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accurate Ambrose Swasey American Machinist analysis arbor axis bevel gears Bilgram Bodmer Brown & Sharpe Brown and Sharpe Buchanan Camus century chine clock makers Codex Atlanticus cone curve cut gears cut spur cutting machines Desargues describing-generating developed device diameter epicycloidal teeth Euler Fellows Gear Shaper finished Flanders formed-tooth friction gear blank gear cutter Gear Shaper gear teeth gear-cutting machine geometry give grinding machine hardened gears Hawkins helical Hindley Hire hobbing machines Hooke's Imison invention involute gear involute teeth later lathe London Mach Machinery manufacture mathematical Mech mechanism method milling cutter milling machine motion number of teeth odontograph Paris pinion plane practice precision pressure angle problem produced production machine Ralph Flanders Rehe Rehe's Reid rolling rotary rotated Sang screw shown in Fig shows single-point spiral gears spur and bevel spur gears templet theory tooth form Trans types of gear-cutting types of gears vertical wheel-cutting engine Willis worm