Red object has 3 degrees of freedom in its planar motion: two linear x, y and one angular displacements.
Left motor controls x motion via screw-nut drive.
Right motor controls y motion via rack-pinion drive.
Upper motor turns pink pulley and controls angular displacement via two toothed belt drives (chain drives are possible).
Four pulleys have same diameter (same tooth number).
Transmission ratio between the pink and orange pulley is 1/1.
If the pink pulley is immobile, the object doest not rotate when moving along Ox and Oy axes.
The video shows how the red object moves along Ox axis, along Oy axis and then rotates.