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Below is an article on false grip pullups, which help work towards Archer pullups and muscle ups. A muscle up is essentially doing a pullup and continuing into a dip. A false grip puts your wrist into a position where you are able to get up into a dip. Practicing false grip pullups will help with building up the technique, grip strength and range of motion for muscle ups.
Article page – How to Do a False Grip Pullups
Below is a video on Archer pullups, which help you train for the Iron Cross (a difficult gymnastics skill), Muscle Ups, and one arm pullups. You can use Archer pullups to focus more on the pulling hand or (for muscle ups) on the pushing-outward hand (for Iron Cross).
Working dips on rings is also useful in training for muscle ups and Archer pullups. For training progressions for pullups, one arm pullups, dips and more check out the book Overcoming Gravity. It has charts, gymnastics based progressions, diagrams and explanations of the skills, and a ton more information. Check out the product page, which includes a PDF of the book, and gymnastics rings. I don’t make a cent from any purchases made through this page – I just think a lot of their products!
Check out my previous posts on working the grip, and training towards one arm pullups.
Wrist roller training for Judo
One arm pullups and the Hartigen method
This article is also included in the Johnston Karate Guide to Functional Strength