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.