Methods of robotics and the pseudoinverse to obtain the least-squares fit of measured points on line-profiles

J. K. Davidson, S. B. Savaliya, Y. He, Jami J. Shah

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations

Abstract

Tolerances on line profiles are used to control cross-sectional shapes of parts, such as turbine blades. A full life cycle for many mechanical devices depends (i) on a wise assignment of tolerances during design and (ii) on careful quality control of the manufacturing process to ensure adherence to the specified tolerances. This paper describes a new method to improve the quality control of a manufacturing process by converting measured points on a part to a geometric entity that can be compared directly with tolerance specifications. The focus of this paper is the development of a new computational method for obtaining the least-squares fit of a set of points that have been measured with a coordinate measurement machine along a line-profile. The pseudo-inverse of a rectangular matrix is used to convert the measured points to the least-squares fit of the profile. A numerical example is included for a convex line-profile that is formed from line- And circular arc-segments.

Original languageEnglish (US)
Title of host publicationASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2012
Pages347-358
Number of pages12
DOIs
StatePublished - Dec 1 2012
EventASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2012 - Chicago, IL, United States
Duration: Aug 12 2012Aug 12 2012

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
Volume5

Other

OtherASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2012
CountryUnited States
CityChicago, IL
Period8/12/128/12/12

ASJC Scopus subject areas

  • Modeling and Simulation
  • Mechanical Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design

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    Davidson, J. K., Savaliya, S. B., He, Y., & Shah, J. J. (2012). Methods of robotics and the pseudoinverse to obtain the least-squares fit of measured points on line-profiles. In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2012 (pp. 347-358). (Proceedings of the ASME Design Engineering Technical Conference; Vol. 5). https://doi.org/10.1115/DETC2012-70203