In this movie, you animate the lines that connect the rings together. There are different ways you can go about that, some more complex than others, but you will use a simple approach as it works well enough in this scene.

Making-of the Channel Trailer - Part 6

The official learning channel for Autodesk® 3ds Max® software, a comprehensive 3D modeling, animation, rendering, and compositing solution for games, film, and motion graphics artists. The Autodesk® 3ds Max® Learning Channel provides tutorials of all levels to help you learn Autodesk® 3ds Max®.