I did zero math! It’s all about good software. I use Stella, Sketchup, and Inkscape. I rely on guides a great deal to keep things aligned, and I use clones to make multiple copies of parts. Using clones lets me make changes to the design later on that will carry through to the final design (things like slot thickness etc).
Good software is key. Stella is great for exploring and designing shapes. Sketchup or something other 3D model software lets you scale and simulate the design with scale material thicknesses, then it’s all vector editing after that.
Further reading: