A general method is presented for the determination of the minimum number of teeth that can be cut in a spur gear without undercutting by a rounded-tooth tip hob. The minimum number of teeth to produce undercutting was investigated for three trochoid/tooth-profile relations: (1) trochoid tangent to the involute profile at the base circle, (2) trochoid tangent to a straight portion of the tooth flank, and (3) trochoid intersecting the involute profile at the base circle. It was found that in order to avoid undercutting, the minimum number of teeth cut into a gear occurs when the trochoid is tangent to the involute at the base circle. There is no set of hob parameters such that the trochoid intersects the involute profile at the base circle nor does the case of the trochoid being tangent to a straight flank exist. A set of figures representing the variation of the amount of undercutting versus the number of teeth, radius of hob-tooth tip, hob addendum, cutting pressure angle, and the corresponding derivatives are included for a typical gear.

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