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ANSWERED on Mon 24 Sep 2007 - 3:52 pm UTC by Roger Browne

Question: What shape would be the best to make a human hamster ball?

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happyengineer 

Customer

 19 Sep 2007 08:18 UTCWed 19 Sep 2007 - 8:18 am UTC 

I asked another question about how to build a truncated icosahedron (a buckyball). See:
    http://uclue.com/?xq=831
However, I've decided that perhaps it would be better to approach this from a different angle.

What is a good geometric shape that I can make which will allow me to make a human hamster ball (a 6 foot diameter ball).

The only problem with a truncated icosahedron is that it wouldn't really roll that well.

Instead, I'd like to start with a hamster wheel shape. See:
    http://www.boston.com/news/odd/articles/2006/05/19/friends_repay_joker_with_human_cage_prank/
and then build out the sides to be a sphere shape. That way it'd actually roll well.

Building a hamster wheel would be easy. One side is just a 90 degree angle for the connections. The other side is the angle of whatever 2D shape is determined by the number of sides of the wheel. I could then put in flat boards and end up with a wheel.

However, how do I go from there to making a ball shape? It wouldn't need to roll along any axis other than the wheel axis.

I'm pretty much looking for instructions on what angles to drill the holes into the balls that would sit at each vertex.

 

myoarin 

User

 19 Sep 2007 10:38 UTCWed 19 Sep 2007 - 10:38 am UTC 

Hi again,

If it is going to be a cage, maybe plastic or aluminum pipe and internal connectors would  be easier, assuming the latter can be found or made.
I was looking at this:
http://www.creative-science.org.uk/c60model.html

Of course, you would have to make a compromise where the pipes join with the round cage.  If you could do with a more open lattice, a dodecahedron might do (again with the compromise):
http://en.wikipedia.org/wiki/Dodecahedron

or this:
http://en.wikipedia.org/wiki/Pentakis_dodecahedron

One advantage of internal connectors, as seen in the first site, is that if they were made of a somewhat flexible plastic, the angles wouldn't have to be so perfect.

BUT, I just checked a truncated icosahedron soccer ball.  There are circumferences that cut perpendicularly through the hexagons and from the middle of one side of the pentagons to the opposite point.  Joints to the round cage would be either 90° or 72°,  but you still have to make your truncated icosahedron. Using flexible internal connectors would be easy  - 120°. Fastening the pipes together would have to be solved, but may not be necessary if the internal connectors are stiff enough.

Spheres at its verteces would extend beyond the circumference of the round cage, depending on their size, but I suspect that the construction would have enough "give" that this would not hinder its rolling.

Let me know if this is any help  - or none.

Cheers, Myo

 

happyengineer 

Customer

 19 Sep 2007 21:22 UTCWed 19 Sep 2007 - 9:22 pm UTC 

Using flexible rods for the side is an interesting idea. I had originally nixed that idea because then the sphere wouldn't support my weight when inside it. But if I make the hamster wheel part out of rigid rods and then using flexible rods for the hemispherical sides then that would work fine.

The key there is to find rigid rods and flexible rods that look like they are made of the same material. Ideally, it'd be nice to have both types of rods be transparent (like lucite) because I think that'd look very nice.

I don't know the various material types. If you look at the order page:
    http://www1.mscdirect.com/CGI/N2DRVSH?SISECT=0000001935&SIS0NO=660723
and click the materials drop down list, can you tell what each of those materials is? Some are labelled as clear, but can you tell which ones are rigid (with a half inch diameter) and which ones are flexible (with a half inch diameter)?

I've already ordered a few of those rods just so I can see what the materials feel like. But I only selected 5 types and the materials list is pretty long.

 

myoarin 

User

 19 Sep 2007 23:36 UTCWed 19 Sep 2007 - 11:36 pm UTC 

Hi Happy,
I mentioned flexible rods on your first idea as a way to connect the spheres  - in anticipation that it would be very difficult to get all those holes perfectly placed.
The internal connectors I envisage would be Y-shaped pieces of some material, cut from maybe 1/4" or 3/8" nylon sheeting.  (It's a lot easier to envisage something than to make it.)
As to the materials on the site you linked, I could only find on Wikipedia that Acetal is less flexible than nylon.

