A method is proposed for planning an optimal machining sequence on automatic NC programming for turning. The method can determine a machining sequence which needs the least cutting time. In a process to determine the sequence, suitability of cutting conditions as well as interference between a tool and a workpiece is checked. A planning problem is represented as a graph based on the concept of "cycle". In the graph, an optimal transition is found among sets consisting of machining processes. And an algorithm is proposed to solve the problem applying the dynamic programming of optimality. Numerical evaluation of the algorithm shows that it needs less calculating cost than exhaustive search and Dijkstra's algorithm to determine an optimal machining sequence. Machining sequences determined by the algorithm are compared with those determined by a skilled worker. As a result, machining sequences determined by the algorithm always had less or equal cutting time than those determined by a skilled worker.
