A differential is a planetary gearset that allows two output shafts to rotate at different speeds while both receiving torque from a single input. In a rear-wheel-drive car, the propeller shaft drives a ring gear; spider gears mounted on the carrier mesh with two side gears connected to the left and right axles. When the car goes straight, all gears rotate as a unit. During a corner, the spider gears rotate on their own axes, letting the outer wheel spin faster than the inner wheel.
The open differential always splits torque equally between both outputs, following the rule that the side with less resistance receives no extra torque. This becomes a problem on low-traction surfaces: a spinning wheel requires almost zero torque, so the differential sends half the available power to it and leaves the gripped wheel equally under-powered. Limited-slip differentials (LSD) add clutch packs or Torsen worm gears to bias torque toward the faster-spinning wheel up to a set ratio.
This simulator animates the ring gear, carrier, spider gears, and axle shafts, letting you vary corner radius and speed to observe how speed and torque are split. It demonstrates epicyclic gearing principles used in automatic transmissions, wind turbines, and robotic joints.
What does a car differential do?
It lets the driven wheels rotate at different speeds during cornering. The outer wheel travels a longer arc, so it must turn faster. Without a differential the tyres would be forced to scrub sideways, stressing the drivetrain and making tight turns impossible.
How does an open differential split torque?
Open differentials always deliver equal torque to both output shafts. Spider gears let the side gears turn at different speeds, but the torque division stays 50/50. On a slippery surface this means power is wasted on the spinning wheel instead of the gripped one.
Why does an open differential fail on ice?
A wheel with no traction requires almost zero torque to spin. The differential routes equally matched torque to both sides, so the gripped wheel only receives as much torque as the spinning wheel needs — which is nearly nothing. Limited-slip differentials add resistance to prevent this runaway spin.
Torsen (Torque-Sensing) differentials use helical worm gears that resist speed difference due to friction. They automatically bias torque toward the slower wheel by a ratio of 2:1 to 5:1, providing limited-slip characteristics without clutch plates or electronics — purely through gear geometry.
Yes — epicyclic (planetary) gearsets derived from differential principles appear in automatic transmissions, electric motor drives, bicycle gear hubs, wind turbine nacelles, robotic wrists, and even early mechanical computers. The principle of combining two speeds into one output (or splitting one into two) is extremely versatile.
A differential gear mechanism allows two output shafts to rotate at different speeds while receiving power from a single input, a critical requirement for vehicles negotiating turns. When a car turns, the outer wheels must travel a longer arc than the inner wheels in the same time — requiring different rotation speeds. A solid axle would force equal speeds, causing wheels to scrub and skid. The differential's epicyclic (planetary) gear train automatically apportions the speed difference between the two output axles while transmitting torque from the driveshaft.
The standard open differential consists of a ring gear (driven by the driveshaft via the pinion), a differential case (the spider housing), and spider gears (bevel gears inside the case) that mesh with two side gears connected to the output axles. The fundamental constraint is: omega_left + omega_right = 2 times omega_ring (the sum of the two output speeds equals twice the ring gear speed). On a straight road, both wheels rotate at the same speed. In a turn, the spider gears rotate on their own axes, allowing the inner wheel to slow and the outer wheel to speed up by equal and opposite amounts — automatically, without electronic control.
This simulator lets you rotate the ring gear and interactively apply drag to either output shaft, observing how the spider gears redistribute speed and how torque is split. You can explore the limitation of the open differential: it sends torque to the wheel with least resistance — a wheel spinning on ice gets all the torque while the gripped wheel gets none, leaving the vehicle stuck. Limited-slip differentials (LSD) and torque-vectoring differentials address this limitation, illustrated by varying the friction model.
Why do vehicles need a differential?
When a vehicle turns, the outer wheels must travel a longer path than the inner wheels in the same time period. If both wheels on an axle were locked together, they would scrub across the road surface during turns — generating heat, wear, and understeer forces. A differential allows each wheel to rotate at the speed appropriate for its turning radius, transmitting engine torque to both wheels while permitting the speed difference needed for smooth cornering. Without a differential, the drivetrain would bind in turns, making steering difficult and causing tire wear.
How does the differential divide torque between the two wheels?
An open differential always delivers equal torque to both output shafts, regardless of their speed difference. This is a fundamental property of the epicyclic gear train: the spider gears act as a balance beam that equalizes torque. The speed can differ (allowing turns), but the torque must be equal. This creates the open differential's key weakness: on slippery surfaces, torque flows to the wheel with lower traction (spinning freely), leaving the gripped wheel with no driving force.
What is a limited-slip differential (LSD) and how does it work?
A limited-slip differential (LSD) adds friction or locking mechanisms to prevent excessive speed difference between the two wheels. Clutch-type LSDs use clutch packs that engage when speed difference exceeds a threshold, partially locking the axles together and transferring some torque to the slower (higher-traction) wheel. Viscous coupling LSDs use a fluid that thickens under shear between rotating plates. Torsen differentials use worm gears with self-locking properties to automatically bias torque toward the wheel with more traction — purely mechanical torque biasing.
The fundamental differential kinematic equation is: omega_left + omega_right = 2 times omega_ring, where omega_ring is the ring gear (input) speed. On a straight road both outputs rotate at the ring gear speed. In a turn where the outer wheel rotates at omega_ring + delta-omega, the inner wheel rotates at omega_ring minus delta-omega — the ring gear speed stays constant while the spider gears rotate on their own axes to accommodate the difference. This can be derived from the general epicyclic gear train formula.
Traditional differentials are purely mechanical and reactive — they respond to speed differences but cannot actively direct torque to a specific wheel. Modern torque-vectoring systems use electronically controlled clutches or electric motors at each wheel to actively over- or under-speed individual wheels on demand, allowing preemptive torque distribution for optimal cornering balance. Electric vehicles with individual wheel motors are the ultimate torque-vectoring platform — each wheel is independently controlled with millisecond response time.