Derivation of Topological Graphs of Some Planar 4DOF Redundant Closed Mechanisms by Contracted Graphs and Arrays

Some planar redundantly closed mechanisms (RCMs) have better dexterity, less singular configuration, and higher stiffness. In this paper, the derivation of valid topology graphs (TGs) of some planar four degrees of freedom (4DOF) RCMs is studied based on the contracted graph (CG), arrays, and topology graph with digits (DTG). First, some CGs without any binary links are constructed for the planar 4DOF RCMs, some curves with only binary links are distributed over CGs, and some valid TGs of the planar 4DOF RCMs are derived. Second, a complicated derivation of TG is transformed into an easy derivation of array and DTG, and some programs are compiled in VISUAL BASIC; all valid arrays corresponding to nonisomorphic TGs are derived, and some invalid arrays corresponding to the isomorphic TGs and invalid TGs are determined and removed by the compiled programs. Third, many valid TGs of the planar 4DOF RCMs with various basic links are derived from valid arrays and DTGs. Finally, some application examples are illustrated.