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عدد المساهمات : 19002 التقييم : 35506 تاريخ التسجيل : 01/07/2009 الدولة : مصر العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
| موضوع: كتاب Robot Analysis - The Mechanics of Serial and Parallel Manipulators الإثنين 27 يونيو 2022, 6:07 pm | |
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أخواني في الله أحضرت لكم كتاب Robot Analysis - The Mechanics of Serial and Parallel Manipulators LUNG-WEN TSAI Department of Mechanical Engineering and Institute for Systems Research University of Maryland
و المحتوى كما يلي :
CONTENTS Preface xi 1 Introduction 1 Historical Development / 2 A Sense of Mechanisms / 6 Robotic Systems / 17 Classification of Robots / 19 Position, Orientation, and Location of a Rigid Body / 29 Homogeneous Transformations / 42 Mechanics of Robot Manipulators / 45 Summary / 48 References / 48 Exercises / 50 2 Position Analysis of Serial Manipulators 2.1 Introduction / 54 2.2 Link Parameters and Link Coordinate Systems / 56 2.3 Denavit-Hartenberg Homogeneous Transformation Matrices / 60 2.4 Loop-Closure Equations vVI CONTENTS 2.5 Other Coordinate Systems / 69 2.6 Denavit-Hartenberg Method / 69 2.7 Method of Successive Screw Displacements / 91 2.8 Summary / 109 References / 109 Exercises / 1 1 1 3 Position Analysis of Parallel Manipulators 3.1 Introduction / 116 3.2 Structure Classification of Parallel Manipulators / 118 3.3 Denavit-Hartenberg Method versus Geometric Method / 123 3.4 Position Analysis of a Planar 3RRR Parallel Manipulator / 124 3.5 Position Analysis of a Spatial Orientation Mechanism / 129 3.6 Position Analysis of the University of Maryland Manipulator / 1 3 4 3.7 Position Analysis of a Spatial 3RPS Parallel Manipulator / 1 4 2 3.8 Position Analysis of a General Stewart-Gough Platform / 1 5 1 3.9 Position Analysis of a Nearly General Stewart-Gough Platform / 1 5 6 3.10 Position Analysis of a 3-3 Stewart-Gough Platform / 158 3.11 Summary / 161 References / 161 Exercises / 1 6 4 116 4 Jacobian Analysis of Serial Manipulators 4.1 Introduction / 1 6 9 4.2 Differential kinematics of a Rigid Body / 171 4.3 Differential Kinematics of Serial Manipulators / 177 4.4 Screw Coordinates and Screw Systems / 182 4.5 Manipulator Jacobian Matrix / 184 4.6 Conventional Jacobian / 186 4.7 Screw-Based Jacobian / 192 4.8 Transformation of Screw Coordinates / 205 169CONTENTS Vii 4.9 Relationship between the Two Methods / 2 1 1 4.10 Condition Number / 211 4.11 Singularity Analysis / 2 1 5 4.12 Summary / 2 1 9 References / 220 Exercises / 221 5 Jacobian Analysis of Parallel Manipulators 5.1 Introduction / 223 5.2 Jacobian Matrices / 224 5.3 Singularity Conditions / 225 5.4 Conventional Jacobian / 226 5.5 Wrenches and Reciprocal Screws / 241 5.6 Screw-Based Jacobian / 247 5.7 Summary / 257 References / 257 Exercises 6 Statics and Stiffness Analysis 6.1 Introduction / 260 6.2 Statics of Serial Manipulators / 261 6.3 Transformation of Forces and Moments / 275 6.4 Stiffness Analysis of Serial Manipulators / 279 6.5 Statics of Parallel Manipulators / 282 6.6 Stiffness Analysis of Parallel Manipulators / 288 6.7 Summary / 293 References / 293 Exercises / 294 260 7 Wrist Mechanisms 7.1 Introduction / 298 7.2 Bevel-Gear Wrist Mechanisms / 3 0 1 7.3 Structure Representation of Mechanisms / 303 7.4 Structure Characteristics of Epicyclic Gear Trains / 307 7.5 