Unitrack was a term first coined by Kawasaki way back in the late 1970's. I think they were the first to activate the rear spring/damper by using levers instead of direct action from either attaching the units at some point along the swing arm OR (Yamaha & Vincent) by mounting the damper(s) on top of the engine - but still pushed directly by the swinging arm.
Basically, the main trick that Kawasaki were employing was to get rising rate and long travel suspension for the MX bikes. Soon Suzuki followed (with the FullFloater system), then just about everyone else. Mounting the damper inboard had packaging advantages, it also allowed you to configure the linkages to get almost any rising rate (or falling I suppose
) curve that your heart desires. A rising rate curve is hard to achieve (not impossible) when mounting the damper on the swing arm (some early long travel systems created a falling rate).
The first Kawasaki links were arranged with push rods and a bell crank that was pushed up by the swing arm, which in turn pushed down on the damper. Soon people realised that you could arrange the cranks lower down and have the damper pushed upwards - this was simpler to achieve and stronger. You certainly saw plenty of early Kawasaki MXers with bent push rods
.
Mounting the damper like this puts terrific bending loads into the swing arm, which is why they soon ditched the old tubular steel arms in favour of ally box section - soon followed by the contoured/tapered arms you see today (Have a look at the pivot mounts and you will usually see massive castings there).
Rising rate suspensions are not popular in cars because they can confuse chassis setup, but in motorbikes (especially MX bikes) rising rate really helps let the wheel follow small bumps with a soft spring and yet absorb the big hits (like jumps) as if the the spring was much stronger.
I wouldn't be surprised if many of the MotoGP & Superbikes don't have much rising rate at all, but they still retain the system because it packages the masses much closer to the CofG of the bike (& makes it easier to feed loads into the structure). Mass centralisation is something that bike engineers spend a lot of time working on.
So, it started with a need for long travel and rising rate suspension (dirt bikes) and finishes because it's a great way to package the spring/damper unit.
