system 18 the screwed joint 16 comprises a screw 12 in the form of a cylindrical bolt with a cruciform slot and with a flat collar and a nut 14 in the form of a hexagonal nut with a flat collar the mating holding head 26 is provided with a suitable open ended wrench 34 which forms an interlocking connection with the nut 14 in this case the mating holding head 26 is mounted in a floating manner on the second robot 24 with a defined zero position in the direction of its three mutually perpendicular main coordinate axes x y z on assuming a respective deflected position the mating holding head 26 is pressed in the direction of the zero position by means of an appropriately acting resilient restoring force the floating bearing can be produced on the second robot 24 for example by means of a pneumatic cylinder system with the inclusion of proportional valves the mating holding head 26 is furthermore mounted in a floating manner within a defined pivoting angle double headed rotating arrow 30 about a rotation axis 28 which extends parallel to the screw longitudinal axis 29 the screw driving head 22 contains a screw driving tool 32 which is connected in an interlocking manner to the screw 12 for automated tightening of the screwed joint 16 on the component 10 the screw driving head 22 is provided with a screw.