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 |  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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