Forward displacement analysis of a quadratic planar parallel manipulator: 3-RPR parallel manipulator with similar triangular platforms

Xianwen Kong, Clément M. Gosselin

Research output: Contribution to journalArticle

9 Citations (Scopus)

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 else where 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. Using an algebraic approach, 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-free region in which it works is specified. © 2009 by ASME.

Original languageEnglish
Pages (from-to)1-3
Number of pages3
JournalJournal of Mechanisms and Robotics
Volume1
Issue number2
DOIs
Publication statusPublished - May 2009

Keywords

  • Forward displacement analysis
  • Parallel mechanism
  • Quadratic parallel manipulator
  • Singularity

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