The four phases of the strict ring muscle up are the grip, the pull, the transition and the dip. However, sometimes it's just best to let the movement speak for itself.
I took the above sequence of photos at a recent muscle up clinic and it shows from the top of the pull to the bottom of the dip. This is called the transition phase and is typically the most difficult part of the strict ring muscle up.
Here is a breakdown of each picture frame:
Frame 1: I am leaning the back while pulling the rings down toward my sternum. I'm also squeezing the rings in toward the center of my body with my palms facing in.
Frame 2: I'm beginning to transition my body forward as I continue to pull the rings down my body.
Frames 3 and 4: In the third frame, you can see that my hands have rotated from facing each other to facing down toward the ground. At this point, the "pull" on the rings has transitioned to a "push" downward on the rings. In the fourth frame you can see how my elbows have transitioned from below to above the rings.
Frame 5: This frame is probably a touch shy of being fully in the catch, but nonetheless, you can see that I'm comfortably on the top of the rings in a good position to finally dip out. From there, I would simply press to the top of the dip.
Here's a video I shot awhile back (please excuse my weak videoing skills ;)) that shows the points of performance for the strict muscle up and is a good visual for someone getting familiar with the strict ring muscle up.
Strict ring muscle up points of performance
Start with a false grip: As I've mentioned in previous posts, the false grip is KEY. You can't do a strict muscle up on the rings without a solid false grip. If you aren't there, practice false grip holds and get some strength in your forearms.
Begin in a full hang: A full hang is definitely NOT required, but it should be the eventual goal. You can absolutely do your first strict muscle up from a bent elbow position (and, yes I would count it as a first muscle up!).
Pull the shoulders first: Retracting your shoulder blades back is an action that is already natural if you have strong pull-ups. However, if you are still building your pulling power, this is something you'll want to practice often by doing shoulder depressions.
Pull elbows to hips: This is actually just a coaching cue that I'll tell athletes to help generate some pep in their pull. By thinking of drawing your elbows down, it tends to help engage the lats and core for a more powerful pull.
Hold rings into center: Keeping active tension on the rings inward will help keep from them from getting outside of your body where you will have less leverage. Hold them in!
Press over the top: Transitioning from under to above the rings requires a lot of pressing power from your triceps. Press yourself to that support position on top!
Catch shoulders on rings: The best position to catch the rings is where the shoulders rest on TOP of the rings. Sometimes people will get caught "between" the rings. This is is different than "on top" of the rings as you will experience struggle dipping out.
Press to support: The final action is to dip out. I covered this pretty heavily in a recent post all about the dip.
I hope these visuals are helpful. At the end of the day, you're just going to need to commit and spend as much time as you can getting comfortable on the rings. We have a 4-week free muscle up program that you can download right now and begin working toward your muscle up.