PURPOSE: To provide a robot track interpolating device which sets and interpolates a track so that the acceleration caused by the shift of a tip part serving as a working point never exceeds a prescribed upper limit level.

CONSTITUTION: A teaching point string data P include plural interpolating points that secure the standard of a track where a tip part of a robot shifts, a shift instruction which designates a track shape based on a teaching point, and the largest path error caused between the track and the teaching point. Then the data P are inputted and an interpolating method selecting means 11 selects one of a straight line interpolation arithmetic means 12, a circular arc interpolation arithmetic means 14 and a parabola interpolation arithmetic means 13. Then the data P are outputted to the selected interpolation arithmetic means, and this means carries out an interpolation arithmetic operation based on the corresponding interpolation method. In this case, it is prevented that the acceleration generated at the tip part of the robot exceeds a prescribed upper limit level.