getting position relative to normal

Im trying to get the xyz coordinates relative to normal
after doing a bunch of translations and rotations while drawing a model.
Basically i have modeled an arm that moves around depending on the values of several global variables and i want to get the XYZ cooridinates of the center of the hand, i could do all the trig but im thinking i can just get the values after i translate to the center of the hand when i draw it.
does that make sense?

but the results were not what i expected.

thanks in advance.