An efficient methodology for the structural synthesis of geared kinematic chains

Through the use of acyclic graphs, an efficient methodology has been developed for the synthesis of the kinematic structure of geared kinematic chains with any number of links. First, a systematic approach is proposed for the enumeration of N-vertex acyclic graphs. For each N-vertex acyclic graph, all the N-vertex geared graphs are generated by adding (N — F — 1) geared edges to the acyclic graphs, eliminating geared graphs which violate the fundamental rules, and non-isomorphic geared graphs are obtained by comparing the structural codes. Finally, the catalog of the graphs of one-degree-of-freedom (DOF) geared kinematic chains with N links are synthesized from the catalog of acyclic graphs with N vertices. As a result, the structural synthesis of one-DOF geared kinematic chains with up to eight links has been successfully constructed.