Re: Elliptical Motion path conundrum

I might try parenting your lines to a a null which you animate along the y access at a constant rate. This gives you your constant vertical scrolling. I'd then turn off all lines but one, and animate its position along the x axis placing keyframes at the top and bottom of your curve as it scrolls up the y, and one at the apex of the curve that you set to "rove across time". I'd then adjust the easing/speed of the first and last keyframes so that your one line follows the curve. Once the one line looks good, I'd copy and paste those keyframes to your other lines and offset them so that they all repeat the same movement.

Am I making sense?

-Matt