Translations: 'Crack' as in 'Crack Knuckles' How to translate 'crack'?

As in:

To crack ones knuckles?

To crack ones fingers?

and other joints/bones/etc?

(Supposedly in 四川话 it's 'pi' - I don't know the character, hopefully @Huang can let us know).
This depends on the method used to generate the sound. The actual "cracking" is not generally mentioned when speaking about this phenomena in Chinese. Instead, the act that you perform to get the sound is the focus of the phrase.

For example, "cracking your knuckles" would become something like "squeezing your fingers", which is "捏手指", 捏 being "to pinch". As a direct translation, "pinch" doesn't make much sense in English, but just imagine the action of squeezing when pinching two pieces of skin together.

Chinese people don't always use this method of cracking fingers, however. Many people choose, instead, to twist their their individual fingers one by one. This has a different term: "掰手指", "掰" being something like "to twist".