Hypocyclic Mechanism

This Demonstration simulates a mechanism used to convert rotary motion into rectilinear motion.
A planet gear rolls inside a static ring tracing an epicyclic trajectory. The trajectory reduces to a straight line when the planet (green) is half the diameter of the ring (red).


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The parametric equation of the hypocycloid formed by rolling a circle of radius inside a circle of radius is:
With and , the right-hand side becomes , which is the parametric equation of a line segment between the points and .


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