The sprocket ratio for a chain drive system having a driven sprocket with 54 teeth and a driver sprocket with 18 teeth is __________.

To determine the sprocket ratio for a chain drive system, you calculate the ratio of the number of teeth on the driven sprocket to the number of teeth on the driver sprocket. In this case, the driven sprocket has 54 teeth, while the driver sprocket has 18 teeth.

The sprocket ratio is calculated using the following formula:

[

\text{Sprocket Ratio} = \frac{\text{Number of Teeth on Driven Sprocket}}{\text{Number of Teeth on Driver Sprocket}} = \frac{54}{18}

]

When you perform this calculation, you get:

[

\frac{54}{18} = 3

]

Thus, the sprocket ratio is 3. This means that for every rotation of the driver sprocket, the driven sprocket will make a third of that rotation, demonstrating a mechanical advantage that affects speed and torque in the system.

Understanding the sprocket ratio is crucial as it influences the performance characteristics of the chain drive system, such as speed reduction and torque multiplication. This is why the value of 3 accurately represents the ratio in this scenario.