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GEARS: Minimum Number of Teeth

To avoid interference without undercutting, the addendum circles of both the pinion and the gear should intersect the common tangent *AB* to the base circles within the points of tangency *A* and *B*. When the addenda are equal, obviously, then the interference will always occur first at number of teeth on the pinion (for a given speed ratio) for this situation can be determined as now explained.

The addendum length *a = O*_{2}A – O_{2}P. From ΔO_{2}AP, we can write, with α as the pressure angle,

For a given speed ratio *ω2/ω1 = λ,* a can be expressed as