What Is a Pulley and Belt? How the Pair Transmits Power

A pulley is a rimmed wheel that carries a belt; the belt wraps two or more pulleys and is held on by tension, transmitting power through friction on a plain or grooved rim, or through teeth on a synchronous one.

That single sentence contains the whole principle, and almost every practical question about belt drives follows from it: how much power a pair can carry depends on how hard the belt is pressed onto the rim, how much of the rim it wraps, and whether the drive relies on friction or on teeth.

What a pulley actually is

A pulley is a wheel mounted on a shaft, with a rim that either guides a belt or drives it. In a belt drive there are usually two: the driver on the input shaft and the driven pulley on the output shaft. A third, smaller pulley is often added as an idler to take up slack or to increase the wrap angle on a small pulley.

The dimensions that matter are not the ones you can measure with a ruler on the outside:

• Pitch diameter — the diameter at which the belt's tension member runs. On a V-belt pulley this is measured at the pitch line inside the groove; on a synchronous pulley it is measured at the cord line. Outside diameter is larger than pitch diameter and is not the number used for ratio calculations.
• Groove angle — the included angle of a V-groove, typically 34° to 40°. It is what produces the wedge action described below, and it must match the belt section.
• Number of grooves or teeth — for V-ribbed and synchronous pulleys, this sets the contact area or the exact ratio.
• Crown — a slight convexity across the face of a flat-belt pulley, which keeps a flat belt centred instead of letting it wander off the edge.

A pulley is not a gear. A gear pair transmits motion by direct tooth contact at a fixed centre distance. A pulley pair transmits motion through a belt, so the shafts can sit far apart, the drive can tolerate misalignment and shock, and the ratio is set by diameter rather than by tooth count. That flexibility is the reason belt drives persist next to much more compact gearboxes.

What a belt actually is

A belt is an endless loop built from three functional layers:

• Tension member (cord) — steel, aramid, glass fibre or polyester; it carries the pulling load and decides how much the belt stretches under tension.
• Body compound — rubber or polyurethane; it holds the cord, forms the profile, and provides the surface that contacts the pulley.
• Facing or cover — fabric, coating or bare compound; it protects the body and, on some belts, supplies the friction the drive depends on.

Two transmission mechanisms exist, and they behave very differently:

• Friction drives — flat belts, V-belts, V-ribbed belts and round belts. The belt grips the rim. Slip is possible, and it is both a protection (it limits torque overload) and a failure mode (it wastes speed and wears the belt).
• Positive drives — synchronous (timing) belts. Teeth on the belt engage grooves in the pulley. There is no slip in normal operation, so the ratio is exact and the angular position is repeatable.

How the pair transmits power

The sequence is short, and understanding it makes the rest of the topic predictable.

1. Tension pulls the belt onto the rim. A belt installed with tension T₁ on the tight side and T₂ on the slack side presses against the pulley across the arc it wraps.
2. Contact pressure generates friction. The friction force is what resists the belt sliding backwards, and the difference between the two tensions is the useful force the drive delivers: Fₑ = T₁ − T₂.
3. That force moves at belt speed. Power is force times speed: P = Fₑ × v, where belt speed is v = π × D × n / 60 000 with D in millimetres and n in rpm, giving v in metres per second.
4. The ratio comes from diameters. For a friction drive, i = n₁ / n₂ = D₂ / D₁, corrected for the small amount of slip. For a synchronous drive the same relation holds exactly, using pitch diameters.

The limit on step 2 is where most design decisions are made. The classical relationship between the two tensions is T₁ / T₂ = e^(μθ), where μ is the coefficient of friction and θ is the wrap angle in radians. Read it as a statement about grip: more friction or more wrap means a larger tension ratio the belt can sustain before it slips.

Two practical consequences follow directly from that equation.

Wrap angle matters more than most people expect. On an open drive with unequal pulley diameters, the small pulley wraps less than half its circumference: θ ≈ 180° − 2 × arcsin((D − d) / 2C), with C the centre distance. As a rule of thumb in design practice, friction drives are kept above roughly 120° of wrap on the small pulley; below that, the drive needs a larger centre distance, a smaller diameter difference, or an idler.

A V-groove multiplies friction without adding tension. A V-belt does not sit on the bottom of its groove; it wedges into the flanks. The effective friction becomes μ / sin(β/2), where β is the groove angle. At a 38° groove, sin(19°) ≈ 0.33, so the effective friction is roughly three times that of a flat belt at the same μ and the same tension. This is why a narrow V-belt carries far more power than a flat belt of similar width, and why the groove angle has to match the belt section — a worn groove that has opened up loses part of that advantage.

