The input or driver gear in a
gear train is the gear directly connected to the motor or other power source. Thus the driver is the gear that transmits power to the other gears in the gear train. In a simple 2-gear system, the second gear (the gear which is
turned by the driver) is called the output or driven gear. In a gear train consisting of more than 2 gears, the final gear (the gear connected to a wheel axle or other rotating mechanical component) is the output gear.
gear ratio (gr) = (number of teeth on output or driven gear)/(number of teeth on input or driver gear)
If we assume that in the photo the smallest gear is connected to the motor, then it is the driver gear. The somewhat larger gear on the upper left is called an
idler gear -- it is not connected directly to either the motor or the output shaft and serves only to transmit power between the input and output gears. There is a third gear in the upper-right corner of the photo. If we assume that gear is connected to the machine's output shaft, it is the output or driven gear.
The idler gear in this particular gear train has 21 teeth and the input gear has 13.
Considering for the moment only those two gears, we can regard the idler as the driven gear. Therefore, the gear ratio is driven/driver = 21/13 = ~1.62 or 1.62:1.
The ratio means that the driver gear must make 1.62 revolutions to turn the driven gear 1 revolution. It also means that for every one
revolution of the driver, the driven gear has made 1/1.62, or 0.62, revolutions. In
practical terms, the larger gear turns more slowly.
Now suppose the third gear in the picture has 42 teeth. The gear ratio between the idler and third gear is thus 42/21, or 2:1, and hence the final gear ratio is 1.62x2=~3.23. For every 3.23 revolutions of the smallest gear, the largest gear turns one revolution, or for every one revolution of the smallest gear, the largest gear turns 0.31 (1/3.23) revolution, a total
reduction of about 1:3.23 (Gear Reduction Ratio (GRR) = 1/Gear Ratio (GR)).
Since the intermediate (idler) gear contacts directly both the smaller and the larger gear it can be removed from the calculation, also giving a ratio of 42/13 = ~3.23.
Since the number of teeth is also
proportional to the
circumference of the gear wheel (the bigger the wheel the more teeth it has) the gear ratio can also be expressed as the
relationship between the pitch circles of both wheels (where d is the pitch diameter of the input wheel and D is the pitch diameter of the output wheel):
Pitch circles have diameters that would give the same gear ratio, but with cylindrical surfaces that do not slip.
Since the diameter is equal to twice the
radius;
as well.
and so