The strength of the rotator cuff plays a key, major role in the muscle up. The transition phase of the muscle up is a heavy internal rotation of the scapula.
The targeted muscle with all internal rotational work is the subscapularis muscle, which is the dominant muscle in internally rotating the shoulder. Teres major also internally rotates the shoulder, but not as much.
In order to maintain the structural balance in the shoulder and allow the rotator cuff to strengthen with great efficiency, both internal rotation and external rotation should be trained to prevent injuries, improve athleticism, and build strength.
The majority of the individuals fall into the group where their internal rotators (subscapularis) are well-developed, but their external rotation (infraspinatus) lacks strength.
Any weakness in the rotator cuff hinders the development of the other muscles because the body always aims to maintain structural balance by default.
I was part of the rare group where my internal rotators were significantly weaker than my external rotators.
Almost everyone on the Internet taught me to train external rotations (because they are often the weak part of the rotator cuff for most people).
There are good chances you are part of the rare few whose internal rotators are the weak link!
Weak rotator cuff can be the missing link in your training if you have already mastered every other element of the muscle up.
Regardless of your desire to master the muscle up, focusing on developing rotator cuff strength will improve general fitness and muscle up performance by leaps and bounds.
I recommend doing rotator cuff work after the muscle up workout or after your normal workout. Rotator cuff work can also be done as part of the warm-up routine.
In order to do rotator cuff mobility work, you will need elastic bands, small weights, or a cable machine.
When your internal rotators and external rotators are strong, this is possible:
How To Train Internal Rotation
My recommended variation is to perform internal rotation lying on the floor.
There are other ways to train your internal rotators as well, but why spend time with less effective exercises when you can do this one?
I believe this is the most effective and best variation you can do. The form is flawless and the range of motion as much as you need.
The entire motion should be comfortable in all musculature. If it is not, then you will need to just focus on performing the internal rotation just with your arm without any extra weight.
Progress in small increments. It is not always necessary to add more weight.
Rotator cuffs are easy to injure, so start low and stay safe.
How To Train External Rotation
This variation of external rotation can be performed lying on the floor, sitting, or standing. This exercise is also called "cuban rotations".
My recommended variation of the external rotation is the standing external rotation, because it is the most demanding with the best range of motion.
Instead of dumbbells, standing external rotation can also be done with a barbell.
Start with small weights and gradually increase the load every week.
Rotator Cuff Workout
Sets x Reps
Lying internal rotations
5 to 10 repetitions with light weight (2.5-7.5kg / 5-15lbs)
Standing external rotations
5 to 10 repetitions with light weight (2.5-7.5kg / 5-30lbs)
As the final exercise of your muscle up workout.
To find your sweet spot for both internal rotation and external rotation, try 1.25 kg (2.5lbs) for 10 reps, and if it is too easy, try 2.5 kg (5lbs).
After you have found your sweet spot, perform the 5 x 5-10 and gradually increase the weight every week or every two weeks. It all depends on how your body feels.
This is not a strength feat - this is just mobility work, so focus on the perfect form and safe execution.
Stay safe, train hard.