In this paper the trajectory planning problem is solved for a 2PRR parallel manipulator which works in cooperation with a 1 degree-of-freedom (dof) platform. The whole kinematic chain is considered as a redundant 3-dof manipulator, and an algorithm is presented to solve the redundancy by using the joint velocities in the null space of the jacobian matrix. The internal motion of the assisted manipulator allows globally optimize the condition number of the jacobian matrix during the accomplishment of a desired task. Consequently, the accuracy of the manipulator is maximized and singular or degenerate poses are avoided. A case of study is presented to show the effectiveness of our approach.