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Generalized Jacobian analysis of lower mobility manipulators
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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. 831844. ISSN 0094114X

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Official URL: http://dx.doi.org/10.1016/j.mechmachtheory.2011.01...
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 endeffector, 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 endeffector, 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 wellknown 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 
Library of Congress Subject Headings (LCSH):  Manipulators (Mechanism)  Mathematical models, Jacobians 
Journal or Publication Title:  Mechanism and Machine Theory 
Publisher:  Elsevier BV 
ISSN:  0094114X 
Official Date:  June 2011 
Volume:  Vol.46 
Number:  No.6 
Number of Pages:  14 
Page Range:  pp. 831844 
Identification Number:  10.1016/j.mechmachtheory.2011.01.009 
Status:  Peer Reviewed 
Publication Status:  Published 
Access rights to Published version:  Restricted or Subscription Access 
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), 2009ZXO4014021 (NNCKP) 
References:  [1] L.W. Tsai, Robot analysis: the Mechanics of Serial and Parallel Manipulators, New York, John Wiley & Sons, 1999. 
URI:  http://wrap.warwick.ac.uk/id/eprint/41475 
Data sourced from Thomson Reuters' Web of Knowledge
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