I'm working on a mechanical engineering design presentation about guni

Hey everyone,

As part of my dynamics course I have to throw together a presentation about a mechanical device of my choice. Nothing fancy…just a 12 min powerpoint presentation. Anyways, my group and I are going to talk about a 3-gear hub for unicycles. We thought that we might be able to spruce up the slides a bit by inserting quotes from people on here.

At the start, we’re going to be describing the limitations of having a fixed gear ratio, and later on in the presentation we’ll be determining design criteria and constraints. We thought these would be the best points to insert quotes, so feel free to answer either of the following questions for the chance to have your words echo through the minds of impressionable 3rd year engineering students. And, of course, credit will be given where credit is due.

  1. What problems or limitations are associated with unicycles having a fixed gear ratio?
  2. What criteria do you think is most important in designing a geared unicycle?

Also, any ideas on good ways to control the gear selection would be appreciated…we haven’t completely decided on that yet.

Are you familiar with the current geared hubs that are out there? There are a few that work, one that you can buy, and many others that don’t work. Only one or two are shiftable while riding (Schlumpf). Hopefully you will be using those as a starting point.

  1. Unicycles need a fixed gear. Fixed gear, in cycling language, generally means no freewheeling. Freewheeling does not work on unicycles. Though it’s possible to ride a unicycle with a freewheel hub, it’s not practical, is really difficult, and is basically for fun or novelty. So are we understanding your question?

  2. Important criteria:

  • Mustn’t break (especially since it will be really expensive!)
  • Must have useful gear ratios
  • Since shift-on-the-fly is already available, it wouldn’t be good marketing to make one that can’t be shifted without stopping.
  • Can’t be too heavy.

Thanks John,

Yeah, I’ve seen some of the designs that are available. From what I understand, the ones that work are mainly 2-gear. Since we needed to incorporate some actual design work into our presentation, we chose to try to figure out a way to have 3 gears. Right now, we’re thinking of trying to figure out a planetary hub with a kick mechanism that has a left, centre, and right position for each of the gears, as well as some kind of mechanism to prevent accidentally shifting two gears at once.

Yep, that’s pretty much what I’m going for. Additionally, things like how it’s difficult to climb hills, etc. Thanks.


Hmmm… I tend to agree with joh on number one. Here are my answers anyway (not that I’m like, an expert or anything)

  1. The limitations of a fixed gear ratio are far outweighed by the abilities. The fixed gear ratio allows a unicycle to stop on a dime. I suppose though it makes going up hills more difficult? it means you have to pedal all the time, but a lot of how I keep my balance is not so much balancing as it is correcting my balance constantly. If I were to coast, it would be hard to change where I put more pressure to stay upright.
    2)The gears shouldn’t change too much in regards to how the unicycle feels, and should not make the unicycle become un balanced, i.e. they should be placed somewhere where the weight of it will be evenly distributed between the front and back.

You’ve probably seen Harper’s epicyclic geared hub before, but just in case : http://staff.washington.edu/gharper/. Some pictures or assembly drawings of what is already done might be interesting for your presentation. And more credits to Greg Harper.

To answer your questions :
It’s almost impossible to have the correct gearing ratio for everyday’s ride (road or muni, not freestyle or street…) with only one gear (or a non-geared hub). A coker with short cranks can do the trick, but you have to spin like crazy to go not as fast as you could go on a geared uni. On the opposite, climbing or lots of stop&go on a high gear is not efficient.

Being compatible with existing parts (ie 42mm or maybe 40mm OD bearing, bearing spacing, etc.)
Simple of use and maintenance (the schlumpf hub is nice for that, is you pay some attention tightening bolts correctly)

I don’t have time to read all that you guys wrote, sorry… but as far I understand by the thread title, I believe that this may help you or just be interesting for your project:

Sorry If i’m posting something useless… I have to go sleep and I just read the title and remember that I bookmarked this website!


I am going to answer the question that I think you should have asked:

  1. What problems or limitations are associated with unicycles having direct drive?

You can only spin so fast!

  1. What criteria do you think is most important in designing a geared unicycle?

It needs to be reliable and durable
Gears should be evenly spaced (in terms of percent gain over previous gear)
The weight should not be greater than 1.5x the weight of a schlumpf hub.
Cost should be under $2500, hopefully a lot less :o

On the subject of shifting I would look into the Truvativ HammerSchmidt to see if you could do something similar. I think a grip shift would be easier to operate especially with multiple gears.

