Combination of gear drive and linkage mechanism.
Two gears are identical. Axle distances between revolution joints on the pink and yellow bars are equal.
Equation of drawn ellipse:
(x/a)^2 + (y/b)^2 = 1
a = (m+n)/2
b = (m-n)/2
m, n: center distance of gear axle and its pink slider axle.
Use violet screws to alter m and n, which means a and b, for various ellipse shapes.
To get an ellipse axis coincident with the gear center line, the screws must be arranged in two sides of the line connecting gear centers with an equal angle.