# Gear Sizes

It is common to use gears in power trains when the shafts are very close together, when a large amount of power is being transmitted or in transmissions where selectable speed ratios are needed. The sizes of gears are determined in the same way as those of chains and sprockets. The sprocket equation can be used without modification.

### 6.4. Speed Ratios

In some situations when the speeds of the driver and driven shafts are known, pulley, sprocket, and gear sizes can be determined by using speed ratios instead of the pulley or sprocket equations.

In the previous problem we determined that a 70-tooth sprocket was needed to power the pump. A 70-tooth sprocket will have a large diameter and may be too large to fit on a small tractor. Does this mean that the pump cannot be used?

The solution is to use a smaller sprocket on the pump and then determine the size of sprocket needed for the PTO. In the original problem we saw that a 18 and 70-tooth sprockets would provide the correct speed. Thus we know that the ratio of the two sprockets is 70/18 or 3.9:1. In other words, the sprocket on the PTO must have approximately four times as many teeth as the sprocket on the pump.

With the speed ratio between the two shafts known, different sprocket combinations could be used:

7 70 35 43 — = — or — or — = 3.9 T2 18 9 11

In these situations the ratio does not usually need to be exact for the system to operate. A hydraulic pump that runs slightly faster or slower, because the exact speed ratio cannot be used, usually performs adequately.

Knowing the speed ratio makes it easier to select sprocket combinations that will operate the pump at the correct speed and still fit within the physical limitations of the machine.

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