Vertical and horizontal movement system of one or more cabins (20) for the transport of people and things in a elevator shifter plant with portal structure (10) for the overcoming overhead and not, back and forth even automatic, obstacles such as roads, railways, waterways and other obstacles affected by driveways and not, especially for pedestrians, usable either in an overhead manner that underground and also incorporated in large buildings such as hospitals, airports, railway stations and so on, with two or more runaways running horizontally and vertically, in which one or more runways include vertical and horizontal stops and descents placed at different levels to overcome obstacles also passing under the same; operated by rack, wherein the motor is rigidly coupled to the cabin and acts via a pinion gear on the rack, having inclined toothing, to increase the fluidity of the movement reducing vibration and noise.