A Walking Machine

Hi everyone!  Due to an incredibly busy end to the school year and start to the summer, I’ve been MIA, with no new blog posts in a few months.  But I’m back.  This post is inspired by a gif my brother-in-law shared with me from Beautiful Engineering’s Facebook page.  Here it is:


In the comments, someone mentioned that it looked like one leg of a walking machine.

As soon as I saw it, I thought it looked like something I could create in Desmos.  So I did.  Here’s what I ended up with:


My best friends for this project were the Law of Cosines and parametric equations.

In order to trace the curve, I had to write nearly everything in function notation.  If you want to play around with any of the parameters, you can open the folders and try to make sense of it, but if there’s one thing I’m still learning, it’s how to make a Desmos graph that I can look back at later and understand.  For this graph in particular, what makes my work hard to follow is the fact that I wanted to make the yellow segments have variable lengths.  So each of their lengths is L1, L2, L3, etc. There was no good way to denote which length went with which segment, so I did what I could.  Either way, it was a lot of fun to put this together.

By changing some of the lengths of the segments involved, here are some of the other versions I ended up with.  Click the image to go to the graph.