Reliably mix 3 ingredients for a factory
I took @Fambida and @Paul Z's suggestion to use long inserters, and came up with this:
Should be jam-proof.
Consider making the cogs from iron where they are needed and inserting them directly from one assembler to another.
This way you only need 2 items on the belt, and you completely avoid the difficult issue of feeding your belt with the correct ratios of the 3 items.