Abstract: The motion control of an underactuated manipulator can be realized on dynamic level only, and the motion of the passive joint is controlled by the actuated joint indirectly. The controllability of the underactuated manipulator depends on the dynamic coupling between the actuated joint and the passive one. Ulteriorly, the dynamic coupling of the system is related to the configuration of the manipulator in joint space. Therefore, the dynamic singularity could be happen in the motion of the system, where some passive joints are uncontrollable. In this paper, the dynamic singularity of the underactuated manipulators is analyzed form two points of views, the joint space and task space. Two measures of the dynamic coupling singularity are proposed according to the two aspects. Furthermore, a sliding mode control method based on the nonlinear transformation on inputs is suggested for the continuous trace-tracking task of the underactuated manipulator system. A planar three joint manipulator, which has one actuated joint, is utilized to simulate thes conclusions and to test the suggested control method. The simulation result shows the method is feasible.

Key words: underactuated, manipulators, dynamic singularity, nonlinear control, nonholonomic