authorized licensed use limited to: CALIFORNIA INSTITUTE OF TECHNOLOGY. Downloaded on November 01,2020 at 16:39:13 UTC from IEEE Xplore. Restrictions apply. 2576-3202 (c) 2020 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_11_0000357_s10883-017-9387-2-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000357_s10883-017-9387-2-Figure1-1.png", "caption": "Fig. 1 Schematic model of a spherical robot", "texts": [ " In this paper, we present a derivation of equations for controlled motion in a reference system attached to the pendulum, present integrals of motion and partial solutions, analyze their stability, and give examples of computer simulation of motion using feedback to illustrate the compensation of the pendulum\u2019s oscillations. Consider the rolling of a spherical robot of pendulum type on a horizontal absolutely rough plane (without slipping). The spherical robot is a spherical shell of radius R0 (Fig. 1a) at whose center an axisymmetric pendulum is attached (a Lagrange top). The system is set in motion by forced oscillations of the pendulum. We study a model problem in which it is assumed that the device that causes the pendulum to move generates a control torque applied at the attachment point C of the pendulum. To describe the dynamics of the spherical robot, we define three coordinate systems (Fig. 1b): \u2013 a fixed (inertial) coordinate system Oxyz with unit vectors \u03b1, \u03b2, \u03b3 ; the plane Oxy is horizontal and coincides with the plane of rolling of the spherical robot; \u2013 a moving coordinate systemC\u03be\u03b7\u03b6 with unit vectors \u03be , \u03b7, and \u03b6 attached to the spherical shell and with the origin at the center of mass of the shell C; \u2013 a moving coordinate system Cx1x2x3 with unit vectors e1, e2, e3 attached to the top so that the unit vector e3 is directed along its symmetry axis. The origin of this moving system also coincides with the center of mass of the shell C" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003539_robot.1996.506835-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003539_robot.1996.506835-Figure4-1.png", "caption": "Fig. 4: IdentXcation of dx, dy9 h, ezoff, &ffI", "texts": [ " J(6:m' neglecting the second order terms leads to: din = (Z' - hp) The vector of parameters PI=[& S, d, 62oe 6 3 , ~ l ~ that has to be identified is the one that minimizes for all the number M of measurement points Ni: CI i..I Ei = [zo + 2, + z, + 6, . & - 6, . x, + d, - hp] - di [ X, Y, Z,lr = DKE(eIi +eI, ,ezi +8,, +e3,, 8.) [OIi, OZi, O3is O K J ~ is the nominal configuration given to the robot ccntrolla to reach Ni (no location errors and no offsets are taken into account). \"he non linear minimization problem is solved using MATLAB library. 4.2 Identiflcatioln of d, d, & (91cm9 6 % ~ , &,m) A number I Q\u20ac cylinders are plugged ~n the plane P. The positions are uni ely distributed on a circle Ck (figure 4). So the position and the orientation of each cylinder are accurately in R,. The robot i s moved so the center of the traveling plate Qt describes a circle Ck e laser sensor s on the mobile plate detects the fust edge Blj of the cylinder j. Then the robot moves to detect the second one B, and so on for each cylinder. The configurations Olu, Q2+ e,, (i=l, 2 ; j=l, ..., I) are stored. Using the defmition of \"T,, Bu coordinates are: x, = x, + x, + 6, . (z* + ZJ -6,. r,. = &+Ye +s, . (Z@ +z,)-s,. x, +d, + d, [ x, z,Ir = mz(eli +el, ,ezi + 632zog ,e3i + ew , edi) Using &, 4, d,, eloff, eloff, (330ff values identified with the first procedure, the parameter vector p2=[dx d, &] to be identified is the one that minimizes for all cylinders: i" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003284_0094-114x(94)90025-6-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003284_0094-114x(94)90025-6-Figure3-1.png", "caption": "Fig. 3. The base pyramid of the manipulator.", "texts": [ " The coordinates of O, are obtained from the expressions Xo, = x T - R2L,3, Yo, = y T - RzM,3 , Zo, = z T - R2N,~ where R 2 is the radius of the circle passing through the points 7, 8, 9 (see Fig. 2). This completes the forward displacement analysis. It is interesting to note that rotating the input links with the same angular speeds that the platform makes rotation about the axis O, Z, and the same time remaining parallel to the plane of the base pyramid. 3. NUMERICAL VERIFICATION OF RESULTS A mechanism was chosen with sides 1|.2 : */2.3 : 1;.3 : 17.s : Is., : 17.9 : 145 cms. The remaining parameters can be determined using Fig. 3 which illustrates the base pyramid only since the calculations for the upper pyramid are identical to those for the base pyramid. From Fig. 3, R~ = !,.2 cos 45 \u00b0. The radius of the circumscribing circle of the pyramid base is, R, = (!1.2/2)(1/cos 30 \u00b0) and, RI - - R2. An in-paralkl spherical manipulator 129 The radius of the sphere r = OOt is given by \u2022 and, cos ~z = R,/R3 = i / 2 cos 30 \u00b0 cos 45 \u00b0, cos ~'3 = r / R = (R~ - RZ)'rz/il.2 cos 45 \u00b0, cos ~, = \u2022/R3 cos 45 \u00b0. The coord inates o f the base po ints are 1002 .53 ;0 ;0 ) , 2(0;0; 102.53), 3(0; 102.53;0). The d i rec t ion cosines o f the revolute j o i n t axes are S t { l ;O ;O } , Sz{O;O; ! } and S3{O; I ; 0 } . The leg lengths are it., = 12.3 = 13.6 =/4.7 = ls.s = !~., -- 145 cms. The cosines of the fixed angles are 0 as the stiffness coefficient, Ci ( \u00b7) as the stiffness characteristic, l!ji as the deformed length and l!jiO as the undeformed length of the spring, and dji = r P; p i as the vector from the attachment point Pi of the spring on body i to the attachment point P j on body j. These force relations are in agreement with the above sign convention: 1. For (l!ji - l!jiO) > 0 the two bodies are pulled and the spring is under tension (Figure 6.6). Then F i acts in the direction of eji and Fj acts in the direction of ( -eji)- 6.1 Constitutive relations of planar external forces and torques 247 2. For (R.ji - R.jiO) < 0 the two bodies are pushed and the spring is under compression. Then Fi acts in the ( -eji) direction, and Fj acts in the eji direction. The deformed length .eji of the spring and the associated unit vector eji are computed by (6.6) , (6.7) , and (6.8). 6.1.3.2 Translational damper. Given a translational (point-to-point) damper between the bodies i and j , as shown in Figure 6" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003388_978-3-662-04831-3-Figure5.20-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003388_978-3-662-04831-3-Figure5.20-1.png", "caption": "Fig. 5.20: Vector diagram of a common-point constraint", "texts": [], "surrounding_texts": [ "200 5. Model equations of planar and spatial joints\nComment 5.1.2 (Spatial torsional spring): Spatial as well as planar torsional springs are always assumed to act around the axis of a revolute joint connecting two bodies. In contrast to the \"pseudo-joint\" of Section 5.1.3.1, this joint constrains in the spatial case three translational DOFs and two rotational DOFs of the adjacent bodies.\n5.2 Theoretical modeling of spatial joints\nIn this chapter mathematical models of spatial joints will be derived. As al ready shown in Section 5.1 for planar joints, models of spatial joints will be derived from geometry relations and from suitable representations and pro jections of vector loop equations and/or orientation loop equations that may serve as constraint positionj orientation relations. Associated relative Coordi nates that may be used for measurement or control purposes are isolated by suitable (local or global) representations and projections of these vector or / and orientation loop equations.\nAs there exists a great variety of different spatial joints and massless links, only a few joints of common use in industrial applications will be discussed here. As a first step (Section 5.2.1} several building blocks (BBs} of joint mod els will be derived. Among those, constraint relations of a common-point con straint (BB1}, paraltel-axes constraint (BB2}, straight-line-point foliower con straint (BB3}, rotation-blocker constraint (BB4}, and constant-distance con straint (BB5) will be considered. From these building blocks, constraint rela tions and relative coordinates of the following standard spatial joints will be derived in Beetion 5.2.2 (Table 5.1): spherical joint (BB1}, massless spherical spherical link (BB5}, translational joint (BB2, BB4), universal joint (BB1, BB4}, revolute joint (BB1,BB2}, cylindrical joint (BB2, BB3}, and prismatic joint (BB2, BB3, BB4). A more general universal joint with nonintersecting and nonorthogonal rotation axes will be derived in Appendix A.4.\n5.2.1 BuHding blocks of joint models\nThe discussion in Section 5.1 shows that combining different absolute and relative constraints of two rigid bodies under planar motion already enables the setting up of a large number of different planar mechanisms. Increasing the number of bodies allows the construction of a large variety of different planar kinematic and dynamic mechanisms and machines. It is easy to imag ine that a tremendous variety of different spatial mechanisms can be built from only a small number of rigid bodies that move in space (ffi.3 ). In this section certain geometrical situations associated with spatial joints will be theoretically modeled by constraint position, velocity, and acceleration equa tions. In Section 5.2.2 they serve as building blocks for modeling different types of spatial joints ([4], [40], [41]).", "5.2 Theoretical modeling of spatial joints 201\n5.2.1.1 Common-point constraint (BBl; three constrained transla tional DOFs). A common-point constraint forces two points Qi and Qj of two rigid bodies i and j to a common position Q that may move in space (Fig ure 5.20). This constraint does not allow relative translational motions of the bodies i and j in the points Qi and Qj , but only relative rotations. Let R be an inertial frame and L\" be a local frame with origin P\" (\"' = i , j) on a body \"'\u00b7 Let ARLK be the orientation matrix of R with respect to L\" (\"' = i , j). This geometrical situation is described by the vector loop relation (see Fig ure 5.20)\nThis provides the common-point constraint position equation\nthe associated constraint velocity equation\nor\nor\n(5.19a)", "202 5o Model equations of planar and spatial joints\nRoR Tpio\nWLi LiR (I - ARLi 0 T-Li -I + ARL; 0 T-L; ) 0\n3 ' QPi ' 3 ' QP; RoR = 0, Tp;o\nL; WL;R\n..._____\"_,_._\n=: (v{, vi)T\nand the associated constraint acceleration equation\nor\nRooR ARLi -Li -Li Li ARLi -Li 0 Li RooR TpiQ- 0 WLiR 0 Tqpi 0 WLiR- 0 Tqpi 0 WLiR- TP;O\n+ ARL; 0 wf;R 0 rLQ~o 0 wf;R + ARL; 0 rLQ~o 0 wf;R = o J J 3 3 3\n=: Yp(P) 0 T(p)\nR\"R Tpio\no Lo wL:R\nR .. R rP;O\no L; WL;R\n- +ARL, 0 WL, 0 \".L, 0 WL, - ARL, -L, -L; L; - L,R QP, L,R 0 WL;R 0 TQP; 0 WL;R\ntagether with the constraint Jacobian matrix\n[Jp(P) : = gp(P) 0 T(p) _ (I _ ARLi 0 -Li _I ARL; 0 \".L; ) E oc3,12 - 3 , Tqpi , 3 , QP; o\n(5ol9b)\n(5ol9c)\n(5ol9d)\nThe constraint acceleration equation (5ol9c) will be used as a building block (BB1)o It provides a theoretical model of a spherical joint connecting the hoclies i and j (see Section 5020201)0\nComment 5.2.1 (BBl): In the case that relative rotation angles of the joint are needed, either for sensing or for control purposes, this building block must be reformulatedo\nComment 5.2.2 (Alternative representation of the constraint Ja cobian of BBl): The time derivative of the constraint position equation (5ol9a)\nRd \u00dfg 0 dtg(p) = 8p 0 p = gp(P) 0 T(p) 0 V (5ol9e)\nmay tagether with\n(( R )T T ( R )T T)T p= Tpio ,TJi' Tp;o ,TJj R ( R R R )T Tpio = Xpio' YPio' Zpio" ] }, { "image_filename": "designv10_11_0001741_lra.2021.3065197-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001741_lra.2021.3065197-Figure2-1.png", "caption": "Fig. 2. Model of WRL system with sprayer.", "texts": [ " Thus, in both motion states, the WRL system is expected to provide supporting force for the sprayer to reduce the load force on the user. In this paper, design requirement of WRL system is that the system has the back drivability to provide 80 N continuous supporting force at walking speed of 0-5km/h. The size and weight of system are expected to be as small and light as possible to reduce the extra burden. Also, to prevent frequent charging, the battery capacity should be used for at least 3 hours. As shown in Fig. 2, the WRL system includes three main components: rigid robotic limb, electronic system, and the battery. The rigid robotic limb is fixed in the center of the baseplate of sprayer to support the sprayer effectively and avoid interference with the human legs. When the user wears the sprayer with the WRL, the rigid robotic limb is about 135 mm from the back of the human body in the sagittal plane, and the rigid robotic limb is between the legs in the coronal surface. The rigid robotic limb has a passive wheel, force sensor, supporting rod and linear actuator" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001005_tasc.2020.2990774-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001005_tasc.2020.2990774-Figure3-1.png", "caption": "Fig. 3. 3D FEM of DSRLM at the aligned position.", "texts": [ " Since there are no windings on the mover of DSRLM, only the stator has windings, so the flux linkage of the motor is generated by the stator windings. The magnetic field lines pass successively through the stator tooth, stator yoke, stator tooth, air gap, mover tooth, air gap, stator tooth, stator yoke, stator tooth, air gap, mover tooth and air gap to form a closed loop. The 3D FEM model of DSRLM was established in software Flux, and the magnetic field distributions of unaligned and aligned position motors were obtained as shown in Fig. 2 and Fig. 3 respectively. In this paper, the coincident position of the stator tooth axis and the mover yoke axis is taken as the unaligned position, and the coincident position of the stator tooth axis and the mover tooth axis is taken as the aligned position. Through the 3D FEM model established, it is found that the magnetic field lines of DSRLM pass successively through the stator tooth, stator yoke, stator tooth, air gap, mover tooth, air gap, stator tooth, stator tooth, stator yoke, stator tooth, air gap, mover tooth and air gap to form a closed loop" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000306_ilt-05-2015-0066-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000306_ilt-05-2015-0066-Figure2-1.png", "caption": "Figure 2 The spray angle of traditional oil-air lubrication unit", "texts": [ " Oil has been treated as the secondary phase in our computational simulation analysis (Zeng et al., 2012). The model of oil-air lubrication unit was solved firstly. The influence of the spray angle and spray point position of oil-air lubrication unit on oil-air two-phase flow in ball bearing chamber is investigated in traditional oil-air lubrication system, respectively. The motion state is complicated because the lubricating oil is acted on the surface tension, gravity, centrifugal, pneumatic power and so on. Figure 2 shows the structure parameter of the spray angle ( ) in oil-air lubrication unit. The spray angle is defined as the angle of the center line of the sloped tube with the horizontal line. The lubricating oil may be transported to the exact the lubrication point at the appropriate spray angle of oil-air lubrication unit. The oil-air two-phase flow is investigated at the spray angle of 30, 20 and 0\u00b0, respectively. The velocity of air is 30 m/s in the bearing chamber. Simulation and experiment of oil-air lubrication unit Qunfeng Zeng, Jinhua Zhang, Jun Hong and Cheng Liu Industrial Lubrication and Tribology Volume 68 \u00b7 Number 3 \u00b7 2016 \u00b7 325\u2013335 D ow nl oa de d by L a T ro be U ni ve rs ity A t 1 4: 17 1 6 Ju ne 2 01 6 (P T ) Figures 3 and 4 show the influence of the spray angle on the gas field and oil-air two-phase flow in the bearing chamber, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001788_j.snb.2021.130364-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001788_j.snb.2021.130364-Figure1-1.png", "caption": "Fig. 1. Typical fabrication process of carbon micro/nanostructures. (a) Spin coating. (b) Over-exposure. (c) Development. (d) Oxygen plasma etching. (e) Pyrolysis of the suspended photoresist micro/nanostructures. (f) Carbon micro/nanostructure arrays.", "texts": [ " The carbon micro/ nanostructures were fabricated by oxygen plasma treatment of suspended microstructures and then pyrolyzing. The large thermal stress between the suspended micro/nanostructures, which were produced in pyrolysis process, will result in the formation of the flower-like carbon micro/nanostructures. The decoration of CuO nanofilm on the carbon micro/nanostructures were demonstrated as enzyme free glucose sensors, and the electrochemical performances were evaluated. The schematic for the fabrication of carbon micro/nanostructures is shown in Fig. 1. Single-side polished stainless steel (SS, 310 s) was selected as substrate for the good conductivity and high temperature resistance. The SS substrate was cleaned with acetone, ethanol and deionized water, respectively. Then it was dehydrated at 150 \u25e6C for 15 min. After cooling to room temperature, it was spin-coated with SU-8 2050 (Microchem Corp, USA) at 400 rpm for 20 s and 2000 rpm for 60 s, respectively. The samples were soft baked at 65 for 10 min and 95 for 30 min on the hotplate. In the next step, the overexposure process was carried out using MJB 4 equipment (SUSS MicroTec Group, Germany) and the exposure time was prolonged to obtain suspended photoresist structures through tailoring diffraction-induced light distribution [24] (Fig. 1b). After exposure, the samples were post baked at 65 for 5 min and 95 for 15 min. Finally, the samples were developed in propylene glycol methyl ether acetate (PGMEA) for about 15 min and the suspended photoresist microstructures with different widths were obtained. The suspended photoresist microstructures were then etched with oxygen plasma (Oxford PlasmaLab System 100) and suspended photoresist micro/nanostructures were fabricated. The obtained samples were pyrolyzed in the tubular furnace (MTI GAL 1400x) in 5% H2/95% Ar atmosphere, and the carbon micro/nanostructures were fabricated" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000621_j.matpr.2018.03.039-Figure11-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000621_j.matpr.2018.03.039-Figure11-1.png", "caption": "Figure 11 Load during Acceleration", "texts": [], "surrounding_texts": [ "Jenarthanan M.P et al / Materials Today: Proceedings 5 (2018) 14512\u201314519 14515\nfixed end, all translations are constrained as well as rotations except z-axis. In Shackle end, translation along x-axis and rotation along z-axis are released while all other DOFs are arrested.