Structural Synthesis and Classification of Epicyclic Gear Trains: An Acyclic Graph-Based Approach

Abstract

Graph theory-based representation is commonly used for modeling the kinematic structure of mechanisms thereby facilitating the listing of all feasible mechanisms that meet certain design requirements. The structural synthesis of kinematic structures is then carried out, using graph algorithms. For the case of epicyclic gear trains (EGTs), the overall synthesis involves the successive steps including the enumeration of rotation graphs and then deriving displacement graphs with respect to each rotation graph. The first step (listing of rotation graphs) is crucial and it is generally algorithmically involved than the other step, namely, generation of displacement graphs. Many scientific works have employed the conventional non-recursive scheme, for enumerating the rotation graphs. However, in this work, a new non-recursive method is proposed. This newly proposed scheme uses acyclic graphs of a certain number of vertices as parents for enumerating rotation graphs of EGTs (whose number of links same as number of vertices of the acyclic graph) of any number of DOF. This method can be easily automated using a computer program. It is applied in the synthesis of EGTs with and up to 7 links and the results are verified with that of the literature.