Coordinate system to move with body

[Anonymous]

How can I constrain the displacement of a node to a plane that moves with the body as it deforms?  In the following representative beam analysis:

(see attachment)

- First row shows the simple analysis of a beam cube, base square fixed, load applied to top square. 

- Second row shows the secondary coordinate system.  The midpoints of two vertical members are constrained to have zero displacement in Y in the new coordinate system.  The coordinate system is defined by the new origin point and two other points on that diagonal plane.

- In the deformed result, the constrained midpoints are stuck to the XZ plane of the new coordinate system, which obviously has not moved in space.

I want to make a plane that is defined by three points on the diagonal plane of the cube that travels with the body when it deforms.  If I constrain my midpoints to this kind of plane, there should be no difference between the base scenario and the extra constrained scenario because the midpoints after deformation will still be on the deformed diagonal plane.

Is there a way to do this?