\nAssume Leaf Spring is in static loading condition shown in Figure 5 (without speed factor) and analyze Total Deformation and Von-Mises Stress values of both Steel and Hybrid Composite Leaf Spring. [7] Load Calculation: Weight of Vehicle, W1= 2150 Kg,Additional Weight (Passengers and Luggage), W2= 750 Kg. Total Weight, W= 2900 Kg. Load Acting on Leaf Spring, F= m\u00d7a F= 2900\u00d79.81 F= 28449 N (For all four-Leaf Springs): F= 7112.25 N (For one Leaf Spring)\nThen the assembly is meshed to for finite elements (Figure 6). Then the setup is solved for Total Deformation and Von-Mises Stress for both Steel Spring and Hybrid Composite [10].The results obtained for static structural analysis are listed in Table 4and the results are shown in Figures 7-10.", "14516 Jenarthanan M.P et al/ Materials Today: Proceedings 5 (2018) 14512\u201314519", "Jenarthanan M.P et al / Materials Today: Proceedings 5 (2018) 14512\u201314519 14517\nAssume the vehicle is slowing down from 60 km/h to 30 km/h. Distance covered by vehicle during deceleration is assumed as 20 m. Load acting on a leaf spring:Vf 2 = Vi 2 + 2\u00d7a\u00d7d Where,Vf = Final Velocity = 30 km/h = 8.335 m/s, Vi= Initial Velocity = 60 km/h = 16.67 m/s,a = acceleration,d = distance travelled by vehicle = 20m.(8.335)2 = (16.67)2 + 2\u00d7a\u00d720,208.42 = 40a,a = 5.208 m/s2. Decelerating Force, Fd = ma,Where,m = mass of the vehicle= 2900 kg, a = acceleration= 5.208 m/s2, Fd= 2900\u00d75.208, Fd= 15110.21 N (For all four-leaf springs),For one leaf spring, Fd = 15102.32/4, Fd= 3775.58 N. Total load acting on the leaf spring is Ft = F+ Fd, Ft= 7112.25+3775.58,Ft=10887.83N. The results obtained for transient structural analysis for deceleration are shown in Figures 16-20 and listed in table 6.\nTable 6 Results during Deceleration\nParameter Steel EN45A Carbon/Glass Composite Max Stress 415.79 MPa 545.53 MPa Max Deformation 8.9656 mm 15.005 mm\nFigure 16 Load during deceleration" ] }, { "image_filename": "designv10_11_0000801_j.msea.2019.138161-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000801_j.msea.2019.138161-Figure4-1.png", "caption": "Fig. 4. (a) Schematic illustration of the single\u2010line formation test. (b) Depiction of each experimental operation under the same content of reinforcement.", "texts": [ " The laser spot diameter and hatch spacing were fixed at 80 \u03bcm and 60 \u03bcm, respectively. This hatch spacing was reported to be suitable for overcoming the lack of cohesion between two consecutive scans [16] and producing SLM samples of higher density [18]. The laser power and scanning velocity were selected using a large number of preliminary experiments associated with the single-line formation tests for the pure 304 stainless steel powder being built, which will be discussed in Section 3.1. A schematic illustration of the single\u2010line formation test is shown in Fig. 4(a). The laser power was set between 175W and 200W, while the scan speed was varied from 36.6mm/s to 1098mm/s. A schematic illustration of the main experiments is shown in Fig. 4(b). A total of 39 cubes with dimensions of 7mm\u00d77mm\u00d72mm were fabricated via SLM under various weight percentages of Al2O3 and eutectic mixture of Al2O3\u2013ZrO2, as listed in Table 1. The microstructure of the powder material and built samples were characterized using optical microscopy (OM) and scanning electron microscopy (SEM; a Vega Tescan). For the built samples, the top surface and cross section were investigated; and for the microstructure analysis, the samples were etched using 100mL distilled water, 10mL HCl, and 3mL HNO3 for 70\u201375min prior to the OM and SEM observations" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003522_apec.2003.1179229-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003522_apec.2003.1179229-Figure4-1.png", "caption": "Figure 4. Vector Diagram for Phase Advance Angle Control", "texts": [ " Torque is produced by the q-axis current iq, the current id and i0 related with field are zero usually. Therefore following equation is obtained. qq e e iepT \u03c92 3= (7) From the above equation, iq component can be obtained as following. q e eq ep Ti 1 3 2 \u03c9 = (8) By using field component of the stator current to reduce air gap field produced by permanent magnets, the BLDC motor drives are reached in constant power operation. The principle of proposed phase advance angle control method is shown in Fig. 4. When the motor operating at the high speed, q-axis component of the back-EMF is increased from eq-base to eq1 and q-axis component of current is decreased from iq-base to iq1. However, q-axis component of back-EMF and current are became to eq2 and iq2 by given phase advance angle \u03c6, respectively. These relations are explained by equations as following. . 2 3 constPie p T mqq e e === \u03c9 (9) When the phase advance angle control method was used, back-EMF eadv produced by id2 can be written as following" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001563_s00170-021-07221-0-Figure11-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001563_s00170-021-07221-0-Figure11-1.png", "caption": "Fig. 11 Temperature test of motorized spindle: (a) test rig and (b) schematic of measuring positions", "texts": [ " The steady temperature field [T] of the motorized spindle is outputted until the convergence criterion is satisfied, where the convergence criterion can be given as Hb1\u2212Hb0 Hb0 \u2264\u03b5 \u00f047\u00de Otherwise,Hb0 =Hb1 is assigned, and Eq. (3) is resolved. \u03b5 is the user-defined error threshold, and \u03b5 = (10)\u22124 is found to be exact for the example analysis presented in the next section by repeatedly comparing the simulated results. The temperatures near the outer ring of bearings 3 and 4 are tested using a thermocouple sensor to verify the thermal network model (Fig. 11). The test rig is shown in Fig. 11a, and the position dimensions of the measuring points are L1 = 212.5 mm, L2 = 80mm, L3 = 61.25 mm, and L4 = 63mm (Fig. 11b). In this work, the spindle runs for more than 3 h to ensure that the spindle is in thermal balance. Then, the temperature value on the temperature indicator can be recorded. In this test, the rated speed of the motorized spindle is 3000 rpm, and the ambient temperature is 26 \u00b0C. The cooling oil volume flow rate of the stator is 4 L/min, and the inlet oil temperature is 21 \u00b0C. All bearings are preloaded by positioning, and the initial preload is 150 N. The bearing parameters and materials of the components are shown in Tables 1 and 2, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003096_s0003-2670(01)01408-8-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003096_s0003-2670(01)01408-8-Figure1-1.png", "caption": "Fig. 1. Reaction scheme depicting the role of a mediator for an enzyme-catalysed anodic reaction where PANi is the poly(aniline)\u2013 poly(acrylate) or poly(aniline)\u2013poly(vinyl sulphonate), LDH is the lactate dehydrogenase and GCE is the glassy carbon electrode.", "texts": [ " Its structure has been determined [13], and it can be readily expressed in Escherichia coli [14,15]. The enzyme is an NAD+-dependent dehydrogenase that catalyses the interconversion of l-lactate and pyruvate. The enzyme is stable over a wide temperature and pH range and has been shown to retain activity following mutagenesis such as the introduction of a histidine tag at the N-terminus [15\u201317] and the changing of amino acid residues in the active or cofactor-binding sites [18\u201321]. The proposed scheme for the generation of a bioanodic current from substrate turnover of LDH is shown in Fig. 1. Whilst the modification of proteins with (poly)histidine tags has been used extensively as a means to aid their purification (for example through affinity chromatography) [17,22], recently we have shown that histidine and other peptide tags can also be used as a means of immobilising proteins on modified sensor surfaces [23\u201325]. Recently, it was shown that whilst a biotinylated peptide-tag can often lower the homogeneous (i.e. solution-based) activity of alkaline phosphatase (ALP), the activity was not significantly reduced further on modified surfaces, due to favourable interactions between the tag and the surface" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000453_j.apm.2019.03.008-Figure36-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000453_j.apm.2019.03.008-Figure36-1.png", "caption": "Fig. 36. The film velocity field evolution from engaging-in to recess.", "texts": [ " 35 ) show that the shape of nanoparticles influences the flow of lubricating oil in the contact region, and many vortexes form in the center of the contact region. The backflow that forms around the inlet zone of contact region. In a whole engagement cycle, the entrainment speed, pinion linear velocity, and gear linear velocity dynamically change. Therefore, the film velocity field varies with meshing action. The dynamic film velocity field is investigated considering spherical alumina nanoparticles as additives. Roughness amplitude A is set as 0.2 \u03bcm. Fig. 36 presents the film velocity field evolution from engaging-in to recess, in which x / b is the dimensionless X and z / h represents dimensionless Z ; Z = 0 indicates the pinion surface and Z = 1 indicates the gear surface. The effects of roughness on film velocity distribution are remarkable, and film velocity considerably increases and some concentrated vortexes form and move from gear teeth to pinion teeth with the engaging motion ( Fig. 36 ). There is significant backflow in the inlet zone, probably due to the blocking effect by a large displacement thickness of the laminar flow boundary layer. In this paper, a robust numerical algorithm for lubrication the high-speed spur gears in rough contact was presented, and the algorithm validated based on the classical Dowson minimum film thickness formula. The lubrication mechanism of base oil with the addition of nanoparticles was studied based on EHL contact theory. Taking alumina nanoparticles, for instance, the influences of nanoparticle shape and concentration on tribology performance and load-carrying capacity of gear lube were fully analyzed" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001327_s00170-020-05927-1-Figure15-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001327_s00170-020-05927-1-Figure15-1.png", "caption": "Fig. 15 Example 2 transmission error curve of face gearFig. 14 Example 2 location and size of contact area", "texts": [ " Figure 13 is the topological map of the tooth surface corresponding to Example 2. It can be seen from the figure that the tooth surface modification amount is the largest at the outer diameter position near the tooth root position and the inner diameter near the tooth top position, and the maximum tooth surface modification amount is \u2212 0.089 mm and \u2212 0.132 mm, respectively. The maximum modification amount of Example 2 is greater than the modification amount of Example 1. The tooth contact area and transmission error curves are shown in Fig. 14 and Fig. 15. Compared with Fig. 12, the direction of the contact trace is further inclined, and the transmission error curve is a parabola with an amplitude of 3.6\u2033. The calculation results are consistent with the direction and size of the designed contact area, and the design method achieves control over its meshing characteristics. According to the generation grinding principle of face gear, a five-axis face gear grinding machine has developed to achieve the disk CBN wheel grinding of face gear. In the grinding process, the spindle speed is 4300 rev/min so as to achieve grinding linear velocity 30 m/s, and the feed speed is 1500 mm/min" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003388_978-3-662-04831-3-Figure5.25-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003388_978-3-662-04831-3-Figure5.25-1.png", "caption": "Fig. 5.25: Spherical joint", "texts": [ " r~o ' w~R ' r~o ' w~R (5.39) 5.2.2 Theoretical models of common joints In this section the constraint relations of several spatial joints in common use will be set up from the building blocks of Section 5.2.1. The spatial joints considered are collected in Table 5.1. 5.2.2.1 Spherical joint (BBl; constrains three translational DOFs). A spherical joint is completely modeled by the building block BB1 (cf. Bee tion 5.2.1.1). The constraint position, velocity, and acceleration equations of a spherical joint (Figure 5.25) are as follows. Constraint position equations of a spherical joint rR _ rR + A RLi . rLi _ A RL; . rL; _ 0 PiO P;O QPi QP; - \u00b7 (5.40a) Constraint velocity equations of a spherical joint Rr-R - ARLi . \".Li . wLi - Rr-R + ARL; . rL; . wLL;R = o. (5.40b) PiO QPi LiR P;O QP; , Constraint acceleration equations of a spherical joint [I - ARLi . r-Li -I + ARL; . r-L; J . 3 ' QPi ' 3 ' QP; =: Yp(P) \u00b7 T(p) R .. R rpio . L\u00b7 wL:R R .. R rP;O . L; WL;R - + ARL, . wLL,R. rLq'p . wLL,R- ARL, . wLL,,R. rqL,p\u00b7 , " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000820_tec.2019.2941935-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000820_tec.2019.2941935-Figure1-1.png", "caption": "Fig. 1 Outer rotor PM machine with 8-pole 9-slot", "texts": [ " Outer-rotor motors have higher developed torque, the easier process of winding and a more mechanically robust structure compared to inner-rotor motors. These features make them popular in electrical bicycles [1] and electrical vehicles [2], [3]. One type of outer-rotor PM machines is a consequent-pole machine wherein all permanent magnets have been magnetized in the same direction. In a surface-mounted motor, if for instance, the north poles are unchanged and the south poles are replaced by ferromagnetic poles, a consequent-pole motor is obtained. Fig. 1 shows how a conventional surface-mounted machine is illustratively changed into the consequent-pole structure for an 8-pole, 9- slot outer-rotor PM machine. In consequent-pole machines due to the reduction of the number of magnets and presence of the iron between them, the armature reaction field mostly passes through iron. These features result in several advantages: The lower number of PMs lead to the cost reduction (both fabrication and maintenance), the introduction of reluctance torque results in increasing the torque at speeds above the nominal speed, fringing linkage flux reduction and hence increase in flux linkage, PM losses reduction (eddy current losses in the magnet) due to passing the armature reaction flux through the iron poles" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003925_tmag.2005.846262-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003925_tmag.2005.846262-Figure1-1.png", "caption": "Fig. 1. Two target motors. (a) M-model. (b) K-model.", "texts": [ " If the motor has skewed slots, we have to use one of the multislice model, the coupled method of 2-D and 3-D models [7] and the full 3-D model [8]. The influence of skewing on the radial force and vibration will be the subject of future work. This paper calculates two motors, hereafter K-model and M-model. To build the model for the simulation, the properties of the material used in the actual motor are loaded. The properties and characteristics of interest in this work are presented as follows. For M-model, 1.5 kW, 200 V, 50 Hz, 6.8 A, 4 poles, number of stator slots: 36, number of rotor slots: 44, and one slot-pitch skewing (see Fig. 1). For K-model, 100 V, 50 Hz, 4 poles, number of stator slots: 24, number of rotor slots: 34, stator winding: 66 turns, rotor bar: aluminum, and no skewing [4]. The models were created using a triangular mesh with 13 665 elements and 6907 nodes for the M-model [see Fig. 2(a)]. For the M-model, these numbers are 14 498 elements and 7333 nodes [see Fig. 2(b)]. The values obtained for the aluminum relative conductivity are for the K-model, and for the M-model. 