Diffs are funny things, multiple diffs are just plain weird.
In the below:
"traction" - Wheel is not slipping/spinning. "drive" - Abilty to move.
I'm about 85% certain this is what happens with various drive and diff lock arrangements:
2WD un locked diff, one wheel loses traction, the other stays still, no drive.
2WD locked diff, both wheels are locked together and rotate at the same speed. If one loses traction, hopefully the other will still have traction and you'll have drive.
4WD un locked diffs. One wheel loses traction, you lose traction for that axle. The other axle still has drive.
4WD locked center diff. Both axles are locked and rotate at the same speed, note axle not wheel. A single wheel can lose traction and the other three wheels retain drive. Both wheels on the same axle can lose traction the other axle retains drive. If diagonal wheels loose traction, you loose drive at the other two wheels.
4WD center and axle diffs locked. Everything (axles and wheels) goes round at the same speed, wether any given wheel has traction or not. This can give you one wheel drive...
With a diff locked there is a risk of "transmission wind up" that can lead to broken half shafts or stripped diff gears. You should not lock diffs unless the surface is slippy enough to allow the wheels to rotate at different speeds, as they must do, as you go around corners.
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