A recursive method for finding revolute-jointed manipulator singularities

A geometric application of screw theory is used to develop a recursive algorithm for computing all singular configurations of revolute-jointed manipulators with arbitrary geometry and an arbitrary number of joints. The depth of the recursion is linear in the number of joints, n, while the computational burden is proportional to 2^(n-2). This method does not require explicit construction of the Jacobian matrix elements or a determinant operation. Further, the screw axis of the singular motion is determined at no additional cost. The bifurcations of this algorithm are also explored.