Page images
PDF
EPUB

treatment, and its difficulties are almost entirely those of geometrical construction, which an engineer who is master of his drawing instruments can easily tackle, and not those of analytical mathematics, with the tools of which he is often, unfortunately, not so familiar. A system which allows every plane and spheric mechanism which has yet found application in machinery, from the simplest cases (Figs. 104 to 109) to the most complex ones (Figs. 128 to 131, 239, 244, 288, 299, etc.) to be treated in exactly the same method and with exactly similar constructions, both in its kinematic and its kinetic relations, possesses on this account advantages so great as quite to outweigh, in my opinion, the very small initial difficulty of thoroughly mastering the idea of virtual rotation which forms its foundation. The theorem of the

three virtual centres (p. 73) or axis (p. 490), without which the method of virtual rotations would be practically useless for our purposes, was first given, I believe, by Aronhold, although its previous publication was unknown to me until some years after I had given it in my lectures.

The problems dealt with in Chapters I. to VI. are in reality purely geometric, the velocities dealt with being only the relative velocities of different points in a constrained linkwork. The ideas of acceleration and of force are introduced in Chapter VII. Here I found myself compelled to choose between the adoption of some system of absolute units, and the retaining of the much-abused word "pound" as the name for a unit both of weight and of force. I hope that in § 30 I have succeeded in making clear the vital distinction between these two things, but after the best consideration which I have been able to give to the matter, I have come to the conclusion that the retaining of the word "pound" for both is, for the purposes of this book, the lesser of two evils. Without going further into reasons than I have done in the text, I will only say that the adoption of any other

plan would have made the book practically useless to almost all engineers so long as the thousand-and-one problems of their everyday work come to them in their present form.

In § 28 of Chapter IX. I have given special attention to the construction of diagrams of acceleration from those of velocity, and diagrams of velocity from those of acceleration, showing the constructions necessary in each case both for diagrams on time- and distance-bases. I have found by experience that the only real difficulty in connection with the practical use of these diagrams lies in the determination of their scales. I have therefore gone into this matter in a more detailed fashion than might, at first sight, seem to have been necessary, and have recurred to it frequently in later Chapters.

Problems connected with the static equilibrium of mechanisms are dealt with in Chapter VIII., and with their kinetic equilibrium in Chapter IX. In order to make these latter more complex problems more intelligible to engineers I have chosen purely technical examples, and worked them out in detail, for the most part graphically. The problems treated include those of trains, "Bull" and Cornish engines, and ordinary steam-engines, while the action of flywheels. and of governors is also considered in some detail, and the connecting-rod is used as an example of the kinetic theory of a single constrained link having general plane motion.

In Chapter X. a number of mechanisms intrinsically interesting, but not finding place as examples in the earlier part of the book, are considered. I have here also endeavoured to arrange a general classification of plane mechanisms on a basis which appears to me, at least so far as it goes, to be a scientific one. It has not been consistent with my purpose, or indeed with the size of this book, even to touch upon the enormous number of recently described plane mechanisms (such as many of those of Kempe and

of Burmester), whose interest, although great, is at present entirely kinematic, and the use of which in any actual machine appears extremely unlikely.

The enormous majority of mechanisms with which the engineer has to do have (fortunately for him) only plane. motions. To treat non-plane mechanisms with the same detail as plane mechanisms, would have involved a great enlargement of a volume already too bulky. I have in Chapter XI., therefore, not attempted to do much more. than to show how the principles already discussed apply to non-plane motion. I have dealt in a detailed manner only with two examples: the universal joint, and Mr. Tower's "spherical" engine. In § 65 I have worked out the action of the latter, kinematically and kinetically, in as complete a fashion as formerly the simpler case of the ordinary engine. The results are shown graphically in Figs. 306 and 307.

In Chapter XII., lastly, I have given some general notion of the influence of friction on the working of machines. In doing this I have put entirely on one side the time-honoured "laws" of dry friction, the relation of which to the friction of machines is purely illusory, and have endeavoured to substitute for them some actual relations between pressure; temperature, and velocity, so far as they are yet experimentally determined, which apply to smooth and more or less completely lubricated surfaces. I would like, however, to emphasise here what I have pointed out in the text (p. 577), that the ordinary calculated determinations of frictional efficiencies have seldom any great absolute numerical value. Not only are the different friction factors very imperfectly known, but the pressures due to "fit," tightening of bolts, etc., which in some cases are more important than any other friction-producing forces, are scarcely known at all.

I have endeavoured to mention throughout the book the names of the various authors and others to whom I have

been, in different matters, indebted. I cannot, however, omit to make special reference to the work of Professor Reuleaux. All engineers are indebted to him for the system of analysis of mechanisms first set forth in his Kinematics of Machinery, a system so simple and so obviously true that its essential points have found universal acceptance. The principles of Reuleaux's system I have unhesitatingly made use of, and my first sixty pages are to a great extent a summary of his results. After that our objects have differed widely, and I have followed entirely different lines from those of his work.

I should like to add that although, partly through pressure of work and partly through ill-health, this book appears only now, yet a great part of it has been in type, and a still greater part written and given in lectures, for a number of years. This has rendered it almost impossible for me to make any use of the excellent work of Prof. Cotterill, or of the recently published graphic methods of Prof. R. H. Smith, or the still more recently published (in any complete form) kinematic work of Professor Burmester, as I should otherwise have liked to do.

For a few of my illustrations I am indebted to Reuleaux's Kinematics, but nine-tenths of them I have drawn specially for their present purpose. In any cases where engineering details are shown I have endeavoured to draw them with reasonably accurate proportions, and in all cases where diagrams of force, velocity, etc., occur, they will be found. drawn to scale, and the scales are marked on the figures.

UNIVERSITY COLLEGE, LONDON,

Nov. 27th, 1886.

ALEX. B. W. KENNEDY.

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small]
« PreviousContinue »