Page:The Kinematics of Machinery.djvu/333

 REVERSING LINKS. 311

This shows us that a pair of the form CtC~ or C~C+ moving only in oscillations of small angle ; may be replaced by a pair of the form AA~ or A~A +, so that in such cases

(G) = (A).

We have already ( 69) had occasion to employ this substitu- tion of the pair sector and curved slot, (A), for a cylinder pair. It can now be seen that we were fully justified in doing so, that the change did not in any way alter the nature of the chain.

This circumstance is very frequently taken advantage of in prac- tice; pin expansion, that is to say, occurs there very frequently. The mechanism of Fig. 240 is both known and used, although it has not hitherto been considered identical with the turning slider-crank. It has been shown * that the block when driven by the crank moves

FIG. 240.

exactly in the same way that it would move were it connected with the latter by means of a connecting rod having a length equal to the radius of the slot. It has not been noticed, however, that the little sector I really is itself this connecting rod or coupler. The small space which it occupies makes this form of mechanism very convenient in some cases.-)- We are very familiar with its employ- ment in reversing gear, both in links of the common form, and in Gooch's link, and others. These mechanisms are compound and not simple crank chains, so that we have not to consider them here, but the replacement of (C) by (A) occurs in them in various forms, forming an essential part of each (compare 16).


 * See for instance Giulio, Cinematica, p. 109.

t I have added in a note, p. 320, a somewhat interesting example of the use of this form of expansion in such a way as to render it impossible to alter a im-chauism from (C 1 ^ P-L) to (tf^P*) a thing which it is sometimes very convenient to have the means of doing.