Fundamentals of robotic mechanical systems: theory, methods, and algorithms

Jorge Angeles9780387953687, 038795368X

Modern robotics dates from the late 1960s, when progress in the development of microprocessors made possible the computer control of a multiaxial manipulator. Since then, robotics has evolved to connect with many branches of science and engineering, and to encompass such diverse fields as computer vision, artificial intelligence, and speech recognition. This book deals with robots-such as remote manipulators, multifingered hands, walking machines, flight simulators, and machine tools-that rely on mechanical systems to perform their tasks. It aims to establish the foundations on which the design, control and implementation of the underlying mechanical systems are based. The treatment assumes familiarity with some calculus, linear algebra, and elementary mechanics; however, the elements of rigid-body mechanics and of linear transformations are reviewed in the first chapters, making the presentation self-contained. An extensive set of exercises is included. Topics covered include: kinematics and dynamics of serial manipulators with decoupled architectures; trajectory planning; determination of the angular velocity and angular acceleration of a rigid body from point data; inverse and direct kinematics manipulators; dynamics of general parallel manipulators of the platform type; and the kinematics and dynamics of rolling robots. Since the publication of the previous edition there have been numerous advances in both the applications of robotics (including in laprascopy, haptics, manufacturing, and most notably space exploration) as well as in the theoretical aspects (for example, the proof that Husty’s 40th-degree polynomial is indeed minimal – mentioned as an open question in the previous edition). This new edition has been revised and updated throughout to include these new.

