Screw system approach to physical realization of stiffness matrix with arbitrary rank

Man Bok Hong, Yong Je Choi

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1-8
Number of pages8
JournalJournal of Mechanisms and Robotics
Volume1
Issue number2
DOIs
Publication statusPublished - 2009 May 1

Fingerprint

Stiffness matrix
Hand tools
Eigenvalues and eigenfunctions
Robots
Compliance

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering

Cite this

@article{34a74bca19d34318b9059ee555d80b19,
title = "Screw system approach to physical realization of stiffness matrix with arbitrary rank",
abstract = "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.",
author = "Hong, {Man Bok} and Choi, {Yong Je}",
year = "2009",
month = "5",
day = "1",
doi = "10.1115/1.3046146",
language = "English",
volume = "1",
pages = "1--8",
journal = "Journal of Mechanisms and Robotics",
issn = "1942-4302",
publisher = "American Society of Mechanical Engineers(ASME)",
number = "2",

}

Screw system approach to physical realization of stiffness matrix with arbitrary rank. / Hong, Man Bok; Choi, Yong Je.

In: Journal of Mechanisms and Robotics, Vol. 1, No. 2, 01.05.2009, p. 1-8.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Screw system approach to physical realization of stiffness matrix with arbitrary rank

AU - Hong, Man Bok

AU - Choi, Yong Je

PY - 2009/5/1

Y1 - 2009/5/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=78651595564&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78651595564&partnerID=8YFLogxK

U2 - 10.1115/1.3046146

DO - 10.1115/1.3046146

M3 - Article

VL - 1

SP - 1

EP - 8

JO - Journal of Mechanisms and Robotics

JF - Journal of Mechanisms and Robotics

SN - 1942-4302

IS - 2

ER -