Enumeration of displacement graphs of epicyclic gear train from a given rotation graph using concept of building of kinematic units

摘要

Use of graph theory for enumeration of Epicyclic gear trains (EGTs) is common during conceptual stage. According to theory of structural synthesis of EGTs, two kinds of graphs are defined namely rotation and displacement graphs, for a given number of links and one degree of freedom. In case, all the non-isomorphic rotation graphs are enumerated, then the next stage of synthesis involves the generation of displacement graphs for each rotation graph. To this end, given a rotation graph, the present work proposes an algorithm for generation of all the displacement graphs. Firstly, the rotation graph is decomposed into modules called kinematic units (KUs). Then, for each KU, all the edge-labeling possibilities of turning pairs are evaluated. Finally, displacement graphs are obtained by building the edge labeled KUs in all possible ways. Acyclic graph based representation is employed and displacement graphs with and up to 7 links are enumerated. The enumeration of displacement graphs is treated as two different cases corresponding to rotation graphs enumerated using recursive and non-recursive schemes and the results are in agreement with C.H. Hsu and others. (C) 2019 Elsevier Ltd. All rights reserved.