Helical Springs: Identify the correct combined statement about form, pitch, and angle of helix

Introduction:
This question tests core terminology for helical springs: the geometric form, the concept of pitch, and the angle of helix. Understanding these basics is essential for analyzing stiffness, energy storage, and stress distribution in springs used in machines and structures.

Given Data / Assumptions:

• Standard mechanical design definitions are used.
• “Close-coil” means adjacent turns are nearly touching (small pitch).
• “Open-coil” means turns are more widely spaced (larger pitch and helix angle).

Concept / Approach:
A helical spring is produced by winding a wire into a helix. Pitch is the axial distance between corresponding points on adjacent coils. The angle of helix is the angle between the helical wire path and a plane perpendicular (or parallel, by consistent convention) to the spring axis; practically, a “larger” helix angle corresponds to more open spacing and different load-deflection behavior.

Step-by-Step Solution:
Step 1: Definition—wound wire in spiral form is a helical spring (correct).Step 2: Close-coil springs have very small pitch; turns are nearly contiguous (correct).Step 3: The coil’s incline relative to a reference plane is the angle of helix (terminology point, correct).Step 4: Open-coil springs have a comparatively large helix angle (correct).Step 5: Since all are correct, select the comprehensive option.

Verification / Alternative check:
Mechanical design texts present the same definitions and note that open-coil behavior differs (torsion + bending) due to larger helix angle.

Why Other Options Are Wrong:
a–d: Each is correct in isolation but not complete; the best answer is the combined choice.e: Correct because it aggregates a–d.

Common Pitfalls:
Confusing pitch with wire diameter; assuming close-coil and open-coil formulas are interchangeable; mixing up reference planes for helix angle but keeping the concept consistent.

Final Answer:
All the above.