Cover image for Flexible manipulators : modeling, analysis and optimum design
Title:
Flexible manipulators : modeling, analysis and optimum design
Personal Author:
Series:
Intelligent systems series
Edition:
1st ed.
Publication Information:
Waltham, M.A. : Academic Press ; [Hangzhou] : Zhejiang University Press, 2012
Physical Description:
x, 257 p. : ill. ; 24 cm.
ISBN:
9780123970367

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Item Category 1
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30000010323134 TJ211 G36 2012 Open Access Book Book
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Summary

Summary

The Intelligent Systems Series comprises titles that present state-of-the-art knowledge and the latest advances in intelligent systems. Its scope includes theoretical studies, design methods, and real-world implementations and applications.

Flexible manipulators play a critical role in applications in a diverse range of fields, such as construction automation, environmental applications, and space engineering. Due to the complexity of the link deformation and dynamics, the research effort on accurate modeling and high performance control of flexible manipulators has increased dramatically in recent years. This book presents analysis, data and insights that will of particular use for researchers and engineers working on the optimization and control of robotic manipulators and automation systems.


Author Notes

Dr. Yanqing Gao is a research scientist at University of Arizona, USA. She is an IEEE member and has served in various positions at IEEE and ASME conferences.
Fei-Yue Wang, Professor, NUDT, Chinese Academy of Sciences. Currently, Prof. Wang is the Editor-in-Chief of the IEEE Intelligent Systems and IEEE Transactions on Intelligent Transportation Systems. He is a Fellow of IEEE, INCOSE, IFAC, ASME, and AAAS. In 2007, he received the 2nd Class National Prize in Natural Sciences of China and was awarded ACM Distinguished Scientist for his work in intelligent systems and social computing. In 2011, he received IEEE ITSS Outstanding ITS Research Award.
Dr. Zhi-Quan Xiao is an Assistant Professor at Wuhan Textile University, China.


