Describe gear trains, calculate gear ratio and output speed, and explain how gears change speed, torque and direction of rotation

What this dot point is asking

SEAB wants you to describe gear trains, calculate gear ratio and output speed, and explain how gears change speed, torque and direction of rotation. This is a core calculation outcome: you must compute a gear ratio from tooth counts, find the output speed, and explain the speed-torque trade-off and the effect of idler gears. Gears are a standard structured-question topic.

The answer

What gears do

A gear is a toothed wheel that meshes with another to transmit rotary motion. Gears transmit motion from one shaft to another, and they can change the speed of rotation, the turning force (torque), and the direction of rotation. The driver gear is connected to the power source; the driven gear is the output. Where meshing gears touch, their teeth move at the same speed, which is why tooth counts determine the ratio.

Direction of rotation

Two meshing gears rotate in opposite directions: if the driver turns clockwise, the driven turns anticlockwise. This is a key fact. To make the output turn the same way as the input, an idler gear is added between them.

Gear ratio

The gear ratio compares the driven and driver gears by their number of teeth:

A ratio of $3:1$ (driven has three times the teeth) means the driven gear turns once for every three turns of the driver: it turns more slowly. A ratio less than 1 means the driven turns faster than the driver.

Output speed

The output (driven) speed follows from the ratio:

So a driver at $300\ \text{rev/min}$ through a $3:1$ ratio gives an output of $100\ \text{rev/min}$. A larger driven gear slows the output; a smaller driven gear speeds it up.

The speed-torque trade-off

Gears trade speed for torque. A reduction (driven larger than driver) makes the output turn more slowly but with greater torque (turning force), useful for moving heavy loads. Speeding up (driven smaller than driver) increases speed but reduces torque. You cannot gain both: more torque means less speed, and more speed means less torque. This trade-off is why machines use reduction gears to lift heavy loads slowly with a small motor.

Idler gears

An idler gear is placed between the driver and driven gears. It does two things: it makes the driven gear turn in the same direction as the driver (reversing the reversal), and it bridges a gap when the two main gears are too far apart to mesh directly. Crucially, an idler does not change the overall gear ratio between the driver and driven gears, because its effect cancels out.

Examples in context

Example 1. A reduction gearbox lifting a load. A small electric motor spins fast but with little torque, too little to lift a heavy load directly. A reduction gear train (large driven gears) slows the output shaft and multiplies the torque, so the load rises slowly but powerfully. The gearbox trades the motor's surplus speed for the torque needed, the everyday purpose of reduction gearing in winches and cranes.

Example 2. A clock's gear train. A clock uses a train of gears to drive the hour, minute and second hands at different speeds from one mechanism. Carefully chosen tooth counts give exact ratios (for example $60:1$ between the second and minute hands) so the hands keep correct time. The gear ratios convert one input rotation into precisely timed outputs, showing gears used to set speed rather than torque.

Try this

• Cue. A driver of $15$ teeth meshes with a driven of $45$ teeth. State the gear ratio. Answer: driven over driver $= 45/15 = 3$, so $3:1$.

• Cue. With a $4:1$ reduction and an input of $800\ \text{rev/min}$, find the output speed. Answer: output $=$ input $\div$ ratio $= 800/4 = 200\ \text{rev/min}$.

• Cue. Explain what an idler gear does to direction and to the gear ratio. Answer: it makes the driven gear turn the same direction as the driver and bridges a gap, but it does not change the overall gear ratio.