If the driving gear is smaller than the driven gear, torque increases.

Yes, that's correct. When the driving gear is smaller than the driven gear, the torque does increase. Here's a step-by-step explanation:

1. Torque is the rotational equivalent of linear force. It's calculated by multiplying the force by the distance from the point of rotation.

2. In a gear system, the driving gear is the one that is directly receiving power (usually from a motor or engine).

3. The driven gear is the one that is being turned by the driving gear.

4. If the driving gear is smaller than the driven gear, it will have to turn more times to make the driven gear turn once. This means that the force exerted by the driving gear is effectively multiplied, resulting in increased torque on the driven gear.

5. This principle is often used in machines and vehicles to increase power or speed. For example, in a bicycle, when you shift into a lower gear (making the driving gear smaller), it becomes easier to pedal, especially uphill. This is because the smaller driving gear increases the torque on the driven gear (the wheel), allowing you to exert less force but achieve the same effect.