Abstract: It is well known that the coordinates of any two spatial points in different orthogonal coordinate systems are different, but the distance between the two points of them is the same. This feature leads to the distance error model⁶.Research work has shown that the distance error model is useful to the study of the positioning accuracy of robots.This paper gives a demonstration to the single valued relationship between the distance accuracy and the positioning accuracy of robots. The results of the positioning error compensation on PUMA 560 robot has also been shown in the paper.