https://share.google/images/4ffcOYLvfbjXneqou
Ths picture is from this forum. The link will take you to the thread.
The best and simplest suspension is still a wide tire of 3 inches or larger. Everything else is just a makeshift solution. Always remember that things like suspension seatposts change the center of gravity and saddle height. You donāt necessarily want that. The suspension should act as a shock absorber, meaning it should also be effective when jumping, not just when youāre sitting in the saddle.
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I agree to a certain extent. It is true for hard muni and at slower speeds, but it has 2 main defects :
- not as good precision on smooth road
- more energy lost
I am pretty sure that, as long as you donāt have to pull hard on the saddle, having something that allows for some play, while staying rigid and light might be a really nice thing on our unicycles.
I donāt think that mountain bike shock absorbers are suitable for that, because they are pretty heavy and lead easily to great range of motion. But watching what is used in the gravel bikes world might be the solution. I am mostly thinking about composite springs, such as used on the lauf grit fork :
It would still be the legs that would provide most of the springness, but it would prevent getting a too sore butt after long times on bumpy roads / tracks (it might even prevent hard balls crushing in some specific cases).
That looks like a plausible design for a uni; attach the wheel hub to one side and the cranks to the other. The shaft drive suggested above could be the linkage.
So, Iāve played about with various āthought experimentsā with this suspension thing over the years (better known as day-dreaming). I think the main disadvantage of the shaft drive idea I suggested above is the space requirements and inefficiency of changing the rotation direction 90 degrees and back again, either with straight-cut or hypoid bevel gears. That and keeping the shaft clean so it can slide freely.
My next idea was something quite different, and I think perhaps reasonably viable albeit with reasonable effort to minimise the width. At one point a few years ago I was intending to actually try to make something to check feasibility etc, but time never seems to be on my side, and I donāt think Iāll make my fame and fortune from itā¦
The geometry is pretty much the same as discussed above with a fixed frame with the cranks attached and a suspended wheel which is constrained to move in one axis (I had in mind a limited travel gravel suspension fork ā I think around 45mm or so travel for the original Fox one of these from memory). Drive is transmitted from the cranks to the hub axle via a Schmitd coupling at either side. The two Schmidt couplings are linked by the wheel axle so the cranks are essentially locked together but the wheel can move as constrained by the linear fork (in my day-dreams it could even be curvilinear movement from a leading/training suspension link). The width of the Schmidt coupling would have to be minimised, and I canāt remember if there is an issue with a dead-spot or notā¦.. it is while since I kicked this idea about.
My first cut at āprototypingāā something was going to be making something out of Lego ā take a look at videos on YouTube of various linkages made from Lego Technic parts, there are some wonderful thingsā¦. There are lots of Schmidt coupling videos on YouTube, it is really a beautiful thing to look at.
Anyhow, I think this is an original idea, not that Iāve checked(!), if perchance someone makes one of these and tries to patent the Schmidt Coupling Unicycle , this post will hopefully be the āprior artā that means it isnāt granted 
Something like this picture may be a very viable option though a slight change in the location of the wheel and a tensioner is needed. Iām not at home right now but I can give an example when I do
Ok a bit of a crude drawing but you can use a derailleur as a tensioner by threading the chain through only one idler and it will work both forwards and backwards. Key: Red=wheel, Green=pedal axle, Blue=chain, Orange=derailleur, Black=idler wheel
My idea is exactly the opposite. I think internally geared hubs are the way to go. My idea is to put the springs on the saddle tube. It is obviously more designed for road riding, but for light muni, it might work too.
Iām going to post this one more time since nobody seemed to look at it the first time I posted it. This guy actually made a rideable suspension unicycle. This link will take you to the thread right on this forum. I was not able to find it searching here but was able to Google it. There is also pictures on Corbin Dunnās website corbins tree house.
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I know this setup, it is nice looking, but probably rather heavy, and I think way too much range of motion.
I think a suspension system may be better suited for light rough surface riding apposed to muni. Here it could soften the un even surface making riding more comfortable. Adding suspension will definitely increase cost and weight and take away one of your most useful Muni tools, the ability to stop and hop. Unless you are designing it to be like a pogo stick, the dampening and recoil effects are going to increase the amount of time it takes to perform the hop and lessen its effectiveness.
100% agree with that.
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This would be big and bulky but a modification of this could work and I can make a basic model pretty quick on my break.
On if the modifications I would want to make is to replace the chain with something similar to a capstan drive with string to save about a pound of weight, or maybe a toothed belt
Internally geared hubs are just really expensive. If the only thing it does is suspension, I donāt know if people would pay for it.
The suspension and the geared hub are two different parts, with, at least in my solution, no link in between them.
Even if itās not a Schlumpf itās hard to internally gear a hub though.. Right?
Not necessarily, as long as you can machine the parts or find parts that are close enough itās pretty easy in theory
I would imagine a single speed IGH would be pretty straightforward. Emphasis on āimagineā since Iām not all too familiar with what goes into the making of an IGH other than playing around with planetary gear sets 
Thatās pretty much it, though you could change what sort of gear system it uses if you want to