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Four Quadrants: What Happens Past 90°?
Four Quadrants: What Happens Past 90°?
How do negative coordinates help a robot arm navigate positions in all directions from its base?
Learning Intentions:
Calculate x and y tip coordinates for angles in all four quadrants and interpret negative values as real physical directions, not errors.
Today's Concept:
Set the arm to 120° and calculate x. The answer is negative. That's not a mistake — it means the tip is to the left of the base. Negative doesn't mean wrong; it means a direction.
The formulas x = r·cos(θ) and y = r·sin(θ) still work past 90°. The sign of each coordinate tells you which way the tip has moved: negative x is left of center, negative y is below horizontal. Today, you map those sign patterns across all four quadrants by physically moving the robot, then verify the pattern with calculation. Your user's task might span more than one quadrant. Knowing how to read the signs is how you design for it.
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