Classification of Wrist Mechanisms / 308 7.6 Kinematics of Epicyclic Gear Drives / 309 298viii CONTENTS 7.7 Kinematics of Robotic Wrist Mechanisms / 317 7.8 Static Force Analysis / 321 7.9 Summary / 326 References / 326 Exercises 8 Tendon-Driven Manipulators 333 8.1 Introduction / 333 8.2 Classification of Tendon-Driven Manipulators / 334 8.3 Planar Schematic Representation / 339 8.4 Kinematics of Tendon-Driven Manipulators / 340 8.5 Static Force Analysis / 348 8.6 Feasible Structure Matrices / 351 8.7 Redundant Forces Resolution / 354 8.8 Summary / 366 References / 367 Exercises / 369 9 Dynamics of Serial Manipulators 9.1 Introduction / 372 9.2 Mass Properties / 375 9.3 Momentum / 379 9.4 Transformation of Inertia Matrix / 381 9.5 Kinetic Energy / 382 9.6 Newton-Euler Laws / 383 9.7 Recursive Newton-Euler Formulation / 386 9.8 Lagrangian Formulation / 395 9.9 Inertia Effects of the Rotors / 410 9.10 End-Effector Space Dynamical Equations / 417 9.11 Summary / 4 1 9 References / 419 Exercises 10 Dynamics Of Parallel Manipulators 424 10.1 Introduction / 424 10.2 Newton-Euler Formulation / 426CONTENTS ix 10.3 Principle of Virtual Work / 437 10.4 Lagrangian Formulation / 447 10.5 Summary / 453 References / 454 Exercises / 455 APPENDIXES A Continuation Method A.l Bezout Number / 458 A.2 Traditional Homogeneous Formulation / 458 A.3 M-Homogenization / 460 A.4 Solutions at Infinity / 461 A.5 Continuation Method / 462 A.6 Cheater’s Homotopy / 469 References B Sylvester Dialytic Elimination Method B. l Elimination Procedure / 473 B.2 Example / 474 References C Raghavan and Roth’s Solution C.1 Loop-Closure Equation / 477 C.2 Elimination of and 62 / 480 C.3 Elimination of fti and 95 / 480 References D List of Symbols 483 Index 499INDEX Accessibility, 463^165 Actuator force(s), 260, 265 Actuator space, 260, 317, 319 Actuator torque(s), 321-322 ADAMS, 374 Adept gripper, 19 Adept-one robot, 20-22, 24 Amplitude, 182 Angular momentum, 380-381 Angular velocity, 171-174 Arm, 25-26, 298 Atan2(.v , y), 39, 41, 72, 75-76, 83-85, 102-103, 107-109 Automation flexible, 1 hard, 1 Bezout theorem, 458, 460 Bootstrap method, 457 Canonical graph, 305-306, 324 Carrier, 302-303, 308, 312 Center of mass, 375 Central configuration, 290 Centrifugal forces, 402^103 Characteristic equation, 34 Characteristic value, 34 Chaslcs' theorem, 42, 91 Cheater’s homotopy, 469^-70 Cincinnati-Milacron wrist, 301, 317-319 canonical graph representation, 306 equivalent open-loop chain, 318 graph representation, 304 Classification of robots, 19-29 by degrees of freedom, 19 by drive technology, 21 by kinematic structure, 20 by motion characteristics, 27 by workspace geometry, 25 Closed-form soluiion(s), 55, 70 Closed-loop chain, 8 Coaxiality condition(s), 313-314, 316, 343-344 Compatibility condition, 173 Base, 9, 54, 116 Base frame, 384 Bendix wrist, 302 canonical graph representation, 323-324 equivalent open-loop chain, 323-324 kinematics 323-326 Bezout number, 147, 149, 155-156, 158, 458 multihomogeneous, 461 499500 INDEX Compliance matrix, 279-281 Composite homogeneous transformation, Dynamic synthesis, 48 Dynamical equations end effector space, 417 gercral form, 401 Dynamics, 47, 372, 424 45 Condition number, 211-212 Configuration, 10, 47, 396 folded back, 72, 82, 216 fully stretched, 72, 82, 216 Connectivity, 118-119, 121-123 Constraints, 396 holonormic, 396 