Forward displacement analysis of the general 6-6 Stewart mechanism using Gröbner bases

Dongming Gan; Qizheng Liao; Jian S. Dai; Shimin Wei; L. D. Seneviratne

doi:10.1016/j.mechmachtheory.2009.01.008

Forward displacement analysis of the general 6-6 Stewart mechanism using Gröbner bases

Dongming Gan
, Qizheng Liao
, Jian S. Dai
, Shimin Wei
, L. D. Seneviratne

Mechanical & Nuclear Engineering

Research output: Contribution to journal › Article › peer-review

72 Scopus citations

Abstract

A new algorithm for the solution of the forward displacement analysis of the general 6-6 Stewart mechanism is presented in this paper. Gröbner basis theory is used and the problem of the forward displacement is reduced to a 40th-degree polynomial equation in a single unknown from a constructed 13 × 13 Sylvester's matrix which is relatively small in the size, from which 40 different locations of the moving platform can be derived. Numerical examples confirm the efficiency of the procedure.

Original language	British English
Pages (from-to)	1640-1647
Number of pages	8
Journal	Mechanism and Machine Theory
Volume	44
Issue number	9
DOIs	https://doi.org/10.1016/j.mechmachtheory.2009.01.008
State	Published - Sep 2009

Keywords

Forward displacement analysis
General 6-6 Stewart mechanism
Gröbner basis

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10.1016/j.mechmachtheory.2009.01.008

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title = "Forward displacement analysis of the general 6-6 Stewart mechanism using Gr{\"o}bner bases",

abstract = "A new algorithm for the solution of the forward displacement analysis of the general 6-6 Stewart mechanism is presented in this paper. Gr{\"o}bner basis theory is used and the problem of the forward displacement is reduced to a 40th-degree polynomial equation in a single unknown from a constructed 13 × 13 Sylvester's matrix which is relatively small in the size, from which 40 different locations of the moving platform can be derived. Numerical examples confirm the efficiency of the procedure.",

keywords = "Forward displacement analysis, General 6-6 Stewart mechanism, Gr{\"o}bner basis",

author = "Dongming Gan and Qizheng Liao and Dai, \{Jian S.\} and Shimin Wei and Seneviratne, \{L. D.\}",

note = "Funding Information: This work is partially supported by a National Key Basic Research Project of China (2004CB318000), partially supported by National Natural Science Foundation of China (50775012).",

year = "2009",

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doi = "10.1016/j.mechmachtheory.2009.01.008",

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volume = "44",

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journal = "Mechanism and Machine Theory",

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T1 - Forward displacement analysis of the general 6-6 Stewart mechanism using Gröbner bases

AU - Gan, Dongming

AU - Liao, Qizheng

AU - Dai, Jian S.

AU - Wei, Shimin

AU - Seneviratne, L. D.

N1 - Funding Information: This work is partially supported by a National Key Basic Research Project of China (2004CB318000), partially supported by National Natural Science Foundation of China (50775012).

PY - 2009/9

Y1 - 2009/9

N2 - A new algorithm for the solution of the forward displacement analysis of the general 6-6 Stewart mechanism is presented in this paper. Gröbner basis theory is used and the problem of the forward displacement is reduced to a 40th-degree polynomial equation in a single unknown from a constructed 13 × 13 Sylvester's matrix which is relatively small in the size, from which 40 different locations of the moving platform can be derived. Numerical examples confirm the efficiency of the procedure.

AB - A new algorithm for the solution of the forward displacement analysis of the general 6-6 Stewart mechanism is presented in this paper. Gröbner basis theory is used and the problem of the forward displacement is reduced to a 40th-degree polynomial equation in a single unknown from a constructed 13 × 13 Sylvester's matrix which is relatively small in the size, from which 40 different locations of the moving platform can be derived. Numerical examples confirm the efficiency of the procedure.

KW - Forward displacement analysis

KW - General 6-6 Stewart mechanism

KW - Gröbner basis

UR - https://www.scopus.com/pages/publications/67349285399

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DO - 10.1016/j.mechmachtheory.2009.01.008

M3 - Article

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SN - 0094-114X

VL - 44

SP - 1640

EP - 1647

JO - Mechanism and Machine Theory

JF - Mechanism and Machine Theory

IS - 9

ER -

Forward displacement analysis of the general 6-6 Stewart mechanism using Gröbner bases

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Keywords

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