Mathematical description of spatial hob-generating motion for an arbitrary gear tooth profile

The purpose of this study is to develop a new kind of technology for the formation of an arbitrary gear tooth profile. In terms of spatial gear meshing theory, a universal transmission mathematical model for forming an arbitrary gear tooth profile has been constructed based on a standard involute gear hob. The coordinate relationship between an arbitrary point on hob cutting-edge curve and the generated point on workpiece has been deduced in detail. Hereby, an arbitrary gear tooth profile can be generated by means of computer flexible controlling each enveloped position on workpiece, and we do not need to spend so much money again to fabricate a special kind of gear cutting tool while cutting a special shape of gear tooth profile. So, this study has great economic importance, and has established the basis of generating an arbitrary gear tooth profile by means of an ordinary involute gear hob and a CNC (Computer Numerical Control) hobbing machine.