The ring with no gap

An unbroken loop has no exit to align. Spend your attention on the objects attached to it. Identify each pin, neighbouring open ring, and clamp that still keeps the loop in the structure.

Release those surrounding constraints one at a time and observe the loop after each change. It should depart only when its connections allow it. Rotating a solid loop repeatedly cannot create an opening.

In a crowded diagram, write down the closed ring’s number first. This gives you a fixed reference while the surrounding pieces disappear.