I believe what you are describing would fit the SCARA-style RepRap Morgan design (http://reprap.org/wiki/RepRap_Morgan), which has a cylindrical build volume bounded by the two motors that define the rotational position and the deflection from that rotational vector in order to provide (X,Y) coordinate values within the print volume. There are currently three basic lines of RepRap design development (delta, cartesian and polar), with variations in construction such as Z-axis variations (dropping build plate, raising extruder, or building upside-down from suspended build plate, etc). Delta RepRaps are like the common Rostock design, Cartesian models include the standard RepRaps like the Mendel and Prusa designs, while Polar variations include options like the recent Morgan design. All accomplish the same thing - they move the extruder between (X,Y,Z) coordinates to build one layer at a time. A few DLP liquid designs use voxels that are cured all at once, but otherwise extruders deposite material sequentially - whether through a heated nozzle, syringe, or through an extruder-screw enabled conduit. SLA printers work more like the DLP designs, curing a liquid polymer one layer at a time as the build plate settles to create each new layer, and really-fine resolution material comes from multi-photon systems that only cure material where two beams intersect within the liquid-filled 3D build space. Other deisgns are mostly granular binding using sprays of material or glue similar to ink-jet printers, or they rely on laminated cutouts of paper stacked atop one-another and glued together for the final design. Beyond that are the blown-powder or wire-feed systems that use lasers or electron beams to melt or sinter materials together at the point of the extruder.
Kalani Kirk Hausman
A true Cylindrical "3dPrinter" (additive manufacturing device) is definitely a do-able and robust device to build.
The above reply doesn't do what you asked. Scara is a series robot with 2 revolute (rotational) and one prismatic (sliding) joints in a "kinematic chain", this robot basically which transforms rotary motion into cartesian space, it doesn't directly perform cylindrical coordinates. (Though of course it can be programmed to do whatever you want in 3DOF)
The device linked to is very loosely a scara robot with additional supporting parallelogram arms.
For native cylindrical geometry there are many alternatives (they all need to be sorted out kinematically and dynamically for proper control).
With CNC machines it is common to separate the "kinematic chain (linked joints) from what is thought of as a robot, into a more robust machine (for rigidity and accuracy) too many series links becomes less accurate due to flex. So that is why 3D printers and 3 axis CNC machines usually only have 2 axes on one mechanical system and the third axis is connected to a different part of the machine as in the z-axis is connected to the base and x and y axes are supported by the top frame, or some other arrangement. This is why a CNC machine isn't usually thought of as a robot, though it is. (Parallel kinematic chain robots (think hexapod / stewart platform / parallel pick-and-place robot) are much more complicated to develop but all axes of motion can be attached to one mechanical member, usually with a lower range of motion but higher accuracy.)
One very robust way to achieve true cylindrical action would be using either a prismatic joint (linear actuator, variable radius) for the x axis ( (R )radially on the cylinder), OR a revolute joint with a fixed length arm which sweeps across the surface of the cylinder (like a record player stylus) for a combined x-and C-axis (Rotation around Z ), the the first option is fairly trivial to control position, while the second option is a little more complicated,but the maths isn't really very difficult (combining the 2 would lead to variable radius arcs and straight lines ) . (Note that linear encoders and actuators are cheaper, easier to make and more accurate when home building a machine, high quality rotary encoders and actuators are "more cool" and results in a more flexible system (faster traverse higher variation in speed) but for a higher cost and programming complexity.
Using a Vertical z-axis for lowering the table, and a C-axis for rotating the table is very practical, however, you won't be able to do both of these actions with any accuracy using a single screw. If you use a very fine (ball) screw (say with 0.1mm pitch), then this system will only be good for lowering the table at the same time as rotating the plate once (fixed layer thickness), while this may be good for making varying wall-thickness pipes, or simple cylindrical structures it doesn't allow for varying the polar position at-will independently of the z-axis (this system will have a linearly dependent transformation and control matrix. ie. you will only be able to control 2 of the axes.)
Having a machine which natively created circles will mean that truly round objects will be more accurately represented than with a low end traditional cartesian machine (no linear interpolation). At the same time, straight lines may not be as straight as what a rep-rap may do it (along the principal axes.) However for all CNC machines, getting a good result is more to do with the homework done on designing the system and the controller than the actual geometry of the machine. If a 6 axis robotic arm can draw/make/machine true circles, straight lines and any mathematical (1D to 3D) function , anything is possible.
Using cheap controllers and mechanical components, adding extra axes for performing circles and straight lines (in any orientation is likely to result in a better outcome (more rotations and linear transforms). For professional high end machines, spending more money on development and using well engineered parts, less axes to do any given task is better (as it results in a stronger (not really necessary for 3d printing) simpler and more reliable machine.
(I have lots of Ideas in this space, I just have to get my ass into gear with doing one of them...)
There have been a number of rotary variations, including one system that pairs multiple extruders with the rotational base plate to allow higher feed rates and some interesting variations in material integration. A rotary system that performed full circles could also support fully automated fabrication with a depositing mechanism to release the final products before beginning the next. Many variations are possible, but you may have to "roll your own" electronics since the G-code translation fits the standard configurations (cartesian, polar, delta) and the firmware variations are coupled to those positional calculations. Using a more robust platform like a BeagleBone instead of the Arduino-based electronics (Microprocessor vs. Microcontroller) would be a good way to start, as it supports more common language development IDEs and could assist you towards your goal. There are Linux CNC Capes (like Shields for Arduinos - add on boards) that can handle fairly robust steppers and such along the way.
I think that was sort of what Ed was asking, it seems that he doesn't really know much about robotics / CNC equipment.
your insights were helpful.. Yes using several deposition heads on a single layer would truly take these machines to the next level (just have to ensure that the programming allows for conflict resolution. Also as used for multiple material, variable colour etc in different structural regions of the object. Again, using it like an automatic tool changer would allow for mature milling code to be used.
A true native cylindrical machine is more like a 3 axis Lathe (most likely to be mounted vertically to allow deposition on the cirfular face (mo reason why it couldn't have its Z-axis in any orientation.
All automatic machines need to have the G-codes translated for their specific kinematics, it is just that using a conventional XYZ system someone has already done the transformations.
As you know we are only playing with the bottom end of CNC gear with (home built, one man rolled) fused deposition machines, a dedicated machine geometry (to perform a particular type of manufacturing) has a better chance of producing the required geometry than a generalist machine in this space..
Anyhow hopefully it is useful for Ed. (I realise the question was asked nearly a year ago.)
Some students at Imperial College in London designed the first recorded cylindrical 3D printer. You can find more details here: http://www.scribd.com/doc/147351838/Lathe-Type-3D-Printer#scribd
I was wondering if there would be any advantage to to a 3D printer that operated in a cylindrical coordinate space instead of a cartesian space? Would it be feasible to come up with a very fine threaded rod that would attach to the center of the print table to permit rotary positioning and Z-axis advancement at the same time?