The Linear Representation of the Screw Triangle: A Unification of Finite and Infinitesimal Kinematics

Abstract This paper presents the linear representation of the screw triangle. The resultant twist of two finite twists is shown to be a linear combination of five screws. The linear representations of all degenerate screw triangles are also derived. The limiting cases of these results of finite displacements confirm the theory of screws in infinitesimal kinematics. The finite kinematic analysis of multi-link serial chains is performed by using the linear representation of the screw triangle to demonstrate a unification of finite and infinitesimal kinematics.