Inverse Kinematics of the General 6R Manipulator and Related Linkages

This paper elaborates on a method developed by the authors for solving the inverse kinematics of a general 6R manipulator. The method is shown to be applicable to determining the joint variables associated with all series-chain manipulators and closed-loop linkages constructed in a single loop with revolute, prismatic, or cylindric joints. The method is shown to yield a single polynomial, of minimum degree, in terms of just one of the joint variables. Once the roots of this polynomial are found, the remaining variables are then usually determined from linear sets of equations. It is shown that this method works equally well for general geometries and for special geometries such as those chararcterized by intersecting or parallel joint axes.