I'm working on a graphic simulation (just for fun, for an open-source screensaver) of an Aerotrim - a "human gyroscope", one of those exercise/training machines with a human in the middle, perched on a ring that swivels on an axis with respect to another ring, which swivels on an axis perpendicular to the first axis, on another ring. (AFAICT there could be 2 or 3 such axes that turn, each at right angles to the next. If I can simulate 2 axes / 3 rings, that would be sufficient. A general solution for n rings would be lovely. :-)

Simulating the thing turning, with each axis rotating at a constant rate, is no problem. But it would "feel" more real if I could apply some realistic acceleration from the interaction between the rings and the mass of the rider.

In the Youtube videos, you sometimes see a bystander push on one of the rings, to help get the rider going. Not only does that ring accelerate, but others start spinning too. And the pushed ring does not accelerate smoothly, but undergoes resistance from the other rings, apparently transferring acceleration to them.

I am not up on angular momentum, torque, and all that, so answers will need to take my ignorance into account, though I'm obviously willing to learn a few things as necessary.

I don't feel like it's necessary to take into account the asymmetry of the person's mass - modeling the person as a point mass in the center of the rings should be fine, I think. In other words I don't plan on modeling the way that the rider accelerates the rings by leaning one way or another.

I was thinking that in order to make things a little more interesting, I would have the program occasionally apply a force like a hand pushing on one of the rings. I can figure out what the torque on that ring would be if it were independent of the others, but I don't know to model a set of 3 rings connected on axes.

Any thoughts on how I could model the interaction between the rings, each affecting the others? Simplifications are fine. My intent is not to discover new phenomena through accurate physical modeling, but to create a visual display that looks more realistic than just rings turning at constant rates.


P.S. Part of my uncertainty is, how much does the Aerotrim really behave like a gyroscope? The gyroscope's main properties are focused on the mass in the middle spinning fast on its axis, and therefore its axis tends not to move. This is obviously different from the aerotrim, where the person is often not rotating much around the inner axis, and the inner axis is certainly not staying still. I wonder if other factors, like the conservation of angular momentum of the outer rings, plays more of a part in the Aerotrim that is negligible with gyroscopes.

If it is essentially just a gyroscope... I've looked at the "fundamental equation" at http://en.wikipedia.org/wiki/Gyroscope#Properties, but as a non-physicist I find it difficult to imagine how to turn that into code computing what happens when a force is applied. Pointers to example code for simulation of gyroscopes would be appreciated.



  • $\begingroup$ Bump... can anyone tell me how to calculate the torque on each ring, if I apply a force to one of the rings? $\endgroup$
    – LarsH
    Nov 5, 2010 at 3:42
  • $\begingroup$ As mbq explains, "aerotrims" have absolutely no connection, whatsoever, to gyroscopes. (Except that they look sort of similar - but then "a ball" looks similar to a gyroscope.) There is, utterly, no connection or relationship. $\endgroup$
    – Fattie
    Jan 21, 2015 at 4:00
  • $\begingroup$ @JoeBlow: It's helpful to know that the motion of an Aerotrim-like device is not significantly affected by the forces that dominate in gyroscopes, despite the fact that both are mounted in gimbal sets. I suppose if you mounted a mass of the right shape in an Aerotrim, you'd have a gyroscope, but that's not what they're made for. $\endgroup$
    – LarsH
    Jan 21, 2015 at 16:19
  • $\begingroup$ Just BTW Lars it's super-simple to implement an "aerotrim" in Unity3D or any PhysX based game engine. It is literally maybe 2 minutes work. $\endgroup$
    – Fattie
    Jan 22, 2015 at 6:05
  • $\begingroup$ Regarding your question why does torqueing on one axis, in fact typically make it "go" on all three? it's nothing more than that there's a bit of friction here and there. on a "perfect" device you can easily spin it on one. Yes, the human moving his body mass introduces incredibly complicated forces. Youcould not simulate those - in a game you just add random jiggle :) $\endgroup$
    – Fattie
    Jan 22, 2015 at 6:06

2 Answers 2


Partial answer, but still. Aerotrim has almost nothing to do with gyroscopes, except that the gyroes are usually mounted in gimbal set similar to aerotrim.

  • $\begingroup$ That helps... but can you elaborate on how/why they are dissimilar, despite being mounted in a gimbal set? $\endgroup$
    – LarsH
    Nov 4, 2010 at 21:24
  • $\begingroup$ @LarsH Gyro is a basically an object with a high angular momentum, so that it could hold its orientation due to angular momentum conservation principle. Human in a aerotrim doesn't have a big inertial moment and what's worse is not spinning among his anteroposterior axis at all. $\endgroup$
    – user68
    Nov 4, 2010 at 21:48
  • $\begingroup$ The reason you say that not spinning about his anteroposterior axis is "worse" is that that kind of rotation would produce the most angular momentum for a given angular velocity, due to the body's dimensions? $\endgroup$
    – LarsH
    Jan 21, 2015 at 16:16

One promising way of implementing arbitrary physics simulations, is by programming in terms of 'constraints'. I highly recommend reading this article that covers constraints very well:


I was very surprised when I first saw this myself, because by declaring things like 'keep this point at some fixed distance' you are actually able to model things like a swinging pendulum without even considering torque.

The constraints for this problem could look something like this for the first circle: circle 1
Where A and B would be fixed and C and D could move. The lines would be constraints that keep C and D at the right place. Instead of drawing the constraints, you would draw a ring so that it lines up with the points.

The second ring would look something like this:

circle 2
I left A&B out, but they're all attached. E and F would be closer than C and D and all constraints would have the appropriate length.

  • $\begingroup$ OK... does this help model the acceleration of the rings at all? $\endgroup$
    – LarsH
    May 17, 2016 at 18:03
  • $\begingroup$ If you implement this, adding acceleration will be varily easy. You can just apply an acceleration to one of the points and if the constraints are stiff enough they should accelerate without deforming. $\endgroup$ May 17, 2016 at 21:19

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