The invention relates to an articulated-arm three-dimensional measurement apparatus having a plurality of articulation axes with angle encoders integrated in said arms for individually measuring the angles of rotation about each of said articulation axes. In accordance with the invention, at least one of the arms (4; 5) of the apparatus (1) includes a hollow tube (4.11; 5.11) interposed between two arm segments, one of which receives an angle
encoder measuring the
angle of rotation about the longitudinal axis of said arm, said hollow tube presenting at each of its ends respective
abutment configurations complementary to
abutment configurations at the adjacent arm segment ends so as to ensure alignment on the axis of the arm that is accurate, stable, and repeatable independently of the clamping of the abutting ends in question one against the other,
coupling between said hollow tube and said arm segment being provided at said abutting ends by demountable clamping means (10) enabling the hollow tube to be replaced on site by another hollow tube of different length without it being necessary to recalibrate the entire apparatus.