0018-9464/$20.00 \u00a9 2005 IEEE Fig. 3 shows the measured and calculated torque and current", " The space variation of the radial electromagnetic force is presented in Fig. 4. It is shown that the radial force is big at the position where sthe flux density is big as shown in Fig. 4, and is approximately flat in the teeth and becomes a small value at the positions where the rotor slot exists. Fig. 5 shows the time variation of the force at the different teeth. It is shown that the force at tooth 1 is the same as that at tooth 4 and is bigger than those at teeth 2 and 3, because the stator winding is distributed in three slots as shown in Fig. 1(a). Figs. 6 and 7 show the radial force and its spectrum at a tooth for different slips. It is shown that the force at the teeth is bigger than that at the slots and have a fundamental frequency of two times the line frequency 50 Hz. The radial force at a low speed is very different from that at slip . Here, we discuss the frequencies of radial force. The electromagnetic flux harmonics are produced due to the relative movement between the rotor and stator. Seeing it from the stator\u2019s side where the main flux is generated, the permeance varies periodically due to the presence of the slots in the rotor" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000238_1.4033045-Figure14-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000238_1.4033045-Figure14-1.png", "caption": "Fig. 14 Three-dimensional models of the pinion (a) and the gear (b)", "texts": [ " In this optimization, the locations of the contact points, which are limited at the middle of the tooth surfaces, are set as the objective function, the machine-tool settings are taken as design variables, and the optimization process is realized in the software ANSYS through iterative computation. Note that, since the tooth surfaces of noncircular spiral bevel gear are different for each tooth and the contact patterns of each tooth are also different, the transition of meshing between teeth has to be analyzed to determine the evolution of the contact area for a meshing cycle. Through setting different cutter locations, iterative computations of FEA are carried out to obtain optimized machine-tool settings for pinion, as listed in Table 4. Figure 14 illustrates the 3D models for the pinion and the gear. Figure 15 illustrates the contact area (a) of the pinion on a concave surface (b) and the gear on a convex surface at the mean position. The contact ellipses with bias are located approximately at the center of the tooth surfaces. Based on the machine-tool settings listed in Tables 3 and 4 and the kinematical model of each machine axis (Eq. (43)), the generation is implemented in a six-axis CNC bevel gear cutting machine with SINUMERIK 840D system" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001051_j.engfracmech.2020.107305-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001051_j.engfracmech.2020.107305-Figure1-1.png", "caption": "Fig. 1. (a) Sample geometry for fatigue crack growth test (in mm); (b) Orientations and entities of the samples.", "texts": [ " In this study, the main purpose was to investigate the single tensile overload influence on crack growth of SLM Inconel 625 superalloy. Firstly, the FCG tests of SLM Inconel 625 superalloy CT specimens were carried out by the load-controlled method. Crack propagation rate data were obtained and discussed. The phenomena of crack growth behavior induced by single overload application were analyzed. And plastic zone size was calculated by different measures, and scanning electron microscope (SEM) was used to examine and explain the mechanism of the FCG behavior. Based on the ASTM E647 specification, as shown in Fig. 1a, for the samples (CT specimens) employed in this investigation, the D. Ren et al. Engineering Fracture Mechanics 239 (2020) 107305 width (W) was 32 mm and the thickness (B) was 5 mm. Through electro-discharge machining, the notch was machined with the length of 6.4 mm (in the test, the initial crack length was set as the notch length). In this study, each specimen was cut from the SLM Inconel 625 plate. The as-received plate was subjected to solution annealing heat treatment at 1100 \u25e6C/h in an argon protected environment to eliminate the residual stress and optimize the anisotropy of microstructure. The samples entity and cutting orientation for the fatigue test is shown in Fig. 1b. Samples were obtained from different orientations, i.e. perpendicular and parallel to building directions Z of SLM Inconel 625 plate. That is, the crack propagation directions of the CT specimens were along two directions parallel to the Y and Z axes, respectively, which are marked as Z-Y and Y-Z, respectively, as displayed in Fig. 1b. Chemical compositions of SLM Inconel 625 used in this single peak overload study are presented in Table 1. The tensile fatigue crack growth test used CT specimen with sides clamped between two fixtures, and was placed in a working cell of an Electro-hydraulic servo fatigue testing machine, INSTRON 8872 (USA, INSTRON company). For the pre-crack preparation stage, the initial experimental methods and parameters were as follows: The loading frequency f = 15 Hz. Decreasing \u0394K-method was used in the pre-crack preparation stage" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003288_00207170110112250-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003288_00207170110112250-Figure4-1.png", "caption": "Figure 4. Rotational/translation proof mass actuator.", "texts": [], "surrounding_texts": [ "The benchmark non-linear problem involving the design of a stabilizing controller for the non-linear RTAC or TORA system has been extensively examined in recent years. Several stabilizing controllers have been developed, based on integrator backstepping and passivity approaches for the state-feedback and output-feedback stabilization problems (Wan et al. 1994, Bupp et al. 1995, 1996, Jankovic et al. 1996, Diong 1997, Jiang et al. 1998, Escobar et al. 1999, Jiang and Kanellakopoulos 1999). Since the dynamic model of this RTAC is not globally feedback linearizable, we can obtain a cascade form as considered in this paper by partial feedback linearization methods. We can, then, derive the composite sliding control scheme for the RTAC system. As shown in \u00aegure 4, the translation oscillator consists of a cart of mass M connected by a linear spring of sti ness k to a wall. The rotational actuator, which is mounted on the cart, consists of a proof mass of mass m and moment of inertia I located at a distance e from its centre of rotation. The control torque applied to the proof mass is denoted by N and the disturbance force exerting on the cart by F . If the translational position of the cart from its equilibrium position is denoted by q; and the counterclockwise rotational angle of the eccentric mass by \u00b3; then the equations of motion are given by D ow nl oa de d by [ U ni ve rs ity o f W es t F lo ri da ] at 2 1: 57 0 5 O ct ob er 2 01 4 As in Wan et al. (1994), if one de\u00aenes the normalized variables xd M m I me2 r q; Fd 1 k M m I me2 r F u M m k I me2 N; \u00bd k M m r t and the parameter \" me I me2 M m p which represents the coupling between the translational and rotational motions, then equations (63) and (64) are simpli\u00aeed to xd xd \" \u00b3 cos \u00b3 _\u00b32 sin \u00b3 Fd 65 \u00b3 \" xd cos \u00b3 u 66 In the new coordinates de\u00aened by y xd \" sin \u00b3, _y _xd \" _\u00b3 cos \u00b3; \u00b1 \u00b3 and _\u00b1 _\u00b3, one can obtain the di erential equations from (65) and (66) y y \" sin \u00b1 Fd 67 \u00b1 1 1 \"2 cos2 \u00b1 u \" cos \u00b1 1 \"2 cos2 \u00b1 y \" sin \u00b1 Fd \"2 sin \u00b1 cos \u00b1 1 \"2 cos2 \u00b1 _\u00b12 68 which is in the form of equations (25) and (26). According to the notations given in } 3, we note that fm y, gm \", F \u00b1 sin \u00b1, fa \" cos \u00b1 1 \"2 cos2 \u00b1 y \" sin \u00b1 Fd \"2 sin \u00b1 cos \u00b1 1 \"2 cos2 \u00b1 _\u00b12 and ga 1 1 \"2 cos2 \u00b1 For simulation, the parameters for the RTAC testbed given in Bupp et al. (1995) are used as follows: M 65 oz, m 2:44 oz, k 18:6 oz/in, e 2:33 in and I 0:74 oz-in2: Let f\u0302m fm M x 0 ; f\u0302a fa N x; \u00b1 0 and 0:1 min m gm max m 0:2; 1 min a ga max a 2: We have Gm 1 min m max m p 7:0711 Ga 1 min a max a p 0:707 and m max m min m s 2 a max a min a s 2 Taking \u00ac1 1, \u00ac2 1 such that F \u00b1 is subjected to a sector-bound condition (27) gives \u00bc \u00ac2 \u00ac1 =2 1: Choose \u00bb \u00af 20 > \u00bc; then k1 \u00bc= \u00bb 1=20: Set \u00b6a \u00b6m 1:0, Fa Fm 0:1, \u00b2a 0:1 and \u00b2m 0:45 > \u00bb \u00bc Fa max m 2\u00b6a 0:21 The function \u00bf x can be computed from (49), (50) and (51), where Km m \u00b2m M m 1 k1 f\u0302m w\u0302m : The overall controller can, therefore, be obtained by Theorem 1 with Ka a \u00b2a N a 1 f\u0302a w\u0302a : For comparison, we simulated the non-linear system using both the proposed composite complementary sliding control and composite sliding control, where the control functions vm and va in (51) and (59), respectively, were replaced with Km 1 k1 sat sm Fm \u00b3 \u00b4 and Ka sat sa Fa \u00b3 \u00b4 The responses of the normalized cart displacement xd for the system with disturbance Fd 0 and initial conditions: xd 0 ; _xd 0 ; \u00b3 0 ; _\u00b3 0 0:1; 0; 0; 0 ; and 0:5; 0; 0; 0 were depicted in \u00aegures 5 and 6, respectively. We note that the settling time for xd to reach and stay less than 0:01 is about three units of \u00bd for the former case: By comparison, this result is superior to other alternative design methods such as Wan et al. D ow nl oa de d by [ U ni ve rs ity o f W es t F lo ri da ] at 2 1: 57 0 5 O ct ob er 2 01 4 (1994), Bupp et al. (1995), and Diong (1997), where the settling times are, respectively, 12:5, 51 and 17 units of \u00bd: To examine the disturbance\u00b1rejection property a orded by the proposed control, we considered Fd 0:0472 sin 2\u00bd; or F 0:4 sin 2\u00bd and simulated the system with zero initial condition. Figure 7 shows that xd settles down to a steady-state amplitude of 0:014 (0:02 when the composite complementary sliding control (composite sliding control) was applied. This means a 69% (58%) reduction in the steady-state amplitude of xd can be achieved by the proposed control. In contrast, the controllers proposed in Wan et al. (1994), Bupp et al. (1995) and Diong (1997) gave reductions of 59%, 56%, and 44%, respectively. We note that these remarkable results were obtained without involving too much control e orts, as were shown in \u00aegure 8." ] }, { "image_filename": "designv10_11_0003456_tia.2003.810643-Figure11-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003456_tia.2003.810643-Figure11-1.png", "caption": "Fig. 11. Modification and measurement of inter-bar resistance.", "texts": [ " However, there are simplifications in the method used in [2] that may lead to incorrect estimates of the inter-bar resistance. A study of an inter-bar resistance measurement technique is put forward here. A skewed rotor was prepared by removing the end-rings and drilling and tapping two holes into one end of each bar, alternating the end which is drilled with successive bars. These gave tappings for current injection and voltage measurement. Direct current was then injected between adjacent bars as shown in Fig. 11 at 5 and 10 A for all the bars. The voltage was measured using a high-quality micro-voltmeter. Since the voltage was very low, the current was varied across a wider range for one connection to ensure the V\u2013I characteristic went through the origin (i.e., there was no voltage offset giving false results). The rotor bars had a cross-sectional area of 38.8 mm and there was a distance of 82 mm between the current terminals. The resistance of the bar between the current terminals was calculated as 0.073 m " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001089_tia.2020.3046195-Figure20-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001089_tia.2020.3046195-Figure20-1.png", "caption": "Fig. 20. IR thermal image and predicted temperature distribution across the motor components at 600 s after power turning ON for coolant flow rates of 10 LPM.", "texts": [ " The IR temperatures at monitor point on the windings end turn (blue line) and lamination (light blue line) are extracted. The input data of thermal resistances listed in Table III for the simulation are calibrated by the IR thermography measurement. The predicted temperatures on the windings end turn (pink dash line) and lamination (red dash line) match the measurement very well during both heat up and cool down periods. Parameter study of the contact resistance and effective windings density was carried out to achieve these results. Fig. 20 shows the IR and CFD images across the motor components at 600 s after power turning ON, and Fig. 21 shows measured (with error bar) and predicted temperature histories on stator end turn and lamination, both for the flow rates of 10 LPM. As expected, the temperatures of 10 LPM are lower than that of 3 LPM because more heat removed at high flow rate. The predicted temperatures match the measured data. Fig. 22 shows the IR and CFD images across the motor components at 600 s after power turning ON, and Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003864_s00419-006-0027-7-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003864_s00419-006-0027-7-Figure2-1.png", "caption": "Fig. 2 Scheme of the \u201cfitting\u201d of the reference configuration of the markers to the current one in a least squares sense", "texts": [ " the position and rotation of the original or reference configuration of the cluster of markers is fitted to the current configuration of the markers in a least squares sense. In the case of a perfectly rigid body segment, the position of the marker j in the global frame is described by the position vector r M j = Si r O M j + r Oi , (2) where Si is the rotation matrix of a body-embedded frame , r Oi is the position vector of the origin of this frame, and r O M j is the position vector of the marker j in the body-embedded coordinate system, see Fig. 2. Because the segments are not perfectly rigid and the cluster of markers deforms due to the skin artefacts and the measurements errors, a rest vector, r R j , is subtracted from the left hand side of Eq. (2) yielding r M j = Si r O M j + r Oi \u2212 r R j . (3) The extent of the deviation of the current marker position to the correspondent one in the reference configuration is given by the Euclidean norm of the rest vector |r R j | = \u221a rT R j r R j . (4) Now the rotation matrix Si and the position vector r Oi are searched that optimize the position and orientation of the reference configuration with respect to the current configuration of the markers. In a least squares sense, this means to minimize the sum of the norms of all the rest vectors. An interesting analogy to this problem can be formulated as minimizing the elastic potential energy stored in linear springs connecting the markers of the current and reference configurations, as shown in Fig. 2. With Eqs. (3) and (4) the optimization problem can be then written as min { 1 mi mi\u2211 j=1 |r R j |2 } = min { 1 mi mi\u2211 j=1 (Si r O M j + r Oi \u2212 rM j ) T (Si r O M j + r Oi \u2212 r M j ) } , (5) where mi represents the number of markers used in the reconstruction. In order to eliminate the vector r Oi from the expression, the centroids of the positions of the markers in the body-embedded and global coordinate systems, respectively, are introduced as r\u0304 O M = 1 mi mi\u2211 j=1 r O M j and r\u0304 M = 1 mi mi\u2211 j=1 r M j " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000508_s11740-019-00922-2-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000508_s11740-019-00922-2-Figure4-1.png", "caption": "Fig. 4 Cutter feed directions at different faces with respect to orthogonally rotating scan direction and build direction", "texts": [ " For side milling (ae < De/2) and a single round insert (ap < D/2), the chip thickness can be calculated from Eq.\u00a0(2) as h = 0.00137\u00a0mm. The schematic diagram of the experimental setup is shown in Fig.\u00a03. (1)De = Dc + \u221a D2 \u2212 (D \u2212 2ap) 2 (2)h = 4fz DDe \ufffd\ufffd ap(D \u2212 ap) \u00d7 \u221a ae(De \u2212 ae) \ufffd . To investigate the effect of feed direction with respect to faces of the additively fabricated nickel alloy Inconel 625 workpieces, side milling along different directions on three different faces were performed. At first, the workpiece was fed along the y-direction on the XY face, which is the Case 1 as indicated in Fig.\u00a04. After that, the workpiece was fed along the x-direction on the XZ face which is the Case 2. In Case 3, the workpiece was fed along the z-direction on the YZ face. All test conditions that are listed in Table\u00a01 were performed for each case of the side milling experiments. The influence of scan strategy (or stripe pattern) rotation on the machinability of the LPBF nickel alloy Inconel\u00a0625 was also investigated. Two workpieces with different scan strategy rotations were used in this work; a workpiece built with scan strategy rotation of 90\u00b0, and another one built with 67\u00b0 rotation. Both workpieces were side milled by following climb (down) milling engagement in three cases as indicated in Fig.\u00a04. In the force measurement setup, the force in X-direction, Fx, indicates the cutting force component measured along the feed rate direction. The force in Y-direction, Fy, indicates the cutting force component along radial depth of cut direction and the force in Z-direction, Fz, indicates the cutting force component along the axial depth of cut direction. All side milling force signals (Fx, Fy, Fz) depict a similar signal form which can be divided into three stages of climb milling cutter engagement, including the stages of cut-in, stable cut, and cut-out as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001379_tec.2020.3030042-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001379_tec.2020.3030042-Figure7-1.png", "caption": "Fig. 7. 