An agricultural machine with a mechanism involving rotating fingers for gathering crops towards an entry port, such as a rotating auger tube, has fingers mounted to be rotatable about a shaft that is itself movable inside the rotating tube, as the ends of the shaft are supported by a pair of cams. The ends of the shaft are movable along cam tracks which impose movement of the shaft along a pre-defined trajectory. Through a suitable coupling mechanism, the rotation of the tube drives the movement of the shaft ends in the cam tracks and hence the movement of the shaft itself, while the shaft remains parallel to the tubes rotation axis.