I was trying to model an epicycloid for my math assignment but none of the parametric equations I found ended up helping me model it on desmos.
One of the more prominent equations I found on the internet was the following:
$$ x=(a+b)\cos \theta -R\cos \theta \left(\frac{a+b}{5}\theta\right) $$ and $$ y=(a+b)\sin \theta -R\sin\theta \left(\frac{a+b}{5}\theta\right) $$
However, when I input these functions and substitute $a=16m, b = 2m, R = 8m$
it should give me something like this Prolate epicycloid.
My math assignment revolves around modeling a fountain to trace that shape from a bird's eye view perspective. I must find out the velocity which the fountain must trace at to clearly see the shape while it is in motion.
However, since the prolate epicycloid isn't a function, it cannot be integrated to find the velocity, so if there are some other methods that can be used please let me know, regardless of how complex they are.
If modeling the following shape can be done another way to make it easier, then please let me know as well.