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Goemetric shape of the rotary housing in a engine called?

The geometric shape of the rotary housing in a rotary engine is called an epitrochoid.

Here's why:

* Rotary engine: This refers to a type of internal combustion engine where the combustion chamber is formed by a rotating element (the rotor) within a stationary housing. The most famous example is the Wankel engine.

* Epitrochoid: This is a mathematical curve traced by a point on a circle rolling around the outside of another circle. This curve defines the shape of the rotary housing in a Wankel engine. The rotor itself is an hypocycloid, another mathematical curve generated by a point on a circle rolling inside another circle.

The unique shape of the epitrochoid housing allows for the complex movement of the rotor and the creation of a combustion chamber that changes volume during the engine cycle.