Mechanism - Dunkerley

MECHANISM

BY S. DUNKERLEY
PROFESSOR OF ENGINEERING AND DIRECTOR OF THE WHITWORTH LABORATORY IN THE UNIVERSITY OF MANCHESTER

LONGMANS, GREEN, AND CO.; NEW YORK; 1920
    

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PREFACE

The subject-matter of this book treats of pure mechanism, or the kinematics of machines. It is intended for use in the University and Technical Colleges, and is not meant to be a philosophical treatise on the subject; we have the works of Willis, Rankine, and Reuleaux for that It is the outcome of experience gained in lecturing on the subject at the Universities of Cambridge and Liverpool, and at the Royal Naval College, Greenwich. The logical treatment of the subject admittedly presents great difficulties, and it was only after anxious thought that the present arrangement was adopted as being, in the author's opinion, the most suitable for the average student.

It was thought desirable to insert an elementary descriptive chapter, which includes an account of various machine tools, and of mechanisms required for special purposes. As far as possible, those illustrations have been selected which, in the writer's opinion, are of most general interest. The remaining chapters include a full discussion of straight-line motions, indicator mechanisms, quick-return motions, couplings, velocity diagrams, approximate solutions to link motions and radial valve gears, acceleration diagrams, toothed wheels, non- circular wheels, cams, and machines for cutting teeth; and a number of numerical examples are added at the end of the book.

I am indebted to many engineering firms - of which acknowledgment is made in the proper place - for kindly supplying me with photographs and descriptions of machines; and also 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,


CHAPTER I. - INTRODUCTORY.

1. Object of a Machine.  The subject of mechanism consists of the study of machines. Following Rankine, 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, 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. In this, as 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 moves to and fro parallel to a plane, the crank pin always moves in a plane perpendicular to the axis, and any other point in the connecting-rod always describes the same path. This perfectly definite motion, which must of necessity be characteristic of all machines, is brought about by the connection of the various pieces with the frame and with each other. Thus the crosshead is guided to and fro in a straight line by contact with straight guides; in order that the crank shaft should continually rotate, it is enclosed within circular bearings which, like the guides, are rigidly attached to the frame; to transmit the motion from the crosshead to the crank pin, each is attached to the connecting-rod. At each end the connecting-rod embraces pins on the crank arm and crosshead respectively, so that as the crosshead moves to and fro, relative angular motion between the connecting-rod and the other two moving pieces is free to take place.

4. Surface and Line Contact, In ordinary machines, considerations of wear and of withstanding steam or water pressure make it desirable that the contact between any two pieces which have relative motion should be a surface contact. In the machine just discussed this condition is satisfied. The crosshead is in contact with the guides over one or more flat surfaces, the crank shaft is in contact with the frame, and the connecting-rod with the crank and crosshead pins, over a cylindrical surface. In the case of the crosshead and guides there is a pure sliding or translation; in the remaining cases there is turning or rotation. We might also have two pieces in which the relative motion is partly translational and partly rotational, but yet in which there is surface contact; as, for example, in the case of the true screw. But with these three exceptions, 1 there is no other type of motion possible in which the motion is governed by the contact of two pieces with each other, and in which, also, the contact is over a surface. It is very important that this point should be thoroughly understood, and to make it quite clear, consider the following illustration.

5. Kinematic Pair of Elements. Lower and Higher Pairs. The form of the slot in B, obtained in the manner just described, may be defined as the envelope of the successive positions of A, and may always be found by plotting A in different positions. In many cases, the motion of A is so simple that it is unnecessary to draw it in successive positions (as, for example, in Figs. 3 and 5), in order to determine the proper form of B ; but in other cases this operation has actually to be performed (for example, in toothed wheels), and in all cases it is done, either consciously or unconsciously.

A combination of the above type, in which one body is constrained to move in a definite manner by means of an envelope, is termed a kinematic pair of elements. If the two pieces or elements are in contact over a surface, the pair is said to be a lower pair ; if in contact over a line, straight or curved, a higher pair. Lower pairs are restricted to the three kinds already pointed out; namely, sliding, turning, or screw pairs. Higher pairs occur in a variety of forms, but one of the most common is toothed wheels.

6. Kinematic Chain. Mechanism. Machine. Instrument. Again, if a number of pairs be successively coupled up so that each element is common to two consecutive pairs, and if, when so coupled up, the motion transmitted is perfectly definite, the combination is termed a kinematic chain. If one of the links of that chain be fixed, the chain is termed a mechanism; and if some natural source of energy sets into motion an element of that mechanism, we obtain what has been called throughout a machine. If the modification of motion is independent of the magnitude and direction of the forces acting, the chain may be said to be self closed.

7. Relative Motions. Point Paths. A mechanism has been derived from a kinematic chain by fixing any one of the links of the latter. By fixing one link, it must not be inferred that that link is absolutely fixed that is, of course, impossible or even that it is fixed relative to the earth; the link may be attached to a moving frame, q in a locomotive or ship. To a person standing on the footplate of a locomotive, or in the engine-room of a ship, the motions (say) of the crosshead and crank pin are exactly the same as if the bedplate of the engine were bolted to the earth, and the observer were to stand on the earth. All points of the mechanism and the observer have impressed upon them exactly the same motion, namely, the motion of the locomotive or ship; and impressing the same motion on every point cannot possibly affect the relative motion or paths of the different points.


CONTENTS

- INTRODUCTORY
- SIMPLE MACHINES AND MACHINE TOOLS, ETC.
- MECHANISMS POSSESSING SOME PARTICULAR GEOMETRICAL PROPERTY
- MECHANISMS CONSISTING OF FOUR LOWER PAIRS
- VELOCITY. RATIO DIAGRAMS. APPROXIMATE SOLUTIONS TO LINK MOTIONS AND RADIAL VALVE GEARS
- ACCELERATION DIAGRAMS
- TOOTHED CIRCULAR WHEELS AND MACHINES FOR CUTTING TEETH
- NON-CIRCULAR WHEELS ROTATING ABOUT PARALLEL AXES. CAMS
- SPECIAL KINEMATIC CHAINS


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