Unified terminal constraint and kinematics modeling of lower mobility serial-parallel mechanisms composed of two parallel mechanisms

Serial-parallel mechanisms have attracted continuous interests in the field of robotics in recent years. However, the researches for lower mobility serial-parallel mechanisms (LMS-PMs) formed by two PMs have not been attempted. This paper establishes the basic theory framework of terminal constraint and kinematics for this class of mechanisms. First, an approach for determining the terminal constraints of LMS-PMs formed by two PMs based on Grassmann-Cayley algebra is proposed. Second, using elimination method and superposition principle, the terminal coupling equations and the forward/inverse displacement solving models of this class of mechanisms are established. Third, combining the velocity mapping relations and the derived terminal constraints, the unified full 6×6 form Jacobian matrix is derived. Finally, the terminal constraint/mobility, forward and inverse displacements, 6×6 form Jacobian of a novel (2-RPU+UPR)+(UPR+RS) LMS-PM are established to demonstrate the established modeling.