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Inverse statics analysis of planar parallel manipulators via Grassmann-Cayley algebra

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Abstract

The wrench Jacobian matrix plays an important role in the statics and singularity analysis of planar parallel manipulators (PPMs). The Jacobian matrix can be calculated based on the conventional Plücker coordinate method. However, this method cannot be applied when two links are in parallel. A new approach is proposed for the analysis of the forward and inverse wrench Jacobian matrix using Grassmann-Cayley algebra (GCA). A symbolic formula for the inverse statics analysis is obtained based on the Jacobian. The proposed method can be applied when two links are in parallel. The approach is explained in detail based on a planar 3-RPR PPM example, and the analysis procedure for nine other PPMs is also presented. This novel approach to deriving the statics can be applied to spatial parallel manipulators and redundant cases of PPMs.

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Authors and Affiliations

  1. School of Mechanical Engineering, Yeungnam University, 280 Daehak-ro, Gyeongsan, Gyeongbuk, 712-749, Korea

    Kefei Wen, Jeh Won Lee & TaeWon Seo

Authors
  1. Kefei Wen
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  2. Jeh Won Lee
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  3. TaeWon Seo
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Corresponding authors

Correspondence to Jeh Won Lee or TaeWon Seo.

Additional information

Recommended by Editor Fuchun Sun. This study was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2014R1A1A4A01009290).

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Wen, K., Lee, J.W. & Seo, T. Inverse statics analysis of planar parallel manipulators via Grassmann-Cayley algebra. Int. J. Control Autom. Syst. 14, 1389–1394 (2016). https://doi.org/10.1007/s12555-014-0471-z

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  • DOI: https://doi.org/10.1007/s12555-014-0471-z

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