Algorithms and measurements the slope and straightness deviation line 2D with stiff probe on manual coordinate measuring machine

Abstract

A mathematical method and the computer algorithm have been developed for determining the slope, straightness deviation and root-mean square roundness deviation for a line in space. The parameters describing the line location have been determined using the orthogonal regression analysis and the least squares method. The lines approximating true line location have been assumed to include the gravity center for the measured points set. satisfying the condition for the minimum value of a Lagrange function with side condition, one can derive a system of homogeneous equations with two unknowns for two unknowns for the spatial line case. By solving these equations, the eigenvalue, n , i =1, 2 and the i eigenvector l (2, 2) could have been determined; l (2, 2) being the normal vectors of the approximating lines including the gravity center. The normal vector to the line to be determined corresponds to the minimum eigenvalue l , i =1, 2.W artykule przedstawiono podstawy matematyczne i obliczenia nachyleń prostych, o prostolinowości i odchyłek prostolinowości wzgldem prostej 2D i odchyłkę prostolinowości średnio kwadratową. Parametry prostej wyznaczono za pomocą regresji stosując metodę najmniejszych kwadratów