Involute gear geometry — the centre distance between two meshing involute gears is equal to which quantity?

Introduction / Context: The centre distance between two gears determines correct meshing, backlash, and pressure angle at the operating pitch point. For standard involute gears without intentional center-distance modification, a simple geometric relationship applies.

Given Data / Assumptions:

• Standard involute spur gears in mesh.
• Pitch diameters d₁ and d₂; pitch radii r₁=d₁/2 and r₂=d₂/2.
• No profile shift or intentional center-distance alteration.

Concept / Approach: For involute gears, the theoretical pitch circles roll without slip at the pitch point. The distance between gear centers equals the sum of their pitch radii: r₁ + r₂ = (d₁ + d₂)/2. This remains the reference even when working pressure angle differs slightly due to manufacturing tolerances or minor adjustments.

Step-by-Step Solution:

Verification / Alternative check: Using module m and teeth numbers z₁, z₂, the nominal distance is C = m(z₁ + z₂)/2, consistent with the pitch-diameter relation.

Why Other Options Are Wrong:
sum of base radii — base circles define involute generation, not center distance.
half the sum of addendum diameters — addendum circles are outside the pitch circles and do not set centers.
difference between pitch radii — would only apply to external-internal gear pairs for clearance checks, not two external gears.
geometric mean — no such standard relation.

Common Pitfalls: Mixing base circle parameters with center-distance calculations; overlooking module-teeth relation C=m(z₁+z₂)/2.

Final Answer: the sum of the pitch radii (i.e., (d₁ + d₂)/2).