Method for Determining the Probing Points for Efficient Measurement of Freeform Surface
In inspection and workpiece localization, sampling point data is an important issue. Since the devices for sampling only sample discrete points, not the completely surface, sampling size and location of the points will be taken into consideration. In this paper a method is presented for determining the sampled points size and location for achieving efficient sampling. Firstly, uncertainty analysis of the localization parameters is investigated. A localization uncertainty model is developed to predict the uncertainty of the localization process. Using this model the minimum size of the sampled points is predicted. Secondly, based on the algebra theory an eigenvalue-optimal optimization is proposed. Then a freeform surface is used in the simulation. The proposed optimization is implemented. The simulation result shows its effectivity.
[1] Y. Li and S. Chen, "Automatic recalibration of an active structured light
vision system," Robotics and Automation, IEEE Transactions on, vol. 19,
pp. 259-268, 2003.
[2] W. Cochran, "Sampling Techniques," New York, 1953.
[3] T. Woo and R. Liang, "Dimensional measurement of surfaces and their
sampling," Computer Aided Design, vol. 25, pp. 233-9, 1993.
[4] T. C. Woo and R. Liang, "Efficient sampling for surface measurements,"
J. Manuf. Syst, vol. 14, pp. 345-354, 1995.
[5] R. Liang, T. Woo, and C. Hsieh, "Accuracy and Time in Surface Measurement,
Part 1: Mathematical Foundations," Journal of Manufacturing
Science and Engineering, vol. 120, p. 141, 1998.
[6] R. Liang, T. C. Woo, and C. C. Hsieh, "Accuracy and Time in Surface
Measurement, Part 2: Optimal Sampling Sequence," J,. Manu. Sci. Eng,
vol. 120, pp. 150-155, 1998.
[7] G. Lee, J. MOU, and Y. Shen, "Sampling strategy design for dimensional
measurement of geometric features using coordinate measuring machine,"
International Journal of Machine Tools and Manufacture, vol. 37, pp. 917-
934, 1997.
[8] W. Kim and S. Raman, "On the selection of flatness measurement points
in coordinate measuring machine inspection," International Journal of
Machine Tools and Manufacture, vol. 40, pp. 427-443, 2000.
[9] K. Summerhays, R. Henke, J. Baldwin, R. Cassou, and C. Brown, "Optimizing
discrete point sample patterns and measurement data analysis on
internal cylindrical surfaces with systematic form deviations," Journal of
the International Societies for Precision Engineering and Nanotechnology,
vol. 26, pp. 105-121, 2001.
[10] M. Dowling, P. Griffin, K. Tsui, and C. Zhou, "Statistical Issues in
Geometric Feature Inspection Using Coordinate Measuring Machines,"
TECHNOMETRICS, vol. 39, p. 3, 1997.
[11] C. Prakasvudhisarn and S. Raman, "Framework for Cone Feature
Measurement Using Coordinate Measuring Machines," Journal of Manufacturing
Science and Engineering, vol. 126, p. 169, 2004.
[12] C. Menq, H. Yau, G. Lai, and R. Miller, "Statistical Evaluation of Form
Tolerances Using Discrete Measurement Data," Advances in Integrated
Product Design and Manufacturing, vol. 47, pp. 135-149, 1990.
[13] Y. Zhang, A. Nee, J. Fuh, K. Neo, and H. Loy, "A neural network
approach to determining optimal inspection sampling size for CMM,"
Computer Integrated Manufacturing Systems, vol. 9, pp. 161-169, 1996.
[14] Z. LIN and W. LIN, "Measurement point prediction of flatness geometric
tolerance by using grey theory," Precision engineering, vol. 25, pp. 171-
184, 2001.
[15] R. Raghunandan and P. Rao, "Selection of an optimum sample size
for flatness error estimation while using coordinate measuring machine,"
International Journal of Machine Tools and Manufacture, vol. 47, pp.
