Forward displacement analysis of a quadratic planar parallel manipulator

3-RPR parallel manipulator with similar triangular platforms

Xianwen Kong, Clement M. Gosselin

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A quadratic parallel manipulator refers to a parallel manipulator with a quadratic characteristic polynomial. This paper revisits the forward displacement analysis (FDA) of a quadratic parallel manipulator: 3-RPR planar parallel manipulator with similar triangular platforms. Although it has been revealed numerically elsewhere that for this parallel manipulator, the four solutions to the FDA fall, respectively, into its four singularity-free regions (in its workspace), it is unclear if there exists a one-to-one correspondence between the four formulas, each producing one solution to the FDA, and the four singularity-free regions. This paper will prove that such a one-to-one correspondence exists. Therefore, a unique solution to the FDA can be obtained in a straightforward way for such a parallel manipulator if the singularity-tree region in which it works is specified. Copyright © 2008 by ASME.

Original languageEnglish
Title of host publication2008 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC 2008
Pages1151-1158
Number of pages8
Volume2
EditionPART B
Publication statusPublished - 2009
Event2008 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - New York City, NY, United States
Duration: 3 Aug 20086 Aug 2008

Conference

Conference2008 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
Abbreviated titleDETC 2008
CountryUnited States
CityNew York City, NY
Period3/08/086/08/08

Fingerprint

Manipulators
Polynomials

Cite this

Kong, X., & Gosselin, C. M. (2009). Forward displacement analysis of a quadratic planar parallel manipulator: 3-RPR parallel manipulator with similar triangular platforms. In 2008 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC 2008 (PART B ed., Vol. 2, pp. 1151-1158)
Kong, Xianwen ; Gosselin, Clement M. / Forward displacement analysis of a quadratic planar parallel manipulator : 3-RPR parallel manipulator with similar triangular platforms. 2008 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC 2008. Vol. 2 PART B. ed. 2009. pp. 1151-1158
@inproceedings{584c1471d262468a98b3a495cddb1d3c,
title = "Forward displacement analysis of a quadratic planar parallel manipulator: 3-RPR parallel manipulator with similar triangular platforms",
abstract = "A quadratic parallel manipulator refers to a parallel manipulator with a quadratic characteristic polynomial. This paper revisits the forward displacement analysis (FDA) of a quadratic parallel manipulator: 3-RPR planar parallel manipulator with similar triangular platforms. Although it has been revealed numerically elsewhere that for this parallel manipulator, the four solutions to the FDA fall, respectively, into its four singularity-free regions (in its workspace), it is unclear if there exists a one-to-one correspondence between the four formulas, each producing one solution to the FDA, and the four singularity-free regions. This paper will prove that such a one-to-one correspondence exists. Therefore, a unique solution to the FDA can be obtained in a straightforward way for such a parallel manipulator if the singularity-tree region in which it works is specified. Copyright {\circledC} 2008 by ASME.",
author = "Xianwen Kong and Gosselin, {Clement M.}",
year = "2009",
language = "English",
isbn = "9780791843253",
volume = "2",
pages = "1151--1158",
booktitle = "2008 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC 2008",
edition = "PART B",

}

Kong, X & Gosselin, CM 2009, Forward displacement analysis of a quadratic planar parallel manipulator: 3-RPR parallel manipulator with similar triangular platforms. in 2008 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC 2008. PART B edn, vol. 2, pp. 1151-1158, 2008 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, New York City, NY, United States, 3/08/08.

Forward displacement analysis of a quadratic planar parallel manipulator : 3-RPR parallel manipulator with similar triangular platforms. / Kong, Xianwen; Gosselin, Clement M.

2008 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC 2008. Vol. 2 PART B. ed. 2009. p. 1151-1158.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

TY - GEN

T1 - Forward displacement analysis of a quadratic planar parallel manipulator

T2 - 3-RPR parallel manipulator with similar triangular platforms

AU - Kong, Xianwen

AU - Gosselin, Clement M.

PY - 2009

Y1 - 2009

N2 - A quadratic parallel manipulator refers to a parallel manipulator with a quadratic characteristic polynomial. This paper revisits the forward displacement analysis (FDA) of a quadratic parallel manipulator: 3-RPR planar parallel manipulator with similar triangular platforms. Although it has been revealed numerically elsewhere that for this parallel manipulator, the four solutions to the FDA fall, respectively, into its four singularity-free regions (in its workspace), it is unclear if there exists a one-to-one correspondence between the four formulas, each producing one solution to the FDA, and the four singularity-free regions. This paper will prove that such a one-to-one correspondence exists. Therefore, a unique solution to the FDA can be obtained in a straightforward way for such a parallel manipulator if the singularity-tree region in which it works is specified. Copyright © 2008 by ASME.

AB - A quadratic parallel manipulator refers to a parallel manipulator with a quadratic characteristic polynomial. This paper revisits the forward displacement analysis (FDA) of a quadratic parallel manipulator: 3-RPR planar parallel manipulator with similar triangular platforms. Although it has been revealed numerically elsewhere that for this parallel manipulator, the four solutions to the FDA fall, respectively, into its four singularity-free regions (in its workspace), it is unclear if there exists a one-to-one correspondence between the four formulas, each producing one solution to the FDA, and the four singularity-free regions. This paper will prove that such a one-to-one correspondence exists. Therefore, a unique solution to the FDA can be obtained in a straightforward way for such a parallel manipulator if the singularity-tree region in which it works is specified. Copyright © 2008 by ASME.

UR - http://www.scopus.com/inward/record.url?scp=69949132133&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9780791843253

SN - 9780791843260

VL - 2

SP - 1151

EP - 1158

BT - 2008 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC 2008

ER -

Kong X, Gosselin CM. Forward displacement analysis of a quadratic planar parallel manipulator: 3-RPR parallel manipulator with similar triangular platforms. In 2008 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC 2008. PART B ed. Vol. 2. 2009. p. 1151-1158