Two shafts need to transmit torque between them — say, a motor driving a pump. In theory, you bolt their flanges together and spin. In practice, the shafts are never perfectly collinear: bearings settle, frames flex, thermal growth shifts the pump 0.3mm sideways during operation. A coupling is the component that transmits torque while tolerating this real-world misalignment.

Misalignment comes in three flavors, and they often combine:

• Parallel (offset): shaft axes are parallel but laterally displaced
• Angular: shaft axes meet at a point but at an angle
• Axial (end float): shafts move toward/away from each other, usually from thermal expansion

Coupling types, roughly in order of misalignment tolerance:

• Rigid couplings (sleeve, clamp, flange): zero misalignment tolerance. Used when shafts are machined as one assembly or when you specifically want to enforce alignment. Cheap and stiff.
• Jaw couplings: two metal hubs with interlocking jaws separated by an elastomeric "spider." Handles ~1° angular, ~0.4mm parallel. The spider dampens vibration and fails predictably — when it shreds, the coupling stops transmitting torque (a feature for protecting downstream equipment).
• Beam (helical) couplings: single piece of metal with a helical cut. Zero backlash, good for encoders and servos. Limited torque capacity.
• Disc couplings: flexible metal discs between hubs. High torque, high speed, very low backlash. Standard for turbomachinery.
• Gear couplings: two hubs with crowned external teeth meshing with an internal-tooth sleeve. Massive torque density, used in steel mills and large pumps.
• Universal joints (U-joints): for large angular misalignment (up to 30°+). But a single U-joint produces velocity fluctuation — you need two U-joints with phased yokes (or a CV joint) to maintain constant velocity. This is why driveshafts have two joints.

Rule of thumb — coupling selection torque:

Calculate nominal torque from T (N·m) = 9550 × P(kW) / N(rpm), then multiply by a service factor: 1.0 for smooth loads (centrifugal pumps), 1.5 for moderate shock (gear pumps, fans), 2.5+ for severe shock (reciprocating compressors, crushers). A 7.5 kW motor at 1750 rpm driving a piston compressor: 9550 × 7.5 / 1750 = 41 N·m × 2.5 = 103 N·m minimum coupling rating.

The critical install step: couplings tolerate misalignment, they don't fix it. Aligning shafts to within the coupling's spec (laser alignment for anything serious) dramatically extends bearing and seal life on both connected machines. A jaw coupling "running" at 5x its rated misalignment will still spin — but it'll eat bearings in months.