the plate about the toroidal axis 18 of the toroid the tool 19 rotates about the longitudinal geometrical axis 34 of a tool carrier 22 the axis 34 being tangential to the mean longitudinal internal axis 33 of the toroidal bend this type of machining can be carried out on a boring machine or a milling machine fitted with a conventional plate or a cast iron plate with controlled rotation the shape of the bend and the different relative values of the angle 7 of the bend of the radius 20 of the bend and of the internal diameter 21 of the bend define the limits of the boring process described above the tool carrier 22 abuts against the projecting edge formed by the face of the bend and its toroidal internal surface at the point 23 furthest from the center the operation can be continued by repeating the machining operation through the opposite orifice in the blank for example the process can be used to machine the bore in a curved pipe 25 in which the angle 7 is equal to 90 u00b0 and of which the radius of curvature is equal to the internal diameter 24 fig5 on the other hand less sharp curves or bends such as those having an angle 7 of 60 u00b0 and having a radius of curvature in excess of three times the internal diameter for example cannot be machined internally by the above described process even by gaining access to the.