Notes on Screw Product Operations in the Formulations of Successive Finite Displacements

Abstract

Geometrical interpretations of two line-based formulations of successive finite displacements, Dimentberg’s formulation and a linear formulation, are discussed in this paper. The interpretations are based on the fact that the pitch of the screw product of two unit line vectors is consistent with Parkin’s definition of pitch. Finite twists in Dimentberg’s formulation are shown to be the screw product of unit line vectors divided by the scalar product of unit line vectors. On the other hand, Finite twists in the linear formulation are interpreted as the screw product of unit line vectors divided by the scalar product of direction-cosine vectors.