3D structures of the stator core.", "texts": [ "org/publications_standards/publications/rights/index.html for more information. > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 7 A. Calculation of the Natural Frequencies of Stator Core In this paper, the natural frequencies of the stator core of a 7.5kW variable-speed PMSM is calculated. The main parameters of the stator core and the simplified structures of stator tooth are shown in Tab. I and Tab. II, respectively. The 3D structure of the stator core is shown in Fig. 7. In order to ensure that the mechanical performance parameters used in the analytical calculation are consistent with that of the laminated stator prototype, the density of the stator core is determined by measuring the mass and volume of the prototype, and the radial and tangential elastic modulus are obtained by changing it in the 3D finite element model until the simulation results converges to the measured value with the axial modal order m=0. The selection of the axial elastic modulus is referred to [26] and [28]" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001781_s12046-021-01650-z-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001781_s12046-021-01650-z-Figure6-1.png", "caption": "Figure 6. Comparison of cooling effect with and without flux barriers, [13].", "texts": [ " A forced water cooling method was imparted to cool the interior permanent magnets [34]. The cooling area and cooling effect are increased considerably as the coolant flow through the flux barriers in the stator which is surrounded by a water-cooling jacket. The flux barrier water jacket cooling had enhanced the cooling effect by 10.5 % compared to the simple water jacket cooling without flux barriers for this PMSM. The flux barrier cooling method caused a lot of turbulences which eventually increased the heat dissipation, figure 6 [13]. A self-adaptive energy-saving cooling system is studied to remove the heat generated in the machine for its effective use. A fuzzy law-controlled cooling pump and cooling fan are designed. Matlab/Simulink is used in developing the simulation model considering the topology and fuzzy controller parameters including the temperature of critical constituents viz. wheel hub temperature, battery temperature, power electronic converter temperature, etc. [50]. Glass fiber stator sleeve placed in the airgap facilitate to cool the stationary components effectively by liquid coolant with minimum windage as the rotor components run dry" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001747_tro.2021.3062306-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001747_tro.2021.3062306-Figure2-1.png", "caption": "Fig. 2. Visual representation of the hand\u2013eye problem AX = XB formulation, which is based on relative geometrical transformations. .", "texts": [ " In the literature, the solution to the hand\u2013eye calibration problem can be formulated using relative or absolute geometrical transformations. The relative transformation method makes use of the geometrical differences between the same frame of reference at different moments in time, which requires the execution of several arm motions to gather sufficient data for the calibration. The hand\u2013eye calibration formulation makes use of transformations that relate the same coordinate frames in distinct positions. This is depicted in Fig. 2 and can be formulated as AX = XB (1) where A and B are transformations that relate the different time frames of the robotic arm and the camera, respectively, and X is the unknown transformation from the hand to the eye [2]. The arm transformations are provided by the robotic system itself, 1552-3098 \u00a9 2021 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: Miami University Libraries" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003511_s0094-114x(00)00024-0-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003511_s0094-114x(00)00024-0-Figure1-1.png", "caption": "Fig. 1. Relationship between the cutting blade and worm.", "texts": [ " The in\u00afuence of hob cutter regrinding, assembly errors and transmission ratio on the bearing contact and kinematical errors of the ZN-type worm gear set are also investigated in this paper. The proposed analysis procedures and the developed computer programs are most helpful in designing and analyzing worm gear sets, as well as in designing oversize hob cutters. The ZN-type worm is cut by a straight-edged cutting blade, and the cutting blade is placed on the groove normal section of the produced worm, as shown Fig. 1. Parameter b1 is the lead angle of the worm. The surface equations of the straight-edged cutting blade, represented in the blade coordinate system Sc Xc; Yc; Zc , as shown in Fig. 2(b), can be expressed by: xc rt l1 cos a1; yc 0; 1 zc l1 sin a1; where l1 is the surface parameter of the straight-edged cutting blade and lmin6 l16 lmax. Design parameter a1 is the half-apex blade angle formed by the straight-edged cutting blade and Xc-axis, as shown in Fig. 2(a) and (b). The plus sign of zc expressed in Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000939_j.advengsoft.2019.102722-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000939_j.advengsoft.2019.102722-Figure1-1.png", "caption": "Fig. 1. Structure of mechanical elastic wheel.", "texts": [ " To improve the ride comfort of vehicles equipped with MEW, a quarter-car model matching hydro-pneumatic suspension and MEW is built, considering the continuously changing sprung mass. After that, the Iterative Deletion Artificial Fish Swarm Algorithm (IDAFSA) is put forward as the optimization algorithm. The parameter \u03b4 is also selected as the optimization variable besides the structural parameters of the suspension system. Finally, the optimal match of the MEW and the hydro-pneumatic suspension is obtained, and the ride comfort of the vehicle with MEW is improved. The MEW is made up of the elastic wheel, hinge groups and hub as shown in Fig. 1. The hub is hung in the centre of the elastic wheel by the hinge groups. The hinge groups are evenly distributed in the circumferential direction to connect the elastic wheel and hub. One hinge group generally consists of three single hinges. The elastic wheel is consisted of the rubber layer, snap rings and elastic bead rings. The elastic bead rings are fastened by snap rings and the entire frame is wrapped by the rubber layer. The vehicle load is transmitted to the hub through axle when a MEW is assembled on a vehicle" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000327_j.mechmachtheory.2017.05.014-Figure21-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000327_j.mechmachtheory.2017.05.014-Figure21-1.png", "caption": "Fig. 21. FEM models with different meshing tooth.", "texts": [ "Taking the conclusion shown in Figs. 11-15 into consideration, the contact ellipse on tooth 3 is the worst one, so the contact situation on tooth 3 is the worst and it determines the transmission characteristics of curve face gear. 5. FEM analysis During the meshing process, the contact ratio of helical curve face gear pair is ranging from 1.3 to 2.5, so the FEM analysis of helical curve face gear pair will be divided into single meshing and double meshing. The FEM analysis in this paper was obtained with \u03d5 1 = \u22120 . 01 \u03c0 , Fig. 21 (a) shows the analysis with single meshing and Fig. 21 (b) shows the analysis with double meshing. With the help of ANSYS, the contact stress can be shown on the surface of helical curve face gear with single meshing and double meshing. As Fig. 22 (a) and (b) shown, the contact area on the surface of helical curve face gear are appeared at the inner part of tooth. The area is ellipse at every moment and the errors for the theoretical contact stress compared with FEM analysis are shown in Fig. 23 . From Fig. 23 , the theoretical contact stress is different from FEM analysis during the meshing process" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003511_s0094-114x(00)00024-0-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003511_s0094-114x(00)00024-0-Figure5-1.png", "caption": "Fig. 5. Three-dimensional computer graphic of the ZN-type worm gear set.", "texts": [ " In order to satisfy this criterion, the setting angle c of the oversize hob cutter in the cutting process must be set smaller than that of the worm in the meshing process (i.e., angle c1), as shown in Fig. 4(a), and it can be expressed by: c c1 \u00ff b1 bo 89\u00b03505900; 31 where b1 and bo are the lead angles of the worm and oversize hob cutter, respectively. According to the developed mathematical model of the worm gear set, a three-dimensional computer graphic of the ZN-type worm gear set is shown in Fig. 5. Based on the developed mathematical model of the worm gear set, the contact surface topology method and TCA computer simulation programs, the bearing contact of worm gear sets can be obtained. Fig. 6(a)\u00b1(c) show the bearing contacts on the worm gear surfaces when pitch diameters of the oversize hob cutter are 85.00 mm (6.92% oversize), 80.00 mm (0.63% oversize) and 79.50 mm (without oversize), respectively. It is worth of mentioning that line contact is occurred when the pitch diameter of hob cutters is reground to 79" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001395_s12206-020-1240-y-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001395_s12206-020-1240-y-Figure6-1.png", "caption": "Fig. 6. Circumferential temperature distributions of the coil: (a) crown (x = -79 mm); (b) cross-section (x = 0 mm); (c) welded (x = 75 mm).", "texts": [ " At the top, oil is injected through two inlets per flow path, and flows along the stator. The oil that flows along the flow path of the stator is integrated with the oil that flows along the coil at the bottom of the motor. One-third of the lower part of the motor is immersed in oil, which flows to the outlet at the bottom of the welded side. The temperature distribution of the coil can be observed from two perspectives. Firstly, we can see the temperature distribution in the circumferential direction of the coil in Fig. 6. The top of the end-winding is the spot that the sprayed oil touches earlier. Therefore, the top is the coldest part of the coil. The top of the welded part is approximately 6 % hotter than the crown part. It is because the protruding part with the insulation, welding and epoxy causes influence. The bottom of the coil is submerged in oil flowing through the stator flow path and the outer surface of the coil. Therefore, the highest temperature is observed at 4:30 and 7:30 in Figs. 6(a) and (c), respectively, at location above the bottom of the coil. At the crown part, the 4:30 and 7:30 positions in Fig. 6(a) are approximately 4 % hotter than the bottom. In the welded part, the 4:30 and 7:30 positions in Fig. 6(c) are approximately 3 % hotter than the bottom. It is because the 4:30 and 7:30 are not submerged in oil below and cooled by oil which flows from the reservoir. When comparing the welded part with the crown part, the welded part is generally approximately 4 % hotter. Because the welded part exhibits lesser heat transfer than the crown part due to the insulating, welding, and epoxy at the coil ends. The temperature distribution in the cross-section of the coil in Fig. 6(b) is similar to the temperature distribution of the endwinding. The lowest temperature occurs at the top, and the highest temperature is observed at the 4:30 and 7:30 positions. However, the temperatures differ by approximately 5 %. This is because heat transfer in the circumferential direction is inhibited by the insulating paper located between the stator and coil. Second, we can see the temperature distribution in the longitudinal direction of the coil in Fig. 7. The end-winding of the coil are cooled directly with oil, and no oil flows through the center of the coil" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001005_tasc.2020.2990774-Figure10-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001005_tasc.2020.2990774-Figure10-1.png", "caption": "Fig. 10. Magnetic flux tube division of stator at the aligned position.", "texts": [ " \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 R11 4Rsp1 4Rsp1 4Rsp2 4Rsp2 4Rsp1 R22 4Rsp1 4Rsp2 0 4Rsp1 4Rsp1 R33 0 \u22124Rg1 4Rsp2 4Rsp2 0 R44 4Rsp2 4Rsp2 0 \u22124Rg1 4Rsp2 R55 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 \u00b7 \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 \u03c61 \u03c62 \u03c63 \u03c64 \u03c65 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 = \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 4(F1 + F2 + F3) 4F1 4F1 4F2 4F2 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 (31) In this formula: R11 = 4 ( Rsp1 +Rsp2 +Rsp3 +Rg3 + 1 2 \u00b7Rmp + 1 2 \u00b7Rsy2 +Rsy1 ) (32) R22 = 4(Rsp1 +Rg1) (33) R33 = 4(Rsp1 +Rg1) (34) R44 = 4(Rg1 +Rsp2 +Rg2) (35) R55 = 4(Rg1 +Rsp2 +Rg2) (36) Next, the reluctance of each part of the air gap is specifically determined. In the aligned position, the division of the stator tooth is basically the same as that in the unaligned position, except that the lengths of h1 and h2 are different. In Fig. 10, h1 = Lp/5, h2 = 7Lp/10. Rg1 = \u03c0 \u00b7 Cs 2 \u00b7 \u03bc0 \u00b7 Ls \u00b7 h1 (37) Rg2 = Cs \u03bc0 \u00b7 Ls \u00b7 h2 (38) At the aligned position, the reluctance of the air gap is composed of Rg3a, left-right symmetrical Rg3b, and front and back symmetrical Rg3c. In Fig. 11, h3 = Lp/20. Rg3a = \u03b4 \u03bc0 \u00b7 ((Bs +Bm)/2) \u00b7 (Ls + Lm)/2 (39) Rg3b = \u03c0 \u03bc0 \u00b7 ((Ls + Lm)/2) \u00b7 ln((\u03b4/2)/(\u03b4/2 + h3)) (40) Rg3c = \u03c0 \u03bc0 \u00b7 ((Bs +Bm)/2) \u00b7 ln((\u03b4/2)/(\u03b4/2 + h3)) (41) Then the expression of Rg3 is: Rg3 = 1 1/Rg3a + 2/Rg3b + 2/Rg3c (42) In the division of the flux tube in the stator tooth part, the calculation method and expression of the reluctance of the aligned position and the unaligned position are the same, except that the length of h1 and h2 changes" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000686_0954406219832333-Figure10-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000686_0954406219832333-Figure10-1.png", "caption": "Figure 10. Progressive damage of the thickest reticula, letters refer to Figure 6 (vM stress).", "texts": [ " The second peak of load (F2), associated with the end of the elastic phase of the upper and lower rows of trusses, was as expected higher than the first one (B2). This was due to the different stiffness of the central cell with respect to the upper and lower cells, caused by different geometrical configurations (full Kagome cell vs. half Kagome cell). After D2, the decrease of the load was not due to the instability of the trusses but due to the fracture of the material corresponding to the upper hinges (Figure 10), resulting in a detachment of the trusses from the plates. The same happened in F2 for the lower connections. Then, the complete packing took place. In Figure 11, a comparison between numerical simulations and actual deformed structure is presented, showing that the FE has excellent capability of predicting the overall deformation during plastic collapse. In this study, a damage model taking into account only the effect of triaxiality on the strain at fracture was selected and tuned. With the availability of more advanced models, in a future work, the dependency on the Lode parameter also will be investigated to achieve an even more accuracy in FEA" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003448_1.1539514-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003448_1.1539514-Figure6-1.png", "caption": "Fig. 6 Line and flat pencil singularities of the derivatives of the matrix A", "texts": [ " Transactions of the ASME 17 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F The importance of this proof is that it is easy to visualize the lines of ]A/]xj for planar manipulators and special cases of spatial manipulators. One should recall that the lines of ]A/]xj pass through the joints in the base platform and are perpendicular to the actuators. For planar robots, when more than two lines of ]A/]xj intersect at one point it causes flat pencil singularity of the Jacobian derivatives. Figure 6 shows a flat pencil singularity @Fig. Journal of Mechanical Design rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 08/23/20 6~a!# and point singularity @Fig. 6~b!