Cool project. Good luck. Are you guys thinking about using a single gear set or compound gears? There are several gear ratios available with a single set of gears but all of the negative ones are useless, except for those with facility riding two-stacks which have reverse pedal-wheel behavior. The useful ratios are the positive ones of which I think there are three. The simplest is locked gear, or 1:1. The positive overdrive ratio is 1:1+P/S where the sun, with S teeth, is locked to the frame, the planets, with P teeth, are driven, and the ring gear, with R teeth, is engaged with the hub. The underdrive ratio is 1:1/(1+P/S), where the ring gear is driven, the planet gears are engaged with the hub, and the sun is again locked to the frame.

Some of the gear engagement schemes are simple but some are tricky. The two gear is of course simplest. Trying to switch the engagement of the ring gear and the hub with the planet gears and the axle while riding always seemed sketchy to me. I hope you guys can find out a way to do it. Then the idea of having an underdrive on a unicycle is questionably useful. This is the point where you have to ask yourself if compound gears are what you want to use. It seems to me that compound gears would be easier to shift and provide more useful gear ratios. The trade off is that they are substantially heavier, weaker, or both.

I hope you guys pursue this and report back with your progress. Again, good luck.

Thanks for all the advice and comments so far!
I’m sure we’ll end up using a lot of this stuff…

In response to question #1: When I read the phrase “fixed gear ratios,” what comes to my mind is having set gear ratios that are not interchangeable or modifiable.

On a “standard” drivetrain on a bicycle, you can change the gear ratios by replacing your chainwheels or rear cassette or cogs with ones of different size. On a rear-wheel drive car, you can change your gear ratios by replacing your rear differential with one of a different ratio or by using larger or smaller tires, or by replacing the transmission.

On an internally geared hub, with actual “gears,” you are pretty much stuck with whatever ratio you build it with, short of changing your wheel size or tire diameter.

However, I am not sure if you’ve seen the NuVinci CVP transmission that’s available now, that actually does not have fixed gear ratios, but rather a continuously variable continuum along which you can shift until you find the right ratio for your pedaling speed.


It’s a pretty cool technology, and one of the first production bicycles available with the NuVinci CVP hub was the Ellsworth “Ride,” essentially a carbon-fiber cruiser bike. It originally used a belt-drive system that was permanently attached to the frame, with no way of replacing the belt. However, it appears that Ellsworth has wised up and redesigned their frame and drivetrain system to use a standard bicycle chain that no longer goes around the chainstay.

In response to question #2, in addition to all the things that others have posted, I feel that versatility is a key feature in designing a geared unicycle.


You want to minimize slop (slop being the wiggling forward and backwards of the cranks with geared hubs.)

Oops. It’s funny what will bolt you out of a deep sleep.

That should be 1:1+S/R.

That should be 1:1/(1+S/R).



Alrighty, here’s what we’ve come up with so far…

We wanted something that would:

-Minimze the amout of gears required (especially weird shaped, expensive ones)
-Have gear ratios: 1:1, 1:1.5, and 1:2.25, which on a 24" wheel would give equivalent wheel size of 24",36", and 54"
-Have simple, reliable shifting
-Minimize dead-zone between gears, i.e. no excessive travel by any gear-changing mechanism. This is also tied in to trying to make the device as compact as possible
-Be compatible with most unicycles
-Be mechanically robust, and minimize the chance of seizing or accidental gear changes

I should probably also mention that (for the purposes of our presentation) we’re envisioning this on a 24". That way, the cycle is small enough to do some street, large enough to do muni, and geared to make commuting easier.

Alright, on with the design thus far:

We tried a lot of designs that involved sliding a kick-shifter along the axle to shift, but we found that there were too many gears. The shifter would have a left, middle, and right position which would cause it to jut out from either of the cranks. We also found that it was difficult to find a good way to mesh gears by sliding them into different gear combinations, especially since several combinations were required, and the gears had to be spaced out enough to avoid binding with adjacent gears.

Eventually, we determined that the gear ratios that we wanted could be obtained by having a single planetary gear with two different diameters, driven by two sun gears which could be locked to the frame independently. The larger end of the planet drives the ring gear.

We found that we could get our desired gear ratios of 1:1, 1:1.5, and 1:2.25, by using the following gear diameters (where the smaller sun gear has been arbitrarily set to 1), which can be scaled as needed.

Sun_1 = 1
Planet_1 = 0.5
Sun_2 = 1.25
Planet_2 = 0.25
Ring = 2.0

Figure 1 (which is not labelled well!) is a scale drawing of the planetary hub that will give the desired gear ratios. Note that there is a single planetary gear with two diameters, that the sun gears can be locked independently, and that the larger end of the planet always drives the ring gear.

