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📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 9: A robotic arm in a factory applies sealant along a seams that follow a helical path with 4 full turns over 2 meters of linear travel. If the arm moves at 0.5 meters per second, how many seconds does it take to complete the entire sealant application, including travel distance and path elongation due to helicity?

📌 First, linear distance = 2 m.

📌 Helical turns: 4 over 2 m → pitch = 0.5 m per turn.

📌 Length of one helical turn: circumference endpoint distance = \( \sqrt{(2\pi r)^2 + \text{pitch}^2} \), but radius not given.

📌 Wait — underdetermined.

📌 Alternative: if we assume the pitch is 0.5 m per turn along a surface, and no radius specified, but in such problems, often the helix length per turn is approximated or:

📌 But absence of radius, perhaps assume unit radius? Not stated.

📌 Better: in robotics, for a helical path with step-by-step, the total path length ≈ \( \sqrt{(\text{linear})^2 + (\text{total circumferential distance})^2} \)

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