Transmission of Motion between Gears:

The gears when transmitting motion may be replaced by their pitch cylinders as illustrate in figure 1 on first page. Let ω₁ and ω₂ be angular velocities of gears 1 and 2 respectively. Assume t₁ and t₂ be respectively the number of teeth on gears 1 and 2. The two mating gears contain same module 'm'. Referring to given figure. The pitch circle radius of gear 1,

O₁ P = m t₁/2

The pitch circle radius of gear 2,

O₂ P = mt₂/2

The velocity of pitch point 'P' letting gear 1,

The velocity of pitch point 'P' letting gear 2,

Thus,

                            . . . (9.1)

 Therefore, the gear ratio is inversely proportional to ratio of number of teeth.

The centre distance among the two gears,

               . . . (9.2)