A device for actuating a rotating shaft selected from a plurality of parallel rotating shafts, comprising a driving shaft supported and actuated by corresponding rotation means, which is provided with a driving gear for the transmission of torque, a plurality of driven shafts each one of which is provided with a corresponding driven gear that is designed to be meshed with the driving gear, the driven gears being arranged on the respective driven shaft in an axial position that is offset with respect to the other driven gears, the driving gear being capable of performing a translational movement axially with means of translational motion for alternate meshing with one of the driven gears, the device further comprising means of prevention of rotation for the driven shafts whose driven gear is not meshed with the driving gear.