Statics, Instantaneous Kinematics and Singularity Analysis of Planar Parallel Manipulators via Grassmann-Cayley Algebra

Ke Fei Wen; Jeh Won Lee

doi:10.4028/www.scientific.net/AMM.532.378

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vol. 532Statics, Instantaneous Kinematics and Singularity...

Statics, Instantaneous Kinematics and Singularity Analysis of Planar Parallel Manipulators via Grassmann-Cayley Algebra

Abstract:

The wrench Jacobian matrix plays an important role in statics and singularity analysis of planar parallel manipulators (PPMs). It is easy to obtain this matrix based on plücker coordinate method. In this paper, a new approach is proposed to the analysis of the forward and inverse wrench Jacobian matrix used by Grassmann-Cayley algebra (GCA). A symbolic formula for the inverse statics and a coordinate free formula for the singularity analysis are obtained based on this Jacobian. As an example, this approach is implemented for the 3-RPR PPMs.

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Periodical:

Applied Mechanics and Materials (Volume 532)

Pages:

378-381

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.532.378

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Online since:

February 2014

Authors:

Ke Fei Wen, Jeh Won Lee*

Keywords:

Grassmann-Cayley Algebra, Planar Parallel Manipulators, Plücker Coordinates

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