Douglas Harper's Etymology Dictionary
1958, from transmission axle.
Wiktionary
n. (context automobiles English) A single unit combining transmission gearbox, clutch, final drive, and differential are combined into a single unit connected directly to the driveshaft, used mostly in rear-engine cars.
Wikipedia
In the automotive field, a transaxle is a major mechanical component that combines the functionality of the transmission, the differential, and associated components of the driven axle into one integrated assembly.
Transaxles are near universal in all automobile configurations that have the engine placed at the same end of the car as the driven wheels: the front-engine, front-wheel drive layout; rear-engine, rear-wheel drive layout; and rear mid-engine, rear-wheel drive layout arrangements.
Many mid- and rear-engined vehicles use a transverse engine and transaxle, similar to a front wheel drive unit. Others use a longitudinal engine and transaxle like Ferrari's 1989 Mondial t which used a "t" arrangement with a longitudinal engine connected to a transverse transaxle, a design the company continues to this day. Front-wheel drive versions of modern Audis, from the A4 upwards, along with their related marques from the Volkswagen Group (which share the same automobile layout) also use a similar layout, but with the transaxle also mounted longitudinally.
Usage examples of "transaxle".
The thing was huge, maybe five hundred feet long, with eight one-hundred-foot-high globular wheels affixed to massive transaxles, banks of superspot running lights, hidden particle-projection cannon turrets, and multiple-missile launch racks.