Table of Contents

Prefacep. ix
Chapter 1 Introductionp. 1
1.1 Background and Problem Statementp. 1
1.2 Motivationsp. 3
1.3 Organization of the Bookp. 3
Referencesp. 3
Chapter 2 Past and Recent Worksp. 5
2.1 Earlier Research on Flexible Manipulatorsp. 5
2.2 Recent Work on Flexible Manipulatorsp. 6
Referencesp. 11
Chapter 3 Modeling of Flexible Manipulatorsp. 15
3.1 Introductionp. 16
3.2 Problem Description and Energy Calculationsp. 17
3.2.1 Problem Statementp. 17
3.2.2 Kinetic Energy of the Beamp. 19
3.2.3 Kinetic Energy of the Tip Loadp. 20
3.2.4 Total Potential Energyp. 21
3.2.5 Work Done by External Forcesp. 21
3.3 Derivation of Equations of Motionp. 21
3.3.1 Euler-Bernoulli Beam Model Derivationp. 22
3.3.2 Equations of Motion for Euler-Bernoulli Beam Modelp. 26
3.3.3 Timoshenko Beam Model Derivationp. 27
3.3.4 Equations of Motion for Timoshenko Beam Modelp. 33
3.4 Linearization of the Beam Dynamic Modelsp. 34
3.4.1 Introductionp. 34
3.4.2 Euler-Bernoulli Model after Linearizationp. 35
3.4.3 Timoshenko Model after Linearizationp. 35
3.4.4 Dimensionless Functions, Variables, and Parametersp. 36
3.5 Finite-Dimensional Modeling of Flexible Manipulatorsp. 37
3.5.1 Natural Frequency and Modal Shapesp. 37
3.5.2 Finite Modal Model of Euler-Bernoulli Beamp. 41
3.5.3 Finite Difference Modelp. 47
3.5.4 Finite Element Modelp. 51
Referencesp. 57
Chapter 4 Analysis of Flexible Manipulatorsp. 59
4.1 Introductionp. 60
4.2 Dynamic Analysis of Vibrations of Flexible Manipulators Considering Effects of Rotary Inertia, Shear Deformation, and Tip Loadp. 60
4.2.1 Introductionp. 60
4.2.2 Dynamic Models for One-Link Flexible Manipulatorsp. 61
4.2.3 Characteristic Equations for Modal Frequencies and Vibration Modesp. 64
4.2.4 Asymptotic Behavior of Modal Frequencies and Vibration Modesp. 70
4.2.5 Experimental Verification and Numerical Analysisp. 72
4.2.6 Natural Frequencies and Modal Shape Functionsp. 80
4.2.7 Step Responses and General Solutionsp. 88
4.3 Passivity, Control, and Stability Analysisp. 91
4.3.1 Nonlinear Dynamic Equations of Motionp. 91
4.3.2 Discretization of Nonlinear Modelp. 92
4.3.3 Stability Analysisp. 94
Referencesp. 97
Chapter 5 Optimization of Flexible Manipulatorsp. 99
5.1 Optimum Design of Flexible Beams with a New Iteration Approachp. 100
5.1.1 Introductionp. 101
5.1.2 Basic Equationsp. 102
5.1.3 Analysis of Singularity at the Free Endp. 104
5.1.4 Solution by Successive Iterations: New Formulationp. 106
5.1.5 Numerical Examplesp. 111
5.2 Geometrically Constrained and Composite Material Designsp. 116
5.2.1 Minimum and Maximum Radius Constraintsp. 116
5.2.2 Uniform and Variable Tunnel Cross-Section Designsp. 116
5.2.3 Composite Material Designsp. 119
5.3 Optimum Shape Design of Flexible Manipulators with Tip Loadsp. 120
5.3.1 Problem Setupp. 120
5.3.2 Euler-Bernoulli Equationsp. 122
5.3.3 Analytical Solutionsp. 125
5.3.4 Segmentized Optimization Approachp. 133
5.3.5 Multiple Tip Load and Multiple Link Optimum Designsp. 142
5.3.6 Sensitivity Analysisp. 146
5.4 Optimum Shape Construction with Total Weight Constraintp. 148
5.4.1 Basic Equations and the Variation Formulationp. 148
5.4.2 Analytical Approach of Unconstrained Shape Designp. 151
5.4.3 Optimization Approach of Constrained Shape Designp. 156
5.4.4 Numerical Examples and Discussionp. 159
5.4.5 Sensitivity Analysis of the Optimal Frequencyp. 164
5.5 Minimum-Weight Design of Flexible Manipulators for a Specified Fundamental Frequencyp. 166
5.5.1 Basic Equationsp. 166
5.5.2 Problem Formulationp. 168
5.5.3 Solution by Iterationsp. 169
5.5.4 Numerical Examplesp. 172
5.6 Optimum Design of Flexible Manipulators: The Segmentized Solutionp. 172
5.6.1 Basic Equationsp. 174
5.6.2 Segmentized Solutionsp. 175
5.6.3 Optimization Formulations for Linear Mass and Bending Rigidity Distributionsp. 178
5.6.4 Practical Issues in Link Constructionp. 181
Referencesp. 182
Chapter 6 Mechatronic Design of Flexible Manipulatorsp. 185
6.1 Introductionp. 186
6.2 Overview of Mechatronics Designp. 187
6.2.1 Why Mechatronic Design?p. 187
6.2.2 What is Mechatronic Design?p. 188
6.2.3 How Does Mechatronic Design Work?p. 189
6.3 Mechatronic Design of Flexible Manipulators Based on LQR with IHR Programmingp. 190
6.3.1 Dynamics of Flexible Manipulator Systemsp. 190
6.3.2 LQR Formula: Inner Loop Optimizationsp. 193
6.3.3 IHR Algorithm: Outer Loop Optimizationp. 195
6.3.4 Integrated Optimization Processp. 196
6.3.5 Results and Discussionp. 196
6.4 Mechatronic Design of Flexible Manipulators-Based on H ∞ with IHR Algorithmp. 210
6.4.1 State-Space Formulas for H ∞ , Control Problemsp. 210
6.4.2 Generalized Plant of a Flexible Beam Systemp. 212
6.4.3 H ∞ Controller Designp. 215
6.4.4 Simulation Resultsp. 216
6.4.5 System Robustness Analysisp. 225
6.5 Closed-Loop Design of Flexible Robotic Linksp. 229
6.5.1 Dynamics of Single-Link Flexible Manipulator Systemsp. 230
6.5.2 Transfer Functions of the Integrated Systemsp. 231
6.5.3 Segmentized Solution for Transfer Functionsp. 232
6.5.4 Optimization Formulations for Mechatronic Designp. 234
6.6 Concurrent Designp. 237
6.6.1 General Conceptsp. 238
6.6.2 Existing Representation of Special Concurrent Designsp. 239
6.6.3 Problemsp. 240
6.7 Concurrent Design of a Single-Link Flexible Manipulator Based on PID Controllerp. 241
6.7.1 Dynamics of Single-Link Flexible Manipulator Systemsp. 241
6.7.2 Implementation of Concurrent Designp. 243
6.7.3 Simulation Resultsp. 245
Referencesp. 248
Chapter 7 Conclusions and Future Researchp. 251
Indexp. 253