的绳子

…'s rope

→ 的
phrase Rare #23,853
…'s rope 的 links 绳子 to a preceding description or possessor; the full meaning depends on what comes before 的.
CH: 他拿起桌上的绳子。
EN: He picked up the rope on the table.

是想让他们的绳子更滑吗?

Are you trying to make their rope smoother?

我把婆婆他们的绳子割断了

I cut the rope belonging to my mother-in-law and the others.

— 天空之城 (1986)

死者脖子上的绳子打了很紧的结

The rope around the dead person's neck was tied in a very tight knot.

— 杀人回忆 (2003)

在尸体旁边有一条很滑稽的绳子

There is a very comical rope next to the corpse.

— 罗生门 (1950)

快去拿准备好的绳子

Quick, go get the rope we prepared.

— 风之谷 (1984)