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Parallel Manipulators in Terms of Dual Cayley-Klein Parameters

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Computational Kinematics

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 50))

Abstract

Cayley-Klein parameters are an alternative to Euler parameters for describing the spherical motion group. Based on Study’s and Kotelnikov’s “Principle of Transference” one can use dual Cayley-Klein parameters for the motion study of oriented lines in Euclidean 3-space. In this paper we focus on the transformation of points in terms of dual Cayley-Klein parameters and show that these parameters imply a very compact symbolic expression of the sphere condition, which is the central equation for computational algebraic kinematics of parallel manipulators of Stewart-Gough type. Moreover it is shown that the compactness of this formulation is passed on to the symbolic expression of the singularity loci. We also adopt our results to the analogue in planar kinematics and point out the difference to the well-known approach of isotropic coordinates.

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Acknowledgements

The author is supported by Grant No. P 24927-N25 of the Austrian Science Fund FWF within the project “Stewart Gough platforms with self-motions”.

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Authors and Affiliations

  1. Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Vienna, Austria

    G. Nawratil

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  1. G. Nawratil
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Correspondence to G. Nawratil .

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Editors and Affiliations

  1. Institut PPRIME, UPR 3346, University of Poitiers, Poitiers, France

    Saïd Zeghloul

  2. American University of Sharjah, UAE, on leave from the National School of Engineering of Sousse , Sousse Erriadh, Tunisia

    Lotfi Romdhane

  3. SP2MI, Téléport 2, University of Poitiers, Poitiers, France

    Med Amine Laribi

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Nawratil, G. (2018). Parallel Manipulators in Terms of Dual Cayley-Klein Parameters. In: Zeghloul, S., Romdhane, L., Laribi, M. (eds) Computational Kinematics. Mechanisms and Machine Science, vol 50. Springer, Cham. https://doi.org/10.1007/978-3-319-60867-9_30

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  • DOI: https://doi.org/10.1007/978-3-319-60867-9_30

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-60866-2

  • Online ISBN: 978-3-319-60867-9

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