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 |  موضوع: كتاب Fundamentals of Robotic Mechanical Systems السبت 04 يناير 2014, 1:30 pm | |
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Fundamentals of Robotic Mechanical Systems
Theory , Methods , and Algorithms
Third Edition
Jorge Angeles
و المحتوى كما يلي :
Contents
Prefac e t o th e Thir d Editio n x v
Prefac e t o th e Firs t Editio n xi x
1 An Overvie w of Roboti c Mechanica l System s 1
1.1 Introduction 1
1.2 The General Architecture of Robotic Mechanical Systems . . . . 3
1.2.1 Types of Robots by Functio n 6
1.2.2 Types of Robots by Siz e 7
1.2.3 Types of Robots by Application 7
1.3 Manipulators 7
1.3.1 Robotic Arms 9
1.3.2 Robotic Hand s 10
1.4 Motion Generators 12
1.4. 1 Parallel Robots 12
1.4. 2 SCARA Systems 16
1.5 Locomotor s 17
1.5.1 Legge d Robots 17
1.5.2 Wheeled Robots 19
1.6 Swimming Robots 22
1.7 Flyin g Robots 23
1.8 Exercise s 24
2 Mathematica l Backgroun d 27
2.1 Preamble 27
2.2 Linea r Transformations 28
2.3 Rigid-Bod y Rotations 33
2.3.1 The Cross-Produc t Matrix 36
2.3.2 The Rotation Matrix 38
2.3.3 The Linea r Invariants of a 3 x 3 Matrix 4 2
2.3.4 The Linea r Invariants of a Rotation 4 3
2.3.5 Example s 4 5
2.3.6 The Euler-Rodrigue s Parameters 51
2.4 Composition of Reflections and Rotations 54Contents
2.5 Coordinate Transformations and Homogeneou s Coordinates . . . 56
2.5.1 Coordinate Transformations Between Frame s
with a Common Origin 56
2.5.2 Coordinate Transformation with Origin Shift 60
2.5.3 Homogeneou s Coordinates 62
2.6 Similarity Transformations 65
2.7 Invariance Concepts 71
2.7.1 Applications to Redundant Sensing 75
2.8 Exercise s 79
Fundamental s of Rigid-Bod y Mechanic s 89
3.1 Introduction 89
3.2 General Rigid-Bod y Motion and Its Associated Screw 89
3.2.1 The Screw of a Rigid-Bod y Motion 93
3.2.2 The Pliicker Coordinates of a Lin e 95
3.2.3 The Pose of a Rigid Body 98
3.3 Rotation of a Rigid Body About a Fixe d Point 102
3.4 General Instantaneous Motion of a Rigid Body 103
3.4. 1 The Instant Screw of a Rigid-Bod y Motion 104
3.4. 2 The Twist of a Rigid Body 107
3.5 Acceleration Analysis of Rigid-Bod y Motions 110
3.6 Rigid-Bod y Motion Referred to Moving Coordinate Axe s 112
3.7 Static Analysis of Rigid Bodies 114
3.8 Dynamics of Rigid Bodies 118
3.9 Exercise s 122
Geometr y of Decouple d Seria l Robot s 129
4. 1 Introduction 129
4. 2 The Denavit-Hartenber g Notation 129
4. 3 The Geometric Model of Six-Revolut e Manipulators 138
4. 4 The Inverse Displacement Analysis of Decoupled Manipulators . 14 1
4.4. 1 The Positioning Problem 14 2
4.4. 2 The Orientation Problem 157
4. 5 Exercise s 162
Kinetostatic s of Seria l Robot s 167
5.1 Introduction 167
5.2 Velocity Analysis of Serial Manipulators 168
5.3 Jacobia n Evaluation 175
5.3.1 Evaluation of Submatrix A 175
5.3.2 Evaluation of Submatrix B 178
5.4 Singularity Analysis of Decoupled Manipulators 180
5.4. 1 Manipulator Workspace 182
5.5 Acceleration Analysis of Serial Manipulators 186
5.6 Static Analysis of Serial Manipulators 190
5.7 Planar Manipulators 192Contents xi
5.7.1 Displacement Analysis 193
5.7.2 Velocity Analysis 195
5.7.3 Acceleration Analysis 198
