A pulley-and-belt CVT is a continuously variable transmission that changes drive ratio by sliding the two halves of each pulley closer together or farther apart, forcing the belt to ride at a different pitch radius. As the primary sheave squeezes shut, the belt climbs higher; the secondary sheave opens, letting the belt drop deeper — ratio shifts smoothly with no fixed gears. The point is to keep the engine at its torque or efficiency peak across all road speeds. Toyota's Direct Shift CVT, Polaris snowmobiles, and nearly every modern scooter use this layout to deliver stepless ratio change between roughly 0.4:1 and 2.5:1.
Pulley-and-belt CVT Interactive Calculator
Vary pulley pitch radii, input speed, and efficiency to see CVT speed ratio, output RPM, and torque multiplication.
Equation Used
The belt pitch-line speed is the same on both pulleys, so the output-to-input speed ratio equals primary pitch radius divided by secondary pitch radius. A smaller primary radius and larger secondary radius gives low range; the opposite gives high range. Efficiency is applied to estimate ideal torque multiplication.
- Belt does not slip and pitch-line speed is equal on both pulleys.
- Primary pulley is the engine/input side and secondary pulley is the output side.
- Efficiency only affects torque transfer, not the geometric speed ratio.
Inside the Pulley-and-belt CVT
Two pulleys, one belt, and a clever trick with geometry. Each pulley is a pair of conical sheaves facing each other — when you push the halves together the belt has nowhere to go but outward, riding on a larger pitch radius. Pull the halves apart and the belt drops down into the V, riding on a smaller radius. Because the belt length is fixed, the secondary pulley must do the opposite of the primary at every instant. That coupled movement is the entire ratio-change mechanism.
On a scooter or snowmobile the primary sheave closes via centrifugal weights flying outward as engine RPM rises. The secondary sheave is held closed by a torque cam and a spring — it opens reluctantly, only when belt tension overcomes the cam ramp. That balance between centrifugal force on the primary and spring-plus-cam force on the secondary sets the operating ratio at any given throttle and load. In a passenger car like the Subaru Lineartronic or a Toyota K310, hydraulic pressure replaces the weights, and an ECU commands the pitch radius directly.
Tolerances matter more than people expect. The belt's V-angle must match the sheave angle within about 0.5° or you get edge-loading and the belt cooks itself in a few hundred kilometres. Sheave faces need to stay smooth — once you see glazing or hairline scoring, friction drops and the belt slips, which heats the rubber, which glazes the sheaves further. That's the classic CVT death spiral. Pitch radius mismatch from a stretched belt causes the same symptom: the primary closes fully but the secondary won't open, and you lose top ratio.
Key Components
- Primary (drive) pulley: Splits into two conical halves, one fixed and one sliding on the input shaft. On engine-driven units the moving half is shoved inward by centrifugal weights — typically 6 weights of 8 to 18 g on a 150cc scooter — as RPM rises past the engagement speed of around 2,500 RPM.
- Secondary (driven) pulley: Mirrors the primary but spring-loaded shut. A torque cam with ramp angles between 40° and 55° forces the sheaves together harder when output torque rises, preventing belt slip during acceleration or hill climbs.
- Drive belt: Either a reinforced rubber V-belt for scooters and snowmobiles or a Van Doorne steel push belt for cars. The push belt is built from 2 stacks of 9 to 12 thin steel rings threaded through 400+ trapezoidal steel elements — it transmits torque by compression between elements, not tension.
- Centrifugal weights or hydraulic actuator: Sets primary clamping force. Mechanical weights are tuned by mass to shift the upshift curve — heavier weights upshift sooner at lower RPM, lighter weights hold the engine higher in its powerband.
- Torque cam and spring (secondary): Provides the back-pressure that determines ratio. Spring rates around 60-100 N/mm and cam angles in the 45° range are typical on sport snowmobile setups like a Polaris TEAM clutch.
- Sheave faces: Hardened steel surfaces ground to a precise included angle — usually 26° total. Surface finish must stay below Ra 0.8 µm; once worn or glazed, friction collapses and belt slip starts within minutes of hard riding.
Who Uses the Pulley-and-belt CVT
Pulley-and-belt CVTs show up wherever you want an engine to sit at its happy RPM regardless of road speed — and where the cost or complexity of a planetary automatic isn't justified. The ratio spread you can extract from a single belt-and-variator pair is between 4 and 6, which covers most light-duty applications cleanly. Above that, you start running into belt-life problems and need a hybrid approach with a launch device or planetary auxiliary.
