Abstract: The present invention discloses a universal abrader capable of grinding, polishing, waxing, cutting (including groove and block cutting), and boring on surfaces having various shapes and tilting positions, for various architectural members. The abrader comprises a main body, a movable headstock supported movably on the main body; a rotatable arm supported rotatively on the movable headstock; a processing tool assembly mounted at the free end of the rotatable arm and carrying a rotatable processing tool; a driving mechanism for rotating the processing tool; a motion supporting mechanism for supporting the movable headstock on the main body and enabling the movable headstock with respect to the main body not only to rotate but also to displace in a direction perpendicular to a plane, in which, the processing tool rotates; a rotation supporting mechanism for supporting the rotatable arm on the movable headstock; and a walking mechanism mounted under the main body, for carrying the abrader to walk.