O PRINCIPLES OF MECHANISM. DESIGNED FOR THE USE OF STUDENTS IN THE UNIVERSITIES, AND FOR ENGINEERING STUDENTS GENERALLY. BY ROBERT WILLIS, M.A. F.R.S. Jacksonian Professor of Natural and Experimental Philosophy in the University of Cambridge; the Royal Institute of British Architects; Corresponding Member of the Royal Academy of Sciences, Turin; Member of the Board of Visitors of Royal Observatory, Greenwich; Member of the Imperial Legion of Honor; Member of the Society of Arts; President of the British Association for the Advancement of Science at Cambridge, 1862; formerly Fellow of Caius College, Cambridge. SECOND EDITION. C. LONDON: LONGMANS, GREEN, AND CO. PREFACE. In the present work I have employed the term Mechanism as applying to combinations of machinery solely when considered as governing the relations of motion. Machinery as a modifier of force, has in the science of Mechanics occupied the attention of nearly every mathematician of eminence who has arisen in the world; but, by some strange chance, very few have attempted to give a scientific form to the attractive and valuable results of mechanism; for it cannot be said that the few and simple machines which form the examples in books of mechanics, are to be regarded as even forming a foundation for the principles upon which is to be based a science that will enable us either to reduce the movements and actions of a complex engine to system, or to give answers to the questions that naturally arise upon considering such engines; for example, are the means by which the results are obtained the best that might have been employed? or what are the various methods that might have been substituted for them? Yet there appears no reason why the construction of a machine for a given purpose should not, like any usual problem, be so reduced to the dominion of the mathematician, as to enable him to obtain, by direct and certain methods, all the forms and arrangements that are applicable to the desired purpose, from which he may select at pleasure. At present, questions of this kind can only be solved by that species of intuition which long familiarity with a subject usually confers upon experienced persons, but which they are totally unable to communicate to others. When the mind of a mechanician is occupied with the contrivance of a machine, he must wait until, in the midst of his meditations, some happy combination presents itself to his mind which may answer his purpose. Yet upon analysing the mental operations by which the nascent contrivance is gradually made to assume form and consistency, it will generally be observed, that the motions of the machine are the principal subject of contemplation, rather than the forces applied to it, or the work it has to do. For every machine will be found to consist of a train of pieces connected together in various ways, so that if one be made to move they all receive a motion, the relation of which to that of the first is governed by the nature of the connection. The work which the machine has to do will require that the pieces appropriated to this work shall move with respect to each other in some given manner, and the forces applied to the machine to set it in motion must also move the piece which receives them in some other manner. Thus the question of contriving a machine by which a given kind of power may be made to perform given work, is reduced to a problem of mere motion-to a question of connecting the pieces which receive the power and those which do the work; so that when the first move according to the law required by the economy of the power, the last shall necessarily receive the motion which will enable them to do the work. There are, of course, many essential considerations of force and arrangement which must be entered into before the machine can be completed, but they admit of being abstracted in the first instance; and it is only by so doing that we can hope to create a science of mechanism. Yet this view seems to have presented itself but lately, with due clearness, to the minds of writers on this subject; and it may be interesting to trace the history of its rise and progress. Apart from the writings on the science of Mechanics, the history of which is well known, a number of books have been produced from time to time, having for their subject Machinery. At first, however, the leading principle of classification in these is derived from the purpose for which each machine is designed, and accordingly these books are either confined to machines destined for one particular kind of work, as in the early treatises of Valturius (1472) and Agricola (1550) on warlike and mining machinery respectively; or else they are collections of machines classed and described with reference to the objects for which they are constructed; divided, for example, into machines for raising water, for grinding flour, sawing timber, and so on. The earliest of these collections are the treatises of Besson (1569), Ramelli (1580), Strada (1618), Zonca (1621), Branca (1629), Bockler (1662); and the list might be continued without interruption to the present day.* The voluminous Theatrum Machinarum' (1724) of Leupold, although it falls under the same description, yet in its first volume contains the first attempt to consider the parts of machinery separated from their work, and referred to the modifications of motion. And although these parts are made to follow the usual mechanical powers, and are mixed up with considerations of force, yet we find chapters on the crank, on cams, on machines for converting a circular motion into a rectilinear, or a back and forwards motion, and for converting a back and forwards motion into a continued circular motion, and so on. This must, in fact, be considered as the first attempt to produce a systematic treatise on Mechanism. But the first clear statement of the true principles upon which the science of Kinematics must be based, was made by Euler, *This list might be preceded by Vitruvius, Book x., the works of Hero and other Greek mechanists, &c. Vide Veterum Mathematicorum Opera. Par. 1693. |