Measurement Techniques

, Volume 61, Issue 6, pp 588–594 | Cite as

Analysis of Basic Data of Unstable Problems of Coordinate Measurements of Geometrical Parameters of Products

  • M. F. DanilovEmail author
  • A. A. Savel’eva

The conditions for the appearance of instability have been analyzed in solving typical problems of coordinate measurements of the geometric parameters of products. The connection is shown between unstable problems of coordinate measurements and ill-conditioned systems of linear equations, and also with the parameters of the geometric elements that show signs of degeneracy. Formulas have been derived for estimating measurement error of the parameters of a circle, coaxiality of cylinders, and parallelism of planes. It has been established that the experimental results are consistent with the theoretical ones.


coordinate measurements unstable problems ill-conditioned problems 


  1. 1.
    V. P. Suslin and A. V. Dzhunkovskii, “Application of the method of regularization to solve ill-conditioned problems of coordinate measurements,” Izmer. Tekhn., No. 7, 23–26 (2009).Google Scholar
  2. 2.
    A. E. Umnov, Analytical Geometry and Linear Algebra: Textbook, MFTI, Moscow (2011).Google Scholar
  3. 3.
    I. B. Petrov and A. I. Lobanov, Lectures on Computational Mathematics: Textbook, Internet University of Information Technologies, BINOM, Moscow (2006).Google Scholar
  4. 4.
    GOST P 53442–2015, Characteristics of Geometric Products. Establishment of Geometric Tolerances. Tolerances for Form, Orientation, Location, and Runout.Google Scholar
  5. 5.
    M. F. Danilov, A. P. Ivanov, and A. A. Savel’eva, “Evaluation of the error of coordinate measurements of the geometric parameters of a component based on a priori data,” Izmer. Tekhn., No. 3, 23–27 (2018).Google Scholar
  6. 6.
    Ya. S. Bugrov and S. M. Nikol’skii, Higher Mathematics. Elements of Linear Algebra and Analytical Geometry, Nauka, Moscow (1980).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Research Institute for Optoelectronic InstrumentationSosnovyi BorRussia

Personalised recommendations