A winding machine is disclosed for winding yarn on a tube to form a package. A package holder arm is pivotally mounted to a fixed structure of the winding machine for rotation about a pivot. A pneumatic actuator causes the package holder arm to be raised or lowered, rotating about the pivot. The actuator has a cavity with two cylindrical chambers of different diameters and a correspondingly shaped piston. The pneumatic actuator is associated with a pressurized air supplying system comprising a control valve. The valve separately supplies and discharges the first, wider cylindrical chamber (41) and the second, narrower cylindrical chamber chamber through two separate first and second conduits. The first conduit, communicating with the wider chamber comprises a choked nozzle for causing a first loss of pressure in the fluid flowing through the first conduit. This first loss off pressure is greater than a second loss of pressure which takes place in the fluid flowing through the second conduit, which communicates with the narrower cylindrical chamber.