PURPOSE: To improve machining accuracy by obtaining two delayed speed instructions available from a speed instruction delayed with different time constants, and applying one of the two delayed speed instructions to all axes of a machine and a difference of both instructions to a moving axis only with a tracer head shifted as superimposed on the motion of all the axes.

CONSTITUTION: An axis is provided for moving only a tracer head as superimposed on the motion of all axes of a machine, and two delayed speed instructions (Vxm, Vzm) and (Vxb, Vzb) delayed from a speed instruction with a time constant are obtained. Then, one of the instructions, or (Vxm, Vzm) is applied to all the axes of a machine, and a difference (Vxs, Vzs) of the instructions is applied to a moving axis only with the tracer head. As a result, the tracer head advances always ahead of a cutter, and when an axis speed drops due to the collision of the tracer head with a corner part, the advance amount of the tracer head is cancelled correspondingly, or the tracer head relatively returns.