477-482, 2007.
[16] R. Hocken, J. Raja, and U. Babu, "Sampling Issues in Coordinate
Metrology," MANUFACTURING REVIEW, vol. 6, pp. 282-282, 1993.
[17] C. H. Menq, H. T. Yau, and G. Y. Lai, "Automated precision measurement
of surface profile in CAD-directed inspection," Robotics and
Automation, IEEE Transactions on, vol. 8, pp. 268-278, 1992.
[18] J. Canny and E. Paulos, "Optimal Probing Strategies," The International
Journal of Robotics Research, vol. 20, p. 694, 2001.
[19] W. Cai, S. Hu, and J. Yuan, "A Variational Method of Robust Fixture
Configuration Design for 3-D Workpieces," Journal of Manufacturing
Science and Engineering, vol. 119, p. 593, 1997.
[20] D. Simon, Fast and accurate shape-based registration: Carnegie Mellon
University Pittsburgh, PA, USA, 1996.
[21] A. Nahvi and J. M. Hollerbach, "The noise amplification index for
optimal pose selection in robot calibration," in Robotics and Automation,
1996. Proceedings., 1996 IEEE International Conference on, 1996, pp.
647-654 vol.1.
[22] Z. Xiong, M. Wang, and Z. Li, "A Near-Optimal Probing Strategy for
Workpiece Localization," IEEE Transactions on Robotics, vol. 20, pp.
668-676, 2004.
[23] M. Wang and D. Pelinescu, "Optimizing fixture layout in a point-set
domain," Robotics and Automation, IEEE Transactions on, vol. 17, pp.
312-323, 2001.
[24] L. Zexiang, G. Jianbo, and C. Yunxian, "Geometric algorithms for
workpiece localization," Robotics and Automation, IEEE Transactions
on, vol. 14, pp. 864-878, 1998.
[1] Y. Li and S. Chen, "Automatic recalibration of an active structured light
vision system," Robotics and Automation, IEEE Transactions on, vol. 19,
pp. 259-268, 2003.
[2] W. Cochran, "Sampling Techniques," New York, 1953.
[3] T. Woo and R. Liang, "Dimensional measurement of surfaces and their
sampling," Computer Aided Design, vol. 25, pp. 233-9, 1993.
[4] T. C. Woo and R. Liang, "Efficient sampling for surface measurements,"
J. Manuf. Syst, vol. 14, pp. 345-354, 1995.
[5] R. Liang, T. Woo, and C. Hsieh, "Accuracy and Time in Surface Measurement,
Part 1: Mathematical Foundations," Journal of Manufacturing
Science and Engineering, vol. 120, p. 141, 1998.
[6] R. Liang, T. C. Woo, and C. C. Hsieh, "Accuracy and Time in Surface
Measurement, Part 2: Optimal Sampling Sequence," J,. Manu. Sci. Eng,
vol. 120, pp. 150-155, 1998.
[7] G. Lee, J. MOU, and Y. Shen, "Sampling strategy design for dimensional
measurement of geometric features using coordinate measuring machine,"
International Journal of Machine Tools and Manufacture, vol. 37, pp. 917-
934, 1997.
[8] W. Kim and S. Raman, "On the selection of flatness measurement points
in coordinate measuring machine inspection," International Journal of
Machine Tools and Manufacture, vol. 40, pp. 427-443, 2000.
[9] K. Summerhays, R. Henke, J. Baldwin, R. Cassou, and C. Brown, "Optimizing
discrete point sample patterns and measurement data analysis on
internal cylindrical surfaces with systematic form deviations," Journal of
the International Societies for Precision Engineering and Nanotechnology,
vol. 26, pp. 105-121, 2001.
[10] M. Dowling, P. Griffin, K. Tsui, and C. Zhou, "Statistical Issues in
Geometric Feature Inspection Using Coordinate Measuring Machines,"
TECHNOMETRICS, vol. 39, p. 3, 1997.
