TY - JOUR

T1 - Forward displacement analysis of a quadratic planar parallel manipulator

T2 - 3-RPR parallel manipulator with similar triangular platforms

AU - Kong, Xianwen

AU - Gosselin, Clément M.

PY - 2009/5

Y1 - 2009/5

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 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.

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 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.

KW - Forward displacement analysis

KW - Parallel mechanism

KW - Quadratic parallel manipulator

KW - Singularity

UR - http://www.scopus.com/inward/record.url?scp=78651581361&partnerID=8YFLogxK

U2 - 10.1115/1.3046180

DO - 10.1115/1.3046180

M3 - Article

VL - 1

SP - 1

EP - 3

JO - Journal of Mechanisms and Robotics

JF - Journal of Mechanisms and Robotics

SN - 1942-4302

IS - 2

ER -