Analytic Jacobian of in-parallel manipulators

A general formulation to obtain an analytic Jacobian matrix for in-parallel manipulators has not been developed yet, although several authors addressed it. This paper suggests a consistent approach to obtain the instantaneous kinematic relation of in-parallel manipulators, by extending the results of screw theory to the forward and inverse instantaneous relations, and gives a formula that can obtain a reciprocal screw analytically without considering geometric relations.