Now we can get going on the cylinders and steam chests. If the boiler is the heart and steam dome the lungs, we could say the fire box is the belly, and the plumbing is the arteries and veins. To keep up the analogy, the cylinders and the steam chests are the muscle. Included in this discussion we will include the boiler/cylinder saddle. First a couple of pictures of the pieces.
Picture for the
San Diego Railroad Museum
The saddle does a few things. One of its most important jobs is a support for the boiler. It is a heavy cast iron affair that is bolted to the locomotive frame and supports the weight of the boiler at the front. It also acts as a hanger for the cylinders and steam chests. But it is not a solid bit of iron. It is rather a set of “pipes”. In the line drawing you can see that one set of pipes connects to the steam chest and the other set of pipes connects to the cylinders. The piping for the inlet of the saddle comes from the steam dome and runs through the boiler. When the throttle is applied the steam leaves the dome, runs through the pipe and into the saddle to the steam chests.
The steam chests is a fancy valving mechanism. When the locomotive is shifted between forward, neutral, and reverse in the cab it is translated to the steam chest via some linkages attached to the Johnson bar.

Picture from Highball Sim
In this picture we see the linkage from the Johnson bar entering into the side of the steam chest. It moves forward and backward. When the johnson bar is in the forward position, steam from the saddle enters the steam chest and is applied to one side of the cylinder piston. Switch it in neutral and the steam from the saddle enters the chest and is directed immediately out the exhaust. Switch it in reverse and it applies steam to the opposite side of cylinder piston reversing the locomotive. As the locomotive moves this rod moves in and out in time with the drivers on a elliptical linkage on the axle. So it is alternating applying steam to one side then the other of the cylinder piston. So the piston is powered in both directions, one way then the other. During what we will call the opposite stroke, where the steam is applying force to one side of the piston the other side is opened up to the saddle to exhaust the steam from the previous cycle. This is the chuffing we get as the steam is exhausted on side then the other then back again, chuff chuff chuff.
Oh, I better add this now or we will be confused. So I said that rod moves back and forth. and I said it is attached to an elliptical linkage on the axle. Well that elliptical linkage is what is actually attached to the Johnson bar. So what happens to reverse the direction the drivers is the Johnson bar changes the relationship of that elliptical linkage and the bar sliding in and out. I realize this is about as clear as mud, Heck I am confusing myself just talking about it. It was also very hard to wrap my brain around until I watched video animations of it. So I am going to leave it here and just say that its magic and it works.
Once the steam leaves the cylinders it travels back through the saddle and into the smoke box where it is ejected out the stack. Remember here that not only is this just a good way of getting rid of it, but it is also acting like a super charger to draw more draft through the fire tubes.