The system, object of the invention consists of a unit for scanning a mould produced from the sample from a patient's mouth, an image which is sent to digital generation equipment of a removable dental prosthesis, producing a file that is transmitted to metal piece manufacturing equipment by means of sintered powder applying a high-energy ray. The design stages consist of the relief of the mould, the calculation of the insertion axis, the paralleling of the teeth, designing of the elements or components of the prosthesis such as lattice, clamp, stop, major connector, minor connector, bristle, pearls, lingual bars, extrusion of the different elements designed, smoothing of the sharp edges, elimination of the superpositions of the different elements designed and conversion of a closed continuous connected surface to a three-dimensional one.