Winding apparatus for the fully automated wrapping of a bundle of wires in an adhesive tape, comprising - a winding unit having an outer ring, which is open on one side and on the inside of which an annular winding rotor, which is open on one side, is arranged such that it can be rotated relative to the outer ring about an axis of rotation running in the longitudinal direction (x) of the winding apparatus, wherein a holder for accommodating a roll of adhesive tape is fastened in a rotatable manner on the winding rotor; - a bracing device for bracing the bundle of wires in the longitudinal direction (x) of the winding apparatus; - a delivery unit, by means of which the winding unit can be moved, in a direction transverse to the longitudinal direction (x) of the winding apparatus, between an operating position, in which the winding unit encloses the braced bundle of wires, and a set-back position, in which the braced bundle of wires is arranged outside the winding unit; - an advancement unit, by means of which the winding unit can be moved in the longitudinal direction (x) of the winding apparatus; - a control device, by means of which the winding unit, the bracing device, the delivery unit and the advancement unit can be activated for the fully automated wrapping of the bundle of wires, wherein the bracing device has a fixing gripper for fixing the bundle of wires and also has a bracing unit for prestressing the bundle of wires prior to the prestressed bundle of wires being wrapped, and wherein the bracing unit for prestressing the bundle of wires has a bracing gripper, which can be moved in the longitudinal direction (x) of the winding apparatus, wherein the winding apparatus has a centring device, by means of which the bundle of wires can be arranged, at least locally, concentrically in relation to the winding rotor, wherein the centring device has a centring unit with two centring arms, which comprise respective depressions for accommodating the bundle of wires, and, in a centring position of the centring unit, these depressions jointly enclose the bundle of wires and thus arrange them concentrically in relation to the winding rotor, characterized in that the centring arms are mounted on the outer ring of the winding unit by means of a four-bar linkage and, in order for the centring arms to be opened and closed, are connected to an extensible cylinder. - a winding unit having an outer ring, which is open on one side and on the inside of which an annular winding rotor, which is open on one side, is arranged such that it can be rotated relative to the outer ring about an axis of rotation running in the longitudinal direction (x) of the winding apparatus, wherein a holder for accommodating a roll of adhesive tape is fastened in a rotatable manner on the winding rotor; - a bracing device for bracing the bundle of wires in the longitudinal direction (x) of the winding apparatus; - a delivery unit, by means of which the winding unit can be moved, in a direction transverse to the longitudinal direction (x) of the winding apparatus, between an operating position, in which the winding unit encloses the braced bundle of wires, and a set-back position, in which the braced bundle of wires is arranged outside the winding unit; - an advancement unit, by means of which the winding unit can be moved in the longitudinal direction (x) of the winding apparatus; - a control device, by means of which the winding unit, the bracing device, the delivery unit and the advancement unit can be activated for the fully automated wrapping of the bundle of wires, wherein the bracing device has a fixing gripper for fixing the bundle of wires and also has a bracing unit for prestressing the bundle of wires prior to the prestressed bundle of wires being wrapped, and wherein the bracing unit for prestressing the bundle of wires has a bracing gripper, which can be moved in the longitudinal direction (x) of the winding apparatus, wherein the winding apparatus has a centring device, by means of which the bundle of wires can be arranged, at least locally, concentrically in relation to the winding rotor, wherein the centring device has a centring unit with two centring arms, which comprise respective depressions for accommodating the bundle of wires, and, in a centring position of the centring unit, these depressions jointly enclose the bundle of wires and thus arrange them concentrically in relation to the winding rotor, characterized in that the centring arms are mounted on the outer ring of the winding unit by means of a four-bar linkage and, in order for the centring arms to be opened and closed, are connected to an extensible cylinder. wherein the winding apparatus has a centring device, by means of which the bundle of wires can be arranged, at least locally, concentrically in relation to the winding rotor, wherein the centring device has a centring unit with two centring arms, which comprise respective depressions for accommodating the bundle of wires, and, in a centring position of the centring unit, these depressions jointly enclose the bundle of wires and thus arrange them concentrically in relation to the winding rotor, characterized in that the centring arms are mounted on the outer ring of the winding unit by means of a four-bar linkage and, in order for the centring arms to be opened and closed, are connected to an extensible cylinder.