Hamming number technique .2. Generation of planar kinematic chains

Synthesis of planar kinematic chains is in general tedious and time consuming. This paper reports a very simple and direct method for the generation of n-link f-degree-of-freedom (d.o.f) chains from (n - 2)-link and f-d.o.f. chains. Hamming number technique reported earlier [A. C. Rao and D. Varada Raju, Mechanism and Machine Theory 26, 55-75 (1991)] for testing isomorphism among kinematic chains is extended to reveal identity and symmetry among the links and joints of a chain. This in turn enables generation of distinct n-link chains directly from each distinct (n - 2)-link without having to test for degeneration and isomorphism. The formulae suggested will give the number of such chains. Chains with (n - 1)-links and (f + 1)-d.o.f. are obtained as a by-product. The distinct n-link, f-d.o.f. chains obtained from all the basic chains need, however, to be tested for isomorphism among themselves. The advantage of this method can be perceived from the fact that only about 400 10-link chains need be tested to get the already established 230 distinct chains. (C) 1997 Elsevier Science Ltd.