Paper Title
An Alternative Method to Specify Undercut Point of Involute Spur Gear with Low Number Teeth

Nowadays, the lightweight design concept is becoming more popular. In parallel with, Involute spur gears with a low number of teeth are used in small and precise mechanisms increasingly. However; Undercutting, which is undesirable matter, occurs for this type involute spur gears since it reduces strength and active profile of gear tooth. For this reason, starting of undercut has to be determined for high accurate contact stress and FEM calculations. In this study, an alternate method is presented to obtain undercut point. Essentially undercut point is the intersection point of involute and trochoid curves of the gear tooth. To obtain intersection point, the mathematical equations of rack cutter is derived. After that, the points of the involute and trochoid curve are obtained by using coordinate transformation, differential geometry, and gearing theory. Lines could represent part of a curve if it is divided a great number of points. Based on this; the lines are generated between points from involute and trochoid areas. Finally, these lines are checked if any intersection exists or not between them. A MATLAB program is generated for specifying coordinates of undercut point. Proposed approach is validated with different methods from previous studies. Keywords- Involute spur gear, Undercutting, Undercut point