How does that work? I'm not sure we're using the same terminology here -- I know that when I'm programming a Fanuc vs a KUKA, and using my hand to work out what angles I need to use, I have to rotate in completely different sequences.
Its a property of extrinsic (always rotating about world frame) vs intrinsic (rotating about the frame created from the previous rotation (the ' and '' notations)) Euler rotations.
To quote the wiki article on it:
Any extrinsic rotation is equivalent to an intrinsic rotation by the same angles but with inverted order of elemental rotations, and vice versa. For instance, the intrinsic rotations x-y’-z″ by angles α, β, γ are equivalent to the extrinsic rotations z-y-x by angles γ, β, α.