5.7.4 Static Analysis 199
5.8 Kinetostati c Performance Indices 201
5.8.1 Positioning Manipulators 207
5.8.2 Orienting Manipulators 210
5.8.3 Positioning and Orienting Manipulators 211
5.8.4 Computation of the Characteristic Length : Applications
to Performance Evaluation 218
5.9 Exercise s 227
6 Trajector y Planning : Pick-and-Plac e Operation s 233
6.1 Introduction 233
6.2 Background on PPO 234
6.3 Polynomial Interpolation 236
6.3.1 A 3-4- 5 Interpolating Polynomial 236
6.3.2 A 4-5-6- 7 Interpolating Polynomial 24 0
6.4 Cycloidal Motion 24 3
6.5 Trajectories with Via Poses 24 5
6.6 Synthesis of PPO Usin g Cubic Splines 24 6
6.7 Exercise s 252
7 Dynamic s of Seria l Roboti c Manipulator s 257
7.1 Introduction 257
7.2 Inverse vs. Forwar d Dynamics 257
7.3 Fundamental s of Multibody System Dynamics 259
7.3.1 On Nomenclature and Basic Definitions 259
7.3.2 The Euler-Lagrang e Equation s of Serial
Manipulators 260
7.3.3 Kane' s Equation s . 268
7.4 Recursive Inverse Dynamics 269
7.4. 1 Kinematic s Computations: Outward Recursions 269
7.4. 2 Dynamics Computations: Inward Recursions 275
7.5 The Natural Orthogonal Complement in Robot Dynamics . . . . 280
7.5.1 Derivation of Constraint Equation s and
Twist-Shap e Relations 285
7.5.2 Noninertial Base Lin k 288
7.6 Manipulator Forwar d Dynamics 289
7.6.1 Planar Manipulators 293
7.6.2 Algorithm Complexit y 306
7.6.3 Simulation 310
7.7 Incorporation of Gravity Into the Dynamics Equation s 312
7.8 The Modeling of Dissipative Force s 313
7.9 Exercise s 316xii Contents
8 Specia l Topic s in Rigid-Bod y Kinematic s 323
8.1 Introduction 323
8.2 Computation of Angular Velocity from Point-Velocit y Data . . . 324
8.2.1 A Robust Formulatio n 330
8.3 Computation of Angular Acceleration from Point-Acceleratio n
Data 331
8.3.1 A Robust Formulatio n 337
8.4 Exercise s 339
9 Geometr y of Genera l Seria l Robot s 34 3
9.1 Introduction 34 3
9.2 The IDP of General Six-Revolut e Manipulators 34 4
9.2.1 Preliminaries 34 5
9.2.2 Derivation of the Fundamenta l Closure Equation s . . . . 34 9
9.3 The Univariate-Polynomia l Approach 357
9.3.1 The Raghavan-Rot h Procedure 357
9.3.2 The Li-Woernle-Hille r Procedure 364
9.4 The Bivariate-Equatio n Approach 367
9.4. 1 Numerical Conditioning of the Solutions 369
9.5 Implementation of the Solution Method 370
9.6 Computation of the R,emaining Join t Angles 371
9.6.1 The Raghavan-Rot h Procedure 372
9.6.2 The Li-Woernle-Hille r Procedure 373
9.6.3 The Bivariate-Equatio n Approach 374
9.7 Example s 375
9.8 Exercise s 384
10 Kinematic s of Alternativ e Roboti c Mechanica l Systems 387
10.1 Introduction 387
10.2 Kinematic s of Parallel Manipulators 388
10.2.1 Velocity and Acceleration Analyses of Parallel
Manipulators 40 1
10.3 Multifingered Hand s 40 8
10.4 Walking Machines 41 3
10.5 Rolling Robots 41 6
10.5.1 Robots with Conventional Wheels 41 7
10.5.2 Robots with Omnidirectional Wheels 42 2
10.6 Exercise s 42 6
11 Trajector y Planning : Continuous-Pat h Operation s 42 9
11.1 Introduction 42 9
11.2 Curve Geometry 430
11.3 Parametric Path Representation 43 5
11.4 Parametric Splines in Trajectory Planning 44 9
11.5 Continuous-Pat h Tracking 45 4
