A Complete Solution for the Inverse Kinematic Problem of the General 6R Robot Manipulator

The inverse kinematic problem of the general 6R robot manipulator is completely solved by means of a 16th degree polynomial equation in the tangent of the half-angle of a revolute joint. An algorithm is developed to compute the desired joint angles of all possible configurations of the kinematic chain for a given position of the end-effector. Examples for robots with maximal 16 different configurations show that the polynomial degree 16 is the lowest possible for the general 6R robot manipulator. Further, a numerical method for the determination of the boundaries of the workspace and its subspaces with different numbers of configurations is developed. These boundaries indicate the singular positions of the end-effector.