Type synthesis of unified planar–spatial mechanisms by systematic linkage and topology matrix-graph technique

A systematic linkage technique and a topology matrix-graph approach are put forward for type synthesis of unified planar–spatial mechanism. By using the systematic linkage technique, numerous associated linkages of unified planar–spatial mechanism are created. The equivalent relations between the actual mechanism and the associated linkage are determined, and the formulas for calculating the number of DOF, the complexity, and acceptable associated linkage are derived. By using the topology matrix- graph approach, corresponding topology matrices are constructed, and some topology embryonic graphs and their isomeric topology embryonic graphs of the unified planar–spatial mechanism are constituted. Finally, the numerous topology graphs for type synthesis of unified planar–spatial mechanism are derived. The results show that the two approaches are simple and effective for type synthesis of unified planar–spatial mechanisms.