Lie Group Based Type Synthesis Using Transformation Configuration Space for Reconfigurable Parallel Mechanisms With Bifurcation Between Spherical Motion and Planar Motion

This paper investigates novel reconfigurable parallel mechanisms with bifurcation between planar subgroup SE(2) and rotation subgroup SO(3) based on a transformation configuration space. Having recollected necessary theoretical fundamentals with regard to compositional submanifolds and kinematic bonds, the motion representation of the platform of reconfigurable parallel mechanisms are investigated. The transformation configuration space of a reconfigurable parallel mechanism with motion branches is proposed with respect to the fact that the intersection of Lie subgroups or submanifolds is the identity element or a non-identity element. The switch conditions of the transformation configuration space are discussed, leading to establishment of a theoretical foundation for realizing a switch of motion branches. The switch principle of reconfigurable parallel mechanisms is further investigated with respect to the common motion between SE(2) parallel-mechanism motion generators and SO(3) parallel-mechanism motion generators. Under this principle, the subchains with common motion generators are synthesized and divided into two types of generators. The first type of generators generates kinematic chains with a common intersection of three joint axes, and the second type of generators generates a common intersection of two joint axes. Following this, two types of reconfigurable parallel mechanisms with three identical subchains are synthesized, resulting in 11 varieties in which platforms can be switched between SE(2) and SO(3) after passing through the singularity configuration space.