(Update: I have a solution now).
I want to make two balls stay a fixed distance from each other, and rotate around a point at a fixed radius. The body on the right is what I want.
Try to interact with both bodies using the mouse. Observe that the one on the right thrashes around violently at the slightest perturbation. Observe that this does not happen for the body on the left, which is the same except for the location of the pivot.
How do I make this work properly?