Linear Pentapods with a Simple Singularity Variety – Part II: Computation of Singularity-Free Balls

  • Arvin RasoulzadehEmail author
  • Georg Nawratil
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)


The configuration space of a linear pentapod can be defined as the set of all points (u, v, w, px , py , pz) 6 located on the singular quadric Γ : u 2 + v2 + w2 = 1, where (u, v, w) determines determines the orientation of the linear platform and (px , py , pz) its position. In such terminology, 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. We study the computational aspects of the determination of singularity-free balls under the design restrictions that Σ is either (1) linear in position variables or (2) linear in orientation variables. It turns out that for these pentapod designs the computation of singularity-free balls in the configuration space simplifies considerably. One can even obtain a closed form solution, which is paving the way for a real-time singularity-free path planning/optimization in the configuration space.


Linear pentapods Distance computation Singularity-free balls 


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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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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Center for Geometry and Computational DesignVienna University of TechnologyViennaAustria

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