How can i achieve this motion?

If you want to keep it AE-native / no third-party tools, take a look at the CC Cylinder effect.
You could probably pull this off using one line animation in a precomp, and several instances with different Y rotations. 

Would be easy enough with Trapcode 3D Stroke or TAO and a suitable mask path, so seriously consider this. Otehrwise this could also be created using a spline extrude in C4D Lite with a twist deformer applied. there are of course other, more complicated ways like rigging a particle emitter with expressions to form the curves, but try the simple stuff first.

Mylenium