The bars create parallelograms.
Yellow parts are fixed together.
Blue parts are fixed together.
Input: green bar.
Z1: tooth number of the small gear.
Z2: tooth number of the large gear.
Z2 = 2.Z1
L2: length of blue and green bars.
L1: length of yellow and orange bars.
If L1 / L2 = 0.267
The pink table translates along almost straight line (in green) (without a runway).
Length of the straight line is around 1.5 X L2 (the input turn +/- 30 deg.).
The video last scene is for case when the pink table moves in horizontal plane.