I am trying to find pivot point locations for two connected objects by filming them and analyzing their relative positions to each other. So, for a simple example, suppose we have two rigid bodies connected by a ball-and-socket joint. Now suppose I am tracking features/markers on the two objects with cameras, and triangulating multiple camera views to get the 3d locations of those features.
So, if I have three features on one object, I can determine the position and orientation of that body over time. If I then have at least one feature on the other object, I can transform that feature's position into the coordinate system of the other object. So, that feature will sweep across the surface of a sphere, relative to the other object, and the center of that sphere is the location of the pivot point. Problem solved.
Now, suppose I only have two features on each object. I can't find an exact position and orientation for either object by themselves. So, has anyone heard of a way to determine the pivot location in this case?