This study deals with the development of an automatic system for measuring and evaluating the thickness of free curved plates, called Orthros. We proposed a method to generate a measuring path with high continuity of the measuring postures by using a quaternion to represent a change in posture with an interpolation algorithm, called squad. In this paper, a new method is proposed to determine the positions and postures of the representative points for interpolation that affect continuity of the measuring path. The validity of the proposed method was confirmed using evaluations of the continuity of a path according to changes in the joint angle of a robot.