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Linear Pentapods with a Simple Singularity Variety – Part I: Determination and Redundant Designs

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Book cover Advances in Mechanism and Machine Science (IFToMM WC 2019)

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 73))

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Abstract

There exists a bijection between the configuration space of a linear pentapod and all points (u, v, w, px , py , pz) ∈ ℝ6 located on the singular quadric Γ : u 2 + v2 + w2 = 1, where (u, v, w) determines the orientation of the linear platform and (px , py , pz) its position. Then the set of all singular robot configurations is obtained by intersecting Γ with a cubic hypersurface Σ in ℝ6, which is only quadratic in the orientation variables and position variables, respectively. This article investigates the restrictions to be imposed on the design of this mechanism in order to obtain a reduction in degree. In detail we study the cases where Σ is (1) linear in position variables, (2) linear in orientation variables and (3) quadratic in total. Finally we propose three kinematically redundant designs of linear pentapods with a simple singularity surface.

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Acknowledgement

The research is supported by Grant No. P 24927-N25 of the Austrian Science Fund FWF. Moreover the first author is funded by the Doctoral College “Computational Design’’ of Vienna University of Technology.

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Authors and Affiliations

  1. Center for Geometry and Computational Design, Vienna University of Technology, Vienna, Austria

    Arvin Rasoulzadeh & Georg Nawratil

Authors
  1. Arvin Rasoulzadeh
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  2. Georg Nawratil
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Corresponding author

Correspondence to Arvin Rasoulzadeh .

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Editors and Affiliations

  1. Robotics & Machine Dynamics Group, University of Mining and Metallurgy, Kraków, Poland

    Tadeusz Uhl

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Rasoulzadeh, A., Nawratil, G. (2019). Linear Pentapods with a Simple Singularity Variety – Part I: Determination and Redundant Designs. In: Uhl, T. (eds) Advances in Mechanism and Machine Science. IFToMM WC 2019. Mechanisms and Machine Science, vol 73. Springer, Cham. https://doi.org/10.1007/978-3-030-20131-9_69

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