# of ]A/]xj for a planar 3 DOF non-redundant manipulator. In both configurations the matrix J\u0303 has a rank of 2, which means that Eq. ~43! has no exact solution for an arbitrary Kj. Figure 7~a! and 7~b! show flat pencil and point singularities of the matrix A ~and J!. Figure 8 illustrates a redundant planar parallel manipulator with six linear actuators. The dimension of the nullspace of the Jacobian of this planar robot is 3 or higher. This means that we can control the stiffness elements in the j th column of the stiffness matrix provided that rank of the matrix J\u0303 associated with this column is no less than 3" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003733_iros.2006.282470-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003733_iros.2006.282470-Figure3-1.png", "caption": "Fig. 3. Model of an underactuated compass-like biped robot with semicircular feet. Only the hip-joint torque uH can be exerted to the robot.", "texts": [ " (5) shows that the ankle-torque effect f1 yields being parallel to the swing leg and that of the hip-torque f2 yields central force as shown in Fig. 2. This can be also understood from the angular momentum point of view. Let L [kg\u00b7m2/s] be angular momentum of the robot, and its time-derivative satisfies the relation L\u0307 = u1 + MgXg. (7) Since only u1 appears in this equation, it can be found that the equivalent transformed force vectors of all joint torques except ankle\u2019s should yield in the direction of rg; they are parallel to rg as seen from f2 \u2208 span {rg} in Fig. 3. Only u1 directly affects L\u0307. It is true that, as seen from Fig. 2, the two force vectors must be exerted suitably to drive the CoM forward, but why is the ankle-torque required much more than hip-torque one? In order to prove this question, let us consider the following condition |f1| |f2| = mb|u1| Mrg|u2| = 1 (8) which means the condition that the ankle-torque effect f1 is the same as the hip-torque one. The torque ratio is then TABLE I PHYSICAL PARAMETERS mH 10.0 kg m 5.0 kg a 0.5 m b 0.5 m arranged as |u1| |u2| = Mrg mb = (mb)\u22121 ( (mH l + ma + ml)2 + m2b2 \u22122mb(mH l + ma + ml) cos \u03b8H)1/2 \u2265 mH l + 2ma mb = Ml mb \u2212 2", " The swing phase dynamic equation with only hip-joint actuation is then given by M (\u03b8)\u03b8\u0308 + C(\u03b8, \u03b8\u0307) + g(\u03b8) = [ 1 \u22121 ] uH . (11) The details of the matrix M and the vector C are as follows. M(\u03b8) = [ M11 M12 M21 M22 ] , C(\u03b8, \u03b8\u0307) = [ C1 C2 ] M11 = m ( R2 + (a \u2212 R)2 + 2R(a \u2212 R) cos \u03b81 ) +(mH + m) ( R2 + (l \u2212 R)2 + 2R(l \u2212 R) cos \u03b81 ) M12 = M21 = \u2212mb (R cos \u03b82 + (l \u2212 R) cos \u03b8H) M22 = mb2 C1 = \u2212mR(a\u2212 R)\u03b8\u0307 2 1 sin \u03b81 \u2212 (mH + m)R(l \u2212 R)\u03b8\u0307 2 1 sin \u03b81 +mb\u03b8\u0307 2 2(R sin \u03b82 \u2212 (l \u2212 R) sin \u03b8H) C2 = mb(l \u2212 R)\u03b8\u0307 2 1 sin \u03b8H R [m] is the foot radius (see Fig. 3) and it is the main adjust parameter in this paper. The transition equation on the other hand is modeled by assuming inelastic collision with the ground but the details are omitted. The time-derivative of mechanical energy of this model then satisfies the relation E\u0307 = \u03b8\u0307HuH (12) and thus the power input is given only by the hip-joint torque. Unreasonableness then arises with it as mentioned before. The rolling effect, however, can overcome it as shown in the next section. The reason can be intuitively explained as follows" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003598_ias.1999.798761-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003598_ias.1999.798761-Figure7-1.png", "caption": "Fig. 7: Plot of Flux Linkage Versus Current Showing Torque as the Change in Stored Energy as a Function of Position for a Fixed Flux Linkage", "texts": [ " 222 1 The average torque is equal to the area enclosed by this change in co-energy divided by the change in position. I The instantaneous torque is the differential co-energy as the change in position tends toward zero. 111. OPERATING POINT TORQUE MODEL IN AN SRM USING FLUX LINKAGE AND ROTOR POSITION AS STATE VARIABLES To begin the operating point analysis of the SRM in terms of flux linkage and rotor position, the expression for torque must first be derived for the linear portion of the flux linkage versus current curve. Fig. 7 shows the change in stored field energy with a change in rotor position for the linear part of the flux linkage versus current curve. The change in stored field energy is the difference between the triangular areas of the flux linkage versus current curves. The base of both of these triangular areas is the constant flux linkage, shown as ho in Fig. 7. The heights of the two triangles are the corresponding currents, shown as i l and i2. The equation for torque for the linear magnetic case for one phase of the SRh4 in terms of the flux linkage and rotor position is given by (21) The relationship between flux linkage and current with reluctance is given by (22). h i(h,0) = g % ( h , 0 ) (22) where N2 %(h,0) = - L(h,0) When the machine is not saturated, the inductance and therefore reluctance are no longer functions of flux linkage. They are still, however, functions of rotor position" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001327_s00170-020-05927-1-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001327_s00170-020-05927-1-Figure5-1.png", "caption": "Fig. 5 The coordinate system of wheel grinding face gear", "texts": [ " The rotational motion in the A, B, and C directions realizes the rotation of the face gear about its own axis, the swinging of the face gear about the virtual axis, and the rotating of the wheel around its own axis. It can realize the generating motion on face gear tooth surface by controlling the linkage of the above five axes. According to the research conclusions of the partners [11], combined with the actual structure of the machine tool and the tool holder, the grinding wheel base is designed into a cup shape, and the tool parameters are determined as shown in Table 1. During the face gear grinding, the coordinate system shown in Fig. 5 needs to be established. The coordinate systems Sa, Sb, and Sc are attached to the axial, tangential, and radial slide, respectively. Sf and Sd are attached to the disk CBNwheel and face gear, respectively. Se and Sg are attached to the workpiece swivel axis and the frame of machine, respectively. The radial rectilinear motion Dx is used to create the tooth surface along the tooth width. The axial rectilinear motion Dy is applied to create the tooth depth and allow additional motion between the disk CBN wheel and the face gear" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001034_tie.2020.3009578-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001034_tie.2020.3009578-Figure2-1.png", "caption": "Fig. 2. Configurations of 24-slot/Nr-pole SWFFSM with complementary armature coils. (a) Nr=2k+1, k\u22603i+1. (b) Nr=2(2k+1), k\u22603i+1.", "texts": [ " 1 2 2 1 , 0,1, 2,...r s N j k k N (17) Therefore, for 24-slot F2Ay-OW-SWFFSMs, when the armature coils C1 and Cj exhibit the complementarity, the rotor pole numbers, Nr, can be given by 6 2 1 r k N h (18) For further analysis, the rotor pole numbers can be listed in Table \u2164 when the h takes different values. Similarly, according to the formula (12), it can be found that the 3-phase armature WCs can be effectively constituted only when h=3, 6, or 9 and k\u22603i+1(i=0, 1\u2026). In other words, as shown in Fig.2 (a), for these 24-slot F2Ay-OW-SWFFSMs with (2k+1) rotor poles, only the armature coil C13 possesses the Authorized licensed use limited to: CMU Libraries - library.cmich.edu. Downloaded on August 18,2020 at 09:24:07 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. complementarity with armature coil C1. Correspondingly, every armature coil Cj in 24-slot/(2k+1)-pole F2Ay-OWSWFFSMs possesses the complementarity with the armature coil Cj+12. Furthermore, for these 24-slot F2Ay-OW-SWFFSMs with 2(2k+1) rotor poles shown in Fig.2 (b), both the armature coil C7 and C19 possess the complementarity with armature coil C1. Further, every armature coil Cj in 24-slot/2(2k+1)-pole F2Ay-OW-SWFFSMs possesses the complementarity with the armature coil Cj+6. In addition, considering the polarity of armature coils, the armature coils with complementarity in 24-slot/(2k+1)-pole F2Ay-OW-SWFFSMs should be in series-opposing connection while the armature coils with complementarity in 24-slot/2(2k+1)-pole F2Ay-OWSWFFSMs should be in series-aiding connection" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001395_s12206-020-1240-y-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001395_s12206-020-1240-y-Figure7-1.png", "caption": "Fig. 7. Longitudinal temperature distributions of coil: (a) view from the side; (b) inside and outside of the welded part.", "texts": [ " The temperature distribution in the cross-section of the coil in Fig. 6(b) is similar to the temperature distribution of the endwinding. The lowest temperature occurs at the top, and the highest temperature is observed at the 4:30 and 7:30 positions. However, the temperatures differ by approximately 5 %. This is because heat transfer in the circumferential direction is inhibited by the insulating paper located between the stator and coil. Second, we can see the temperature distribution in the longitudinal direction of the coil in Fig. 7. The end-winding of the coil are cooled directly with oil, and no oil flows through the center of the coil. The coil center is wrapped in an insulating paper, which makes it difficult to transfer heat in the circumferential direction. The coil center is generally approximately 5 % warmer than the end-winding. Therefore, heat transfer in the longitudinal direction is more dominant than that in the circumferential direction. As depicted in Fig. 7(a), the hot spot in the longitudinal direction of the coil appears at the center, and not at the end-winding. Fig. 7(b) depicts the temperature distribution outside and inside the insulating paper of the welded part. Inside, the insulating paper is approximately 15 % hotter than the outside. As can be seen from the circumferential temperature distribution, the temperature is approximately 4 % lower in the crown part than it in the welded part; this is due to the influence of the insulating paper, welding, and epoxy. This implies that heat transfer is more efficient at the crown part than at the welded part. Therefore, hot spot in the longitudinal direction appears to be biased toward the welded part" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000894_j.jfranklin.2019.05.018-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000894_j.jfranklin.2019.05.018-Figure1-1.png", "caption": "Fig. 1. 3D model of a quad-rotor aircraft.", "texts": [ " By a rigorous proof, under the roposed controller, the finite-time attitude tracking task can be achieved for the quad-rotor ystem in the presence of disturbances and input saturation. Finally, the simulation results are rovided to verify that the proposed active finite-time control method has a faster regulation erformance and stronger performance on disturbance rejection by comparing with some other lgorithms. . Mathematical description and some preliminaries .1. Mathematical model of attitude control problem of quad-rotor system As shown in Fig. 1 , the flight of quad-rotor is powered by four motors, which are mounted n the rigid cross structure evolving in a three dimensional space, towing the propellers to enerate the input of the quad-rotor attitude system. The propeller rotation rate \u03c9 i , i = 1 , 2, 3 , 4 determines the thrust of each motor T i and hree torques: the yaw, pitch and roll moment. Taking the geometric center of quad-rotor as rigin, the body-fixed frame \u03c7b = { x b , y b , z b } is set up along the angle bisector formed by the otor-arms, where x and y are coordinates in the horizontal plane, z is the vertical position" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003122_s0094-114x(96)00033-x-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003122_s0094-114x(96)00033-x-Figure6-1.png", "caption": "Fig. 6. Singularity corresponding to case 2 for S~.", "texts": [ " (28) To give a geometric interpretation of this curve, we set joint rates of the passive rotary joints in the R~P2S2SsPsR3 loop to zero. Then, the line SzS3 is fixed and the tangent at Sip must be perpendicular to the platform. So, if a common tangent exists, the line SsSI and the line $2S~ must intersect the joint RI axis. This is similar to Condition (1) described in the previous section, applied to the first and third loops. In this case, the mechanism gains one degree of freedom and this particular singularity occurs along three curves corresponding to the three legs. Figure 6 shows this singular configuration. 4.1.3. C a s e 3. Singularity may also occur when two terms of [J*], which are neither in the same row nor in the same column, are zero. This also results in three symmetrical curves. For D~2 = F36 = 0, the equat ion o f the curve is _ 256k2x 2 + 32k4x 2 _ k6x 2 _ _ 256k2x 3 + 16k4x 3 + 256x 4 - 128k2x 4 + 3k4x 4 + 256x 5 - 32k2x 5 + 96x 6 - 3k2x 6 + 16x 7 + x 8 q- 4 8 k 2 x z 2 _ 12k4xz 2 + 32x2z 2 _ 2k2x2z ~ _ 6k4x2z 2 _ 48x3z 2 q-2X47, 2 q- 4k2x4g 2 \"t- 12xSz 2 + 2x6z 2 + 7- 4 - 2k2z 4 + k4z 4 - 4xg 4 + 4k2xg 4 + 6x2g 4 - - 2 k Z x 2 z 4 - - 4x3z 4 + x4z 4 = O" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003665_iecon.2005.1569239-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003665_iecon.2005.1569239-Figure2-1.png", "caption": "Fig. 2. Robot mechanical structure.", "texts": [ " Fortunately, in the market, there are very low cost battery operated electrical screwdrivers, proving it all in a single set, which may be adapted to a low cost mobile robot. These screwdrivers (or battery operated drills), can be bought for just a few euros (for the one presented in figure 1, the cost was 7.5 Euros). When disassembled, they include a DC motor, a gearbox, batteries and charger. Buying any one of these products in the specific robots market would immediately exceed the cost of the electrical screwdriver. Figure 2 shows the mobile robot mechanical structure made up of two electrical screwdrivers. In the image, it is easily seen that the screwdrivers were cut; the batteries, which were inside the screw-driver, were put along the robot, to keep the robot with a reason-able size. Nowadays many students already have their own laptop computer. They have plenty of accessories, like webcams, which mainly interface the computer through USB ports which are rapidly replacing the old serial and parallel interfaces. However, regarding data acquisition and control cards, usual PCI cards are not suitable for laptops and PCMCIA data acquisition cards are still very expensive" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003388_978-3-662-04831-3-Figure1.1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003388_978-3-662-04831-3-Figure1.1-1.png", "caption": "Fig. 1.1: Examples of multibody systems", "texts": [ "............. 313 A.4.2.4 Fourth constraint equation ................. 316 A.4.3 Computation of the shortest distance between two rotation axes ...................................... 319 References ................................................. 321 Index ...................................................... 329 List of figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333 1. lntrod uction The mechanical systems discussed in this book (e.g., Figure 1.1) are collec tions of rigid-badies connected by translational and torsional spring, damper and friction elements, and by joints, links, bearings and gear boxes, in which some or all ofthe bodies can move relative to each other. They may be driven by external forces or torques to achieve specified performance requirements as well as desired loading and operation conditions. They are called rigid-body systems or mechanisms. A rigid body is defined as an assembly of particles that do not move relative to each other" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000374_tie.2018.2795525-Figure11-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000374_tie.2018.2795525-Figure11-1.png", "caption": "Fig. 11. Reciprocal power-fed test rig for linear induction motor (a) Bogie and Primary (b) Distribution of the sensors.", "texts": [ " FORCES OF SLIMS WITH THE LATERAL DISPLACEMENTS In order to compare to the characteristics of SLIM with ladder-slit and flat-solid secondary, the forces is calculated and shown in the following figures, the input currents are 160 A. Variations of secondary constructions and the difference of end effect lead to the variation of forces in the SLIMs with asymmetry. The thrust and vertical force of the SLIMs with different secondaries are shown in the Fig.10. The range of the slip is 0-2. In order to verify the correctness of the result, the experiments are carried out by the reciprocal power-fed test rig as shown in Fig. 11, and the test SLIMs are driven by a variable voltage and variable frequency inverter. Besides, the SLIMs installed on the rig with the different displacements are used to simulate the possible operating conditions. In the Fig.10 (a)-(b), when the primary is in the asymmetrical position, the thrust Fx and the vertical force Fz in the SLIM with the ladder-slit and the flat-solid secondary change with the variations of velocity at different frequencies. 