I developed some ideas about this from first principles ten years ago, and then discovered that they were already known and were being explored by a few forward looking machine tool manufacturers. The architecture is called 'hexapod' or 'Stewart Platform'. Stewart did not patent the idea, and it has been in the public domain since. The hexapod mechanism is a variable triangulated frame which controls the position of a platform with six degrees of freedom. The frame has six or more extendable legs, connected to the movable platform and to the support structure with universal joints.
Various configurations are possible.
The one I favour is shown in this ray-traced snapshot of our software model. Some of the top structure and the bed support framing have been omitted for clarity. The architecture has a number of advantages over the conventional approach. Most of the member forces are axial, so it is inherently more rigid. It is very regular, so cost reductions through design refinement will really pay off.