You Won't Believe They Roll: How to Build Half Circle and Elliptical Wobblers

How to Build Half Circle and Elliptical Wobblers

You Won't Believe They Roll: How to Build Half Circle and Elliptical Wobblers

If you thought the last post on Two Circle Wobblers was wild, then wait until you see what happens when you build wobblers out of two half circles or two ellipses. In both of these cases, the center of gravity still remains constant in the vertical direction, allowing them to roll down the slightest of inclines or even travel a significant distance on a level surface if given a push or even when blown on.

For the two half circle wobbler, while the center of mass remains at a constant height, it varies significantly in the horizontal direction which causes the motion to look incredibly funky as you can see in the video below.

For the two half ellipse wobbler, the shape looks like it would never roll.  It even has blunt edges! But not only does it roll, but it rolls very easily.

Finally, I'd like to demonstrate that these wobblers can be made out of just about any material. In the last post on two circle wobblers, CDs were used as the circles but anything circular will work. George Hart has made them out of both coins and large wooden discs, and in the following video I made one using Hula Hoops.

For a full mathematical treatment of all of these objects, including the information you would need to design your own variations on the shapes, you can read the paper, "The Two-Disc-Roller – A Combination of Physics, Art and Mathematics".

In the rest of this post, I'm going to show you how to build the two half disc circular wobbler from CDs, the two half elliptical wobbler from foam core board, and how to use any solid circular object to make a two circle wobbler.

Materials

  • Downloadable Two Half Circle Roller Template
  • Downloadable Two Elliptical Roller Template
  • Scissors or Exacto knife
  • At least 2 circular objects for the half circle wobbler (I used CDs)
  • Utility knife to cut CDs
  • Foam core board to cut out ellipses (You can buy at any arts and crafts supply store)
  • Surface to cut on—Do NOT cut while holding in your hand!
  • Optional: Scroll saw or jig saw to cut out multiple CDs at one time and speed up the cutting process.

Project 1: Two Half-Circle Wobbler  Made out of CDs

Step One: Download, Print, and Cut Out Template

Download the template and print it out at 100%. Do not scale to fit, this will not work. Once you have printed out the template, use scissors or exacto knife to cut the circle out of the template. It's important to be careful in this step.

You Won't Believe They Roll: How to Build Half Circle and Elliptical Wobblers

Step Two: Place Template Onto a CD and Tape It Down

Carefully place the template onto the CD so that it covers it symmetrically. Tape it onto the CD using multiple points of attachment so that the template will not slip as you are cutting the CD. 

You Won't Believe They Roll: How to Build Half Circle and Elliptical Wobblers

If you are going to cut through multiple CDs at once using a scroll or jig saw, make sure you tape around the entire stack.

You Won't Believe They Roll: How to Build Half Circle and Elliptical Wobblers

Step Three: Use a Cutting Tool to Cut the CD Using the Template

Carefully cut along the line on the template through the CD. You do not need to worry about the width of the slot yet, as long as you don't make it wider than the thickness of a CD. If using only a box knife, you are going to have to press hard and make numerous passes in order to make it through the CD.  

You Won't Believe They Roll: How to Build Half Circle and Elliptical Wobblers

If using a scroll or a jig saw, make sure that you have a stack of at least 4 CDs. If you do not, you will probably break the CDs. All you have to do with these is cut down the center of the line and stop at the end of the line. A scroll saw is my tool of choice for this project because it is so easy, and can handle many CDs at the same time.  

Step Four: Widen Slots and Friction Fit the CDs

Remove the template and tape. Widen the slots by using the box knife to cut more on the sides of the cut and scrape the sides. Each time you make the slot wider, check to see if it is the right width by trying to slide an edge of the CD into the cut. You need to make sure that it is still quite tight since this is the only thing that is going to hold the object together. Once you have both CDs the correct width, slide them into each other.

You Won't Believe They Roll: How to Build Half Circle and Elliptical Wobblers

Slide the two CDs into each other until their centers are aligned. They should hold with just friction, but you might need to use some adhesive.

