Introduction:
Interference may only be avoided, if the point of contact between the two teeth is always on the involute profiles of both the teeth.
Minimum number of teeth on the pinion in order to avoid interference

The minimum number of teeth on the pinion which will mesh with any gear (also rack) without interference are given in the following table.

The number of teeth on the pinion (TP) in order to avoid interference may be obtained from the following relation :
where

AW = Fraction by which the standard addendum for the wheel should be multiplied,

G = Gear ratio or velocity ratio = TG / TP = DG / DP,

φ = Pressure angle or angle of obliquity.