Bit of a maths question here for you…
Imagine you were stood in the positive Z direction, and your feet were facing outwards (like a ballet dancer) with your right foot pointing negative X and your left foot positive X. The rotations of your right ankle would result in the following:
Z rotation - the amount of elevation (-Z elevating you higher onto your tip-toes)
Y rotation - the amount of turnout (90deg pointing your toe directly along the X-axis)
X rotation - twisting your foot forwards and backwards
Now imaging your feet were not aligned directly along the X-axis with the Y rotation being at around 45deg (ten to two).
If you use the rotate tool at the ankle on a joint chain replicating this setup in world mode, the foot bone falls between the X and Z rotation axis. If you switch to local mode, the Z rotation lines up nicely with the foot bone, the X axis lines up nicely with the foot twist and the Y axis lines up nicely with the foot turnout.
The rotate XYZ values in the channel box for the ankle joint however are all affected when you change the turnout or elevation, and only the foot twist affects only the rotateX.
I am aware that these are the world rotation values which are displaying and there must be some underlying maths which calculates this based on the local rotation.
From what I can gather, this calculation may be based on Euler angles. Perhaps it is matrix algebra or something more geometrical?
If anyone has any ideas as to the maths behind it or can direct me towards a solution it would be much appreciated.