Abstract: The cuff (25) for connecting a tube (26) to two pipes (2) or two equipments together includes, at each end, a knuckle joint mechanism (31) bearing on a clamp (3) integral with the pipe (2) and which forces the end of the tube (26) against the mouth (4). The knuckle joint (31) is two pairs of rods (32, 35), whose interference produces a compressive stress on spring washers (37). The fixing force is consequently applied in simple and reliable manner and can be interrupted just as easily. The bearing surfaces of the connecting parts and the tube (26, 30, 43) with respect to one another, on the clamp (3) and the mouth (4) must be spherical and concentric in order to enable the pipes (2) to be angularly displaced by a few degrees relative to the tube (26).