Verification of form tolerances part II: Cylindricity and straightness of a median line

Kirsten Carr, Placid Ferreira

Research output: Contribution to journalArticlepeer-review


Most inspectors measure form tolerances as the minimum zone solution, which minimizes the maximum error between the datapoints and a reference feature. Current coordinate measuring machines verification algorithms are based on the least-squares solution, which minimizes the sum of the squared errors, resulting in a possible overestimation of the form tolerance. Therefore, although coordinate measuring machines algorithms successfully reject bad parts, they may also reject some good parts. The verification algorithms developed in this set of papers compute the minimum zone solution of a set of datapoints sampled from a part. Computing the minimum zone solution is inherently a nonlinear optimization problem. This paper develops a single verification methodology that can be applied to the cylindricity and straightness of a median line problems. The final implementable formulation solves a sequence of linear programs that converge to a local optimal solution. Given adequate initial conditions, this solution will be the minimum zone solution. This methodology is also applied to the problems of computing the minimum circumscribed cylinder and the maximum inscribed cylinder. Experimental evidence that the formulations are both robust and efficient is provided.

Original languageEnglish (US)
Pages (from-to)144-156
Number of pages13
JournalPrecision Engineering
Issue number2
StatePublished - Apr 1995


  • coordinate measuring machine
  • cylindrical size
  • cylindricity
  • inspection
  • maximum inscribed cylinder
  • minimum circumscribed cylinder
  • minimum zone solution
  • straightness

ASJC Scopus subject areas

  • General Engineering


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