Inverse kinematics of six-degree of freedom "general" and "special" manipulators using symbolic computation

This paper presents an algorithm that solves the inverse kinematics problem of all six degrees of freedom manipulators, "general" or "special". A manipulator is represented by a chain of characters that symbolizes the position of prismatic and revolute joints in the manipulator and the special geometry that may exist between its joint axes. One form of the loop closure equation is chosen and the Raghavan and Roth method is used to obtain symbolically a square matrix. The determinant of this matrix yields the characteristic polynomial of the manipulator in one of the kinematic variables. As an example of the use of this algorithm we present the solution to the inverse kinematics problem of the GMF Arc Mate welding manipulator. In spite of its geometry, this industrial manipulator has a non-trivial solution to its inverse kinematics problem.