IN text books on gears and gear teeth the form of the tooth below the base circle is usually dismissed with a few words of advice on the evils of undercutting, and while formulae for calculating the form of the involute curve abound, no one worries about the epitrochoid which is the form of the curve below the base circle. This may be because the involute is a self‐respecting curve that never varies except in size while the epitrochoid varies as the distance below the base circle and the ratio of the rolling circles vary. Of course in the case of generated gears, provided that the root diameter gives sufficient clearance the cutter will sweep out its own correct path, but with gears ground with formed wheels the question of the form below the base circle does arise, especially with small pump gears of about nine to sixteen teeth. The easiest way to examine the form of the root is by projection and here comes the problem of drawing the correct form.
Pepper, H.C. (1947), "Developing the Epitrochoid Curve in Gear Teeth Below the Base Circle", Aircraft Engineering and Aerospace Technology, Vol. 19 No. 10, pp. 320-320. https://doi.org/10.1108/eb031559
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