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

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

Centre for Robotics Research

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

64 Citations (Scopus)

Abstract

A new algorithm for the solution of the forward displacement analysis of the general 6-6 Stewart mechanism is presented in this paper. Grobner 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 x 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. (C) 2009 Elsevier Ltd. All rights reserved.

Original language	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
Publication status	Published - Sept 2009

Access to Document

10.1016/j.mechmachtheory.2009.01.008

Cite this

@article{360178ae92024b03b8674284b30c9c16,

title = "Forward displacement analysis of the general 6-6 Stewart mechanism using Grobner 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. Grobner 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 x 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. (C) 2009 Elsevier Ltd. All rights reserved.",

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

year = "2009",

month = sep,

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

language = "English",

volume = "44",

pages = "1640 -- 1647",

journal = "Mechanism and Machine Theory",

publisher = "Elsevier",

number = "9",

}

TY - JOUR

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

AU - Gan, Dongming

AU - Liao, Qizheng

AU - Dai, Jian S.

AU - Wei, Shimin

AU - Seneviratne, L. D.

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. Grobner 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 x 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. (C) 2009 Elsevier Ltd. All rights reserved.

AB - A new algorithm for the solution of the forward displacement analysis of the general 6-6 Stewart mechanism is presented in this paper. Grobner 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 x 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. (C) 2009 Elsevier Ltd. All rights reserved.

U2 - 10.1016/j.mechmachtheory.2009.01.008

DO - 10.1016/j.mechmachtheory.2009.01.008

M3 - Article

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 Grobner bases

Abstract

Access to Document

Fingerprint

Cite this