Understanding Gear Tooth Geometry: Identifying the Fillet Radius

Gears are fundamental components in many mechanical systems, used to transmit power and motion. Each tooth on a gear has specific features defined by various circles and curves. Understanding these features is key to understanding gear design and operation.

Let's look at the question: "The radius that connects the root circle to the profile of the tooth is known as ________." This is asking about a specific curved part at the base of the gear tooth.

Analyzing the Options

We need to identify which term correctly describes the radius connecting the root circle and the tooth profile (also known as the flank).

• arc of approach: This term relates to the path traced by the contact point between two mating gear teeth from the start of contact until the pitch point. It is part of the path of contact, not a physical radius on a single tooth.
• fillet radius: The root circle is the circle tangent to the bottom of the tooth spaces. The tooth profile is the working surface of the tooth (usually an involute curve). The region where the tooth profile meets the root circle is typically rounded to reduce stress concentration. This rounded corner is called the root fillet, and its curvature is defined by the fillet radius. This description perfectly matches what the question is asking.
• profile: The profile refers to the shape of the working surface of the tooth flank, usually an involute curve or cycloidal curve. It is the shape itself, not a radius connecting different parts.
• pitch radius: The pitch circle is a theoretical circle on which mating gears are considered to roll without slipping. The pitch radius is the radius of this pitch circle. It is an important reference circle but does not describe the radius connecting the root circle to the tooth profile.

The Correct Term

Based on the definitions, the radius that creates the smooth transition between the root circle and the tooth profile is the fillet radius. This radius is crucial for the strength of the gear tooth as it helps distribute stress at the root.

Therefore, the radius connecting the root circle to the profile of the tooth is known as the fillet radius.