Abstract: A review of seven significant DOF formulas proposed over the past ten years with their main characteristics is presented. On this basis, significant aspect related DOF on their basic form of constraint-analysis-based DOF formulas of motion-analysis-based DOF formulas is presented, their procedures are given. The characteristics of a mechanism topology structure are determined based on DOF formulas, such as mechanism DOF, position and orientation characteristic (POC) set of moving platform and its dimension, number of independent position equations, over constraint degree, redundant DOF and the determination of passive and active kinematic pairs. The mapping relationship among mechanism DOF, topology structure and POC set is further revealed with the invariance property of the mechanism topology structure and the POC set as the theoretical foundation for constructing this mapping relationship is presented.

Key words: constraint analysis, degree of freedom, motion analysis, parallel mechanism, position and orientation characteristic, topological structure, topology structure characteristics