11.6 Exercise s 46 3Contents xiii
12 Dynamic s of Comple x Roboti c Mechanica l System s 46 9
12.1 Introduction 46 9
12.2 Classification of Robotic Mechanical Systems with Regard to Dynamics 470
12.3 The Structure of the Dynamics Models of Holonomi c Systems . . 47 1
12.4 Dynamics of Parallel Manipulators 47 4
12.5 Dynamics of Rolling Robots 48 4
12.5.1 Robots with Conventional Wheels 48 5
12.5.2 Robots with Omnidirectional Wheels 49 3
12.6 Exercise s 502
A Kinematic s of Rotations : A Summar y 507
B Numerica l Equation-Solvin g 513
B.l The Overdetermined Linea r Case 514
B.1.1 The Numerical Solution of an Overdetermined
System of Linea r Equation s 515
B.2 The Underdetermine d Linea r Case 519
B.2.1 The Numerical Solution of an Underdetermine d
System of Linea r Equation s 520
B.3 Nonlinear-Equatio n Solving: The Determined Case 521
B.3.1 The Newton-Raphso n Method 522
B.4 Overdetermined Nonlinear Systems of Equation s 524
B.4. 1 The Newton-Gaus s Method 525
B.4. 2 Convergence Criterion 525
Reference s 529
Inde x 54 3
Index
ABB-IR B 1000 robot, 164 , 229
acatastatic systems, 47 1
acceleration analysis
of parallel manipulators, 40 3
of rigid bodies, 110
of serial manipulators, 186
affine transformation, 29, 62
Agile Eye, 12
AI, see artificial intelligence
algorithm definition, 24
angle of rotation, 38
angular acceleration
computation, 331
invariant-rat e relations, 110
matrix , 110
vector, 110
angular velocity
dyad, 121, 259
invariant-rat e relations, 108, 508-
511
matrix , 102
vector, 102
Appendix A, 507
Appendix B, 513
arc-welding , 430
operation, 44 4
path-tracking , 45 9
architecture of a
kinematic chain, 131
manipulator, 129
articulated-bod y method, 290
artificial intelligence, 4 , 24
axia l component of a vector, 31
axia l vector of a 3 x 3 matrix , 4 2
base frame, 139
basis of a vector space, 31
Bezout' s method, 400
bivariate-equatio n approach, 345 , 357,
367
C, 25
C++ , 25
Canadarm, see Canadarm2
Canadarm2, 5, 6
canonical form of a rotation, 4 1
Carausius morosus, 17, 534
Cartesian coordinates
of a manipulator, 129
also, see Cartesian variables
Cartesian decomposition, 4 2
Cartesian variables
of a manipulator, 138
caster wheel, 417 , 48 5
catastatic system, 47 1
Cayley' s Theorem, 81
Cayley-Hamilto n theorem, 36
change of basis, 65
characteristic equation , 33, 36
of a manipulator, 145 , 367
characteristic length, 206, 211, 216
characteristic polynomial, 33
of a manipulator, 184 , 344 , 364 ,
367, 390, 40 1
Chasles' Theorem, see Mozzi-Chasles '
Theorem
Chebyshev norm, 206, 45 9
Cholesky-decompositio n algorithm,
290, 309
closure equations , 139
compatibility conditions
for acceleration, 332
for velocity, 326
composite rigid-bod y method, 29054 4 INDEX
composition of reflections and
rotations, 54
condition number, 205, 369
configuration of a manipulator, 129
constraint wrenches, 167
continuous path, 234 , 34 5
operations, 42 9
tracking, 45 4
control vector, 280, 310
coordinate transformation, 56-6 5
Coriolis
acceleration, 113
and centrifugal forces, 283, 284 ,
290
Couette flow, 314
Coulomb
dissipation function, 315
friction, 261, 315
CP, see continuous path
cross-produc t matrix , 36
curvature, 43 1
derivative w. r. t.
