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Introduction to Fitting Substitute Geometry

Abstract

We address the need for fitting substitute geometry from measured data and highlight its significance in coordinate, roundness and surface metrology. We describe how fitting criteria is important when a data set is over-sampled; that is, more points are collected than is needed to determine parameters of a best-fit geometry. We briefly survey the literature to demonstrate the varied approaches that have been reported to efficiently and accurately solve the problem of determining best-fit geometry parameters. We present an overview of part III in this chapter.

Keywords

Precision Engineer Support Vector Regression Reference Circle Tolerancing Principle Nominal Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. American Society of Mechanical Engineers 1972, ASME B89.3.1-1972, Measurement of Out-of-Roundness, ASME. New York, NY, USA.Google Scholar
  2. American Society of Mechanical Engineers 1994a, ASME Y14.5M-1994, Dimensioning and Tolerancing, ASME. New York, NY, USA.Google Scholar
  3. American Society of Mechanical Engineers 1994b, ASME Y14.5.1M-1994, Mathematical Definition of Dimensioning and Tolerancing Principles, ASME. New York, NY, USA.Google Scholar
  4. Bosch, R. (ed) 1995, Coordinate Measuring Machines and Systems, 1st edn, CRC Press. New York, USA.Google Scholar
  5. Carr, K. and Ferreira, P. 1995, ‘Verification of form tolerances part I: Basic issues, flatness, and straightness’, Precision Engineering, 17, pp. 131–143.CrossRefGoogle Scholar
  6. Cheraghi, S.H., Lim, H.S. and Motavalli, S. 1996, ‘Straightness and flatness tolerance evaluation: an optimization approach’, Precision Engineering, vol. 18, pp. 30–37.CrossRefGoogle Scholar
  7. Dhanish, P.B. and Shunmugam, M.S. 1991, ‘An algorithm for form error evaluation – using the theory of discrete and linear Chebyshev approximation’, Computer Methods in Applied Mechanics and Engineering, vol. 92, pp. 309–324.CrossRefzbMATHGoogle Scholar
  8. Etesami, F. and Qiao, H. 1990, ‘Analysis of two-dimensional measurement data for automated inspection’, Journal of Manufacturing Systems, vol. 9, pp. 21–34.CrossRefGoogle Scholar
  9. Feng, S. and Hopp, T. 1991, A Review of Current Geometric Tolerancing Theories and Inspection Data Analysis Algorithms, NISTIR 4509, National Institute of Standards and Technology. Gaithersburg, Maryland.Google Scholar
  10. Forbes, A.B. 1989, Least-Squares Best-Fit Geometric Elements, NPL Report DITC 140/89, National Physical Laboratory. Teddington, UK.Google Scholar
  11. Hodgson, T.J., Kay, M.G., Mittal, R.O. and Tang, S. 1999, ‘Evaluation of cylindricity using combinatorics’, IIE Transactions, vol. 31, pp. 39–47.Google Scholar
  12. Huang, J. 1999, ‘An exact minimum zone solution for three-dimensional straightness evaluation problems’, Precision Engineering, vol. 23, pp.204–208.CrossRefGoogle Scholar
  13. Kanada, T. 1996, ‘Computation of sphericity from minimum circumscribing and maximum inscribing centers by means of simulation data and downhill Simplex method’, International Journal of Japan Society for Precision Engineering, vol. 30, no. 3, pp. 253–258.Google Scholar
  14. International Organization for Standardization 1985, ISO 4291:1985, Methods for the Assessment of Departure from Roundness – Measurement of Variations in Radius, ISO. Geneva, Switzerland.Google Scholar
  15. Lai, H.Y., Jywe, W.Y., Chen, C.K. and Liu, C.H. 2000, ‘Precision modeling of form errors for cylindricity evaluation using genetic algorithms’, Precision Engineering, vol. 24, pp. 310–319.CrossRefGoogle Scholar
  16. Lai, K. and Wang, J. 1988, ‘Computational geometry approach to geometric tolerancing’, Proceedings of the XVI North American Manufacturing Research Conference, pp. 376–379. Urban-Campaign, IL, USA.Google Scholar
  17. Murthy, T.S.R. and Abdin, S.Z. 1980, ‘Minimum zone evaluation of surfaces’, International Journal of Machine Tools Design and Research, vol. 20, pp. 123–136.CrossRefGoogle Scholar
  18. Prakasvudhisarn, C., Trafalis, T. and Raman, S. 2003, ‘Support vector regression for determination of minimum zone’, Transactions of the ASME: Journal of Manufacturing Science and Engineering, vol. 125, pp. 736–739.CrossRefGoogle Scholar
  19. Rajagopal, K. and Anand, S. 1999, ‘Assessment of circularity error using a selective data partitioning approach’, International Journal of Production Research, vol. 37, no. 17, pp. 3959–3979.CrossRefzbMATHGoogle Scholar
  20. Shakarji, C. 1998, ‘Least-squares fitting algorithms of the NIST Algorithm Testing System’, Journal of Research of the NIST, vol. 103, no. 6, pp. 633–641.Google Scholar
  21. Srinivasan, V. 2007, ‘Computational metrology for the design and manufacture of product geometry: A classification and synthesis’, Transactions of the ASME: Journal of Computing and Information Science in Engineering, vol. 7, no. 1, pp. 3–9.CrossRefGoogle Scholar
  22. Suen, D.S. and Chang, C.N. 1997, ‘Application of neural network interval regression method for minimum zone straightness and flatness’, Precision Engineering, vol. 20, pp. 196–207.CrossRefGoogle Scholar
  23. Traband, M.T., Joshi, S., Wysk, R.A. and Cavalier, T.M. 1989, ‘Evaluation of straightness and flatness tolerances using the minimum zone’, Manufacturing Review, vol. 2, pp. 189–195.Google Scholar
  24. Ventura, J.A. and Yeralan, S. 1989, ‘The minimax center estimation problem for automated roundness inspection’, European Journal of Operations Research, vol. 41, pp. 64–72.CrossRefMathSciNetzbMATHGoogle Scholar

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© Springer London 2009

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