A Note on the Screw Triangle

Abstract

This paper derives the expressions of an equivalent finite screw of two successive screw motions in a simplified form using purely vectorial analysis. This is achieved by tracing the trajectories of specific points on the moving body, which together with the known axis and angle of combined rotation, yield the expressions of the screw triangle. This paper also gives a short overview of different known expressions of the screw triangle and shows that the one given in this paper reduces the number of arithmetic operations by about a third compared with the most efficient algorithm in the literature.