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Rigid Body Dynamics Algorithms

By: Roy Featherstone

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Hardcover | 1 December 2007 | Edition Number 2

At a Glance

Hardcover
288 Pages

Edition Type
Revised

Dimensions(cm)
23.39 x 15.6 x 1.75

Hardcover

$486.75

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Rigid Body Dynamics Algorithms presents the subject of computational rigid-body dynamics through the medium of spatial 6D vector notation. It explains how to model a rigid-body system and how to analyze it, and it presents the most comprehensive collection of the best rigid-body dynamics algorithms to be found in a single source. The use of spatial vector notation greatly reduces the volume of algebra which allows systems to be described using fewer equations and fewer quantities. It also allows problems to be solved in fewer steps, and solutions to be expressed more succinctly. In addition algorithms are explained simply and clearly, and are expressed in a compact form. The use of spatial vector notation facilitates the implementation of dynamics algorithms on a computer: shorter, simpler code that is easier to write, understand and debug, with no loss of efficiency.

Unique features include:

A comprehensive collection of the best rigid-body dynamics algorithms

Use of spatial (6D) vectors to greatly reduce the volume of algebra, to simplify the treatment of the subject, and to simplify the computer code that implements the algorithms

Algorithms expressed both mathematically and in pseudocode for easy translation into computer programs

Source code for many algorithms available on the internet

Rigid Body Dynamics Algorithms is aimed at readers who already have some elementary knowledge of rigid-body dynamics, and are interested in calculating the dynamics of a rigid-body system. This book serves as an algorithms recipe book as well as a guide to the analysis and deeper understanding of rigid-body systems.

Industry Reviews

From the reviews: "This book deals with a numerical treatment of different problems in the dynamics of rigid-body systems which arise mainly in robotics ... . is centered on mechanical models made up of many rigid bodies connected by joints. ... The book is written in a clear way. Each chapter begins by stating the objectives to be achieved. The algorithms presented are well documented and worked examples are also given. ... the bibliography close this useful book on the computational approach to the dynamics of rigid-body systems." (A. San Miguel, Mathematical Reviews, Issue 2011 h)

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Preface	p. v
Introduction	p. 1
Dynamics Algorithms	p. 1
Spatial Vectors	p. 3
Unity and Notation	p. 4
Readers' Guide	p. 5
Further Reading	p. 6
Spatial Vector Algebra	p. 7
Mathematical Preliminaries	p. 7
Spatial Velocity	p. 10
Spatial Force	p. 13
Plucker Notation	p. 15
Line Vectors and Free Vectors	p. 16
Scalar Product	p. 17
Using Spatial Vectors	p. 18
Coordinate Transforms	p. 20
Spatial Cross Products	p. 23
Differentiation	p. 25
Acceleration	p. 28
Momentum	p. 31
Inertia	p. 32
Equation of Motion	p. 35
Inverse Inertia	p. 36
Planar Vectors	p. 37
Further Reading	p. 38
Dynamics of Rigid Body Systems	p. 39
Equations of Motion	p. 40
Constructing Equations of Motion	p. 42
Vector Subspaces	p. 46
Classification of Constraints	p. 50
Joint Constraints	p. 53
Dynamics of a Constrained Rigid Body	p. 57
Dynamics of a Multibody System	p. 60
Modelling Rigid Body Systems	p. 65
Connectivity	p. 66
Geometry	p. 73
Denavit-Hartenberg Parameters	p. 75
Joint Models	p. 78
Spherical Motion	p. 84
A Complete System Model	p. 87
Inverse Dynamics	p. 89
Algorithm Complexity	p. 89
Recurrence Relations	p. 90
The Recursive Newton-Euler Algorithm	p. 92
The Original Version	p. 97
Additional Notes	p. 99
Forward Dynamics - Inertia Matrix Methods	p. 101
The Joint-Space Inertia Matrix	p. 102
The Composite-Rigid-Body Algorithm	p. 104
A Physical Interpretation	p. 108
Branch-Induced Sparsity	p. 110
Sparse Factorization Algorithms	p. 112
Additional Notes	p. 117
Forward Dynamics - Propagation Methods	p. 119
Articulated-Body Inertia	p. 119
Calculating Articulated-Body Inertias	p. 123
The Articulated-Body Algorithm	p. 128
Alternative Assembly Formulae	p. 131
Multiple Handles	p. 136
Closed Loop Systems	p. 141
Equations of Motion	p. 141
Loop Constraint Equations	p. 143
Constraint Stabilization	p. 145
Loop Joint Forces	p. 148
Solving the Equations of Motion	p. 149
Algorithm for C - [tau superscript a]	p. 152
Algorithm for K and k	p. 154
Algorithm for G and g	p. 156
Exploiting Sparsity in K and G	p. 158
Some Properties of Closed-Loop Systems	p. 159
Loop Closure Functions	p. 161
Inverse Dynamics	p. 164
Sparse Matrix Method	p. 166
Hybrid Dynamics and Other Topics	p. 171
Hybrid Dynamics	p. 171
Articulated-Body Hybrid Dynamics	p. 176
Floating Bases	p. 179
Floating-Base Forward Dynamics	p. 181
Floating-Base Inverse Dynamics	p. 183
Gears	p. 186
Dynamic Equivalence	p. 189
Accuracy and Efficiency	p. 195
Sources of Error	p. 196
The Sensitivity Problem	p. 199
Efficiency	p. 201
Symbolic Simplification	p. 209
Contact and Impact	p. 213
Single Point Contact	p. 213
Multiple Point Contacts	p. 216
A Rigid-Body System with Contacts	p. 219
Inequality Constraints	p. 222
Solving Contact Equations	p. 224
Contact Geometry	p. 227
Impulsive Dynamics	p. 230
Soft Contact	p. 235
Further Reading	p. 239
Spatial Vector Arithmetic	p. 241
Simple Planar Arithmetic	p. 241
Simple Spatial Arithmetic	p. 243
Compact Representations	p. 245
Axial Screw Transforms	p. 249
Some Efficiency Tricks	p. 252
Bibliography	p. 257
Symbols	p. 265
Index	p. 267
Table of Contents provided by Ingram. All Rights Reserved.

Rigid Body Dynamics Algorithms

At a Glance

Hardcover

Industry Reviews

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