Yellow head is controlled by three step motors via spatial linkage. Green and pink bars create 3 parallelogram mechanisms. In some designs the revolution joints between them are replaced with spherical ones.
The video shows the head motion from central position when three blue input cranks turn with the same angle, first one after another and then at the same time.
The head is kept always horizontal and moves without rotation. By combination of positions of the input cranks the head can reach any position in 3D space. However, the calculation is not simple.
It can be used for 3D printers, pick and place devices.
See a real mechanism:
/watch?v=Gv5B63HeF1E