How important is it to have the thing really roll well?
I'm thinking that a truncated icosahedron with internal connectors would roll well enough, and certainly be more aesthetically pleasing  - nice decoration for your garden or patio; it's not going to be in use most of the time.

But maybe I have the wrong conception of the project.  I'm a little tempted to try to make a smaller one, myself.

Cheers, Myo

 

happyengineer 

Customer

 20 Sep 2007 00:14 UTCThu 20 Sep 2007 - 12:14 am UTC 

It's part of a Halloween costume where I'm dressed as one of the monkeys from the video game Super Monkey Ball. In that game you're a monkey that runs around inside a ball. So for this costume I'll be a monkey running around inside this thing. It might be acceptable to just stand inside it and shuffle around, but I think the costume would be cooler if it actually rolled while I was running inside it.

Having internal connectors might make it roll smoother (no balls would be hitting the floor as it rolls), but I'm not sure how I would cut out those Y-shaped pieces. Cutting them from something means that they'd be square. I guess maybe a square connector could grip the insides of a round tube, but I imagine it wouldn't be a strong grip where an adhesive would actually help much.

When the rods that I ordered arrive, hopefully some will be rigid and some flexible. If not then perhaps I could just use smaller diameter rods for the curved parts (which should be more flexible) and thicker rods for the hamster wheel part.

If it was just a sculpture then making the whole thing a buckyball would probably be prettiest.

 

happyengineer 

Customer

 20 Sep 2007 07:46 UTCThu 20 Sep 2007 - 7:46 am UTC 

myoarin, do you think you can do the angles that I asked for in my previous question? I'm curious about them even if I'm probably not going to use them with this modified version of the project. If you figure them out I can repost the previous question.

 

myoarin 

User

 20 Sep 2007 12:16 UTCThu 20 Sep 2007 - 12:16 pm UTC 

Happy,
I think I can do half the calculation.  Someone else will have to calculate the final angle, since everything I once knew about angle functions is gone.
I will try to explain so that someone can check my work.  Since I can’t find a square root symbol, I will use  V-

Here is an image of vertex:
http://en.wikipedia.org/wiki/Image:Truncated_icosahedron_vertfig.png
and here is information on 30-60-90 triangles:
http://mathworld.wolfram.com/30-60-90Triangle.html

The area of the hexagon within the equilateral triangle (white line) is a 120-30-30 triangle, two 30-60-90 triangles.
If the edges between the surfaces are A, then the shorter leg is ½ A and the longer one ½V-3A, so the sides of the equilateral triangle are twice that = V-3A (square root of 3A).

Let’s call this B.

The vertex in the middle of that image is ¼ B for each side, since we are still dealing with 30-60-90 triangles, being ½ of 1/2B. 
The line bisecting the triangle as the length of 1/2V-3B  (in terms of A:  ½V- 3/2V-3A)

Looking at the image from the side, we have a hypotenuse A and a longer leg:
1/2 V-3B  -  1/4B.

The calculation of the shorter leg is simple pythogoram, but unnecessary for someone who understand sines and cosines.

“Someone” please help.

However, the beauty of flexible internal connectors is that they will be forced in the correct angle as the thing is constructed, and  - I am hoping -  if the arms of the Y-shaped connectors (120-120-120) are long enough, the thing will be so stable that it won’t want to fall apart.  Screws through the pipes into the arms of the connectors could assure that.

I don’t know how neat you want the vertices to be.  I belong to the duct tape and coat hanger wire school.  (Come to think of it, the connectors could be made of the latter and inserted in holes drilled in the ends of solid rods for the edges.)

Good luck,  Myo

 

Roger Browne 

Researcher

 20 Sep 2007 16:39 UTCThu 20 Sep 2007 - 4:39 pm UTC 

Hi happyengineer and myoarin,

I've been following along with interest, but my 3-D math is too rusty to attempt to answer the question as asked. I'm OK on trigonometry, but I'm not sure myo's approach will work because it only considers the hexagons - and the pentagons are likely to complicate things.

I would certainly build this with flexible rods. That will make the construction much easier, and will also give a more spherical shape. I'd cut up old hula hoops, which (at a pinch) can be joined by flattening the ends and stapling to a wooden connector. Let's face it - with 90 edges (180 ends) you won't be able to spend too long doing anything fancy if you want this finished by Halloween.

