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A Geometric Modeling and Computing Method for Direct Kinematic Analysis of 6-4 Stewart Platforms
Joint Authors
Wei, Shimin
Zhang, Ying
Liu, Xin
Wang, Yaobing
Zhang, Xiaodong
Zhang, Pei
Liang, Changchun
Source
Mathematical Problems in Engineering
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-02-26
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
A geometric modeling and solution procedure for direct kinematic analysis of 6-4 Stewart platforms with any link parameters is proposed based on conformal geometric algebra (CGA).
Firstly, the positions of the two single spherical joints on the moving platform are formulated by the intersection, dissection, and dual of the basic entities under the frame of CGA.
Secondly, a coordinate-invariant equation is derived via CGA operation in the positions of the other two pairwise spherical joints.
Thirdly, the other five equations are formulated in terms of geometric constraints.
Fourthly, a 32-degree univariate polynomial equation is reduced from a constructed 7 by 7 matrix which is relatively small in size by using a Gröbner-Sylvester hybrid method.
Finally, a numerical example is employed to verify the solution procedure.
The novelty of the paper lies in that (1) the formulation is concise and coordinate-invariant and has intrinsic geometric intuition due to the use of CGA and (2) the size of the resultant matrix is smaller than those existed.
American Psychological Association (APA)
Zhang, Ying& Liu, Xin& Wei, Shimin& Wang, Yaobing& Zhang, Xiaodong& Zhang, Pei…[et al.]. 2018. A Geometric Modeling and Computing Method for Direct Kinematic Analysis of 6-4 Stewart Platforms. Mathematical Problems in Engineering،Vol. 2018, no. 2018, pp.1-9.
https://search.emarefa.net/detail/BIM-1208283
Modern Language Association (MLA)
Zhang, Ying…[et al.]. A Geometric Modeling and Computing Method for Direct Kinematic Analysis of 6-4 Stewart Platforms. Mathematical Problems in Engineering No. 2018 (2018), pp.1-9.
https://search.emarefa.net/detail/BIM-1208283
American Medical Association (AMA)
Zhang, Ying& Liu, Xin& Wei, Shimin& Wang, Yaobing& Zhang, Xiaodong& Zhang, Pei…[et al.]. A Geometric Modeling and Computing Method for Direct Kinematic Analysis of 6-4 Stewart Platforms. Mathematical Problems in Engineering. 2018. Vol. 2018, no. 2018, pp.1-9.
https://search.emarefa.net/detail/BIM-1208283
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1208283