This activity belongs to the GeoGebra book Linkages. Since three-dimensional space has one more dimension than the plane, the constraint imposed by the fixed length of each bar is weaker, which gives the mechanism greater freedom. While our flat rhombus had 1 internal degree of freedom, its spatial version has 2, as we can see in this construction. This implies that even the very idea of a rhombus as a "parallelogram" loses its meaning. Instead, it is better to think of a hinge. Note that now, to match the total number of degrees of freedom with the number of internal degrees of freedom, in addition to fixing points O and U, we have also fixed the plane in which point E is held.
Now, although the construction transmits the movement from F to E and vice versa, it is not comfortable to handle. On this occasion, it is more practical to preserve the dependence of F on E, so that when F moves point E remains in its position. This is what the following construction does, typical of Dynamic Geometry (without scripts).
Author of the construction of GeoGebra: Rafael Losada