A motorization device comprises two substantially parallel winding cylinders, at least one longitudinal link element to maintain a predetermined distance between the cylinders, and wound around said winding tracks, the link element consequently having a crossover point between the winding cylinders, two flexible tracks fixed to the winding cylinders and arranged facing and in contact with one another at the point of contact, a winding cylinder and flexible track assembly forming a fitting, a prestressing force being applied at the point of contact under the effect of the link element. The flexible tracks have a spiral form configured that the point of contact between the two flexible tracks in spiral form, situated between said winding cylinders, is offset relative to the crossover point, such that a torque dependent on the distance between the point of contact and the crossover point is applied, to provoke the mutual rotation of the fittings.