The present invention provides certain additional improvements for such mechanical-type multi-axis machine tools. These improvements include: (1) permitting the spindles to be rotated about their respective axes relative to the member independently of one another, (2) providing a low-cost, and yet highly-effective, sensor apparatus for determining the angular position of the member relative to the frame without the use of an expensive encoder or the like, (3) mounting the rotatable member more precisely relative to the frame, and (4) providing a zero-backlash tool slide on the frame for imparting an action to a workpiece.