nonholonomic, 396 Constraint equation(s), 447, 450 Constraint function(s), 448 Continuation method, 56, 117, 156, 457, 462-163 Continuation parameter, 463 Coordinate systems base, 60 end effector, 58 hand, 58, 60 link, 56-60 Coriolis forces, 402- 403 Eigenvalue(s), 34, 212-213, 273, 275, 281-282, 378 Eigenvectors, 35, 212-213, 273, 275, 281-282, 378 Elbow manipulator position analysis, 98-103 screw-based Jacobian, 198-202 singular configurations, 218-219 Eliminant, 150-151, 473 Elimination method, 56, 473, 477 Ellipsoid, 212-213, 215, 273-275, 281 End effector, 17—18, 54, 65-66 End-cffector force space, 274-275, 282 End-effector space, 169, 185, 213, 215-216, 260, 279, 317-318 Equivalent joint torque(s), 261, 265-266, 321-322, 348 Equivalent open-loop chain, 300, 317-319, 323-326, 411-412, 414 Euler anglc(s), 31, 37-41, 65, 131, 133, 427-429 roll-pitch-yaw angles, 38 w-u-w Euler angles, 39 w-v-w Euler angles, 41 Euler’s equation, 16 Euler’s equation of motion, 385, 432 Euler’s theorem, 34 Extraneous solutions, 56, 155, 460, 462, d’Alembert’s principle, 374, 437 DADS, 374 Degree of a polynomial system, 458-460, 470 Degrees of freedom, 6, 9-15, 118, 298, 307, 334-337, 396-397, 448 passive, 12-13, 122, 152 DELTA robot, 134, 166, 167 Denavit and Hartenberg’s convention, 57 Denavit-Hartenberg method, 69, 123-124 Dextrous hand, 18 Differential kinematics, 171, 177 Differential speed reducer, 315 Differential transformation matrix link, 178 overall, 179 Direct dynamics, 47, 372 Direct kinematics, 46, 54, 66, 98, 117 Direct position problem, 54 Direct velocity problem, 169 Direction cosine representation, 31 DOF, 6 Dual matrix method, 55 DYMAC, 374 Dynamic analysis, 47 473 F-circuit, see Fundamental circuits) Fanuc arc welding robot, 373 Fanuc LR Mate robot, 261 Fanuc S-900W robot, 4. 20-21, 77, 109, 115 position analysis, 77-85 Fanuc spray painting robot, 170 Five-bar linkage, 11-12 Forward kinematics, 46, 142 Four-bar linkage, 11 Frame Fixed frame, 29 Moving frame, 29INDEX 501 Free-body diagram, 261, 282, 288, 293 Functional schematic representation, 303-304 Fundamental circuit(s), 300, 308, 311-312, 314, 316, 319, 323 Fundamental circuit equation(s), 312, 314, 316, 319, 324, 342-343 manipulator, 399, 401, 403, 418 transformation of, 381 Inertia tensor, 376. See also Inertia matrix (ces) Initial Instantaneous system,screw 463—165 axis , ,467 174-175, 177 Intensity, 182-183, 241, 248 Inverse dynamics, 47, 372-373, 385, 425, 427, 436, 443, 448 Inverse kinematics, 40, 46, 54-56, 66, 69. 85, 98 Inverse position problem, 54 Inverse transformation, 33, 44, 62 Inverse velocity problem, 169, 209, 211 Isomorphic structure matrices, 352 Isotropic point(s), 212-214, 273 Isotropic torsional stiffness, 292 Isotropic translational stiffness, 292 Iterative method, 55 General 6R manipulator, 85-86, 459, 466 Generalized coordinates, 395-397, 438, 450-452 independent, .397, 403, 406, 425 redundant, 397, 447^148, 450 Generalized 410, 448forces , 450, 395, 400—101, 405, Generalized inner product, 243 Geometric method, 55-56, 123 Griibler criterion, 11-12, 14 Graph representation, 304 Gripper, 18 universal, 18 Jacobian, 169-171, 184, 211-213, 215-216, 223, 225, 226, 373 conventional, 170, 185-186, 226-227 screw-based, 170, 185, 192, 247 Jacobian matrix(ces), see also Jacobian link, 398-399, 402, 439, 441, 442, 444 manipulator, 184, 439^140, 443 