Page:The Kinematics of Machinery.djvu/595

 SIX LINKED CYLINDER CHAINS.

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�make the links e and / infinite, and further make the axes of the pairs in each of the ternary k links (1, 2, 5 and 2, 3, 7,) conplane, we obtain the combination shown in Fig. 428. If we make the original chain (6 1 "), a, &, c, d, a parallelogram (as here shown) we obtain a combined chain which has some remarkable properties, although they have not yet been utilised. The line 7'4' parallel to a is always=2'l, and the length 1*4' is constant, the lines 5'6 and 1*4 therefore always intersect in the same point 0. If we place the chain on d we obtain a mechanism in which the bar e will

��move so that its axis passes always through a fixed point beyond the mechanism, and which therefore may be itself inaccessible.

If we make e finite and therefore / and 3*7 infinitely long, we obtain the chain shown in Fig. 429, which is essentially different from the last.

��FIG. 429.

The combination of cylinder-pairs already described in 60, which is again represented in Fig. 430, is a combined chain. The closure of the links 4*7 and 3'6 of the (C" 4 ') chain makes the other- wise incompletely closed five-linked chain 1. 2. 3. 4. 5 constrained. This chain finds several useful applications in " parallel motions/ 1 trains in which one or more points move in (accurately or ap- proximately) straight paths. One of these, for instance, given by Tchebyscheff, * and another by Harvey,^ are formed on this


 * Dingler's Journal, 1862, vol. 163, p. 403.

t Practical Mechanic 1 & Journal, 1850, volil, p. 174.

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