Figure 1: Planetary gear system drawn to scale for 1:1, 1:1.5, 1:2.25 gear ratios

The method of locking the sun gears is a little more tricky. We wanted it to be reliable, and to minimize dead-zones in between gears. Our design can be seen in Figure 2.

Figure 2: Gear changing mechanism

The axle is powered by the cranks, and is directly connected to the planet arm. Over the axle, there is a sleeve which is attached to the frame on the left side of the drawing. Over this sleeve, there is another sleeve which also does not rotate relative to the frame, but slides left/right over the first sleeve. This left and right sliding controls the gears. The outer slider has several holes it in which house ball bearings. The inner-side of the sun gears are curved inwards, as well as ridged along their circumferece to create ball-shaped “pockets” of low energy for the ball bearings to become trapped in. This stops motion of the sun gear, causing it to become locked relative to the frame.

To control the 1:1 ratio, the slider continues farther, and eventually pushes a portion of the planet arm which is free to slide along the pin. This meshes with the hub, and stops relative motion of the planet arm and ring gear, making the system 1:1. The sliding portion of the arm returns to its normal position via a spring or something similar.

Several of the parts involved are drawn in more detail in Figure 3.

Figure 3: Pictorial views of some of the parts involved in the mechanism

To test the feasibility of the design, I made some measurements of the hub of my Bedford 24" and drew a 1:1 scale drawing of the design, using gear sizes that would provide the required gear ratios. The smallest sun gear was chosen to be 3cm in diameter, which makes the ring gear 6cm in diameter. Figure 4 shows our design so far.

Figure 4: 1:1 scale drawing of planetary hub based on measurements of Bedord 24" unicycle hub

I sectioned the figure down the exact centre of the axle to show the cut-away view on the top half. The ball/slider is shown in the position relating to the highest gear. The ring gear is contacting the larger side of the planet gear. Everything that moves relative to the crank input is hatched down and to the right. The curved inner-surface of the sun gears can be seen, as well as both sliders. The one without hatching slides left/right. I need a mechanism to control the movement of this part, which is why I kept the left part of the diagram somewhat ambiguous (unfinished).

As a side note, with this design there is the potential to have a neutral gear for gliding. If the slider moves left one more time (shifting up from the highest gear), both suns are disengaged and are free to spin as they please. I’m not sure if that’s an idea worth developing, but it’s there.

So, among minor complications, the biggest thing we’re trying to figure out right now is how to control movement of the slider that determines the gear.

A typical bike cable could be used, which would allow gear control at the front of the seat or somewhere simliar. We’re also trying to figure out a ratcheting kick-lever mechanism. This would allow gears to be changed by steping on a small lever which sticks out between the frame and the wheel. Our most current design involves a a small lever sticking forwards to control upshifting, and a small lever sticking backwards to control downshifting. These would thread the sleeve forward a specific amount each time they are stepped on.

Anyways, that’s where we’re at for now.

This is a really cool looking shifting scheme. Are the balls spring loaded to assist engagement or do they engage with centrifugal force? I’m trying to understand how they can remain engaged when desired and then easily shifted when desired.

At first I did not see where the 1:2.25 gear ratio was coming from until I realized that you said that only the large planets ever drive the ring. Then it was clear how you were compounding the gears. Have you ever ridden a geared unicycle? At 1:1.5 they are already finicky and, in my opinion, the smaller the wheel the more apparent that twitchy behavior is. I have ridden Pete Perron’s 1:1.89 jackshaft Coker and it’s a very unfriendly machine to control. I believe that the 1:2.25 24" will require a tremendous amount of rider energy to control.

Hey Greg,

For the time being, we’re just saying that the balls need to be forced out of the concave indents in the sun gears…pure elastic strain for all parts involved:). It would take a bit of force to transition between gears. We haven’t gone into too much detail about how clearance should be given at each point as the balls move between gears. I was just talking to one of my teammates though, and we noticed that a CNC mill could probably control the depth of the grooves on the inner slider fairly well, so the clearance of the balls should be fairly controllable. The slider could even be made of some kind of hard plastic so it would strain a bit easier (but not so much as to contact the axle).

As for me, I don’t have any real live experience with geared unicycles. We’re just guessing at gear ratios that seem appropriate. What do you mean by finicky? It is the give in the gears when they change direction? Also, are you recommending switching to a larger sized wheel? We were intending to keep it small enough to do street-type tricks on.

