The characteristic pair of joints-an effective approach for the inverse kinematic problem of robots

The inverse kinematic problem of robot manipulators requires the computation of the joint coordinates to execute prescribed trajectories. It implies the determination of six dependant joint coordinates in a kinematic multibody loop by six nonlinear algebraic constraint equations. The approach presented yields a nonredundant system of constraint equations which is always partitioned into an implicit core system and explicitly solvable equations. General rules have been derived for the generation of these equations. For numerous classes of manipulator designs even the complete system of equations can be solved in closed form. The effectiveness of the method has been proved by several technical applications in cooperation with the West German robot industry