Let's look at a really simple suspension. In the next picture, you can see that the tractor has a simple solid axle for the front wheels. There are no springs, the axle is just rotating about the pin at the center (There is no suspension at all for the rear axle).
The pin is the roll center of the front axle. In this particular (really simple) suspension, no matter how the «sprung» mass (the tractor frame) is positioned with respect to the «unsprung» mass (the front axle), the roll center position is always clearly known.
Now, this tractor is not built for cornering, but let's imagine that the rear axle is built the same way and that there are left & right springs between each axle and the tractor frame. The roll axis would be the imaginary line linking both rear and front pins.
If that tractor would be under lateral acceleration, the centrifugal force (
ma) would act at the center of gravity of the sprung mass. The distance between the center of gravity and the roll axis would create the moment arm for the centrifugal force. That moment (or couple) would begin a rotation of the sprung mass around the roll axis. This rotation (or this moment) will be opposed by the moment created by the spring force and how far it is from the roll center. These moments will be balanced when the rotation stops to a certain angle. The larger the lateral acceleration, the larger the final angle.
Now imagine that the pins are moved high enough that the roll axis goes through the center of gravity. In such a case, there will be no moment created since the moment arm length is zero. Hence there will be no rotation initiated and the tractor would stay perfectly parallel to the ground under any amount of lateral acceleration.
For more complex suspensions (with more links), the position of the roll center depends on the position of each link. Since those links are constantly moving, the roll center is also constantly moving. And that's where the fun begins in suspension design ...
