It's just very difficult to place cogs down when moving along the grid :(
You have to click in place, do not drag where you want.
Stacking the pillars all the way to the ceiling soft locks it, and sometimes you can place invalid cogs when moving around when placing cogs. As well sometimes they feel like they should connect but don't. Also syncing the animation between all the cogs would be really nice.
But also for anyone who placed an out of reach pillar, you can remove pillars above large cogs if you move back far enough.