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Table of contents :
Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms……Page 1
Series Preface……Page 9
Preface to the Second Edition……Page 10
Preface to the First Edition……Page 12
How to Use the Book……Page 16
Acknowledgements……Page 17
Contents……Page 20
1.1 Introduction……Page 26
1.2 The General Structure of Robotic Mechanical Systems……Page 28
1.3 Serial Manipulators……Page 31
1.4 Parallel Manipulators……Page 33
1.5 Robotic Hands……Page 36
1.6 Walking Machines……Page 38
1.7 Rolling Robots……Page 40
2.1 Preamble……Page 44
2.2 Linear Transformations……Page 45
2.3 Rigid-Body Rotations……Page 50
2.3.1 The Cross-Product Matrix……Page 53
2.3.2 The Rotation Matrix……Page 55
2.3.3 The Linear Invariants of a 3 × 3 Matrix……Page 59
2.3.4 The Linear Invariants of a Rotation……Page 60
2.3.5 Examples……Page 62
2.3.6 The Euler-Rodrigues Parameters……Page 68
2.4 Composition of Reflections and Rotations……Page 72
2.5 Coordinate Transformations and Homogeneous Coordinates……Page 73
2.5.1 Coordinate Transformations Between Frames with a Common Origin……Page 74
2.5.2 Coordinate Transformation with Origin Shift……Page 77
2.5.3 Homogeneous Coordinates……Page 79
2.6 Similarity Transformations……Page 83
2.7 Invariance Concepts……Page 88
2.7.1 Applications to Redundant Sensing……Page 91
3.1 Introduction……Page 96
3.2 General Rigid-Body Motion and Its Associated Screw……Page 97
3.2.1 The Screw of a Rigid-Body Motion……Page 99
3.2.2 The Pl¨ucker Coordinates of a Line……Page 101
3.2.3 The Pose of a Rigid Body……Page 105
3.3 Rotation of a Rigid Body About a Fixed Point……Page 108
3.4 General Instantaneous Motion of a Rigid Body……Page 109
3.4.1 The Instant Screw of a Rigid-Body Motion……Page 110
3.4.2 The Twist of a Rigid Body……Page 113
3.5 Acceleration Analysis of Rigid-Body Motions……Page 116
3.6 Rigid-Body Motion Referred to Moving Coordinate Axes……Page 118
3.7 Static Analysis of Rigid Bodies……Page 120
3.8 Dynamics of Rigid Bodies……Page 124
4.1 Introduction……Page 130
4.2 The Denavit-Hartenberg Notation……Page 131
4.3 The Kinematics of Six-Revolute Manipulators……Page 138
4.4 The IKP of Decoupled Manipulators……Page 142
4.4.1 The Positioning Problem……Page 143
4.4.2 The Orientation Problem……Page 158
4.5 Velocity Analysis of Serial Manipulators……Page 163
4.5.1 Jacobian Evaluation……Page 170
4.5.2 Singularity Analysis of Decoupled Manipulators……Page 175
4.5.3 Manipulator Workspace……Page 177
4.6 Acceleration Analysis of Serial Manipulators……Page 181
4.7 Static Analysis of Serial Manipulators……Page 185
4.8 Planar Manipulators……Page 187
4.8.1 Displacement Analysis……Page 188
4.8.2 Velocity Analysis……Page 190
4.8.3 Acceleration Analysis……Page 193
4.8.4 Static Analysis……Page 195
4.9 Kinetostatic Performance Indices……Page 196
4.9.1 Positioning Manipulators……Page 201
4.9.2 Orienting Manipulators……Page 204
4.9.3 Positioning and Orienting Manipulators……Page 205
5.1 Introduction……Page 214
5.2 Background on PPO……Page 215
5.3.1 A 3-4-5 Interpolating Polynomial……Page 217
5.3.2 A 4-5-6-7 Interpolating Polynomial……Page 221
5.4 Cycloidal Motion……Page 224
5.5 Trajectories with Via Poses……Page 226
5.6 Synthesis of PPO Using Cubic Splines……Page 227
6.2 Inverse vs. Forward Dynamics……Page 236
6.3.1 On Nomenclature and Basic Definitions……Page 238
6.3.2 The Euler-Lagrange Equations of Serial Manipulators……Page 239
6.4 Recursive Inverse Dynamics……Page 248
6.4.1 Kinematics Computations: Outward Recursions……Page 249
6.4.2 Dynamics Computations: Inward Recursions……Page 255
6.5 The Natural Orthogonal Complement in Robot Dynamics……Page 259
6.5.1 Derivation of Constraint Equations and Twist-Shape Relations……Page 265
6.6 Manipulator Forward Dynamics……Page 269
6.6.1 Planar Manipulators……Page 273
6.6.2 Algorithm Complexity……Page 286
6.6.3 Simulation……Page 290
Equations……Page 293
6.8 The Modeling of Dissipative Forces……Page 294
7.1 Introduction……Page 298
7.2 Computation of Angular Velocity from Point-Velocity Data……Page 299
7.3 Computation of Angular Acceleration from Point-Acceleration Data……Page 305
8.1 Introduction……Page 312
8.2 The IKP of General Six-Revolute Manipulators……Page 313
8.2.1 Preliminaries……Page 314
8.2.2 The Bivariate-Equation Approach……Page 327
8.2.3 The Univariate-Polynomial Approach……Page 329
8.2.4 Numerical Conditioning of the Solutions……Page 338
8.2.5 Computation of the Remaining Joint Angles……Page 339
8.2.6 Examples……Page 342
8.3 Kinematics of Parallel Manipulators……Page 347
8.3.1 Velocity and Acceleration Analyses of Parallel Manipulators……Page 362
8.4 Multifingered Hands……Page 368
8.5 Walking Machines……Page 373
8.6.1 Robots with Conventional Wheels……Page 377
8.6.2 Robots with Omnidirectional Wheels……Page 383
9.1 Introduction……Page 388
9.2 Curve Geometry……Page 389
9.3 Parametric Path Representation……Page 395
9.4 Parametric Splines in Trajectory Planning……Page 408
9.5 Continuous-Path Tracking……Page 414
10.1 Introduction……Page 425
10.2 Classification of Robotic Mechanical Systems Holonomic Systems……Page 426
10.3 The Structure of the Dynamics Models of Holonomic Systems……Page 427
10.4 Dynamics of Parallel Manipulators……Page 430
10.5.1 Robots with Conventional Wheels……Page 441
10.5.2 Robots with Omnidirectional Wheels……Page 451
Kinematics of Rotations: A Summary……Page 461
The Numerical Solution of Linear Algebraic Systems……Page 469
B.1 The Overdetermined Case……Page 470
B.1.1 The Numerical Solution of an Overdetermined System of Linear Equations……Page 471
B.2 The Underdetermined Case……Page 475
B.2.1 The Numerical Solution of an Underdetermined System of Linear Equations……Page 476
1 An Overview of Robotic Mechanical Systems……Page 479
2 Mathematical Background……Page 481
3 Fundamentals of Rigid-Body Mechanics……Page 489
4 Kinetostatics of Simple Robotic Manipulators……Page 495
5 Trajectory Planning: Pick-and-Place Operations……Page 502
6 Dynamics of Serial Robotic Manipulators……Page 505
7 Special Topics on Rigid-Body Kinematics……Page 511
8 Kinematics of Complex Robotic Mechanical Systems……Page 514
9 Trajectory Planning: Continuous-Path Operations……Page 518
10 Dynamics of Complex Robotic Mechanical Systems……Page 522
References……Page 525
Index……Page 539