Abstract: The invention contemplates an articulating head having bearings of reproducible travel behavior, for precision angular displacment of a mounted probe-pin, about each of two orthogonal component axes of rotation. The precision of angular displacement relies upon high-resolution angle encoders for reading the instantaneous angle for each of these component axes of rotation and for reporting the same to the computer of a coordinate-measuring machine. Active position-control circuits use the angle encoders for controlling drive about the respective component axes of rotation, all in conjunction with a given program of measurements by the coordinate-measuring machine. A probe holder mounted to the articulating head can be oriented to any desired angular aspect with respect to the workpiece feature to be measured or scanned, and measurements can be made solely by controleld actuation via one or both drives on the respective axes of the articulating head, i.e.