Fundamentals Of Robotic Mechanical System Theory

Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms......Page 1
Acknowledgements......Page 0
Contents......Page 2
1.1 Introduction......Page 8
1.2 The General Structure of Robotic Mechanical Systems......Page 10
1.3 Serial Manipulators......Page 13
1.4 Parallel Manipulators......Page 15
1.5 Robotic Hands......Page 18
1.6 Walking Machines......Page 20
1.7 Rolling Robots......Page 22
2.1 Preamble......Page 26
2.2 Linear Transformations......Page 27
2.3 Rigid-Body Rotations......Page 32
2.3.1 The Cross-Product Matrix......Page 35
2.3.2 The Rotation Matrix......Page 37
2.3.3 The Linear Invariants of a 3 × 3 Matrix......Page 41
2.3.4 The Linear Invariants of a Rotation......Page 42
2.3.5 Examples......Page 44
2.3.6 The Euler-Rodrigues Parameters......Page 50
2.4 Composition of Reflections and Rotations......Page 54
2.5 Coordinate Transformations and Homogeneous Coordinates......Page 55
2.5.1 Coordinate Transformations Between Frames with a Common Origin......Page 56
2.5.2 Coordinate Transformation with Origin Shift......Page 59
2.5.3 Homogeneous Coordinates......Page 61
2.6 Similarity Transformations......Page 65
2.7 Invariance Concepts......Page 70
2.7.1 Applications to Redundant Sensing......Page 73
3.1 Introduction......Page 78
3.2 General Rigid-Body Motion and Its Associated Screw......Page 79
3.2.1 The Screw of a Rigid-Body Motion......Page 81
3.2.2 The Pl¨ucker Coordinates of a Line......Page 83
3.2.3 The Pose of a Rigid Body......Page 87
3.3 Rotation of a Rigid Body About a Fixed Point......Page 90
3.4 General Instantaneous Motion of a Rigid Body......Page 91
3.4.1 The Instant Screw of a Rigid-Body Motion......Page 92
3.4.2 The Twist of a Rigid Body......Page 95
3.5 Acceleration Analysis of Rigid-Body Motions......Page 98
3.6 Rigid-Body Motion Referred to Moving Coordinate Axes......Page 100
3.7 Static Analysis of Rigid Bodies......Page 102
3.8 Dynamics of Rigid Bodies......Page 106
4.1 Introduction......Page 112
4.2 The Denavit-Hartenberg Notation......Page 113
4.3 The Kinematics of Six-Revolute Manipulators......Page 120
4.4 The IKP of Decoupled Manipulators......Page 124
4.4.1 The Positioning Problem......Page 125
4.4.2 The Orientation Problem......Page 140
4.5 Velocity Analysis of Serial Manipulators......Page 145
4.5.1 Jacobian Evaluation......Page 152
4.5.2 Singularity Analysis of Decoupled Manipulators......Page 157
4.5.3 Manipulator Workspace......Page 159
4.6 Acceleration Analysis of Serial Manipulators......Page 163
4.7 Static Analysis of Serial Manipulators......Page 167
4.8 Planar Manipulators......Page 169
4.8.1 Displacement Analysis......Page 170
4.8.2 Velocity Analysis......Page 172
4.8.3 Acceleration Analysis......Page 175
4.8.4 Static Analysis......Page 177
4.9 Kinetostatic Performance Indices......Page 178
4.9.1 Positioning Manipulators......Page 183
4.9.2 Orienting Manipulators......Page 186
4.9.3 Positioning and Orienting Manipulators......Page 187
5.1 Introduction......Page 196
5.2 Background on PPO......Page 197
5.3.1 A 3-4-5 Interpolating Polynomial......Page 199
5.3.2 A 4-5-6-7 Interpolating Polynomial......Page 203
5.4 Cycloidal Motion......Page 206
5.5 Trajectories with Via Poses......Page 208
5.6 Synthesis of PPO Using Cubic Splines......Page 209
6.2 Inverse vs. Forward Dynamics......Page 218
6.3.1 On Nomenclature and Basic Definitions......Page 220
6.3.2 The Euler-Lagrange Equations of Serial Manipulators......Page 221
6.4 Recursive Inverse Dynamics......Page 230
6.4.1 Kinematics Computations: Outward Recursions......Page 231
6.4.2 Dynamics Computations: Inward Recursions......Page 237
6.5 The Natural Orthogonal Complement in Robot Dynamics......Page 241
6.5.1 Derivation of Constraint Equations and Twist-Shape Relations......Page 247
6.6 Manipulator Forward Dynamics......Page 251
6.6.1 Planar Manipulators......Page 255
6.6.2 Algorithm Complexity......Page 268
6.6.3 Simulation......Page 272
Equations......Page 275
6.8 The Modeling of Dissipative Forces......Page 276
7.1 Introduction......Page 280
7.2 Computation of Angular Velocity from Point-Velocity Data......Page 281
7.3 Computation of Angular Acceleration from Point-Acceleration Data......Page 287
8.1 Introduction......Page 294
8.2 The IKP of General Six-Revolute Manipulators......Page 295
8.2.1 Preliminaries......Page 296
8.2.2 The Bivariate-Equation Approach......Page 309
8.2.3 The Univariate-Polynomial Approach......Page 311
8.2.4 Numerical Conditioning of the Solutions......Page 320
8.2.5 Computation of the Remaining Joint Angles......Page 321
8.2.6 Examples......Page 324
8.3 Kinematics of Parallel Manipulators......Page 329
8.3.1 Velocity and Acceleration Analyses of Parallel Manipulators......Page 344
8.4 Multifingered Hands......Page 350
8.5 Walking Machines......Page 355
8.6.1 Robots with Conventional Wheels......Page 359
8.6.2 Robots with Omnidirectional Wheels......Page 365
9.1 Introduction......Page 370
9.2 Curve Geometry......Page 371
9.3 Parametric Path Representation......Page 377
9.4 Parametric Splines in Trajectory Planning......Page 390
9.5 Continuous-Path Tracking......Page 396
10.1 Introduction......Page 407
10.2 Classification of Robotic Mechanical Systems Holonomic Systems......Page 408
10.3 The Structure of the Dynamics Models of Holonomic Systems......Page 409
10.4 Dynamics of Parallel Manipulators......Page 412
10.5.1 Robots with Conventional Wheels......Page 423
10.5.2 Robots with Omnidirectional Wheels......Page 433
Kinematics of Rotations: A Summary......Page 443
The Numerical Solution of Linear Algebraic Systems......Page 451
B.1 The Overdetermined Case......Page 452
B.1.1 The Numerical Solution of an Overdetermined System of Linear Equations......Page 453
B.2 The Underdetermined Case......Page 457
B.2.1 The Numerical Solution of an Underdetermined System of Linear Equations......Page 458
1 An Overview of Robotic Mechanical Systems......Page 461
2 Mathematical Background......Page 463
3 Fundamentals of Rigid-Body Mechanics......Page 471
4 Kinetostatics of Simple Robotic Manipulators......Page 477
5 Trajectory Planning: Pick-and-Place Operations......Page 484
6 Dynamics of Serial Robotic Manipulators......Page 487
7 Special Topics on Rigid-Body Kinematics......Page 493
8 Kinematics of Complex Robotic Mechanical Systems......Page 496
9 Trajectory Planning: Continuous-Path Operations......Page 500
10 Dynamics of Complex Robotic Mechanical Systems......Page 504
References......Page 507
End of Book......Page 521