I researched hummingbirds and bumblebees in hover flight and discovered their wings flapped in a figure eight motion. This motion is similar to how you would move your arms and hands when trying to stay afloat in water.
So I researched all kinds of mechanisms and designs that could provide this motion and was surprised with the complexity of every system.
I decided to figure out my own mechanism and started running simulations using a kinematic dynamic software package called Mechanica Motion. NOTE: Mechanica is now ProEngineer which can be found at http://www.ptc.com/products/proengineer/mechanism-dynamics
For my first simulation i was thinking that a figure eight looks like two circles touching each other. Based on that i created a two gear system with two connecting rods. I arranged the gears to first provide a circle as they both spun at the same speed. I then thought if I spun one of the gears twice as fast as the other i should see two perfect lobes. Well i didn't. I got something close to a lopsided figure eight with one side having a convex shape. So i played with phasing of the gears and still no perfect figure eight. A colleague of mine happened to be visiting and asked me to spin the two gears at the same speed. I told her i already tried that and proceeded to show her. It was a truly eureka moment as the mechanism traced a really small figure 8! It was all in the phasing.
So after a few optimizations the perfect figure eight motion was accomplished with 4 basic parts, ie 2 counter rotating gears coupled with two connecting arms.
I was so excited, applied for a patent and two years later the US Patent & Trademark Office gave me the saddest news of my life. The mechanism had already been patented ( #2,775,899 ) in 1957 by C.L. Vagneur .
During the anxious two years i researched features like adding a second pair of connecting rods to flip the "wing" during the figure eight motion.
I looked at other applications like rowing & bike pedaling mechanisms, hair braiding, ceiling fans, wind energy device, etc . I researched the web on all things figure eight and found it was a common motion for polishing, cleaning and mixing.
Anyway, after discovering Instructables I thought it would be great to share all this info for anyone looking for that perfect figure eight motion drive!
The steps are more of slide presentation.