Gear–tooth terminology: What is the radial distance measured from the pitch circle down to the bottom (root) of the tooth space in standard spur or helical gears?

Given data

• A standard gear terminology question asks for the name of the radial distance measured from the pitch circle to the bottom of the tooth space (the root or bottom land).

Concept / Approach
Addendum: radial distance from the pitch circle to the tooth tip (top land).Dedendum: radial distance from the pitch circle to the tooth root (bottom land).Working depth: sum of the addenda of the two mating gears that are actually in contact during meshing.Clearance: the difference between dedendum and the mating gear addendum; provides a small gap so that the tip of one gear does not rub the bottom land of its mate.Total depth: sum of addendum and dedendum of the same gear (full tooth height measured radially).

Step-by-step reasoning
Step 1: Identify what is being measured. The problem explicitly says from the pitch circle down to the bottom of the tooth space. This is a downward radial measure from the pitch circle toward the gear center.Step 2: Map this description to formal terms. Downward from pitch circle to root is not the addendum, because addendum is upward to the tip. It is not working depth, because working depth involves two mating gears and represents engaged height. It is not clearance, which is a small allowance between mating tip and root. It is not total depth, which is addendum plus dedendum of one gear. The only term matching the exact description is the dedendum.Step 3: Confirm using standard definitions. Standard machine design texts define dedendum as the radial distance between the pitch circle and the root circle. That matches the statement precisely.

Verification / Alternative view
Visualize two concentric circles on a gear: the larger is the addendum circle passing through the tooth tips, the intermediate pitch circle is the reference circle for rolling contact, and the smaller root circle passes through the bottoms of the spaces. The distance from the pitch circle to the root circle is the dedendum. The distance from the pitch circle to the addendum circle is the addendum. Their sum is the total depth.

Common pitfalls
Confusing addendum and dedendum due to both being measured from the pitch circle but in opposite directions.Selecting working depth because it sounds like a radial height; however, working depth is a two-gear engagement quantity, not the single gear radial distance to the root.Choosing clearance because it is also associated with the bottom land; clearance is a small difference between dedendum and mating addendum, not the entire radial span from pitch to root.

Why the other options are incorrect
Addendum: measures upward from pitch circle to the tip, not downward to the root.Clearance: a small allowance between the tip of one gear and the bottom land of the other, not a full radial distance from pitch circle.Working depth: equals the sum of addenda of the two mating gears in contact; it is not a single gear radial dimension to the bottom land.Total depth: equals addendum plus dedendum for one gear; this is larger than the dedendum and does not match the problem statement.

Final Answer
Dedendum