Anti-sway or Anti-roll bars if anyone prefers the latter term do two things.
First they reduce body roll which means the C of G stays more laterally centred and also lower therefore reducing the chances of rolling the vehicle at higher speeds
Second they control the amount of stiffness in the suspension transmitted between front and rear and therefore directly affect understeer/oversteer.
Thats why they have the driver adjustable bars in the V8 Supercars etc.
Disconnecting an Anti-sway bar is desirable offroad (and only offroad) because one of the side effects of the bars is the 'coupling' of uneven surfaces from one wheel to both on an axle pair so the ride is much softer with the links disconnected.
Properly tuned bars will not limit overall suspension travel and removing the bar/s is a kinda slack way of not forking out the bucks to properly retune the suspension after lifts etc.
Removing the bars for more flex is pretty much aesthetics only as far as traction is concerned most of the time.
Lifting a wheel is easier with the bars connected and less chance of rolling the vehicle
Lifting a wheel by generating body roll is harder with the bars disconnected and in that config you are more and more likely to roll the whole shebang




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