In mechanical design terminology for standard spur or helical gears, what is the precise radial distance measured from the pitch circle down to the bottom (root) of the tooth space (i.e., the depth below the pitch line)?

Introduction / Context

In gear engineering, clear definitions of tooth proportions ensure correct meshing, strength, and manufacturability. One commonly confused pair of terms is addendum and dedendum. This question tests recognition of the radial distance below the pitch circle that reaches the root of the tooth space in standard spur or helical gears.

Given Data / Assumptions

• Standard involute spur or helical gear terminology applies.
• Pitch circle is the reference circle for speed ratios and conjugate action.
• Root (bottom land) is the lowest point of the tooth space.

Concept / Approach

The pitch circle divides the tooth into two radial portions: above it, the addendum; below it, the dedendum. The dedendum must be greater than the addendum by a small clearance to prevent tip interference of the mating gear.

Step-by-Step Solution

Verification / Alternative check

Standard proportions (for many systems) use addendum ≈ one module and dedendum ≈ addendum + clearance. Thus, the below-pitch portion is the dedendum.

Why Other Options Are Wrong

• Addendum: distance from pitch circle to tooth tip (outside), not to the root.
• Clearance: the extra difference between dedendum of one gear and addendum of its mate, not a full radial depth below pitch.
• Working depth: sum of the two addenda of meshing gears, measured within the engaged region, not a single gear's below-pitch depth.
• Total depth: addendum + dedendum of the same gear; a larger measure than either alone.

Common Pitfalls

• Mixing up addendum and dedendum by focusing on the wrong side of the pitch circle.
• Confusing clearance with dedendum due to both being below the pitch circle.

Final Answer

Dedendum