Puzzletober 2026: Contraption

 The door opens to what at first appears to be an ordinary storeroom. The only other hole in the room is a grate in the ceiling which does not move when rattled. Along the back wall is a panel with several pegs. A box on the floor contains gears which could fit into the pegs. Two gears are already stuck in the panel: one is a wheel with 26 spokes, and the other is directly connected to the grate but has too much friction. Felix suggests that may have to assemble a contraption to slide the grate open.

Rules: Add circles which rest completely within the grid. All circles should be centered on gridpoints and have integer radii. No circles may overlap, but all circles must be tangent to each other in a chain which connects the given partially shown circles.