Page:The Kinematics of Machinery.djvu/575

 BALL AND SOCKET JOINT.

�553

�The " ball and socket " joint which we have here is simply the result of the omission of one of three cylinder pairs, the axes of which intersect at right angles in one point. It is therefore marked 3.4.5. The block / = P~... _[_... P + serves as the piston-rod, the driving-link, of the steam-engine. The contracted formula of the mechanism is therefore (C t -CP P ff )i - c - d. In order to make

���FIG. 395.

�Fio. 396.

�a comparison with the general form (f>+) more easy, I have repre- sented the chain in Fig. 396 so that the two prism pairs, which we may consider as R or C 00, are replaced by the cylinder pairs and 7. The formula for the mechanism in this form, placed on,/, runs(C^CJ-<r+) 8.

The foregoing examples are sufficient to show the importance of the chains (<7+) and (#+) and to serve as an introduction to their complete synthesis. The former appears to have the largest number of links that can be used in any constrained simple chain formed from the lower pairs of elements.

�153.

Prism Chains.

We have already more than once examined ( 64 and 108) the three-linked prism chain, or wedge-chain, (P-). Fig. 397 represents

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