Abstract: A tool fastening apparatus for industrial robots comprises a coupling unit attached to the arm of a robot and a coupling unit attached to a tool to be used with the robot. When the two coupling units are joined together, their relative position can be easily and accurately fixed by means of positioning couplings comprising ball rings carrying a set of annularly arranged balls slightly sticking out from the plane of contact between the two coupling units. Accurate positioning is achieved by bringing the balls on the two ball rings into engagement, which, in turn, is achieved by fitting each ball on one ball ring into between two adjoining balls on the other ball ring.