At 2:1, turning the same way, each blade's path round the part is an ellipse centred on the part's axis and fixed on it, so every pass recuts the same two opposite flats. Off that ratio the flats would not stay in place, and at 2:1 the other way round the faces would come out dished rather than flat. How far the cutter feeds in sets the size across the flats, so one cutter covers a range of hex sizes, while the corners are the round surface the blank arrives with: a 1 in. heavy hex nut, 1.575 to 1.625 in. across the flats and 1.796 to 1.876 in. across the corners (ASME B18.2.2), needs a blank at least 1.796 in. across.
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model dataExample part: a 1 in.-8 heavy hex nut to ASME B18.2.2 (across flats 1.575–1.625 in., across corners 1.796–1.876 in.), drawn with 1.600 in. flats on a round nut 1.81 in. across, so thin round lands stay on the corners. Kinematics as in the polygon-turning patents (cutter and work driven at 2:1, turning the same way; one cutting edge gives two flats): the metal removed is computed from the blade tips' elliptical paths, and the faces' slight crown is shown exaggerated in the close-up. The machine is generic and illustrative: enclosure, collet chuck holding a threaded arbor (the round nut screws onto it, one pitch a turn, and seats on a shoulder smaller than the hex, so the blades run past both faces), cutter head, feed slide and gear train (18 teeth to 18, then 24 to 12: two meshes, so the same direction at twice the speed) show the principle, not a particular machine. Cutter proportions are illustrative (a 3.5 in. cutting circle, three blades); speeds are not shown to time; the nut is drawn without its chamfers, and its 1-8 thread (0.125 in. pitch) is drawn in the bore.
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