Design of automatic gear boxes with better performance is a pursuit goal of the modern automobile industry. In order to develop CAD method for the creative design of automatic gear boxes, this paper proposes an automatic method for the structure synthesis of one degree of freedom (DOF) epicyclic gear trains (EGTs) with one main shaft which serve as the key mechanisms in automatic gear boxes. First, based on the graph representation of EGTs, the canonical perimeter graphs and the corresponding canonical adjacency matrices are obtained. Then, based on the canonical adjacency matrices, the characteristic number strings are obtained and used to identify isomorphism in the synthesis process. Third, an automatic method is proposed to generate the basic graphs of the topological graphs of EGTs, and the basic graphs up to 9 links are synthesized. After that, based on the structural characteristics for the graphs of EGTs, an automatic method is proposed to synthesize the topological graphs of EGTs from the basic graphs, and an algorithm for the detection of rigid subchains in EGTs is also presented. Finally, a program is developed, and 1-DOF EGTs having one main shaft with up to 9 links are synthesized.

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