But a much easier design is available. Take a look at this diagram:

   United States Patent 6651590
   http://www.freepatentsonline.com/6651590.html

If you could get three large hoops (e.g. oversized hula hoops) you would just need a bit of duct tape and you could have this ready in five minutes. Add a few more hula hoops if you want smaller holes.

Now for the whimsy. I rather like this human hamster wheel made by Dug North. This one looks like you could use it to get places:

   Dug North
   http://www.dugnorth.com/rolling-o.jpg

People ride down hills inside large balls, called Zorbs. Man it looks fun!

   Google Image Search - Zorb
   http://images.google.com/images?q=zorb

The inventors don't sell these, but you can get a "lookalike" for a mere $2800:

   Zorb-a-naut
   http://www.zorbasales.com/zorbforsale.html

Only slightly more affordable are the human hamster wheels in this video:

   YouTube - Human Hamster Ball
   http://www.youtube.com/watch?v=sZFRrjxb7mE

You can get them here for $2300 per pair

   GameOps.com store - Human Hamster Ball
   http://www.gameops.com/spot/promo/hamster.php

but if you also want the human hamster costume that will set you back another $700 for two.

On a more realistic budget, Amazon and Target sell the 84 inch (external) diameter Giga Balls for $200:

   Amazon - 84 inch Giga Ball (Red)
   http://www.amazon.com/Kidz-Kraze-84-Giga-Ball/dp/B000HCT7NC

Here's a video of the smaller version in use:

   YouTube - Brady in the Giga-Ball
   http://www.youtube.com/watch?v=9zXYtb6oaLg

These ones are said to be available from CostCo for $100, but I can't find a confirming link:

   Inflatable human beach ball
   http://gizmodo.com/gadgets/gadgets/inflatable-human-beach-ball-138380.php

Here's the video:

   YouTube - Human Hamster Ball
   http://www.youtube.com/watch?v=vVlDZDoD7OQ

Something tells me you're going to have a blast this Halloween.

Regards,
eiffel

 

myoarin 

User

 20 Sep 2007 20:58 UTCThu 20 Sep 2007 - 8:58 pm UTC 

Would you believe, after I started reading Roger's comment, before I got to the Zorb, I was thinking a posting a photo of one in action that I made in Rumania.  For a price, one could roll down a long slope in it.

The high end of human hamster balls is the Rhönrad, which you may have seen somewhere.  Here is a training video:
http://www.youtube.com/watch?v=6k6G8fj9vvI

This is from a Japanese event.  Stick it out into the second minute to see the guy "spiralling":
http://tv.mofile.com/Q7N3Q9FR/

 

happyengineer 

Customer

 21 Sep 2007 07:48 UTCFri 21 Sep 2007 - 7:48 am UTC 

I'm glad to see the giga-ball. I'll consider that my backup. If I can't get my own ball made in time (or if it turns out to be far too difficult) then I'll buy one of those.

 

Roger Browne 

Answer

 24 Sep 2007 15:52 UTCMon 24 Sep 2007 - 3:52 pm UTC 

Hi happyengineer,

I've looked into several options which I'll present here, but in my opinion all except the last have practical problems. The structure needs to be fairly light for several reasons: it must be able to roll easily without damaging the floor, it should not crush someone's foot, etc. Also, you probably need to be able to disassemble it easily for transportation (or to fit through doorways). I fear that a buckyball with its numerous rods and joints may be too cumbersome and heavy.

If you want to start with a hamster wheel and build it out with rounded ends, you have probably considered something like a carbon nanotube shape, with the tube part being very short i.e. just the rolling hamster wheel part, and each end of the tube being capped with half a buckyball. Here's a picture (but imagine the tube being much shorter):

   Carbon Nanotube Molecular Model Kit
   http://www.indigo.com/models/gphmodel/carbon-nanotube-model-W.html

As myoarin says, you can cut a buckyball in half, and the cut will sometimes pass through the vertices and sometimes will pass midway through the edges. That will match up with the hexagons in the tube part, but it's not good news because it means the tube part won't roll very well. Take a look at the animation on the following page to get a feel for how roughly the middle part would roll:

   Wikipedia - Carbon nanotube
   http://en.wikipedia.org/wiki/Carbon_nanotube

You could work around this by making the tube part be a true circle, but then it won't line up with the buckyball halves. That's because every vertex of a buckyball lies on a sphere, but the midpoints of the edges (where some of the cuts to the buckyball will be made) don't lie on the same sphere (they lie on a smaller one).

