A procedure for systematically and completely enumerating all nonfractionated planar kinematic chains having N links and F degrees of freedom has been developed. This procedure employs the theory of finite symmetry groups to eliminate isomorphic chains. The analysis of 8-, 9-, and 10-link chains having 1, 2, and 3 degrees of freedom, respectively, is presented as an example.
Enumeration of Basic Kinematic Chains Using the Theory of Finite Groups
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Tuttle, E. R., Peterson, S. W., and Titus, J. E. (December 1, 1989). "Enumeration of Basic Kinematic Chains Using the Theory of Finite Groups." ASME. J. Mech., Trans., and Automation. December 1989; 111(4): 498–503. https://doi.org/10.1115/1.3259028
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