1. A device for measuring the shape of a three-dimensional object comprising: a movable arm having a plurality of movable arm members coupled in tandem by joints; a probe coupled to the forward end of said movable arm by a universal joint, said probe adapted for contacting the three-dimensional object, the shape of which is to be measured, and said probe being rotatable and having at its forward end a flat surface portion which is provided perpendicular to an axis of said probe and which contacts said three-dimensional object; angle-of-rotation encoder means for detecting the angles of rotation of said probe and said movable arm members during the measurement of the shape of the three-dimensional object; and calculating means for calculating, on the basis of information from said angle-of-rotation encoder means and the dimensions of said movable arm, the orientation of said flat surface portion of said probe in contact with the three-dimensional object, to thereby determine a tangent plane at the contact point between said flat surface portion and said three-dimensional object, and determining the shape of the three-dimensional object from a plurality of tangent planes at contact points between said flat surface portion of said probe and said object.