A linear algebraic procedure in obtaining reciprocal screw systems

This paper presents a linear algebraic procedure in obtaining (6-n) reciprocal screws from an n-screw system of a robotic manipulator. The procedure starts by formulating the reciprocal relationship between a screw system and its reciprocal screw system in matrix form, and augmenting the screw matrix which is assembled with n screws in the screw system. Vectors of cofactors of the augmented row are then produced and the partitioning of the screw matrix is implemented to generate each of the (6-n) reciprocal screws. The theory developed in this paper provides a novel and simple procedure to obtain reciprocal screws from any screw system. The paper illustrates applications to cases with different screw systems. (C) 2003 Wiley Periodicals, Inc.