Joint space, 169, 212, 213, 215, 279, 317-319, 323, 373, 410, 417-418, Hamilton, 374 Home position, 98 Homogeneous Homogeneous coordinates formulation,, 42 457—14 m-homogeneous formulation, 460 1-homogeneous formulation, 459 2-homogeneous formulation, 461 traditional, 458 Homogeneous solution, 351 Homogeneous transformation matrix(ces), 43 D-H transformation matrices, 60-62 Homogeneous variables, 457 Homotopy function, 463-464, 467, 442 Joint torque equations, 390 Joint torque space, 273, 351 Joint variables, 54, 59-60, 65-66, 69, 96, 98, 124, 169, 185, 216, 225, 397, 419, 448 Joinl(s), 6-8. See also Kinematic pair(s) actuated, 15 cylindrical, 7 helical, 7 hinge, 7 passive, 4 pin, 7 prismatic, 7 revolutc, 7 spherical, 7 universal, 8 470 Homotopy method, 85, 457 Homotopy paths, 463 Humanoids, 2-3 Hybrid kinematic chain, 8 IMP, 374 Inertia effects of rotors, 410 Inertia frame, 383-385, 400 Inertia matrix(ces), 375-378, 381-382, 386, 395, 414 Cartesian, 418 end-effcctor space, 418 Kane’s method, 374 Kinematic analysis, 46502 INDEX Kinematic chain(s), 9 Kinematic pair(s), 7. See also Joint(s) cam pair, 8 gear pair, 8 higher pairs, 7-8 lower pairs, 7-8 plane pair, 7 screw pair, 7 sliding pair, 7 surface contact, 246 Kinematic synthesis, 46 Kinematics, 46 Kinetic energy, 382-383, 395-396, 398-399, 401, 412^413, 418, 450 Kutzbach criterion, 11 spatial, 28 spherical, 28 Matrix method, 55 Mechanics, 45 Mechanism(s), 6, 8-9 overconstrained, 14 planar, 27 spatial, 28 spherical, 29 Members, 6 Method of successive screw displacements, 56, 91, 98 Minuteman cover drive, 313 Momcnt(s) of inertia, 375-377 axial , 413 principal, 375, 377-378, 386 Motion planar, 27 spatial, 28 spherical, 28 Lagrangian equations, 374 of the first type, 397, 447 of the second type, 397 Lagrangian formulation, 374, 395, 424, 426, 443, 447 Lagrangian function, 395, 401, 450 451 Lagrangian method(s), 374, 395 Lagrangian multiplier, 425, 448 Legs, 116 Limb(s), 116 Line coordinates, 184 Linear momentum, 379-380 Linear velocity, 174 Link Jacobian submatrix(ces), 395, 398-399, 402 Link parameters, 56, 58-60 Links, 6 Location, 29 description of, 41 Loop mobility criterion, 6, 15-16 Loop-closure equation(s), 16, 65-66, 69-70, 85, 97, 124, 228, 231, 235 NBOD2, 374 Newton-Euler laws, 383 Newton’s equation of motion, 384 Newton-Euler equations, 374, 395 Newton-Euler formulation, 386, 424, 426 NIST RoboCrane, 337, 370 Norm, 212 Number synthesis, 46 0+ operator, 358-366 0 ~ operator, 358-366 Open-loop chain, 8, 15 Orientation, 25, 29, 31, 35, 37, 44 Orthogonal conditions, 33, 66, 144, 151, 153-156 Orthogonal product, 243, 248, 252 Orthogonal transformation, 34 Orthogonality conditions, see orthogonal condition Machine(s), 8-9 Manipulator(s), 1. See also Robot(s) direct drive, 23 hybrid, 21 master-slave, 2 mechanical, 2, 17 open-loop, 20, 54 parallel, 20-21 planar, 27 serial, 20 Pair element, 7 Pantograph mechanism, 12-13, 16, 164, 294 Parallel axes theorem, 375, 377 Parallel manipulators, 20-21, 116 asymmetrical, 118 classification of, 118-123INDEX 503 dynamics, 424 Jacobian analysis, 223 planar, 119 position analysis, 116 spatial, 121 spherical, 28, 119 statics, 282 stiffness analysis, 288 symmetrical, 118 Parameter homotopy, 470 Parameter perturbation method, 457 Particular solution, 351, 354 Path tracking, 466 Pathfinder, 6 Perspective transformation, 43- 44 