MACHINES AND MECHANISMS APPLIED KINEMATIC ANALYSIS Fourth Edition David H. Myszka University of Dayton Prentice Hall Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo Vice President & Editorial Director: Project Manager: Susan Hannahs Vernon R. 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Library of Congress Cataloging-in-Publication Data Myszka, David H. Machines and mechanisms : applied kinematic analysis / David H. Myszka.—4th ed. p. cm. Includes bibliographical references and index. ISBN-13: 978-0-13-215780-3 ISBN-10: 0-13-215780-2 1. Machinery, Kinematics of. 2. Mechanical movements. I. Title. TJ175.M97 2012 621.8'11—dc22 2010032839 10987654321 ISBN 10: 0-13-215780-2 ISBN 13: 978-0-13-215780-3 PREFACE The objective of this book is to provide the techniques 6. Every chapter concludes with at least one case study. necessary to study the motion of machines. A focus is placed on Each case illustrates a mechanism that is used on the application of kinematic theories to real-world machinery. industrial equipment and challenges the student to It is intended to bridge the gap between a theoretical study of discuss the rationale behind the design and suggest kinematics and the application to practical mechanisms. improvements. Students completing a course of study using this book should 7. Both static and dynamic mechanism force analysis be able to determine the motion characteristics of a machine. methods are introduced. The topics presented in this book are critical in machine design 8. Every major concept is followed by an example process as such analyses should be performed on design con- problem to illustrate the application of the cepts to optimize the motion of a machine arrangement. concept. This fourth edition incorporates much of the feedback received from instructors and students who used the first three 9. Every Example Problem begins with an introduction editions. Some enhancements include a section introducing of a real machine that relies on the mechanism being special-purpose mechanisms; expanding the descriptions of analyzed. kinematic properties to more precisely define the property; 10. Numerous end-of-chapter problems are consistent clearly identifying vector quantities through standard boldface with the application approach of the text. Every notation; including timing charts; presenting analytical concept introduced in the chapter has at least one synthesis methods; clarifying the tables describing cam fol- associated problem. Most of these problems include lower motion; and adding a standard table used for selection of the machine that relies on the mechanism being chain pitch. The end-of-chapter problems have been reviewed. analyzed. In addition, many new problems have been included. 11. Where applicable, end-of-chapter problems are It is expected that students using this book will have a provided that utilize the analytical methods and are good background in technical drawing, college algebra, and best suited for programmable devices (calculators, trigonometry. Concepts from elementary calculus are spreadsheets, math software, etc.). mentioned, but a background in calculus is not required. Also, knowledge of vectors, mechanics, and computer Initially, I developed this textbook after teaching mech- application software, such as spreadsheets, will be useful. anisms for several semesters and noticing that students did However, these concepts are also introduced in the book. not always see the practical applications of the material. To The approach of applying theoretical developments to this end, I have grown quite fond of the case study problems practical problems is consistent with the philosophy of and begin each class with one. The students refer to this as engineering technology programs. This book is primarily the “mechanism of the day.” I find this to be an excellent oriented toward mechanical- and manufacturing-related opportunity to focus attention on operating machinery. engineering technology programs. It can be used in either Additionally, it promotes dialogue and creates a learning associate or baccalaureate degree programs. community in the classroom. Following are some distinctive features of this book: Finally, the purpose of any textbook is to guide the students through a learning experience in an effective 1. Pictures and sketches of machinery that contain manner. I sincerely hope that this book will fulfill this inten- mechanisms are incorporated throughout the text. tion. I welcome all suggestions and comments and can be 2. The focus is on the application of kinematic theories to reached at [email protected]. common and practical mechanisms. 3. Both graphical techniques and analytical methods are ACKNOWLEDGMENTS used in the analysis of mechanisms. I thank the reviewers of this text for their comments and 4. An examination copy of Working Model®, a commer- suggestions: Dave Brock, Kalamazoo Valley Community cially available dynamic software package (see Section 2.3 College; Laura Calswell, University of Cincinnati; Charles on page 32 for ordering information), is extensively used Drake, Ferris State University; Lubambala Kabengela, in this book. Tutorials and problems that utilize this University of North Carolina at Charlotte; Sung Kim, software are integrated into the book. Piedmont Technical College; Michael J. Rider, Ohio 5. Suggestions for implementing the graphical techniques Northern University; and Gerald Weisman, University of on computer-aided design (CAD) systems are included Vermont. and illustrated throughout the book. Dave Myszka iii CONTENTS 1 Introduction to Mechanisms and 2 Building Computer Models of Kinematics 1 Mechanisms Using Working Model® Objectives 1 Software 31 1.1 Introduction 1 Objectives 31 1.2 Machines and Mechanisms 1 2.1 Introduction 31 1.3 Kinematics 2 2.2 Computer Simulation of Mechanisms 31 1.4 Mechanism Terminology 2 2.3 Obtaining Working Model Software 32 1.5 Kinematic Diagrams 4 2.4 Using Working Model to Model a Four-Bar 1.6 Kinematic Inversion 8 Mechanism 32 1.7 Mobility 8 2.5 Using Working Model to Model a Slider- Crank Mechanism 37 1.7.1 Gruebler’s Equation 8 Problems 41 1.7.2 Actuators and Drivers 12 1.8 Commonly Used Links and Joints 14 Case Studies 42 1.8.1 Eccentric Crank 14 1.8.2 Pin-in-a-Slot Joint 14 3Vectors43 1.8.3 Screw Joint 15 Objectives 43 1.9 Special Cases of the Mobility Equation 16 3.1 Introduction 43 1.9.1 Coincident Joints 16 3.2 Scalars and Vectors 43 1.9.2 Exceptions to the Gruebler’s 3.3 Graphical Vector Analysis 43 Equation 18 3.4 Drafting Techniques Required in Graphical 1.9.3 Idle Degrees of Freedom 18 Vector Analysis 44 1.10 The Four-Bar Mechanism 19 3.5 CAD Knowledge Required in Graphical Vector 1.10.1 Grashof’s Criterion 19 Analysis 44 1.10.2 Double Crank 20 3.6 Trigonometry Required in Analytical Vector 1.10.3 Crank-Rocker 20 Analysis 44 1.10.4 Double Rocker 20 3.6.1 Right Triangle 44 1.10.5 Change Point Mechanism 20 3.6.2 Oblique Triangle 46 1.10.6 Triple Rocker 20 3.7 Vector Manipulation 48 1.11 Slider-Crank Mechanism 22 3.8 Graphical Vector Addition (+7) 48 1.12 Special Purpose Mechanisms 22 3.9 Analytical Vector Addition (+7): Triangle 1.12.1 Straight-Line Mechanisms 22 Method 50 1.12.2 Parallelogram Mechanisms 22 3.10 Components of a Vector 52 1.12.3 Quick-Return Mechanisms 23 3.11 Analytical Vector Addition (+7): Component 1.12.4 Scotch Yoke Mechanism 23 Method 53 1.13 Techniques of Mechanism Analysis 23 3.12 Vector Subtraction (-7) 55 1.13.1 Traditional Drafting Techniques 24 3.13 Graphical Vector Subtraction (-7) 55 1.13.2 CAD Systems 24 3.14 Analytical Vector Subtraction (-7): Triangle