Limited Slip Differential
A limited-slip differential (LSD) is a type of automotive differential gear arrangement that allows for some difference in angular velocity of the output shafts, but imposes a mechanical limit on the disparity. It transmits equal torque to both wheels which driving a straight line. But, when one wheel spins (slippery surface like ice) the gear provides more power to the wheel that has traction. Most Jeeps were equipped with Dana Trac Loc limited slip differentials.
In an automobile, such limited-slip differentials are sometimes used in place of a standard differential, where they convey certain dynamic advantages. Automotive limited-slip differentials have a few standard elements. They all have a gear train that, like an open differential, allows the output shafts to spin at different speeds while holding the sum of their speeds proportional to that of the input shaft. They also all have a mechanism that applies a torque (internal to the differential) that resists the relative motion of the output shafts. This means they have a mechanism which resists a speed difference between the outputs, by creating a resisting torque between either the two outputs, or the outputs and the differential housing.
Your Jeep may be equipped with Trac-Lok (clutch-type mechanical), Tru-Lok (gear-type mechanical), and Vari-Lok (gerotor pump), Power Lok
For Jeep Cherokee XJ 1991-1995 see Mopar 52068451 Trac-Lok 27 Spline Differential case Assembly with Gears
For Jeep Cherokee XJ 1996-2001 and Jeep Liberty KJ 2002-2005 with 8.25" rear axle see Mopar 52098778AD