- Automotive: Toyota Direct Shift CVT (K313/K314) on the Corolla and C-HR — adds a launch gear so the belt doesn't have to handle stall-torque shock
- Powersports: Polaris P-85 and TEAM Rapid Response primary clutches on RMK and Indy snowmobiles
- Two-wheel transport: Honda PCX 150 and Vespa Primavera scooters — full mechanical CVT with centrifugal primary
- Off-highway / UTV: Can-Am Maverick X3 and Polaris RZR side-by-sides using oversized belts and aggressive sheave cooling ducts
- Agriculture: John Deere variable-speed combine drives on older 9000-series harvesters — hydraulic-actuated split sheaves
- Industrial machinery: Reeves drives and Lenze Disco vario units used on conveyors, mixers, and drill presses where stepless feed adjustment is needed without an inverter
The Formula Behind the Pulley-and-belt CVT
The ratio of a pulley-and-belt CVT comes straight out of the pitch radii of the two sheaves at any given instant. What makes this useful in practice is understanding the *spread* — the ratio at the bottom of your operating range versus the top — because that's what determines whether your engine can stay in its powerband from a standstill to top speed. At the low-ratio end (belt high on primary, low on secondary) you get overdrive for cruising; at the high-ratio end (belt low on primary, high on secondary) you get launch torque. The sweet spot for most applications sits at a total spread of 5:1 to 6:1, beyond which belt-bend stress at the small pulley starts cutting belt life in half for every additional unit of spread.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| i | Instantaneous transmission ratio (input speed divided by output speed) | dimensionless | dimensionless |
| ωin | Angular velocity of the primary pulley | rad/s | RPM |
| ωout | Angular velocity of the secondary pulley | rad/s | RPM |
| Rprimary | Pitch radius of the belt on the primary (drive) pulley | m | in |
| Rsecondary | Pitch radius of the belt on the secondary (driven) pulley | m | in |
Worked Example: Pulley-and-belt CVT in a 150cc delivery scooter retrofit
You are rebuilding the variator on a Honda PCX 150 used by a courier service in Taipei. The fleet manager wants to know what top speed the scooter should hit on flat ground at the engine's 8,500 RPM redline, and what the launch ratio looks like when the belt is fully down on the primary at engagement. Measured pitch radii: at full upshift R<sub>primary</sub> = 52 mm, R<sub>secondary</sub> = 26 mm. At full downshift (engagement) R<sub>primary</sub> = 19 mm, R<sub>secondary</sub> = 58 mm. Final drive ratio is 10.0:1 and the rear tyre rolls at 1.85 m per revolution.
Given
- Rprimary, high = 52 mm
- Rsecondary, high = 26 mm
- Rprimary, low = 19 mm
- Rsecondary, low = 58 mm
- ωengine, max = 8500 RPM
- ifinal = 10.0 :1
- Ctyre = 1.85 m/rev
Solution
Step 1 — compute the CVT ratio at full upshift (cruise condition, belt high on primary):
That's an overdrive of 0.5:1 — the secondary spins twice as fast as the primary. Combined with the 10.0:1 final drive, the total reduction from engine to wheel is 0.50 × 10.0 = 5.0:1.
Step 2 — convert engine speed to wheel speed at redline and find road speed:
That's the theoretical top speed if the engine could pull redline against air drag. In reality a stock PCX 150 tops out around 110-115 km/h because the engine doesn't make enough power to hold redline against drag at that ratio — the variator backshifts and settles around icvt ≈ 0.75 in cruise, giving a real top speed in the 105-115 km/h band.
Step 3 — compute the launch (low-end) ratio at engagement, belt fully down on the primary:
Combined with final drive: 3.05 × 10.0 = 30.5:1 total reduction. At 3,000 RPM engagement that gives wheel speed of 3000 / 30.5 = 98 RPM, or about 3.0 m/s (10.9 km/h) — exactly the slow crawl you feel when a scooter first hooks up off the line.
Step 4 — total ratio spread:
A 6.1:1 spread is at the upper edge of what a rubber V-belt handles reliably. Push it higher with a smaller primary minimum radius and you'll see belt life drop from the typical 20,000-25,000 km down to under 12,000 km because of bending fatigue at the tight wrap.
Result
Nominal full-upshift CVT ratio is 0. 50:1, giving a theoretical top speed near 188 km/h at 8,500 RPM that real-world drag pulls back to roughly 110 km/h. At the low end the 3.05:1 launch ratio delivers about 11 km/h of crawl at engagement RPM — which is what makes the scooter feel positive off the line without bogging the engine. The 6.1:1 ratio spread is right at the practical ceiling for this belt size. If your measured top speed is 15 km/h below predicted, suspect three things: a stretched belt that can no longer climb to full height on the primary (check belt width — under 21.5 mm on a stock PCX belt means scrap it), centrifugal weights that have flat-spotted and won't push the moving sheave fully closed (look for grooved tracks on the weights), or a glazed primary face that's letting the belt slip mid-shift instead of climbing.
