Page:The Kinematics of Machinery.djvu/601

 called this mechanism the. The centroids of c and a and also those of d and b are Cardanic circles.

(7.) By making b and c infinite instead of b and a we obtain an altogether different mechanism, as is shown in Fig. 442. Its formula is (C″C+P+C″2Cz). Placed on c and driven by e we obtain a somewhat complicated reciprocation of b. Among other applications of the train is one by Whitehill for the motion of the needle in a sewing-machine; he makes the two wheels equal.

. 442.

. 443.

. 444.

If we make c an annular wheel we obtain the chain shown in Fig. 443. If here the diameter of d be made half that of c, and 1·5 be made equal to 5·4, the chain takes the form shown in Fig. 444. The point 1, upon the circumference of a smaller Cardanic circle, moves along a diameter of c. Placing the chain on c, therefore, we obtain the well-known hypocycloidal "parallel-motion." This is a very old mechanism, called both after Lahire and after White, and is often used in printing-presses. There is no longer any motion in the turning pair 2, so that the link b may be altogether omitted. If the same chain be placed upon a instead of c we obtain again a parallel-motion, this time for the link c. So far as I know this mechanism is new.