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In gearing, according to Wikipedia and Dr. Rainer Hessmer's involute gear generator, the most popular pressure angles in the industry are 14.5°, 20° and 25°, with 20° being the most abundant. I can appreciate why 20° and 25° might be common values since they are nice round numbers. This then brings up the question; why 14.5°?

I understand that the lower pressure angle of 14.5° will come with some advantages over 20°, such as keeping the lines of action of the forces on the teeth further from the gear axis, reducing the reaction force of the shaft for the same torque transmitted. What I don't get is why a rather peculiar, un-round number such as 14.5° is a common choice? Was there a practical reason behind it, such as the minimum pressure angle before undercutting occurs for gears of a typical number of teeth, or was the value applied when a large quantity of these 14.5° gears existed prior to a standard pressure angle having existed? Perhaps it is a relic of an older standard of gears?

Involute
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    Because $\sin 14.5^\circ$ is very close to $0.25$? Before calculators, engineers liked to work with easy numbers. – alephzero Aug 26 '16 at 19:40
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    It was also the half-angle of the ACME thread (thread angle 29 degrees) used for leadscrews, and developed in 1894. There may be some commonality in tooling between screwcutting and gearcutting (especially hobbing) machinery that makes sharing the angle worthwhile. – user_1818839 May 29 '17 at 22:22

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