Kinematic Calibration of a Six DOF Flexure-based Parallel Manipulator

J.H. Timmer Arends, K.H.J. Voss, W.K. Hakvoort, R.G.K.M. Aarts

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademic

    6 Citations (Scopus)
    548 Downloads (Pure)


    The absence of friction, hysteresis and backlash makes flexure-based mechanisms well-suited for high precision manipulators. However, the (inverse) kinematic relation between actuators and end-effector is far from trivial due to the non-linear behaviour of the deforming compliant joints. In this paper we consider the kinematic modelling and calibration of a flexure-based parallel manipulator for a six degrees of freedom (DOF) mirror mount. The mount is positioned by six arms, each of which has five joints and is driven by a linear actuator.

    Three kinematic models are compared. A simple and computationally fast model that ignores pivot shift is too inaccurate. A flexible multibody model can account for the non-linear deformations of the joints, but is too computationally expensive for real-time applications. Finally, a kinematic model is derived using the Denavit–Hartenberg notation where the pivot shift is described with a polynomial approximation. This model offers nm accuracy with a small
    number of terms from a Taylor series and can be evaluated sufficiently fast.

    In this way a nominal kinematic model can be derived using the (kinematic) parameters from CAD data. However, the achievable accuracy in an experimental set-up remains inadequate. Hence a geometric calibration procedure has been
    developed for the four most critical translations and rotations of the end-effector. The measurement set-up contains two position-sensing detectors to measure these motions. The model is linearized for small errors in the parameters to enable the use of linear regression techniques. With a least squares estimate the errors in the parameters are estimated. The quality of the estimation is checked by combining the singular value decomposition of the (linearised) regression matrix with cross-validation. It was found that the kinematic calibration clearly improves the accuracy of the (inverse) kinematic model.
    Original languageEnglish
    Title of host publicationECCOMAS Thematic Conference on Multibody Dynamics
    Subtitle of host publicationPrague, June 19-22, 2017: conference proceedings
    EditorsMichael Valasek, Zbynek Sika, Tomas Vampola
    Number of pages13
    ISBN (Electronic)978-80-01-6174-9
    Publication statusPublished - 8 Dec 2017
    EventMultibody Dynamics 2017: 8th ECCOMAS Thematic Conference - Czech Technical University, Prague, Czech Republic
    Duration: 19 Jun 201722 Jun 2017
    Conference number: 8


    ConferenceMultibody Dynamics 2017
    Country/TerritoryCzech Republic
    Internet address


    • Kinematic model
    • Geometric calibration
    • Flexure-based parallel mechanisms
    • Flexible multibody analysis
    • Iterative linear parameters estimation


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