Structural implications of the graph theory representation in epicyclic gear trains

Graph theory has been demonstrated by many researchers to be useful during the conceptual phase of mechanism design. In this regard it has been put to use by many works for systematically synthesizing varieties of epicyclic gear trains (EGTs) of one degree of freedom. This paper makes use of the solutions derived using graph theory and introduces a procedure for identifying the constituent links corresponding to the chosen EGT graph concept so that it can be realized into a 3-D CAD model. It is seen that certain EGT graphs do not lead to meaningful 3-D representation. Conditions for a graph to result in a meaningful EGT structure are also derived in the process.