# Figure Eight Motion Drive

13 Steps
Back in the 90s I was very interested in Micro Aerial Vehicles (MAVs).

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!

Sabri Sansoy

The steps are more of slide presentation.
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## Step 1: Frame by Frame Trace

Frame by Frame analysis showing how the point where the two connecting rods are connected traces the figure 8. The two gears must counterrotate at the same speed.
kholmes7 says: Nov 30, 2012. 12:08 PM
What's the exact phasing of C and D to get a perfect figure eight?
ventifact in reply to kholmes7Dec 20, 2012. 7:20 AM
My question too. Measuring Step 6 figure 1 with a screen tool reads: C 28º above and D 28º below horizontal.
The Weekend Project says: May 26, 2010. 4:02 AM
Any chance of posting a close up of the slider mechanism in the above photo?
Hulya says: Aug 9, 2009. 7:35 PM
It takes a genius to design this concept. Great work!
___ says: Feb 12, 2009. 2:11 PM
What program did u use to make the animations? Thanks!
sansoy (author) in reply to ___Feb 12, 2009. 2:31 PM
I made these animations about 10 years ago using an animation package called Lightwave from NewTek.
Basically, I exported the motion data out of Mechanica Motion and imported it into Lightwave.
There is a free animation package you can download today at http://www.blender.org/ .

It has inverse kinematics (IK) which should allow you to make the same mechanism and any of your own design.

http://wiki.blender.org/index.php/Manual/Inverse_Kinematics
mycroftxxx says: Feb 9, 2009. 1:20 AM
Thank you! Great instructable. I know this has nothing to do with the actual subject of the instructable, but the last video is a great explanation for how to drive a boat using a single oar. I had always wondered how single-oar boats worked after seeing one on television. Aside from being an interesting instructable on a fascinating topic, the progression of videos at the end makes it simple to extract both the method for propelling such a boat along with the reason that one would use that particular method. Great job!
rimar2000 says: Feb 8, 2009. 8:05 AM
AMAZING! AWESOME! (what more I can say?) Thanks and congratulations!
budsiskos says: Feb 7, 2009. 1:10 PM
incredible. try making an rc prototype now
sansoy (author) in reply to budsiskosFeb 7, 2009. 1:15 PM
I had begun to build a prototype but i was so crushed when the patent office gave me the news i gave up on this for 10 years. I just checked out your awesome ornithopter instructable. i'm so busy at work but it would be great if you made a figure 8 ornithopter!
budsiskos in reply to sansoyFeb 7, 2009. 2:59 PM
thanks, ill defiantly consider it. but isn't the figure 8 only good for hovering on a flying vehicle? or could you possible use linear motors to move the cranks to change from hovering to accelerating
sansoy (author) in reply to budsiskosFeb 7, 2009. 3:48 PM
I like to use the analogy of a helicopter in hover. Its rotor blades create a downward force just as the figure eight drive. a helicopters forward motion is achieved when you tilt the blade system forward. in theory you should be able to do the same thing with tilting forward the figure eight mechanism. Also in hover both the bumble bee and hummingbird assume the rear bottom down approach, ie improving the center of gravity from a stability standpoint. exactly how its depicted in this image http://pro.corbis.com/images/MD004815.jpg?size=67&uid=%7BF0E77C80-6AA5-4011-8EBF-D66C16121107%7D
Lift the rear portion up and off you go into the forward direction....maybe..its only in theory..lol. i do need to build a prototype.
budsiskos in reply to sansoyFeb 7, 2009. 8:33 PM
good analogy. a prototype would be a big help in proving the viability of the design, and if you need any help just ask as im sure a good amount of people here would be interested. however i do suggest building the boat idea first just as a proof of concept and ease of design. in fact, i may just build one myself :)
Kiteman says: Feb 7, 2009. 1:13 PM
All those avi files... If you uploaded them to YouTube or similar, then embedded them here, you would get a lot more views.
sansoy (author) in reply to KitemanFeb 7, 2009. 1:16 PM
oh ok. thanks for the tip. i'm new here.
Kiteman in reply to KitemanFeb 7, 2009. 1:16 PM
(Oh, and if reality is as promising as those videos, you should definitely build a prototype!)
sansoy (author) in reply to KitemanFeb 7, 2009. 1:18 PM
thanks for the kudos. maybe we can build one as group project.
Kiteman in reply to sansoyFeb 7, 2009. 3:22 PM
Not so easy - we're on different continents.
budsiskos in reply to KitemanFeb 7, 2009. 3:39 PM
and thats what makes the Internet so amazing