GEARS: Minimum Number of Teeth


Figure 5

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 = O2A – O2P. From ΔO2AP, we can write, with α as the pressure angle,

equation

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

equation