Efficient inverse kinematics for serial connections of serial and parallel manipulators

This paper presents a unified and efficient method of solving the inverse kinematics for six degree-of-freedom serial connections of two three degree-of-freedom serial and parallel manipulators. Based on the kinematic analysis of three degree-of-freedom serial and parallel manipulators, the forward kinematics are formulated for six degree-of-freedom serial connections, including parallel-parallel, serial-parallel, parallel-serial, and serial-serial types. A unified method of solving the inverse kinematics for the serial connections is established: for a given task velocity, the inverse kinematics of two arms are obtained separately, thereby significantly reducing a computational cost. This is made possible by projecting a given velocity onto the infeasible velocity space of one arm independently. Through computational analysis, the proposed method is shown to be effective for the serial connections having at least one parallel manipulator.