In the two position theory of finite kinematics, we are concerned with not only the displacement of a rigid body, but also with the displacement of a certain element of the body. This paper deals with the displacement of a line and reveals the regulus that characterizes such a displacement. Residing on a special hyperbolic paraboloid, the regulus is obtained by the intersection of three linear line complexes corresponding to a specific set of basis screws of a 3-system. The degeneration of the regulus when two positions of a line intersect is also discussed. In this paper, the regulus of intersection is obtained geometrically as well as analytically. The discovery of the regulus lays a geometric foundation for dealing with line-based problems in computational kinematics and computational line geometry.
- Design Engineering Division and Computers and Information in Engineering Division
On the Regulus Associated With the General Displacement of a Line
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Huang, C, Kuo, W, & Ravani, B. "On the Regulus Associated With the General Displacement of a Line." Proceedings of the ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 8: 31st Mechanisms and Robotics Conference, Parts A and B. Las Vegas, Nevada, USA. September 4–7, 2007. pp. 1299-1304. ASME. https://doi.org/10.1115/DETC2007-35765
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