Geometric Design of Linkages (Google eBook)

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Springer Science & Business Media, Nov 11, 2010 - Technology & Engineering - 476 pages
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This book is an introduction to the mathematical theory of design for articulated mechanical systems known as linkages. The focus is on sizing mechanical constraints that guide the movement of a work piece, or end-effector, of the system. The function of the device is prescribed as a set of positions to be reachable by the end-effector; and the mechanical constraints are formed by joints that limit relative movement. The goal is to find all the devices that can achieve a specific task. Formulated in this way the design problem is purely geometric in character. Robot manipulators, walking machines, and mechanical hands are examples of articulated mechanical systems that rely on simple mechanical constraints to provide a complex workspace for the end- effector. The principles presented in this book form the foundation for a design theory for these devices. The emphasis, however, is on articulated systems with fewer degrees of freedom than that of the typical robotic system, and therefore, less complexity. This book will be useful to mathematics, engineering and computer science departments teaching courses on mathematical modeling of robotics and other articulated mechanical systems.This new edition includes research results of the past decade on the synthesis of multi loop planar and spherical linkages, and the use of homotopy methods and Clifford algebras in the synthesis of spatial serial chains. One new chapter on the synthesis of spatial serial chains introduces numerical homotopy and the linear product decomposition of polynomial systems.  The second new chapter introduces the Clifford algebra formulation of the kinematics equations of serial chain robots. Examples are use throughout to demonstrate the theory.
  

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Contents

Chapter 1 Introduction
1
Chapter 2 Analysis of Planar Linkages
15
Chapter 3 Graphical Synthesis in the Plane
55
Chapter 4 Planar Kinematics
75
Chapter 5 Algebraic Synthesis of Planar Chains
93
Chapter 6 Multiloop Planar Linkages
125
Chapter 7 Analysis of Spherical Linkages
155
Chapter 8 Spherical Kinematics
179
Chapter 13 Algebraic Synthesis of Spatial Chains
307
Chapter 14 Synthesis of Spatial Chains with Reachable Surfaces
335
Chapter 15 Clifford Algebra Synthesis of Serial Chains
357
Chapter 16 Platform Manipulators
393
Appendix A Solving Constraint Equations
411
Appendix B Graphical Constructions
415
Appendix C Spherical Trigonometry
419
Appendix D Operations with Dual Numbers
425

Chapter 9 Algebraic Synthesis of Spherical Chains
203
Chapter 10 Multiloop Spherical Linkages
231
Chapter 11 Analysis of Spatial Chains
253
Chapter 12 Spatial Kinematics
281
Appendix E Kinematics Equations
427
References
433
Index
441
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About the author (2010)

J.M. McCarthy is a professor in the Department of Mechanical and Aerospace Engineering at the School of Engineering, University of California, Irvine.

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