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Arc Length: How far does the tip travel?
Arc Length: How far does the tip travel?
How can we calculate the exact distance a robot arm tip travels to plan precise motion for a user's task?
Learning Intentions:
Verify the arc length formula s = rθ by measuring a physical arc with string and comparing it to the calculated result.
Today's Concept:
When a robot arm sweeps 90°, the tip doesn't travel 90 centimeters. It travels a curved path — an arc — whose length depends on both the angle and the arm's length. The formula s = rθ calculates that distance, but only when θ is in radians.
Today, you measure the arc with a string first, before using the formula. The string measurement and the formula should agree within 1–2 cm. If they don't, you'll investigate why. That gap between predicted and actual is one of the most important things an engineer can learn to read.
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Arc Length
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