A coordinate positioning machine comprises a fixed structure including a table and a supporting frame, rigidly connected together. A movable arm is suspended from the frame by means of three powered telescopic struts, each of which is universally pivotally connected to both the arm and the frame. As a consequence, the movable arm is able to move with three rotational degrees of freedom. Movement of the arm with each of these degrees of freedom is constrained by a passive device, connected to the arm and the fixed structure, and which eliminates all rotational movement of the arm, while simultaneously permitting translation thereof.