How to make procedural animations for spider-like character?

This is what my character looks like:
image
I want to add (completely) procedural animations to it, but I struggled to find a tutorial. The closest thing I could find was Epic’s FBIK Procedural Dragon Animations video, but there were excessive functions and variables, and a lot of code (variables too) was hidden.

What’s the easiest and possibly cleanest way to implement a procedural animation system for my character?