The Inverse Kinematics Problem of the Generalised Stanford Arm

This paper aims to elaborate a technique to solve the inverse kinematics problem (IKP) of a general RRPRRR serial link manipulator which turns out to be the general case of the Stanford arm robot. Although the IKP of the Stanford arm is well established in the literature, solving its general form is not a trivial problem. The contributions of the paper include elaborating the solution procedure based on the Raghavan–Roth formulation and viewing the root finding process as a polynomial eigenproblem rather than a normal or generalised eigenproblem. In fact the structure of the equations are such that it leads to a quadratic eigenproblem formulation which opens up the scope for broader analysis in the future. It is well-known that the upper bound on the number of solutions would be 16 in the complex plane and the same has been elaborated in this paper through an appropriate example.