Abstract:

Taking a plane 3-RPR parallel manipulator as an example, the motion stability at singular configurations corresponding to the kinematic parameters of the manipulator is investigated. The quadratic term uncoupled particle equation without multipliers for the 3-RPR parallel manipulator is established at first based on Lagrange approach. In this analytical equation, the kinematic parameters are contained apparently. With the aid of the first approximation stability criterion of Lyapunov, the motion stability at singular configurations is analyzed. It is found that when the absolute velocity center of the movable platform locates in the vicinity of the rotation center of the gained degree-of-freedom of the movable platform at singular configurations, the motion stability at singular configurations is worse; increasing the angular speed of the movable platform and/or the values of input parameter items in accord with the rotation direction of the movable platform, the motion stability at singular configurations will be improved. This research has positive theoretical significance in avoiding singularities and enhancing the motion stability at singular configurations through adjusting the kinematic parameters of the manipulator in the design and the actual control stages.

Key words: kinematic parameters, motion stability, singular configuration, trajectory planning, parallel manipulator