Abstract: A hip joint simulator with a 3SPS+1PS spatial parallel manipulator as the core module is proposed. The spatial parallel manipulator has 4 degrees of freedom, including three rotations and one translation. It consists of a fixed base and a moving platform that is connected by three SPS-type active legs and one PS-type central strut. Singularity has great effects on working performance of parallel manipulator, so the singular characterizes of the hip joint simulator need to be studied. Kinematic model based on Rodrigues parameters is provided and a general formulation of static mechanical conversion matrix is deduced that allows one to determine Plücker vectors associated with six analytical lines for Grassmann analysis. Most singular configurations of the simulator are presented, and the expressions describing corresponding singularities are obtained in closed forms. Numerical simulations show the corresponding motion curves and surfaces of singular configurations with different linear variety ranks from 1 through 5, and the distribution characteristics of singular trajectories are studied respectively. The analysis of the singular configurations provided has great significance for trajectory planning, size optimization and control design of the simulator.

Key words: Grassmann line geometry, Parallel hip joint simulator, Rodrigues parameters, Singular configuration