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

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


There exists a bijection between the configuration space of a linear pentapod and 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 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.


Linear pentapods Singularity variety Design Kinematic redundancy 


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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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