Dimensional measurement data analysis, part 1: A zone fitting algorithm

Measured data taken from Coordinate Measuring Machines ( CMMs ) are in the form of Cartesian coordinates of points from a part surface. In order to in terpret the data, a numerical analysis must be performed on them. Currently , delta fitting techniques such as a least squares fit or a min-max fit are employed to compare the measured points to the design model. As the object ives of the various techniques differ, they often yield conflicting results . Since this discrepancy may lean to a different conclusions in the process dimensional inspection, if is critical that inspection procedures are base d on well defined criteria that employ the appropriate technique to achieve the desired inspection goals. If tolerances are represented by tolerance zones, a zone fitting algorithm, introduced in this paper provides a more consistent means of verify confor mance to the tolerance zone. It determines whether a set of measured points fits into a specified tolerance Zone. If the point set can Jit into the zo ne, a rigid body transformation placing the points inside the zone is retur ned The algorithm is numerically stable and addresses a general type of tol erance zone. The examples demonstrate that the zone fitting algorithm is mo re consistent compared to the least squares fit and the min-max fit in tole rance zone conformance verification. A subsequent paper (Part 2) addresses the determination of a minimum zone that extends inspection from a pass/fai l mode to a quality analysis operation.