Institute for Systems Research

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An Application of Graph Theory to the Detection of Fundamental Circuits in Epicyclic Gear Trains
(1995) Tsai, L.W.; ISR
In this paper, a systematic procedure is developed for the identification of fundamental circuits and transfer vertices in epicyclic gear trains. The method utilizes the well-established concepts of graph theory and related matrices. The procedure leads to automated formulation of the kinematic equations in a systematic manner.
An Efficient Algorithm for the Automatic Enumeration of the Topological Structures of Mechanisms
(1993) Hsieh, Hsin-I; Tsai, L.W.; ISR
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.
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.