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Posi is a name for GM's limited slip differential. A limited slip differential is just that, it allows a limited slip between the left and right tires for turning corners, etc. to allow different wheel speeds. A locker is also fairly self explanatory. It physically locks the left and right tires together. Some do have an unlocking action for turning corners, but many do not. These make taking turns difficult because they do NOT allow one wheel to turn slightly faster than the other, so you usually end up chirping a tire around a corner, or hear a ratcheting sound. Bottom line, what's best for you, depends on what you prefer. Something like an Auburn Gear ECTED is a good compromise. It's what is known as an eLocker. It is a limited slip differential that, at the push of a button, can be electrically turned into a full locker. So you would have the limited slip function on the street and for mild off-road conditions, and when it gets really tough, you can lock the differential, because under extreme conditions, even a limited slip will spin 1 wheel at some point. There is also the OX locker, which is the same thing, but uses a custom rear cover and a cable, and the venerable ARB air locker, which uses air lines and an air compressor to engage the locker. All have advantages and disadvantages. A cable will be the hardest to damage, the air line the easiest. A broken cable, however, will be impossible to fix on the trail, while a severed wire is the simplest fix, only requiring some wire and electrical tape. Also, the Auburn and OX both default to limited slip axles, while the ARB, when it's not engaged, is an open differential. This is why I wouldn't use an ARB, in addition to the extra $500+ in parts just to use the thing, needing an air tank, compressor, etc.
LIMITED SLIP - LSD
"The main advantage of a limited slip differential is shown by considering the case of a standard (or "open") differential where one wheel has no contact with the ground at all. In such a case, the contacting wheel will remain stationary, and the non-contacting wheel will rotate freely—the torque transmitted will be equal at both wheels, but will not exceed the threshold of torque needed to move the vehicle, and thus the vehicle will remain stationary. In everyday use on typical roads, such a situation is very unlikely, and so a normal differential suffices. For more demanding use, such as driving in mud, off-road, or for high performance vehicles, such a state of affairs is undesirable, and the LSD can be employed to deal with it. By limiting the angular velocity difference between a pair of driven wheels, useful torque can be transmitted as long as there is some traction available on at least one of the wheels."
LOCKER - Automatic lockers
Automatic lockers lock and unlock automatically with no direct input from the driver. Some automatic locking differential designs ensure that engine power is always transmitted to both wheels, regardless of traction conditions, and will "unlock" only when one wheel is required to spin faster than the other during cornering. They will never allow either wheel to spin slower than the differential carrier or axle as a whole, but will permit a wheel to be over-driven faster than the carrier speed. The most common example of this type would be the famous "Detroit Locker," also known as the "Detroit No-Spin," which replaces the entire differential carrier assembly. Others, sometimes referred to as "lunchbox lockers," employ the stock differential carrier and replace only the internal spider gears and shafts with interlocking plates. Both types of automatic lockers will allow for a degree of differential wheel speed while turning corners in conditions of equal traction, but will otherwise lock both axle shafts together when traction conditions demand it.
Pros: Automatic action, no driver interaction necessary, no stopping for (dis-) engagement necessary
Cons: Increased tire wear and noticeable impact on driving behavior. During cornering, the automatic locker is characterized by heavy understeer which transitions instantly to power over steer when traction is exceeded.
Some other automatic lockers operate as an open differential until wheel spin is encountered and then they lockup. This style generally uses an internal governor to sense a difference in wheel speeds. An example of this would be GM's "Gov-Lok."
Some other automatic lockers operate as an open differential until high torque is applied and then they lockup. This style generally uses internal gears systems with very high friction. An example of this would be ZF "sliding pins and cams" available for use in early VWs.
LOCKER - Manual Selection
Selectable lockers allow the driver to lock and unlock the differential at will from the driver's seat. This can be accomplished many ways.
Compressed air (pneumatics).
Cable operated mechanism as is employed on the "Ox Locker."
Electronic solenoids and (electromagnetics) like Eaton's "ELocker." However, OEMs are beginning to offer electronic lockers as well. Nissan Corporations electric locker found as optional equipment on the Frontier (Navarra) & Xterra. 2011 Ford Super Duty F-250 and SRW F-350 4x4 models have a electronic locker as 390.00 USD option.
Pros: Allows the differential to perform as an "open" differential for improved drivability, maneuverability, provides full locking capability when it is desirable or needed
Cons: Mechanically complex with more parts to fail. Some lockers require vehicle to stop for engagement. Needs human interaction and forward-thinking regarding upcoming terrain. Unskilled drivers often put massive stress on driveline components when leaving the differential in locked operation on terrain not requiring a locker.