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Research Papers

Screw System Approach to Physical Realization of Stiffness Matrix With Arbitrary Rank

[+] Author and Article Information
Man Bok Hong

Department of Mechanical Engineering, Yonsei University, 262 Seongsanno, Seodaemun-gu, Seoul 120-749, Koreacoffeemorphism@gmail.com

Yong Je Choi1

Department of Mechanical Engineering, Yonsei University, 262 Seongsanno, Seodaemun-gu, Seoul 120-749, Koreayjchoi@yonsei.ac.kr

1

Corresponding author.

J. Mechanisms Robotics 1(2), 021007 (Jan 07, 2009) (8 pages) doi:10.1115/1.3046146 History: Received February 22, 2008; Revised October 31, 2008; Published January 07, 2009

It is possible to realize the desired compliance characteristics of a robot in a form of a passive compliance device, which demands the synthesis technique of a stiffness matrix by parallel connections of line and/or torsional springs. In this paper, the stiffness matrix is expressed in terms of the screw coordinates with respect to the basis consisting of its eigenvectors, thereby the synthesis equation is derived. Examination of the numbers of free design parameters involved in the synthesis suggests that a line or free vector for a spring can be freely selected from the induced wrench space depending on the rank of the stiffness matrix. The recursive synthesis method that allows one to select the positions or directions of the springs from the screw system spanned by the induced wrenches of the given stiffness matrix is proposed.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Flowchart of synthesis procedure of the stiffness

Grahic Jump Location
Figure 2

Realization of the given rank 3 stiffness by three line springs

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