Choosing the Pulley-and-belt CVT: Pros and Cons
Pulley-and-belt CVTs compete against geared automatics, hydrostatic transmissions, and toroidal CVTs depending on the application. The choice usually comes down to torque capacity, efficiency at cruise, and whether the application can tolerate belt replacement intervals.
| Property | Pulley-and-belt CVT | Planetary automatic (geared) | Hydrostatic transmission |
|---|---|---|---|
| Ratio spread (typical) | 4.0 to 6.5 | 6.0 to 10.0 (8-10 speed) | infinite — but limited by pump/motor displacement |
| Peak torque capacity | up to ~400 Nm with steel push belt; ~150 Nm with rubber V-belt | 1000+ Nm with no architectural change | 2000+ Nm in heavy off-highway units |
| Cruise efficiency | 86-90% (steel belt) / 78-85% (rubber) | 92-95% | 65-80% |
| Service interval / lifespan | belt: 20,000-50,000 km automotive, 5,000-8,000 km snowmobile | fluid: 100,000+ km, often sealed-for-life | filter and fluid every 1,000-2,000 hours |
| Cost (production) | low to medium | high — many gears, clutches, and valve bodies | high — precision pump and motor |
| Application fit | scooters, snowmobiles, small cars, UTVs, light industrial | trucks, large cars, heavy equipment | skid steers, combines, tractors, marine |
| Cold-temperature behaviour | belt stiffens; harsh engagement below -20°C | shifts smoothly with proper ATF | fluid viscosity dominates; long warmup needed |
Frequently Asked Questions About Pulley-and-belt CVT
The primary clutch is upshifting before the engine has built enough power for the load. The fix is in the centrifugal weights — they're too heavy. Heavy weights produce more clamping force at lower RPM, which forces the upshift to happen below the powerband peak.
Drop weight mass by 1-2 g per arm and the engagement curve moves up the rev range. On a Polaris RMK the standard 60 g weights often need to come down to 56-58 g for high-altitude use because thinner air means less power, so you need the engine sitting higher in its band to make the same wheel torque. The torque cam ramp angle on the secondary also matters — a steeper ramp (45° instead of 40°) holds the belt deeper on the secondary under load and resists premature upshift.
Black dust is rubber being abraded off the belt edges, and yes, it points to a problem — but usually not the belt itself. The cause is almost always a mismatched sheave angle or a sheave face that's no longer flat. The belt sidewall isn't fully seated against the cone, so only a narrow band of contact carries the load, and that band wears fast.
Check the sheave faces with a straightedge and feeler gauge — anything more than 0.05 mm of dish or wear-step means the sheave needs replacement, not the belt. Also confirm the belt's V-angle matches the sheave: most automotive CVT belts run 11° per side (22° included), most scooter belts run 13° per side (26° included). Mixing them produces exactly the dust pattern you're seeing.
Choose CVT when fuel economy at steady cruise is the priority and peak torque is below about 300 Nm. The CVT lets the engine sit exactly on its BSFC sweet spot regardless of road speed, which is why hybrid drivetrains like the Toyota eCVT-style and the Honda i-MMD use belt or chain CVTs.
Choose DCT when shift feel, sport response, or torque capacity above 400 Nm matters more than absolute economy. DCTs have higher mechanical efficiency at full throttle but worse part-load efficiency than a well-tuned CVT. The other deciding factor is cost — a steel-belt CVT is genuinely cheaper to build than a 7-speed DCT, which is why budget compacts almost always run CVT.
Published spreads assume the belt rides at the absolute outer edge of the primary at full upshift and the absolute inner edge at full downshift. In reality the belt almost never gets all the way to either limit, because the moving sheave hits a mechanical stop or the spring tension on the secondary won't let the belt rise high enough.
You typically see 80-90% of the published spread in real operation. If you're below 75%, look for a worn or weak secondary spring (it's letting the belt climb too high on the secondary instead of being forced down), a binding sliding sheave on the primary (debris or dry splines), or the wrong belt length — a belt 2-3 mm short forces the system to operate within a narrower pitch-radius window.
More power means the engine can pull a taller ratio at any given RPM, so you want the upshift curve to happen later in the rev range to keep the engine on the new power peak. Add weight, don't remove it — counterintuitive, but correct.
Rule of thumb: increase weight by roughly 1 g per arm for every 10% power gain, then road-test and watch the tach. The engine should hit peak-power RPM right as the variator starts upshifting in third-gear-equivalent acceleration. If the tach climbs past peak power before upshift starts, weights are still too light. If the tach stalls below peak power during acceleration, weights are too heavy and you need to drop back. Tuning by 0.5 g increments is normal — the variator is that sensitive.
You can, but it's usually pointless. Electric motors produce useful torque from zero RPM and have a usable speed range of typically 0-12,000 RPM with constant power above base speed. That's already a wider effective ratio range than a CVT can add.
The exception is high-performance EVs that want to hold the motor at peak-efficiency RPM during cruise to extend range. The 2024 Porsche Taycan and Audi e-tron GT use a 2-speed gearbox for this exact reason — a CVT would do the same job with smoother ratio change but adds 8-12% drivetrain loss compared to direct gearing, which kills the efficiency gain you were chasing. So unless your motor has a narrow efficient operating band, skip the CVT and use a fixed reduction or 2-speed.
References & Further Reading
- Wikipedia contributors. Continuously variable transmission. Wikipedia
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