A machining apparatus for a workpieces includes an upper turn table support mechanism supporting an upper turn table from above to be vertically movable by a cylinder extending along a rotational axis direction of the table, a horizontal plate fixed to the cylinder so that a main surface thereof becomes perpendicular to a longitudinal axis of the cylinder, at least three displacement sensors which measure horizontal plate surface height positions when the upper turn table has moved down to a fixed position, and a control apparatus to calculate a relative upper turn table height position and an angle formed between the upper turn table rotational axis and the cylinder longitudinal axis from the horizontal plate surface height positions measured by the displacement sensors. A workpiece holding abnormality can be accurately and quickly detected before machining the workpiece to avoid damage, and an cylinder eccentric angle can be detected during machining.