Abstract: By applying the analytical dynamic mechanics theory, transforming the geometric constraints of parallel manipulators into the constraint forces, the dynamic equation of 3-RPR parallel manipulator without the multipliers and the uncoupling quadratic terms is derived with the aid of the Lagrange’s equation of the first class. This equation comprehensively reflects the effects of the velocities of the moving platform, the velocities and the accelerations of the input parameters, and system’s applied loads and gravities on the dynamic behaviors of the manipulator. Based on this equation, the dynamic responses of the parallel manipulator at the turning point singularities under the system’s gravities are analyzed. The research reveals that at the singularity, the dynamic responses of the moving platform under the action of the gravities have the characteristics of keeping the lengths of some input actuators constant. This kind of behavior makes the dynamic response of the moving platform can not be control by the input parameters, and the moving platform loss control. The research on the dynamic stability of the singularity with the aid of the Lyapunov stability criterion shows that through changing the amplitudes and directions of applied forces either separately or jointly, it is not easy to obtain the suitable loads meeting the dynamic stability requirements at the singularity. Therefore, the strategy to enhance the dynamic stability of the manipulator at its singularities by applied loads is not constructive.

Key words: Dynamic response, Dynamic stability, Parallel manipulator, Singularity