If a driver sprocket has 30 teeth and the driven has 90 teeth, what is the driven torque if the driver is 60in-lb?

To determine the driven torque when a driver sprocket has 30 teeth and the driven sprocket has 90 teeth, it's important to consider the relationship between torque and the number of teeth on the sprockets.

The torque relationship between the driver and the driven sprockets can be established using the gear ratio, which is calculated as follows:

Gear Ratio = Number of Teeth on Driven Sprocket / Number of Teeth on Driver Sprocket

In this case, the gear ratio would be:

Gear Ratio = 90 teeth (driven) / 30 teeth (driver) = 3

This means that for every turn of the driver sprocket, the driven sprocket will turn one-third of a turn, but the torque is multiplied by the gear ratio. Therefore, the torque on the driven side can be calculated by multiplying the torque on the driver side by the gear ratio:

Driven Torque = Driver Torque x Gear Ratio

Driven Torque = 60 in-lb x 3 = 180 in-lb

Thus, the driven torque is indeed 180 in-lb, confirming that the answer is correct. This calculation reflects the fundamental principle of mechanical advantage obtained through gearing: the driven sprocket, having a higher number of teeth