There was a thread in Trading post but unfortunately the OP closed it before I could contribute. I have done this, if they are interested. Not sure that this is the right section of the forum for it, but happy to share what I did.
Since there is no “just conversation” thread anymore this is probably as good a place as any. Besides, I will be building a unicycle wheel for it.
I was wondering if your username was about fibers.
I’m certainly interested in seeing what you have done. My first thoughts were to make an open spindle wheel with the spindle above the wheel, and a single treadle in front.
Something like this drawing if you can understand it:
Historically, spindle wheels have tended not to have treadles. I don’t know how much you know about spinning, so excuse me if I am telling you stuff you already know, but the other mechanically inclined readers of the thread will probably be interested. There is a good reason for this - a spindle spinner, like a unicyclist, needs to be able to slow down, stop and temporarily reverse direction frequently while spinning. You spin a length of yarn as long as you can reach back, then you reverse the spin to unwind the bit at the tip of the spindle, then you forward it to wind the spun yarn onto the ‘cop’ or ball of yarn forming at the back of the spindle. A treadle makes that much harder than simply turning the wheel by hand. Treadles come into their own once you put a flyer on the wheel - a flyer being a brilliant mechanism that automatically winds on the yarn as it is spun. So spinning becomes a continuous, fast, regular process, and speeding up the wheel and freeing the hand by adding a treadle makes perfect sense. It is possible to learn to use a treadled spindle wheel - Rachel Brown’s Río Grande wheel being the best known example - but it isn’t easy.
I’m cooking dinner, so I will put up details of the wheel I made later when I have shrunk the photos!
I am really interested in seeing your wheel.
In my art room I try to have opportunities available for students, and in many cases it is materials/techniques that I have limited experience with. Rather than presenting myself as “the expert” I guide students through discovery, practice, and skill development. That said, my basic experience with spinning on a drop spindle is enough to get students started, and having a wheel will be for students who feel a strong motivation to spin.
I have seen videos of people spinning on open spindle wheels, and it started me thinking that it would be a simple enough thing to make. At least in one video the step where the wheel is reversed for winding on the yarn is done quickly, and the spinning starts again almost immediately. That wheel had a spindle that went to a point with no hook.
Based on what you said I think it will be best to plan for a wheel with a flyer. I will probably collect parts, and wait until Summer to build it. In the mean time I will continue spinning with drop spindles, and maybe make a kick spindle. For my classes the kick spindle may make sense since I could have a few of them, and not have to worry about storage.
Educationally, a spindle wheel is excellent because it links the mechanical principle of the drop spindle direct with the wheel in a way that is obvious. I always take one with me for demonstrations. The flyer wheel is too clever - even many experienced spinners don’t really understand how it works, they just know how to operate it. Spindle wheels were the norm for many many centuries and the process can be really fast - the windback/wind on movement becomes automatic. You couldn’t go wrong by making an ultravsimple spindle wheel like mine, and then the students would actually understand what the flyer was doing if you made one subsequently.
I’ve set my wheel up again for the first time in some years, so that I can video it in use. It used a spindle assembly from a small Charkha style wheel which I already owned. I used an old bike front wheel and was inspired by Faroese wheel which were built directly into the wall of the house and mounted it on an existing chest of drawers by the simple method of drilling a hole in the drawer front for the axle and attaching it with the existing nut. The tension adjustment is simply by sliding the clamp for the spindle assembly along the desk. I am very bad at fiddling with photos etc on this forum so it might take me a while to get them to work!
If I was starting with unicycle parts, I think I would get a large base plank and take the seat off the seat post. Then screw the seat post down to the base plank. Then mount the frame and wheel upside down (without tyre) onto the upside down seat post. I would put a smooth peg on the near side pedal crank and use that as a crank handle. Then I would mount the spindle assembly on another seatpost and frame further along the baseboard, preferably with some slide mechanism to adjust tension.
Video of it in action.
http://youtu.be/x4W6ltNiEoA
This has got me thinking how I could make a packable conversion that would let me use a working unicycle as a holiday spinning wheel and unicycle!
I have seen “walking wheels,” and I thought the treadle style spindle wheels seemed like the point was to keep everything a bit more “compact” in the studio.
As it stands I may still make a treadle/spindle wheel, but as I said before I will make it a little differently than I originally planned in order to add a flyer/bobbin in the future. I really don’t think this will happen before Summer. A kick spindle is much more likely in the short term.
Even though I’m fairly familiar with spinning fibers and making yarn, it never occurred to me that your screen name had anything to do with it. I like the double connection with yarn spinning and unicycling. Very clever!
While I’m not into yarn making myself, I am into making a lot of other things (some for fun, some for necessity), and I think your conversion of a bicycle wheel into a spinning wheel is pretty cool. It also looks like you didn’t have to modify the wheel at all, so it could be used again on a bicycle, giving it at least a dual-purpose. Nice! 
Excellent idea! It might also be a way to avoid the extra fees that airlines charge nowadays for transporting sports equipment. This forum has many threads on how to avoid those fees, but you are the first to mention this clever idea!
This is why I love these forums. Sometimes it doesn’t take much for an idea to be planted and for someone to run with it. The conversion should not be very hard. Perhaps the spinning wheel base could double as a unicycle stand when not in use :).
Thanks for the video, I’ve never seen that style of spinning wheel before, and was having trouble visualizing how it would work in jtrops’s sketch.
fascinating thread
I received the hub in the mail today, so I will start looking for a rim. The wheel I originally had planned would have a relatively small main wheel with a low gear ratio, so I will probably stick with something in the 406mm ETRTO size.
The wheel will be the easiest part to build, I still have to figure out the best way to make the flyer. I have seen some good examples that don’t look too tricky to make.
I have a feeling that once I have the wheel built I won’t be able to stop myself from finishing the project.
This book is no longer in print but there seem to be copies around. It includes a whole spinning wheel made from bicycle parts, with a flyer made from wood.
Thomas Kilbride, Spinning and Weaving at Home.
and this… https://uk.pinterest.com/pin/28006828904769672/
scroll down on this ,…there’s loads
Very nice!
It’s in my Amazon cart!
After looking at different flyer designs I don’t think it will be too difficult to make something that works well.
I decided to use a uni wheel because it can be supported on both sides, and still have a crank to be driven by a treadle. My design will probably be overkill for strength and stiffness, but in my experience anything that goes into the art room in a high school needs to be overbuilt or it just won’t last.
For now I have it in my head to design a kick spindle that uses a drop spindle set into a chuck or collet. If i can get it to work smoothly, and without wobble students will be able to use their drop spindles (made by them) in the kick spindle frame.