0278-0046 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000606_j.triboint.2018.02.028-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000606_j.triboint.2018.02.028-Figure7-1.png", "caption": "Fig. 7. Schematic drawing of defect profile.", "texts": [ " The discretization equations of the contact model are presented as >>> 4 Xm n ajbjpj \u00bc Q 8 >>>< >>>>>>: j\u00bc1 1 \u03c0E0 Xm n j\u00bc1 Dijpj \u00bc \u03b4 zi\u00f0xi; yi\u00de Ad \u03c6i\u00f0xi; yi\u00de pj 0; xj; yj 2 \u03a9 pj < 0; xj; yj 62 \u03a9 (4) Where\u03a9 is the solution domain, which is divided intom n units;m and n is the number of grid nodes in the solution region width and length direction, respectively; aj and bj is half length and half width of j unit, respectively; Dij is the flexibility matrix [18]; zi\u00f0xi; yi\u00de and \u03c6i\u00f0xi; yi\u00de is initial clearance and defect topography function of i unit, respectively. The details of the solution process of discretized contact model are illustrated in Fig. 6. It is noted that the initial solution domain needs to be larger than the actual contact area. In this paper, the length and width of solution domain is the roller length and the 1.4 times Hertz line contact width, respectively. In this study defects are considered to be a rectangular depression with uniform depth dd as shown in Fig. 7, the length of defect along roller axial and radial direction is denoted as defect length ld and defect width bd, respectively. The defect profile is chosen so as to simulate the effects of \u201cnon-through\u201d type defect on roller-raceway contact while reducing the model complexity due to irregular natural defect profiles. However, the developed contact model can be use in future to simulate more complex defects. The model of defected roller bearing was performed to demonstrate the effects of defect on roller bearing", " Taking the defect on outer-raceway for example, the contact stiffness of j th roller is represented as Kj; nj \u00bc \u00f0Kd; nd\u00de j\u03b8j \u03d5d j < \u0394\u03d5d=2 \u00f0Kn; nn\u00de non defect area (7) Where \u03b8j is the angular position of jth roller; \u03d5d is the angular position of defect; \u0394\u03c6d is the angular distance of defect; Kd; nd are the stiffness coefficient and index under defect condition; Kn; nn are the stiffness coefficient and index under non-defect condition. The quasi-static model of defected roller bearing is simultaneous nonlinear equations, which can be solved by the Newton-Raphson iteration algorithm. The detailed solution process of defected roller bearing model is illustrated in Fig. 9. The modeling of defected roller bearing is carried out on TRB 32008J with the presented defect modeling method. The parameters of TRB 32008J are shown in Table 1. The defect is positioned to have its axis (Fig. 7) on the center of roller-raceway contact area, and the angular position of defect (Fig. 8) is 0 rad. The processing of roller passing over a defect is simulated to demonstrate the effects of defect on contact pressure and contact stiffness. As shown in Fig. 10, the relative displacement between defect and contact area Dx increases from negative to positive, as the roller passes over defect. When the sum of half contact width bc/2 and half defect width bd/2 is larger than jDxj, the roller will enter the defect area" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003625_robot.2000.846403-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003625_robot.2000.846403-Figure2-1.png", "caption": "Figure 2. Kinematic scheme of the double pendulum manipulator mounted atop of the unicycle.", "texts": [ " (22) One can conclude from (22) that the ASEA IRb-6 manipulator mounted on the track becomes singular only at configurations ( U ( . ) , x) for which cosxl = 0 or sin(x2 - 23) = 0. Exactly the same result have been obtained in [12] by treating the mobile manipulator consisting of the track and the ASEA IRb-6 manipulator as an ordinary 6 d.0.f. manipulator. 3.2 Double pendulum mounted atop of the unicycle In the second example we shall investigate the behaviour of a double pendulum type manipulator mounted on the top of a nonholonomic platform of the unicycle (see figure 2). After choosing as taskspace coordinates the Cartesian coordinates X Y Z the kinematics of such a mobile manipulator take the following form ?/ = k ( q , z ) = qz + ( Z I cos21 + Z2 cos(21 + $2)) sin43 q1 + (11 cos 21 + 12 cos(z1 + 2 2 ) ) cos q3 11 sin z1 + 12 sin(z1 + 2 2 ) The kinematics of the unicycle are represented by a 41 = U1 cosq3 qz = u1 sinq3 (24) 43 = u2, control system where u1, u2 are the platform controls. Without any excessive effort the matrices A( t ) , B(t) , g(q,z) and g(q, 2 ) for the unicycle platform may be computed as 0 0 -211 sin43 6% - ( Q , X ) = &I (11 COSZl + 12 coS(z1 + 22)) COS^^ , (26) -(11 cos 21 + 12 cos(z1 + 2 2 ) ) sin q3 1 0 -(11 sin ri + 12 s i n ( z l + r 2 ) ) s i n q g -12 sin(zl+zZ) s i n q g " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000520_tte.2019.2959400-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000520_tte.2019.2959400-Figure5-1.png", "caption": "Fig. 5. Cross section of the studied SynRel motor", "texts": [ " The final explicit expression for \u0424AG is expressed as: \ud835\udef7\ud835\udc34\ud835\udc3a = \u22122\ud835\udc3f\ud835\udc34(\ud835\udc65\ud835\udc34, \ud835\udc66\ud835\udc34) = 2\ud835\udc3f\ud835\udc350\ud835\udc4e\ud835\udc5f\ud835\udc50\ud835\udc50\ud835\udc5c\ud835\udc60\u210e ( \u221a(\ud835\udc65\ud835\udc34 + \ud835\udc501) 2 + \ud835\udc66\ud835\udc34 2 + \u221a(\ud835\udc65\ud835\udc34 \u2212 \ud835\udc501) 2 + \ud835\udc66\ud835\udc34 2 2\ud835\udc501 ) (29) The MMF drop FED is derived by integrating the magnetic field, (26); along a linear path linking points E and D as follows: \ud835\udc39\ud835\udc38\ud835\udc37 = ( 1 \ud835\udf070 )\u222b \ud835\udc35(\ud835\udc65, 0)\ud835\udc51\ud835\udc65 \ud835\udc45\u2212\u2206\u2212\u210e \ud835\udc45\u2212\u2206 =( \ud835\udc350 \ud835\udf070 ) [\ud835\udc4e\ud835\udc5f\ud835\udc50\ud835\udc60\ud835\udc56\ud835\udc5b ( \u2206 \u2212 \ud835\udc45 + \u210e \ud835\udc501 ) \u2212 \ud835\udc4e\ud835\udc5f\ud835\udc50\ud835\udc60\ud835\udc56\ud835\udc5b ( \u2206 \u2212 \ud835\udc45 \ud835\udc501 )] (30) By inserting (29) and (30) into (27), the explicit analytical expression for the reluctance of a generic hyperbolic flux barrier can be determined: \ud835\udc45\ud835\udc4f = ( \ud835\udc350 \ud835\udf070 ) [ \ud835\udc4e\ud835\udc5f\ud835\udc50\ud835\udc60\ud835\udc56\ud835\udc5b ( \u2206\u2212\ud835\udc45+\u210e \ud835\udc501 ) \u2212 \ud835\udc4e\ud835\udc5f\ud835\udc50\ud835\udc60\ud835\udc56\ud835\udc5b ( \u2206\u2212\ud835\udc45 \ud835\udc501 ) \ud835\udc4e\ud835\udc5f\ud835\udc50\ud835\udc50\ud835\udc5c\ud835\udc60\u210e ( \u221a(\ud835\udc65\ud835\udc34+\ud835\udc501) 2+\ud835\udc66\ud835\udc34 2+\u221a(\ud835\udc65\ud835\udc34\u2212\ud835\udc501) 2+\ud835\udc66\ud835\udc34 2 2\ud835\udc501 ) ] (31) By inserting (18) and (19) in (31); it can be rewritten as follows: \ud835\udc45\ud835\udc4f = 1 2\ud835\udc3f\ud835\udf070 \ud835\udc622 \u2212 \ud835\udc621 \ud835\udc631 = 1 \ud835\udf070 \ud835\udc4b \ud835\udc4c\ud835\udc3f (32) This expression is equivalent to the barrier reluctance in w plane. The methodology presented for analytical computations of the reluctance of a hyperbolic flux barrier is illustrated and assessed by applying it to an eight-pole five-layer-rotor SynRel motor, the cross section of which is shown in Fig. 5. The motor flux barrier design is discussed briefly in Appendix I. Its specifications and some geometrical parameters of the flux barriers are tabulated in Tables I and II, respectively. The stator yoke and winding configuration of the motor are the same as the one in the 2004 Prius IPM motor. An analytical solution based on the MEC method is applied to determine the air-gap flux density of the studied SynRel motor for any rotor position and the stator phase currents. Accuracy of the analytical results is evaluated by comparing them through the FEA simulations [21]-[32]" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003060_s0020-7683(99)00178-x-Figure5-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003060_s0020-7683(99)00178-x-Figure5-1.png", "caption": "Fig. 5. Plane reticulated system with \u00aeve members representing a T-shape, in its reference con\u00aeguration.", "texts": [ " We evaluate fe 4 g, with the following displacements: d K d K 1 85 and d I d I 2 d I 3 DI with kDIk 0O4 86 Since (according to the expression (73)) e 4 A t DI 1 2 DAd I 2 t d I 2 87 then e 4 U1 1 2 m41, \u00ffU1 1 2 m41, U2 \u00ffU3 1 8 m41, U3 1 8 m41 t 88 It does not exist value of U1 solution of the system fe 4 g f0g: Therefore, there is no displacement fd Ig cancelling at order four length variation generated by mechanism fd Kg: So, fd Kg f0, 0, m1, 0gt is an in\u00aenitesimal mechanism of order three, which is in accordance with results from Tarnai (1989) and Kuznetsov (1991a) and displacements expressions that were given by the \u00aerst author. It is interesting to notice that this method gives simultaneously the order of mechanism and values of node displacements fd Kg and fd Ig which cancel length variations until the order of the mechanism (Fig. 4). We notice that another T assembly, comprising \u00aeve members (Fig. 5). which is considered by Kuznetsov (1988) as an order two mechanism, and by Salerno (1992) as a mechanism at least of order three, is also a mechanism of order three. Application of our algorithm leads to a system fe 4 g f0g, which has no U1 solution. Let us search mechanisms of order higher than one for a plane reticulated system submitted by Kuznetsov (1991a, 1991b, 1991c). Length of member 6 (Fig. 6) is parametered by ``a'' a 6 0). It admits two internal independent mechanisms (m = 2): d K1 f0, 1, 0, 0, 0, 1, 0, 0gt and d K2 f0, 0, 0, 1, 0, 0, 0, 1gt 89 The eight components of these vectors \u00aet with the 8 dof (2x, 2y, 3x, 3y, 6x, 6y, 7x, 7y ) of the system" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003196_s0030-3992(99)00116-4-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003196_s0030-3992(99)00116-4-Figure4-1.png", "caption": "Fig. 4. The parameters of the Gaussian function on an inclined plane.", "texts": [ " In theory, the powder stream structure could be expressed by the Gaussian function [7], whose central concentration varies with stand-o distance. Assuming all incident powder from the coaxial jet stream will be captured on the substrate, a simple mode of the powder concentration was proposed in the present study to analyze the e ects of inclined cladding angle. According to the concept of the conservation of the mass, the mode of powder concentration in the coaxial jet stream could be expressed as Eq. (1) and illustrated in Fig. 4 [7] G g h\u00ff y tan f 2 exp \" \u00ff 3y cot y h\u00ff y tan f 2 # 1a s y csc y 1b where g is the peak value of the Gaussian distribution function, y is the axis of the center line, h is the stando distance, f is the half powder spraying angle or half beam divergent angle, y is the inclined cladding angle of the substrate and s is the axis of the inclined plane. With a stand-o distance of 15 mm, half spraying angle of 108 and inclined angles from 0 to 608, the pro\u00aeles of the powder concentration on the projecting plane are shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003805_881587-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003805_881587-Figure1-1.png", "caption": "Figure 1. Optical Arrangement for Oil Film Thickness Measurement", "texts": [ " The angle between the focus optical path and the collection optical path was minimized to limit the optical access required in the engine. The angle is fifteen degrees, set by mechanical interference. Fluoresced light emerges from the optical passage, and a portion of it is focused onto an aperture by a converging lens. The light is then refocused onto the photomultiplier by an additional converging lens. The interference filter is installed in the photomultiplier housing, adjacent to the tube. The photomultiplier output is then amplified and digitized. The optical arrangement is depicted in Figure 1. A Transiac model 2825 4-channel digitizer was used in conjunction with the lab's VAX-750 computer for data acquisition. The digitizer has a frequency response and maximum sample rate of 250 kHz, a 1 megabyte storage capacity, and 12 bit resolution. In addition to the primary signal; cylinder pressure, pulse per crank angle degree, and pulse per revolution were recorded. Sampling was performed on a real-time basis; system limitations precluded the use of crank angle/time sampling at high acquisition rates" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001441_tmag.2021.3081186-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001441_tmag.2021.3081186-Figure4-1.png", "caption": "Fig. 4. Field distributions and flux density under no load. (a) Field distributions. (b) Flux density of GO material. (c) Flux density of NO material.", "texts": [ " See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. BV-04 3 kind of q-axis magnetic flux path goes through SMC cover, rotor, and stator. And Fig. 7 shows the improvement of torque output by utilize reluctance torque. Due to the arrangement of the PMs, the main magnetic flux only pass through the stator in one direction, which can be set as easy magnetization direction, without passing through the stator yoke tangentially. C. No-load Characteristics Fig. 4 shows the stator flux distributions and flux density under no load, showing that the main flux paths go through the easy magnetization direction. It can be seen that the magnetic field distribution is in full agreement with the magnetic principal prediction and GO material is easier to saturate. Due to the smaller area of the inner region of the stator, the inner region of stators, either using NO or GO material, is more susceptible to saturation than that of outer region. It should be noted that even if the GO material is easier to magnetize, the air-gap flux density and back-EMF are not greatly improved under no-load condition, as is shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000625_j.jmatprotec.2018.06.027-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000625_j.jmatprotec.2018.06.027-Figure2-1.png", "caption": "Fig. 2. A schematic of a hydraulic valve (left) and a photo of the valve body of a multiway valve (right).", "texts": [ ", 2015) analyzed the influence of porosity on the lubricated contact by using powder metallurgy austenitic stainless steels. They found the wear rate decreases with increased porosity from 7.6% to 28.8%. Li et al. (Li et al., 2015) compared the tribological performance of PM and standard steel gears materials under typical gear contact conditions. They also found that many large pores enable good lubrication to reduce friction and wear. The application of the current work is to replace the cast hydraulic valve with SLM technology. Fig. 2 shows a schematic of a hydraulic valve. The valve body contains very complex fluid passageways produced by casting using grey cast iron or spheroidal graphite cast iron. By using the AM technology, one can greatly reduce the size and weight of valve bodies. The gap between a valve body and a spool is usually 5 \u03bcm. Thus the surface of the main bore of the valve body requires machining to a Ra \u2248 0.2 \u03bcm or even below. Research reveals that the main failure often takes place on the bore surface due to wear and contaminants, which significantly reduces the lifetime and dynamic response (Amini et al" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000706_0954406219854112-Figure7-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000706_0954406219854112-Figure7-1.png", "caption": "Figure 7. Diagram of the thermal deformation of a gear pair that contains gear backlash.", "texts": [ " Synthesising these factors, the temperature of the gear system can be regarded as a stable. Then, the effect of the temperature on the gear backlash is studied with these prerequisites. After the thermal deformation of the gears, the tooth thickness and the base circle of the gear have both changed. The gear pair has begun meshing in a new pitch circle instead of meshing in the standard pitch circle. However, the centre distance, a, is regarded to be the same. A schematic diagram of the thermal deformation of the gear pair is shown in Figure 7. This figure consists of the gear base circle radii before thermal deformation, ri(i\u00bc 1,2), the gear base circle radii after thermal deformation, rbi, the meshing angle before thermal deformation, , which is also the pressure angle of the standard pitch circle, the meshing angle after thermal deformation, b, and the gear base circle radius after thermal deformation rb:i: rb1 \u00bc \u00f01\u00fe Tl\u00der1 rb2 \u00bc \u00f01\u00fe Tl\u00der2 \u00f018\u00de The temperature difference of the gear, T, refers to the difference between the temperature T1 in the heat balance and the normal temperature, T0\u00bc 20 C" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001120_acsami.9b23093-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001120_acsami.9b23093-Figure1-1.png", "caption": "Figure 1. Bending-induced buckling concept and demonstrations. (a) Schematic illustration of the bending-induced surface wrinkle manufacturing prototype. (b) Mechanism of wrinkling. A liquid UV-curable polymer is coated on a soft elastomer sheet and is cured by UV light on the curved surface. (c) Photo of a 4 \u00d7 4 cm2 surface wrinkle sample fabricated from the roll-to-roll prototype. (d) Atomic force microscope (AFM) image of the 1D sinusoidal wrinkle surface of the sample in (c). The line plot shows the cross-section of the wrinkle profile.", "texts": [ " The potential utility of R2R-manufactured surface wrinkles as a light scattering layer is demonstrated by substantial enhancement of light harvesting and thus the energy conversion efficiency of solar cells under oblique angles of solar illumination. 2.1. Roll-to-Roll Manufacturing Prototype. Owing to its low cost, high speed, and versatility, R2R manufacturing is widely used in industry for large-scale production of various sheet/membrane/paper-based products. The R2R prototype based on bending-induced buckling for surface wrinkle formation is illustrated in Figure 1a (see Figure S1 for a photo of the prototype). The prototype consists of two cylindrical rollers, an elastomeric web, a cylindrical UV light source, and a driving motor. A detailed diagram of the wrinkling process is shown in Figure 1b. The elastomeric substrate made of PDMS (Sylgard 184) is first spin-coated with a thin layer of UV-curable PDMS. The bilayer sheet is wrapped onto a cylindrical roller, experiencing a bending strain. By impinging UV/Ozone (UV/O3) light onto the bilayer, the wrapped portion of UV-PDMS is cured and hardened. Here, the UV/O3 light is chosen because of its highenergy flux (185 and 254 nm wavelength peaks) that facilitates the rapid curing of UV-PDMS, resulting in a high degree of cross-linking. Upon the rotation of the roller, the bending strain in the substrate PDMS layer is released as the bilayer flattens, leading to the formation of surface wrinkles, which can be easily observed with the naked eye. No delamination of the bilayer is observed during processing, suggesting that the two layers have strong adhesion due to their chemical similarities. Based on this prototype, a 4 cm \u00d7 4 cm wrinkle sample is fabricated, as shown in Figure 1c (see Section 4 for more details). The wrinkled region, which covers extensive areas of the sample, appears hazy on a transparent PDMS substrate due to light scattering, which will later be used to enhance light harvesting of solar cells under oblique illumination. Figure 1d shows the atomic force microscope (AFM) image and the https://dx.doi.org/10.1021/acsami.9b23093 ACS Appl. Mater. Interfaces XXXX, XXX, XXX\u2212XXX B cross-sectional profile of the surface wrinkles shown in Figure 1c. In this image, 1D sinusoidal surface wrinkles are apparent with the 4.6 \u03bcm height and the 28.0 \u03bcm wavelength. Examination of the entire sample area shows a roughly 7% variation in the wavelength, possibly due to the nonuniform thickness of the UV-PDMS during spin coating and gravitational flow during the R2R process. 