LAUSR

Machines, automobiles, robots, etc., usually employ epicyclic gear trains (EGTs) in their transmission systems. The graph theory-based representation of an EGT has enabled in the development of structural synthesis algorithms for enumerating all the feasible concepts in the form of non-isomorphic graphs. The enumerated EGTs are of importance to an EGT designer during the conceptual stage of design. One of the important steps in the structural synthesis is that of detection and elimination of those graphs that contain degenerate structure/s as subgraphs. In this work, graph theory-based methods are presented for the detection of degenerate EGT graphs among the enumerated collection. It is shown that the graph of any degenerate structure can be evolved to that of EGTs of single/multi-degree of freedom (SDOF/MDOF) through the addition of graph components thereby giving rise to degenerate EGTs. Through a series of statements, it is concluded that degenerate EGTs can be divided into two classes: those with one or more cut vertices and those without any cut vertex. A simple decomposition scheme is formulated which when applied to any EGT graph would determine whether or not it contains a degenerate structure. The proposed method is applied as a test for degeneracy in the structural synthesis of SDOF and MDOF EGTs, and the results for nondegenerate graphs are verified to be correct.