A comparison between line geometries of point and line displacements

Abstract

This paper deals with the comparison between the line geometries of point and line displacements. The central concept is that two linear complexes of different pitches are associated to a displacement screw. One is pertaining to point displacements, while the other to line displacements. Similarities between the two linear complexes in their construction, elements, properties, and relations to the displacement screw are investigated. This study shows that all of the recently developed theorems and properties in the line geometry of line displacements resemble those in the well-developed line geometry of point displacements. The results provided in this paper can help bridge the gap between point and line displacements in both theoretical treatments and practical applications. © Springer Science+Business Media B.V. 2009.