§1Three jobs on one shaft line
Between any motor and its load sit up to three decisions: join the shafts, interrupt the joining, and remove the energy — and the three families divide the work with almost no overlap.
The coupling is the permanent joint, and its real subject is imperfection: two “aligned” shafts never quite are, and §2’s family is graded almost entirely by how much misalignment each forgives and how it forgives it. The clutch makes the joint switchable, which means it must be able to slip — the property that lets it engage a moving driver to a stationary load — and slipping friction is a torque device, sized by §3’s one line. The brake is the clutch’s twin with one member bolted to the earth: same friction faces, same clamping arithmetic, but its duty is not to transmit torque steadily — it is to swallow a definite quantity of kinetic energy and survive the heat, which is why §4 prices brakes in joules while §3 priced clutches in newton-metres. Hold that torque-versus-energy distinction and the whole page falls into order; lose it and you meet the classic sizing mistakes — a brake chosen on holding torque that fades to nothing on the first long descent, a clutch chosen on torque that cooks its plates on inching duty. §5 is about exactly those.
Contents§2Couplings
A coupling’s catalogue question is never “how much torque” first — it is “what errors between these two shafts must this joint absorb, forever, at speed”.
| Type | Forgives | Signature |
|---|---|---|
| Rigid (flange, sleeve) | nothing | strongest and simplest — demands real alignment |
| Jaw / elastomeric | small angular + parallel | rubber spider cushions shock; a wear part by design |
| Disc (lamina) | angular + axial, zero backlash | flexing steel discs — the servo and machine-tool joint |
| Gear / grid | more of everything, heavy torque | crowned teeth or spring grid; needs its grease |
| Universal (Hooke) joint | large angular | speed pulses with angle — see the caveat below |
| The universal joint’s caveat is kinematic, not a defect: a single Hooke joint at a working angle β transmits rotation whose speed swings between cos β and 1/cos β each half-revolution — at β = 15° that is 0.966 to 1.035, a ±3.5% pulse, twice per turn, felt as vibration and gear rattle. The standard cure is built into every vehicle tailshaft: two joints, equal angles, yokes phased, so the second joint’s pulse exactly cancels the first — or a constant-velocity joint where geometry forbids the pulse entirely. And a family-wide honesty note: flexible couplings forgive misalignment by flexing under it every revolution, and flexing is fatigue duty — which is why the shaft-alignment page that ends this section exists even for machines “on flexible couplings”. | ||
§3The friction clutch
Clamp friction faces together and torque capacity is one multiplication: faces, friction, force, radius — with plates as the designer’s multiplier.
A single driven plate lined both sides gives n = 2 faces. With μ = 0.3, a spring clamp of F = 2 kN, and linings from Ri = 70 to Ro = 100 mm, the mean radius is Rm = 85 mm and the capacity is T = 2 × 0.3 × 2000 × 0.085 = 102 N·m. Every term is a design dial. n is the cheap one: a multi-plate pack alternating driving and driven discs turns the same clamp into four, six, ten faces — the motorcycle and machine-tool solution to torque in no diameter. F comes from springs (so the clutch is engaged at rest and released by the operator through a thrust — release — bearing, the fail-engaged arrangement vehicles use) or from hydraulics and coils where control wants it. Rm’s uniform-wear form carries its own quiet lesson: a worn-in clutch bears hardest at its inner radius, so capacity follows the mean radius, not the outer edge the eye credits. And μ is the term you least control — which is §5’s door, because μ is a function of temperature, and temperature is a function of how the clutch is used.
§4Brakes: joules, not newton-metres
Any brake can generate stopping torque; the sizing question is whether it can swallow the stop’s energy — every stop, all day — without cooking its own friction away.
