The Moineau, or progressing cavity, pump was invented in 1931 by a Frenchman named Rene Moineau (imagine that!). The principle of this pump is best explained and illustrated by Prof. Jens Gravesen here: http://www2.mat.dtu.dk/people/J.Gravesen/MoineauPump/
Select one of the designs, say "Hypo- & epi-cycloids 3:2", to see the details. Excellent illustrations show both the principle of the pump and the geometry creation method. Consult the Wikipedia for the equations for the hypocycloid and epicycloid.
The advantage of this pump design for 3D printing of pastes is that it is rigid and positive displacement. Why is that an advantage? Because the pumping chamber and impeller are both rigid, unlike a syringe or peristaltic pump, the only elasticity is in the material being pumped; usually easier to compensate for. Effects like pulsing are also absent. Positive displacement means that the pumping action starts and stops when the impeller starts and stops. The idea is that these factors result in more precise control of the paste printing process.
"OK, fine," you say. "So how do I create a Moineau pump"
Glad you asked, 'cause that's what this is all about. A Python script will do the math to create the profile for the Moineau chamber and impeller. I will then use the linear extrude function in OpenSCAD to create the Moineau pump impeller and chamber in three dimensions from the profiles. By providing both the Python and the OpenSCAD source, other sizes and geometries of the Moineau may be created. So if my design doesn't suit your fancy, here are the tools to design your own version. Since this is my first time using the HAD tools, I'm not sure yet where to put my code. When I figure that out, I'll post it and add my code snippets. (Maybe github?)