Conputer Mechanics Profile Measurement Without a Standard. Measurement of Flatness along a Circle.

Abstract

This paper describes a method for measuring surface profile without a standard. At first, it is discribed that measurement of straightness along a line on the surface, in general, can not be accomplished without a standard. Next, as a simple case, measurement of a flatness along a circle on the surface is described. For the purpose, the distances between two unknown surfaces located almost in parallel are measured along the circle. One of the surfaces is rotated around the center of the circle and the distances are measured again. This prosedure is repeated many times. The profiles of the two surfaces are calculated with a system of simultaneous linear equations. The equations consist of two types : one is the observation equation formed using many measured distances ; the other is the equation derived from the condition that the surface profile is determined by the deviation from the mean plane defined by the least square method. Computer simulation of the method proves the validity of the method and estimates the effects of the measuring error.