Differentiation-free taylor approximation of finite motion in closed loop kinematics

J.J. de Jong*, A. Müller, J. van Dijk, J.L. Herder

*Corresponding author for this work

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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    Higher-order derivatives of kinematic mappings give insight into the motion characteristics of complex mechanisms. Screw theory and its associated Lie group theory have been used to find these derivatives of loop closure equations up to an arbitrary order. However this has not been extended to the higher-order derivatives of finite motion as given by the inverse or forward kinematic model of closed loop mechanisms. In this paper, a recursive algorithm is presented, consisting solely of matrix multiplications, which is capable of giving these higher-order derivatives of kinematic models of closed loop linkages. It depends on a simplified representation of the higher-order derivatives of an open chain. From these higher-order derivatives a Taylor expansion of a finite motion becomes available. The evaluation of this method on a Taylor approximation (up to 5th order) of the inverse kinematic model of a 5-bar mechanism shows a good approximation in a large part of workspace around the evaluation point.

    Original languageEnglish
    Title of host publicationComputational Kinematics
    Subtitle of host publicationProceedings of the 7th International Workshop on Computational Kinematics, 2017
    EditorsSaid Zeghloul, Lotfi Romdhane, Med Amine Laribi
    Place of PublicationCham
    Number of pages8
    ISBN (Electronic)978-3-319-60867-9
    ISBN (Print)9783319608662
    Publication statusPublished - 2018
    Event7th IFToMM International Workshop on Computational Kinematics, CK 2017 - Futuroscope, Poitiers, France
    Duration: 22 May 201724 May 2017
    Conference number: 7

    Publication series

    NameMechanisms and Machine Science
    ISSN (Print)2211-0984
    ISSN (Electronic)2211-0992


    Conference7th IFToMM International Workshop on Computational Kinematics, CK 2017
    Abbreviated titleCK
    Internet address


    • 5-bar mechanism
    • Higher-order kinematics
    • Screw theory
    • Taylor approximation


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