a parameter, 43 8
derivative w. r. t. the arc length,
43 1
parametric representation, 43 6
time-derivative , 43 3
cycloidal motion, 24 3
Darboux vector, 43 3
time-derivative , 43 4
decoupled manipulators, 133, 138
decoupled robots, 129
Delta Robot, 14
Delta robot, 14
delta-arra y (A-array) , 427 , 49 3
Denavit-Hartenber g
frames, 131
notation, 129
parameters, 133, 134
rotation matrix , 134
vector joining two frame origins,
135
determined system, 521
dexterity , 24
measures, see kinetostatic performance indices
DEXTRE , 5
dextrou s hands, see multifingered hands
dextrou s manipulation, 10
dextrou s workspace, 201
DH , see Denavit-Hartenber g
dialytic elimination, 185, 230
DIESTRO
inverse kinematics, 379
Jacobian , 227
manipulator, 217, 379
differentiation with respect to
vectors, 36, 37
direct kinematic problem
of parallel manipulators, 388
displacement equation s of a
manipulator, 139
dissipation function, 261, 314
duality, 167
dynamic systems, 1
dynamics
of holonomic systems, 47 0
of multibody systems, 259
of parallel manipulators, 47 4
of rigid bodies, 118
of robotic mechanical systems,
470
of rolling robots, 48 4
of serial manipulators, 257
EE, see end-effecto r
elastodynamic, 168
end-effector , 131
Euclidean norm, 38
Euler
angles, 42 , 81, 87
equatio n (for graphs), 47 4
equatio n (in mechanics), 120
parameters, see Euler-Rodrigue s
parameters
Euler' s
formula for graphs, see Euler
equatio n for graphs
theorem, 36
Euler-Lagrang e equations , 258, 260INDEX 54 5
derived with the NOC, 282, 47 2
Euler-Rodrigue s parameters, 51
Fanu c Arc Mate
inverse displacement, 375
Fanu c Arc Mate 120iB, 165
Fanu c Robot Arc Mate
characteristic length, 226
DH parameters, 225
KCI , 226
feasible twists, 167
Firs t La w of Thermodynamics, 191
flight simulator, 389
floating-poin t operation, 24,189 , 289,
515
flop, see floating-point operation
forward dynamics
algorithm complexity , 306
of serial manipulators, 257, 289
fractal, 524
Frenet , see Frenet-Serre t
Frenet-Serre t
formulas, 43 1
frame, 43 0
vectors, 43 1
friction forces, 313
Frobeniu s norm, 204
fuzz y logic, 24
genealogy of robotic mechanical systems, 1, 4
general architecture of a
manipulator, 4
generalize d coordinates, 260, 261, 470
generaUze d forces, 260, 261, 490
generalize d inertia matrix , 262, 49 8
Cholesky decomposition, 291
factoring, 291
time-rat e of change, 298
generalize d speeds, 261, 47 1
Ginger, see Segway
gluing operation, 43 9
grasping matrix , 410
gravity
terms, 312
wrench, 281
hand-ey e calibration, 76
Hex a robot, 15
higher kinematic pair, 130
holonomic systems, 469 , 47 0
homogeneous coordinates, 56
homotopy, 34 5
IDP, see inverse displacement problem
ilonators, 20
inertia tensor, 118
inertia dyad, 120, 259
input, 1, 280
instant screw axis , 104
instrument calibration, 75
intelligent machines, 2, 24
intelligent robots, 2
invariance, 71
inverse displacement problem of
a general 6R manipulator, 34 4
inverse dynamics
of serial manipulators, 257
recursive, 269
inverse kinematics problem of
parallel manipulators, 390
inverse vs. forward dynamics, 257
inward recursions, 275, 278
ISA, see instant screw axi s
isomorphism, 33
isotropic
manipulator, 206
matrix , 203, 206
isotropy, 209
iteration, 24 , 45 8
Jacobia n matrix , 167
condition number, 205
evaluation, 175
invertibility, 201
transfer formula, 173
joint, 130
coordinates, 129, 133
parameters, 133
variables, 133
Kane' s equations , 26854 6 INDEX
KCI , see kinematic conditioning index
kernel of a linear transformation, 29
Kinemate , 108
kinematic
chain, 129
