The Kinematics of Machinery/Preface
PREFACE.
The greater part of the Theoretische Kinematik of Prof. Reuleaux, which I have now the pleasure of presenting to English and American readers, was originally published in chapters in the Berliner Verhandlungen, under the title of Kinematische Mittheilungen. These papers, revised and enlarged, and with the addition of a chapter on Kinematic Synthesis, were published collectively in 1874−5 in the work of which the present is a translation. They have attracted considerable attention in Germany, and the principles laid down in them have already made their way into Polytechnic School instruction, not only in that country but also in Russia and Italy.
The book addresses itself to somewhat different classes of readers, or rather to readers who have had very different training, on the Continent and here. Its readers there are to a great extent the past or present students of the Polytechnic Schools, or at least those who are acquainted with polytechnic teaching. They are familiar with a regularly systematised system of machine instruction and its somewhat extended literature. Here, on the other hand, neither systematised instruction nor extended literature exists. The book addresses itself greatly to practical engineers and mechanicians, men who have often enough worked out their knowledge of the subject for themselves to a far greater extent than they have acquired it from books or lectures. To these readers some sections of the book may appear unnecessary, as referring to opinions or combating conclusions of which they have scarcely heard, and the erroneousness of which they are perfectly ready to admit. No doubt had the work originally been written for its English readers these passages might have been omitted or changed; as it is, I must merely remind those readers of the fact I have just mentioned. Here and there I have made small alterations in the text on this account, otherwise the sections referred to remain as in the original. The conclusions arrived at in them are not the less interesting that they might have been reached here, sometimes, in a more direct manner.
It may be well for me to mention here some of the leading characteristics of Prof. Reuleaux's treatment of his subject, and to point out in what respects it differs from that of his predecessors. In the oldest books upon machinery each machine was taken up as a whole, to be described and treated by itself from beginning to end. Gradually it became recognised that similar parts occurred again and again in different machines, and these parts received the name of mechanisms. They sometimes appear in a more or less abstract form in text-books of Elementary Mechanics, and have received more complete treatment in separate works. With the growth of clear ideas in physical science it became possible to separate the ideas of force, time and motion, and to consider the latter merely for its own sake without reference to the other two. Prof. Willis adopted this treatment unreservedly in his Principles of Mechanism—a work too well known to need any characterisation here—calling the study thus marked out the “Science of Pure Mechanism.” Here, however, the matter stopped, later writers have been content to follow upon Willis's lines, not carrying the analytic process further, and contenting themselves with the examination of mechanisms as a whole in the forms in which they are presented to us by tradition or invention, without attempting to analyse them, or to investigate their mode of formation.
It is unquestionably true that by the aid of mathematics this treatment of mechanisms has given us many most valuable results, but it is equally true that the method itself is defective, and was only used for want of a better. This better method Prof. Reuleaux has attempted, and I think with great success, to indicate. Starting with the idea of motion as change of position only—and limiting himself to cases where such changes are absolutely determinate at every instant,—as always in the machine—he points out that they are conditioned simply by the geometric form of the moving bodies. Two bodies, such for instance as a screw and nut, having such forms that at any instant there is only one possible motion for each relatively to the other, form the simplest combination available for machinal purposes—such bodies he calls a pair of elements. Two or more elements from as many different pairs can be combined into a link, and such links united into kinematic chains, and it is by fixing, that is, preventing the motion of, some one link of such a chain that a mechanism is obtained. Stated thus in a few words the analysis is simple and obvious enough; like many other simple things, however, it leads to most important consequences. As one illustration merely of this, I may point to the collection of "rotary" engines and pumps examined in Chap. IX. Here will be found, among others, over thirty forms of "rotary" engines of which the kinematic chain used in the driving mechanism is absolutely identical with that of the common direct-acting engine! Their constructive forms differ most widely, and have of course too often misled their inventors, but the application of what Prof. Reuleaux calls "kinematic analysis" shows at once both their identity as kinematic chains and their relation as mechanisms. In Fig. 3, Pl. XX., for instance, is shown a rotary engine which has been patented every few years since 1805 in one or another form, and in which no doubt some of my readers will recognise an old friend "schemed" in the days of their apprenticeship. Its driving mechanism is absolutely the same as that of the direct-acting engine, but with the crank fixed and the frame allowed to move round it.
