Table Of ContentMechanical Engineering Series
Frederick F. Ling
Editor- in- Chief
Mechanical Engineering Series
J. Angeles, Fundamentals of Robotic Mechanical Systems:
Theory, Methods, and Algorithms, 3rd ed.
P. Basu, C. Kefa, and L. Jestin, Boilers and Burners: Design and Theory
J.M. Berthelot, Composite Materials:
Mechanical Behavior and Structural Analysis
I.J. Busch-Vishniac, Electromechanical Sensors and Actuators
J. Chakrabarty, Applied Plasticity
K.K. Choi and N.H. Kim, Structural Sensitivity Analysis and Optimization 1:
Linear Systems
K.K. Choi and N.H. Kim, Structural Sensitivity Analysis and Optimization 2:
Nonlinear Systems and Applications
G. Chryssolouris, Manufacturing Systems
G. Chryssolouris, Laser Machining: Theory and Practice
V.N. Constantinescu, Laminar Viscous Flow
G.A. Costello, Theory of Wire Rope, 2nd Ed.
K. Czolczynski, Rotordynamics of Gas-Lubricated Journal Bearing Systems
M.S. Darlow, Balancing of High-Speed Machinery
W. R. DeVries, Analysis of Material Removal Processes
J.F. Doyle, Nonlinear Analysis of Thin-Walled Structures: Statics,
Dynamics, and StabiUty
J.F. Doyle, Wave Propagation in Structures:
Spectral Analysis Using Fast Discrete Fourier Transforms, 2nd ed.
P. A. Engel, Structural Analysis of Printed Circuit Board Systems
A.C. Fischer-Cripps, Introduction to Contact Mechanics
A.C. Fischer-Cripps, Nanoindentations, 2nd ed.
J. Garcia de Jalon and E. Bayo, Kinematic and Dynamic Simulation of
Multibody Systems: The Real-Time Challenge
W.K. Gawronski, Advanced Structural Dynamics and Active Control of
(continued after index)
Jorge Angeles
Fundamentals of Robotic
Mechanical Systems
Theory, Methods, and Algorithms
Third Edition
^ Sprriin ger
Jorge Angeles
Department of Mechanical Engineering
and Center for Intelligent Machines
McGill University
Montreal, Quebec, Canada
Editor-in-Chief
Frederick F. Ling
Earnest F. Gloyna Regents Chair Emeritus in Engineering
Department of Mechanical Engineering
The University of Texas at Austin
Austin, TX 78712-1063, USA
And
Distinguished William Howard Hart
Professor Emeritus
Department of Mechanical Engineering
Aeronautical Engineering and Mechanics
Rensselaer Polytechnic Institute
Troy, NY 12180-3590, USA
Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms, 3'^ Edition
Library of Congress Control Number: 2006927795
ISBN 0-387-29412-0 e-ISBN 0-387-34580-9
ISBN 978-0-387-29412-4
Printed on acid-free paper.
© 2007 Springer Science+Business Media, LLC
All rights reserved. This work may not be translated or copied in whole or in part without
the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring
Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or
scholarly analysis. Use in connection with any form of information storage and retrieval,
electronic adaptation, computer software, or by similar or dissimilar methodology now
know or hereafter developed is forbidden.
The use in this publication of trade names, trademarks, service marks and similar terms,
even if they are not identified as such, is not to be taken as an expression of opinion as to
whether or not they are subject to proprietary rights.
9 8 7 6 5 4 3 21
springer.com
To Anne-Marie, who has given me
not only her love, but also her precious time,
without which this book would not have been possible.
Mechanical Engineering Series
Frederick F. Ling
Editor-in-Chief
The Mechanical Engineering Series features graduate texts and research monographs to
address the need for information in contemporary mechanical engineering, including
areas of concentration of applied mechanics, biomechanics, computational mechanics,
dynamical systems and control, energetics, mechanics of materials, processing, produc
tion systems, thermal science, and tribology.
