An Efficient Algorithm for the Automatic Enumeration of the Topological Structures of Mechanisms
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In this paper, a new algorithm for the automatic enumeration of the topological structures of mechanisms is developed. The algorithm permits the deviation of conventional graphs from contracted graphs by the partition of binary vertices. A row vector is formed to present the binary-vertex chains. The partition of binary vertices is transformed into the solution of one linear equation in several unknown integers. No permutation of binary-vertex chains is necessary. This leads to the development of a highly efficient computer algorithm for the enumeration of conventional graphs.<P>Two tables of conventional graphs with seven and eight vertices, and with up to five loops have been developed. We believe that the results of these conventional graphs are new. Mechanisms of higher pair joints up to five loops and with eight links can now be synthesized from these tables.