This paper presents a study on the higher-order motion of point-lines embedded on rigid bodies. The mathematic treatment of the paper is based on dual quaternion algebra and differential geometry of line trajectories, which facilitate a concise and unified description of the material in this paper. Due to the unified treatment, the results are directly applicable to line motion as well. The transformation of a point-line between positions is expressed as a unit dual quaternion referred to as the point-line displacement operator depicting a pure translation along the point-line followed by a screw displacement about their common normal. The derivatives of the point-line displacement operator characterize the point-line motion to various orders with a set of characteristic numbers. A set of associated rigid body motions is obtained by applying an instantaneous rotation about the point-line. It shows that the ISA trihedrons of the associated rigid motions can be simply depicted with a set of cylindroids. It also presents for a rigid body motion, the locus of lines and point-lines with common rotation or translation characteristics about the line axes. Lines embedded in a rigid body with uniform screw motion are presented. For a general rigid body motion, one may find lines generating up to the third order uniform screw motion about these lines.
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February 2007
Research Papers
On Higher Order Point-Line and the Associated Rigid Body Motions
Yi Zhang,
Yi Zhang
Research Assistant
Center for Manufacturing Research,
Tennessee Technological University
, Cookeville, TN 38505
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Kwun-Lon Ting
Kwun-Lon Ting
Professor
Center for Manufacturing Research,
e-mail: kting@tntech.edu
Tennessee Technological University
, Cookeville, TN 38505
Search for other works by this author on:
Yi Zhang
Research Assistant
Center for Manufacturing Research,
Tennessee Technological University
, Cookeville, TN 38505
Kwun-Lon Ting
Professor
Center for Manufacturing Research,
Tennessee Technological University
, Cookeville, TN 38505e-mail: kting@tntech.edu
J. Mech. Des. Feb 2007, 129(2): 166-172 (7 pages)
Published Online: January 17, 2006
Article history
Received:
February 15, 2005
Revised:
January 17, 2006
Citation
Zhang, Y., and Ting, K. (January 17, 2006). "On Higher Order Point-Line and the Associated Rigid Body Motions." ASME. J. Mech. Des. February 2007; 129(2): 166–172. https://doi.org/10.1115/1.2406086
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