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Kinematic Analysis of Active Ankle Using Computational Algebraic Geometry

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


Active Ankle is a novel 3 DoF parallel mechanism which works in an almost spherical manner. Its geometry provides various advantages like good stress distribution, low link diversity and robust construction. Determining all the solutions to the direct kinematics problem is an important and challenging step in kinematic analysis of any newly invented parallel manipulator due to the coupled nature of the constraint equations. In this paper, we make use of powerful methods in computational algebraic geometry to provide a rational univariate representation of direct kinematics solution in the form of a \(40^\circ \) univariate polynomial. In the presented analysis, up to 16 real solutions of the direct kinematics problem for this mechanism have been obtained. In addition, the results of its torsional motion analysis are presented and singularities of the mechanism are highlighted during this motion. Also, the assembly modes where this mechanism behaves as an almost-spherical device are identified, which is the main contribution of the paper.


  • Parallel manipulator
  • Kinematic analysis
  • Direct kinematics
  • Algebraic geometry

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  • DOI: 10.1007/978-3-319-60867-9_14
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The work presented in this paper was performed within the project Recupera-Reha, funded by the German Aerospace Center (DLR) with federal funds from the Federal Ministry of Education and Research (BMBF) (Grant 01-IM-14006A). The fourth author acknowledges that this work has been partially supported by the Austrian COMET-K2 program of the Linz Center of Mechatronics (LCM).

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Correspondence to Shivesh Kumar .

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Kumar, S., Nayak, A., Bongardt, B., Mueller, A., Kirchner, F. (2018). Kinematic Analysis of Active Ankle Using Computational Algebraic Geometry. In: Zeghloul, S., Romdhane, L., Laribi, M. (eds) Computational Kinematics. Mechanisms and Machine Science, vol 50. Springer, Cham.

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  • Print ISBN: 978-3-319-60866-2

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