What does a differential actually do?
It lets the driven wheels turn at different speeds while both still receive power — which is necessary because when a car turns, the outer wheel travels further than the inner one.
The problem it solves. Going round a corner, the outside wheel follows a larger radius than the inside wheel. If both were locked to the same shaft they would have to rotate at the same speed, so one must scrub — dragging sideways, wearing tyres, stressing the drivetrain, and making the car reluctant to turn. On a go-kart with a solid axle this is exactly what happens.
How it works. An open differential uses a set of bevel gears in a carrier driven by the propshaft or final drive. The arrangement always splits torque equally between the two output shafts while allowing their speeds to differ, with the average of the two matching the input.
The weakness that follows, and it is a big one. Because torque is split equally, the differential can only deliver as much torque to the gripping wheel as the slipping wheel can take. One wheel on ice means both wheels receive almost nothing, and the car goes nowhere while one wheel spins uselessly. This is the classic open-diff failure, and it is a consequence of the design rather than a fault.
The solutions:
Limited-slip differential (LSD). Uses clutches, gears or viscous coupling to resist a large speed difference, transferring torque toward the wheel with grip. Standard on performance cars.
Locking differential. Mechanically locks both outputs together, giving maximum traction off-road and making the car handle badly on tarmac — so it is switchable.
Torsen and helical designs, which bias torque mechanically without clutches.
Electronic brake-based traction control, which brakes the spinning wheel so the differential can send torque to the other side. This is how most ordinary cars now get most of the benefit of an LSD without one — it is sometimes called an electronic differential lock.
Torque vectoring, actively distributing torque side to side to help the car turn.
Four-wheel-drive vehicles need a centre differential as well, to allow front and rear axles to rotate at different speeds.