AFAIK, the only three-cylinder compound built for use in the USA was the 4-10-2 Baldwin demonstrator #60000, which now resides in the Franklin Institute in Philadelphia.
The center cylinder was/is high-pressure, the two outer cylinders low-pressure. The two outer cranks were 90 degrees apart with left-hand lead; the center crank was 135 degrees from both of the outer cranks. Since Alco had the license for the English Gresley valve gear for operating the valve of the center cylinder of a locomotive whose cranks were 120 degrees apart, Baldwin had to resort to a different method.
Again, AFAIK the engine performed well enough, but had a water-tube firebox and steamed at 350 pounds; it had so many novel features that nobody was interested in buying it.
The center cylinder has an inside-admission piston valve getting its motion from an oddly-set eccentric crank on the right side; its combination lever is inside. The left valve is an outside-admission piston valve with the normal arrangement of Walschaerts valve gear. The Walschaerts link for the right valve, also outside admission, gets its motion from the left crosshead, which has a lever that drives a shaft across the frame.
Don't know whether Baldwin really expected to sell any of these, but nobody was interested in either the water-tube firebox (the firebox alone has 200 washout plugs to be removed and replaced every monthly boiler wash; an N&W Y-6 2-8-8-2 had 39 in firebox and boiler combined) or the drive train.
Alco did use the wheel arrangement for 3-cylinder simple engines for the UP and SP, though. The cranks of these engines were 120 degrees apart, and they used the Gresley arrangement.
EdKing
