Mechanisms generating line trajectories

Abstract

In this work the problem of designing mechanisms to guide a line along a ruled surface is considered. This is motivated by the idea of illustrating, by means of a physical model, the set of lines in a general linear line complex. Cylindrical symmetry implies that the problem reduces of designing a mechanism to move a line along the regulus of a rectangular hyperbolic paraboloid. This leads to the study of several simple ruled surfaces and congruences of lines. In particular the paper studies the regulus of the elliptical hyperboloid, the cylindroid and linear line congruences. In each case relatively simple mechanisms are designed to constrain a line in the mechanism to a given space of lines.