**6. Conclusion**

524 Mechanical Engineering

Fig. 16. Generated gear and generating positions of the pinion-cutter with a rounded-tip

Fig. 17. Generated gear and generating positions of the pinion-cutter with symmetric teeth

Fig. 18. Generated gear and generating positions of the pinion-cutter with symmetric teeth

and a fully rounded-tip

and a sharp-tip

In this study, computerized tooth profile generation of involute gears manufactured by rackand pinion-type cutters are studied based on Litvin's vector method. Based on Yang's application mathematical model of rack cutter with asymmetric involute teeth is given. Trochoidal paths of the rack tool tip are investigated. For pinion-type generation Asymmetric involute teeth is adopted to Chang and Tsay's application. The developed computer program provides the investigation of the effect of tool parameters on the generated tool profile before manufactured. Trochoidal paths traced by the generating tool tip are investigated. It has been seen that geometric varieties of the rounded corner of pinion-type cutter determines the position of trochoidal paths relative to the center line of tooth space of the generated gear. Because of the position of the center of the tip rounding, there is a limitation on the geometric varieties of pinion-type cutter tip. Based on the given mathematical models, the simulated motion path of the generating cutters are also investigated. The relative position of the cutter to the workpiece has been illustrated. The simulation of shaper cutting action can be used to determine the chip geometry for further analysis about tool wear and tool life. The mathematical models can be extended to generalized mathematical model of the involute gears including spur and helical beveloid (involute conical) gears.
