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Rolling Out a Straight Line

Mobile Science Museum · Mathematics

Operation: Turn the handwheel and observe the movement path of the little panda. Function Overview: The exhibit consists of a large disc, a small disc, a bear model, and an operating handwheel. When the handwheel is turned, the small disc rolls inside the large disc, and the little bear on the small disc surprisingly moves back and forth in a straight line. Scientific Principle: Why is this? On a plane, when a moving circle rolls along the inside of a fixed circle, the path of a point on this circle is called a hypocycloid. If the radius of the moving circle is exactly half the radius of the fixed circle, the path of any point on the circumference of the moving circle is a straight line. In the exhibit, the diameter of the small disc is exactly half the diameter of the large disc, and the little bear is located exactly on the circumference of the small disc, so its movement path is a straight line. In machining, the reciprocating linear motion of the blade on a planer utilizes this property of the hypocycloid.

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