Algebraic C∗C∗-actions and the inverse kinematics of a general 6R manipulator

Let X   be a smooth quadric of dimension 2m2m in PC2m+1 and let Y,Z⊂XY,Z⊂X be subvarieties both of dimension m   which intersect transversely. In this paper we give an algorithm for computing the intersection points of Y∩ZY∩Z based on a homotopy method. The homotopy is constructed using a C∗C∗-action on X whose fixed points are isolated, which induces Bialynicki-Birula decompositions of X into locally closed invariant subsets. As an application we present a new solution to the inverse kinematics problem of a general six-revolute serial-link manipulator.