The goal is to obtain optimal fillet curve for minimum bending stress using parameterized geometry models.The boundary shape for fillet curve is described by generalized elliptic function.Thus it becomes very easy to describe and obtain optimal fillet curve just making use of the optimization module provided in a commercial finite element package due to the less number of design variables.The gear model is founded by ANSYS

and adopting first step optimization in ANSYS optimize the maximum Von Mises stress of tooth root.As compared to the known solutions in the literature

it was shown that extremely good results could be obtained while using the proposed parameterized equations.