The gear backlash is more of an unavoidable annoyance than a problem. That part can usually be filtered out by the brain. Gearing to a relative large wheel size reduces the balance envelope. The amount of time (or, equivalently, distance) in which the rider has to respond goes down with increasing gear ratio. You have a wheel with small inertia and encounter some variation like a slight slope change or a surface irregularity. This disturbance is amplified by the gear ratio and the rider’s response time is too. All of a sudden, what was perfectly manageable on a 24" wheel becomes very “twitchy” on a 48" effective wheel with the same inertia. This takes energy and concentration on the part of the rider to deal with it.

Hopefully, others have a better description of this. It is more difficult to ride a 24" wheel geared to 36" than it is to ride a 36" wheel. Part (but only part) of that is due to the large inherent difference in inertia between the wheels. This is why I think geared big wheels are more stable than geared small wheels.

Keep us updated with your progress. I would really like to see your shifting scheme unfold successfully.

Either I don’t know how to properly calculate the gear ratio in this system (fairly likely in which case you can ignore most of my post) or your numbers are off.

I got a way higher gear than you for 3rd gear. I ended up with a gear ratio of 1:3.42. I found that you needed the secondary sun gear to be about 1.14 and the secondary planetary gear to be about .36 if we were to leave your other numbers the same.

I think Greg is right about 2.25 being too high of a gear anyway. I would aim for about 33% jumps to end up with something gears looking like

Sun_1 = 1
Planet_1 = 1
Sun_2 = 1.2
Planet_2 = .8
Ring = 3

You end up with a bigger ring gear but the much larger planet gears could let you build it much stronger. I am starting to thing that this three speed hub is really doable.

Warning: I dropped out of engineering 3 years ago partially due to the math aspect.

just an idea for the geared ratios, but if one of them smaller than 1:1. like 1:.5? that would make it really nice for tough hills, commuter and muni riding alike no?

but this looks like a really good project!


This is kind of difficult to describe verbally, but I’ll give it a try. Let’s separate this into parts.

Simple gear system:

First, view the planets as locked and unable to rotate and the sun gear as absent. One revolution of the cranks produces one revolution of the ring gear (hub) as the planets engage the ring gear. Now, free the planets and put the locked sun gear back in. View the planets as walking around the locked sun gear as the planet cage revolves around it. Since the planets are now rotating (in the correct direction in this case), the ring gear is going to go around more than one turn as the planet cage goes one revolution around the fixed sun gear. How much? As one of the planets engages each tooth of the sun gear it also engages a tooth on the ring gear. Each tooth advanced on the sun gear corresponds to a tooth advanced on the ring gear. This means that the ring gear will move an additional amount equal to the sun-ring gear ratio, S/R. For each revolution of the planet cage, the ring gear will advance 1+S/R revolutions.

In Glen’s system, the second gear ratio is a simple planetary system with S=1, P=0.5, and R=2, so 1+S/R=1.5. Importantly, the diameters are consistent with the ring diameter, R, equal to the sum of 2P+S.

Compound gear system:

In Glen’s design ONLY the LARGE diameter planets engage the ring gear. The ring gear is the same size but the sun and planets have changed size. The behavior is everywhere the same except for the engagement of the ring gear as the planets walk around the sun gear. In the third gear, the large planet gear which engages the ring is twice as big as the small planet gear which is engaging the (larger) locked sun gear. This means that for every tooth engaged on the larger sun gear, TWO teeth are now engaged on the ring gear. The compound planet has doubled this part of the overall gearing. In the compound case given here, the ratio is 1:1+2S/R. Glen’s large sun is 1.25 so the ratio is now 1:1+2*1.25/2=1:1+1.25=1:2.25.

The diameters are consistent. This is the compound system. S+2p+(P-p)=R where here S is the large sun diameter, P is the large planet diameter, p is the small planet diameter, and R is the ring diameter.

A final important point for Glen to remember (which bit me hard once) is that the number of sun gear teeth and the number of ring gear teeth must both be integer divisible by the number of planet gears in order to uniformly distribute the planets.

I know that’s a lot of verbiage but I hope that’s kind of clear.

Thanks Greg

That makes a lot of sense and is a lot simpler than what I was doing.

My new proposed numbers with new math :stuck_out_tongue:

Sun_1 = 1
Planet_1 = 1
Sun_2 = 1.4
Planet_2 = .6
Ring = 3

For gear ratios of 1:1.33 and 1:1.78. A gain of 1/3 each time. I hope my math is right this time :slight_smile:

this would give you a nice gearing range with most wheels

                Wheel size
gear	  20  	24  	26	  29	  36
1.00	20.0	24.0	26.0	29.0	36.0
1.33	26.7	32.0	34.7	38.7	48.0
1.78	35.6	42.7	46.2	51.6	64.0