Technical Briefs

A Kinematic Model for Parallel-Joint Coordinate Measuring Machine

[+] Author and Article Information
Jie Li

e-mail: 2000smile@163.om

Lian-Dong Yu

e-mail: liandongyu@hfut.edu.cn

Jing-Qi Sun

e-mail: aqwsxz123456a@163.com

Hao-Jie Xia

e-mail: hjxia@hfut.edu.cn
School of Instrument Science
and Opto-electronics Engineering,
Hefei University of Technology,
Tunxi Road No. 193,
Hefei 230009, China

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received March 1, 2012; final manuscript received January 6, 2013; published online September 11, 2013. Assoc. Editor: Delun Wang.

J. Mechanisms Robotics 5(4), 044501 (Sep 11, 2013) (4 pages) Paper No: JMR-12-1021; doi: 10.1115/1.4025121 History: Received March 01, 2012; Revised January 06, 2013

The typical nonorthogonal coordinate measuring machine is the portable coordinate measuring machine (PCMM), which is widely applied in manufacturing. In order to improve the measurement accuracy of PCMM, structural designing, data processing, mathematical modeling, and identification of parameters of PCMM, which are essential for the measurement accuracy, should be taken into account during the machine development. In this paper, a kind of PCMM used for detecting the crucial dimension of automobile chassis has been studied and calibrated. The Denavit–Hartenberg (D–H) kinematic modeling method has often been used for modeling traditional robot, but the D–H error representation is ill-conditioned when it is applied to represent parallel joints. A modified four-parameter model combined with D–H model is put forward for this PCMM. Based on the kinematic model, Gauss–Newton method is applied for calibrating the kinematic parameters. The experimental results indicate the improvement of measuring accuracy and the effectiveness of the PCMM based on the proposed method.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Minh, T., and Phil, W., 2012, “An Improved Kinematic Model for Calibration of Serial Robots Having Closed-Chain Mechanisms,” Robotica, 30, pp. 963–971. [CrossRef]
Ramua, P., Yagüeb, J. A., Hockena, R. J., and Millera, J., 2011, “Development of a Parametric Model and Virtual Machine to Estimate Task Specific Measurement Uncertainty for a Five-Axis Multi-Sensor Coordinate Measuring Machine,” Precis. Eng., 35, pp. 431–439. [CrossRef]
Denavit, J., and Hartenberg, R. S., 1955, “A Kinematic Notation for Low Pair Mechanisms Based on Matrices,” ASME J. Appl. Mech., 22, pp. 215–221.
Meggiolaro, M. A., and Dubowsky, S., 2000, “An Analytical Method to Eliminate the Redundant Parameters in Robot Calibration,” Proceedings of the IEEE Conference on Robotics and Automation, San Francisco, CA, April 24–28, IEEE, New York, Vol. 4, pp. 3609–3615.
Veitschegger, W. K., and Wu, C.-H., 1987, “A Method for Calibrating and Compensating Robot Kinematic Errors,” Proceedings of the IEEE Conference on Robotics and Automation, March, IEEE, New York, pp. 39–44.
Veitschegger, W. K., and Wu, C.-H., 1988, “Robot Calibration and Compensation,” IEEE J. Rob. Autom., 4(6), pp. 643–656. [CrossRef]
Ding, X., Yang, Y., and Dai, J., 2009, “Design and kinematic analysis of a novel prism deployable mechanism,” Mechanism and Machine Theory, 36(5), pp. 35–49. Available at: http://www.sciencedirect.com/science/journal/0094114X
Zhuang, H., Roth, Z. S., and Hamano, F., 1992, “A Complete and Parametrically Continuous Kinematic Model for Robot Manipulators,” IEEE Trans. Rob. Autom., 8(4), pp. 451–463. [CrossRef]
Ziegert, J., and Datseris, P., 1988. “Basic Considerations for Robot Calibration,” Proceedings of the IEEE Conference on Robotics and Automation, March, Philadelphia, PA, IEEE, New York, pp. 932–938.
Roberts, K. S., 1988, “A New Representation for a Line,” Proceedings of the International Conference on Computer Vision and Pattern Recognition, Ann Harbor, MI, June 5–9, pp. 635–640.
Stone, H. W., 1987, Kinematic Modeling, Identification and Control Robotic Manipulators, Kluwer, New York.
Roth, Z. S., Mooring, B. W., and Ravani, B., 1987, “An Overview of Robot Calibration,” IEEE J. Rob. Autom., 3(5), pp. 377–384. [CrossRef]
Judd, R. P., and Knasinski, A. B.,1990, “A Technique to Calibrate Industrial Robots With Experimental Verification,” IEEE Trans. Rob. Autom., 6(1), pp. 20–30. [CrossRef]
Karpińska, J., and Tchoń, K., 2012, “Performance-Oriented Design of Inverse Kinematics Algorithms: Extended Jacobian Approximation of the Jacobian Pseudo-Inverse,” ASME J. Mech. Rob., 4(2), p. 021008. [CrossRef]
Bai, Y., and Wang, D., 2006, “Fuzzy Logic for Robots Calibration—Using Fuzzy Interpolation Technique in Modeless Robot Calibration,” Advanced Fuzzy Logic Technologies in Industrial Applications, Y.Bai, H.Zhuang, and D.Wang, eds., Springer-Verlag, London.
Bai, Y., 2007, “On the Comparison of Model-Based and Modeless Robotic Calibration Based on a Fuzzy Interpolation Method,” Int. J. Adv. Manuf. Technol., 31, pp. 1243–1250. [CrossRef]
Bai, Y., and Wang, D., 2003, “Improve the Position Measurement Accuracy Using a Dynamic On-Line Fuzzy Interpolation Technique,” IEEE International Symposium on Computational Intelligence for Measurement Systems and Applications, IEEE, New York, pp. 227–232.
Wang, X. Y., Liu, S. G., Zhang, G. C., Wang, B., and Guo, L. F., 2007, “Calibration Technology of the Articulated Arm Flexible CMM,” ISMTII2007, pp. 731–734.
Gao, G., Wang, W., Lin, K., and Chen, Z., 2009, “Structural Parameter Identification for Articulated ARM Coordinate Measuring Machines,” International Conference on Measuring Technology and Mechatronics Automation, Zhangjiajie, Hunan, April 11–12, pp. 128–131.
Santolaria, J., Aguilar, J.-J., Yaguee, J.-A., and Pastor, J., 2008, “Kinematic Parameter Estimation Technique for Calibration and Repeatability Improvement of Articulated Arm Coordinate Measuring Machines,” Precis. Eng., 32, pp. 251–268. [CrossRef]
Jin, Q., 2010, “On a Regularized Levenberg-Marquardt Method for Solving Nonlinear Inverse Problems,” Numer. Math., 115(2), pp. 229–259. [CrossRef]


Grahic Jump Location
Fig. 5

The calibration standard bar with the probe inserted

Grahic Jump Location
Fig. 4

The transformation of modified Denavit–Hartenberg model for revolute joints

Grahic Jump Location
Fig. 3

The transformation of Denavit–Hartenberg model

Grahic Jump Location
Fig. 2

A kinematical representation of the PCMM

Grahic Jump Location
Fig. 1

Photograph of the PCMM under study

Grahic Jump Location
Fig. 6

Reduction of the objective function during iterations

Grahic Jump Location
Fig. 7

Measurement error before and after calibration




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