Let's say someone wanted to learn how to do this. Not just follow a step by step guide, but actually learn how to do this. Where would you find a good resource?
You would need to control a pair of servos. Arduino is the easy way. Some trigonometry to convert x-y positions to the two arm angles. The connectors to the pen are linkages.
I am currently building a whiteboard plotter myself, though a much larger scale.
Feel free to send me questions and I can send you pointers on where to research next.
There are three parts to learn -- the electronics (handled by an Arduino and a few servos), the mechanics (for this design, it's not too complicated -- you could make do with popsicle sticks and some screws if you had to), and the software. The tricky bit with the software is the math. The arms, when free to spin around their centers, can be considered circles. You'd want to learn the geometry of circles and, specifically, how to find the intersection of two circles. The joints on the arms are where the circles meet.
I'm working a new version of my mobile testing robot that looks very similar to this clock. Haven't posted the code, yet, but I did have to go back and re-learn some trig and circle geometry to make the simulator. http://youtu.be/qRzrm4zx82g
A good starting point might be to use Lego + Mindstorm (or Lego + Arduino). You get to use various off the shelf mechanical parts and you get to re-use the Lego parts in your next project.
Yup, that's a fine suggestion, too. I used to do all my prototyping with Lego Technic pieces... Years later, when I needed parts that Lego didn't make (like for connecting servos or Arduino), I used Lego dimensions to create my own 3D printable (but Lego compatible) parts.
You could probably build a similar thing almost out of the box (BYO marker and whiteboard) and you can replace the various parts with your own bits as you get more advanced.
I suppose if you knew what you were doing going an Arduino is a cheaper option though.
This of course depends on what you know already (CS or EE background?), but the easiest way would be to use an arduino. You'd need to have some electronics knowledge (basic circuitry, servo motors) and be able to do some embedded programming (PWM, ADC/DAC, interrupts/timers)
I am currently building a whiteboard plotter myself, though a much larger scale.
Feel free to send me questions and I can send you pointers on where to research next.