The machine control 30 drives the winder 1 according to the invention in such a manner that for the winding of a reel 6, the pair of supporting arms 17 is continuously moved away from the contact roller 4 in accordance with the calculated desired radius of the reel 6 which is building up. The contact roller is exposed to the contact pressure through the cylinder arrangement 24 and remains in its desired position without any perturbations (out-of-round reel, incorrectly calculated desired radius) but in the event of perturbations, can avoid the perturbation due to its floating mounting.