What is the function of the differential in a vehicle's drivetrain?

Differential: a gear arrangement in the drive axle that allows the two drive wheels to rotate at DIFFERENT SPEEDS while still receiving power from the driveshaft/transaxle. Why needed: when a vehicle turns, the OUTSIDE wheel must travel a longer distance than the INSIDE wheel (larger radius), so it must rotate FASTER. Without a differential, both wheels would be forced to spin at the same speed, causing tire skidding/wear, steering difficulty, and stress on drivetrain components. Operation: input from driveshaft → ring gear (large bevel gear) → pinion gear (smaller, drives ring gear); the differential carrier inside the ring gear houses smaller bevel gears (side gears and spider/pinion gears) that allow the two output shafts (to the wheels) to turn at different rates while the total drives the carrier. OPEN DIFFERENTIAL (standard): simplest, lightest, cheapest; sends EQUAL TORQUE to both wheels (but torque follows path of least resistance — so if one wheel has no traction, that wheel spins, the other gets little/no torque); great for cornering on dry roads; terrible for low-traction situations (mud, snow, ice — one wheel slips, vehicle stuck). LIMITED-SLIP DIFFERENTIAL (LSD): uses clutches, gears, or fluid coupling to provide some torque transfer to the wheel with traction when the other slips; reduces wheel-spin loss; types include: CLUTCH-PACK LSDs, HELICAL/TORSEN (gear-based, smooth), VISCOUS-COUPLING (fluid-based, less aggressive). LOCKING DIFFERENTIAL (locker): mechanically links both wheels to spin together; either FULLY LOCKED (no differential action; great traction on/off-road but causes wheel-skidding on turns; off-road vehicles), or SELECTABLE (driver engages when needed). ELECTRONIC LIMITED-SLIP / BRAKE-BASED traction control: uses ABS sensors to detect wheel slip; applies brakes to spinning wheel, transferring torque to the other side via the open differential's torque-equality principle (one wheel braked = more torque to other). Modern AWD/4WD: combinations of front, rear, and CENTER differentials. CENTER DIFFERENTIAL allows front and rear drive shafts to rotate at different speeds (needed for turning since front and rear wheels travel different paths). VISCOUS CENTER DIFFERENTIALS or computer-controlled clutches manage front-rear torque distribution. TORQUE VECTORING: high-performance systems actively control torque to individual wheels for cornering performance. Differential gear ratio: drive shaft RPM / wheel RPM; e.g., 3.73:1 means driveshaft spins 3.73 times for each wheel rotation; affects acceleration vs top speed (lower numerical ratio = higher gearing, better fuel economy at speed; higher numerical = quicker acceleration). Differential fluid: special gear oil (often 75W-90 or 80W-90); usually contains friction modifiers for LSDs; change interval varies (often 30,000-100,000 miles; severe duty more frequent). FWD vehicles have differential integrated into transaxle. RWD vehicles have separate rear differential. AWD/4WD: front differential, rear differential, and transfer case (which routes power between them). RWD and 4WD have a driveshaft running under the vehicle.