PURPOSE: To detect a sharply changing part on the surface of a model in advance of a stylus by providing a position control means for placing a length measuring device and a means to control the feeding speed of a tracer head in accordance with the result of the measured length by said length measuring device, in the proceeding direction of said tracer head.

CONSTITUTION: A length measuring device 2 is placed at a certain length apart from axis of a tracer head 1, in the proceeding direction of the head 1, and measures the distance up to the surface of a model in advance of the head 1. A case body 5 holding the length measuring device 2 and a motor 6 is held on the outer peripheral part of the head 1, rotatably around its axis. Data of measured length from the length measuring device 2 is read in a CPU20 through an A-D convertion circuit 23 and a system bus 21 at a certain period, processed there, and stored in a memory 22. When the CPU20 detects from the data of measured length that the steepness on the model surface is above a certain level, it commands that a remaining part decelerate the copying speed through the system bus 21.