A logic animation system is usually made with the following logic cubes: Delay Cube, Cube Model Hider, Pressure Plate or Lever, and any models you want to animate.
We'll start with 4 frames of the animation, so 4 models. Let's explain the first image.
The number of frames in the animation can be as high as you want/as high as necessary. The Cube model hider's yellow logic connector can only be connected to models; follow the image's example. Each yellow logic connector from Cube model hider should be connected to a model.
Now connect the Delay cubes to the Cube model hiders as the third image shows.
And now the harder part. For orientation, we first edit delay at model, which will begin in the animation (examine the fourth image to understand). Also it means we must set delay to 0. Of course, that's still an example, you can add delay at start also.
Other Delay cubes will have both - if we make an animation without slow-motion between models - same time in seconds as in the first (At our example in the fifth image, it means 0.7 delay and duration in other Delay cubes). However, if you wanna keep the model still at the last "move", then do an exception in the last delay and put duration to 1000 (or a time which is very long for the player).
And at the last, connect Pressure plate or Lever to the orange dot of Delay cube, which we edited first.
NOTE: If you want to make this infinite, use a Pulse Cube!
Well, that stays almost the same, except for the Cube model hiders, instead of them there will be Negate cubes, and instead of models we shall use Text cubes. Also for good effect, set all the Text cubes together after finishing the system.