How to go about filling the gaps between segmented objects connected with hinge joints?

Hey everyone, I am making a palm tree that needs to react to physics. Here, I've rigged it like so, and an average use case for it would look something like this.

Not great, since you can see the clipping/gaps between the individual segments. What would be a good way to tackle that issue? I thought about setting each segment's vertices to the position of the adjacent vertices that belong to its parent, but that doesn't seem all that performant for how many leaves the player might be moving at once.

Any help you can give would be greatly appreciated!