REDUCED CHAINS. 339
this purpose a full cylinder on the end 2 of the coupler is paired with its envelope on the frame, an open annular cylinder having 1 for its centre. Such a chain is written (C" 8 ' P- 1 -) ac.
It is two-linked : in other words it has been reduced to a pair of elements, the two pieces & and d. It can be placed therefore in two ways only. Placed upon d it gives us the turning slider- crank (C" 3 'P- L ) d a c, in a form which might be used in cases where the only motion required is that of the coupler. Placed upon I we have the swinging block, and can utilise the motion of the slider only.
FIG. 273.
Fig. 273, an arrangement which came before us at the very outset of our work, is another example of a reduced chain. It can easily be seen that it is really a portion of a twice reduced skew double-slider chain such as Fig. 253 (Cf. No. 24 page 326). The piece marked aa dd is the skew cross-block, and & c the crank. Its formula is therefore :
Any point p in the crank moves, as we have frequently seen, in an ellipse. The pairing rendered necessary by the omission of the links is here, as in the other cases, higher pairing, the pair of elements obtained by ultimate reduction from a chain is a higher pair. The reduction can be carried no further, for a machinal arrangement cannot be made with less than two bodies.
Practical use is made of this process of reduction in other chains than those which we have been considering. I may just give one example of this. The spur chain (Fig. 274) can be reduced to the higher pair of elements shown in Fig. 275 by
z 2
