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Research Papers: Mechanisms and Robotics

A Geometric Interpretation of Finite Screw Systems Using the Bisecting Linear Line Complex

[+] Author and Article Information
Chintien Huang

Department of Mechanical Engineering, National Cheng Kung University, No. 1 University Road, Tainan City 70101, Taiwan, R.O.C.chuang@mail.ncku.edu.tw

Bahram Ravani

Department of Mechanical and Aeronautical Engineering, University of California, Davis, 1 Shields Avenue, Davis, CA 95616

Wuchang Kuo

Department of Mechanical Engineering, National Cheng Kung University, No. 1 University Road, Tainan City 70101, Taiwan, R.O.C.

J. Mech. Des 130(10), 102303 (Sep 09, 2008) (5 pages) doi:10.1115/1.2965362 History: Received February 20, 2007; Revised May 28, 2008; Published September 09, 2008

This paper uses the concept of bisecting linear line complex of the two position theory in kinematics to present a geometric foundation for finite displacement screw systems, with an emphasis on incompletely specified displacement of points. It is shown that the bisecting linear line complex arising from the finite displacement of points is subject to a reciprocal condition if a specific definition of pitch of finite screws is used. The screw systems of finite displacements are then characterized in terms of intersections of bisecting linear line complexes. The line varieties corresponding to the two-system and four-system associated with finite displacements of two points and a point, respectively, are illustrated. This paper demonstrates that the bisecting linear line complex provides a geometric framework for studying finite and infinitesimal kinematics.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

LLC of an instantaneous screw

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Figure 2

Bisecting LLC of a finite displacement screw

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Figure 3

The displacement of two points

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Figure 4

The linear congruence of a two-point displacement

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