A method of positioning a tool along a circular arc. The tool is carried by an automaton which is moved through a teaching phase during which it is taught coordinates and wrist orientation angles for three reference points. The method then proceeds into a work phase in which calculations are performed to determine coordinates and wrist angles for a series of work points spaced along the circular arc defined by the three reference points. Thereafter the automaton is direction to position the tool at the calculated coordinates and orientations.