2.2. Surface Wrinkle Library and Wrinkling Mechanism. For a given polymer thickness, the bending strain in the cured polymer should depend on the roller curvature (i.e., diameter) and the substrate thickness", " PDMS (Sylgard 184, DOW Chemical Company) was mixed in a 5:1 weight ratio of the base and curing agent and cured at 60 \u00b0C for 5 h as the substrate. UVcurable PDMS (KER 4690, Shin-Etsu Chemical Co., Ltd.) was mixed in a 1:1 weight ratio of components A and B and spin-coated onto the PDMS substrate at 4000 rpm for 1 min. The coated sample was then manually laid on the curved surface of a cylindrical roller to induce prestrain. Both ends were fixed with tapes. The roller was then installed on the R2R machine with a 5 mm distance to the light source for exposures. For the sample in Figure 1c, a large piece of the wrinkle sample was manufactured by rotating the rollers to achieve continuous exposure. After spin coating the UV-curable PDMS on the 4 cm \u00d7 4 cm PDMS substrate, the sample was installed on the two-roller machine with poly(ethylene terephthalate) (PET) sheets taped to form a closed loop around the two rollers. The exposure distance was kept at 5 mm using an 8 mm diameter roller, and the roller speed was set at 0.02 rpm for complete exposure. For samples in Figure 2, stationary exposure of 15 min was used without rotation of the roller" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003612_s1474-6670(17)31356-3-Figure2-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003612_s1474-6670(17)31356-3-Figure2-1.png", "caption": "Fig. 2. Unicycle robot.", "texts": [ ") Let p be the coordinate of (x, y) on the axis along the normal of the centerline at (xr(q), Yr(q)) and rP = 8 8r (q). Then, the robot's motion in the lane can be expressed in terms of (q,p,rP) (see Figure 3): Suppose it is desired that the robot travels in a prescribed lane of width d, with centerline (xr(s),Yr(s)),s ~ 0, 1 dxrd\"i\"' = cos (}r(S) ;; = sin8r (s), xr(O) = Yr(O) = 0, 8r (0) = O. d(}r d; = wr(s) Consider the motion of a unicycle robot moving at unit speed, which is modeled by { X=CoS(} if = sin () iJ = w(t). See Figure 2. With communication constraints, we assume that the motion of the robot is con trolled in a quantized manner such that, on one hand, the control w(t) can only take N different values. On the other hand, the control is piecewise constant. Adjustments are made only at discrete time instants {tj}~o, with tj+l - tj = h. Call h the sampling interval. The data-rate of the control system here is defined as 3. THE PATH FOLLOWING PROBLEM FOR MOBILE ROBOTS RemaTk 1. It is clear from the equations (1) and the form of the feedback law (2) that the solution curves of the closed-loop system depend only on the ratio kz/kl , and not on the magnitudes of k1 and kz" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003836_bf02844015-Figure11-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003836_bf02844015-Figure11-1.png", "caption": "Figure 11 Cross section of finite element model for an oblique impact on a tennis surface (15 m s\u20131 and 30\u00ba) at different stages of the impact: (a) 3 ms and (b) 4 ms. The velocity of the centre of mass is shown, along with an enlarged view of the contact area.", "texts": [ " 10(c) would be equal to the coefficient of friction, while the ball was sliding. However, Fig. 10(d) shows that this ratio only equals \u00b5 until t = 2.8 ms. After this time, there is a long period (almost 2.0 ms) when the ratio of the friction and reaction forces is less than \u00b5. The reason that the frictional force does not instantaneously reverse direction is simply due to the fact that a tennis ball is not a rigid object. During the impact, the frictional force significantly deforms the felt, as illustrated by the deformed mesh in Fig. 11(a). The enlarged view of this figure shows how the felt has deformed in shear. The felt effectively acts as a \u00a9 2005 isea Sports Engineering (2005) 8, 145\u2013158 155 very compliant interface between the rubber core and the rigid surface. Referring back to Fig. 10(b), the surface tangential velocity was calculated using the ball angular velocity and the effective radius of the ball. This surface tangential velocity is actually only an average tangential velocity through the thickness of the felt and rubber", " For example, the rubber core may be moving in one direction while the felt surface is stationary. The main consequence of the compliance of the rubber and felt is that the direction (and magnitude) of the frictional force F does not suddenly switch from F = R to F = \u2013R. In Fig. 10(b) it was seen that the calculated surface tangential velocity exceeded the horizontal COM velocity after a time of 3.5 ms. However, the frictional force did not reverse direction until 4.2 ms. The reason for this is illustrated in Figs. 11(a) and (b). Fig. 11(a) shows the deformed felt at a time of 3 ms. Shortly after this time, the rubber core starts to spin faster than rolling. However, due to the existing shear deformation of the felt, there is a significant time lag before the rubber core has rotated sufficiently to cause the friction to reverse direction. Indeed, Fig. 11(b) shows that a section of the felt is still deformed, which leads to a net frictional force that has still not reversed direction. Therefore, the FE solution has shown that the ball retains much of the spin that it attained during the impact and can leave with a spin ratio that is greater than unity. Our conclusion is that this mechanism significantly contributes to the high spin ratios that have been measured in this and previous studies. 156 Sports Engineering (2005) 8, 145\u2013158 \u00a9 2005 isea In this study, an FE model of a tennis ball impact on a tennis surface has been used to explain two specific phenomena that occur in an oblique impact" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000767_s12206-019-0203-7-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000767_s12206-019-0203-7-Figure4-1.png", "caption": "Fig. 4. Operating pressure angles of a pair of mesh teeth.", "texts": [ " Therefore, for a gear pair with specific parameters, cases (a) and (d) cannot exist at the same time, and the selection of these two cases depends on the angle relation among \u03b1G, \u03b2, N1 and Ic at the present moment. In Fig. 3, \u03b2 increases gradually as the pinion rotates, and finally, the first tooth center line is beyond the separate line, i.e., the first pair of mesh teeth is separated. When the second tooth center line exceeds the gear center line, it becomes the first tooth center, on which \u03b2 is based. \u03b1G is the actual pressure angle, whereas the variable \u03b1m represents the so-called operating pressure angle, which has different calculations under four tooth contact states (see Eqs. (8) and (9)). Fig. 4 shows the operating pressure angles of a pair of mesh teeth. The action line 1 2B B can be calculated as follows according to the geometry relation of triangles and the characteristics of involute profile: \u00bc \u00bc ( ) ( ) 1 2 1 2 1 1 2 2 1 1, 1 2 2, 2 sin sin , G G G b m q b b m q b B B G O a B F B F R R = = = + = + + + a a a q a q (10) where subscript q denotes the ordinal number of pairs of mesh teeth (q = 1 for the first pair of mesh teeth and q = 2 for the second pair) and \u03b8b2 is the half-tooth angle on the base circle of the gear" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003050_s0094-114x(96)00043-2-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003050_s0094-114x(96)00043-2-Figure1-1.png", "caption": "Fig. 1. Coordinate system S~ and geometry of the cup-shaped grinding wheel.", "texts": [ " Many computer problems such as the tooth contact analysis (TCA) program, computer-aided CNC inspection program and corrective machine-tool settings calculation program have been developed and can be used to form a closed loop manufacturing system. An example is given to illustrate application of the proposed mathematical model. Surface deviation between the real cut spiral bevel gear and the proposed mathematical model has been investigated. Bearing contacts and kinematic errors in the sprial bevel gear have also been studied. 2. I. Surface geometry of the cup-shaped grinding wheel The surface geometry of the face mill cutter and the cup-shaped grinding wheel is usually considered a cone surface as shown in Fig. 1 [8, 9]. The axial cross-section of the cup-shaped grinding wheel is straight-edged in the a-a cross-section in Fig. 1. The position vector and unit normal vector of the cup-shaped grinding wheel surface can be represented by [9]: R,(uj,/~) = FJ .7 t 1 Ir~ + (W + uJ sin ~kJ)lsin flJ 1 Ir\" --- (W + uJ sin @J)lc\u00b0s BJ ] - uj ~os @j (1) and where Nj n j - INA' ~Rj ~Sj N j = - ~ u j \u00d7 - ~ j , and j = i , o . Model of spiral bevel and hypoid gears 123 The subscripts \"i\" and \"o\" denote the inside and outside blades, respectively. The \"+_\" sign should be considered a \" + \" sign for the outside blade and a \" - \" sign for the inside blade" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001024_j.promfg.2020.05.072-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001024_j.promfg.2020.05.072-Figure3-1.png", "caption": "Figure 3 Experimental setup in the machining center for milling thin-walled structures", "texts": [ " The step is created due to the shorter cutting length l2 of the tool compared to the height of the workpiece and is thus formed at the end of the cutting length. The step occurs in the area in which material was not milled in the first process step (I. 1st Machining Step) due to deflection. The height of the step is therefore a good indicator of the deflection of the workpiece during the postprocessing of thin-walled structures. 2.2. Experimental methods, material and tool The experimental setup used on the Heller MC12 machining center is shown in Fig. 3. A solid carbide end mill with number of teeth z = 4 and diameter d = 12 mm was used as milling tool. The end mill had a cutting length of l2 = 24 mm. Ti6Al4V workpieces with a height H = 35 mm and a length L = 60 mm were used for milling. In the initial state, the workpieces had a thickness of t = 7 mm. As described in the process cycle, the surface was machined with two cutting depths ap1 = ap2 = 16 mm and an engagement width ae = 0.2 mm. After one machining cycle, the tactile measurement of the surface was carried out with the measuring device MahrSurf XR 20" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0000909_02678292.2019.1609109-Figure6-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0000909_02678292.2019.1609109-Figure6-1.png", "caption": "Figure 6. (Colour online) a) Capillary-based microfluidic device for the preparation of LCE particles: Droplets of the monomer mixture are formed at the capillary\u2019s tip (100 \u00b5m in diameter) and photopolymerized further downstream before the cured particles are collected in a small glass vial. Adapted with permission [29]. Copyright 2009, Wiley-VCH Verlag GmbH & Co. KGaA. b) Formation of shape-anisotropic droplets depending on the diameter of the polymerization tube. Here, diameters of (a) 1000 \u00b5m, (b) 750 \u00b5m, (c) 500 \u00b5m and (d) 250 \u00b5m were chosen. c) Mechanism of the log-rolling process which leads to the formation of a concentric director orientation. b) and c) are reprinted with permission [35]. Copyright 2011, American Chemical Society.", "texts": [ " Stretching of this film induced an orientation of the mesogens inside the droplets along the direction of stretching so that after UV photopolymerization and dissolution of the PVA matrix, elongated LCE particles having a uniform director field could be collected. Much larger uniform LCP particles can be fabricated in flow via a microfluidic approach which will be explained in the following. In order to achieve a uniform director field in large LCP particles (several hundred microns in diameter), an orientation with the aid of surfactants is not possible. A straightforward method for the fabrication of such large particles are microfluidic approaches which were developed in our group. In our general microfluidic setup (Figure 6(a)) droplets of the monomer mixture are formed, at first, at the tip of a thin glass capillary and then transported by a highly viscous silicon oil further downstream where they are photopolymerized. This microfluidic process not only has the advantage that a multitude of equally sized particles can be prepared in a short time, but it also induces an orientation of the liquid crystalline director inside these droplets. This works due to a shear between the monomer mixture and the high viscous silicon oil", " orientation of the mesogens depending on the shear rates, which can either be increased by raising the flow rate ratio between the monomer (dispersed) and oil (continuous) phase or by decreasing the diameter of the polymerization tube. If no shear is applied, also no orientation of the mesogens can be observed. This was experimentally proven by investigating particles which were polymerized while they were standing still inside the tube [38]. In a series of experiments, Ohm et al. varied the diameter of the polymerization tube in order to influence the shear rate (Figure 6(b)). While for large diameters of 1000 \u00b5m almost spherical particles were obtained, highly shape anisotropic fibres could be observed for small inner diameters of 250 \u00b5m. In between disc-like and rod-like morphologies emerged [35]. Wide angle X-ray scattering (WAXS) measurements were performed in order to investigate the director field of these particles. A determination by POM was not possible because the thick particles (several 100 \u03bcm) always appeared opaque in their LC phase. A concentric orientation was found for the disc-like particles, whereas a bipolar orientation was found for the fibres and rod-like particles", " Latter appeared for high capillary numbers (high shear rates) and thus arises from stretching of the droplet by the high viscous silicone oil during the polymerization. This mechanism is equal to the orientation of the mesogens in mainchain LCP films [91,92]. Many other examples are known in which the fabrication of LCE particles, fibres or even tubes leads to a bipolar director orientation [36,37,45,93,94]. In the case of the disc-like particles, which are formed at smaller capillary numbers (smaller shear rate), the mechanism isn\u2019t as obvious. It was assumed that the orientation originates from a logrolling process which is illustrated in Figure 6(c). Due to the shear flow caused by the surrounding oil, a flow inside the droplet is induced leading to an orientation of the director perpendicular to the flow field. The same director orientation was found for the preparation of LCE core-shell particles and photoresponsive particles [39,46]. Beside the microfluidic process, several other approaches are known for the preparation of LCP fibres. Most of them also lead to a director alignment parallel to the fibre axis since they are based on similar processes (elongational flow) during drawing the fibre from a melted monomer mixture or by electro-spinning of a prepolymerized LC mixture [6,32,56,95\u201397]" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001296_s10846-019-01143-6-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001296_s10846-019-01143-6-Figure3-1.png", "caption": "Fig. 3 Actual and reference positions of the manipulator robot with R-S joints", "texts": [ " Then, a dynamic controller is designed to derive the control torques and forces that can converge the robot\u2019s angular and linear velocities (i.e., vP; \u03b8\u0307i i \u00bc 0;\u22ef; n\u00f0 \u00deand \u03b7\u0307 i i \u00bc 1;\u22ef; n\u00f0 \u00de ) to the desired linear and angular velocity inputs obtained from the kinematic controller (i.e., vPd ; \u03b8 \u02d9 i;d i \u00bc 0;\u22ef; n\u00f0 \u00deand\u03b7\u02d9 i;d i \u00bc 1;\u22ef; n\u00f0 \u00de ). To design a kinematic controller for the mentioned robotic system, the tracking error of the entire system (including the traveling base and the links of manipulator) should be evaluated. Figure 3 illustrates the actual and the reference trajectories of the robot base and end-effector. According to this figure, the difference between the actual and the reference positions of the traveling platform (i.e. Point P) is represented by vector 0 r!Pe, which can be expressed in the x0y0z0 local frame as. 0 r!Pe \u00bc 0RG G r!Pr\u2212 G r!Pa \u00bc 0xPe 0 x!0 \u00fe 0yPe 0 y!0 \u00f043\u00de where 0RG is the 3\u2a2f3 rotation matrix showing the orientation of the global reference frame (i.e.,XGYGZG) with respect to the local reference frame attached to the moving base (i", " Moreover, the orientation errors between the actual and reference angular positions of the moving base (i.e., \u03b80, e) and angular and linear positions of the i th link (i.e., \u03b8i, e and \u03b7i, e) can be represented as \u03b80;e \u00bc \u03b80;r\u2212\u03b80;a \u00f044\u00de \u03b8i;e \u00bc \u2211 i j\u00bc0 \u03b8 j;r\u2212\u03b8 j;a \u00bc \u03b8i\u22121;e \u00fe \u03b8i;r\u2212\u03b8i;a i \u00bc 1;\u22ef; n \u00f045\u00de \u03b7i;e \u00bc \u03b7i;r\u2212\u03b7i;a i \u00bc 1;\u22ef; n \u00f046\u00de By differentiation Eq. (43) with respect to time, the difference between Point P\u2019s reference and actual velocities, expressed in the x0y0z0 coordinate system, is determined as. 0 r!