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E-raamat: Constrained Dynamics Computations: Models & Case Studies

(University Of Sydney, Australia), (The University Of Western Australia, Australia), (The University Of Western Australia, Australia)
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Constrained Dynamics Computations: Models & Case StudiesSuurem pilt
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This book introduces a practical approach to the modelling and computation of real-world systems. Multibody dynamics, planar and spatial modelling, and numerical methods are all pursued to obtain information about the behaviour of various dynamical systems. Each study presents the method of modelling and the ensuing differential equations governing the system behaviour. Integration of the equations yields results which are carefully discussed and which indicate how useful information may be obtained from the study. The studies include planar mechanisms, heavy equipment, automobile crash simulation and a spatial planetary system example. Research students, scientists and engineers will appreciate the practical approach taken in this book.
Preface vii
Contents xi
Abbreviations xv
Nomenclature xvii
List of Figures
xxiii
List of Tables
xxv
Overview
1(14)
Introduction
1(1)
Multibody Dynamics
2(7)
Examples of Multibody Systems
3(2)
Generalized Coordinates
5(1)
System Topology and Configuration
6(1)
Dynamic Formulation
7(1)
Dynamic Systems Software
8(1)
Numerical Methods
9(1)
Motivation for this Work
10(1)
Contribution of this Work
11(2)
Structure of this Work
13(2)
Planar Modelling
15(20)
Introduction
15(1)
Multibody System Description
16(2)
The Principle of Virtual Work
18(2)
The Lagrange Equations
20(2)
System Equations
22(4)
Lagrange Multipliers
26(1)
Augmented Formulation
27(1)
Joint Types
28(2)
Revolute Joint
28(1)
Prismatic Joint
29(1)
Force Modelling
30(4)
Spring-Damper-Actuator Force Element
30(2)
Torsional Spring-Damper Force Element
32(1)
Contact Forces
33(1)
Summary
34(1)
Numerical Methods
35(17)
Introduction
35(1)
Differential Algebraic Equations
36(5)
General Perspective
36(1)
Types of DAEs
37(1)
DAE Considered in Multibody Modelling
38(3)
Numerical Integration
41(6)
Single-Step Methods
42(1)
Euler's Method
43(1)
Taylor Series Methods
44(1)
Runge-Kutta Methods
45(1)
Multistep Methods
46(1)
Project Software
47(4)
Summary
51(1)
Planar Multibody Systems
52(25)
Introduction
52(1)
Introductory Planar Systems
53(23)
Slider Crank Mechanism
53(2)
Newton-Euler Equations
55(1)
The Equations of Motion
56(2)
Animation and Graphs
58(5)
Arbitrary Length Pendulum
63(3)
Arbitrary Length Train
66(4)
Aircraft Towing Truck
70(4)
Off-highway Recreational Vehicle
74(2)
Summary
76(1)
Off-highway Track Vehicle
77(16)
Introduction
77(1)
Caterpillar System Modelling
78(11)
Track-Roller Contact Force Model
79(2)
Track-Idler Contact Force Model
81(2)
Track-Sprocket Contact Force Model
83(2)
Surface-Tooth Transformation
85(1)
Tooth-Sprocket Transformation
86(1)
Sprocket-Global Transformation
86(2)
Track-Ground Contact Force Model
88(1)
Results
89(3)
Summary
92(1)
Automobile Crash System
93(20)
Introduction
93(1)
Simplified Body Cluster Model
94(7)
Body Seat Contact Force Model
94(2)
Result Reproduction
96(1)
Foot Floor Contact Force Model
97(2)
Seat Belt Contact Force Model
99(1)
Muscle-Skeletal Joint Restoring Torque Model
100(1)
Simplified Body Cluster Model Constraint Equations
101(1)
Vertebral Body Model
101(3)
Muscle-Skeletal Shoulder Connection Model
102(1)
Vertebral Body Model Constraint Equations
103(1)
Results
104(8)
Result Generation
104(8)
Summary
112(1)
Spatial Modelling
113(11)
Introduction
113(1)
Generalized Coordinates and the Rotation Matrix
114(3)
Kinetic Energy
117(1)
The Lagrange Equations
118(2)
General System Equations
120(1)
Force Modelling
121(1)
Joint Types
122(1)
Summary
123(1)
Spatial Planetary System
124(14)
Introduction
124(1)
Spherical Astronomy
125(5)
Coordinate Systems
126(3)
System Forces
129(1)
Results
130(7)
Summary
137(1)
Conclusions and Future Directions
138(6)
Introduction
138(1)
Summary of Results
139(1)
Project Development
140(1)
Future Directions
141(1)
Conclusions
142(2)
References 144(13)
Appendices 157(4)
Appendix
1. Multibody System Computer Pseudo Code
157(2)
Appendix 1.1 Function Call Trees
157(2)
Appendix
2. Robotics
159(2)
Index 161


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