(Note, we have a newer version of this project at this Instructable)
You can try this project out live at the site
So, the challenge is taking a hobby servo and getting 2-3 feet of linear motion out of it. ServoCity is working on servo linear actuators, but we'd prefer lower power, lower cost, and longer reach that they currently offer (though new ones may be pending). We also built a basic SCARA type arrangement with 3" lazy susans, servos, and counter weights. This works OK, but the workspace was limited, and due to the polar approach with hobby servos, the resolution is uneven - higher nearer the servos. This may not be a huge problem, but the approach shown here yields the same precision over the entire workspace. We could also consider a hybrid - using one rotational arm with a liner slider on it - the math would be easy in that it would use polar coordinates directly. We could also reverse the two - use on linear slider and add a rotating arm to it. A project for another day!
Using Hobby Servos
With a Hobby Servo, you typically get just 90 or 180 degrees of rotation, so the trick is getting that to work over a longer span - 2-3 feet. We could modify a servo for continuous rotation, but then you lose the positioning capability and we'd like to keep the internal PID circuitry and potentiometer approach. If you use the internal potentiometer and add a big servo horn, you could get a wider range of travel. With a circular horn, the distance traveled is Pi * Diameter of the horn / 2 - that last divide by two is to account for the max 180 degree of travel (we'll get into that later). So, for a 2' travel, you'd need a servo horn with a diameter of over 15"! We could use that approach with a lazy susan type of setup, but the momentum in moving that much material puts a huge mechanical strain on the servos (the same issue we had with the SCARA prototype). Another approach is to gear up the output, so you get more motion on the output. We didn't dig into this, and there may be issues with the power required to move those gears, and in addition, using gears is a bit ticker mechanically - we came up with a much simpler approach.
So, for our system, we pulled the potentiometer out of the servo case, and replaced it with a 10-turn potentiometer. So, right away, you can multiply the distance traveled by 10, so for the above case, it takes the horn diameter for a 2' travel from 15" to 1.5" - much more reasonable!
In terms of coupling the output we could drive a threaded shaft with a follower nut (ACME threading seems to be preferred). This appears to be the most common drive mechanism for homebrew XY Tables - due to it's power and precision. It does result in slower travel, though, and again, a lot of gearing to get the potentiometer to move at the right speed to cover the span of travel.
What we opted for was a very simple timing belt approach where the servo drives a timing belt pulley, and the 10-turn potentiometer is connected directly to the shaft. With this very simple arrangement, then, we get 2-3' of travel in a few seconds with no complex mechanics. You could scale this approach up by gearing down the drive or potentiometer to the limits of the mechanics of a hobby servo.