Ever since I saw Sublime's Tantillus 3D printer using spectra fishing line, I've ben really intrigued by the idea, in fact I built 2 Hbot prototypes using the idea.
The fundamental issue that comes up is that the fishing line "walks" as it wraps around the pulley, this changes the angle of the line, which in turn affects the tension. The problem is worse on a HBot because of the single long belt the number of times that the belt wraps around the pulley to go extent to extent can be large. In fact on my first prototype where I didn't try and address this there is a noticeable change in tension.
There are basically two way to approach the drive Tantillus passes the line through the "pulley" and wraps the filament on and off, this makes it impossible for the line to slip, but it's also difficult to address the walking filament, on Tantillus the combination of short axis and linear line path make this a minor issue that doesn't seem to impact the print quality.
The other option is to have sufficient friction on the drive pulley to prevent slipping, this requires a significant contact area between the line and the pulley and significant tension on the line.
The idea of the figure 8 line drive above is to use an idler to continually reset the filament position, basically the drive pulley in this case has 4 grooves, and the idler 3 that are offset by 1/2 the groove spacing. The filament always rolls onto the top groove on the drive pulley and off the bottom one.
There is no filament walking, and the equivalent of multiple wraps around the drive pulley to provide additional friction.
You can see the prototype running here
As a point of reference I'm running it off the LPC1768 based electronics discussed in other posts.
The idler has 2 9mm bearings in it's center.
I stole the idea for this from somewhere, I think the first time I ever saw it suggested was on the CNC Zone forums regarding wire drives for routers.
I'm pretty happy with the friction from the 3 figure8's, I might reduce the groove spacing on the drive and idler from 1.5mm to 1mm, but 1.5mm seems to work well.
My intent is to use this mechanism on my 4th HBot prototype, though I intend to use the CoreXY mechanics rather than the HBot mechanics, I have most of the X/Y Gantry laid out in CAD, hopefully I can get the CAD work complete this week.