Back when Australia's main tin-top category used cars with live rear axles, the rear roll centre used to be a thing.
Actually, it still is a thing even in vehicles with an independent rear suspension (IRS), it's just that it can't be adjusted without relocating the suspension pick-up points on the chassis during vehicle design and assembly.
The rear roll centre is a point in space, about which the rear of the vehicle pivots when it rolls side to side (like a clock's hands pivoting around the centre of a clock). With an IRS, that point is calculated from the angles of the rear wishbones or control arms.
In configurations with a Watt's linkage, that point in space is actually physical, because it is the centre of the bellcrank in the middle of the Watt's linkage system.
Invented by James Watt in 1784, the Watt's linkage was used in all Falcon sedans from the XE in 1982 to the EL in 1998 (and lower-spec AUs). When used for lateral control of a rear axle its job is to stop the body and the axle moving from side to side (however, also note that rubber bushes still allow some deflection when cornering). It has two arms that sit sideways, and a bellcrank in the middle.
In road cars the height of that bellcrank (and therefore the roll centre height) is not adjustable, but in live axle race cars it often is. And in the aforementioned tin-tops, it was adjustable in-car by the driver.
The reason for wanting this adjustment is to affect the behaviour of the car in corners. Generally speaking, raising this height helps turn-in but too high can induce lift-off oversteer, while lowering it can increase rear-end stability at corner entry.
The configuration of a Watt's link also affects vehicle behaviour. On production cars, it's usually fixed to the diff, whereas in race cars, it's usually fixed to the body. As you might have deduced, that means road car versions keep the roll centre pretty much fixed in relation to the road, whereas in race cars it will move up and down as the car squats under power, dives under brakes, and generally deals with humps and bumps.
This sounds like the road car version is more desirable, but it isn't. The actual tendency for the rear to roll is calculated from the vertical distance between the rear roll centre and the rear's centre of gravity.
This distance is called the roll couple, and it's like an invisible lever making the car roll. The longer a lever, the easier it is to make an object move in a given direction (body roll in this case) and in road car Watt's links this measurement (and therefore the leverage) changes constantly with the squatting, diving, humps and bumps.
However, when the roll centre position is fixed to the body, this roll couple measurement only changes when the roll centre height is adjusted (or the centre of gravity is moved, with ballast or a different fuel load). That makes the car's behaviour more consistent as you accelerate and brake.
The Watt's link isn't the only system of lateral control that live axles can use though. Plenty of vehicles, like older Commodores, used the much simpler panhard rod instead.
The panhard is a single rod that connects to the diff at one end, and the body of the vehicle at the other. It does the same basic job of lateral control as the Watt's linkage, but its roll centre is not physical, it's a calculated point in space.
The roll centre will be where the vertical centreline of the axle intersects the panhard bar, so it too is affected by the vertical movement of the body, changing the roll couple length as it does so (but not as much as a road car Watt's link).
Lowering its mounting point (on the body, the diff, or both) also lowers the roll centre height, having the same effect as lowering the bellcrank of a Watt's linkage. A panhard rod will also make the diff move just a little bit sideways as it goes through its range of motion, but with correct geometry this deflection is so small it doesn't matter.
Sam Hollier is an ACM journalist and a motoring fanatic who builds cars in his shed in his spare time.