Contents
Preface
1. Introduction
1.1 Dynamics Algorithms
1.2 Spatial Vectors
1.3 Units and Notation
1.4 Readers' Guide
1.5 Further Reading
2. Spatial Vector Algebra
2.1 Mathematical Preliminaries
2.2 Spatial Velocity
2.3 Spatial Force
2.4 Plücker Notation
2.5 Line Vectors and Free Vectors
2.6 Scalar Product
2.7 Using Spatial Vectors
2.8 Coordinate Transforms
2.9 Spatial Cross Products
2.10 Differentiation
2.11 Acceleration
2.12 Momentum
2.13 Inertia
2.14 Equation of Motion
2.15 Inverse Inertia
2.16 Planar Vectors
2.17 Further Reading
3. Dynamics of Rigid Body Systems
3.1 Equations of Motion
3.2 Constructing Equations of Motion
3.3 Vector Subspaces
3.4 Classification of Constraints
3.5 Joint Constraints
3.6 Dynamics of a Constrained Rigid Body
3.7 Dynamics of a Multibody System
4. Modelling Rigid Body Systems
4.1 Connectivity
4.2 Geometry
4.3 Denavit-Hartenberg Parameters
4.4 Joint Models
4.5 Spherical Motion
4.6 A Complete System Model
5. Inverse Dynamics
5.1 Algorithm Complexity
5.2 Recurrence Relations
5.3 The Recursive Newton-Euler Algorithm
5.4 The Original Version
5.5 Additional Notes
6. Forward Dynamics — Inertia Matrix Methods
6.1 The Joint-Space Inertia Matrix
6.2 The Composite-Rigid-Body Algorithm
6.3 A Physical Interpretation
6.4 Branch-Induced Sparsity
6.5 Sparse Factorization Algorithms
6.6 Additional Notes
7. Forward Dynamics — Propagation Methods
7.1 Articulated-Body Inertia
7.2 Calculating Articulated-Body Inertias
7.3 The Articulated-Body Algorithm
7.4 Alternative Assembly Formulae
7.5 Multiple Handles
8. Closed Loop Systems
8.1 Equations of Motion
8.2 Loop Constraint Equations
8.3 Constraint Stabilization
8.4 Loop Joint Forces
8.5 Solving the Equations of Motion
8.6 Algorithm for C – T[sup(a)]
8.7 Algorithm for K and k
8.8 Algorithm for G and g
8.9 Exploiting Sparsity in K and G
8.10 Some Properties of Closed-Loop Systems
8.11 Loop Closure Functions
8.12 Inverse Dynamics
8.13 Sparse Matrix Method
9. Hybrid Dynamics and Other Topics
9.1 Hybrid Dynamics
9.2 Articulated-Body Hybrid Dynamics
9.3 Floating Bases
9.4 Floating-Base Forward Dynamics
9.5 Floating-Base Inverse Dynamics
9.6 Gears
9.7 Dynamic Equivalence
10. Accuracy and Efficiency
10.1 Sources of Error
10.2 The Sensitivity Problem
10.3 Efficiency
10.4 Symbolic Simplification
11. Contact and Impact
11.1 Single Point Contact
11.2 Multiple Point Contacts
11.3 A Rigid-Body System with Contacts
11.4 Inequality Constraints
11.5 Solving Contact Equations
11.6 Contact Geometry
11.7 Impulsive Dynamics
11.8 Soft Contact
11.9 Further Reading
A. Spatial Vector Arithmetic
A.1 Simple Planar Arithmetic
A.2 Simple Spatial Arithmetic
A.3 Compact Representations
A.4 Axial Screw Transforms
A.5 Some Efficiency Tricks
Bibliography
Symbols
Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Z