The separating device comprises: an actuating device (8) translatable along a first axis (A1) between a retracted position and a separated position, at least one separating element (28, 60) translatable along a second axis (A2) between a retracted position and a separated position, a transfer device (26) connecting the actuating device (8) and the separating device (28, 60). The transfer device (26) comprises at least two links (46), rotatable relative to one another and relative to the actuating device (8) and the separating element (28, 60), and a guide element (36) receiving said links (46), said links being moved along a movement path by the actuating device (8) and moving the separating element (28, 60).