Page:The Kinematics of Machinery.djvu/550

 528 KINEMA TICS OF MA CHINEE Y. elements and of several series of mechanisms and complete machines. These propositions have more and more limited the road to the solution of the problem, so that we already know something of the general nature of the results to which we may expect kinematic synthesis to lead us. The methods, however, in which the problem may be treated differ very greatly, and we must in the first place endeavour to determine which form of application of the synthesis promises the best results in the treatment of its problems. There are, I think, two principal methods by which the desired end can be attained ; 4hese maybe called direct and indirect synthesis respectively. Each of these again divides itself into two branches, according as its treatment is general or special. We shall attempt to determine, a priori, the usefulness of these different forms of synthesis. . Direct Kinematic Synthesis. The general direct synthesis should give us immediately the mechanisms which are required in each machine to effect a given change of place or form in its work- piece, or to utilise in it a given natural force. It is evident at once, however, that we cannot hope to arrive at useful results by this method. For our analytical investigations have shown us that one and the same motion can be obtained in different and often very many different ways. The synthesis must therefore'either give us a great number of different simultaneous solutions to the one problem, or must be able to furnish us with that one out of them all which is the best. The latter is, however, impossible, for the practical merits or defects of each single result lie to a considerable extent beyond the sphere of kinematics ( 3). Two steam-engines, for instance, in different circumstances may be equally good, equally useful, equally " practical," although they may be kinematically very different. We cannot expect, therefore, to build up any system of general direct analysis which can be useful to us. The function of special direct synthesis would be to furnish us