Forward Displacement Analysis of a Quadratic Planar Parallel Manipulator: 3-RPR Parallel Manipulator With Similar Triangular Platforms 1

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-RP̱R 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. 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.

Related Papers

• → Singularity of a novel five-DOF parallel manipulator(2010)2 cited
• Current status of workspace in parallel manipulator research(2004)
• → Workspace Investigation of a Novel Parallel Manipulator(2009)1 cited
• STUDY OF WORKSPACE IN PARALLEL ROBOT MANIPULATOR(1991)
• → Workspace Optimal Design of Parallel Mechanisms Reflecting the Singularity Locations(2012)