This book is the outgrowth of a somewhat smaller treatise which was prepared and printed by the writer in 1894 for the rise of the classes in mechanical and electrical engineering at Sibley College, Cornell University.
After having used the original for several years, it was decided to issue the work in revised form, making such corrections and changes as experience suggested.
The present volume was prepared especially to bring together, and to present to the students in a condensed text-book, those principles and methods which are deemed most important in a general course on Kinematics. This is the only excuse offered for another - book on a subject about which so much has been written. No pretension is made to originality except in the arrangement and manner of presenting a few subjects. Neither is the present work offered as in any sense a complete treatise on the Kinematics of Machinery. The treatment of many topics has been much abridged; particularly the portion relating to toothed gearing, a subject which is exhaustively treated in numerous available works. On the other hand, the discussions of the applications of such important conceptions as instantaneous centres, velocity diagrams, etc., are rather fuller than are found in many of the shorter works on Mechanism.
The treatment of these subjects follows closely that given by Professor Kennedy in his admirable work on the Mechanics of Machinery.
It is believed that the presentation of principles and methods, with illustrations of their applications, is the proper line to adopt in a text-book intended for a short general course on such a subject as Kinematics. The detailed description of usual forms, and the discussion of the innumerable considerations with which the expert in any line must be familiar are to be sought in special treatises.
Messrs. A. T. Bruegel, D. S. Kimball, and W. N. Barnard, all of whom have given instruction in the course to which it applies, have rendered valuable assistance in the preparation of the present book. Mr. Bruegel contributed most of the problems, which were developed during his six years as instructor in Kinematics at Cornell University. Professor Kimball kindly wrote the articles on "Acceleration Diagrams" and "Epicyclic Trains," and he and Mr. Barnard have cooperated in other ways in the revision.
Many earlier works have been consulted and drawn on in the preparation of the present book. The following, especially, should be mentioned: Principles of Mechanism, by Professor Willis; Machinery and Mill work, by Professor Rankine; Kinematics of Machinery, by Professor Reuleaux; Mechanics of Machinery, by Professor Kennedy; Kinematics, by Professor MacCord; Machine Design, by Professor Unwin; Elementary Mechanism, by Professors Stahl and Woods; Teeth of Gears, by Mr. George B. Grant; A Practical Treatise on Gearing (Beale), published by the Brown and Sharpe Manufacturing Company.
The writer desires to acknowledge his obligations to all who have in anyway aided in the preparation of this little book.
CHAPTER I - Fundamental Conceptions of Motion. The Nature of a Machine
CHAPTER II - General Methods of Transmitting Motion in Machines
CHAPTER III - Pure Rolling in Direct-contact Mechanisms. Frictional Gearing
CHAPTER IV - Outlines of Gear-teeth. Systems of Tooth-gearing
CHAPTER V - Cams and Other Direct-contact Mechanisms
CHAPTER VI - Linkwork
CHAPTER VII - Wrapping-connectors. Belts, Ropes, and Chains
CHAPTER VIII - Trains of Mechanism
Problems and Exercises
FUNDAMENTAL CONCEPTIONS OF MOTION. THE NATURE OF A MACHINE.
1. Motion is a change of position; and it is measured by the space traversed. Time is not involved in this conception. A train, in running between two stations fifty miles apart, has the same motion, whether the time occupied be one, two, or three hours. The motion of a crank-pin in making a revolution is independent of the time required.
2. Linear Velocity, or simply velocity, is the rate of motion of a point along its path in space. It is a function of both space and time, and is measured in compound units of these fundamental quantities; as feet per second, feet per minute, miles per hour, etc.
If, in the illustration of the preceding article, the time of the run between the stations is one hour, the train has an average, or mean, linear velocity of fifty miles per hour; if the time be two and a half hours, the mean velocity, or speed, as it is often called, is twenty miles per hour, etc.
3. Acceleration, or linear acceleration, is the rate of change of velocity. Acceleration is expressed in the same system of space and time-units as the velocity itself (as feet and seconds, feet and minutes, miles and hours, etc.); but acceleration involves one space- factor and two time-factors.
If a velocity is uniformly increased from 10 feet per second to 18 feet per second, the change of velocity is 8 feet per second. If this change takes place in 2 seconds, the rate of change, or the acceleration, is 4 feet per second per second, or 4 foot-seconds per second, or 4 feet per square second. If the increase of velocity is not uniform, the mean acceleration is 4 feet per square second in the above illustration, although the actual increase of velocity in any one second is not necessarily 4 feet per second.
4. Uniform and Variable Velocity. - If the motion of a body is uniform (that is, if all equal increments of space are traversed in equal increments of time) the velocity is uniform, and is equal to the space traversed in any time divided by that time. If the velocity is uniform, the acceleration is zero. If a body moves 120 feet in 10 seconds, with a uniform velocity, the velocity is 12 feet per second, equivalent to 720 feet per minute.
If the velocity is not uniform, the space divided by the time gives only the mean or average velocity, and the velocity may vary between the widest limits during the motion. If the law of the motion is known, the velocity at any instant may be determined from the space and time; otherwise, only the mean velocity can be determined from these data.
The velocity of a body may vary uniformly, the velocity increasing or decreasing by equal increments with each equal increment of time, in which case the acceleration is constant; or it may vary according to any other law. For our present purposes it is only necessary to discriminate between uniform, or constant, and varying velocity.
Although the velocity may be constantly changing, it is customary to speak of a body as moving at a certain velocity, as 25 feet per second, 30 miles per hour, etc. ; and such expressions are perfectly correct, even though the velocity does not remain constant for a single instant. For example: a train of cars in getting up speed passes through every velocity from zero to the maximum velocity attained; at a certain stage the velocity may be, say, ten miles per hour, and in coming to rest the velocity again passes through this same value. Perhaps the train does not maintain this particular velocity for a single foot; yet, for the instant, it is said to have this velocity; meaning that if it continued to move with the velocity that it has at this instant it would move 10 miles in one hour.
5. Relative and Absolute Motion. - All known motions are relative, for change of position can only be noted with reference to objects at rest (or assumed to be at rest), or by reference to objects the motion of which is known (or assumed to be known). We know of no body absolutely at rest, nor do we even know the absolute motion of anybody in the universe. In treating of the motion of a body, only its change of position with regard to some other body, or its motion relative to that other body, can be considered.
In ordinary problems of terrestrial mechanics the earth is taken as the standard from which to reckon, and a body which does not change its position relative to the earth is said to be at rest, stationary, or fixed ; of course recognizing that it partakes of the motion which the earth has about its axis, around the sun, and in common with the sun through space.
In problems of machinery the motions of the parts are usually most conveniently taken with reference to the frame of the machine as a standard. In "stationary" or "fixed" machines this is equivalent to referring these motions to the earth, for the frame has no appreciable motion relative to the earth; but in such cases as locomotives and marine engines, for example, the parts have very different motions relative to the frame and to the earth. In these latter cases we are usually concerned with the motion of the parts relative to the frame, or with the motion of the machine as a whole (including everything connected with it) relative to the earth.
The function of the machine, in these cases, is to impart motion, relative to the earth, to the attached train or ship, and incidentally to itself; but this motion of the entire system, and the motion of the parts, as members of a machine, may generally be treated as quite distinct, though related, problems. A marine engine can be studied as an engine just as a mill engine can be treated, without considering the application of the energy beyond the engine itself. As we know nothing of the absolute motion of a body, and can only know its motion relative to other objects, it can have as many relative motions as there are objects with which to compare its changes of position.