Geometric Design of Linkages

J. Michael McCarthy, Gim Song Soh (auth.)0387989838, 9780387989839, 9780387227351

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 workpiece, 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.

This new edition includes research results of the past decade on the synthesis of multiloop 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 the linear product decomposition of polynomial systems and polynomial continuation solutions. The second new chapter introduces the Clifford algebra formulation of the kinematics equations of serial chain robots. Examples are used throughout to demonstrate the theory.

Review of First Edition: “…I found the author had provided an excellent text that enabled me to come to terms with the subject. Readers with an interest in the area will find the volume rewarding.” -The Mathematical Gazette (2001)

Table of contents :
Front Matter….Pages i-xxviii
Introduction….Pages 1-14
Analysis of Planar Linkages….Pages 15-53
Graphical Synthesis in the Plane….Pages 55-74
Planar Kinematics….Pages 75-92
Algebraic Synthesis of Planar Chains….Pages 93-123
Multiloop Planar Linkages….Pages 125-154
Analysis of Spherical Linkages….Pages 155-178
Spherical Kinematics….Pages 179-201
Algebraic Synthesis of Spherical Chains….Pages 203-229
Multiloop Spherical Linkages….Pages 231-251
Analysis of Spatial Chains….Pages 253-279
Spatial Kinematics….Pages 281-306
Algebraic Synthesis of Spatial Chains….Pages 307-333
Synthesis of Spatial Chains with Reachable Surfaces….Pages 335-356
Clifford Algebra Synthesis of Serial Chains….Pages 357-392
Platform Manipulators….Pages 393-410
Back Matter….Pages 411-448