This paper presents a simple and direct approach to the problem of the definition of the root profile for standard and nonstandard external spur gear teeth. Equations are developed for the location of the tooth center-line intercept at the constant-stress parabola. Also, the expression for the location of the point of tangency of the parabola with the root trochoid is given as well as the derivative of this expression. The AGMA Standards present charts of geometry factors, but the method by which these factors were determined is graphical and in some instances is not sufficiently accurate nor convenient to use. Although other investigators have considered this problem, their methods are either graphical or very complicated analytically. This treatment of the problem has been developed because it is not available in the open literature. Tables and charts are given for both Y and J factors for many profile variations.

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