conditioning index , 204
constraints, 281
constraints for serial manipulators, 285
pair, 130
kinematic chain
architecture of a , 131
kinetostatic performance indices, 201
kinetostatics, 167
least-squar e error, 525
least-squar e solution, 525
Le e vs. Li , 34 5
Lee' s manipulator, 376
Lee' s procedure, 373
left hand, 15
legged robots, 17
L i vs. Lee , see Le e vs. L i
Li' s manipulator, see Lee' s manipulator
linear invariants, 4 2
of rotation, 4 3
linear transformations, 28
local structure of a manipulator, 133
locomotors, 17
lower kinematic pair, 130
L U decomposition, 171
machine (definitions of), 24
main gauche, see left hand
maneuverability, 42 6
manipulability, 201
of decoupled manipulators, 231
manipulator
angular velocity matrix , 261
architecture, 129
configuration, 129
dynamics, 257, 47 4
general architecture, 4
mass matrix , 261
posture, 129
twist, 261
wrench, 261
manipulators, 7, 129
matrix
norm, 204
representation, 32
mechanical system, 2
mechatronics, 24
Mekanum wheels, 20
minimum-tim e trajectory, 283
mobile wheeled pendulums, 21
module, 35
moment of inertia, 118
moment invariants, 71
moment of a line
about a point, 96
about another line, 122
momentum screw, 121
motor, 108
Mozzi-Chasles ' Theorem, 91
MSS, 5
multibody system
dynamics, 259
Euler-Lagrang e equations , 268
multicubic expression , 14 1
multifingered hands, 10
multilinear expression , 14 0
multiquadrati c expression , 14 1
multiquarti c expression , 14 1
natural orthogonal complement, 259
applied to holonomic systems,
47 2
applied to parallel manipulators,
47 4
applied to planar manipulators,
293
applied to rolling robots, 485 ,
49 6
Newton
-Eule r algorithm, 278
-Gaus s method, 45 5
-Raphso n method, 77
equation , 120
methods, 345 , 45 5INDEX 54 7
NOC, see natural orthogonal complement
nonholonomic systems, 258, 469 , 48 4
noninertial base link, 288
nonlinear system, 521
norm
also, see Frobeniu s norm
norm (matrix -) , 204
normal component of a vector, 31
normality condition, 526
nullspace of a linear transformation,
29
numerical conditioning, 357, 369
object-oriente d programming, 25
Odetics series of hexapods , 17
ODW, see omnidirectional wheels,
see omnidirectional wheels
off-line , 4 , 145 , 176
omnidirectional wheels, 20, 49 3
dynamics, 49 3
kinematics, 42 2
on-line , 24
operation point, 133
orientation problem, 157
orthogonal complement, 282
orthogonal decomposition of a vector, 31
orthogonal decoupled manipulator,
152
orthogonal projection, 29
orthogonal RRR manipulator
dynamics, 294 , 297
inverse kinematics, 153, 155
recursive dynamics, 304
workspace, 159
OSU ASV, 17
OSU Hexapod , 17
output, 1
outward recursions, 269
overdetermined system, 524
Pappus-Guldinu s theorem, 231
parallel axes , theorem, 120
parallel manipulators
acceleration analysis, 40 1
dynamics, 47 4
kinematics, 388
velocity analysis, 40 1
parallel robots, 12
parametric
path representation, 43 5
representation of curvature, 43 6
representation of curvature derivative, 43 8
representation of torsion, 43 6
representation of torsion derivative, 43 8
splines, 44 9
path-trackin g for arc-welding , 45 9
pick-and-plac e operations, 233, 234
Pliicker coordinates
of a line, 95
transfer formula, 98
planar manipulators, 192
acceleration analysis, 198
displacement analysis, 193
dynamics, 263
static analysis, 199
velocity analysis, 195
platform manipulators, 389, 398, 47 4
polar-decompositio n theorem, 202
polynomial interpolation
with 3-4- 5 polynomial, 236
with 4-5-6- 7 polynomial, 24 0
pose
array, 99
of a rigid body, 98
positioning problem, 14 2
