RESEARCH PAPERS: Mechanisms Papers

On a Set of Displacements in Space

[+] Author and Article Information
O. Bottema

Department of Mathematics, Technological University of Delft, Delft, The Netherlands

J. Eng. Ind 95(2), 451-454 (May 01, 1973) (4 pages) doi:10.1115/1.3438176 History: Received June 22, 1972; Online July 15, 2010


In this paper we study sets of screw displacements in three-dimensional space when the displacements are not uniquely specified. The two cases considered are displacements which transform a row of points onto a congruent row of points, and displacements which transform a line onto a line. In the first case the locus of all screw axes is shown to be a regulus which is either cubic (a cylindroid) or quadratic (a hyperbolic paraboloid), depending upon, respectively, if the displacement is direct or indirect (a reflection). In the second case the locus of screw axes is shown to be a line congruence of order 3 and class 1.

Copyright © 1973 by ASME
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