0
Research Papers

Kinematic Calibration of a Three Degrees-of-Freedom Parallel Manipulator With a Laser Tracker

[+] Author and Article Information
Leiying He

Faculty of Mechanical Engineering
and Automation,
Zhejiang Sci-Tech University,
928 Second Avenue, Xiasha Higher
Education Zone,
Hangzhou 310018, China
e-mail: hlying@zstu.edu.cn

Qinchuan Li

Faculty of Mechanical Engineering
and Automation,
Zhejiang Sci-Tech University,
928 Second Avenue, Xiasha Higher Education
Zone,
Hangzhou 310018, China
e-mail: lqchuan@zstu.edu.cn

Xubiao Zhu

Faculty of Mechanical Engineering
and Automation,
Zhejiang Sci-Tech University,
928 Second Avenue, Xiasha Higher
Education Zone,
Hangzhou 310018, China
e-mail: 447690649@qq.com

Chuanyu Wu

Faculty of Mechanical Engineering
and Automation,
Zhejiang Sci-Tech University,
928 Second Avenue, Xiasha Higher
Education Zone,
Hangzhou 310018, China
e-mail: cywu@zstu.edu.cn

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received January 4, 2017; final manuscript received October 8, 2018; published online November 22, 2018. Assoc. Editor: Manish Kumar.

J. Dyn. Sys., Meas., Control 141(3), 031009 (Nov 22, 2018) (10 pages) Paper No: DS-17-1007; doi: 10.1115/1.4041749 History: Received January 04, 2017; Revised October 08, 2018

Kinematic calibration is commonly used to improve the accuracy of a parallel mechanism. This paper presents an effective method for calibrating an overconstrained three degrees-of-freedom parallel manipulator employing a direct kinematic model. An error-mapping function is formulated from the differential of its kinematic model which is established through vector chains with the geometrical errors. To simplify the measurement of the error, the positioning and orientation error of the moving platform is replaced by the positioning error of the tool center point, which can be measured by a laser tracker accurately. Three different objective functions F1, F2, and F, respectively, representing 1-norm, 2-norm, and inf-norm of the error vector are used to identify the geometrical parameters of the manipulator. The results of computer simulation show that parameters after kinematic calibration through minimizing the objective function F2 is highly accurate and efficient. A calibration experiment is carried out to verify the effectiveness of the method. The maximum residual of calibration points reduces greatly from 3.904 to 0.256 mm during parameter identification. The positioning errors of all points on and inside the space surrounded by the calibration points are smaller than 0.4 mm after error compensation.

FIGURES IN THIS ARTICLE
<>
Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.

