Planetary Gear Train

This Demonstration simulates a planetary gear train with cycloidal gears. A typical planetary gear train has three components: the ring gear, the Sun gear, and the planet carrier connecting the two together.
You can see a wide range of reductions by holding stationary any one of these components and using the remaining ones as inputs and outputs.


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For the gears to mesh, they need to have the same pitch. For cycloidal gears, this means that the radius has to be proportional to the number of teeth.
For the Sun and planet gears to fit within the ring gear, these geometric constraints are needed: , .
For the angular speeds of the gears to match, the following kinematic constraints are needed: and .
There are thus four equations in eight variables. In this Demonstration, and are inputs, and the system has two degrees of freedom. These are the combinations that you can choose:
1. Lock the ring gear and drive the Sun gear ().
2. Lock the Sun gear and drive the planet carrier ().
3. Lock the planet carrier and drive the ring gear ().
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