Hmm. Looks like it could be made to work. But the orange gear hooks look too deep, I think that as the gear rotates the hook would fail to let go on the other side. Then the entire thing would jam up.
the legnth of the chain depends of the distance beiween the rails. The moment, the orange gear pushes the chain into the narrower rails, it needs all the power to lift the chain to it length. the little diagonal bit of rail, where that force is induced, is just missing!
after rereading your concept i finally got the point with the moving hooks as part of the chane.
now i see, there are two regions of acceleration; 1. when the chane is forced to bend by means of theorange wheel (so the hooks can come into 'long'-position), and 2. when it is forced to straiten while leaving the orange wheel. that moment the 'inner' wheel of the chane needs to seperate from it's following one.
which it cannot in your design, because it's hooked to the orange wheel...
assumpting the 'outer' wheels of the chane arefree moving, they can be driven by bended rail which carrys the full weight of the chanes (like a virtuel fulcrum).
the orange wheel may not have any teeth to allow a smooth liftoff of the chane, but there can be a smaller excentric teethwheel to transmit the power. i don't see why it should not work...
Do the hooks of the chain easily lock/unlock just by gravity, if the chain is bend in the propper way?
It should be possible than, to place the chain in a double-U-shaped channel just sawn out of a wooden board by a jig-saw. Friction would certainly be quite high, but could be eleminated by using ball-bearing at the chainlink-wheels etc.It would omit any hooks or teeth, which hinder the in and outfolding of the chainlinks. it might not be running smoothly but good enough to see if it is working at all (and for me it seems much easyer than computersimulation)
I guess, the funktion is somehow similar to sitting on a swing gaining momentum by lifting and lowering the barycenter - an issue I spent a lot of concideration upon...
I wasn't notified by RG, so I've got Your answer today.
As far as I understand the set, the main-thing is the "acceleration" of the chain taking place while bending (black circle A) and unbending (black circle B on my scetch), when the hooks are taking affekt.
If the chain is carryed by the red band-convayer and guided by the green one, traveling at equal speed, and the slower orange wheel, there are the yellow spaces, where the speed-changing may take place whithout mangeling up the elements.