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Update Oct 2019: Wow, just ran across these two free pdfs by Mori, Hiroshi about how to make self-balancing gyroscopic monotrain. Includes all the theory and practical aspects. A must read: thebbb.net/fre...
and: thebbb.net/fre...
My free ebook to help you construct your own vehicle:
demej00.wordpr...
I present some lessons learned about using a gyroscope to balance a structure or vehicle by constructing a model to demonstrate free precession. I have been able to balance this demonstration model over 15 seconds now before the gyro runs down.
UPDATE: just occurred to me that I don't need the extra weight - as one side of the gyroscope is already heavier than the other so I just spin up the gyro then swivel the heaviest side to the top and it actually balances longer and smoother than if I add weights.
You can actually make a motor/rotor gyroscope balance itself on two legs without any gimbal control - just by making the rotor or motor the heavier side of the motor/rotor pair. By being top heavy in a vertical axis gyroscope or one side heavy in a horizontal axis gimbal, it will correct itself as it falls to one side or the other. Also I have calculated and measured the total gyroscope weight to torque produced by the gyroscope and found that it is a 26% ratio - in other words the total gyroscope weight needs to be 26% of the torque produced by the gyroscope (can be calculated at gyroscopes.org/maths) to be able to keep itself balanced on two legs. Interesting stuff!