Skip to main content

An Iterative Approach to Profile Evaluation Using Interpolation of Measured Positions and Surface Normals

  • Chapter

Abstract

This paper describes a method to adoptively select sample points on a 2 dimensional profile based upon interpolation between sample points. The interpolant uses the measured deviations from nominal position and surface normals at a pair of sample points to predict the form errors between these samples. Additional sample points are selected if the interpolant exceeds a set of sampling criteria and the evaluation process is repeated iteratively until no new sample points are identified. An example of the algorithm’s performance using data containing non-random errors from a machining process is given at’ the end of the paper.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aoyama, H. and Inasaki, I., “Surface Classification and Model Construction Based on Processing Position Vectors and Unit Normal Vectors”, Transactions of NAMRI/SME, 24, (1996), 211–216

    Google Scholar 

  2. Aoyama, H., Kawai, M. and Kishinami, T., “A New Method for Detecting the Contact Point between a Touch Probe and a Surface”, Annals of the CIRP, 1989, 34/1, 593–596

    Google Scholar 

  3. Aoyama, H. and Kishinami, T. “A Proposition of and Interpolation Form Defined by Position Vectors and Unit Normal Vectors”, International Journal Japan Society of Precision Engineering, 25,3, (1991), 239–241.

    Google Scholar 

  4. Carr, K. and Ferriera, P., “Verification of Form Tolerance Part I: Basic Issues, Flatness and Straightness”, Precision Engineering, 17:131–143, 1995

    Article  Google Scholar 

  5. Carr, K. and Ferriera, P., “Verification of Form Tolerance Part II: Cylindricity and Straightness of a Median Line”, Precision Engineering, 17:144–156, 1995

    Article  Google Scholar 

  6. Cheragi, S., Huay S., and Motavalli S., “Straightness and Flatness Tolerance Evaluation: an Optimization Approach”, Precision Engineering, 18:30–37, 1996

    Article  Google Scholar 

  7. DeVries, W. R. and Li, C-J. “Algorithms to Deconvolve Stylus Geometry from Surface Profile Measurements”, Journal of Engineering for Industry, 1985, 107, 167–174.

    Article  Google Scholar 

  8. Duffie, N., Bollinger, J., Piper, R., and Kroneberg, M., “CAD Directed Inspection and Error Analysis Using Surface Patch Databases”, Annals of the CIRP, 33/1, 1984, 347–350.

    Article  Google Scholar 

  9. Edgeworth, R. (1996), “Contouring Data Used for Sampling Algorithm Example”, URL http://www.coe.uncc.edu/∼rmedgewo/Coordinate_Measurement/Contour_data.html

  10. Farin, G. Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide (3rd) Academic Press, San Diego, (1993)

    Google Scholar 

  11. Kim, N. and Kim S., “Geometrical Tolerances: Improved Linear Approximation of Least Squares Evaluation of Circularity by Minimum Variance”, Int. J Mach. Tools Manufact. 36(3), 1996, 355–366

    Article  Google Scholar 

  12. Lai, J. and Chen I., “Minimum Zone Evaluation of Circles and Cylinders”, Int. J. Mach. Tools Manufact. 35(4), 1996,435–451

    Article  Google Scholar 

  13. Menq, C-H., Yau, H-T. and Lai, G-W., “Automated Precision Measurement of Surface Profile in Cad Directed Inspection”, IEEE Transactions on Robotics and Automation, 82, (1992), 268–278.

    Article  Google Scholar 

  14. Mestre, M. and Abou-Kandil, H., “Measuring the errors of form of industrial surfaces: prediction and optimization”, Precision Engineering, 164, (1994), 268–275

    Article  Google Scholar 

  15. Summerhays, K. D., et. al., “New Algorithms for the Evaluation of Discrete Point Measurement Data and for Sample Point Selection on Surfaces with Systematic Form Deviations”, Proceedings of the ASPE-1995, 12,388–391

    Google Scholar 

  16. Vidic, M., Harb, S., Smith, S. T., “Observations of Contact Measurements Using Resonance Based Touch Sensor”, Proceedings of the American Society of Precision Engineers, 1996, 41–46.

    Google Scholar 

  17. Wilhelm, R. G., Srinivasan N., Farabaugh, F., and Hocken, R., “Machine Tool Performance and Part Errors: Experimental Summary”, to appear in the Transactions of the North American Manufacturing Research Institute of the SME, 1997.

    Google Scholar 

  18. Woo, T. C. and Liang, R. “Dimensional Measurement of Surfaces and their Sampling”, Computer Aided Design, 254,233–239

    Google Scholar 

  19. Yamazaki, K., Aoyama, H., Lee, K. S., and Sawabe, M, “Non-Contact Probe for Continuous Measurement of Surface Inclination and Position using Dynamic Irradiation of Light Beam”, Annals ofCIRP, 42/1, 585–588

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Edgeworth, R., Wilhelm, R.G. (1998). An Iterative Approach to Profile Evaluation Using Interpolation of Measured Positions and Surface Normals. In: ElMaraghy, H.A. (eds) Geometric Design Tolerancing: Theories, Standards and Applications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5797-5_27

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-5797-5_27

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7656-9

  • Online ISBN: 978-1-4615-5797-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics