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Technical Briefs

A Note on the Screw Triangle

[+] Author and Article Information
David Zarrouk

Robotics Laboratory, Department of Mechanical Engineering, Technion–Israel Institute of Technology, Haifa 32000, Israelzadavid@tx.technion.ac.il

Moshe Shoham

Robotics Laboratory, Department of Mechanical Engineering, Technion–Israel Institute of Technology, Haifa 32000, Israelshoham@technion.ac.il

J. Mechanisms Robotics 3(1), 014502 (Jan 06, 2011) (4 pages) doi:10.1115/1.4002943 History: Received November 21, 2009; Revised October 24, 2010; Published January 06, 2011; Online January 06, 2011

This paper derives the expressions of an equivalent finite screw of two successive screw motions in a simplified form using purely vectorial analysis. This is achieved by tracing the trajectories of specific points on the moving body, which together with the known axis and angle of combined rotation, yield the expressions of the screw triangle. This paper also gives a short overview of different known expressions of the screw triangle and shows that the one given in this paper reduces the number of arithmetic operations by about a third compared with the most efficient algorithm in the literature.

FIGURES IN THIS ARTICLE
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Copyright © 2011 by American Society of Mechanical Engineers
Topics: Screws
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References

Figures

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Figure 1

The screw triangle: Sij is screw ij(i,j=1,2,3,i≠j), Ni is common perpendicular of screw Sij axis, and tij and θij are translation along and rotation about Sij

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Figure 2

The equivalent screw for given rotation and translation of a rigid body

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Figure 3

The path traveled by a23′

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Figure 4

The path traveled by a12′

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