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A Constrained L2 Based Algorithm for Standardized Planar Datum Establishment

Published

Author(s)

Craig M. Shakarji, Vijay Srinivasan

Abstract

For years (decades, in fact) a definition for datum planes has been sought by ASME and ISO standards writers that combines the contacting nature of traditional surface plate mating with a means of balancing rocking conditions when there is a centrally positioned extreme point or edge on the datum feature. This paper describes a completely self-balancing method for datum plane establishment that matches traditional surface plate mating while automatically stabilizing rocker conditions. The method is based on a constrained L2 minimization, which, when seen mathematically, elegantly combines the desirable contact properties of the constrained L1 minimization with the stable properties of the unconstrained least-squares and does so in a manner that avoids the drawbacks of either of those two definitions. The definition is shown along with proofs of a mathematical development of an algorithm that relies on a strategically chosen singular value decomposition that allows for an elegant, robust solution. Concise code is included for the reader for actual use as well as to full clarify all the algorithmic details. Testing has shown the definition defined here does indeed provide attractive balancing of full contact with rocker stability, leading to guarded optimism on the part of the key standards committees as an attractive default definition. Since both the ISO and ASME standardization efforts are actively working to establish default datum plane definitions, the timing of such a rigorously documented study is opportune.
Proceedings Title
Proceedings of the ASME 2015 International Mechanical Engineering Congress & Exposition
Conference Dates
November 13-19, 2015
Conference Location
Houston, TX, US

Keywords

coordinate metrology, datum, geometric and dimensional tolerancing, least-squares, plane

Citation

Shakarji, C. and Srinivasan, V. (2015), A Constrained L2 Based Algorithm for Standardized Planar Datum Establishment, Proceedings of the ASME 2015 International Mechanical Engineering Congress & Exposition, Houston, TX, US, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=921833 (Accessed April 18, 2024)
Created November 18, 2015, Updated April 4, 2022