i would love to see that! that is my favorite machine at the gym!

I remember being at a parade and one of the groups in it was riding bikes from 1900 or so, they had a few ordinaries (the ones with the huge wheel in front) and a safety bike (the kind we all know) and one that used a pumping motion to make it go (like your eliptical idea) it had two pedals that were more like wood planks that ran all the way back to the rear axle, the rider ( a woman dressed in period dress) pumped the pedals alternately to make it go. I couldn't figure out exactly if they were linked so that one went up when the other went down or if there was a spring that caused them to return to the up position. I do remember that the riding position was much more upright and the pedal travel was longer than a crank would be. I think there were cables or chains that ran to a drum in the rear to pull the rear tire.
So it looks like the idea was manufactured a long time ago, however back during that time period, almost every town had people making bikes as well as selling the larger brands. That is how the wright brothers were employed before airplanes.

These are the guys that were at the Maker Faire two weeks ago...