Error Mohr Circle and Invariants of Cofactor Coefficient

Abstract

In this paper, Mohr's circle is used as an implement to show the position error distribution. Using the circle, the four components of the cofactor coefficient matrix, in the two-dimensional case, can be expressed conveniently. Although Mohr's circle is rooted in classical mechanics, its application to deformation analysis is a new achievement. In surveying engineering, the relevant error ellipse is an important method to test the deformation of the network. Mohr's circle, compared to the error ellipse, possesses higher efficacy in testing movements since its confidence area is consistent with the theoretical value. This advantage is shown by a computer imitating example. The difference of the results, obtained by the two methods, is dependent upon point error distribution. In the three-dimensional case, there are three invariants of cofactor coefficients, whose values do not change when the coordinate axis is changed, for a point, and they indicate the situation of error distribution.