Summary

High capacity bubble machine capable of 14,000 bubbles (more on that bellow) per minute. Uses a 5 gallon bucket, some aluminum extrusion and a 50rpm motor. Everything else is 3d printed. Video and another Video that google highlights made
Be sure to check out http://www.thingiverse.com/thing:973742 to eliminate the need for the aluminum extrusion!

Instructions

EDIT 2: Added a picture of the motor coupling and replaced the pin and link pieces for ones that are oriented 90 degrees to help with layer lines and strength. The motor coupling is just 6.35mm x 1.25mm aluminum rod ($2 at an RC store) cut to length with a small hole drilled for a paper clip key.
EDIT: Added BOM and updated the motor carrier to suck a bit less.
A quick word on the math. Some totally legit questions have sprung up about the actual capacity of this machine. The math I used is (40 wands 6 bubblers 8 bubbles each) * 10 rpm which comes out to 19.2 . No chance all of the bubblers will fire though so I took 70% of that to get the max which is roughly 14,000 per minute. In practice it's anywhere from 2,000 to what I estimate to be around 8,000. At 8k you can't stand in front of the thing, but it has to be a calm day for that to work. The videos are somewhere in the 2k range because it was a windy day. Hope you enjoy making one on your own, let me know if I screwed up the math (I am not a smart man).

You'll need to print around 40 of the wands, 80 pins and 40 links to make one the same size as the one I made. The bottom sprocket is held into the extrusion with T-Nuts and a bolt (the bolt acts as the axel, no bearing is needed as this sprocket stays submerged in soapy water) while the top sprocket uses a shaft coupler or some 4mm ID aluminum stock (hobby stores carry this).

BOM
Gear Head motor
Shaft Coupler You can use this type or make your own, like I did, out of aluminium stock
20x20 aluminum extrusion or whatever else you want to use to hold things together
Various bolts, tnuts, etc
5 Gallon bucket

Be sure to check out http://www.thingiverse.com/thing:973742 to eliminate the need for the aluminum extrusion!

Things to improve
I need a better mount for the bottom sprocket. It wobbles a little just using a bolt and that lets the chain eventually come off.
A better housing for the motor. A bit of soup eventually gets on the motor and Im worried that will impact it over time. Could just make the housing bigger, not the solution Im looking for.

Bubble bucket