A synchronous belt replaces this whole mechanism with teeth. Wrap angle still affects how many teeth are in mesh and therefore how the load is spread, but it no longer sets a slip limit.

The five belt-and-pulley systems

The table below compares the five systems. Mechanism and profile designations are definitional; efficiency, speed and tension are industry-typical values.

Source: mechanism and section designations follow the ISO 4183 / ISO 4184 (V-belt), ISO 22 (flat belt) and ISO 5296 / ISO 13050 (synchronous) families. Efficiency, speed and tension figures are industry-typical ranges for a single stage in good alignment and correct tension — they are not test data for any specific belt, and a real drive should be sized from the manufacturer's rating tables.

Six things that decide whether the pair works

Teaching a belt drive usually means teaching these six, because each one turns a concept into a consequence you can see on the machine.

1. Wrap angle — the arc the belt covers on the small pulley sets the tension ratio the drive can sustain → a large diameter difference on a short centre distance is the classic reason a correctly sized belt still slips.
2. Installation tension — tension provides the normal force that friction depends on → too little slips and glazes the belt, too much overloads the bearings and shortens cord life; the window is narrower than most people assume.
3. Groove or tooth condition — a worn V-groove loses wedge angle, and a worn pulley tooth loses contact area → either one drops capacity without changing the belt, which is why a new belt on a worn pulley often fails quickly.
4. Pulley diameter against belt thickness — every revolution bends the belt around the small pulley → a diameter below the belt's minimum raises bending stress and is a common cause of cracking at the back or at the tooth root.
5. Alignment — parallel and angular misalignment both concentrate load on one edge → edge wear and cord exposure appear long before the belt is worn out across its width.
6. Ratio and speed — diameter ratio sets the output speed, and belt speed sets the centrifugal load → beyond the practical speed for the belt type, the belt lifts off the rim and grip falls away even though tension is unchanged.

Where each system is used

• Flat belts — long centre distances, high speed and low torque: line shafting, some agricultural and woodworking machinery, and light conveying where a thin belt must wrap a small pulley.
• V-belts — the general-purpose industrial default: pumps, fans, compressors and machine tools where shock tolerance and low cost matter more than exact speed.
• V-ribbed belts — compact drives with small pulley diameters and high speed, especially where a thin, flexible belt must follow a serpentine path around several pulleys.
• Synchronous belts — anywhere the ratio must be exact or the position repeatable: conveyors with indexing, packaging machinery, printing, and any drive where slip would ruin the product.
• Round belts — light conveying and transmission on small pulleys, including lines that need a quick on-site joint.

FAQ

Does a pulley and belt have to be replaced as a pair?

Replace the pulley when its groove or teeth are worn, even if the belt is new. A worn groove has lost part of its wedge angle and a worn tooth has lost contact area, so a fresh belt on a worn pulley starts with reduced capacity and typically fails early. Measuring groove width or tooth profile is the cheap check; replacing only the belt on a worn pulley is the expensive habit.

Why does a V-belt carry more power than a flat belt of similar width?

Because the V-shape wedges into the groove instead of sitting flat on the rim. The effective friction becomes μ divided by sin(β/2), which at a 38° groove angle is roughly three times the flat-belt value at the same friction coefficient and the same tension. The belt is not pressing harder — the geometry converts the same tension into a much larger normal force on the flanks.

Can a synchronous belt slip?

Not in normal operation, because teeth carry the load rather than friction. It can still ratchet — jump a tooth — if tension is too low for the torque, if the pulley teeth are worn, or if a shock load exceeds what the teeth in mesh can hold. That distinction matters when diagnosing a fault: ratcheting leaves the teeth intact but scuffs the flanks and the pulley grooves, while a genuine overload shears the teeth off.

Standards referenced

• ISO 22 — flat transmission belts: widths and lengths.
• ISO 4183 / ISO 4184 — classical and narrow V-belt sections and datum lengths.
• ISO 5296 — synchronous belt drives: belt pitch codes and dimensional characteristics (trapezoidal profiles).
• ISO 13050 — synchronous belt drives: metric pitch curvilinear profile systems.
• ISO 254 — belt drives, pulleys: quality, finish and balance requirements.
• ISO 1813 — antistatic characteristics of endless V-belts, joined V-belts and V-ribbed belts, where a static-dissipative drive is required.