References

Li, Q. , and Herve, J. M. , 2014, “ Type Synthesis of 3-DOF RPR-Equivalent Parallel Mechanisms,” IEEE Trans. Rob., 30(6), pp. 1333–1343. [CrossRef]
Sun, T. , Song, Y. , Dong, G. , Lian, B. , and Liu, J. , 2012, “ Optimal Design of a Parallel Mechanism With Three Rotational Degrees of Freedom,” Rob. Comput. Integr. Manuf., 28(4), pp. 500–508. [CrossRef]
Wu, J. F. , Rui, Z. , Wang, R. H. , and Yao, Y. X. , 2014, “ A Systematic Optimization Approach for the Calibration of Parallel Kinematics Machine Tools by a Laser Tracker,” Int. J. Mach. Tools Manuf., 86, pp. 1–11. [CrossRef]
Gao, M. , Li, T. M. , and Yin, W. S. , 2003, “ Calibration Method and Experiment of Stewart Platform Using a Laser Tracker,” IEEE International Conference on Systems, Man and Cybernetics (SMC), Washington, DC, Oct. 8, pp. 2797–2802.
Takeda, Y. , Gang, S. , and Funabashi, H. , 2004, “ A DBB-Based Kinematic Calibration Method for In-Parallel Actuated Mechanisms Using a Fourier Series,” ASME J. Mech. Des., 126(5), pp. 856–865. [CrossRef]
Ni, Y. B. , Zhang, B. , Guo, W. X. , and Shao, C. Y. , 2016, “ Kinematic Calibration of Parallel Manipulator With Full-Circle Rotation,” Ind. Rob., 43(3), pp. 296–307. [CrossRef]
Renaud, P. , Andreff, N. , Lavest, J. M. , and Dhome, M. , 2006, “ Simplifying the Kinematic Calibration of Parallel Mechanisms Using Vision-Based Metrology,” IEEE Trans. Rob., 22(1), pp. 12–22. [CrossRef]
Traslosheros, A. , Sebastián, J. M. , Castillo, E. , Roberti, F. , and Carelli, R. , 2010, “ One Camera in Hand for Kinematic Calibration of a Parallel Robot,” IEEE/RSJ International Conference on Intelligent Robots and Systems, Taipei, Taiwan, Oct. 18–22, pp. 5673–5678.
Traslosheros, A. , Sebastián, J. M. , Torrijos, J. , Carelli, R. , and Castillo, E. , 2013, “ An Inexpensive Method for Kinematic Calibration of a Parallel Robot by Using One Hand-Held Camera as Main Sensor,” Sensors, 13(8), pp. 9941–9965. [CrossRef] [PubMed]
Majarena, A. C. , Santolaria, J. , Samper, D. , and Aguilar, J. J. , 2011, “ Modelling and Calibration of Parallel Mechanisms Using Linear Optical Sensors and a Coordinate Measuring Machine,” Meas. Sci. Technol., 22(10), p. 105101. [CrossRef]
Joubair, A. , Slamani, M. , and Bonev, I. A. , 2012, “ Kinematic Calibration of a 3-DOF Planar Parallel Robot,” Ind. Rob., 39(4), pp. 392–400. [CrossRef]
Ren, X. D. , Feng, Z. R. , and Su, C. P. , 2008, “ Kinematic Calibration of Parallel Robots Using Orientation Constraint,” IEEE International Symposium on Industrial Electronics, Cambridge, UK, June 30–July 2, pp. 1435–1440.
Ren, X. , Feng, Z. , and Su, C. , 2009, “ A New Calibration Method for Parallel Kinematics Machine Tools Using Orientation Constraint,” Int. J. Mach. Tools Manuf., 49(9), pp. 08–721. [CrossRef]
Yang, G. L. , Chen, I. M. , Yeo, S. H. , and Lim, W. K. , 2002, “ Simultaneous Base and Tool Calibration for Self-Calibrated Parallel Robots,” Robotica, 20(4), pp. 67–374. [CrossRef]
Hesselbach, J. , Bier, C. , Pietsch, I. , Plitea, N. , Büttgenbach, S. , Wogersien, A. , and Güttler, J. , 2005, “ Passive-Joint Sensors for Parallel Robots,” Mechatronics, 15(1), pp. 3–65. [CrossRef]
Daney, D. , 2003, “ Kinematic Calibration of the Gough Platform,” Robotica, 21(6), pp. 77–690. [CrossRef]
Gatti, G. , and Danieli, G. , 2008, “ A Practical Approach to Compensate for Geometric Errors in Measuring Arms: Application to a Six-Degree-of-Freedom Kinematic Structure,” Meas. Sci. Technol., 19(1), p. 015107. [CrossRef]
Huang, T. , and Whitehouse, D. J. , 2000, “ A Simple Yet Effective Approach for Error Compensation of a Tripod-Based Parallel Kinematic Machine,” CIRP Ann. Manuf. Technol., 49(1), pp. 85–288. [CrossRef]
