Characterization and Coordination of Point-line Trajectories

[+] Author and Article Information
Kwun-Lon Ting

Professorkting@tntech.eduResearch Assistantkting@tntech.eduResearch Assistantkting@tntech.eduCenter for Manufacturing Research,  Tennessee Technological University, Cookville, TN 38505kting@tntech.edu

Yi Zhang, Ruj Bunduwongse

ProfessorResearch AssistantResearch AssistantCenter for Manufacturing Research,  Tennessee Technological University, Cookville, TN 38505

J. Mech. Des 127(3), 502-505 (Jul 08, 2004) (4 pages) doi:10.1115/1.1867504 History: Received March 18, 2004; Revised July 08, 2004

A point-line refers to a rigid combination of a directed line and an endpoint along the line. To trace a point-line trajectory, one must control not only the trajectory of the endpoint (the directrix) but also the direction of the point-line (the indicatrix). This paper addresses three issues on point-line trajectories. First of all, by considering the relationship between the point trajectory and the corresponding point-line direction, it offers the complete characterization of point-line trajectories. It presents the coordination of the point-line axis with a free point trajectory and also with a point trajectory constrained on a free form surface. The issue of maintaining an invariant orientation relationship between the point-line axis and the point trajectory is also addressed.

Copyright © 2005 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Trihedrons {R} and {T}, and the geodesic angle

Grahic Jump Location
Figure 2

A point-line trajectory on a surface



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