Power Transmission — Gears, Belts & Chains — Basic Mechanical Engineering Notes

Last reviewed 16 Sept 2026 · 10 min read

Methods of power transmission

Drive	Features	Typical use
Belt drive	Flexible, quiet, absorbs shock; slip possible; moderate centre distances	Pumps, compressors, conveyors, machine tools
Rope drive	Large distances and powers	Cranes, hoists, elevators, ropeways
Chain drive	No slip (positive drive), moderate distances, compact	Bicycles, motorcycles, conveyors, concrete mixers
Gear drive	Positive, exact velocity ratio, compact, high power; short centre distances	Gearboxes, machine tools, cranes, winches, mixers
Shafts and couplings	Direct transmission	Motor–pump sets
Hydraulic/pneumatic	Flexible layout, high force	Excavators, loaders, jacks

Shafts

FormulaPower, torque and torsion

Power: $P = T ω = \frac{2 π N T}{60}$ (W; T in N·m, N in rpm)

Torsion of a solid circular shaft:

\frac{T}{J} = \frac{τ}{r} = \frac{Gθ}{L}, τ_{ma x} = \frac{16 T}{π d ^{3}}, J = \frac{π d ^{4}}{32}

Hollow shaft: $τ_{ma x} = \frac{16 T d _{o}}{π ( d _{o}^{4} - d _{i}^{4} )}$ — hollow shafts are lighter for the same strength.

Shafts may also carry bending (from pulleys, gears) — combined bending and torsion design.
Axles carry bending but not torque; spindles are short shafts in machine tools.

Keys and couplings

Keys (sunk rectangular/square, saddle, feather, Woodruff, splines) transmit torque between shaft and hub; designed for shear and crushing.
Couplings join shafts:
- Rigid couplings (sleeve/muff, flange coupling) — shafts must be accurately aligned.
- Flexible couplings (bush-pin type, universal/Hooke's joint, Oldham coupling) — accommodate misalignment and absorb shocks.

Clutches and brakes

Clutch — engages/disengages driving and driven shafts while running: friction clutches (single-plate, multi-plate, cone, centrifugal), jaw (positive) clutches.
Brakes — absorb kinetic energy to slow or stop motion: block/shoe brakes, band brakes, internal expanding shoe brakes, disc brakes, hydraulic and electromagnetic brakes (hoists).
Friction torque of a single-plate clutch with uniform wear: $T = μ W \frac{r _{1} + r _{2}}{2} n$ ( $n$ = number of friction surfaces).

Belt drives

Types

Flat belts — long centre distances, high speeds, lower power per belt.
V-belts — wedge action increases grip → higher power, less slip, shorter centre distances; multiple belts used; common in compressors, pumps, generators.
Timing (toothed) belts — no slip, synchronous.
Open belt — both pulleys rotate in the same direction; crossed belt — opposite directions (larger contact angle, more wear).

Velocity ratio

FormulaVelocity ratio of belt drives

\frac{N _{2}}{N _{1}} = \frac{D _{1}}{D _{2}}

With belt thickness t: $\frac{N _{2}}{N _{1}} = \frac{D _{1} + t}{D _{2} + t}$ With total slip s%: $\frac{N _{2}}{N _{1}} = \frac{D _{1}}{D _{2}} (1 - \frac{s}{100})$

Creep — slow relative motion due to unequal stretching on tight and slack sides.

Length of belt

Open belt: $L = \frac{π}{2} (D_{1} + D_{2}) + 2 C + \frac{( D _{1} - D _{2} ) ^{2}}{4 C}$
Crossed belt: $L = \frac{π}{2} (D_{1} + D_{2}) + 2 C + \frac{( D _{1} + D _{2} ) ^{2}}{4 C}$

Tensions and power

FormulaBelt tensions and power

Ratio of tensions (flat belt): $\frac{T _{1}}{T _{2}} = e^{μ θ}$ ( $θ$ = angle of contact in radians on the smaller pulley) V-belt: $\frac{T _{1}}{T _{2}} = e^{μ θ / s i n β}$ ( $2 β$ = groove angle) Power transmitted: $P = (T_{1} - T_{2}) v$ , $v = \frac{π D N}{60}$ Centrifugal tension: $T_{c} = m v^{2}$ ( $m$ = mass per unit length) Maximum tension $T_{ma x} = T_{1} + T_{c}$ ; maximum power is transmitted when $T_{c} = T_{ma x} /3$ Open belt angle of contact: $θ = π - 2 sin^{- 1} \frac{D _{1} - D _{2}}{2 C}$

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