This multi-axis pivoting head of a machine tool, of the type comprising a fork block (2) mounted pivoting around a first axis C, a support shaft (12) mounted rotating around a second axis B in the fork block (2), first means (3) for driving the fork block in rotation (2) around said first axis C, second means (18-20) for driving in rotation of said support shaft (12) around said second axis B, and two pins (30, 40) mounted on said support shaft (12) and axis (aa, bb) orthogonal to said second axis B, the pins (30, 40) being mounted offset on the shaft -support (12) so that its axis (aa, bb) is distant from said second axis B.
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