Cycloids

[crabbass]

I have asked this before, but with newer software versions available I again would like to know...
How do you sketch a cycloid?
I'm no math major, but my understanding is this shape is a generated curve,(like the old toy with gears called spirograph)
to create an external cycloid (hypocycloid) a circle would trace a point while rotating around another circle
to create an internal cycloid (epicycloid) a circle would trace a point while rotating along the ID of another circle.
I see alot of examples of 3-d modeling software drawings with cycloidad gears and wankel style rotary engines.
I believe this is a parametric function, can an cycloid be plotted with a closed spline? What is the difference in a parametric spline and a Nurbs spline?
What kind of spline is Inventor drawing in sketch mode?

thanks for any info.

[mcphill]

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