Hypocyclic Mechanism

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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).


Contributed by: Erik Mahieu (October 2016)
Open content licensed under CC BY-NC-SA



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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