Research Papers

On the Regulus Associated With the General Displacement of a Line and Its Application in Determining Displacement Screws

[+] Author and Article Information
Chintien Huang

Department of Mechanical Engineering, National Cheng Kung University, Tainan 701, Taiwanchuang@mail.ncku.edu.tw

Wuchang Kuo

Department of Mechanical Engineering, Hsiuping Institute of Technology, Taichung 412, Taiwan

Bahram Ravani

Department of Mechanical and Aeronautical Engineering, University of California at Davis, Davis, CA 95616

J. Mechanisms Robotics 2(4), 041013 (Oct 14, 2010) (6 pages) doi:10.1115/1.4001729 History: Received November 21, 2008; Revised December 18, 2009; Published October 14, 2010; Online October 14, 2010

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 unveils the regulus that corresponds to such a displacement. The regulus is then used as a basic entity to determine the displacements of a rigid body from line specifications. 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 three-system. When determining the displacements of a rigid body from line specifications, a displacement screw is obtained by fitting a linear line complex to two or more line reguli. When two exact pairs of homologous lines are specified, we obtain a unique linear line complex, which determines the corresponding displacement screw. When more than two pairs of homologous lines with measurement errors are specified, it becomes a redundantly specified problem, and a linear line complex that has the best fit to more than two reguli is determined.

Copyright © 2010 by American Society of Mechanical Engineers
Topics: Screws , Displacement
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Figure 1

The LLC and nullplanes of homologous lines

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Figure 2

The screw system associated with the displacement of a line

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Figure 3

The LLCs corresponding to the basis screws

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Figure 4

The congruence of intersection of SB1 and SB2

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Figure 5

The regulus of the intersection of SB1, SB2, and SB3

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Figure 6

Degeneration of the regulus when t is close to zero

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Figure 7

A displacement with two line elements specified

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Figure 8

A redundantly specified displacement problem

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Figure 9

The deviation between calculated and specified lines after a displacement




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