A drive with I = 2 kg·m² of inertia at 1500 rpm (ω = 157.1 rad/s) carries E = ½Iω² = 24.7 kJ of kinetic energy. Stop it in 3 seconds and the brake linings absorb a mean 8.2 kW for those seconds — a bar-radiator’s worth of heat delivered into a few square centimetres of lining, and the number that actually sizes the brake: repeat the stop every minute and the duty is a continuous thermal load the friction material must live at. The failure of an under-sized brake has a name every driver of a long descent knows: fade — friction coefficients fall as linings overheat, so the harder the brake works, the less it grips, a feedback §1 warned about. Geometry manages the heat: the disc brake’s exposed, air-swept rotor sheds it best and fades least, which is why it owns high-duty braking; the drum brake encloses its heat but pays itself back with self-energisation — the leading shoe’s geometry uses the drum’s own rotation to wedge the shoe harder, multiplying pedal effort at the cost of touchier, direction-sensitive behaviour. Holding still is the easy case, and even there the standing rule applies: parking and crane brakes are spring-applied, power-released, so losing power means gaining brake.
§5Engagement and the heat bill
A clutch taking up a load must slip, and the slip phase has an exact and slightly shocking energy account: the heat equals the kinetic energy delivered — no matter how the clutch is built.
Watch one engagement from a constant-speed driver. The clutch transmits torque T through the whole slip; the load needs angular impulse Iω to reach speed, so the slip lasts t = Iω/T and the driver does work T·ω·t = Iω². The load banks only ½Iω². The other half — exactly half, by algebra, independent of T, μ, plate count or skill — became heat in the friction faces. Slip faster with a fiercer clutch and the same joules arrive in less time; feather it gently and they arrive slowly; they arrive regardless. That identity writes the duty rules. Clutches on inching, positioning and frequent-start service are sized like §4’s brakes — by joules per hour, not peak torque — and this is the natural home of the wet clutch: running in oil costs friction coefficient (bought back with §3’s plate count) but turns the lining’s heat problem into the oil cooler’s, buying near-indefinite slip life; the automatic transmission’s packs and every serious motorcycle clutch live here. Dry clutches keep the higher μ and the compact package, and pay in lining life exactly proportional to how much of §5’s arithmetic their duty invokes. The friction pair, in the end, is a consumable bought by the kilojoule — the only question is how fast the account is drawn down.
§6Overload protection
Somewhere in a drive line it pays to install the weakest link on purpose — a torque fuse that fails cheaply, predictably and exactly where you chose.
Fit a Ø6 mm pin at a radius of 40 mm in a coupling flange, in a material shearing at 300 MPa: it carries F = τA = 8482 N, so the joint lets go at T = 339 N·m — and a jammed auger or fouled propeller costs one pin instead of a gearbox. The shear pin is the honest extreme of a family. Friction torque limiters — §3’s clutch with its clamp set by adjustable springs — slip at the set torque and re-engage when the jam clears, the resettable fuse for machines that jam routinely. The jaw coupling’s elastomer spider is a soft fuse of sorts, absorbing shocks below the damage line and tearing sacrificially above it. And the discipline that makes any of them work is placement and honesty: the fuse must be the calculated weakest link — weaker than the keys of the next page, the gear teeth, the shaft — and must stay so, which is why replacing a sheared pin with “whatever bolt fits” is the classic way to convert the next overload from a five-minute pin change into the gearbox failure the pin existed to prevent. A drive line, like a circuit, protects what its designer fused — and only that.
| Device | On overload | Afterwards |
|---|---|---|
| Shear pin | breaks at its set torque — 339 N·m in Example 3 | fit a new pin of the same grade |
| Friction torque limiter | slips at the spring setting | re-engages itself when the jam clears |
| Elastomer spider (jaw coupling) | cushions below, tears above its damage line | replace the spider |
| Vee-belt drive | squeals and slips (§ belts) | re-tension; replace if glazed |
| One rule spans the family: the fuse works only while it remains the calculated weakest link — and only if what replaces a spent one restores the calculation, not just the connection. | ||
§7Quick reference
The working core of the page on one card rack.
Couplings
graded by forgiveness
Hooke joint: pair and phase
Clutch
T = nμFR_m = 102 N·m
plates multiply n
Brake
E = ½Iω² = 24.7 kJ → 8.2 kW
fade: hot linings lose μ
Slip law
heat = KE delivered, exactly
wet clutch: oil pays the bill
Torque fuse
Ø6 pin @ 40 mm → 339 N·m
the weakest link, on purpose