Evaluation of minimum zone for flatness by normal plane method and simplex search

This paper presents an optimization approach for evaluating the minimum zone flatness for a data set obtained from a Coordinate Measuring Machine. The search for the minimum zone is performed in the parameter space of a plane. The perpendicular distance (p) from the origin to a normal plane intersecting each point in the data set is determined. The difference between the maximum ‘p’ and the minimum ‘p’ for a particular set of parameters (direction cosine angles) determines the minimum zone for flatness. The parameters defining the orientation of a plane through each point in the data set are searched systematically. The set of parameters that determine the minimum zone is found by simplex search. The new method is applied to six example data sets and the results are compared with other methods.