Mobility analysis for parallel manipulators based on intersection of screw manifolds

In order to overcome the exceptional cases of the classical CGK formula for mobility analysis, a novel approach based on intersection of screw manifolds is proposed in this paper. This approach can deal with both the mobility of the moving platform and the full-cycle mobility. Furthermore, this approach can identify the redundant and passive mobilities, and guide the allocation of actuators. The procedure of the intersection operation of screw manifolds is presented in detail using the proposed concept of the complementary screw. And in special conditions, the intersection of two screw manifolds can be achieved instantly without the calculation of complementary screws. Moreover, this approach needs no investigation of the structures and properties of subgroups or submanifolds, and needs no reference to tables that are generalized to demonstrate operational rules for intersection of two subgroups. The proposed notion of the intersection of screw manifolds has the explicit kinematic sense, so that the nature of the mechanical motion of parallel robotic mechanisms can be profoundly understood.