My first step was researching various commerically available mixers and shakers were out there.  For this application, I felt a vibrating table would be the best solution.  I had given some thought to a physical shaker that would move the vial vertically that would mimic a hand motion, but it seemed there were plenty of table top devices that worked well with vibration.

     Next, I spent some time sketching a few drafts and decided to make an internal frame supported by springs.  The motor would be mounted under the top table with a counterweight to cause the vibration.  I experimented with various spring types but landed on the lightest ones I had available.  The first proof of concept consisted of 2 plates separated by 4 springs and 4 bolts.  I attached an old vibration motor from a video game controller and drew up a quick mount for the vial and hot glued the whole thing together.  It gave promising results.

      It was time to move on.  I found an old lamp setup and decided to reuse the base.  I took my mock up and used it as a roadmap.  I got some aluminum brackets and cut them to a size that would fit the base and then moved my springs, bolts and any other hardware I would need.  Next, I mounted the internal system into the base, cutting the plastic away to make room.  

      At this point, it was starting to form into something that resembled and actual machine.  I made a cover to help hide some of the internal frame work, added a few mounts for the vials (angleing them to 15degs to help agitate things), and hot glued the video game motor.  It would agitate still but it wasn't as strong as I would have liked it.