In the field of cutting processes, the current trend is to produce more and more in the shortest time. A solution to this consists of shortening the total machining time by increasing the motion speeds of the tool supply systems that equip the machining centers, thus minimizing the idle time needed for replacing the tools during the machining process. Actual idle times needed for replacing the tools through the supply systems are high, especially for machining housing type work pieces on boring and milling machining centres. With the help of the method being proposed through this work, the motion times of the moving elements in the structure of the tool supply systems can be decreased, by following up, at the same time, their dynamic behavior.