Eyolf, after reading you post , i wondered why you were not getting the motion figured out, so I went back to the Rad-cam site and discovered the movie doesnt work anymore, which was an animation of the principle..I will try an explain it.
It is a variation of the Scotch-yoke principle, which maybe what you are describing in that steam engine, as i am aware of that design being used long ago.
In the Rad-cam, the rod is round and has no rocking motion, like a scotch yoke, it goes straight in and out of the crankcase. Their is a cam inside to take the place of the crank journal..but not a cam like a V-8 camshaft, but what he calles a rotor design.
The bottom end of the rod has a round bearing that rides in a track, captured on both top and bottom by this cam/rotor. the center of the rotor being the longitudinal axis of the output shaft.
TDC dwell time is therefore not a function of rod angle and rod length, but the radius of the track in which the bottom rod bearing follows. In the rad-cam design this enables a dwell time many times longer than a conventional crank and rod.
Picture 2 horeshoes placed feet to feet..sort of a double U shape..or a circle with flat sides, with the track for the rod bearing to follow on the outer edge of the rotor. This is the shape of the cam/rotor in the RAD-CAM, so that pistons 180 degrees apart are on the SAME stroke ...both down or both up you might say, so you have 2 pistons fireing at the same time, directly opposite of one an other. It is not complicated..in fact VERY simple with few moving parts.
I believe The scotch yoke design, like a Bourke-cycle design, or a De-Vaux engine design are all similiar to this theory, and in discussions with the inventor of this Rad-Cam design he admits as much. He told me that he first actually built a scotch yoke style but couldnt make it satisfy him so , with the advent of Computer-controlled machining centers..this cam/rotor design was made possible.
Here are a couple of links to some more current scotch-yoke designs, if it interests you.
http://devauxengines.com/
http://bourke-engine.com/ani.htm