In rating the bending strength of the hobbed gear teeth, the critical point located within the root fillet, where the fracture
occurs due to the tensile bending stress, is necessary to be determined. Hofer, Lewis, Niemann, and Colbourme propose
their methods to find this point approximately, in which a numerical iteration method is needed to solve nonlinear
one-variable equations established to find their critical points. This paper presents equations expressed easily and in a
similar way for finding these four critical points as well as the general gear tooth profile equations derived based on the
vector analysis method. These equations are assuredly solved by the finite difference Newton- -Raphson iteration
algorithm. Position comparison of their points was achieved with computer- aided graphical and numerical output.