Page:The Kinematics of Machinery.djvu/334

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KINEMATICS OF MACHINERY.

The mechanism shown in the following figure, which occurs sometimes in slotting machines, furnishes us with another illustra- tion of pin-expansion. The whole forms a turning slider crank having the formula (C^P-^i . The link b, the coupler, is formed essentially as it was in the last case, but here the profiles against which it works are concave on both sides of the pin 2, the upper profile being of large, and the lower of very small radius, but both forming part of the block c. The block c is in this case so closed

by the binder d that the profiles repre- senting the pin 3 lie entirely within the prism-pair 4. We have here, therefore, the elements of the slider crank chain so proportioned that 2 lies within 3 and 3 within 4, an illustration of the w r ay in which the method of expansion can be applied also to the fourth pair. To show how, conversely, W T C may place 4 within 3 we may take the chain shown in Fig. 242. Here the pin 3 of the link c is made so large that the open prism of the pair 4 can be

formed within it. Upon 3 there now oscillates the open cylinder of the coupler &, which, however, must be cut away at the sides so as to allow it to clear the frame d. The extent to which this

FIG. 241.

FIG. 242.

cutting away must take place can be found, as the figure shows, by drawing d in the two positions in which it encloses the greatest angles with I. These occur when a and d are at right angles. We shall have to consider some applications of this form of expansion further on.