Geared Unicycle Engineering Challenges

I own three geared unicycles that use three different designs. One is a “mass-produced” commercial design and the other two are one-off custom designs.

One risk with buying a custom built geared unicycle is that it may not have gone through as rigorous a design process as a commercial unicycle, and there may be some unexpected engineering problems. Due to this, and due to user error, I almost ripped apart one of my geared unicycles because of unforeseen stresses.

Also, no user manual.

I hit this problem when changing gears on Red Menace, my dual-chain geared unicycle.

(see Riding Faster on One Wheel and Riding Fast on One Wheel–Ignite Talk for more on my geared unicycles)

Red Menace is an experimental unicycle which I purchased from its creator, and it is capable of being set to practically any gear ratio. It allows unicycling speeds limited only by the skill and bravery of the rider. To change gears you take off the right crank, change the sprocket on it, and change the sprockets on the jack shaft.

The picture below shows a typical setup of the crank and attached sprocket. Apologies for the non-metric ruler – it’s all I had at hand. We can see that the crank has a radius of 6+11/16” or about 170 mm. Meanwhile the 22 cog gear I currently have mounted on the crank has a radius of 1+13/16” or about 46 mm.

image

According to the standard calculations of mechanical advantage that gives a force multiplier of 3.7x. If I put my full 180 pound weight on one pedal then this says that the tension on the chain will be 666 pounds.

I’ve never measured how much force I actually put on the pedals of my unicycles. The requirement that pedal force be used both for forward progress and for balance makes it harder to put all your weight on the pedals, but when I climb hills I often pull up on the seat, so it’s possible that the peak pressure is even greater than my weight.

666 pounds is a lot of pull on that chain. Bicycle chains can handle that, but other parts are not so lucky.

Jackshaft

The chain goes to a jackshaft and pulls on one side of it with that 666 pounds of force, pulling it towards the wheel/crank axle. The jackshaft axle transfers the force to its other side, to a slightly larger sprocket. That sprocket then transfers the force down to a fourth sprocket that is attached to the wheel. That second chain is also pulling the jackshaft towards the wheel/crank axle. The force is slightly reduced because the inner sprocket is larger than the outer – I currently have a 22/20 cog pair – but that’s still another 605 pounds of force on the jackshaft, for a total of about 1271 pounds of force.

Ouch.

There are a pair of chain tensioners which are used to pull the jackshaft to the appropriate location after changing gears. They each consist of a bolt that is attach to the jackshaft axle at one end and attached to the frame box at the other end by a bracket. You can see one of the brackets circled in green on the left side of the picture below, together with the estimated forces on the chains, and the slightly different sized cogs:

P1040476 cropped annotated

imageThe brackets are flimsy things made out of thin metal. In hindsight it is obvious that they were never meant to take over 600 pounds of force each. You can see one of the chain tensioner brackets to the right, together with the damage caused by the excessive forces. The top surface has been pulled down and started to tear apart. Meanwhile the sides are bowing out. The entire thing is a lot less square than it used to be, and is very close to failing.

What was supposed to happen was that the jackshaft axle was supposed to be tightened enough so that friction between it and the frame box stops the jackshaft from moving. I didn’t tighten the jackshaft axle nearly enough so the force was born almost completely by the tensioner brackets, and they buckled under the load.

The fix is in

imageI was pretty bummed about damaging my wonderful toy and I mentioned this to one of my coworkers, along with my concern that I wouldn’t be able to find replacement parts. Their response was to remind me that we have a machine shop at work. Cool!

I took the old parts to one of my coworkers and asked if he could make replacements. About ten minutes later I received a CAD model (shown to the right) of the parts that he was going to custom mill for me.

 

The old and new parts can be seen below. You can see the damage on the original parts at the bottom, and the much stronger and very nice looking new parts at the top.

image

Lessons learned

The new parts are much stronger than the old ones and can probably handle the forces, but the other components of the chain tensioners still can’t. The nuts were showing signs of stripping, and the welds probably weren’t designed for that sort of force. Therefore it is very important that I keep the jackshaft tightened up as much as possible.

The designer of the unicycle hadn’t realized the magnitude of the forces involved and he is now wishing that he’d made the frame box out of sturdier materials. If anybody makes a new unicycle based on this design they should keep that in mind.

I’m lucky to have been able to buy this unicycle, and I’m lucky to have received some great helping in fixing it when I broke it. Time to go break my personal top-speed records now…

About brucedawson

I'm a programmer, working for Google, focusing on optimization and reliability. Nothing's more fun than making code run 10x faster. Unless it's eliminating large numbers of bugs. I also unicycle. And play (ice) hockey. And juggle.
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10 Responses to Geared Unicycle Engineering Challenges

  1. Pingback: Riding Faster on One Wheel: Geared Unicycles | Random ASCII

  2. kurtfeller says:

    Thanks. As an ME who plays with trikes, I found it . . . just interesting!

  3. kurtfeller says:

    Sorry, just can’t get this out of my head. Actually the new design is not that much ”stronger.” The stress these parts carry is primarily in the sides, and with the thru-hole in the middle little load carrying material has been added. If the hole has too large a tolerance, the additional length (thickness) of the new design could cause the threaded member passing through it to bend under load. However that is not how the parts began to fail but where the nuts have begun to “pull through.” Depending on the abilities of the shop I think brazing thick washers atop the original parts would have been the better solution. But what you’ve done works so it’s all good. You are certainly right that the most important thing is to keep the jackshaft axel fully tightened to the frame.

    • brucedawson says:

      The sides of the new parts are thicker than the old sides which should give them some extra strength. The other advantage of the new parts is that they aren’t already horribly damaged — the original parts were almost ripped apart and I think were unsalvageable.

      The tolerance of the hole in the new parts is extremely good. It’s pretty much a perfect fit for the bolt. The width of the channel is not as good — its a mm or two too thick which weakens the parts and lets them move sideways in an undesirable way.

      You should replicate the design with better stress analysis — I’ll test drive it for you!

    • Jeff Sweeney says:

      I think the same arrangement but using gears instead of cogs and chains might work better. No tensioner would be required.

      • brucedawson says:

        Indeed this has been done and it has some advantages, including allowing shifting between two gears while riding. This is discussed in an earlier article:

        https://randomascii.wordpress.com/2012/11/25/riding-faster-on-one-wheel-geared-unicycles/

        • K Feller says:

          When I read Jeff S’s comments I understood him to mean an arrangement similar to the Dual Chain Drive but using four meshing gears instead of four sprockets with chains, not a planetary gear system.  I understood that his suggestion was one way of eliminating the required chain tension which lead to the failure and subsequent redesign of the tesioner.   While the planetary Schlumpf drive is elegant and allows multiple gearing shift-able on the fly, Jeff S’s suggestion has an appeal in its simplicity for a single-speed geared wheel.  If I only had the time …

          • brucedawson says:

            If you make one then I will test drive it. I have proven experience riding more different geared unicycles than perhaps anyone else.

            The ideal four-geared system would allow removing the four gears as a set, for faster gear changes. That would probably require having a total of six gears, but how glorious it would be.

  4. Pezz says:

    Bruce, I have been trying to find and contact the designer of the hub you are referring to in this article. I have another cycling application I am working with my sons this may be appropriate to use in. Pete Perron, or Dave Stockton are the names I have found that make the hub?

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