In order to utilise the kinematic analysis Prof. Reuleaux has devised and elaborated the notation which is explained in Chap. VII. and used in the later part of the book. That this notation is both exceedingly simple and of practical use will be admitted by all readers of Chap. IX., but its full advantages will only be realised by those who use it for themselves. The way in which it aids the resolution of apparently complex mechanisms into quite familiar forms is often most remarkable. Use will no doubt suggest modifications and improvements in its details, but Prof. Reuleaux is very anxious that its essential features, and especially the symbols for the elements (which have been so chosen as to be as suitable as possible for the principal European languages) should not be altered.
I may mention here only one other feature in Reuleaux's work, namely, his treatment of fluids when they occur in mechanisms or machines (Chap. IV. &c.). It has long been customary, of course, to treat cords, chains, belts &c., as organs which could legitimately form part of machines, but fluids have been universally (so far as I know) excluded from consideration in this way. Reuleaux points out that fluids—"pressure-organs"—are simply contrapositives of the "tension-organs" just mentioned, and that if one be included in the study of "pure mechanism" there can be no reason for excluding the other. He gives also many instances of the way in which engineers use the one or the other as the column of fluid or the cord best suits their purpose. In examining mechanisms we consider the motions of each body as a whole, ignoring altogether its molecular condition, or more strictly assuming that it is so arranged that its molecular stability is not disturbed during the motion. This pre-supposition is made tacitly in the case of "rigid" bodies, where molecular stability is independent of the application of external force. It is made also in the case of ropes, belts, &c., for when these occur in machines it is always assumed that they are kept in tension by some force external to themselves, in any other case their motions would be quite indeterminate. With fluids it is not necessary to make any other assumption than this, but the external force must be a pressure instead of a pull, and must be supplied in directions other than that in which motion takes place. § 126 shows some of the interesting results to which this treatment of fluid organs may lead.
My own work in connection with Prof. Reuleaux's book has been chiefly, of course, that of translation; but a comparison of this edition with the German one will show several not unimportant improvements. Some of these have been suggested by the author; in all cases where they involved more than the changing of a few words they have been submitted to him. I may take this opportunity of acknowledging the assistance I have received from him and the interest he has taken in the progress of this English edition of his work, (which has been already published in Italian, and is now being translated into French). I have also great pleasure in acknowledging the help I have received on many occasions from my friend and colleague Prof. Henrici, F.R.S.
The references given in footnotes are mostly those of the original edition; in Chapters IX and X I have added English references where I was able to do so. The longer footnotes I am responsible for, except in cases where I have placed "R" after them. Of the notes at the end of the book I have added those which are placed in square brackets. A few of the notes in the original, which referred to matters with which English readers would probably be unacquainted, or to passages which have been altered in the text, have been shortened or omitted.
The names which Prof. Reuleaux gives to the various mechanisms have in most cases been invented by himself, and in several other instances he has had to coin words to express ideas to which individual distinctness has now first been given. Such names and words I have not tried to translate, but only to replace by equally good English ones, with what success I must leave my readers to judge. I shall be happy to receive suggestions for improvements in this matter. The names have, however, been very carefully considered, and so arranged as to fit in with each other—I venture to hope, therefore, that those who use them for instruction will not alter them without good reason. For the word "centroid," for which I anticipate great usefulness, I have to thank Prof. Clifford.
Prof. Reuleaux uses the word Kinematics in a limited sense, for the Science of constrained motion—that is, motion as it occurs in machines—without reference to the ideas of either time or force (p. 40, &c.), and has therefore called his book Theoretische Kinematik. Grundzüge einer Theorie des Maschinenwesens. Whether this use of the word be advisable or not, it was obviously impossible to adopt it in this country, where it has obtained firm hold in a much more extended, but quite legitimate, sense. While retaining the second part of Prof. Reuleaux's title I have therefore been compelled to change the first part to Kinematics of Machinery. It is very unfortunate that we have as yet no word for the study of motion as change of position merely. Phoronomy, which is used in Germany very nearly in this sense, is very unpreposessing;—I would suggest Metastatics for the purpose, unless a better word can be found. It has at least the merit of expressing the idea clearly, and with both philologic and scientific accuracy.
Alex. B. W. Kennedy.
I may add that Prof. Reuleaux has sent over some three hundred models, a portion of his Kinematic collection at the Berlin Gewerbe-Akademie, to the Exhibition of Scientific Apparatus now (May 1876) being held at South Kensington, where they will remain throughout the summer. Among these models are a great number of the mechanisms described in the following pages, along with many others. They will well repay a visit, or more than one, and as close examination as circumstances permit. Herr Kirchner, of the Berlin Akademie, has charge of the models, and will be as well pleased as he is well able to give explanations about them.