## Sprocket Sizes

Roller chains and sprockets, Figure 6.3, have two advantages over belts and pulleys. They are capable of transmitting greater amounts of power, and because it is impossible for the chain to slip, the sprockets stay in time.

The equation used with pulleys can be used to determine sprocket sizes by replacing the diameter of the pulley with the teeth for each sprocket. For sprockets,

FIGURE 6.3. Roller chain and sprockets.

the pulley equation becomes:

Problem: A hydraulic pump will be powered by a tractor power take-off (PTO). The pump must turn at 2100 rpm, and the PTO operates at 540 rpm. What sizes of sprockets are needed?

Solution: This problem is the same as the previous one where we determined the size of pulleys needed to power the fan. The first step is to select the size of one of the sprockets. In this example the driven sprocket (pump) will have fewer teeth than the driver sprocket (PTO). For this example, we will start by selecting an 18-tooth sprocket for the pump. We need to determine the size of the PTO sprocket.

Rearranging the sprocket equation for the number of teeth in the driver sprocket give us:

T2 x N2 18 teeth x 2,100 rpm

1 Ni 540 rpm

The pump will turn at the correct speed if the PTO sprocket of the tractor has 70 teeth.