Jim - On all the "direct drive" Cats from the 1940's, 1950's and 1960's .. the power goes from the clutch, via a short jackshaft with double universal joints, to the sliding gear or countershaft-type transmission.
From the transmission, power then travels via the transmission output shaft, to a straight pinion and bevel gear.
There is no differential in most crawlers .. apart from a few oddball machines, such as some Cletrac/Oliver, some European machines, and some Massey Ferguson crawler models.
The bevel gear is bolted to a solid cross-shaft, which transfers power crosswise, to the steering clutches, and thence to the final drives.
The steering clutches are operated via levers and crank mechanism, most times power-assisted in some way.
Around the steering clutch drums are mounted foot operated brakes.
Disengaging a steering clutch, disables power to that track .. and applying the brake stops the track for a sharper turn.
Early machines of the 1930's, 1940's, and early 1950's used dry steering clutches and main clutches. These are prone to heat build-up and rapid wear under heavy working conditions.
Around the early to mid 1950's, oil main clutches were introduced, and in the early 1960's, oil-immersed steering clutches were introduced.
Both of these features, are very worthy improvements to any tractor you buy, if you wish to do some serious work. The dry clutches are adequate for hobby work.
The power goes from the steering clutches, to a gear reduction called the final drive, which drives the big sprocket that propels the tractor along the track.
Most larger machines have double-reduction final drives (a pinion drives an intermediate gear, which then drives a bull gear, which is bolted to a hub that the sprocket is splined onto).
Most smaller machines, or cheaper models, have only a single reduction final drive (a pinion driving directly onto a bull gear).
Caterpillars have a 'dead axle' .. a large diameter shaft, tapered both ends, that is pressed into the final drive/steering clutch case, and which supports the track frame.
The sprocket and bull gear are attached to a tubular 'sprocket shaft', which fits neatly over, and which rotates around, the dead axle.
Vintage International crawlers of the 1930's used a different drivetrain setup, with steering clutches turned 90° so they were parallel to the transmission. These were accessible from the rear housing.
Later Internatiional crawlers used planetary gearsets in the final drives, and the track frame was supported by, and pivoted on, a large shaft that ran across the full width of the tractor, in front of the final drives.
The Caterpillar D2 also used this track frame pivot shaft arrangement .. the only Cat to do so.
Here's a couple of exploded views of a D6 drive train, that may assist you. The details listed are more selling points, than a drivetrain precise parts description .. but I'm sure you'll get the idea.
img339.imageshack.us/img339/7064/d6drivetrain1gk4.jpg
img182.imageshack.us/img182/7066/d6drivetrain2do8.jpg