If t and T are the number of teeth on pinion and gear, G is gear ratio, Ap is the fraction by which the standard addendum of one module is multiplied and ϕ is the pressure angle, the expression of the minimum number of teeth on the pinion to avoid interference when pinion and gear have an equal number of teeth is given as
1
\(t = \frac{{2{A_p}}}{{\sqrt {1~- ~3\;si{n^2}\phi } ~ +~ 1}}\)
2
\(t = \frac{{2{A_p}}}{{\sqrt {1~ +~ 3\;si{n^2}\phi } ~+ ~1}}\)
3
\(t = \frac{{2{A_p}}}{{\sqrt {1~ -~ 3\;si{n^2}\phi } ~ - ~1}}\)
4
\(t = \frac{{2{A_p}}}{{\sqrt {1 ~+~ 3\;si{n^2}\phi } ~-~ 1}}\)