Abstract: A multiple-axis machine (11) for working on an object (131) and a machine tool head (27) therefor. The machine (11) includes abase (13) housing an annular bearing (19), which has a central axis (21) along which the object (131) being be worked on is disposed. A ring journal (23) is concentrically and rotatably disposed within the bearing (19). A journal drive (25) is mounted to the bearing (19) for engaging and controlledly driving the ring journal (23) in rotation or counter-rotation relative to the bearing (19). The machine tool head (27) includes a holder (73) for a tool (85) to be connected thereto for working the object (131) and three fingers (75) for engaging and supporting the holder (73) in a variety of orientations relative to a main axis or plane of the object (131). Three corresponding cylinders and barrels (77) are provided for accommodating and changing the position of the fingers (75) to orient the holder (73) relative to the main axis or plane in any of the variety of orientations.