A machine for the harvesting of plants, movable in a direction of advance, comprises an arm movable between work and transport configurations, a tool comprising lateral ends and being able to occupy a work position and another position, a connecting device via which the tool is connected to the arm and enabling a first movement of the tool relative to the arm, during which the lateral ends move vertically relative to the arm in the same vertical direction relative thereto, the connecting device comprising means making it possible to operate a second transverse and horizontal movement of the tool relative to the arm and making it possible to operate this second movement independently of the first movement. The connecting device comprises an arm oriented in the direction of advance when the support arm is in the work configuration, this arm is articulated on the support arm about a first transverse and horizontal axis when the support arm is in the work configuration, and this arm can, by pivoting about the first axis, move vertically relative to the support arm in the work configuration.