The complete set of 12-bar planar simple-jointed kinematic chains is enumerated using the stratified or hierarchical representation, of Fang and Freudenstien (1990) in which post-priori isomorphism testing is not needed. This is achieved by directly enumerating the simplified and contracted graphs from which the kinematic chains are built up. The number obtained is compared with those from previous studies, and the list is catagorized by the link sets and by the numbers of major vertices and edges in the simplified graphs. A major feature of the technique is the use of an efficient rote-based technique for eliminating degenerate chains.

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