Interesting topic but extremely technical. I think also that most of it's knowledge is lost to the steam locomotive designers long gone. Anyway, here's a taste, and it's only my brief conclusion and a tip of the iceberg based upon what I know are concrete foundations.
Without any kind of synchronization between seperate driving forces on a single locomotive, the problem of inertia being acted upon by unbalanced forces becomes a liability. According to Newton's First Law of Motion, every body continues in it's state of uniform motion in a straight line unless acted upon by external forces so applied to the body that the direction of motion is changed. That is why railway engineers super-elevate fast curves, provide restraining rail at sharp curves, removed the comfortable resilient wheels on Boston PCC trolleys for solid steel uncomfortable ones, etc. Now this would seem to be fine with a loco heading in only one direction at a time, but there is a problem. The problem is that there are actually numerous directions of uniform motion in a steam locomotive, which even in a simple loco must be compensated. ( A simple example of compensation is the weighted quarter wheel disc often found on the opposite side of the loco's wheel from where the driving rod is attached.) All these different motions (energy) have to go somewhere. If these different motions are not calculated and compensated, dangerous competing and conflicting motion occurs, all desiring to go on their own seperate straight lines and all being compromised by the other motions going in different straight lines. As I mentioned before, dangerous rhythm and vibrations can result. A phenomenon known as "Center of Percussion" (CP) may also effect power in the other entire drive train by these unbalanced forces effecting it's inertia. The classic example of this phenomenon is displayed in the class room with a vertical body of some sort (usually a wooden post) that's attached by a loop to a horizontal wire at the top. Hit the body with a hammer above the CP, the body slides away horizontally. Hit the body below the CP, the body moves towards you in rotation. Hit the body dead on the CP, the body doesn't move. It seems to me that a steam engine would be highly susceptible to these types of unbalanced forces, probably more so than an electric motor.
Ok, if I haven't put you to sleep yet, I'll stop here. If you've read this far, you've earned a physics degree from the U of Joyce. Suffice to say, all these considerations have to be made when building something as complex as an articulated or compound steam locomotive. Now, after all this, does a steam locomotive run as smoothly as a prima ballerina during Swan Lake ? No. But the counter-forces that would dangerously effect the operation of a steam locomotive are brought down to a workable level, and as Alan said above, further fine tuned by "proper engine control, liberal use of sanding, etc.", and other techniques of a long time ago. I'll add that to have a basic understanding of the work that goes into planning the basics for these locomotives is to realize even more what a thing of beauty that they really were.
~Paul Joyce~
Moderator: Toy Trains, Model Railroading, Outdoor and Live Steam
Paul Joyce passed away in August, 2013. We honor his memory and his devotion at railroad.net.