Chain Drive

How a chain transmits power

A roller chain is a row of pin-jointed links, each carrying a steel roller that turns freely on a bushing. A sprocket is a toothed wheel whose teeth fit between the rollers. When the drive sprocket rotates, each tooth picks up the next roller and pulls the chain forward; the chain wraps the driven sprocket and the rollers settle into its tooth pockets, spinning that sprocket. Because rollers physically engage tooth pockets, the chain cannot slip relative to either sprocket — power transfer is positive.

The same tooth-ratio arithmetic that governs gears applies to chain sprockets. With N_1 teeth on the driver and N_2 teeth on the driven sprocket:

R = N_2 / N_1
ω_2 = ω_1 / R
τ_2 = τ_1 × R × η
P_out = P_in × η  (η ≈ 0.98 to 0.99)

The chain itself preserves exact rotational phase between sprockets — critical in engine timing drives, where the camshaft must stay aligned with the crankshaft to millisecond accuracy across millions of revolutions. Belts can stretch and skip teeth; chains under reasonable tension maintain alignment for the engine's life.

Worked example: cycling power transfer

Take a road cyclist averaging 250 W on a 1-hour climb, with a 50-tooth chainring and a 21-tooth rear cog. Crank radius is 172.5 mm; rear wheel diameter is 700 mm.

• Cadence: 80 RPM = 8.38 rad/s
• Crank torque: P / ω = 250 / 8.38 = 29.8 N·m
• Pedal force: 29.8 / 0.1725 = 173 N at the pedal
• Gear ratio: 50 / 21 = 2.38:1
• Rear wheel speed: 80 × 2.38 = 190 RPM = 19.9 rad/s

The chain delivers power to the rear wheel at 99% efficiency (typical clean, oiled chain). Wheel torque: 29.8 / 2.38 × 0.99 = 12.4 N·m. At a tire rolling radius of 0.34 m, that's 12.4 / 0.34 = 36.5 N of forward thrust. At 19.9 rad/s × 0.34 m = 6.77 m/s, the rider is moving at 24.4 km/h — and the chain has wasted only about 2.5 W out of the 250 W. A worn chain or dry chain loses 5-15 W — measurable on a power meter.

Chain vs belt vs gear comparison

	Chain drive	V-belt	Timing belt	Direct gears	Worm drive	Cardan shaft
Slip	None	1-3%	None	None	None	None
Efficiency	98-99%	95-98%	96-98%	97-99%	40-90%	98-99%
Center distance	0.3 to 3+ m	0.3 to 3+ m	0.2 to 1 m	Touching	Touching	Up to 5+ m
Noise	Medium-high	Low	Medium	High	Low	Low
Maintenance	Lube every ~500 km	Tension check	Replace 60-100k km	Oil change 50k km	Oil change 5k hrs	U-joint grease
Typical use	Bikes, motorcycles, conveyors	Cars, HVAC, washers	Engine cams, 3D printers	Transmissions, robots	Hoists, lifts	Truck driveshafts

Chains win on efficiency and load capacity. Belts win on noise and cost. Direct gears win when shafts touch. Worm drives win when self-locking matters. Cardan shafts win when bridging long distances with angular flexibility. Engineers pick based on cost, environment, load, and noise budget.

Chain types and configurations

• Standard roller chain (ANSI/ISO). Pitch 12.7 mm (1/2") to 76.2 mm (3"). Workhorse for industrial and bicycle drives. Standardized for interchangeable parts.
• Silent (inverted-tooth) chain. Articulating link plates engage sprocket teeth on their inner edges. Much quieter than roller chain, used in engine timing, gearboxes (Borg-Warner). Higher cost.
• Leaf chain. Pure-tension chain with no rollers, used in forklifts and counterweight applications.
• Block chain. Solid steel blocks pinned together; used in old industrial conveyors and large transport machinery.
• Bicycle (narrow) chain. 12.7 mm pitch but narrow (5-7 mm inner width) to fit modern derailleurs with 11-13 rear cogs.
• Motorcycle (O-ring/X-ring) chain. Roller chain with sealed lubrication via elastomer O-rings between pin plates. Extends life from ~10,000 km to 20,000+ km.

Real-world specifications

• SRAM Red bicycle chain (12-speed). 50-tooth chainring + 10-33T cassette. Pitch 12.7 mm. Rated for 1,000+ W sprint loads. Life ~3,000 km before 0.5% elongation.
• RK Takasago 525X-XW motorcycle chain. 15.875 mm pitch, X-ring sealed, 6,000 N working load. Common on 600-1000 cc sportbikes. Service life 20-30,000 km.
• Honda B20A engine timing chain. 9.525 mm pitch, two-row roller chain, lasts 250,000+ km without replacement (one of the reasons Honda engines have a reliability reputation).
• Conveyor chain (50-pitch). 38.1 mm pitch, 7-15 m long, drags packages at 0.5-2 m/s. Lubricated continuously via drip oilers; replaced every 5-10 years.
• Garage door chain. 9.525 mm pitch open chain wrapping a 30 mm pulley + 10:1 reduction. Lifts 50 kg door 2.5 m in 12 seconds. Annual lube only.

Common misconceptions

• Chains stretch like rubber. No — they elongate from pin/bushing wear. The steel doesn't stretch; the joints loosen.
• Tighter chain is better. Over-tensioned chains accelerate bearing wear and reduce efficiency. A bicycle chain should have 12-15 mm vertical play at the midpoint.
• Chains never slip. They don't slip on the sprocket, but they can skip teeth if very worn, derailleur-shifted under load, or jammed by debris.
• Belt is always quieter. Silent (inverted-tooth) chains rival belts for noise in modern engines.
• Lube is optional. Dry chain efficiency drops to 92-95% and wear accelerates 5-10×. Every 500 km of bicycle riding (or every 1,000 km of motorcycle) is the typical re-lube interval.
• One chain length fits all. Chain length must match the sprocket pair and center distance. Too long → slack and skipping; too short → won't engage. Replace as a set: chain + chainring + cassette every 2-3 chain replacements.