Piteh(cs), 39, 176, 182-183, 207, 241, 243-247 Pliicker coordinates, 184 Planar 2-dof manipulator conventional Jacohian, 187-188 force ellipsoid, 275 locus of isotropic points, 214 Lagrangian dynamics, 403^105 Newton-Euler dynamics, 391-394 stiffness analysis, 281-282 velocity ellipsoid , 215 Planar 3-dof manipulator conventional Jacobian, 188-189 D-H transformation matrices, 62-63 position analysis, 70-74 singular configurations, 216-217 statics, 266-268 Planar 3-dof, 3-PRP manipulator, 120, Principle of virtual work, 272, 285, 321 Prismatic 348,-437 spherical —438, dyad 442-443 , 245 Product of inertia, 376-377 Projective space, 460, 462 Pseudoisomorphic graphs, 305 Pseudoisomorphic mechanisms, 305 Pseudolriangular structure matrix(ces), 354, 360, 366 Quarternian algebra method, 55 Radius of gyration, 376 Raghavan and Roth’s solution, 477-482 Reciprocal screw(s), 241-250, 253-254 of some kinematic chains, 245 of some kinematic pairs, 244 Rectifier, 354, 359-360 Recursive method, 264 Redundant forces resolution, 354 Reference coordinate system, 29 Reference frame, 30, 42, 44 instantaneous, 193 - 195, 199, 203, 205 Reference position, 96-100, 104, 318 Resultant, 473 Resultant screw, 91, 95 Revolute-spherical dyad, 245 Robot(s), 2. See also Manipulators) articulated, 26 Cartesian, 25, 26 Cincinnati Milacron T , 4 cylindrical, 25, 27 deficient, 19 gantry, 25 general-purpose, 19 historical development, 2-6 master-slave, 5 PUMA, 4 redundant, 19 SCARA, 26. See also SCARA arm serial, 20 spherical, 25 Unirnate, 3 Robotic systems, 17 Robotics, 45 Rodrigues’s formula, 36, 93 Roll, 39 Root, 305 165 Planar 3-RRR manipulator, 50, 120 conventional Jacobian, 227-231 position analysis, 124-129 statics, 283-284, 286-287 Planar linkages, 27 Planar schematic representation, 339 Platform manipulators, 116, 136 Position vector, 29-30 Posture, 47, 55 Potential energy, 395-396, 400-401, 414-415 ^ Power product(s), 473-474, 477, 479 Primary links, 412 Principal axes, 212, 273, 281-282, 378, 386, 435504 INDEX Rotation matrix(ces), 33, 36-42 basic, 38 Skew-symmetric matrix, 172-173, 176, 179-180, 207, 277 Slidcr-and-crank mechanism, 9 Smoothness, 463^165 Solutions at infinity, 461-462 Spatial 3-PPSR, 168 screw-based Jacobian, 252-257 Spatial 3-RPS manipulator, 51 position analysis, 142-151 Spatial 3-UPU manipulator, 52, 165-166 Spatial orientation mechanism, 129 conventional Jacobian, 231-234 position analysis, 129-134 Spherical 3-RRR manipulator, 28 Stanford manipulator, 113 conventional Jacobian, 189-192 position analysis, 103-109 screw-bascd Jacobian, 195-198 singular configurations, 217-218 statics, 268-271 Stanford/JPL finger, 339-342 abbreviated planar representation, 342 force resolver schematic diagram, 365 kinematics, 345-346 planar schematic diagram, 341 redundant forces resolution, 363-365 schematic diagram, 340 structural matrix, 350 Slanford/JPL hand, 18, 338 Statics, 47, 260 Stewart-Gough platform, 13, 14, 426 conventional Jacobian, 239-240 dynamics, 432—436 equations of motion, 442^443 kinematics, 426-432 link Jacobian matrices, 439^441 position analysis, 151-158 screw-based Jacobian, 250-252 statics, 284-285, 287-288 3-3 Stewart-Gough platform position analysis, 158-161 stiffness analysis, 289-293 Stiffness analysis parallel manipulators, 288 serial manipulators, 279 Stiffness constant, 280 Stiffness matrix, 261, 280-281, 289, 