Extension of the Second Paden-Kahan Sub-problem and its´ Application in the Inverse Kinematics of a Manipulator

Three basic sub-problems of screw theory are acceptable for some particular configuration manipulators´ inverse kinematics, which can not solve the inverse kinematics of all configuration manipulators. A new sub-problem is extended based on sub-problem 2, that is, rotation about two disjoint axes, and the inverse kinematics thereof is solved in this paper. Based on the extended sub-problem, a manipulator, the inverse kinematics of which can not be solved by the three sub-problems without the participation of the new sub-problem, is constructed. The inverse kinematics of the manipulator is solved with the help of the extended sub-problem, therefore a close-form solution expressed by motion screw is gained.