The Differential Gear: How One Box Lets Wheels Spin at Different Speeds

Why a rigid axle cannot turn a corner

Take a car through a bend and the two driven wheels no longer travel the same distance. The outer wheel follows a bigger circle than the inner wheel, and over a tight turn the difference is not small - on a typical family car it can be several percent of the wheel's rotation. Bolt both wheels to one solid shaft and something has to give: either a wheel scrubs sideways against the tarmac every time the car turns, chewing through tyres and fighting the steering, or the axle itself twists and binds. Every practical road vehicle instead puts a small gearbox, the differential, between the final drive and the two half-shafts, so each wheel can spin at its own speed while both still receive torque from the engine.

Bevel gears and the spider

Inside a live axle, the propeller shaft turns a small pinion gear, which meshes with a large ring gear (also called the crown wheel) bolted to a rotating cage, the carrier. Mounted inside the carrier on a cross-shaped pin are two or four small spider gears (planet pinions), and they mesh with two side gears, one bolted to each half-shaft. Driving straight ahead, both wheels want to turn at the same speed as the carrier, so the spider gears sit still relative to the cage and just orbit with it, passing torque straight through. In a turn, the two side gears want different speeds, so the spider gears start spinning on their own pin as well as orbiting - rolling a little faster onto the slower side gear and a little slower onto the faster one, exactly the way a see-saw's pivot lets both ends move by different amounts around a fixed centre.

omega_left + omega_right = 2 * omega_carrier      // speed relation, always true
torque_left  = torque_right = torque_ring / 2     // open diff: equal split, always true

Those two equations are the whole story of an open differential. The speed equation is pure kinematics - it falls out of the gear geometry and holds whatever is happening at the wheels. The torque equation falls out of the spider gears themselves: each one presses on both side gears with the same tooth force by construction, so however the speeds split, the torque always splits fifty-fifty.

The open differential's fatal flaw

That fixed fifty-fifty torque split is exactly what strands a car with one wheel on ice. A spinning wheel on a frictionless surface needs almost no torque at all to keep accelerating - it offers next to no resistance. Because the differential forces the other wheel, the one with grip, to receive the same torque as the slipping one, and that torque is capped at whatever the low-grip wheel can react, the gripping wheel is starved of torque too. The engine can be producing full power and the car still will not move, because the weak link sets the ceiling for both sides.

Fixing it: limited-slip, viscous and torque vectoring

A limited-slip differential (LSD) adds a friction path across the two half-shafts, most commonly a pack of clutch plates squeezed by a preload spring and by ramps that push harder as torque rises. That friction path can sustain a torque difference between the wheels, so it lets the gripping wheel take more than half the torque instead of being capped by the slipping one; the ratio between the two is the diff's bias ratio, typically 2:1 to 4:1 on a road car. A viscous coupling does the same job with shear-thickening silicone fluid between two sets of perforated plates instead of a clutch pack, resisting large speed differences without needing a mechanical preload. A Torsen (torque-sensing) diff uses worm gears whose mesh geometry is deliberately non-back-drivable, so it biases torque purely through gear friction with no clutches at all. The most capable modern systems skip the mechanical compromise entirely: dual-motor electric cars drive each axle, or each wheel, with its own motor and let software send exactly the torque each one calls for, actively vectoring more drive to the outside wheel in a bend to help the car rotate into the corner rather than merely stopping it from spinning a wheel.

Try it yourself

Open the simulation and put one wheel on a low-friction patch. Watch the torque gauges on each side collapse together even as the wheel speeds fly apart - that single picture is the entire reason winter driving on an open diff is such a struggle.

Frequently asked questions

Try it live

Everything above runs in your browser - open Differential Gear and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.