Gear Train Example
The applet below shows four (or three) gears in a gear train. We may think of the green gear as the gear driving the motion of the other gears. The blue and purple gears are mounted on the same arbor (axle) and rotate at the same frequency.
The jagged-edged gears are not circles, obviously, but for any gear, the pitch circle is the imaginary circle where it would roll without slipping against the pitch circle of its neighbor. Because the circumference of a circle is linearly related to its diameter, the number of teeth on a gear is linearly related to the diameter. The module, is the constant of proportionality. In particular, a gear with teeth and pitch diameter satisfies This implies that if two gears with and teeth and pitch diameters of and mesh, then the distance between their centers (called the center distance) is
Because of this relationship, the sum of the number of teeth on two meshing gears depends only on the center distance. So, when we refer to two meshing gears, the distance between them carries the same information as the sum of the numbers of teeth. The gear ratio of two meshing gears is
# teeth on driven gear / # teeth on driving gear.
In a gear train, the gear ratio is the product of the gear ratios of the meshing gears in the train. In our example, the gear ratio is(# blue teeth / # green teeth)(# red teeth / # purple teeth).
When we replace the purple and blue gears with a single (blue) gear, it is called an idler gear. The gear ratio does not depend on the number of teeth on the idler gear because(# blue teeth / # green teeth)(# red teeth / # blue teeth) = # red teeth / # green teeth.
Lastly, note that when two gears mesh, the direction of rotation changes. So, although adding the idler gear doesn't change the gear ratio between the green and red gears, the rotation direction of the red gear is different when the gear train is green-red and green-blue-red. Note: In the applet below, you can zoom in and out using a scroll wheel and can pan the view by clicking and dragging.