How Does a Pulley (Belt-Driven) System Work?

A belt-driven pulley system transfers rotary motion and power from a rotating input shaft to an output shaft. It can change rotational speed, torque, and direction by using pulleys of different diameters or by changing the belt arrangement.

The input pulley is the driver, while the output pulley is the driven pulley. As the driver rotates, friction between its rim and the tensioned belt moves the belt. The belt then applies a tangential force to the driven pulley, causing its shaft to rotate.

In an ideal system with no belt slip, the belt has the same linear speed around both pulleys. Therefore:

$$\pi D_{\text{driver}}N_{\text{driver}} = \pi D_{\text{driven}}N_{\text{driven}}$$

This gives:

$$\frac{N_{\text{driven}}}{N_{\text{driver}}} = \frac{D_{\text{driver}}}{D_{\text{driven}}}$$

where $D$ is pulley diameter and $N$ is rotational speed.

For example, a $100\text{ mm}$ driver rotating at $600\text{ rpm}$ drives a $300\text{ mm}$ pulley:

$$N_{\text{driven}} = 600 \times \frac{100}{300} = 200\text{ rpm}$$

The output rotates more slowly but ideally produces greater torque. In practice, friction, belt deformation, and slip reduce efficiency.

Correct belt tension is essential: insufficient tension allows slip, while excessive tension increases bearing loads and wear. Belt drives are quieter than many gear systems and can transmit motion across larger shaft distances, but their ratio is generally less precise because belts stretch and slip.

A common misconception is that a larger driven pulley increases output speed. It does the opposite: it reduces speed while increasing torque, assuming approximately constant power.

For A3.3 Introduction to mechanical systems (HL only), an examiner may ask you to identify the driver and driven components, calculate an output speed, or explain the speed-torque trade-off. Always state the no-slip assumption when applying the pulley-ratio equation.