A Line Geometric Approach to Determining Displacements Based on Line Specifications

This paper presents a systematic approach to determining the displacements of a rigid body from line specifications. The underlying concept of the proposed approach pertains to screw theory and line geometry. We utilize the correspondence between a pair of homologous lines and a regulus and that between a screw and a linear line complex. In this paper, a displacement screw is obtained by fitting a linear line complex to two or more line reguli. When two exact pairs of homologous line are specified, we obtain a unique linear line complex, which determines the displacement screw correspondingly. When more than two pairs of homologous lines with measurement errors are specified, it becomes a redundantly specified problem, and a linear line complex that has the best fit to more than two reguli is determined. A numerical example with the specification of four pairs of homologous lines is provided.