Higher-order Taylor approximation of finite motions in mechanisms

J.J. De Jong*, A. Müller, J.L. Herder

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    3 Citations (Scopus)
    1 Downloads (Pure)


    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. In this paper, this is extended to the higher-order derivatives of the solution to these loop closure equations to provide an approximation of the finite motion of serial and parallel mechanisms. This recursive algorithm, consisting solely of matrix operations, relies on a simplified representation of the higher-order derivatives of open chains. The method is applied to a serial, a multi-DOF parallel, and an overconstrained mechanism. In all cases, adequate approximation is obtained over a large portion of the workspace.

    Original languageEnglish
    Pages (from-to)1190-1201
    Number of pages12
    Issue number7
    Early online date29 Jun 2018
    Publication statusPublished - 1 Jul 2019


    • UT-Hybrid-D
    • Bennet linkage
    • Higher-order kinematics
    • Screw theory
    • Taylor approximation
    • 5-bar mechanism


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