Gear Ratio - Speed Ratio

Speed Ratio

The teeth of a gear are distributed on the circumference of the pitch circle so that the thickness of each tooth t and the space between two teeth are the same. The pitch p of a gear, which is the distance between the equivalent points on two teeth, is equal to twice the thickness of a tooth,

The pitch of a gear G_A can be computed from the number of teeth N_A and the radius r_A of its pitch circle

In order to mesh smoothly two gears G_A and G_B must have the same sized teeth and therefore they must have the same pitch p, which means

This equation shows that the ratio of the circumference, the diameters and the radii of two meshing gears is equal to the ratio of their number of teeth,

The speed ratio of two gears rolling without slipping on their pitch circles is given by,

therefore

In other words, the gear ratio, or speed ratio, is inversely proportional to ratio of the radii of the pitch circles and the number of teeth of the two gears.