Week of 1/27

I spent the better part of this week doing research on a feedback loop for my monorail, as I've realized in the past few weeks that relying on the gyroscopes on their own for balance is impossible. The reason for this is because while Gyroscopes can exert a torque onto the monorail to resist disturbances, it can only do so for a finite amount of time before reaching a state called "Gimbal Lock" where the gyro is unable to exert the torque any longer.

The graph below measures torque on the rig over a period of time. The blue line is the amount of torque the gyro can exert in response to a disturbance, and the red line shows the amount of disturbance that is pushing the monorail over.

When a disturbance is put onto the rig (in this case, because the rig is negatively stable due to only having one rail to balance on, there is a constant disturbance on the rig) The gyro is able to rotate, or 'Precess' which turns the gyro and creates a torque that counteracts the resistance(think of it as the gyro trying to twist forwards and applying that torque to the monorail).

Gyro resisting a disturbance by Precessing, or rotating

However, if the disturbance is constant, the gyro will also have to constantly precess in order to keep up with the disturbance and keep stable. because the Gyro's torque is always perpendicular to it's position, the direction of the force will turn away from the direction of the disturbance, and the precession will become less and less effective. So while the gyroscope can initially exert significant resistance to a disturbance, as to begins to precess to one side or the other, it will become less and less effective. This is why tapping the sides of the rig sharply will often cause little to no change, putting even very slight, constant pressure will slowly overpower the gyro until it becomes completely ineffective and the rig will tip over. This state is known as gimbal lock, and because of the inherent instability of the balancing rig, just running the gyroscopes unassisted will always cause them to eventually reach gimbal lock and fall over.

Gimbal Lock. The gyro turns itself out and is no longer to apply a force against a disturbance

In order to fix this issue, there needs to be a system in place that can increase the gyroscopes' natural precession and multiply it. Doing this means that when a disturbance is applied to the rig, instead of the gyros simply matching its torque, they will respond with a greater torque than the resistance, which will actually cause the rig to overpower the disturbance and bring the rig back to its balancing point, instead of just resisting the disturbance and slowly falling over.

So, this week I started doing research on designing a feedback loop for my gyroscopes, so that I can actively control their precession, and keep the rig perfectly balanced.

This is the start of my new design, which will sit with the flywheel face-down, and being rotated with either a server motor or a brushed DC motor, which I'm going to use I haven't decided on yet.

I also came up with some ideas for balancing my flywheels, as I still have the issue from last week of the flywheels' vibrations causing the rig to lose control, and the flywheels coming loose from their mounts in a few cases. As you can imagine, heavy aluminum discs spinning at 8,000 RPM are things that need to be kept secure. Thankfully I never had a catastrophic failure where the flywheels could have completely removed themselves from the mounting shaft. If that had happened, the flywheels would have shot off the mounting in a random direction(FLY-wheels haha). I had this happen on several occasions at the very beginning of this project, when I just hot-glued wooden flywheels to my motors, and they would often go shooting off the motor in every direction when brought up to speed. Now that I have much heavier flywheels however, I have to get this issue fixed before I can do any high-speed tests with my design.

Original Motor design for reference