In an automatic controlled machining system including a spindle, means for rotating said spindle, a cutting tool holder for holding a cutting tool, a cross slide means for moving the cutting tool holder reversably along an x axis and an axial slide means for moving one of the spindle and the cross slide means reversably along a y axis, a positional reference system comprising:
- a metering bar assembly including X and Y coordinate reflective reference surfaces disposed parallel to the X and Y axis slides of said machining system;
- a mounting plate carried by said spindle for supporting a workpiece thereon to be rotated about an axis parallel to said Y axis;
- a plurality of interferometers for monitoring the displacement of said tool holder and said mounting plate carried by said spindle at predetermined points thereon relative to the points of contact of said tool with said workpiece with reference to said X and Y coordinates of said metering bar assembly;
- and
- a control means responsive to the outputs of said plurality of interferometers and workpiece machining contour description data in the form of X and Y axis components of programmed displacement of the cutting tool relative to the centerline of rotation of said spindle for generating x and y axis error signals and applying said signals to the cross slide means and the axial slide means, respectively, so that the cutting tool is positioned relative to the workpiece according to the workpiece description data with positional reference of the tool holder and the workpiece to said metering bar assembly.