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I'm working on a very low poly model (Minecraft style) for a game, I've rigged it by parent with empty groups, then manually assigning bones to groups. I want to have bend in the arm, but when I do so the joint "pinches" Example Notice how the elbow isn't as thick as the rest of the arm. How can I fix this?

Blend file

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It is the way vertices are deformed to obtain a smooth transition angle between the two parts of arm. If you rotate an edge, by projection, it will look like the size is smaller from the hand point of view. (Simple trigonometry rule.)

On a average higher poly model, you would have more vertices on the elbow, with different weights depending of proximity with the other bone. So the arm have same thickness and elbow will smoothly do transition.

In you case you would need the join edge to change size to keep arm thickness, but even if it is possible, it could give weird results.

In this case, since your inspiration come from minecraft, I would suggest you to separate each bone as a distinct piece (with different object or in one, like you want). Topo example

Minecraft character

If you don't want same minecraft bone separation effect, you'll need to add more vertices to elbow.

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