Skip to main content
Log in

Approximation by circles

  • Published:
Zeitschrift für Operations Research Aims and scope Submit manuscript

Zusammenfassung

Wir entwickeln Algorithmen, mit deren Hilfe die Einhaltung der Positionstoleranzen ebener Lochbilder untersucht werden kann. Die Gruppe der Ist-Zentren wird dabei gegenüber der Gruppe der Soll-Zentren so eingepaßt, daß der maximale Abstand zwischen den Soll- und den Ist-Werten minimal ausfällt.

Abstract

We derive algorithms which permit the inspection of plane hole patterns for their position tolerance. The entire hole pattern is measured by a coordinate measuring machine and then is fitted into the nominal pattern in such a way as to minimize the maximum of the distances between the nominal and the actual positions.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Avriel M (1976) Nonlinear programming. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  2. Bänninger E (1982) Die Prüfung von Positionstoleranzen mit Berücksichtigung des MMC-Prinzips. VSM-Normenbüro, Zürich

    Google Scholar 

  3. Bihlmayer W (1987) Algorithmen zur Prüfung von Positionstoleranzen mit Berücksichtigung des MMC-Prinzips. Thesis, Ulm

  4. Dörflinger J (1986) Approximation durch Kreise: Algorithmen zur Ermittlung der Formab-weichung mit Koordinatenmeßgeräten. Thesis. Ulm

  5. Courant R, Robins H (1973) Was ist Mathematik. Springer-Verlag, Berlin, pp 98–102

    Google Scholar 

  6. Elzinga J, Hearn D (1972) Geometrical solutions for some minimax location problems. Transportation Science 6:379–394

    Google Scholar 

  7. Fletcher R (1981) Practical methods of optimization, vol 2. J Wiley & Sons, New York

    Google Scholar 

  8. Frost EL (1982) Description of the computer program COCOMP. Sandia National Laboratories, Report SAND 79-0028

  9. Halpin WJ (1978) Details of the mathematics associated with COCOM and COCOMP. Sandia National Laboratories, Report SAND 77-1316

  10. Hogan W (1973) Directional derivatives for extreme-value functions with applications to the completely convex case. Operations Research 21:188–209

    Google Scholar 

  11. Krabs W (1983) Einführung in die lineare und nichtlineare Optimierung für Ingenieure. Teubner, Stuttgart

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bihlmayer, W., Forst, W. Approximation by circles. ZOR - Methods and Models of Operations Research 33, 315–339 (1989). https://doi.org/10.1007/BF01416079

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01416079

Key words

Navigation