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Theory and Algorithms for L1 Fitting Used for Planar Datum Establishment in Support of Tolerancing Standards

Published

Author(s)

Craig M. Shakarji, Vijay Srinivasan

Abstract

We present the theory and algorithms for establishing a datum plane consistent with ASME Y14.5 standard definitions corresponding to a planar datum feature sampled with coordinate data that is weighted,. The method uses a one-sided minimization search based on the L_1 (L1) norm. We prove that the problem reduces to a simple minimization search between the weighted centroid and the convex hull. The practice of unweighted fitting works well enough when point sampling is controlled and can thus be made uniform (e.g., using a discrete point contact Coordinate Measuring Machine). However, we show by example that nonuniformly sampled points (arising from many new measurement technologies) coupled with unweighted fitting can lead to erroneous results. When needed, the algorithms presented also solve the unweighted cases simply by assigning the value one to each weight. Terse Mathematica code is included for the reader. The code is sufficient for constrained and unconstrained planar fitting as well as a 3-2-1 datum reference frame generation, which is also described in detail. We additionally prove convergence from the discrete to continuous cases of datum establishment as the point sampling becomes dense.
Proceedings Title
Proceedings of the ASME 2012 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference
Conference Dates
August 4-7, 2013
Conference Location
Portland, OR

Keywords

datum, datum feature, datum plane, datum reference frame, fitting, geometric dimensioning and tolerancing, L1, L1 norm, plane, plane fitting, standards

Citation

Shakarji, C. and Srinivasan, V. (2013), Theory and Algorithms for L1 Fitting Used for Planar Datum Establishment in Support of Tolerancing Standards, Proceedings of the ASME 2012 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Portland, OR (Accessed March 3, 2024)
Created October 15, 2013, Updated February 19, 2017