I don't have Illustrator, so I used Affinity Designer for this project. Drawing the gears in that program was easy, but as far as I can determine Affinity Designer has nothing like the Transparency window for dealing with the grunge texture. After many experiments, I finally just applied the texture to the background, and arranged for it to show through on the gears by choosing suitable layer blending modes.

In this version the background is very dark grey, the texture is black, the blending mode for the red gear is Vivid Light, and the blending mode for all the grey gears is Colour Dodge.

I created a second colour way simply by changing the background colour to dark red. Without changing anything else, all the circles turned various shade of red.

Finally I created three different gears, filled them with corroded metal textures, and made them look a bit three dimensional.

Thank you, Helen, for a fun class. Changing the rotation centre so many times was good practice.