A coordinate positioning machine comprises a fixed structure including a table and a supporting frame (314), rigidly connected together. A moveable arm (310) is suspended from the frame by means of three powered telescopic struts (316), each of which is universally pivotally connected to both the arm and the frame. As a consequence the moveable 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 (340), connected to the arm and the fixed structure, and which eliminates all rotational movement of the arm, while simultaneously permitting translation thereof.