An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

# Computational investigations for a new, constrained least-squares datum definition for circles, cylinders, and spheres

Published

### Author(s)

Craig M. Shakarji, Vijay Srinivasan

### Abstract

For engineering drawings and CAD definitions, the problem of a suitable datum definition for datum features of circles, spheres, and cylinders has been sought by standards writers over decades. The maximum-inscribed and minimum-circumscribed definitions that have often been used have known problems relating to stability in many common, industrial cases. Examples of these problem cases include cylindrical datum features having an hourglass shape, barrel shape, or the shape of a tapered shaft and circular or spherical datum features that are dimpled. For these problematic cases, many resort to using a least-squares fit whose diameter is scaled to be just inside (or just outside) the datum feature. However, we show this shifted least-squares solution has its own drawbacks. This paper investigates a new datum definition based on a constrained least-squares criterion. The use of this definition for datum planes has already elegantly solved the problem of providing a full contact solution when that solution is stable, while providing a balanced, stable solution in the case of rocker conditions. With that success as motivation, we now investigate using this definition for circles, spheres, and cylinders. We demonstrate that the constrained least-squares is an excellent choice for several known problematic cases. This datum definition maintains stability in cases where the maximum- inscribed fits are not unique and thus not stable. Yet they also maintain close adherence to the maximum- inscribed solution when such solutions are stable. We also show that the constrained least- squares solution has clear benefits over the shifted least squares solution. While not being fully comprehensive, these initial findings indicate that the constrained least-squares appears to be a safe and advantageous datum definition choice and provide substantial optimism that results in future investigated cases will be pleasing as well.
Proceedings Title
Proceedings of the ASME 2016 International Mechanical Engineering Congress & Exposition
Conference Dates
November 11-17, 2016
Conference Location
Phoenix, AZ
Conference Title
The ASME 2016 International Mechanical Engineering Congress & Exposition

### Keywords

circle, coordinate metrology, cylinder, datum, dimensional metrology, fitting, geometric dimensioning and tolerancing, least-squares, optimization, sphere, standards

## Citation

Shakarji, C. and Srinivasan, V. (2016), Computational investigations for a new, constrained least-squares datum definition for circles, cylinders, and spheres, Proceedings of the ASME 2016 International Mechanical Engineering Congress & Exposition, Phoenix, AZ, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=924366 (Accessed June 23, 2024)