Ways for printing overheads with no support?

The only thing that prevents the mendel from printing overheads is gravity. On the other hand, mendel relies on gravity to get the heated goo in place.

What if instead of a print bed there would be a spit?
The spit will have three directions of movement: Moving along the mendel Y, rotating along its axis, and rotating along one of its tips. I believe that could be explained as: Forward \ reverse, roll, and pitch.
The print head will still move along the X and Z.

This should allow great freedom of design and very complex shapes.

It might be hard when it comes to proper syncing of the print head though. Pitch change will also require X and Z change, for example.
Also it means every design will have a hole going through it.

I think that the greater design possibilities outweigh the unwanted hole. Many designs probably won't mind it. And if the spit is optional and easily interchangeable with the print bed (perhaps the bed can clamp onto the spit), it will allow one to print without a hole when desired.

If the spit isn't perfectly round, it will prevent the design from losing grip and rotating freely along the axis.
If the spit is coated with some sort of thin plaster, it will prevent the design from losing grip and moving freely along the spit's length. Once the design is finished, the plaster can be softened and washed off with water in order to release the design.

Any thoughts?

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The only thing that prevents the mendel from printing overheads is gravity. On the other hand, mendel relies on gravity to get the heated goo in place.

Neither of those statements is true. Mendel has been shown to work fine upside down. The filament is pressed onto the layer below, no need for gravity. And the reason you can't print an overhang is there is nothing for the filament to stick to, so when the nozzle turns a corner the filament doesn't. It would follow the head like an elastic band would.

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[www.hydraraptor.blogspot.com]

But if the bed would be the one rotating, wouldn't it stick to the right place?

If you extrude a vertical tower and then rotate the base 90 degrees so that it was vertical then yes you could build a projection on the side, which would now be the top, but that would only work for a limited number of shapes as the head would collide with bits of the object already made.

Similarly you could mount an extruder on a 5 axis robot, but again you would not be able to make arbitrary shapes with overhangs, just some special cases.

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[www.hydraraptor.blogspot.com]

Doing anything except the one-layer-at-a-time method would required skeinforge to treat the extruder nozzle like a tool head. Things are about as simple as they can get at the moment because there's nothing for the extruder to run into; everything is below it. That means nothing really matters except the position of the table and how fast the extruder is extruding. If you want the extruder to print "around" an object all of a sudden you have to carefully calculate both the size and position of the nozzle, and of the already printed object.

Also, you'd have to make the bot's frame a lot bigger to allow for the build surface to be moving around inside it on more than one axis.

If you want to try that it might be better to start smaller. Maybe design the bot so that the user can manually reposition the extruder or the build platform while the print is paused. Plenty of CNC machines wait for the user to change out tool heads or move the piece around or something. That's a lot easier than having the bot take care of everything itself. You could even have the bot print out a calibration mark (like an 'X') that the user could line up with the tip of the extruder when they reposition the build platform.