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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. 831-844. doi:10.1016/j.mechmachtheory.2011.01.009
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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 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 |
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| 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: | 0094-114X | ||||
| Official Date: | June 2011 | ||||
| Dates: |
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| 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 | ||||
| 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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