The present invention relates to a clamping device having a mounting element with an axis of rotation X, an actuator, a support that has an opening of axis X in which opening the mounting element and the actuator are positioned. The mounting element includes a slide in which there are positioned a ring and a locking wedge which collaborate with at least one angle transmission. The support has an interior groove arranged in the opening and the ring and the locking wedge collaborate with the interior groove. The mounting element can thus easily be angularly positioned. There are preferably two angle transmissions positioned such that they are diametrically opposed.