I can't really tell how the device works exactly from the stills or video. It 
appears that the large pedal driven disc is merely a shutter, and the video 
camera looks through the shutter to something on the other side, and then the 
video projector displays that image on the screen in front of the user. Is that 
it? What is that something on the other side of the disc?

How does this work without the projector? What spatial relationships are 
required between the viewer, the disc and the thing behind the disk -- how 
close do they have to be to each other? How does the size of the disk play into 
this? If the disc has to be the size it is in the existing device, and the 
viewer has to be as close to the disc as the video camera is now, you won't be 
able to use the recumbant pedaling position unless the viewer is looking 
through the bottom of the disc, which would make the whole thing pretty tall 
and probably defeat the purpose of portabiity...

--
One thing you might try to use as a 90 degree transmission is a close-quarter 
drill attachment, such as this: http://tinyurl.com/6y4ftrc

I don't know if the gears in this one are strong enough to take the inertial 
force of your disc. I assume you can get similar devices from other sources 
that would be sturdier than what Harbor Freight sells, though more expensive.

You'd mount the attachment at the hub height of the disc, with the disc linked 
to the part of the attachment that goes into the drill. The attachment would 
not hold the weight of the disc axle, so the axle would have to be supported 
independently, with one end connected to the drill attachment to drive it. The 
bicycle gear, then, would be on a similar axle, independently supported again, 
probably on both sides, as inside a bike fork, that would extend on one side 
and clamp into the drill chuck. This gear would be driven by the pedals in the 
sort of 90 degree horizontal to vertical chain path you have now.

Making these axles and attachments sounds like a lot of hacking work, though...

--
It's possible a beat-up old bike chain might have enough play in it that it 
could could make a 90 degree twist over a long enough run. That would be 
simple, but probably wear out or break easily.

--
Another possibility would be to use automotive type pulleys and rubber belts. A 
belt of the length required should handle a 90 degree twist. I think they even 
make such belts and pulleys with teeth, for a more positive grip and drive. 
(Without teeth, you'd just need to build in a tensioner to keep the belt 
taut...) You might talk to an auto mechanic or an industrial supply company... 
This method, I think, would be more reliable than the drill attachment thingy, 
and perhaps easier to construct...

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