### 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 language | English |
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Title of host publication | 2008 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC 2008 |

Pages | 1151-1158 |

Number of pages | 8 |

Volume | 2 |

Edition | PART B |

Publication status | Published - 2009 |

Event | 2008 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - New York City, NY, United States Duration: 3 Aug 2008 → 6 Aug 2008 |

### Conference

Conference | 2008 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference |
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Abbreviated title | DETC 2008 |

Country | United States |

City | New York City, NY |

Period | 3/08/08 → 6/08/08 |

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### Cite this

*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)

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*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 -