Vectors of Cofactors of a Screw Matrix and Their Relationship with Reciprocal Screws

This paper studies the vectors of cofactors in a screw matrix assembled by n screws and investigates the properties and different arrangements of cofactors. An augmentation screw which is linearly independent of n screws in the screw matrix is proposed and is used to relate the vector of cofactors to a reciprocal screw and subsequently to the reciprocal screw system. The paper proposes a new algebraic procedure to evaluate a reciprocal screw and the subsequent (6-n)-reciprocal screw system. The method is invariant and based upon the cofactors of the screw matrix.