Differentials: The Gearbox That Lets Two Wheels Disagree

September 28, 2026 · by Mechanism Lab

Here is the problem every car faced from day one: drive around a corner and the outside wheel must cover a longer arc than the inside wheel. Connect them with a rigid axle and something must slip — tyres scrub, driveline winds up, steering fights back. The differential is the bevel-gear arrangement that resolves the conflict: one input, two outputs, each free to spin at its own speed.

The gear family inside the drum

An open differential mid-corner. The cage turns at one fixed rate, but the outer wheel must travel farther than the inner one — so the spider gears spin on their own axes, letting one axle slow while the other speeds up. Their average remains exactly the cage speed.

An open differential has three kinds of gears:

Ring gear and cage — the final drive. The engine (through the driveshaft’s pinion) turns the ring gear, which is bolted to a cage — the drum that carries everything else. The cage speed is the average of the two wheel speeds.
Side gears — splined to the left and right axles, one at each end of the drum.
Spider (planet) gears — small bevels on a cross-shaft inside the cage, meshing with both side gears simultaneously.

When the car drives straight, the whole assembly turns as one block: spiders don’t spin on their own axes, both axles turn at cage speed. In a corner, the spiders begin to walk, letting one side gear lag while the other leads — the animation shows exactly this dance.

The elegant arithmetic

The differential enforces one inviolable identity, no matter what:

speed_left + speed_right = 2 × speed_cage

Check the animation: the left axle rotates at 2/3 of cage speed, the right at 4/3, and the average is exactly cage speed. Torque, however, is always delivered equally to both wheels (minus small friction) — which leads directly to the open differential’s famous flaw.

The flaw: one wheel in the air

Because torque splits equally, grip does not matter to the split. Put one wheel on ice and it needs almost no torque to spin — so it takes all the engine’s offered torque at zero resistance, and the other wheel, though on dry tarmac, receives the same near-zero torque. The car does not move. This is why:

Limited-slip differentials (LSDs) add clutches or gears that resist the speed difference, forcing torque across.
Locking differentials mechanically join the two axles solid for off-road and heavy towing.
Torque-vectoring systems use extra clutches to deliberately overdrive one wheel, actively steering the car with torque.

One differential per axle

A four-wheel-drive vehicle carries two differentials (front and rear axle), plus a centre device splitting engine torque between the axles — often another differential. The same bevel-gear logic scales from a toy car to a mining dump truck.

Where else differentials appear

Analogue computers — WWII bombsights and fire-control systems used differential gears to sum and average rotating quantities. Mechanical addition, in bevel gears.
Mechanical odometers — a differential averages wheel revolutions with time to compute distance in older designs.
Wind turbines and mixers — splitting one input into two synchronised, load-sharing outputs.

Key takeaways

Spider bevel gears let two outputs share one input while spinning at different speeds.
Speeds average, torque splits equally: (left + right) / 2 = cage.
Equal torque split is the open diff’s weakness; LSDs and lockers exist to fight it.
The same gear set is a mechanical analog computer — summing rotations since the 1800s.