The appts. to join two polymeric monofilaments (2, 4), such as in warping, has them between an anvil (3) and a sonotrode (7) to generate ultrasonic vibrations. The anvil (3) has a hollow cylindrical channel (9) to take the two monofilaments (2, 4). The channel (9) has at least two facing lateral walls (11) or main walls, joined by a base (13). They are inclined to and symmetrical with the centre line (P), to give a concave shape aligned to the sonotrode (7). The two walls (11) hold the first monofilament (2). The sonotrode (7) is cylindrical with a lower surface (19) curved in a concave aligned to the interior of the channel (9). The sonotrode (7) has a disengaged rest position, and a working position to press the second monofilament (4) against the first (2).
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