THE EFFECTIVE UTILIZATION OF FIVE-AXIS MACHINING CENTERS, IN THE CONTEXT OF FLEXIBLE AUTOMATION, MAY BE ACCOMPLISHED THROUGH THE USE OF A RULE-DRIVEN KNOWLEDGE- BASED SYSTEM FOR DESIGN FOR MANUFACTURE. ONE GEOMETRICAL PROBLEM, CHARACTERISTIC TO THIS CLASS OF COMPUTER-CONTROLLED MACHINES, MAY BE ADDRESSED THROUGH FIVE-AXIS GEOMETRICAL INTERPOLATIONS. THE PROBLEM ARISES WHILE THE TOOL IS SWEEPING THROUGH CORNERS DURING SIDE MILLING, OR ROLLING OVER EDGES DURING FACE MILLING. THE NATURE OF THE PROBLEM IS DESCRIBED AND AN ALGORITHMIC APPROACH TO ITS SOLUTION IS OUTLINED. THE OVERALL IMPLEMENTATION OF THE KNOWLEDGE-BASED SYSTEM AND COMPUTER HARDWARE ON WHICH IT IS IMPLEMENTED ARE DESCRIBED.