posture of a manipulator, 129
PPO, see pick-and-plac e operations
Principle of Virtual Work, 191
prismatic pair, 130, 179
programmable robot, 2
projection, 29
theorem, 515
Puma robot, 132, 133, 150
DH parameters, 133
inverse kinematics, 14 2
workspace, 151
pure reflection, 3054 8 INDEX
quaternions , 53
Raghavan and Roth' s procedure, 34 5
Raghavan-Roth' s procedure, 357
range of a linear transformation, 29,
79
Rayleigh dissipation function, see dissipation function
real-time , 24 , 257
reciprocal bases, 76, 175, 48 3
reciprocal product, 117
recursion, 24
redundant sensing, 75
References, 528
reflection, 30, 346 , 352
composition with rotations, 54
regional structure of a manipulator,
133
revolute pair, 130
rheonomic systems, 47 0
robot design, 168
robotic hands, 10
robotic mechanical systems, xiii , 1
Rodrigues, see Euler-Rodrigue s
vector, 81
rolling robots
dynamics, 48 4
kinematics, 41 6
rotating pair, 130
rotation, 33
rotation matrix , 38
exponentia l representation, 4 0
run-time , 24
Runge-Kutt a methods, 311
RVS, xiv , 235
SARAH , 11
Schonflies-motio n generators, 16
scleronomic systems, 47 0
screw
amplitude, 93
axis , 93
motion, 89
pitch, 93
Segway, 22
self-inverse , 31
serial manipulators
acceleration analysis, 186
dynamics, 257
kinematics, 130
statics, 190
velocity analysis, 168
workspace, 183
service angle, 201
similarity transformations, 65
simple manipulation, 10
simulation, 310
singular-valu e decomposition, 203
singular-values , 203
singularities, 167
singularity analysis of decoupled manipulators, 180
sliding pair, 130
SPDM, 5
spherical wrist, 133, 158, 159
workspace, 160
spline(s), 24 6
interpolation of 4-5-6- 7 polynomial, 251
natural, 250
nonparametric, 247 , 44 9
parametric, 44 9
periodic, 24 7
squar e root of a matrix , 52
Star robot, 15
state
of a dynamical system, 280
of parallel manipulators, 480
of serial manipulators, 280, 310
variable, 261, 280, 310
variable equations , 310
vector, 280
static analysis
of rigid bodies, 114
of serial manipulators, 190
static, conservative conditions, 167
stationary point, 526
Steiner, theorem, 120
Stewart platform, see Stewart-Goug h
platform
Stewart-Goug h platform, xix , 390
direct kinematics, 388INDEX 54 9
leg kinematics, 390
structural design, 168
structure of mechanical systems, 9
structured environment, 3
Sutherland, Sprout & Assocs. Hexa -
pod,17
Swedish wheels, 20
system, 1
telemanipulators, 5
tensors, 27, 279, 280
Titan series of quadrupeds , 17
torsion, 43 1
derivative w. r. t.
a parameter, 43 8
derivative w. r. t. the arc length,
43 1
parametric representation, 43 6
time-derivative , 43 3
trace of a squar e matrix , 4 2
trajectories with via poses, 24 5
trajectory planning, 233, 42 9
truncation error, 311
Trussarm, 15
TU Munich Hand , 11
TU Munich Hexapod , 17
twist, 104
axi s coordinates, 108
of a rigid body, 107
ray coordinates, 108
transfer formula, 109
twist-shap e relations, 282
for serial manipulators, 285
unimodular group (of matrices), 97
unstructured environment, 3
vector of a 3 X 3 matrix , 4 2
vector space, 28
velocity analysis
of parallel manipulators, 40 1
of rolling robots, 41 8
of serial manipulators, 168
via poses, 24 5
virtual work, see Principle of Virtual Work
viscosity coefBcient, 314
viscous forces, 313
walking machines
kinematics, 41 3
leg architecture, 413-41 5
walking stick, 17
weighting matrix , 525
wheeled robots, 19
workspace of positioning manipulators, 182
wrench
acting on a rigid body, 115
axis , 115
pitch, 115
transfer formula, 117
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