Oldham Coupling

What an Oldham coupling does

Real machines almost never line up perfectly. A motor bolted to one bracket and a pump bolted to another will have their shaft centrelines a fraction of a millimetre apart, and that small parallel offset is enough to chew through bearings if the two shafts are rigidly coupled. The Oldham coupling solves the pure-offset case elegantly: it lets the two shafts sit side by side, axes parallel but displaced, and still spin as one. It does this by inserting a floating disc between two hubs and letting that disc slide.

The geometry is the whole trick. The input hub presents a flat tongue along one diameter. The output hub presents a tongue along a diameter rotated 90° from the first. Between them sits the central disc, with a slot on each face — one slot mating with the input tongue, the other with the output tongue, the two slots themselves 90° apart. Each tongue can slide freely along its slot, but it cannot rotate relative to the disc. So rotation is passed through rigidly, while radial position is free in two perpendicular directions — and two perpendicular sliding freedoms are exactly enough to span any offset vector in the plane.

The kinematics: why it is constant velocity

Let the input shaft centre be at the origin and the output shaft centre be displaced by a fixed offset e along the x-axis. Call the instantaneous input angle φ. The input tongue lies along a diameter at angle φ; the disc's slot that mates with it must be parallel to that tongue, so the disc itself rotates with the input. Because the second slot is fixed 90° from the first on the disc, and the output tongue must lie along that second slot, the output hub is forced to the same angle φ as the input.

Input angle      φ_in  = φ
Output angle     φ_out = φ          ← identical, always
Velocity ratio   ω_out / ω_in = 1   (constant, independent of offset e)

That is the defining property: the output angle equals the input angle at every instant, so the angular velocity ratio is a rock-steady 1.0 no matter how large the offset. The offset is absorbed purely by translation of the disc, not by any rotational lead or lag. This is what makes the Oldham a genuine constant-velocity coupling — unlike a single universal joint, whose output speed wobbles up and down twice per revolution whenever the shafts are at an angle.

Now track the disc's geometric centre. It must sit on the line joining the two slot engagements, and that line's midpoint traces a circle as the shafts turn. The disc centre orbits a circle of diameter equal to the offset e, and it completes that orbit twice for every one shaft revolution:

Disc-centre orbit radius   = e / 2
Disc-centre orbit frequency = 2 × shaft frequency
Sliding stroke per slot     = 2e per revolution (one full back-and-forth)

The 2× term is the source of every practical limitation. The disc carries mass, and a mass orbiting a circle of radius e/2 at twice the shaft rate generates an unbalanced inertial force F = m·(e/2)·(2ω)² = 2 m e ω² — proportional to offset, to disc mass, and to the square of speed. Double the rpm and the shaking force quadruples. This is why Oldham couplings are kept to modest speeds, made with the lightest practical disc, and used with the smallest offset the installation can be aligned to.

Torque transmission and contact pressure

Torque passes from the input tongue, through the disc, to the output tongue as a pair of opposing contact forces on the slot flanks. For a transmitted torque T on a slot of effective lever arm r (roughly the disc radius), the flank force is on the order of F = T / r, and the contact pressure is that force spread over the engaged tongue area. Designers keep this pressure below the bearing strength of the disc material; for a plastic centre disc the allowable is far lower than for steel, which caps the torque rating.

Slot flank force         F ≈ T / r
Sliding-friction torque  T_fric ≈ μ · F · (e/2)   per slot pair
Power lost to sliding    P_loss ≈ T_fric · ω

Because the tongues slide while loaded, the friction is genuine rubbing friction, not rolling — so efficiency drops as offset grows. A well-lubricated metal Oldham at small offset can exceed 98% efficient; the same coupling run dry at a large offset can lose several percent and heat up. That trade between offset capacity and frictional loss is the central design tension of the device.

Oldham vs other misalignment couplings

The Oldham occupies a specific niche — pure parallel offset, true constant velocity, short axial length. The table below places it against the other common shaft couplings.

