Angular momentum for these strange nonplanar gears?

[FallenApple]

I wonder what would the angular momentum vector look like for these gears.

As it rotates, there is no clear direction on where the angular momentum vector is pointing. This object is symmetric.

Here's the video about these.

 

[A.T.]

As it rotates, there is no clear direction on where the angular momentum vector is pointing.

It's just 3 spinning rings, simply add their vectors.