Tian, H. , Chetwynd, D. G. , Whitehouse, D. J. , and Wang, J. S. , 2005, “ A General and Novel Approach for Parameter Identification of 6-DOF Parallel Kinematic Machines,” Mech. Mach. Theory, 40(2), pp. 19–239.
Bai, S. , and Teo, M. Y. , 2003, “ Kinematic Calibration and Pose Measurement of a Medical Parallel Manipulator by Optical Position Sensors,” J. Rob. Syst., 20(4), pp. 201–209. [CrossRef]
Majarena, A. C. , Santolaria, J. , Samper, D. , and Aguilar, J. J. , 2013, “ Analysis and Evaluation of Objective Functions in Kinematic Calibration of Parallel Mechanisms,” Int. J. Adv. Manuf. Technol., 66(5–8), pp. 751–761. [CrossRef]
Chen, G. , Wang, H. , and Lin, Z. , 2014, “ Determination of the Identifiable Parameters in Robot Calibration Based on the POE Formula,” IEEE Trans. Rob., 30(5), pp. 1066–1077. [CrossRef]
Varziri, M. S. , and Notash, L. , 2007, “ Kinematic Calibration of a Wire-Actuated Parallel Robot,” Mech. Mach. Theory, 42(8), pp. 960–976. [CrossRef]
Imoto, J. , Takeda, Y. , Saito, H. , and Ichiryu, K. , 2009, “ Optimal Kinematic Calibration of Robots Based on Maximum Positioning-Error Estimation (Theory and Application to a Parallel-Mechanism Pipe Bender),” Fifth International Workshop on Computational Kinematics, Duisburg, Germany, May 6–8, pp. 133–140.
Fan, C. , Zhao, G. , Zhao, J. , Zhang, L. , and Sun, L. , 2015, “ Calibration of a Parallel Mechanism in a Serial-Parallel Polishing Machine Tool Based on Genetic Algorithm,” Int. J. Adv. Manuf. Technol., 81(1–4), pp. 27–37. [CrossRef]
Song, Y. , Zhang, J. , Lian, B. , and Sun, T. , 2016, “ Kinematic Calibration of a 5-DOF Parallel Kinematic Machine,” Precis. Eng., 45, pp. 242–261. [CrossRef]
Sun, T. , Zhai, Y. , Song, Y. , and Zhang, J. , 2016, “ Kinematic Calibration of a 3-DoF Rotational Parallel Manipulator Using Laser Tracker,” Rob. Comput. Integr. Manuf., 41, pp. 78–91. [CrossRef]
Lee, S. , Zeng, Q. , and Ehmann, K. F. , 2017, “ Error Modeling for Sensitivity Analysis and Calibration of the Tri-Pyramid Parallel Robot,” Int. J. Adv. Manuf. Technol., 93(1–4), pp. 1319–1332. [CrossRef]
Ahmed, J. , Mohamed, S. , and Ilian, A. , 2012, “ Kinematic Calibration of a Five-Bar Planar Parallel Robot Using All Working Modes,” Rob. Comput. Integr. Manuf., 29(4), pp. 15–25.
Wang, F. , Chen, Q. , and Li, Q. , 2015, “ Optimal Design of a 2-UPR-RPU Parallel Manipulator,” ASME J. Mech. Des., 137(5), pp. 054501–054504. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Computer-aided design model of the parallel manipulator

Grahic Jump Location
Fig. 2

Schematic diagram of the mechanism

Grahic Jump Location
Fig. 3

Schematic diagram of the position measurement

Grahic Jump Location
Fig. 4

Procedure of the kinematic calibration for the parallel mechanism

Grahic Jump Location
Fig. 5

System of the parallel manipulator

Grahic Jump Location
Fig. 6

Reachable workspace of the TCP

Grahic Jump Location
Fig. 7

Positioning error after parameter identification

Grahic Jump Location
Fig. 8

Residuals of calibration with three objective functions

Grahic Jump Location
Fig. 9

Calibration experiment using a laser tracker

Grahic Jump Location
Fig. 10

Distribution of calibration points and testing point

Grahic Jump Location
Fig. 11

Flow diagram of manipulator calibration

Grahic Jump Location
Fig. 12

Residuals of all calibration points before and after calibration

Grahic Jump Location
Fig. 13

Positioning errors after compensation

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In