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Abstract：The systematic method for topological structural synthesis of parallel mechanism based on POC equations is introduced considering the development of SCARA parallel robot, the complete procedure for structural synthesis of 3T-1R parallel mechanism is discussed using this method. Thirteen types of 3T-1R parallel mechanisms (including 3 types of 3T-1R parallel mechanisms already used for the SCARA parallel robot) were obtained. The structural synthesis method based on POC equations is easy to use since there are explicit formulas or criteria for each step of the synthesis process.

This paper proposes a geometric way to generate metamorphic configurations and investigates metamorphic principles based on geometrized displacement group. Metamorphic reconfiguration techniques are revealed as the variations of kinematic joints, kinematic links and geometric orientation constraints particularly by examining the invariant configuration properties of a mechanism. The nature of all these configuration changes belongs to geometric constraint category. Metamorphic configuration units are proposed as the irreducible reconfiguration modules to envelop these reconfiguration techniques. It can self-reconfigure or be combined to generate metamorphosis. Moreover, the geometrized displacement group is lent to achieve a geometric representation for configuration modelling and further reconfiguration operations. Based on seting up kinematic group extended qualitatively according to its group structure, geometrized displacement group modelling is proposed for these identified metamorphic configuration units. The investigated group motion-matrix is an integration of its displacement group properties and kinematic extensions. Then defined geometric constraint relations and the proposed dependence rules lead to metamorphic principles. In this way, metamorphic process is mapped to matrix operations under group extensions and their compositions. Design examples and a metamorphic joint with six configurations are given to illustrate the feasibility of these metamorphic principles.

Based on the units of single-opened-chain limb, some topological characteristics of rank-degenerate parallel robot mechanisms are revealed, and a systematic methodology for the structural synthesis of a class of five degree-of-freedom parallel robot mechanisms is put forward in this paper. 49 new mechanisms with three translational and two rotational degrees of freedom are synthesized and classified. The method proposed in this paper is of universal significance and has been used for the structure synthesis of rank-degenerate parallel robot mechanisms with other kinematics output types.