A winding machine for winding yarn on a tube to form a package, the winding machine comprising: - a fixed structure; - a package holder arm supporting a fixed center and a movable center, which centers can be opened and closed to release the package or to receive a new tube, said holder arm being pivotally mounted to the fixed structure for rotation about a pivot; - an actuator comprising a pneumatic cylinder, supplied by a source of pressurized air, wherein the actuator has a first end connected to the fixed structure of the winding machine and a second end connected to the package holder arm, whereby actuation of the actuator causes the package holder arm to be raised or lowered rotating about the pivot, and the actuator is associated with a supplying system comprising a control valve connectable to the source of compressed air or an equivalent pressurized operation fluid, the actuator comprising a casing defining a cavity for slidingly accommodating a piston, and a piston slidingly accommodated within the cavity; characterized in that - the cavity is so shaped as to form an end portion with a first, wider cylindrical chamber and a second, narrower cylindrical chamber; - the piston comprises two superimposed, respectively wider and narrower cylindrical portions (45, 46) having shapes and sizes corresponding to the cylindrical chambers (41, 42); - the control valve controls the pressure supplied to the cavity as a result of control signals from a control unit which controls operation of the winding machine, and that the control valve separately supplies and discharges the first and second chamber through two separate first and second conduits, and that at least the first conduit comprises a means for causing a first loss of pressure in the fluid flowing through the first conduit, whereby the first loss of pressure is greater than a second loss of pressure in the fluid flowing through the second conduit, and that - the cavity is mushroom-shaped in its lower end portion, with the wider cylindrical chamber arranged above the narrower cylindrical chamber. - a fixed structure; - a package holder arm supporting a fixed center and a movable center, which centers can be opened and closed to release the package or to receive a new tube, said holder arm being pivotally mounted to the fixed structure for rotation about a pivot; - an actuator comprising a pneumatic cylinder, supplied by a source of pressurized air, wherein the actuator has a first end connected to the fixed structure of the winding machine and a second end connected to the package holder arm, whereby actuation of the actuator causes the package holder arm to be raised or lowered rotating about the pivot, and the actuator is associated with a supplying system comprising a control valve connectable to the source of compressed air or an equivalent pressurized operation fluid, the actuator comprising a casing defining a cavity for slidingly accommodating a piston, and a piston slidingly accommodated within the cavity; - the cavity is so shaped as to form an end portion with a first, wider cylindrical chamber and a second, narrower cylindrical chamber; - the piston comprises two superimposed, respectively wider and narrower cylindrical portions (45, 46) having shapes and sizes corresponding to the cylindrical chambers (41, 42); - the control valve controls the pressure supplied to the cavity as a result of control signals from a control unit which controls operation of the winding machine, and that the control valve separately supplies and discharges the first and second chamber through two separate first and second conduits, and that at least the first conduit comprises a means for causing a first loss of pressure in the fluid flowing through the first conduit, whereby the first loss of pressure is greater than a second loss of pressure in the fluid flowing through the second conduit, and that - the cavity is mushroom-shaped in its lower end portion, with the wider cylindrical chamber arranged above the narrower cylindrical chamber.