### Abstract

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 language | English |
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Title of host publication | ECCOMAS Thematic Conference on Multibody Dynamics |

Subtitle of host publication | Prague, June 19-22, 2017: conference proceedings |

Editors | Michael Valasek, Zbynek Sika, Tomas Vampola |

Pages | 199-211 |

Number of pages | 13 |

ISBN (Electronic) | 978-80-01-6174-9 |

Publication status | Published - 8 Dec 2017 |

Event | Multibody Dynamics 2017: 8th ECCOMAS Thematic Conference - Czech Technical University, Prague, Czech Republic Duration: 19 Jun 2017 → 22 Jun 2017 Conference number: 8 http://multibody2017.cz/ |

### Conference

Conference | Multibody Dynamics 2017 |
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Country | Czech Republic |

City | Prague |

Period | 19/06/17 → 22/06/17 |

Internet address |

### Fingerprint

### Keywords

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

### Cite this

*ECCOMAS Thematic Conference on Multibody Dynamics: Prague, June 19-22, 2017: conference proceedings*(pp. 199-211)

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*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic

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

SP - 199

EP - 211

BT - ECCOMAS Thematic Conference on Multibody Dynamics

A2 - Valasek, Michael

A2 - Sika, Zbynek

A2 - Vampola, Tomas

ER -