# Self Balancing Unicycle

Here is a link to a video of a self-balencing unicycle. I'm curious as to how this works. In particular:

• What provides the torque to keep the rider from falling over? I know it's somehow provided by the motor, but this isn't an external torque (if we define the unicycle as our system), and I assume we need an external torque to change the angular momentum of the unicycle.

• If you were to try to ride this thing on ice, I assume that it could not prevent the rider from falling over. Is this correct?

• What would the free body diagrams look like for this unicycle when it is in the act of falling over? When it is righting itself?

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en.wikipedia.org/wiki/Self-balancing_unicycle should get you started. – Noldorin Dec 13 '10 at 21:09

Basically it works on the following principle.

There is a gyroscope used to determine what is the current angle between the vertical and the seat of the monocycle. This can be done because the gyroscope will tend to maintain the same position no matter what the orientation of the monocycle.

The gyroscope is connected to the engine, so that when it detects torque towards the front, the engine will generate more torque oriented backwards correspondingly (spin up); when it detects torque towards the back, the engine will spin down accordingly.

The engine torque mentioned is generated by increasing (or the decreasing) the angular velocity of the wheel.

So this has two purposes:

1. It corrects any imbalances of the passenger and keeps the wheel directed up.
2. The corrections have a net effect of speeding up or slowing down the linear motion (i.e. how fast the monocycle goes), so it's an effective way of controlling the monocycle. If you want to brake you lean back.
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Hope you don't mind the slight grammatical edit. – Noldorin Dec 14 '10 at 0:06
@Noldorin I think you accidentally a word. – AttackingHobo Dec 16 '10 at 19:18

It is in principle possible for a unicycle to prevent the rider from falling over, even on a frictionless surface, by spinning up the (hopefully massive) wheel enough for the resulting torque to pull the axis under the rider. Naturally, locomotion on a frictionless surface has its own set of problems.

If the rider is falling sideways, the unicycle would need an additional motor to twist the wheel in an appropriate direction relative to the seat to compensate. Such twisting could be a potential problem for people whose legs aren't tentacles.

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