Inverse dynamic analysis of parallel manipulators with full mobility

An approach is presented for automatically generating inverse dynamic solutions for planar parallel manipulators with 3-DOF and spatial parallel manipulators with 6-DOF, thereby eliminating the errors and tedium associated with hand derivations. Kinematic and dynamic equations are formulated using a combination of linear graph theory, the principle of virtual work, and symbolic programming. A planar RRR manipulator and a Gough–Stewart platform are used to validate the inverse dynamic analyses, and to compare the efficiencies of several different computer implementations.