The system has a form of a movable and fixable structure node, equipped with hinges and/or pins. It consists of a head bush adapted to be fixed in an articulator, said head bush consisting of the dish (1), the lid (2), of the hub (3) with an internal through-orifice, of the ball pin (4), of the cylinder (5), of the plate (6), and of the control element (7). In case the fixation is required, the control element (7) contacts the plate (6) which pushes on the cylinder (5). Said cylinder (5) acts on the ball pin (4) and the force from the ball pin (4) is transferred further on the hub (3) to ensure its fixation against the dish (1). In a variant it can be completed with a counterpart having shape of the structure element (9) which contains the disk plate (109) on the opposite side of which two pairs of movable plates (104) are fixed and equipped with an internal longitudinally-shaped opening. The arrested screw (105) passes through the internal openings of the movable plates (104). In another variant it can be completed with a calibrating pillar which contains two disks (201, 201a) joined with the movable bottom element (203) and with the movable top element (203a) which are joined with a set of ball hinges (202, 202a, 206).