Page:The Kinematics of Machinery.djvu/293

 FORMULA FOE MECHANISMS.

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as a rule, will occupy this position, there being only one fixed link to be indicated. An illustration will make the method quite dis- tinct.

Let it be required to write contracted formulae for the mecha- nisms in the form of which the four-linked chain, Fig. 190, can be used. We first give to the four links the signs a, b, c, d in the way schematically indicated in Fig. 191 : these signs are arbitrarily

FIG. 190.

chosen in the first instance, but once chosen they must of course be adhered to. The lengths of the links are so proportioned that if d be fixed the link a (the crank) can revolve while c swings in circular arcs. So long as the chain is unfixed its contracted for- mula we have already found to be (") If now d be ^ xe( i as * ts form in Fig. 191 indicates the formula will become (C" 4 ') d in words " C parallel four on d" The particle on indicates that the

2 _--

FIG. 191.

chain is, as it were, placed on the link d, that this link becomes its base. If d were released and a fixed instead, the new mechanism would be (C") a ; in the same way the water-wheel of 61 would be (C'C zX F x ) c, the paddle-steamer (G'C zX V x ) b , and so on. It will be seen that this very short method of symbolization enables us easily to distinguish by distinct symbols the different mecha- nisms which can be made from one and the same chain. It pos- sesses always the limitation, however, that the letters a, I, c, etc., are