LinuxCNC is a very cost effective method for controlling complex movement of devices mounted to an XZ stage.
Bill mounted a Quick Change Tool Post (QCTP) to his stage, and that is used to hold the cutting frame which is moved along the X or Z axes (or both). The object is held on a midi-lathe.
Dewey used his stage as the headstock, moving the object around whist the cutting frame remains fixed. (Dewey has stated that he'd take Bill's approach if he did it over).
Disclaimer: eMail comments to me at OTBookOfKnowledge @ Gmail.com. The process of woodturning involves the use of tools, machinery and materials which could cause injury or be a health hazard unless proper precautions are taken, including the wearing of appropriate protective equipment.