Was there a steam locomotive valve gear linked to pistons both in front of and behind the driving wheels, connected to the same set of linking rods?
score:3
The closest thing I've been able to find to your suggested layout is the Baltimore and Ohio class N-1: a 4-4-4-4 locomotive (front and rear pistons, like you describe, but powering independent sets of wheels).
The reason your design is unlikely to ever see use is a matter of balance. Two-piston locomotives cannot be fully balanced: there will always be residual vibration from the motion of the pistons, valve gear, and main rods. This vibration limits the speed of the locomotive. Four-piston locomotives can eliminate the linear vibrations that a two-piston locomotive experiences, but only if the additional two pistons are moving opposite their counterparts. Thus, anyone going to the extra effort of putting four pistons on a locomotive is going to take the opportunity to reduce vibration.
The "pistons-at-the-rear" design you propose has an additional problem: the back of a steam locomotive is crowded. You've already got the firebox and the cab, and now you somehow need to fit two large pistons and their steam pipes as well.
The "push-pull" argument doesn't work, either. Virtually every steam locomotive ever made has used double-acting pistons, which give the benefit of continuous power without the complexity of additional pistons.
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