| Description |
1 online resource (ix, 272 pages) : illustrations |
| Contents |
1.1 Dynamics Algorithms 1 -- 1.2 Spatial Vectors 3 -- 1.3 Unity and Notation 4 -- 2 Spatial Vector Algebra 7 -- 2.1 Mathematical Preliminaries 7 -- 2.2 Spatial Velocity 10 -- 2.3 Spatial Force 13 -- 2.4 Plucker Notation 15 -- 2.5 Line Vectors and Free Vectors 16 -- 2.6 Scalar Product 17 -- 2.7 Using Spatial Vectors 18 -- 2.8 Coordinate Transforms 20 -- 2.9 Spatial Cross Products 23 -- 2.10 Differentiation 25 -- 2.11 Acceleration 28 -- 2.12 Momentum 31 -- 2.13 Inertia 32 -- 2.14 Equation of Motion 35 -- 2.15 Inverse Inertia 36 -- 2.16 Planar Vectors 37 -- 3 Dynamics of Rigid Body Systems 39 -- 3.1 Equations of Motion 40 -- 3.2 Constructing Equations of Motion 42 -- 3.3 Vector Subspaces 46 -- 3.4 Classification of Constraints 50 -- 3.5 Joint Constraints 53 -- 3.6 Dynamics of a Constrained Rigid Body 57 -- 3.7 Dynamics of a Multibody System 60 -- 4 Modelling Rigid Body Systems 65 -- 4.1 Connectivity 66 -- 4.2 Geometry 73 -- 4.3 Denavit-Hartenberg Parameters 75 -- 4.4 Joint Models 78 -- 4.5 Spherical Motion 84 -- 4.6 A Complete System Model 87 -- 5 Inverse Dynamics 89 -- 5.1 Algorithm Complexity 89 -- 5.2 Recurrence Relations 90 -- 5.3 The Recursive Newton-Euler Algorithm 92 -- 5.4 The Original Version 97 -- 5.5 Additional Notes 99 -- 6 Forward Dynamics -- Inertia Matrix Methods 101 -- 6.1 The Joint-Space Inertia Matrix 102 -- 6.2 The Composite-Rigid-Body Algorithm 104 -- 6.3 A Physical Interpretation 108 -- 6.4 Branch-Induced Sparsity 110 -- 6.5 Sparse Factorization Algorithms 112 -- 7 Forward Dynamics -- Propagation Methods 119 -- 7.1 Articulated-Body Inertia 119 -- 7.2 Calculating Articulated-Body Inertias 123 -- 7.3 The Articulated-Body Algorithm 128 -- 7.4 Alternative Assembly Formulae 131 -- 7.5 Multiple Handles 136 -- 8 Closed Loop Systems 141 -- 8.1 Equations of Motion 141 -- 8.2 Loop Constraint Equations 143 -- 8.3 Constraint Stabilization 145 -- 8.4 Loop Joint Forces 148 -- 8.5 Solving the Equations of Motion 149 -- 8.6 Algorithm for C -- [tau superscript a] 152 -- 8.7 Algorithm for K and k 154 -- 8.8 Algorithm for G and g 156 -- 8.9 Exploiting Sparsity in K and G 158 -- 8.10 Some Properties of Closed-Loop Systems 159 -- 8.11 Loop Closure Functions 161 -- 8.12 Inverse Dynamics 164 -- 8.13 Sparse Matrix Method 166 -- 9 Hybrid Dynamics and Other Topics 171 -- 9.1 Hybrid Dynamics 171 -- 9.2 Articulated-Body Hybrid Dynamics 176 -- 9.3 Floating Bases 179 -- 9.4 Floating-Base Forward Dynamics 181 -- 9.5 Floating-Base Inverse Dynamics 183 -- 9.6 Gears 186 -- 9.7 Dynamic Equivalence 189 -- 10 Accuracy and Efficiency 195 -- 10.1 Sources of Error 196 -- 10.2 The Sensitivity Problem 199 -- 10.3 Efficiency 201 -- 10.4 Symbolic Simplification 209 -- 11 Contact and Impact 213 -- 11.1 Single Point Contact 213 -- 11.2 Multiple Point Contacts 216 -- 11.3 A Rigid-Body System with Contacts 219 -- 11.4 Inequality Constraints 222 -- 11.5 Solving Contact Equations 224 -- 11.6 Contact Geometry 227 -- 11.7 Impulsive Dynamics 230 -- 11.8 Soft Contact 235 -- A Spatial Vector Arithmetic 241 -- A.1 Simple Planar Arithmetic 241 -- A.2 Simple Spatial Arithmetic 243 -- A.3 Compact Representations 245 -- A.4 Axial Screw Transforms 249 -- A.5 Some Efficiency Tricks 252 |
| Summary |
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 |
| Bibliography |
Includes bibliographical references (pages 257-264) and index |
| Notes |
Print version record |
| In |
Springer e-books |
| Subject |
Dynamics, Rigid.
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Recursive functions.
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Robots -- Dynamics.
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Engineering.
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Robotics.
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Automation.
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Engineering
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Robotics
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Automation
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engineering.
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automation.
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TECHNOLOGY & ENGINEERING -- Robotics.
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Recursive functions.
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Robots -- Dynamics.
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Dynamics, Rigid.
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Informatique.
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Dynamics, Rigid
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Recursive functions
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Robots -- Dynamics
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| Form |
Electronic book
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| LC no. |
2007936980 |
| ISBN |
9781489975607 |
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1489975608 |
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1281117307 |
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9781281117304 |
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9780387743158 |
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0387743154 |
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