It appears that the left gear is the driving gear and the right is the driven. This means that the angular speed of the right gear is the ratio of the left radius to the right radius (speed_right = speed_left*radius_left/radius_right). Because the angular speed of the left gear is constant the only change to the angular speed of the right will come from the changing radius ratio of the two gears.

This behavior can be seen a bit more clearly with nautilus gears that have constantly changing radii.

I imagine the red gear is the one backed with a motor rotating at a constant speed. Which would explain why it never slows down or speeds up.

The blue one is being entirely driven by the red. It slows down because moving 2 notches at a greater diameter requires less rotation than moving 2 notches at a lesser diameter. It then speeds up because moving 3 notches at a lesser diameter requires more rotation than moving 3 at a greater diameter.

Others have talked to the changing ratio, however I think the possible implications(use cases) of this are also interesting. I'm imagining making room for something, also rotating at a the same speed, to slip into place by arresting the second gears speed before catching it up.

I'd love to get into watch building which likely utilizes a lot of these tricky movements.

I have recently became interested with the inner workings of watches and found this 1949 video to be a perfect explanation of the underlying concept of a watch movement mechanism: https://www.youtube.com/watch?v=WYBvt9kA3bE

That was a great video. Tourbillon from scratch; one day.

Gear ratios. Think bicycle.

By adjusting the distance from the center the ratio can be changed. Closer to the center on the driving cog (the left red one) will reduce rotation ratio and further away, will increase the rotation.

Only relative speed will be determined by the geometry (these gears, in effect, change the gear ratio throughout one revolution).

In this animation, the author decided that the left gear is driving the right one (while itself, presumably, being driven by a motor at constant speed or something similar).

As others have mentioned, the movements make perfect sense intuitively as soon as you realize that the red gear is rotating constantly (driven by a motor), and the blue gear is spinning freely.

It does indeed thinking about it like that. But since the gears would be bumping into each other rather than just pushing each other would that cause them to deteriorate faster?

Gears are always bumping into each other, one tooth at a time. In practice, the friction of the teeth sliding on each other causes much more wear than the impacts.

In a properly constructed (shaped) gear, the teeth should roll against each other rather than sliding (i.e. the velocities of the contact points are the same).

Sloped / beveled edges, a strong material, and a ratcheting mechanism should keep gear lifetime about the same if I had to guess.

Also lubricated with grease or even bathed in oil which serves as a cushion.

The left wheel rotates at fixed speed, it's the source of the movement (connected to the source of power). The right wheel rotates according to the relative radii between them, the constant speed of the left wheel dictating its speed.

They are indeed identical but they're spinning in opposite directions, which in effect means one is flipped (going small->big instead of big->small). I believe that's how they can behave differently.

the gear on the left is the driving gear, moving at a constant rate. When the gear on the left allows the gear on the right to fit closer to the center of that left gear, the gear on the right moves more slowly. Similarly, when the gear on the right fits farther from the center of the left gear, the gear on the right moves more quickly

Red is being driven by the axle at a constant rate, blue is being driven by the teeth of red