\u0307Pe \u00bc 0 v!Pe \u00bc 0x\u02d9 Pe\u2212 0yPe \u03b8\u02d9 0;a 0 x!0 \u00fe 0y\u02d9Pe \u00fe 0xPe\u03b8 \u02d9 0;a 0 y!0 \u00f047\u00de Based on Fig. 3, the difference between the actual and the reference velocities of Point P, stated in the x0y0z0 local frame, can also be obtained as. 0 v!Pe \u00bc 0 v!Pr\u2212 0 v!Pa \u00bc vPrcos\u03b80;e\u2212vPa 0 x!0 \u00fe vPr sin\u03b80;e\u22120 0 y!0 \u00f048\u00de The dynamics of the moving base position errors can be attained by equating Eqs. (47) and (48). 0x\u02d9 Pe \u00bc vPrcos\u03b80;e\u2212vPa \u00fe 0yPe \u03b8\u02d90;a \u00f049\u00de 0y\u02d9Pe \u00bc vPr sin\u03b80;e\u2212 0xPe\u03b8 \u02d9 0;a \u00f050\u00de The dynamics of the orientation and position errors of the moving base and manipulator links can be determined by differentiating Eqs" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003122_s0094-114x(96)00033-x-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003122_s0094-114x(96)00033-x-Figure3-1.png", "caption": "Fig. 3. The R S S R - S C mechanism.", "texts": [ " We can thus conclude that: in a loop containing an S - - S link, if the line joining the centres of the spherical joints intersects any passive R joint axis, the loop becomes singular. Also, the partial derivative of the loop-closure function with respect to that particular R joint variable becomes zero. In the case of multi-loop mechanisms, singularity in one loop causes singularity of the mechanism, though the converse is not necessarily true. This fact is illustrated in the next example. For the singularity analysis of multi-loop mechanisms, we consider two examples: (1) the one-degree-of-freedom RSSR-SC mechanism shown in Fig. 3 and (2) the two-degree-of-freedom RSSRR-SRR mechanism shown in Fig. 4. 3.1.1. The R S S R - S C mechanism. Figure 3 shows the RSSR-SC mechanism with three coordinate systems, {O1}, {02} and {03}. Assuming that 01 is the actuated joint, when 0, is locked, the first link is fixed and singularity due to the spherical joint $1 is impossible. Next, we consider the possibility of singular configurations due to the spherical joint $2. We cut the mechanism at $2 and denote the point $2 of the platform as S2p and that of the link 2 as $2~. In the loop RtStS3CR1, we have three joint variables which must satisfy the corresponding loop-closure equation" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001278_j.mechmachtheory.2020.103865-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001278_j.mechmachtheory.2020.103865-Figure1-1.png", "caption": "Fig. 1. 3D structure mode and structure diagram of the hybrid robot: (a) main structure of hybrid robot, (b) structure diagram which shows the main junctions, main kinematic pairs and coordinate system.", "texts": [ " The correlation coefficients between every two terms of dimensional parameters and objective functions in the optimal-set are analyzed to conclude some instructive conclusions for improving the design of optimization objectives. To begin with, the kinematic pairs are defined as follows: the rotating pair R; the prismatic pair P; the Hooke hinge U, consisting of two mutually perpendicular rotating pairs, which forms U \u2261RR; the ball pair S, consisting of three intersecting but not coplanar rotating pairs, which forms S \u2261RRR. The structure diagram of the 2U P R-R P S- RR (drive pairs are underlined) hybrid robot is shown as Fig. 1 a. It is divided into a fixed platform, a moving platform, three limbs connecting the two platforms, two joints in series and end effector. The end effector is represented by a spindle in this paper. The fixed platform is fixed on the base; the moving platform is connected to the series structure; and the three limbs in the middle are driving limbs. Limb1 and limb2 are two symmetrical linear motion limbs, which are connected with the fixed platform at one end via a Hooke hinge, and with the moving platform at the other end via a rotating pair. limb3 is connected to the fixed platform in the form of a rotating pair and to the moving platform via a ball pair. As shown in Fig. 1 b, points B 1 , B 2 and B 3 are the junctions of limb1, limb2, limb3 and the fixed platform, respectively; points A 1 , A 2 and A 3 are the junctions of limb1, limb2, limb3 and the moving platform, respectively. The midpoint of the long side B 1 B 2 is the coordinate origin B 0 of absolute coordinate system B 0 \u2212 xyz while axis x is along line B 0 B 3 , axis y is along line B 0 B 2 and axis z is perpendicular to axes x and y , respectively. Similarly, relative coordinate system A 0 \u2212 u v w is established on the moving platform", " The second joint in series is connected to the first joint in series, the intersection point is C 2 , and the rotating axis of the second joint is perpendicular to the axis of the first, and parallel to the plane of the moving platform. Point C 3 is the intersection of two lines, one is the line of the first joint rotating axis, the other is parallel to the moving platform and passing the point C 2 . The distance from C 3 to C 1 is denoted as d , and the distance between C 2 and C 3 is denoted as p . The distance from the end point C 4 of the spindle to the other points has been fixed and presented in the Fig. 1 b below. The differences between the robot in this paper and the well-known Tricept and Exechon in parallel structure are illustrated by the schematic diagrams ( Fig. 2 ). There are fewer passive pairs in the proposed robot than those in Tricept, which can effectively reduce the motion error produced by pair clearance. Compared to Exechon, the kinematic pairs which connect limb3 to the fixed platform and to the moving platform are interchanged in this hybrid robot, which makes it possible to use one-piece precision ball pair instead of three rotating pairs and thus avoid the assembly error", " And the limb with prismatic joint is regarded as a cantilever beam in which the lead screw and the connecting rod are connected in parallel. The fixed platform and the moving platform are regarded as rigid bodies. And the effects of friction and damping forces between the connectors are not considered. Then, the element stiffness matrix K is introduced to solve the terminal stiffness matrix K p . The whole parallel structure is divided into four elements, and the nodes are A 1 , A 2 , A 3 and A 0 as shown in Fig. 1 b . The terminal stiffness of the parallel structure is strongly coupled with the stiffness of three limbs which is independent of each other. Therefore, it can be determined that element stiffness matrix K is non-diagonal and can be defined as follows K = \u23a1 \u23a2 \u23a3 K 11 0 0 K 22 0 K 14 0 K 24 0 0 K 41 K 42 K 33 K 34 K 43 K 44 \u23a4 \u23a5 \u23a6 (23) where K ii ( i = 1 \u00b7 \u00b7 \u00b7 4 ) is the stiffness of four nodes; K 4 i ( i = 1 \u00b7 \u00b7 \u00b7 3 ) is the coupling stiffness relating the corresponding node A i to node A 0 ; K i 4 ( i = 1 \u00b7 \u00b7 \u00b7 3 ) is the coupling stiffness relating node A 0 to corresponding node A i " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001327_s00170-020-05927-1-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001327_s00170-020-05927-1-Figure3-1.png", "caption": "Fig. 3 Grinding wheel and pinion position relationship", "texts": [ " The pinion tooth profile equation is as follows: Mst \u03c6s\u00f0 \u00de \u00bc rst \u03bct;\u03d1t;\u03c6s\u00f0 \u00de \u00bc Mst \u03c6s\u00f0 \u00dert \u03bct;\u03d1t\u00f0 \u00de f t \u03bct;\u03c6s\u00f0 \u00de \u00bc nt v st\u00f0 \u00de t \u03bct;\u03c6s\u00f0 \u00de \u00bc 0 cos\u03c6s sin\u03c6s 0 rps sin\u03c6s\u2212\u03c6scos\u03c6s\u00f0 \u00de \u2212sin\u03c6s cos\u03c6s 0 rps cos\u03c6s \u00fe \u03c6ssin\u03c6s\u00f0 \u00de 0 0 1 0 0 0 0 1 2 664 3 775 \u00f04\u00de where v st\u00f0 \u00de t represents the relative speed of the rack and pinion. The meshing equation in Eq. (4) satisfies the following formula: f t ut;\u03c6s\u00f0 \u00de \u00bc ut\u2213rps\u03c6ssin\u03b3t \u00bc 0 \u00f05\u00de Therefore, the virtual spur gear cutter and normal vector equation are expressed as: rs ut;\u03d1t;\u03c6s ut\u00f0 \u00de\u00f0 \u00de \u00bc Rs ut;\u03d1t\u00f0 \u00de ns \u03c6s \u03bct\u00f0 \u00de\u00f0 \u00de \u00bc Lst \u03c6s \u03bct\u00f0 \u00de\u00f0 \u00dent \u00f06\u00de where the matrix Lst is a 3 \u00d7 3 submatrix of the matrix Mst. The positional relationship between the grinding wheel and the pinion is shown in Fig. 3. The coordinate systems Sd, Ss, and Sd0 are rigidly connected to the wheel, pinion, and frame, respectively. rd represents the radius of the grinding wheel, \u03d5d is the tooth profile parameter of the grinding wheel, and Ed represents the distance between the center of the grinding wheel and the central axis of the pinion, Ed = rd \u2212 rps. The tooth profile equation of the grinding wheel is as follows: Mds \u03d5s\u00f0 \u00de \u00bc rd ut;\u03d5c\u00f0 \u00de \u00bc Mst \u03c6s\u00f0 \u00dert \u03bct;\u03d1t\u00f0 \u00de nd \u03d5d;\u03c6s ut\u00f0 \u00de\u00f0 \u00de \u00bc Lds \u03d5s\u00f0 \u00dens 1 0 0 0 0 cos\u03d5d sin\u03d5d \u2212Edcos\u03d5d 0 \u2212sin\u03d5d cos\u03d5d Edsin\u03d5d 0 0 0 1 2 64 3 75 \u00f07\u00de where \u03c6s \u00bc ut rpssin\u03b3t " ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0003055_(sici)1521-4109(199809)10:11<779::aid-elan779>3.0.co;2-u-Figure1-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0003055_(sici)1521-4109(199809)10:11<779::aid-elan779>3.0.co;2-u-Figure1-1.png", "caption": "Fig. 1. Cyclic voltammogram for the oxidation of the modified carbon paste electrode at different scan rates; 0.1 M KNO3; pH 3. a)100 mV/s; b) 50 mV/s; c) 20 mV/s; d)10 mV/s.", "texts": [ " Aliquots of the analyte (cysteine or glutathione), standard and unknown were added, respectively, to the supporting electrolyte for calibration and estimation. Quantitative determination along with the stability of the electrode was carried out at constant potential in a stirred system. All experiments were carried out in deaerated solutions to avoid aerial oxidation of the sulfhydryl compounds. 3.1. Characterization of the Modified Electrode 3.1.1. Oxidation Studies The cyclic voltammogram of the modified carbon paste electrode is shown in Figure 1. An anodic peak at \u00fe0.38 and a cathodic peak at \u00fe0.22 V (vs. SCE) were observed for a scan rate of 100 mV/s. The scan rate variation studies showed both the anodic and the cathodic peaks shifts towards each other at lower scan rate. The anodic and cathodic peaks at lower scan rate (10 mV/s) were observed at \u00fe0.30 V and \u00fe0.29 V respectively. There was also a decrease in the peak current as the scan rate was decreased. The DEp values show a quasireversible electron transfer. The decrease in DEp as a function of scan rate shows that the electron transfer reaction at the electrode/ solution interface tending towards reversibility" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001278_j.mechmachtheory.2020.103865-Figure4-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001278_j.mechmachtheory.2020.103865-Figure4-1.png", "caption": "Fig. 4. Interfere position: (a) a position where the motor interferes with the limb, (b) another position where the motor exactly interferes with the limb and the fixed platform respectively.", "texts": [ " l Z = l A 0 B 0 \u00b7 cosG (15) where l Z and l A 0 B 0 represent the motion ranges projected on axis z and along line A 0 B 0 , respectively. The intermediate variable G is related to the limb length q 3 . When the intermediate variable G equals to 90 \u25e6, the motion range l Z in the direction of axis z reaches the maximum distance h which can be regarded as one of the indexes. Keep axis x of absolute coordinate system B 0 \u2212 xyz parallel to axis u of relative coordinate system A 0 \u2212 u v w so that the plane PL on the moving platform falls on the coordinate plane yB 0 z . As shown in Fig. 4 below, the motion range in the direction of axis z can be described by the distance h between the coordinate origin B 0 of absolute coordinate system B 0 \u2212 xyz and the coordinate origin A 0 of relative coordinate system A 0 \u2212 u v w . A kind of plane rectangular bounding box is used to solve the value of h while considering the interference. As shown in Fig. 4 , rectangular bounding boxes in different colors are drew to represent the approximate geometries of components. In Fig. 4 a, when the two bounding boxes in green and purple intersect exactly, the moving platform reaches its lower limit of position and thus motion interference occurs. When the length of limb q 1 reaches the maximum q 1 max and the two rectangular bounding boxes intersect exactly at point P O 2 , distance h reaches its maximum value h max . Therefore, quadrilateral A 1 A 2 B 2 B 1 constitutes a theoretical structural model, in which point A 0 and point B 0 are the midpoints of line A 1 A 2 and line B 1 B 2 , respectively", " In addition, the lines P O 1 P O 2 , P O 2 P O 3 , P O 3 P O 4 , P O 4 A 1 and A 1 P O 1 are defined to be r 1 , ad, r 2 , r 3 and r 4 , respectively; the angles P O 1 A 1 P O 4 , P O 1 A 1 P O 2 and P O 2 A 1 P O 4 are defined to be \u03d5 1 , \u03d5 11 and \u03d5 12 , respectively. The distance can be solved through b 1 , a, q 1 max and \u03d51 according to Eq. (16) h max = \u221a q 1 max 2 + a 2 \u2212 b 1 2 \u2212 2 q 1 max acos \u03d5 1 (16) where \u03d51 can be obtained by the geometrical relations shown in triangle A 1 P O 2 P O 1 and triangle A 1 P O 2 P O 4 . \u03d5 1 = \u03d5 11 + \u03d5 12 = arctan r 1 r 4 + arctan ad + r 2 r 3 r 4 = \u221a r 3 2 + ( ad + r 2 ) 2 \u2212 r 1 2 (17) In Fig. 4 b, the rectangular bounding box is marked in yellow. When the bounding box in purple exactly intersects those in green and yellow as shown above, the moving platform reaches its upper limit of position and the motion interference occurs, and distance h reaches the minimum value h min . Similar to the definition above, polygon P O 1 \u2032 P O 2 \u2032 P O 6 \u2032 P O 5 \u2032 P O 7 \u2032 A 0 \u2032 P O 3 \u2032 constitutes an interference structural model, in which the points P O 1 \u2032 , P O 3 \u2032 and P O 4 \u2032 locate on line A 1 \u2032 B 1 \u2032 , P O 2 \u2032 P O 4 \u2032 and A 1 \u2032 A 0 \u2032 , respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_11_0001041_j.ijmecsci.2020.106020-Figure3-1.png", "original_path": "designv10-11/openalex_figure/designv10_11_0001041_j.ijmecsci.2020.106020-Figure3-1.png", "caption": "Fig. 3. Simultaneous meshing of a rotary cutter, a virtual shaper cutter and a spur face gear.", "texts": [ " As a result, the equation of the tooth surface o aking the origins of coordinate systems coincide is used to simplify the he simplified theoretical radial vector of spur face gears obtained by s \u20d7 \ud835\udc53 ( \ud835\udf07\ud835\udc50 , \ud835\udf03\ud835\udc50 , \ud835\udf19\ud835\udc60 ) = \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 \ud835\udc5f \ud835\udc4f\ud835\udc50 [ cos \ud835\udf19\ud835\udc53 ( sin \ud835\udf13 \ud835\udc60 \u2212 \ud835\udf03\ud835\udc50 cos \ud835\udf13 \ud835\udc60 ) \u2212 sin \ud835\udf19\ud835\udc53 \ud835\udc5a \ud835\udc60\ud835\udc53 cos \ud835\udf13 \ud835\udc60 ] \u2212 \ud835\udc5f \ud835\udc4f\ud835\udc50 [ \ud835\udc60\ud835\udc56\ud835\udc5b\ud835\udf19\ud835\udc53 ( sin \ud835\udf13 \ud835\udc60 \u2212 \ud835\udf03\ud835\udc50 cos \ud835\udf13 \ud835\udc60 ) + cos \ud835\udf19\ud835\udc53 \ud835\udc5a \ud835\udc60\ud835\udc53 \ud835\udc50\ud835\udc5c\ud835\udc60\ud835\udf13 \ud835\udc60 ] \u2212 \ud835\udc5f \ud835\udc4f\ud835\udc50 ( cos \ud835\udf13 \ud835\udc60 + \ud835\udf03\ud835\udc50 sin \ud835\udf13 \ud835\udc60 ) 1 \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 here \ud835\udf13 \ud835\udc60 = \ud835\udc5a \ud835\udc50\ud835\udc60 \ud835\udf19\ud835\udc60 + ( \ud835\udf03\ud835\udc500 + \ud835\udf03\ud835\udc50 ) . In contrast to the tooth surface equation of spur face gears derived i his work verifies the correctness of the spur face gear shaving method face gear based on the simultaneous meshing in Fig. 3. io. e obtained as Eq. (15) . The transformation matrixes M f,f0 , M f0,p , M p,k , cos \ud835\udf19\ud835\udc60 ( cos \ud835\udefd sin \ud835\udf19\ud835\udc53 \u2212 cos \ud835\udf19\ud835\udc53 sin \ud835\udefd) \ud835\udc45 sin \ud835\udf19\ud835\udc53 sin \ud835\udf19\ud835\udc60 \ud835\udc3b os \ud835\udf19\ud835\udc60 ( sin \ud835\udefd sin \ud835\udf19\ud835\udc53 + cos \ud835\udefd cos \ud835\udf19\ud835\udc53 ) \u2212 \ud835\udc45 cos \ud835\udf19\ud835\udc53 0 1 \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 (15) (16) ) . The detailed calculation process for this relationship is shown in the (17) cos \ud835\udf19\ud835\udc60 ( sin \ud835\udefd sin \ud835\udf19\ud835\udc53 + cos \ud835\udefd cos \ud835\udf19\ud835\udc53 ) . (18) al positions of tools and gears to facilitate the reader\u2019s understanding face gear is too long to write easily in this paper. Thus, the method of h surface equation of the face gear" ], "surrounding_texts": [] } ]