A security device includes a stop member for a rotary drilling instrument used in particular in dental surgery. The stop member is capable of being positioned at a desired depth of drilling and of preventing the depth from being exceeded. The two elements drilling instrument and the stop member include coupling elements directly or indirectly linking them together and co-operating elements capable of transforming their movement, such that when the device is operating, the drilling instrument is retracted rearwards relative to the drilling direction and to the position of the stop member under the action of the elements when the front part of the stop member comes in contact with a neighboring surface. The co-operating elements preferably consist of a screw-nut system, the direction of the thread(s) of the system and the rotating direction of the drill being opposite. A device comprising a gauge containing a piston enables to pre-calibrate and store the desired drilling depth.
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