Four slotted bars create a parallelogram. The blue bars rotate with a same speed but opposite directions due to three identical bevel gear drive.

Equation of drawn ellipse:

(x(a+b))^2 + (y(a-b))^2 = 1

a: center distances between pivots of the long slotted bars.

b: center distances between pivots of the short slotted bars.

Use screws to alter a and b for various ellipse shapes.