A cutting head comprising: • a hollow cylindrical core having a longitudinal axis (X-X') and a bottom end; • a helical flight being mounted on an outside face of the hollow cylindrical core; • a threading tooth presenting an extended position in which the threading tooth projects outside a volume defined by the periphery of the flight and a retracted position in which the threading tooth is disposed inside said volume; • displacement means for displacing said threading tooth between said retracted position and said extended position, said displacement means comprising: • an inner hollow tubular member mounted to move into said hollow cylindrical core in translation along said longitudinal axis and disposed at least at the bottom end of said hollow cylindrical core; • control means for causing said threading tooth to be displaced between said retracted position and said extended position in response to the translation of the inner hollow tubular member relative to at least the bottom end of said hollow cylindrical core; the cutting head being characterized in that the control means comprises: • a rack fixed to the inner hollow tubular member, • at least a gear cooperating with the rack, said gear being mounted on the bottom end of the hollow cylindrical core, • a lever connected to the gear; • a connecting rod pivotally connected to the lever and to the threading tooth, whereby the translation of the rack causes the displacement of the threading tooth. • a hollow cylindrical core having a longitudinal axis (X-X') and a bottom end; • a helical flight being mounted on an outside face of the hollow cylindrical core; • a threading tooth presenting an extended position in which the threading tooth projects outside a volume defined by the periphery of the flight and a retracted position in which the threading tooth is disposed inside said volume; • displacement means for displacing said threading tooth between said retracted position and said extended position, said displacement means comprising: • an inner hollow tubular member mounted to move into said hollow cylindrical core in translation along said longitudinal axis and disposed at least at the bottom end of said hollow cylindrical core; • control means for causing said threading tooth to be displaced between said retracted position and said extended position in response to the translation of the inner hollow tubular member relative to at least the bottom end of said hollow cylindrical core; • an inner hollow tubular member mounted to move into said hollow cylindrical core in translation along said longitudinal axis and disposed at least at the bottom end of said hollow cylindrical core; • control means for causing said threading tooth to be displaced between said retracted position and said extended position in response to the translation of the inner hollow tubular member relative to at least the bottom end of said hollow cylindrical core; • a rack fixed to the inner hollow tubular member, • at least a gear cooperating with the rack, said gear being mounted on the bottom end of the hollow cylindrical core, • a lever connected to the gear; • a connecting rod pivotally connected to the lever and to the threading tooth, whereby the translation of the rack causes the displacement of the threading tooth.