What is the concave portion of the tooth profile at the bottom of the tooth called?

The correct answer is the fillet curves. In the context of gear tooth design or other similar mechanical components, the fillet curves refer to the smooth contours connecting the root of the tooth to the base of the tooth profile. This area helps to reduce stress concentrations and can improve the fatigue strength of the gear or mechanical part by allowing for a gradual transition rather than a sharp corner.

The fillet curves assist in ensuring smoother operation as they minimize the risk of failure due to stress concentrations that might occur at sharper angles. They also play a crucial role in the manufacturing process, as a well-designed fillet can contribute to easier milling or casting of the gears.

In contrast, the root circle specifies the diameter of the circle at the bottom of the tooth profile, while the terms "fillet radius" and "fillet" typically refer to general rounding practices in engineering but do not specifically define the concave profile at the tooth's root. Understanding these definitions allows designers to make informed decisions about the design and functionality of toothed elements in machinery.