Huang, Tian, Liu, H. T. and Chetwynd, D. G. (2011) Generalized Jacobian analysis of lower mobility manipulators. Mechanism and Machine Theory, Vol.46 (No.6). pp. 831-844. doi:10.1016/j.mechmachtheory.2011.01.009 ISSN 0094-114X.

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Abstract

Mainly drawing on screw theory and linear algebra, this paper presents a general approach for Jacobian analysis of lower mobility manipulators. Given the definitions of twist/wrench spaces and their subspaces of the end-effector, the underlying relationships amongst these subspaces are identified using the virtual work principle. Using the orthogonal and dual properties of these subspaces and variational representation to account for the permitted and restricted instantaneous motions of the end-effector, a general and systematic procedure for the formulation of a generalized Jacobian is proposed. The merit of the generalized Jacobian allows the first order kinematic and static modeling (velocity, accuracy, force and
stiffness) to be integrated into a unified mathematical framework. The generalized Jacobians for three well-known parallel manipulators are derived as examples to illustrate generality and effectiveness of this approach.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics T Technology > TJ Mechanical engineering and machinery
Divisions:	Faculty of Science, Engineering and Medicine > Engineering > Engineering
Library of Congress Subject Headings (LCSH):	Manipulators (Mechanism) -- Mathematical models, Jacobians
Journal or Publication Title:	Mechanism and Machine Theory
Publisher:	Elsevier BV
ISSN:	0094-114X
Official Date:	June 2011
Dates:	Date Event June 2011 Published
Volume:	Vol.46
Number:	No.6
Number of Pages:	14
Page Range:	pp. 831-844
DOI:	10.1016/j.mechmachtheory.2011.01.009
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	19 December 2015
Date of first compliant Open Access:	19 December 2015
Funder:	Guo jia zi ran ke xue ji jin wei yuan hui (China) [National Natural Science Foundation of China] (NSFC), National NC Key Program
Grant number:	50535010 (NSFC), 50775158 (NSFC), 2009ZXO4014-021 (NNCKP)

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