Full forward kinematics of redundant kinematic hybrid manipulator

A unified recursive mathematic model is established for full forward kinematics analysis of various redundant kinematic hybrid manipulators which are formed by several different parallel manipulators connected in series. In the established model, the relationships between the general input velocity/acceleration and the general output velocity/acceleration are discovered. The Jacobian matrices for mapping the general output velocities to the general input velocity and the Hessian matrices for mapping the general output velocities to the general input acceleration are derived. The unified iteration recursive formulae are derived for solving the general output velocity/acceleration of the end moving platform of the redundant kinematic hybrid manipulator by only giving the general input velocity/acceleration of every parallel manipulator. A 3D model of a novel (4SPS + SPR )+ (4SPS/SP) + 3SPR type hybrid manipulator is constructed and its full forward velocity/acceleration formulae are derived from the established unified recursive mathematic model and are proved to be correct by utilizing a simulation solution of the novel redundant kinematic hybrid manipulator.