	Oldham coupling	Single universal (Hooke) joint	Double U-joint / CV joint	Jaw / spider (Lovejoy)	Disc / diaphragm coupling	Gear coupling
Handles parallel offset	Yes (its specialty)	No (angular only)	Yes (with offset shaft)	Small	Small	Small
Handles angular misalignment	No (≈0.5° max)	Yes (up to ~30°)	Yes	~1°	~0.5°	~1.5°
Constant velocity?	Yes, exactly	No (±secθ ripple)	Yes (if phased)	Approx.	Yes	Approx.
Axial length	Very short	Short	Long	Short	Medium	Medium
Backlash	Low–medium (slot fit)	Low	Low	Damped, near zero	Zero	Medium
Main wear mode	Sliding tongue/slot abrasion	Needle-bearing wear	Bearing/race wear	Elastomer fatigue	Disc-pack fatigue	Tooth wear, lube
Speed limit driver	2× disc orbit inertia	Speed ripple, bearings	Bearings, balance	Elastomer heating	Critical speed	Lube slinging
Typical use	Offset motor-to-pump, encoders, packaging drives	Steering, PTO at an angle	Driveshafts, front axles	General pumps/fans	High-speed turbomachinery	High-torque industrial

Design choices and materials

• Three-piece metallic. Hardened steel hubs and a steel or bronze disc, lubricated. Highest torque density and stiffness; requires grease, limited speed, and the slot fit must be controlled to trade backlash against friction.
• Plastic-disc (sacrificial centre). Two metal hubs with an acetal (POM) or nylon centre disc. The plastic is self-lubricating, quiet, cheap, electrically isolating, and acts as a torque-overload fuse — it shears before the driven machine is damaged, and is trivial to replace. Dominant in motion-control and instrument drives.
• One-piece flexure ("zero-backlash" Oldham). A precision variant machined so the disc is captured with a spring preload, eliminating slot backlash for servo and encoder use where lost motion cannot be tolerated.
• Disc mass. Always minimized: the 2× orbital inertia force scales directly with disc mass, so lightening the centre is the cheapest way to raise the speed limit.
• Slot clearance. Tight clearance gives low backlash but high friction and wear; loose clearance reverses both. The chosen fit is a deliberate compromise tuned to the application's precision and duty.

Concrete examples and specs

• Encoder and stepper drives. A zero-backlash plastic-disc Oldham 20–25 mm in diameter coupling a stepper to a leadscrew accepts ~0.2 mm offset, transmits a few N·m, and isolates motor vibration from the encoder.
• Offset pump drives. When a pump and motor cannot be made coaxial on a fabricated baseplate, a metallic Oldham of 60–100 mm diameter bridges a millimetre or two of offset while passing tens to low hundreds of N·m at a few hundred rpm.
• Packaging and printing machinery. Constant-velocity output is essential for registration; the Oldham's exact 1:1 ratio avoids the speed ripple a single U-joint would inject into the web feed.
• Indexing and instrument mechanisms. Light loads, small offsets, and the need to absorb thermal growth between two precision-located shafts.

Failure modes and trade-offs

• Slot/tongue abrasion (primary). Each tongue slides a full 2e stroke per revolution under the torque load, so the faces wear. Metal designs need lubrication and a speed cap; plastic discs accept the wear as the sacrificial element.
• Backlash growth. As the sliding faces wear, slot clearance opens up and lost motion increases — fatal in servo positioning, which is why zero-backlash flexure variants exist.
• Vibration from 2× orbit. The disc's offset orbit at twice shaft speed produces a synchronous shaking force ∝ m·e·ω². At high speed or large offset this excites the structure and can resonate near 2× the running speed.
• Heat at large offset. Sliding friction power P ≈ μ·(T/r)·(e/2)·ω rises with offset; a large offset run fast can overheat a plastic disc and soften it.
• No angular capacity. An Oldham forced to take an angular bend binds and wears rapidly — the wrong tool for that job; use a U-joint or flexible coupling instead.
• Torque overload shear (by design, plastic disc). A deliberate failure: the centre shears to protect the machine. Good for safety, but means stocking spare discs and accepting downtime on overload.