in cartesian co-ordinates is in spherical co-ordinates.
where is the distance of the end of the arm from the origin, is the pitch, and is the yaw. This is assuming your arm is a single straight line pivoting about a fixed origin, in which case, there would be no way to find roll, since a change in roll does not cause a change in (x,y,z) position...the arm just rotates about its central axis, leaving the endpoint in the same position.
What exactly is the setup of your arm? I guess it's more complicated than a single straight line, and you have joints in it.