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.
['Stefan Dutre', 'Hans Bruyninckx', 'J. De Schutter']
The analytical Jacobian and its derivative for a parallel manipulator