The key distinguishing detail is the rolling surface: hypocycloid and epicycloid both involve one circle rolling on another circle (inside or outside), while cycloid specifically means rolling along a straight line, exactly as the question describes.
Trochoid is a broader umbrella term for curves traced by any point rigidly attached to a rolling circle, including points off the circumference, so cycloid is the more precise, specific name for a point exactly on the circumference rolling on a straight line.
Therefore, the correct answer is Cycloid.
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Approach Solution -2
Thinking of a concrete real-world example for each term also confirms the answer.
Hypocycloid: Seen in mechanisms like the Spirograph pattern traced inside a fixed ring, a circle-inside-circle motion.
Epicycloid: Seen in gear-tooth profile design where a circle rolls around the outside of another circle.
Cycloid: Seen classically in the path traced by a reflector mounted on a bicycle wheel as the wheel rolls along a straight road, the textbook example of this exact curve.
Trochoid: Seen in the more general path of any fixed point on a rolling wheel, such as a point inside the wheel's rim, not necessarily on the tread itself.
The bicycle-wheel-on-a-straight-road example is the standard illustration of a cycloid, matching the question precisely.