A system of movement of the transport cabin mobile for the transport of people and things, along an overpass constituted of a portal of an urban elevator translator plant, of the overhead type across the obstacle and which joins in and from two stations respectively of departure and arrival opposed to each other, and vice-versa, comprising vertical guide columns (11, 12, 13, 14) and horizontal guide beams (15, 16) to which the said cabin is bound by means of slide means adapted to perform the horizontal movement with respect to said guide beams (15, 16), and with carriage means acts to make the vertical movement with respect to the vertical guide columns (11, 12, 13, 14) said carriage means being of the type engageable with said slide means to perform the said vertical movement with respect to the vertical guide columns (11, 12, 13, 14), and wherein the said cabin is moved vertically and horizontally by means of a chain ring closed to which is bound the slide, said chain of the type moved by a motor means, so as to allow movement and support of the cabin along the horizontal and vertical axis (x, y), the connection between the flanks, the cabin, the vertical guide columns (11, 12, 13, 14) and horizontal guide beams (15, 16), is obtained by means of at least one slide, said slide constrained to the drive cabin being provided with a row of upper wheels parallel with respect to a row of lower wheels so as to slide in the case of the translation of the cabin along the horizontal axis (x) with respect to the parallel guide rails (17, 18) which are parallel, made longitudinally and in correspondence with the vertical inner faces of said horizontal guide beams (15, 16), said horizontal guide beams (15, 16), joined with the ends to said vertical guide columns (11, 12, 13, 14) so as to allow the cabin, by means of hollow guides the achievement also of the vertical movement with the aid of carriages engaged from the corresponding slide, sliding with respect to each pair of columns (11, 13) and (12, 14) of said portal along the vertical axis (y), and wherein in correspondence of the inner faces of said columns of vertical guide (11, 12, 13, 14) are provided guides (190, 191) of the carriages. wherein for translating the cabin in a vertical direction along at least one of said pairs of vertical guide columns (11, 12, 13, 14), in correspondence of the interior side of said carriages there are extension rails (170, 180) of the rails (17, 18) of said horizontal guide beams (15, 16), said extension rails (170, 180) which allow the slides which laterally support the cabin to take and to engage said carriages, wherein the ring chain allows to move the cabin along the vertical and horizontal directions (x, y) through a single motor, said chain is arranged in closed ring through a series of pinions and crowns so as to follow the trajectory of the cabin and remaining attached through a pin which is integral with the slide and wherein the chain is fixed to the pin which also acts as rope-head for the two ends of the chain which close the ring, said pin which can rotate on itself so as to follow the variations in direction, in such way that acting directly or indirectly on the chain, by means of the motor, it is possible to realize the movement in both directions, forwards and backwards, so as to move the cabin in all directions, vertical and horizontal by means of the same motor,comprising a device for suspension of the carriages to which engages, through the slides, the said cabin, said suspension device of the carriages with ropes or chains which are bound to their opposite ends (401, 402) to the two opposite carriages of the same arch, and that through returns (405, 410) raise a slide attachment on which they insist the hydraulic cylinders for the balancing, so as to apply alternately, to both opposite carriages of each of the two arches the traction of a single balancing system, characterized in that the balancing device of the carriages, is adaptive, with hydraulic cylinders fed by hydropneumatic accumulators in which some pressurized gas in the inside of an elastic bag, allows to maintain pressure in an oil reservoir, in such a way that acting by means of appropriate suspension system the weight of the cabin being balanced, the elements rigidly coupled thereto, as well as the load being transported, said balancing device, being able to vary the power of the counterweight according to the actual load, being that the hydraulic cylinders present bore and stems different between them, and wherein said device interacts with weighing means, which detect the weight that insists on the cabin and an electronic system which supervises the management of the balance, based on the load detected by said load cells, so as to open the valves of those cylinders which can realize a thrust as close to that necessary to maintain in equilibrium the cabin and its load.