2 DOF with Belts (a planetary with belts, not gears)

Hi,
So today my boss and my self got in a debate about a design for a powersplit. We have been working on hybrids for a while, and talk
about powersplit designs often. One thing that comes up is doing the powersplit with belts, instead of a planetary gearset as normaly used in vehicles such as the toyota prius.
This basicly comes from something in one of his old text books saying you could build a device the same as a planetary but with a system of belts. But it doesn't show how it's done or give any pictures or equations. Just says it can be done. In the vehicles we have built so far (no powersplits yet) we have used Gates Syncronous Belts for various parts of the drive line since they are simple, durably, no need for oiling and so forth. Plus cheap to do on a prototype or a one off like University Built hybrids. So to be able to do a simple powersplit with belts would be great.
I have looked all over the net but have yet to find anything about such a device. It might be out there, but I don't know what to call it. So I was wondering If anyone here knows of such a device, basicly a drawing(s) and the equations for it.
We have a design (as in a markerboard of sketches) we belive works, but there is still some debate if it would work. Neither of us has had time to work it out. But apparently there is a way to do this. I can come up with a description of what we have if no one has any info at all. I would think if it's possible some where there must be some info on doing this. But then again trying to find info on doing a powersplit with a planetary is kinda hard since most things only use planetary gear sets for speed reducers, not 2 DOF systems.
Thanks for any links or help.
Brad
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Well, after work at this some more I pretty much got my answer. In the end I found out how to do it. I also figured out that what we had come up with was correct but did not work as my boss thought, but worked as I thought it did. You know, it's a real pain to think out the mechanics of a planatary in your head some times. Everytime you think you got the reactions and the motion right you relize something else.
Still took me a bit to truely belive it works. Also after I figured it out I finaly found a drawing (well animation infact) or a planetary gear set that has no inside ring gear, can be done with just plain old gears, and thus could be done with belts. Infact it look just like what I was working on but with a minor differance.
Never the less, it would be nice to find some info on doing it with belts, save a lot of work doing the equations and checking I get it right. Plus to find out what you call such a thing. This is more of a mind exercise, but we all want to know how to do it if we do decide to make one.
Have a nice day.
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I think that, kinematically, the solution is pretty straightforward if we look at the problem in 2D and draw with an HB pencil. The realization might be pretty awful.
I'll propose two general equivalence procedures:
1. To replace ordinary pinion and gear with belt and sprockets, we a.) replace pinion and gear with sprockets that have the same diameter ratio and b.) connect them with a crossed belt to maintain directionality.
2. To replace internal-pinion-external-ring-gear with belt and sprockets, we a.) replace pinion and gear with sprockets that have the same diameter ratio, b.) separate the shafts to place the pinion sprocket outside the ring sprocket, and c.) connect them with an uncrossed belt to maintain directionality.
and one geometric constraint:
3. The shaft separation between two engaged belt sprockets must be greater than the sum of their radii.
Starting with the basic planetary gear set arrangement with three concentric (hollow) shafts, replacement of the sun and planet gears with sprockets and a crossed belt is straightforward, and the planet-to-ring relationship can be maintained if we recognize that the planetary orbit size with belts is now independent of the gear ratio between sun and planet and their ratio. We establish the desired ratio between planet and ring, then place the planetary orbit outside the ring sprocket and engage them with an uncrossed belt.
Things might not be quite as bad as the first sketches with the HB pencil show, once we recognize that the we can fit two different size sprockets on a common planetary shaft to engage the sun and the ring belts.
The described belted device should have the same kinematics as the geared device as far as the reversing and gear reduction properties are concerned. If you use uncrossed belts, you'll get different behavior that might or might not be usable.

That's easy. "Sunbelt."

Hth, Fred Klingener
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