Down below is my thought about how "the X of Y" can be used. Can you help me check if my understanding is grammatically correct? I think this post might help other learners.
The structure "the X of Y" usually implies that Y has only one X.
The heart of a human body
The engine of a car
The cushion of the armchair
But in my opinion, sometimes, according to the context, "the X of Y" can mean the special X that Y has.
A: Now, the enemies are coming and they are too strong.
B: We have a weapon that can defeat them. Look, this is the weapon of our army.
This suggests the weapon is special and does not mean it is the only weapon.
A: I found that one of the legs of the new table is problematic. Here, this is the leg of the table.
This suggests the leg is special (or has some special quality) and does not mean it is the only table leg.