Dynamic line drawing

I have a line drawing that I have to animate it has curved lines like the image attached.

I have tried tweening however it looks terrible and not smooth in it drawing. so I thought I would try and action script it. I can actions script the lines but not animate them can anyone help.

this is the action script I already have so far.

createEmptyMovieClip (“curveLine”, 1);
with (curveLine) {
lineStyle (2,0xffffff, 600);
curveTo (50,0,80,50);
curveLine._x = 300;