Proper thickness of gymnastics rings to learn the false grip

I am training to do a proper muscle-up on gymnastics rings. A muscle-up has 3 components:

I do have the strength to do pull-ups and dips on rings separately. However, in a muscle-up you join two movements together - you transition from a pull-up to a dip. For the transition to be possible you have to hold the rings with a false grip, as it shortens the distance from your chest to the rings. For quite some time I was having big trouble with the false grip.

I could not support my full body weight with a false grip, not to mention pulling myself up. It hurt the spot that touched the ring, at the hand joint area. Pushing through pain is an idiotic approach to exercise, and I did not want an injury. I did some research on the web and decided to try rings with a greater diameter.

The rings I was having trouble with were 28 mm in diameter, and they were made of plastic. I bought new wooden ones with a diameter of 32 mm.

Here are my new beautiful wooden rings: 



Here is a thickness comparison between the old ones and the new ones. It is quite a big difference.



After my first try with the new wooden rings I could do a pull-up with a false grip, with my full body weight. There was no pain, and my grip was strong.

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