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This paper attempts to establish unified topological models and corresponding mathematical representations for planar simple joint, multiple joint, and geared (cam) kinematic chains. First, the conventional topological representation models of kinematic chains are introduced. Then, new topological models of multiple joint and geared (cam) kinematic chains, which are derived from the topological model of simple joint kinematic chains, are presented. The characteristics of the new topological graphs and their associations with the topological graph of simple joint kinematic chains are also addressed. The most important merit of the new topological graphs is that it makes it much easier to undertake unified structure synthesis and further to establish conceptual design platform for various planar mechanisms. Synthesis examples of both multiple joint and geared chains are given, which show the effectiveness of the unified topological models.
Ding et al. (2009) studied this question.