Primary unbalanced force — the primary inertia force of a reciprocating mass attains its maximum value when the crank angle with the line of stroke is at which positions?

Introduction / Context: The primary unbalanced force in a reciprocating mechanism varies sinusoidally with crank angle. Recognizing where it peaks is important for balancing strategies and bearing load estimation.

Given Data / Assumptions:

• Primary force F_p=m r ω² cos θ (first harmonic).
• θ is the angle between crank and line of stroke.
• Constant speed ω.

Concept / Approach: The magnitude of F_p is maximum when |cos θ|=1 and minimum when cos θ=0. Therefore, maxima occur at θ=0° and 180° (along the line of stroke), not at quadrature.

Step-by-Step Solution:

Verification / Alternative check: A plot of F_p against θ shows peaks at 0° and 180° and zeros at 90° and 270°.

Why Other Options Are Wrong:
0° and 90° — includes one maximum and one zero.
90° and 180° — includes a zero and a maximum.
180° and 360° — 360°≡0°, duplicates same position but omits the other distinct maximum at 180°.

Common Pitfalls: Mixing primary and secondary components; forgetting that the cosine term peaks on the line of stroke.

Final Answer: 0° and 180°.