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Kinematic Analysis of Active Ankle Using Computational Algebraic Geometry

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Computational Kinematics

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

Abstract

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.

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References

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Acknowledgements

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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Authors and Affiliations

  1. Robotics Innovation Center, German Research Center for Artificial Intelligence (DFKI GmbH), 28359, Bremen, Germany

    Shivesh Kumar, Bertold Bongardt & Frank Kirchner

  2. Fachbereich Mathematik und Informatik, Arbeitsgruppe Robotik, Universität Bremen, 28359, Bremen, Germany

    Frank Kirchner

  3. IRCCyN, Ecole Centrale de Nantes, 44321, Nantes, France

    Abhilash Nayak

  4. Institute of Robotics, Johannes Kepler University Linz, 4040, Linz, Austria

    Andreas Mueller

Authors
  1. Shivesh Kumar
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  2. Abhilash Nayak
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  3. Bertold Bongardt
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  4. Andreas Mueller
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  5. Frank Kirchner
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Corresponding author

Correspondence to Shivesh Kumar .

Editor information

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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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. https://doi.org/10.1007/978-3-319-60867-9_14

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  • DOI: https://doi.org/10.1007/978-3-319-60867-9_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-60866-2

  • Online ISBN: 978-3-319-60867-9

  • eBook Packages: EngineeringEngineering (R0)

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