The speed ratio of the fourth gear to the first gear in a compound gear train (gear 2 and gear 3 are mounted on the same shaft) as shown below is
where T1, T2 , T3 and T4 are numbers of teeth on gears 1, 2, 3 and 4 respectively.
1
\(\frac{N_4}{N_1} = \frac{T_4}{T_1}\)
2
\(\frac{N_4}{N_1} = \frac{T_4}{T_2} \times \frac{T_3}{T_4}\)
3
\(\frac{N_4}{N_1} = \frac{T_4}{T_2} \times \frac{T_4}{T_3}\)
4
\(\frac{{{N_4}}}{{{N_1}}} = \frac{{{T_1}}}{{{T_2}}}\times \frac{T_3}{T_4}\)