Here's a first pass on comments. If you could work on these changes, I'll come back with some more comments in a second round.
First off, I'd put a mouse over on the word "tangent" or something else to help explain that last requirement. It's a bit vague and confusing.
Under your last sentence, is there a way to have a picture of each of the things you've just mentioned? It would be good to have an example of with a point on the inside and then on the outside.
Under hypocycloid, you don't say what a and b are... so I'm pretty confused by what's going on there. Also, remember to have links by each of the animations that you didn't personally create.
Under involute, I'm not clear on what you mean by "pole" Could you put in a separate sentence explaining that?
When you say the word catenary, you should link to that page :)
Tyler Sammann RPI 7/5/11
Any chance that some of this material could be related to the toy "spirograph".
Here's a link http://en.wikipedia.org/wiki/Spirograph