A coordinate measuring device (10) comprises a housing (12) rotatively supported on a base (11) and mounting a vertical pillar (13) along which rides a carriage (14) engaged by a horizontally translating arm (15). A turret (18, 19) at each end of the aim houses a rotating body (20, 21) connected to a probe (22, 23). The rotation of the base, the vertical movement of the carriage, the horizontal movement of the arm and the rotation of the probes are driven by motors (27, 28, 29, 30) in the housing. The rotation of the motors are transmitted by a cable and pulley assembly to the arm and carriage. The cable (43) controlling the transversal movement of the arm has its opposite ends attached to the opposite extremity (16, 17) of the arm, and is run respectively up and down the portion of the pillar above and below the carriage in order to maintain constant lengths and tension of the cables as the carriage moves up and down the pillar. The rotation of the probes and that of the base are coordinated to keep the probes at a constant angle in relation to the measured surface.