Gears and Power Transmission

Power transmission is how a motor’s torque and speed reach the load: through gears, belts, chains, shafts, couplings and bearings. The choices decide the efficiency, the noise, the life and the cost of a machine, and a mistake in any element (an undersized gear, a belt that slips, a bearing that is overloaded) shows up as heat, vibration or a broken part. This guide goes through the elements one at a time with the formulas, worked numbers and diagrams, from the geometry of a tooth to the choice of a bearing and its lubricant. It continues from Motion Control and Actuators (the motors and drives that turn the shafts) and connects to Structures and Strength of Materials (the stresses in shafts, bolts and housings).

Start here: what do you need?

I need to…	Go to
understand module, pitch, pressure angle, tooth terms, and gear ratio	Gear Basics and Terminology
choose between spur, helical, bevel, worm and planetary gears	Gear Types and Selection
check that a gear is strong enough, or size one for a given power	Gear Strength and Design Calculations
work out a multi-stage reduction, planetary ratio or choose tooth counts	Gear Trains, Ratios and Efficiency
size a belt or timing belt drive, or find belt length and tension	Belts and Pulleys
choose a roller chain and sprockets	Chains and Sprockets
size a shaft, a key or a coupling	Shafts, Keys and Couplings
choose a bearing and estimate its life	Bearings and Bearing Selection
pick a lubricant or find out why a drive is hot or noisy	Lubrication, Wear and Gear Failures

A suggested order

If you are new to the subject, read the pages in this order: the first three build the gear theory, the next two cover flexible drives, and the last pages are the parts that every drive needs.

1. Gear Basics and Terminology: Module and pitch, pressure angle, tooth terms, speed and torque ratios, contact ratio, undercut and how two gears mesh.
2. Gear Types and Selection: Spur, helical, bevel, worm, rack, internal and planetary gears compared: efficiency, noise, thrust and where each is used.
3. Gear Strength and Design Calculations: Tooth forces, bending stress by the Lewis equation, contact stress, safety factors and sizing a gear pair for a given power.
4. Gear Trains, Ratios and Efficiency: Simple, compound and planetary gear trains, overall ratio, losses, backlash and the choice of the number of teeth.
5. Belts and Pulleys: Flat, V and timing belts: speed ratio, belt length, wrap and tension, power rating, sizing and the pulley and tooth counts for timing drives.
6. Chains and Sprockets: Roller chain, pitch and speed, the polygon effect, power rating, lubrication, tension and a worked drive selection.
7. Shafts, Keys and Couplings: Shaft torque capacity, keys and keyways, splines, shaft stiffness and critical speed, and rigid and flexible couplings.
8. Bearings and Bearing Selection: Ball, roller and plain bearings, the life equation, radial and axial loads, fits and preload, mounting and failure signs.
9. Lubrication, Wear and Gear Failures: Oils and greases, viscosity and film thickness, gear failure modes, inspection and a symptom table for noisy or hot drives.

Quick reference: formulas

Topic	Formula	Page
Module and pitch diameter	m = d ÷ z; d = m z	Gear Basics and Terminology
Center distance	a = m (z1 + z2) ÷ 2	Gear Basics and Terminology
Gear ratio, torque	i = z2 ÷ z1; T2 = T1 i η	Gear Basics and Terminology
Tooth force	Ft = 2T ÷ d; Fr = Ft tan φ	Gear Strength and Design Calculations
Lewis bending stress	σ = Ft ÷ (b m Y)	Gear Strength and Design Calculations
Planetary ratio (ring fixed)	i = 1 + zring ÷ zsun	Gear Trains, Ratios and Efficiency
Belt tension ratio	T1 ÷ T2 = eμθ	Belts and Pulleys
Chain speed	v = N p n ÷ 60 000 (m/s, p in mm)	Chains and Sprockets
Shaft torque capacity	T = π τ d³ ÷ 16	Shafts, Keys and Couplings
Bearing life	L10 = (C ÷ P)p million rev	Bearings and Bearing Selection

Gears, belts or chains?

	Gears	Belts (timing)	Roller chains
Efficiency	96 to 99 % per mesh	95 to 98 %	95 to 98 %
Center distance	Fixed and short	Flexible, up to several meters	Flexible, up to several meters
Slip	None	None (timing belts)	None
Noise	Moderate to loud (hum)	Quiet	Rattle at speed
Lubrication	Oil or grease	None	Required
Load capacity	Highest	Moderate	High
Cost	Medium to high	Low	Low to medium
Typical use	Gearboxes, machine tools, vehicles	Printers, light machinery, automotive cams	Conveyors, agricultural, motorcycles

Calculators and related guides

• Gear Ratio, Torque and Speed Generator: ratio, speed and torque for a pair or a train.
• Motor Torque and Inertia Matching Calculator: reflected inertia through a gearbox.
• Fits and Tolerances: shaft and bore fits, press fits.
• GD&T: drawing the gear and housing tolerances.
• Structures and Strength of Materials: shaft stresses, bolts and fatigue.
• Mechanical Transmission: screws, backlash and inertia matching for servo axes.

Safety

• Guard every moving part: gears, belts, chains and couplings catch clothing, hair and fingers in an instant. Fit fixed guards that cannot be removed without a tool.
• Lock out and de-energize before servicing, and block against stored energy (see Workshop Safety).
• Hot surfaces and oil: gearboxes and bearings get hot and the oil can scald.
• Failures can throw parts: a broken gear or a flying belt can be dangerous: guard against it, and never exceed the speed ratings.
• Lifting: gearboxes are heavy; use lifting points and proper slings.

FAQ

Where should I start?

With Gear Basics and Terminology for the vocabulary, then Gear Types and Selection. If you need a drive designed, go to Gear Strength and Design Calculations once you know the type.

What happened to the Belts and Pulleys page?

It is now Belts and Pulleys, one page of this guide, with more worked examples and the belt-tension and power calculations.

Do I need a gearbox or a belt?

A belt is quiet, light and cheap with no lubricant, but only for modest loads. A gearbox gives the highest load for the size and a fixed ratio. A chain is robust in dirty places. See the comparison above and the individual pages.

Is there a calculator?

Yes: the Gear Ratio, Torque and Speed Generator. The strength and life calculations are worked by hand in the pages, with the formulas given so you can reproduce them in a spreadsheet.

References

• Shigley, J. E. and Mischke, C. R., Mechanical Engineering Design, McGraw-Hill.
• Dudley, D. W., Handbook of Practical Gear Design; Machinery’s Handbook (gearing, belts, chains, bearings).
• AGMA and ISO standards for gears (ISO 6336, AGMA 2001); ISO 281 (rolling bearing life); ISO 606 (roller chains).
• KHK, Gear Technical Reference; SKF and Timken, Bearing handbooks.

Last reviewed: October 2026. Values are typical: use the manufacturer’s data and the relevant standard for real designs.