You Won't Believe They Roll: How to Build Half Circle and Elliptical Wobblers

Project 2: Two Half Elliptical Wobbler 

Step One: Download, Print and Cut Out Template

Download the template and print it out. You can scale this to whatever size you like since you are actually going to cut out the form of the ellipse. Once you have printed out the template, use scissors or an exacto knife to cut around the ellipse.

You Won't Believe They Roll: How to Build Half Circle and Elliptical Wobblers

Step Two: Place Template Onto a CD and Tape It Down

Place the template onto the foam core board. Tape it onto the board using multiple points of attachment so that the template will not slip as you are making the cuts. 

You Won't Believe They Roll: How to Build Half Circle and Elliptical Wobblers

Step Three: Use a Cutting Tool to Cut the CD Using the Template

Now carefully cut along the line on the template through the foam core board. I recommend using an exacto knife and cutting through the board in multiple passes. You do not need to worry about the width of the slot yet, as long as you don't make it wider than the thickness of the board.

You Won't Believe They Roll: How to Build Half Circle and Elliptical Wobblers

Step Four: Widen Slots and Friction Fit the Ellipses

Remove the template and tape. Widen the slots by using the exacto knife to cut more on the sides of the cut and scrape the sides. Each time you make the slot wider, check to see if it is the right width by trying to slide an edge of the board into the cut. You need to make sure that it is still quite tight since this is the only thing that is going to hold the object together. Once you have both ellipses the correct width, slide them into each other.

You Won't Believe They Roll: How to Build Half Circle and Elliptical Wobblers

The finished product should look like this:

You Won't Believe They Roll: How to Build Half Circle and Elliptical Wobblers

Project 3: Make Two Circular Wobbler from Two Circles of any Material

Step One: Determine Your Diameter

In order to make a two circle wobbler you must find a diameter of the circle you are making it from. The easiest way to do this is to use a theorem from geometry. If a right triangle is inscribed in a circle, then its hypotenuse is a diameter. To use this, take any object that has a right angle in it. Place the right angle so that it is on the edge of the circle. Mark the two points where the edges of the object intersect the circle.

You Won't Believe They Roll: How to Build Half Circle and Elliptical Wobblers

Now use these two marks and a straight edge to draw the diameter.

You Won't Believe They Roll: How to Build Half Circle and Elliptical Wobblers

Step Two: Measure the Diameter and Calculate Slot Length

The slots that must be cut for a two circle wobbler are 29% of the radius or 14.5% of the diameter. Measure the diameter of the circle and use this to calculate the slot length.

You Won't Believe They Roll: How to Build Half Circle and Elliptical Wobblers

Step Three: Make a Two Circle Wobbler

Now use your calculation to mark and cut the slots out of the circler. Widen the slots to the width of your material and friction fit the two circles. For more information on how to do this, see my previous post on making the Two Circle Wobber from CDs.

The finished product should look like this:

You Won't Believe They Roll: How to Build Half Circle and Elliptical Wobblers

Step Four: Amaze Your Friends and Show Off Your Results!

These objects never cease to amaze me and most of the people I show them to. If you and a friend make one, you can always have a race! You can try and find out which wobbler is faster, the full circular, the half circular, or the half elliptical.

If you build one or all of them, let us know by posting a picture or video up on the corkboard. If you have any ideas of how to make these better or faster, be sure to comment.

7 Comments

So cool! this was in that article.

Yep. I knew when I read the article I just had to build the elliptical ones. You could probably make a lot of money betting people that it would win a race against some other object....perhaps a heavy metal hoop with a high moment of inertia. Everyone would pick the wheel over this!

Yes... good idea!

Now just to find two monster truck wheels

Hah! That would be awesome. I'd be a little worried about the thickness though. If you had something really thick you'd probably want to round the edges a little. Two large tire tubes would probably work though...but you'd have to cut through one and then reattach in such a way you could still inflate...

How do you come up with the 29% cut? The distance between the centers is the square root of 2 times the radius.

If there was no cut the distance between the centers would be twice the radius. You have to subtract twice the cut length from that. So you end up needing to solve the equation 2R-2C=sqrt(2)*R. If you solve this for the ratio of C to the radius you find that C/R=1-sqrt(2) which gives you approximately 0.29.

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