Gear Layout — Teeth vs Spaces When laying out a gear, should the number of spaces equal the number of teeth (one space between each pair of teeth), or should there be twice as many spaces as teeth as claimed?

Introduction / Context:
In spur, helical, and many other gear types, the pitch circle is divided into equal angular segments corresponding to tooth count Z. Each segment contains one tooth and one space alternating around the circumference. Thus, the total number of spaces equals the total number of teeth.

Given Data / Assumptions:

• Pitch division is 360/Z degrees per tooth (and per space).
• Tooth and space alternate around the pitch circle.
• Standard involute systems maintain uniform spacing.

Concept / Approach:
Geometric layout divides the circle into Z equal parts. Indexing machines and CAD constructions step by the pitch angle to mark tooth flanks. Because each tooth is followed by a space, counts are equal: Z teeth and Z spaces. The claim that spaces are twice the number of teeth is mathematically and geometrically incorrect.

Step-by-Step Solution:
1) Choose tooth count Z.2) Compute pitch angle = 360/Z degrees.3) Index around the pitch circle, marking alternating tooth and space positions.4) Confirm that counts match (Z each).

Verification / Alternative check:
Physical inspection of any standard gear shows alternating teeth and spaces in equal numbers; metrology confirms one space per tooth across the pitch circle.

Why Other Options Are Wrong:
Correct repeats the false claim. Even tooth count and Bevel gear qualifiers are irrelevant. Partially correct still suggests a ratio other than 1:1.

Common Pitfalls:
Confusing addendum/dedendum details with counting logic; misreading CAD polar arrays.

Final Answer:
Incorrect