Dynamics and Balancing of Multibody Systems / Edition 1

Dynamics and Balancing of Multibody Systems / Edition 1

by Himanshu Chaudhary, Subir Kumar Saha
     
 

ISBN-10: 3540781781

ISBN-13: 9783540781783

Pub. Date: 10/28/2008

Publisher: Springer Berlin Heidelberg

This monograph develops a unified methodology for dynamic analysis and minimization of the inertia-induced forces occurring in high speed multiloop planar as well as spatial mechanisms based on the multibody system modeling approach. Dynamic analysis is prerequisite for the dynamic balancing of mechanisms. The balancing of mechanisms is one of the crucial steps in

Overview

This monograph develops a unified methodology for dynamic analysis and minimization of the inertia-induced forces occurring in high speed multiloop planar as well as spatial mechanisms based on the multibody system modeling approach. Dynamic analysis is prerequisite for the dynamic balancing of mechanisms. The balancing of mechanisms is one of the crucial steps in design of high speed machinery and is a difficult one due to trade-off amongst various dynamic quantities, e.g., shaking force, shaking moment, bearing reactions, and driving torques/forces. Hence, it is essentially an optimization problem where various dynamic quantities are computed repeatedly.

Product Details

ISBN-13:
9783540781783
Publisher:
Springer Berlin Heidelberg
Publication date:
10/28/2008
Series:
Lecture Notes in Applied and Computational Mechanics Series, #37
Edition description:
2009
Pages:
176
Product dimensions:
6.30(w) x 9.40(h) x 0.60(d)

Table of Contents

1 Introduction 1

1.1 Dynamics 1

1.2 Formulation of Dynamic Analysis 3

1.2.1 DAE vs. ODE 4

1.2.2 Recursive formulations 6

1.2.3 Velocity transformation methods 7

1.3 Balancing of Mechanisms 10

2 Dynamics of Open-loop Systems 11

2.1 Kinematic Constraints in Serial Systems 11

2.2 Kinematic Constraints in Tree-type Systems 16

2.3 Equations of Motion 19

2.4 Constraint Wrench for Serial Systems 22

2.5 Constraint Wrench in Tree-type Systems 25

2.6 Algorithm for Constraint Wrenches 26

2.7 Applications 29

2.7.1 Two-link manipulator 29

2.7.2 Four link gripper 32

2.7.3 Two six-link manipulators 37

2.8 Summary 40

3 Dynamics of Closed-loop Systems 45

3.1 Equations of Motion 45

3.1.1 Spanning tree 46

3.1.2 Determinate and indeterminate subsystems 48

3.1.3 The DeNOC matrices for the spanning tree 49

3.1.4 Constrained equations of motion for a subsystem 49

3.1.5 Constrained equations of motion for the spanning tree 52

3.2 Algorithm for Constraint Wrenches 52

3.3 Four-bar mechanism 55

3.3.1 Equations of motion 56

3.3.2 Numerical example 60

3.4 Carpet Scrapping Machine 63

3.4.1 Subsystem III 66

3.4.2 Subsystem I 69

3.4.3 Subsystem II 71

3.4.4 Numerical example 72

3.4.5 Computation efficiency 76

3.5 Spatial RSSR Mechanism 76

3.5.1 Subsystem approach 78

3.5.2 Numerical example 83

3.5.3 Computation efficiency 86

3.6 Summary 86

4 Equimomental Systems 87

4.1 Equimomental Systems for Planar Motion 87

4.1.1 Two point-mass model 89

4.1.2 Three point-mass model 90

4.2 Equimomental Systems for Spatial Motion 93

5 Balancing of Planar Mechanisms 99

5.1 Balancing of Shaking Force and Shaking Moment 100

5.1.1 Equimomentalsystem in optimization 101

5.2 Balancing Problem Formulation 102

5.2.1 Equations of motion 102

5.2.2 Equations of motion for a point-mass system 106

5.2.3 Shaking force and shaking moment 110

5.2.4 Optimality criterion 112

5.2.5 Mass redistribution method 113

5.2.6 Counterweighting method 114

5.3 Hoeken's Four-bar Mechanism 118

5.3.1 Balancing of shaking force 119

5.3.2 Optimization of shaking force and shaking moment 121

5.4 Carpet Scrapping Mechanism 130

5.5 Summary 135

6 Balancing of Spatial Mechanisms 137

6.1 Balancing Problem Formulation 138

6.1.1 Dynamic equations of motion 138

6.1.2 Shaking force and shaking moment 141

6.1.3 Optimization problem 142

6.2 Spatial RSSR Mechanism 147

6.3 Summary 157

Appendix A 159

Appendix B 163

References 165

Index 173

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