Elements of Mechanism PETER SCHWAMB, S. B. Professor of Machine Design Retired, Massachusetts Institute of Technology ALLYNE L. MERRILL, S. B. Professor of Mechanism, Massachusetts Institute of Technology WALTER H. JAMES, S. B. Associate Professor in the Department of Mechanical Engineering, Massachusetts Institute of Technology THIRD EDITION, REWRITTEN, ENLARGED, AND RESET TOTAL ISSUE FORTY-EIGHT THOUSAND NEW YORK JOHN WILEY SONS, INC. LONDON CHAPMAN HALL, LIMITED COPYKIQHT, 1904, 1905, BY PETER SCHWAMB AND ALLYNE L. MERRILL COPYRIGHT, 1921, BY PETER SCHWAMB ALLYNE L. MERRILL WALTER H. JAMES Printed in U. S. A. PREFACE TO THE THIRD EDITION This revised edition embodies many changes suggested by instructors who have used the second edition during the last sixteen years. The authors-acknowledge their indebtedness to all of these gentlemen, and especially to Prof. George W. Swett, who has read a large part of the manuscript and given much valuable criticism. Professor Walter H. James, in charge of the instruction in Mechanical Engineering Drawing and Machine Drawing at the Massachusetts Institute of Technology, and also an Instructor in Mechanism for many years, has been in charge of the revision, and joins in the authorship of the book. PETER SCHWAMB. ALLYNE L. MERRILL. WALTER H. JAMES. CAMBRIDGE, MASS., December, 1920 PREFACE TO SECOND EDITION The main subject-matter of this work was written during 1885 by Peter Schwamb and has been used since then, in the form of printed notes, at the Massachusetts Institute of Technology, as a basis for instruction in mechanism, being followed by a study of the mechanism of machine tools and of cotton machinery. The notes were written because asuitable text-book could not be found which would enable the required instruction to be given in the time available. They have accomplished the desired result, and numerous inquiries have been received for copies from various institutions and individuals desiring to use them as text-books. This outside demand, coupled with a desire to revise the notes, making such changes and additions as experience has proved advisable, is the reason for publishing at this time. Very little claim is made as to originality of the subject-matter which has been so fully covered by previous writers. Such available matter has been used as appeared best to accomplish the object desired. Claim for consideration rests largely on the manner of presenting the subject, which we have endeavored to make systematic, clear, and practical. Among the works consulted and to which we are indebted for sug gestions and illustrations are the following Kinematics of Machinery, and Der Konstrukteur, by F. Reuleaux, the former for the discussion of linkages, and the latter for various illustrations of mechanisms Principles of Mechanism, by S. W. Robinson, for the discus sion of non-circular wheels Kinematics, by C. W. MacCord, for the discussion of annular wheels and screw-gearing Machinery and Millwork, by Rankine Elements of Mechanism, by T. M. Goodeve and Elements of Machine Design, by W. C. Unwin. PETER SCHWAMB. ALLYNE L. MERRILL. October 20, 1904 CONTENTS PAQB CHAPTER I INTRODUCTION 1 CHAPTER II REVOLVING AND OSCILLATING BODIES 12 CHAPTER III BELT, ROPES AND CHAINS 21 CHAPTER IV TRANSMISSION OF MOTION BY BODIES IN PURE ROLLING CONTACT 63 CHAPTER V GEARS AND GKAR TEETH 86 CHAPTER VI WHEELS IN TRAINS 153 CHAPTER VIIEPICYCLIC GEAR TRAINS 166 CHAPTER VI11 INCLINED PLANE, WEDGE, SCREW, WORM AND WHEEL 180 CHAPTER IX CAMS 197 CHAPTER X FOUR-BAR LINKAGE. RELATIVE VELOCITIES OF RIGIDLY CONNECTED POINTS 221 CHAPTER XI LlNKWORK 244 CHAPTER XII STRAIGHT-LINE MECHANISMS PARALLEL MOTIONS 291 CHAPTER XIII MISCELLANEOUS MECHANISMS AGGREGATE COMBINATIONS PULLEY BLOCKS INTERMITTENT MOTION 306 PROBLEMS 336 INDEX 367 vii Elements of Mechanism CHAPTER I INTRODUCTION 1...