292 Structure characteristics, 300, 307, 351, Scaling factor, 43^44, 458 SCARA arm, 26, 64, 112, 406 D-H transformation matrices, 63-65 Scorbot Lagrangian robot,dynamics 56-57, 67,,405 114—410 D-H transformation matrices, 64—65 loop-closure equation, 66-69 position analysis, 74-76 Scorbot-ER HI robot, 24 Screw algebra method, 55 Screw axis, 34-35, 92, 94-95, 182-183, 241 Screw axis representation, 31, 35-37 Screw coordinates, 182-1 84 Screw cylindroid, 183 Screw displacement(s), 91, 182 Screw parameters, 92, 94 Screw systems, 182-183 H-system, 183 one-system, 183 two-system, 183 Screw(s) reciprocal, 241-247 transpose of, 243 SD-EXACT, 374 Second moment, 375 Secondary links, 412 Self motion, 218 Serial manipulators, 20 dynamics, 372 Jacobian analysis, 169 position analysis, 54 statics, 260 stiffness analysis, 279 Significant solutions, 88, 462 Singular condition(s), 170, 216, 225-226 Singular configuration(s), 84, 108, 127, 215, 223, 225-226 Singularity(ies), 215 boundary, 216 combined, 226, 230, 234, 238 direct kinematic, 226, 229, 232, 236, 240 , 256 interior, 216 inverse kinematic, 225, 228, 232, 236, 240, 256 354INDEX 505 epicyclic gear trains, 308 tendon-driven manipulators, 352 Structure matrix, 322-323, 349-350 Successive screw displacements, 56, 91, 95-96, 98 Sylvester, 150, 158, 473 redundant forces resolution, 364-366 structural matrix, 350-351 Utah/MIT hand, 18, 20-21, 338-339 VARIAX machining center, 117, 224, 424-425 Vector algebra method, 55 Vector of gravitational forces, 395, 402 Vector-loop equation(s), 124, 223-224, 228, 231, 428 Vector-loop method, 73, 226 Velocity coupling vector, 395, 402 Virtual coefficient, 243 Virtual displacemeot(s), 272-273, 285-286, 321, 348-349, 400, 438-439 Virtual work, 242-243, 272, 282, 285-286, 321, 348-349, 395, 400-401 Target position, 96-98, 100, 105 Target system, 463-465, 469 Tendon driven manipulators classification of, 334-339 closed-loop tendon drives, 334 feasible structure matrices, 351 kinematics, 340 open-ended tendon drives, 334 planar schematic representation, 339 redundant forces resolution, 354 static force analysis, 348 structure characteristics, 352 Tendon force space, 351 Tendon routing, 339, 340, 342-345 crossed type, 343-344 parallel type, 343 Train value, 323 Transfer vertex, 308 Transformation of forces, 273 of forcc(s) and moment(s), 260, 275 of screw coordinates, 205 Transmission line(s), 309, 322-323, 340, 342-345, 349 Trigonometric identities, 82, 88, 127, 134, 149, 480 Triviality, 463-^165 Tsai and Morgan’s solution, 85, 466 Twist, 182-183 Type synthesis, 46 Workspace, 25-26 dextrous, 25 reachable, 25 regional, 25 Wrench axis, 241 Wrench(es), 241-244, 263, 275-277, 438-439, 441-442, 444 Wrist, 25. See also Wrist mechanisms nonspherical, 299, 309 oblique, 309 simple, 309 spherical, 299, 309 Wrist mechanisms, 14, 298. See also Wrist basic mechanism, 309-310 canonical graph representation, 305 classification of, 308 derived mechanism, 309 graph representation, 304 kinematics, 317 static force analysis, 321 structure characteristics, 307-308 Universal-spherical dyad, 245 University of Maryland manipulator conventional Jacobian, 234-239 position Lagrangian analysis dynamics , 134-, 449 142—453 Ulah/MIT finger force resolver schematic diagram, Yaw, 39 367 Zero position, 96 kinematics, 346-348
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