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An approach to determining the unknown twist/wrench subspaces of lower mobility serial kinematic chains

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Huang, Tian, Yang, Shuofei, Wang, Manxin, Sun, Tao and Chetwynd, D. G. (2015) An approach to determining the unknown twist/wrench subspaces of lower mobility serial kinematic chains. Journal of Mechanisms and Robotics, 7 (3). 031003. doi:10.1115/1.4028622 ISSN 1942-4302.

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Official URL: http://dx.doi.org/10.1115/1.4028622

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Abstract

Mainly drawing on screw theory and linear algebra, this paper presents an approach to determining the bases of three unknown twist and wrench subspaces of lower mobility serial kinematic chains, an essential step for kinematic and dynamic modeling of both serial and parallel manipulators. By taking the reciprocal product of a wrench on a twist as a linear functional, the underlying relationships among their subspaces are reviewed by means of the dual space and dual basis. Given the basis of a twist subspace of permissions, the causes of nonuniqueness in the bases of the other three subspaces are discussed in some depth. Driven by needs from engineering design, criteria, and a procedure are proposed that enable pragmatic, consistent bases of these subspaces to be determined in a meaningful, visualizable, and effective manner. Three typical examples are given to illustrate the entire process. Then, formulas are presented for the bases of the twist/wrench subspaces of a number of commonly used serial kinematic chains, which can readily be employed for the formulation of the generalized Jacobian of a variety of lower mobility parallel manipulators.

Item Type: Journal Article
Divisions: Faculty of Science, Engineering and Medicine > Engineering > Engineering
Journal or Publication Title: Journal of Mechanisms and Robotics
Publisher: A S M E International
ISSN: 1942-4302
Official Date: 1 August 2015
Dates:
DateEvent
1 August 2015Published
4 December 2014Available
5 March 2013Submitted
Volume: 7
Number: 3
Article Number: 031003
DOI: 10.1115/1.4028622
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

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