A piece of equipment for the mechanical machining of sheet-shaped elements, comprising: - at least a press bending machine having: - at least a bearing structure which has a work surface having at least a containment seat for containing at least a portion to be bent of a sheet-shaped element to be bent; - pressing means associated in a movable manner with said bearing structure along a direction of sliding moving close to / away from said work surface and adapted to bend said portion to be bent; - at least a central management unit operatively connected to said pressing means and programmed to control the movement thereof along said direction of sliding; - at least an accompanying device having: - at least a base frame for resting on the ground; - at least a supporting surface of said sheet-shaped element associated with said base frame and movable in rotation with respect to a relative axis of oscillation; - actuating means for actuating the rotation of said supporting surface with respect to said axis of oscillation; said accompanying device comprises: - detection means for detecting the position of said pressing means along said direction of sliding; and - at least an independent management unit, distinct from said central management unit and programmed for the adjustment of the rotation of said supporting surface depending on the position detected by said detection means, characterized by the fact that it comprises removable positioning means interposable between said machine and said accompanying device for the positioning of said accompanying device in a configuration of alignment with respect to said machine depending on said axis of oscillation, wherein said removable positioning means comprise at least a first abutment surface arranged in contact with at least a portion of said supporting surface and at least a second abutment surface arranged in contact with at least a portion of said containment seat, and said second abutment surface has a pointed profile substantially complementary with the profile of said containment seat, in such a way as to enable its substantial fitting to measure inside the containment seat itself in the configuration of alignment. - at least a press bending machine having: - at least a bearing structure which has a work surface having at least a containment seat for containing at least a portion to be bent of a sheet-shaped element to be bent; - pressing means associated in a movable manner with said bearing structure along a direction of sliding moving close to / away from said work surface and adapted to bend said portion to be bent; - at least a central management unit operatively connected to said pressing means and programmed to control the movement thereof along said direction of sliding; - at least a bearing structure which has a work surface having at least a containment seat for containing at least a portion to be bent of a sheet-shaped element to be bent; - pressing means associated in a movable manner with said bearing structure along a direction of sliding moving close to / away from said work surface and adapted to bend said portion to be bent; - at least a central management unit operatively connected to said pressing means and programmed to control the movement thereof along said direction of sliding; - at least an accompanying device having: - at least a base frame for resting on the ground; - at least a supporting surface of said sheet-shaped element associated with said base frame and movable in rotation with respect to a relative axis of oscillation; - actuating means for actuating the rotation of said supporting surface with respect to said axis of oscillation; - at least a base frame for resting on the ground; - at least a supporting surface of said sheet-shaped element associated with said base frame and movable in rotation with respect to a relative axis of oscillation; - actuating means for actuating the rotation of said supporting surface with respect to said axis of oscillation; - detection means for detecting the position of said pressing means along said direction of sliding; and - at least an independent management unit, distinct from said central management unit and programmed for the adjustment of the rotation of said supporting surface depending on the position detected by said detection means,