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Accuracy characterization and measurement point planning for workpiece localization

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Abstract

This paper addresses the problem of accuracy characterization and measurement point planning for 3-D workpiece localization in the presence of part surface errors and measurement errors. Two frame-invariant functions of the infinitesimal rigid body displacement are defined to quantify the localization accuracy required by manufacturing processes. Then, two kinds of frame-invariant indices are derived to characterize the sensitivities of the accuracy measures to the sampling errors at the measurement points. With a dense set of discrete points on the workpiece datum surfaces pre-defined as candidates for measurement, planning of probing points for accurate recovery of part location is modeled as a combinatorial problem focusing on minimizing the accuracy sensitivity index. Based on an interchange rule, a greedy algorithm is developed to efficiently find a near-optimal solution. It is also shown that if the number of the measurement points is sufficiently large, there is no need to optimize their positions. Example confirms the validity of the presented indices and algorithm.

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References

  1. Ding, H., Zhu, L. M., Xiong, Z. H., A survey on coordinate measurement, geometric modeling and PR or NC code generation from measured data points, Chinese Journal of Mechanical Engineering, 2003, 39(11): 28–37.

    Article  Google Scholar 

  2. Zhu, L. M., Xiong, Z. H., Ding, H. et al., A distance function based approach for localization and profile error evaluation of complex surface, Transactions of ASME, Journal of Manufacturing Science & Engineering, 2004, 126(3): 542–554.

    Article  Google Scholar 

  3. Zhu, L. M., Ding, H., Application of kinematic geometry to computational metrology: distance function based heirarchical algorithms for cylindricity evaluation, International Journal of Machine Tools & Manufacture, 2003, 43(2): 203–215.

    Article  Google Scholar 

  4. Li, Z., Gou, J., Chu, Y., Geometric algorithms for workpiece localization, IEEE Transactions on Robotics and Automation, 1998, 14: 864–878.

    Article  Google Scholar 

  5. Sourlier, D., Bucher, A., Surface-independent, theoretically exact bestfit for arbitrary sculptured, complex, or standard geometries, Precision Engineering, 1995, 17: 101–113.

    Article  Google Scholar 

  6. Forbes, A. B., Least-squares best-fit geometric elements, in Algorithms for Approximation II (ed. Mason, J. C., Cox, M. G.), London: Chapman and Hall, 1990, 311–319.

    Google Scholar 

  7. Hong, J. W., Tan, X. L., Method and apparatus for determining position and orientation of mechanical objects, U.S. Patent 5208763, 1990.

  8. Yan, Z. C., Meng, C. H., Uncertainty analysis and variation reduction of three-dimensional coordinate metrology, International Journal of Machine Tools & Manufacture, 1999, 39: 1199–1261.

    Article  Google Scholar 

  9. Yau, H. T., Uncertainty analysis in geometric best fit, International Journal of Machine Tools and Manufacture, 1998, 38: 1323–1342.

    Article  Google Scholar 

  10. Murray, R. M., Li, Z., Sastry, S. S., A Mathematical Introduction to Robotic Manipulation, Boca Raton: CRC Press, 1994.

    MATH  Google Scholar 

  11. Wang, M. Y., Characterizations of localization accuracy of fixtures, IEEE Transactions on Robotics and Automation, 2002, 18(6): 976–981.

    Article  Google Scholar 

  12. Chu, Y. X., Gou, J. B., Li, Z. X., Workpiece localization algorithms: performance and reliability analysis Journal of Manufacturing System, 1999, 18(2): 113–126.

    Article  Google Scholar 

  13. Lin, Q., Burdick, J. W., Objective and frame-invariant kinematic metric functions for rigid bodies, International Journal of Robotics Research, 2000, 19: 612–625.

    Article  Google Scholar 

  14. Wang, M. Y., Tolerance analysis for fixture layout design, Assembly Automation, 2002, 22(2): 153–162.

    Article  Google Scholar 

  15. Soderberg, R., Carlson, J., Locating scheme analysis for robust assembly and fixture design, in Proc. of the ASME Design for Manufacture Conference, Las Vegas, Nevada, UAS, 1999.

  16. Asada, H., By, A. B., Kinematic analysis of workpart fixturing for flexible assembly with automatically reconfigurable fixture, IEEE J. of Robotics & Automation, 1985, 1(2): 86–94.

    Google Scholar 

  17. Wang, M. Y., Pelinescu, D., Optimizing fixture layout in a point set domain, IEEE Trans. on Robotics and Automation, 2001, 17(3): 312–323.

    Article  Google Scholar 

  18. Fang, K. T., Applied Multivariate Statistical Analysis (in Chinese), Shanghai: East China Normal University Press, 1989.

    Google Scholar 

  19. Zhu, L. M., Distance function-based models and algorithms for fitting of geometric elements to measured coordinate points, Postdoctoral technical report (No. 2002-2), School of Mechanical Science & Engineering, Huazhong University of Science & Technology, 2002.

  20. Choudhuri, S. A., Demeter, E. C., Tolerance analysis of manufacturing fixture locators, Trans of ASME, Journal of Manufacturing Science & Engineering, 1999, 121(2): 273–281.

    Article  Google Scholar 

  21. Rong, Y., Hu, W., Kang, Y. et al., Locating error analysis and tolerance assignment for computer-aided fixture design, International Journal of Production Research, 2002, 39(15): 3529–3545.

    Google Scholar 

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Authors and Affiliations

  1. School of Mechanical Engineering, Shanghai Jiaotong University, 200030, Shanghai, China

    Zhu Limin, Luo Honggen & Ding Han

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  1. Zhu Limin
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  2. Luo Honggen
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  3. Ding Han
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Correspondence to Zhu Limin.

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Zhu, L., Luo, H. & Ding, H. Accuracy characterization and measurement point planning for workpiece localization. Sci. China Ser. E-Technol. Sci. 47, 676–690 (2004). https://doi.org/10.1360/03ye0505

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  • DOI: https://doi.org/10.1360/03ye0505

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