DeltaBot: Intro

A few weeks ago, in a search for inspiration for a new mechanical build project, I came upon the following Youtube video: 

Needless to say, I was, well, inspired. 
A Delta Robot is a type of parallel manipulator developed by Raymond Clavel as a professor at his alma mater, the Federal Institute of Technology of Lausanne, Switzerland. It is a design that was engineered to solve a very specific problem: high-speed high-precision pick-and-place manipulation of small, light objects in a manufacturing environment. Circuit Board population comes to mind, as does I Love Lucy. 

It is a 3-DOF robot whose end effector can move in XYZ, but cannot rotate in Pitch, Roll, or Yaw. Through clever geometry I have yet to fully comprehend, the end effector is always parallel to the base. There are 3 two-link arms (the bottom link being twin parallel links) which are actuated by three feedback-controlled motors at the top. The top links are constrained by the top actuators but the bottom links are held to the top link and end effector by ball joints. 

Before I could build one of these, there are some questions I need answered:

1. What are the robot kinematic and differential equations? (Find end effector position and speed (X, Y, Z, Vx, Vy, Vz) based on actuator angles: (Theta1, Theta2, Theta3) and their first derivatives). Also Inverse Kinematics (What Theta1, Theta2, and Theta3 are necessary to get the end effector to a desired XYZ?))
2. What magic engineering makes the end effector always parallel to the base?
3. Why do most Delta robots I see online have L1 (topmost link) smaller than L2 (the second, bottommost link) ?
4. What will changing the lengths of L1 and L2 do to limit or enhance my workspace range?
5. Where should my workspace be? If I am picking and placing, how high above my work plane should I put my robot? If I am 3D Printing?
6. How should I alter my transmission to be able to bear more load, gain more speed, or gain more accuracy?
7. What is the greatest load I can bear before the strain (% of deformation) on the links becomes unacceptable? (unacceptable being greater than my design end effector positioning tolerance, which I will now shoot for the stars and make an arbitrary .001" in X Y and Z. Interestingly enough, the layer size (and thus accuracy) of a MakerBot Replicator 2 is .1 mm, equal to ~.004". If I can achieve comparable or greater accuracy than a MakerBot Replicator, I can totally use this as a 3D printer!)
8. Finally, how can I improve on this design?

Here is a Solidworks assembly I put together in a few hours by looking at a bunch of designs online. This is nowhere near a final product, but it is to help me visualize the robot while I work out the kinematics. In this attempt I made L1 and L2 the same length (L1 = L2) and the size of the Base and Effector exactly the same. 

Here are the top joints, whose angles make up the robot's generalized coordinates, thetaOne, thetaTwo and thetaThree. These will eventually probably each be driven by a geared motor with encoder feedback. Like my Pittman 655s. 

Both joints for each of link 2's twin links are ball joints, which each have two rotational degrees of freedom. 

As you can see in the above photos, the DeltaBot end effector is indeed parallel to the base platform. I've determined this to be due to the fact that the each arm is identical (L1_1 = L1_2 = L1_3, etc) and the bottom links of all L2s are tethered together. 

But why? 
Pretty soon I'll start applying all this 2.12 I've been doing and work out the forward and inverse kinematics. Between all this schoolwork. And Melonchopper. According to Shane, the difficulty of solving the Delta robot forward kinematics is more difficult than solving the inverse kinematics, which is completely opposite from your standard serial link manipulator. 

I'll asplain later. I have a Pset to finish.