The muscle up on rings involves pulling yourself on top of the rings from a full hang beneath them and then pressing to support. It is a combination of a pull-up and dip connected by a transition to connect the two movements.
Execution
Start by securing the false grip. This grip allows you to do both the pull-up and dip without having to change your hand position on the rings. It is the most efficient way to hold the rings to handle the transition for this reason.
Hang fully allowing the arms to go straight. From here, pull high, until your thumbs touch your chest. The higher you pull the easier the next step will be. Once you are up, twist the rings into the dip position by dragging your hands around your chest and into your armpits. Stronger athletes can allow the hands to go wide during this transition, but when it learning it is best to keep them in close to maintain maximal leverage.
The muscle up is in essence complete at this point. Finish by pressing to support with fully locked elbows and turning the rings out so the palms face forward. Keeping the rings close initially will require less strength much like keeping the rings against your torso during the transition. As you develop strength you can control the rings away from you while maintaining your support.
Purpose
In gymnastics the muscle up is not considered a formal skill. It is a pre-requisite for skills that take place from a position from above the rings.
That being said, it is a worthy achievement for any non-gymnast and those interested in advancing their fitness through the incorporation of bodyweight training. It requires strong muscles throughout the upper body and the training for this skill develops strength, flexibility, coordination and attention to detail. Often requiring months to years of diligent training, you will be ready for new skills as well as capable of handling more basic skills like traditional pull-ups and push-ups with ease.
Pre-requisites
You must be able to do a single pull-up to the specification demonstrated in the demo video above. You must have the ability to support yourself strongly above the rings at support and in a deep dip position. Accomplishing many reps of pull-ups, or dips, at a high speed and partial range of motion will not translate to a muscle up. Your movement must be well-defined and cleanly executed to ensure success.
The transition need be learned with the feet on the ground to understand the movement. Once the pattern is understood it can be progressively loaded in many creative ways including this transition I find helpful as a teaching method – Ring Row to Muscle up – Transition. The important factor is to clearly understand the highest point of the pull-up and lowest point of the dip required at the end points of the transition. This drill makes these positions clear when coupled with Ring Dip – Support and other strengthening exercises.