IEEE International Conference on Robotics and Automation, Albuquerque, New Mexico, USA, pp. 2961--2966, 1997

This paper finds an analytical expression for the Jacobian matrix of a parallel manipulator, as well as for its derivatives (with respect to time or to a change in joint angles) of any order. The most important part in the presented procedures is the closed-form expression for the velocity closure equations of the manipulator