to the Council of the Institution of Mechanical Engineers, and the Editors of the professional papers, for their kind permission to make use of articles and illustrations appearing in their publications. In dealing with velocity and acceleration diagrams, I have adopted the methods explained by Professor R. H. Smith in his paper published in the Proceedings of the Royal Society of Edinburgh for January, 1885. S. DUNKERLEY. R. N. COLLEGE, GREENWICH, PREFACE TO THE SECOND EDITION EXCEPT for slight verbal alterations, the first eight chapters remain as in the First Edition. A ninth chapter has been added, dealing with special subjects. The new matter includes a discussion of freedom and constraint of a point and rigid body, geometrical slides and clamps, Sarrut's parallel motion, the Amsler planimeter, a description of a milling machine, a treatment of worm-gearing, and a new four-piece mechanism by Mr. Bennett, Fellow of Emmanuel College, Cambridge. I am indebted to the Council of the Institution of Mechanical Engineers, and to the Cambridge University Press, for kindly giving permission to use the matter contained in the following articles. MANCHESTER, March 4, 1907. S. DUNKERLEY. 1 MECHANISM CHAPTER I. INTRODUCTORY. § 1. Object of a Machine. The subject of mechanism consists of the study of machines. Following Rankine,1 the use of every machine, of whatever type or size, is to modify motion and force. Some natural source of energy sets into motion a part of the machine usually termed the "driver"; the motion and force imparted to the driver are transmitted through a "train of mechanism" to a part of the machine called the "follower," at which the useful resistance is overcome; and in the transmission between the driver and follower the force and motion are modified to such an extent, both in magnitude and direction, as to be made available for the particular purpose for which the machine is designed. The train of mechanism may be complex or simple, according to the nature of the machine, and in direct-acting machines may be absent. § 2. Design of a Machine.-The first step in the design of a machine is to thoroughly grasp the precise nature of the problem that has to be solved, and the principles underlying it. Most frequently the follower has to move in some definite way, depending on the kind of work that has to be done; whilst the motion. of the driver depends on the kind of natural source of energy which is available. The follower has to be connected with the driver by a train of mechanism, so that when the driver receives its motion, the follower will have impressed upon it the precise motion required by the nature of the problem. A general outline, “Machinery and Mill Work." B or skeleton, of a suitable arrangement would first be sketched without any respect to the detailed proportions or forms of the individual parts; and from that general outline, by means of pure geometry alone, the displacement, velocity, and acceleration of each of the moving parts could generally be accurately determined. Secondly, the force acting on each part would be determined, and each part would be given its proper form and dimensions to withstand these forces; so that the "skeleton " could be clothed with a suitable combination of mechanical parts which would transmit and modify the motion and force according to the necessary requirements. Thirdly, having designed the machine, the dynamical effects of the moving parts could be accurately determined. The first part of this operation belongs to the subject known as the Kinematics of Machines; the second, to the Design of Machine Parts; and the third, to the Dynamics of Machines. The present book deals only with the kinematics of machines. § 3. Parts of a Machine.-Consider any machine, and see how it is made up; for purposes of illustration, take a very familiar form, namely, the direct-acting machine (Fig. 1). In this, as crank arm connecting rod crosshead bedplate FIG. 1. in the majority of cases, the various parts-neglecting the slight deformations due to elasticity or change of temperature—are rigid. It is made up of four pieces, namely, the frame or bedplate, the crosshead, the connecting-rod, and the crank shaft, to which is rigidly attached the crank arm and pin. The frame is usually considered as fixed, and the motions of all the other pieces are referred to it; but the frame itself might move, as, for example, in a locomotive or ship. But whether the frame be moving relatively to the earth or not, so long as we imagine ourselves to be carried with the frame, the character of the motions of the other pieces are always the same. The crosshead always |