The present disclosure includes a method for use on a machine tool system having a controller, three linear axes of motion and at least one rotary axis, for determining the orientation of the rotary axis relative to the linear axes, including mounting a sphere to a system component that rotates about the rotary axis, rotating the component to move the sphere to at least three positions about the rotary axis, measuring a center of the sphere at each of the positions by using the controller to move a probe mounted to a spindle of the system into contact with the sphere, computing, using the controller, a plane fitting the center measurements, and computing, using the controller, a vector normal to the plane passing through a center of rotation of an arc lying in the plane and fitting the center measurements, the vector corresponding to the orientation of the rotary axis.