Mechanism Design Enumeration of Kinematic Structures According to Function Mechanical Engineering Series Frank Kreith - Series Editor Published Titles Entropy Generation Minimization Adrian Bejan Finite Element Method Using MATLAB Young W. Kwon & Hyochoong Bang Fundamentals of Environmental Discharge Modeling Lorin R. Davis Intelligent Transportation Systems: New Principles and Architectures Sumit Ghosh & Tony Lee Mathematical & Physical Modeling of Materials Processing Operations Olusegun Johnson Ileghus, Manabu Iguchi & Walter E. Wahnsiedler Mechanics of Composite Materials Autar K. Kaw Mechanics of Fatigue Vladimir V. Bolotin Mechanism Design: Enumeration of Kinematic Structures According to Function Lung-Wen Tsai Nonlinear Analysis of Structures M. Sathyamoorthy Practical Inverse Analysis in Engineering David M. Trujillo & Henry R. Busby Thermodynamics for Engineers Kau-Fui Wong Viscoelastic Solids Roderic S. 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Mechanism design : enumeration of kinematic structures according to function / Lung-Wen Tsai p. cm.--(Mechanical engineering series) Includes bibliographical references and index. ISBN 0-8493-0901-8 1. Machinery, Kinematics of. 2. Machine design. I. Title. II. Advanced topics in mechanical engineering series. TJ175 .T78 2000 621.8′11--dc21 00-056415 This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. 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Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe. © 2001 by CRC Press LLC No claim to original U.S. Government works International Standard Book Number 0-8493-0901-8 Library of Congress Card Number 00-056415 Printed in the United States of America 1 2 3 4 5 6 7 8 9 0 Printed on acid-free paper Preface This textbook has evolved from class notes used for a course in systematic design of mechanisms that the author has taught for over a decade. Although it is written primarily for senior and first-year graduate level students in engineering, it is equally valuable for practicing engineers, particularly for mechanism and machine designers. Traditionally, mechanisms are created by the designer’s intuition, ingenuity, and experience. This ad hoc approach, however, cannot ensure the identification of all feasible design alternatives, nor does it necessarily lead to an optimum design. Two approaches have been developed to alleviate the problem. The first involves the development of atlases of mechanisms grouped according to function for use as a primary source of ideas. The second makes use of a symbolic representation of the kinematic structure and the combinatorial analysis as a tool for enumeration of mechanisms. This textbook introduces a systematic methodology for the creation and classifi- cation of mechanisms. The approach is partly analytical and partly algorithmic. It is based on the idea that, during the conceptual design phase, some of the functional requirements of a desired mechanism can be transformed into structural characteris- tics that can be employed for systematic enumeration of mechanisms. The kinematic structure of a mechanism contains the essential information about which link is con- nected to which other link by what type of joint. Using graph theory, combinatorial analysis, and computer algorithms, kinematic structures of the same nature, i.e., the same the number of degrees of freedom, type of motion (planar or spatial), and com- plexity can be enumerated in an essentially systematic and unbiased manner. Then each mechanism structure is sketched and evaluated with respect to the remaining functional requirements. This results in a class of feasible mechanisms that can be subject to dimensional synthesis, kinematic and dynamic analyses, design optimiza- tion, and design detailing. This textbook is organized as follows: Chapter 1 provides a brief review of the design process and a systematic method- ology for creation of mechanisms. Some terminologies related to the kinematics of mechanism are defined. Mechanisms are classified according to the nature of motion into planar, spherical, and spatial mechanisms. Chapter 2 is concerned with the basic concepts of graph theory, which is essential for structural analysis and structural synthesis of mechanisms. This material is extremely important since the design methodology employs graphs to represent the mechanism structure and mechanism structures are enumerated with the aid of graph theory. Chapter 3 introduces several methods of representation of the kinematic structure of mechanisms. The kinematic structure, which contains the essential information about which link is connected to which other links by what types of joint, will be used for enumeration of mechanisms. Chapter 4 examines the structural characteristics of mechanisms. The correspon- dence between graph and mechanism is established, from which several important mechanism structural characteristics are derived. The degrees of freedom of a mecha- nism, the loop-mobility criterion, the concept of structural isomorphism, and various methods of identification of structural isomorphism are described. Chapter 5 deals with the enumeration of graphs of kinematic chains. Systematic algorithms for the enumeration of contracted and conventional graphs are presented. Atlases of contracted graphs and conventional graphs are developed. Using these atlases, an enormous number of mechanisms can be developed. Chapter 6 describes a general procedure for the enumeration and classification of mechanisms. Planar bar linkages, geared mechanisms, cam mechanisms, spherical mechanisms, and spatial mechanisms are enumerated and classified according to the number of degrees of freedom, the number of independent loops, etc. Chapter 7 covers the enumeration and classification of epicyclic gear trains (EGTs). The structural characteristics of EGTs are identified. Variousmethods of enumeration including Buchsbaum and Freudenstein’s method, the genetic graph approach, and the parent bar linkage method are discussed. Furthermore, the theory of fundamental circuits is introduced for the speed-ratio analysis of EGTs. Chapters 8 and 9 offer several conceptual design examples to demonstrate the power of the methodology. Chapter 8 concentrates on the enumeration of automotive mechanisms, whereas Chapter 9 involves the enumeration of robotic mechanisms. Atlases of parallel manipulators and robotic wrist mechanisms are developed. Appendix A presents an algorithm for solving a system of m linear equations in n unknowns. A nested do-loops algorithm serves as the basis for systematic enumera- tion of mechanisms. Appendix B provides an atlas of contracted graphs having two to four independent loops. Appendix C is comprised of an atlas of graphs of kinematic chains having up to three independent loops and eight links. Appendix D offers an atlas of planar linkages with one, two, and three degrees of freedom. Appendix E contains an atlas of spatial one-dof, single-loop kinematic chains. Appendix F in- cludes an atlas of epicyclic gear trains classified according to the number of degrees of freedom, the number of independent loops, and the vertex degree listing. Appendix G furnishes the schematic diagrams and clutching sequences of some commonly used epicyclic transmission gear trains. Prerequisites for readers of this textbook include the basic concepts of combinato- rial analysis, graph theory, matrix theory, and the kinematics of mechanisms that are usually taught at the undergraduate level. Thomas Edison said, “genius is one percent inspiration and ninety-nine percent perspiration.” Inspiration can occur more readily when perspiration is properly directed and focused.