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Author Topic: "Limbo" Gyro Top  (Read 4941 times)

Jeremy McCreary

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Re: "Limbo" Gyro Top
« Reply #60 on: June 05, 2020, 11:54:37 PM »

So, I'm compiling a list of all the solid observations we now have on both tops to see what the total body of evidence has to tell us. Including the Limbo video evidence. Just the facts, ma'am.

Think they can fool iTopSpin, do they?

Forgot about this diagram from the Limbo folks. Guessing that the Toupie Lumineuse has similar internals and uses the same strategy to stay up without spin decay.

In the Limbo, at least, this confirms the use of (1) an accelerometer, and (2) a coin-type eccentric rotating mass (ERM) motor like the ones used to vibrate mobile phones. The claimed PID motor controller presumably resides on the IC (integrated circuit) shown on the electronics deck below the battery. The accelerometer is probably capable of measuring both tilt and precession rate.

It's also worth noting what's fixed to what...

Unit A: Rotating as one rigid unit are (1) the shell, (2) the motor base and shroud (not shown), (3) the electronics deck, (4) the battery, and presumably (5) the ball tip.

Unit B: The other rigid unit consists of (1) the motor rotor and shaft, and (2) the ERM keyed to the shaft.

For the Limbo, we also know some important facts relating to angular momentum balance...
1. B's rotational inertia is tiny compared to A's.
2. But B can spin up to 10,000 RPM faster than A.
3. Meanwhile, a good twirl can probably spin A at up to 2,000-3,000 RPM relative to the table.
4. So, B could spin as fast as 12,000-13,000 RPM relative to the table in normal operation.

Motor torque is probably the only significant mechanical coupling between A and B. The torque delivered to the ERM is net of any frictional couplings in the motor bearings (which belong to A). Direct aerodynamic coupling between the ERM and A could also be negligible, as the ERM shroud belonging to A could well lie outside the ERM's boundary layer by design.

Nonetheless, the aerodynamic braking torque on B itself could still be significant in this setting. An  asymmetric ERM spinning at 10,000 RPM could be an effective impeller. The reaction torque on A would be equal and opposite to the motor torque needed to drive the B impeller.

The air and tip resistances acting directly on A are then primarily external. Each resistance always acts to oppose A's rotation relative to the table -- with no direct effect on B's spin rate relative to A.

B's speed relative to A is instead up to the PID controller based on programmed responses to the instantaneous accelerometer readings.

Controlling motor voltage adjusts the rate and direction of B's spin relative to A. When motor torque changes their relative spin rate, air and tip resistance and Unit A's large rotational inertia limit the torque reaction on A relative to the table. This effectively shunts most of the change in spin rate into B -- relative to both A and the table.

The Toupie Lumieuse appears to maintain a steady A spin rate relative to the table. The Limbo promos imply that its A also keeps spinning relative to the table in normal operation.

So these tops really are overcoming their air and tip resistances in the steady state. They may be staying up in part by spinning B relative to the table like a caged toy gyro. But that's not all they're doing.

Pretty confident about all of these statements, but still puzzling over what B's actually doing to beat spin decay in A. :-\
« Last Edit: June 06, 2020, 07:07:35 PM by Jeremy McCreary »
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