FORMULA FOR REDUCED CHAINS.
335
indicate it in the contracted formula for the new chain by writing the latter :
The chain so reduced has three links; it can therefore "be placed in three ways only, so that only three mechanisms can be formed from it. These are: (C'^P^-Y 6; the turning slider- crank, (01 P-L) a - I the turning block, and (<7J P^-f - I the swinging slider-crank. All three mechanisms occur in practice.
Instead of removing I any other of the links may be taken away, provided only that the particular motion required can be obtained without it. The two following figures show two methods
FIG. 268.
FIG. 269.
of reducing the chain (CJ P x ) by omitting the block c, they re- present therefore (C'J P- 1 -) - c. In the first of them there is added to the coupler, conaxially wifch the former cylinder pair 3, a solid cylinder, and this is paired with its envelope in the slider, which is a straight slot, or negative prism. In Fig. 269, on the other hand, the slider is made a positive prism, and paired with its envelope in the end of the coupler. The latter takes the form of an X-shaped recess, which lies closely on the slider only at the points of greatest pressure, (i.e., when the axes of a and I are at right angles), but in all other positions has considerable freedom, and works therefore under force-closure. The pair- closure could be complete only if the prism d were infinitely
