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

    3 Citations (Scopus)
    172 Downloads (Pure)

    Abstract

    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
    Pages199-211
    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
    http://multibody2017.cz/

    Conference

    ConferenceMultibody Dynamics 2017
    CountryCzech Republic
    CityPrague
    Period19/06/1722/06/17
    Internet address

    Fingerprint

    Manipulators
    Kinematics
    Calibration
    Inverse kinematics
    End effectors
    Linear actuators
    Polynomial approximation
    Taylor series
    Singular value decomposition
    Linear regression
    Hysteresis
    Computer aided design
    Mirrors
    Actuators
    Friction
    Detectors

    Keywords

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

    Cite this

    Timmer Arends, J. H., Voss, K. H. J., Hakvoort, W. K., & Aarts, R. G. K. M. (2017). Kinematic Calibration of a Six DOF Flexure-based Parallel Manipulator. In M. Valasek, Z. Sika, & T. Vampola (Eds.), ECCOMAS Thematic Conference on Multibody Dynamics: Prague, June 19-22, 2017: conference proceedings (pp. 199-211)
    Timmer Arends, J.H. ; Voss, K.H.J. ; Hakvoort, W.K. ; Aarts, R.G.K.M. / Kinematic Calibration of a Six DOF Flexure-based Parallel Manipulator. ECCOMAS Thematic Conference on Multibody Dynamics: Prague, June 19-22, 2017: conference proceedings. editor / Michael Valasek ; Zbynek Sika ; Tomas Vampola. 2017. pp. 199-211
    @inproceedings{6e0778233df84e208c7b9d75c232b05a,
    title = "Kinematic Calibration of a Six DOF Flexure-based Parallel Manipulator",
    abstract = "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 smallnumber 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 beendeveloped 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.",
    keywords = "Kinematic model, Geometric calibration, Flexure-based parallel mechanisms, Flexible multibody analysis, Iterative linear parameters estimation",
    author = "{Timmer Arends}, J.H. and K.H.J. Voss and W.K. Hakvoort and R.G.K.M. Aarts",
    note = "ATA, KV and WH acknowledge the support from the Horizon2020 program of the EU under project grant no. 637045 (“ADALAM”).",
    year = "2017",
    month = "12",
    day = "8",
    language = "English",
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    }

    Timmer Arends, JH, Voss, KHJ, Hakvoort, WK & Aarts, RGKM 2017, Kinematic Calibration of a Six DOF Flexure-based Parallel Manipulator. in M Valasek, Z Sika & T Vampola (eds), ECCOMAS Thematic Conference on Multibody Dynamics: Prague, June 19-22, 2017: conference proceedings. pp. 199-211, Multibody Dynamics 2017, Prague, Czech Republic, 19/06/17.

    Kinematic Calibration of a Six DOF Flexure-based Parallel Manipulator. / Timmer Arends, J.H.; Voss, K.H.J.; Hakvoort, W.K.; Aarts, R.G.K.M.

    ECCOMAS Thematic Conference on Multibody Dynamics: Prague, June 19-22, 2017: conference proceedings. ed. / Michael Valasek; Zbynek Sika; Tomas Vampola. 2017. p. 199-211.

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

    TY - GEN

    T1 - Kinematic Calibration of a Six DOF Flexure-based Parallel Manipulator

    AU - Timmer Arends, J.H.

    AU - Voss, K.H.J.

    AU - Hakvoort, W.K.

    AU - Aarts, R.G.K.M.

    N1 - ATA, KV and WH acknowledge the support from the Horizon2020 program of the EU under project grant no. 637045 (“ADALAM”).

    PY - 2017/12/8

    Y1 - 2017/12/8

    N2 - 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 smallnumber 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 beendeveloped 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.

    AB - 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 smallnumber 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 beendeveloped 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.

    KW - Kinematic model

    KW - Geometric calibration

    KW - Flexure-based parallel mechanisms

    KW - Flexible multibody analysis

    KW - Iterative linear parameters estimation

    M3 - Conference contribution

    SN - 978-80-01-06173-2

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    EP - 211

    BT - ECCOMAS Thematic Conference on Multibody Dynamics

    A2 - Valasek, Michael

    A2 - Sika, Zbynek

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    ER -

    Timmer Arends JH, Voss KHJ, Hakvoort WK, Aarts RGKM. Kinematic Calibration of a Six DOF Flexure-based Parallel Manipulator. In Valasek M, Sika Z, Vampola T, editors, ECCOMAS Thematic Conference on Multibody Dynamics: Prague, June 19-22, 2017: conference proceedings. 2017. p. 199-211