A movement device, comprising a cutting torch, particularly a cutting torch of the plasma type, a working head that can move along three Cartesian axes (3, 4, 5) which are mutually perpendicular and supports said cutting torch for cutting mechanical pieces, means for the combined rotary and translational motion of said cutting torch with respect to said working head being further comprised in order to vary the inclination of the cutting flow with respect to said mechanical piece, the centre of instantaneous rotation of said cutting torch with respect to which said means for combined rotary and translational motion operate coincide substantially with the focal point of said cutting torch, wherein said working head comprises a box-like body which is slideably associated with a frame along two straight guides that belong to said frame and are substantially parallel, respectively, to a second one and a third one of said Cartesian axes (3, 4, 5), characterized in that the working head comprises an impeller which supports said cutting torch and is accommodated rotatably within said box-like body by means of a first gear which can be actuated by second drive means which are accommodated in said box-like body, wherein said cutting torch is associated with said working head by way of two supporting arms (27, 28), of which the first one is integral with said impeller and the second one is associated with said cutting torch, said first supporting arm extending from said impeller substantially parallel to a first axis of revolution, which is substantially parallel to a first of one of said Cartesian axes (3, 4, 5), and eccentrically with respect to said first axis of revolution and said second supporting arm being associated kinematically with said first supporting arm by way of an articulated quadrilateral structure, which lies on a plane which is substantially parallel to said first axis of revolution and can be actuated by third drive means accommodated within said box-like body by means of mechanical transmission elements which are defined inside said supporting arms (27, 28), said articulated quadrilateral structure, said third drive means and said mechanical transmission elements defining part of said means for combined rotary and translational motion, said cutting torch being connected kinematically to said mechanical transmission elements for its opposite rotation about said second axis of revolution with respect to the direction of rotation of said second supporting arm relative to said first supporting arm, wherein said third drive means and said mechanical transmission elements comprise a third electric motor, which is associated with a third speed reduction unit on the output shaft of which a third pinion is keyed and engages a second toothed wheel which is fitted rotatably on the shaft of said impeller, said second toothed wheel being integral in rotation with a third toothed wheel, which is fitted rotatably on the shaft of said impeller and is associated kinematically with a screw-and-nut coupling which is accommodated at least partly in said first supporting arm and produces a translational motion of a second rack, which engages two actuation pinions (37, 38) of said articulated quadrilateral structure, wherein said articulated quadrilateral structure comprises two linkages (39, 40), which are integral in rotation, at their ends, with said actuation pinions (37, 38) and with two driving pulleys (41, 42) which are accommodated within said second supporting arm and one of which is connected, by way of a belt transmission, to a driven pulley, which is provided on an actuation shaft associated with a supporting base of said cutting torch, the axis of said actuation shaft coinciding with said second axis of revolution, the distance between the pivots of each one of said linkages (39, 40) being equal to the distance between said focal point and said second axis of revolution, said linkages (39, 40) being oriented parallel to said second axis of revolution.