Reconfiguration-aimed and manifold-operation based type synthesis of metamorphic parallel mechanisms with motion between 1R2T and 2R1T

This paper presents a novel approach for synthesizing metamorphic parallel mechanisms with an ability of reconfiguring motion between 1R2T and 2R1T based on quotient operation of manifolds. With the theoretical fundamentals of Lie subgroups and submanifolds, the principle of configuration change is proposed in the synthesis with a submanifold switch, that reconfigures the mechanism to provide a various motion, leading to reconfiguration of the metamorphic parallel mechanism platform. The synthesis starts from a quotient operation of manifolds to generate a manifold subchain, the synthesis of these subchains is aiming at the reconfiguration of the platform between 1R2T and 2R1T based on the same composition form of submanifold subchains with various motions. Three new subchains are synthesized with metamorphic joints, revolute joints and prismatic joints based on manifold-operation, which leads to a configuration switch of each subchain in terms of the phase change of the metamorphic joint with respect to relative positions of rotational axis and links, resulting in different constraints and motions of the subchains, leading to a platform with an ability to realize multiple motions. The design of new metamorphic joints is a key factor to realize the different motion of platform in terms of the principle of configuration change and manifold-operation. Further, the special geometrical properties and several specific phases of the metamorphic joint are analyzed. The approach of synthesis based on manifold-operation provides a distinct rationale for this paper. Under this guidance, analysis of motion and constraint conditions transmitted to the platform through subchains is essential, to enable the reconfiguration aimed type synthesis of metamorphic parallel mechanisms.