Go find and speak to Arniel Gane , who will ask for help with a special project of his. He’ll want you to go and bring him TEN Dwemer Cog’s , but he WON’T tell you what he’s going to use them for…
I swear we’re too nice. Ok, Dwemer Cogs are, of course, fairly common in any Dwemer ruins. Personally, I went and fast-traveled to Mzulft (southeast of Windhelm, you have to go through it to complete the college’s questline) and got all ten there. You can get 3-4 from a storage building before you even enter Mzulft proper, then you just need to search Mzulft high and low until you have ten of these. They are often behind locked doors and can be found on the corpses of spiders and guardian spheres.
There are also cogs in the Dwemer Museum in Markarth (you’d need to steal them ). If you don’t quite have ten, go find another Dwemer Ruin (there are a lot in the mountains west of Windhelm) and make it happen.
Return to Arniel and give him the cogs. He’ll be quite happy and will give you 750 Gold as a reward.