[11] C. Prakasvudhisarn and S. Raman, "Framework for Cone Feature
Measurement Using Coordinate Measuring Machines," Journal of Manufacturing
Science and Engineering, vol. 126, p. 169, 2004.
[12] C. Menq, H. Yau, G. Lai, and R. Miller, "Statistical Evaluation of Form
Tolerances Using Discrete Measurement Data," Advances in Integrated
Product Design and Manufacturing, vol. 47, pp. 135-149, 1990.
[13] Y. Zhang, A. Nee, J. Fuh, K. Neo, and H. Loy, "A neural network
approach to determining optimal inspection sampling size for CMM,"
Computer Integrated Manufacturing Systems, vol. 9, pp. 161-169, 1996.
[14] Z. LIN and W. LIN, "Measurement point prediction of flatness geometric
tolerance by using grey theory," Precision engineering, vol. 25, pp. 171-
184, 2001.
[15] R. Raghunandan and P. Rao, "Selection of an optimum sample size
for flatness error estimation while using coordinate measuring machine,"
International Journal of Machine Tools and Manufacture, vol. 47, pp.
477-482, 2007.
[16] R. Hocken, J. Raja, and U. Babu, "Sampling Issues in Coordinate
Metrology," MANUFACTURING REVIEW, vol. 6, pp. 282-282, 1993.
[17] C. H. Menq, H. T. Yau, and G. Y. Lai, "Automated precision measurement
of surface profile in CAD-directed inspection," Robotics and
Automation, IEEE Transactions on, vol. 8, pp. 268-278, 1992.
[18] J. Canny and E. Paulos, "Optimal Probing Strategies," The International
Journal of Robotics Research, vol. 20, p. 694, 2001.
[19] W. Cai, S. Hu, and J. Yuan, "A Variational Method of Robust Fixture
Configuration Design for 3-D Workpieces," Journal of Manufacturing
Science and Engineering, vol. 119, p. 593, 1997.
[20] D. Simon, Fast and accurate shape-based registration: Carnegie Mellon
University Pittsburgh, PA, USA, 1996.
[21] A. Nahvi and J. M. Hollerbach, "The noise amplification index for
optimal pose selection in robot calibration," in Robotics and Automation,
1996. Proceedings., 1996 IEEE International Conference on, 1996, pp.
647-654 vol.1.
[22] Z. Xiong, M. Wang, and Z. Li, "A Near-Optimal Probing Strategy for
Workpiece Localization," IEEE Transactions on Robotics, vol. 20, pp.
668-676, 2004.
[23] M. Wang and D. Pelinescu, "Optimizing fixture layout in a point-set
domain," Robotics and Automation, IEEE Transactions on, vol. 17, pp.
312-323, 2001.
[24] L. Zexiang, G. Jianbo, and C. Yunxian, "Geometric algorithms for
workpiece localization," Robotics and Automation, IEEE Transactions
on, vol. 14, pp. 864-878, 1998.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:55339", author = "Yi Xu and Zexiang Li", title = "Method for Determining the Probing Points for Efficient Measurement of Freeform Surface", abstract = "In inspection and workpiece localization, sampling point data is an important issue. Since the devices for sampling only sample discrete points, not the completely surface, sampling size and location of the points will be taken into consideration. In this paper a method is presented for determining the sampled points size and location for achieving efficient sampling. Firstly, uncertainty analysis of the localization parameters is investigated. A localization uncertainty model is developed to predict the uncertainty of the localization process. Using this model the minimum size of the sampled points is predicted. Secondly, based on the algebra theory an eigenvalue-optimal optimization is proposed. Then a freeform surface is used in the simulation. The proposed optimization is implemented. The simulation result shows its effectivity.
", keywords = "eigenvalue-optimal optimization, freeform surface inspection,sampling size and location, sampled points.", volume = "2", number = "2", pages = "183-6", }
