Page:The Kinematics of Machinery.djvu/322

 3^0 KINEMATICS OF MACHINERY.

and the crank a becomes a coupler and makes complex oscillations. We shall call the mechanism, on account of the swinging of the link b, a swinging slider-crank. This mechanism is little known, but does here and there find applications. Among others there is the apparatus sketched in Fig. 222, which is used in disc-polishing machines in order to give the polishing wheel a to-and-fro motion axially along with its rotation. The train is set in motion by the link a (by means of the worm), and its special formula is there- fore (Og'P- 1 -)*-. I have elsewhere described* another application of this mechanism in the same form, and I shall come further on to another very notable one.

Our analysis has shown that four mechanisms can be obtained from the chain (C^ 1 J ), of which the first is extremely familiar, the last very little known; the connection between them, however,

FIG. 222.

has remained until now completely unseen. At the same time we see that we have exhausted the chain which is before us; we know that no more mechanisms than these four can be formed out of it. If we now put these together and consider them once more, we shall be able to recognise, by the help of their formulae, still closer relationships between them. With this object let us write the formulae at length, one above the other, so that they may be easily compared. We then have :

a b c d

= c^riuTo^

= C+ ... || ... (0) ... ||... (fl) ... _]_ ... (P)..._L... C-

= 0+ ... || ... (O) ... || ... (C) ... _L ... (P)..._L,..fc

If we recollect that these formulse are expressions which return upon themselves, that they can also be read, or written, from


 * Civil-ingtnieur, vol. iv. 1858, p. 4.