Advisory Board/Series Editors
Applied Mechanics F.A. Leckie
University of California,
Santa Barbara
D. Gross
Technical University of Darmstadt
Biomechanics V.C. Mow
Columbia University
Computational Mechanics H.T. Yang
University of California,
Santa Barbara
Dynamic Systems and Control/ D. Bryant
Mechatronics University of Texas at Austin
Energetics J.R. Welty
University of Oregon, Eugene
Mechanics of Materials I. Firmie
University of California, Berkeley
Processing K.K. Wang
Cornell University
Production Systems G.-A. Klutke
Texas A&M University
Thermal Science A.E. Bergles
Rensselaer Polytechnic Institute
Tribology W.O. Winer
Georgia Institute of Technology
Series Preface
Mechanical engineering, and engineering discipline born of the needs of the indus
trial revolution, is once again asked to do its substantial share in the call for indus
trial renewal. The general call is urgent as we face profound issues of productivity
and competitiveness that require engineering solutions, among others. The Me
chanical Engineering Series is a series featuring graduate texts and research mono
graphs intended to address the need for information in contemporary areas of me
chanical engineering.
The series is conceived as a comprehensive one that covers a broad range of
concentrations important to mechanical engineering graduate education and re
search. We are fortunate to have a distinguished roster of consulting editors, each
an expert in one of the areas of concentration. The names of the consulting editors
are listed on page vi of this volume. The areas of concentration are applied me
chanics, biomechanics, computational mechanics, dynamic systems and control,
energetics, mechanics of materials, processing, thermal science, and tribology.
Contents
Preface to the Third Edition xv
Preface to the First Edition xix
1 An Overview of Robotic Mechanical Systems 1
1.1 Introduction 1
1.2 The General Architecture of Robotic Mechanical Systems . . .. 3
1.2.1 Types of Robots by Function 6
1.2.2 Types of Robots by Size 7
1.2.3 Types of Robots by Application 7
1.3 Manipulators 7
1.3.1 Robotic Arms 9
1.3.2 Robotic Hands 10
1.4 Motion Generators 12
1.4.1 Parallel Robots 12
1.4.2 SCARA Systems 16
1.5 Locomotors 17
1.5.1 Legged Robots 17
1.5.2 Wheeled Robots 19
1.6 Swimming Robots 22
1.7 Flying Robots 23
1.8 Exercises 24
2 Mathematical Background 27
2.1 Preamble 27
2.2 Linear Transformations 28
2.3 Rigid-Body Rotations 33
2.3.1 The Cross-Product Matrix 36
2.3.2 The Rotation Matrix 38
2.3.3 The Linear Invariants of a 3 x 3 Matrix 42
2.3.4 The Linear Invariants of a Rotation 43
2.3.5 Examples 45
2.3.6 The Euler-Rodrigues Parameters 51
2.4 Composition of Reflections and Rotations 54
Contents
2.5 Coordinate Transformations and Homogeneous Coordinates . .. 56
2.5.1 Coordinate Transformations Between Frames
with a Common Origin 56
2.5.2 Coordinate Transformation with Origin Shift 60
2.5.3 Homogeneous Coordinates 62
2.6 Similarity Transformations 65
2.7 Invariance Concepts 71
2.7.1 Applications to Redundant Sensing 75
2.8 Exercises 79
Fundamentals of Rigid-Body Mechanics 89
3.1 Introduction 89
3.2 General Rigid-Body Motion and Its Associated Screw 89
3.2.1 The Screw of a Rigid-Body Motion 93
3.2.2 The Pliicker Coordinates of a Line 95
3.2.3 The Pose of a Rigid Body 98
3.3 Rotation of a Rigid Body About a Fixed Point 102
3.4 General Instantaneous Motion of a Rigid Body 103
3.4.1 The Instant Screw of a Rigid-Body Motion 104
3.4.2 The Twist of a Rigid Body 107
3.5 Acceleration Analysis of Rigid-Body Motions 110
3.6 Rigid-Body Motion Referred to Moving Coordinate Axes 112
3.7 Static Analysis of Rigid Bodies 114
3.8 Dynamics of Rigid Bodies 118
3.9 Exercises 122
Geometry of Decoupled Serial Robots 129
4.1 Introduction 129
4.2 The Denavit-Hartenberg Notation 129
4.3 The Geometric Model of Six-Revolute Manipulators 138
4.4 The Inverse Displacement Analysis of Decoupled Manipulators . 141
4.4.1 The Positioning Problem 142
4.4.2 The Orientation Problem 157
4.5 Exercises 162
Kinetostatics of Serial Robots 167
5.1 Introduction 167
5.2 Velocity Analysis of Serial Manipulators 168
5.3 Jacobian 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 192