If you had a bit of flexibility in your end caps, you could attach them to a circular hamster wheel like the one in the boston.com article that you referenced. The small photo in the top-left of the following article shows how half a buckyball has been joined to a circle:

   Model buckyball tops Bristol nanoscience lab
   http://www.vnunet.com/vnunet/news/2198278/four-meter-diameter-carbon

If you're using a buckyball, I have been able to work out the angles to drill the holes into the balls that would sit at each vertex.

First, drill a hole from the "equator" of the ball into the center. Then, rotate the ball 120 degrees on its polar axis, and drill another hole from the equator into the center.

Now, use this second hole as the axis of rotation and rotate the ball 41 degrees 49 minutes on this axis. What we have done here is to "adjust" the orientation of the ball from the plane of one hexagon to the plane of the adjoining hexagon of the buckyball. Using the polar axis again (but the "new" polar axis obtained after the previous rotation), rotate the ball 120 degrees and drill the third hole.

The significance of the angle (41 deg 49 mins) is that it is 180 degrees minus the angle between adjacent hex-hex planes of a truncated icosahedron:

   Polyhedra - Truncated icosahedron
   http://www.coolmath.com/reference/polyhedra-truncated-icosahedron.html

I do feel that a buckyball-based design will be too unwieldy for party use, and I would like to present a much lighter and simpler design based around plastic water pipe - the kind of pipe that is used for water reticulation inside the home. It's light and fairly stiff, yet flexible enough for our purposes because it can easily be bent into a circle of diameter 6 feet. It's relatively cheap, and readily available from building supply stores or "Home Depot" type outlets.

Start with two twenty-foot lengths. Lay them on the floor parallel, about 18 inches apart. This will form the hamster wheel part. Cut eight pieces of wooden dowelling, each about 22 inches long, and lay them on top like railway sleepers, equally spaced (each 2 and a half feet apart). Ideally the dowelling will be of a diameter that will fit inside the plastic pipe. Attach the railway sleepers somehow - I would just bind them with tape. Each "sleeper" will overhang the "railway lines" by about 2 inches on each side - that overhang will be what we used to join the pipes that will form each hemisphere.

Now roll up the construction to form the hamster wheel. Join the ends of the 20 foot circumpherences by inserting a short length of dowel into the join and stapling it, then taping the join.

To build out the sphere, use eight ten-foot pieces of plastic pipe, four per side. Bend each of these into a semicircle, slip the ends over the projecting ends of the "sleeper" dowels, staple and tape.

Now all that's left to be done is to provide a walking surface for the wheel. It's tempting to use "boards" as you mentioned in your question, but this will be heavy and will complicate the construction. I'd be tempted just to cover the outside of the hampster wheel with fabric (e.g. strips cut from old sheets). When you walk inside the wheel, you step on this fabric to bring a new part it to the ground with each footstep - but the fabric doesn't need to support your full weight because your foot will be pressing directly through it onto the ground.

Add some lighting using the EL wire suggested in the responses to your other question, and you will have quite a spectacular wheel that can be disassembled and transported without too much trouble.

I hope this addresses your needs. If not, please request clarification.

Regards,
eiffel


GOOGLE SEARCH STRATEGY

angles truncated.icosahedron
http://www.google.com/search?q=angles+truncated.icosahedron

half model nanotube buckyball OR icosahedron
http://www.google.com/search?q=half+model+nanotube+buckyball+OR+icosahedron

nanotube
http://www.google.com/search?q=nanotube


ADDITIONAL REFERENCES

This Wikipedia article confirms that every vertex of a buckyball lies on a sphere:

   Wikipedia - Truncated icosahedron
   http://en.wikipedia.org/wiki/Truncated_icosahedron

Also this page includes some worthwhile links:

   Nanotubes and Buckyballs
   http://www.nanotech-now.com/nanotube-buckyball-sites.htm

 

myoarin 

User

 24 Sep 2007 20:58 UTCMon 24 Sep 2007 - 8:58 pm UTC 

Roger has come up with a fine solution, I believe.
One point:  if the ten-foot pieces are fastened to arch from opposite sides of the rim, they will all cross at one point  - longitudes meeting at the pole.  An alternative would be to fasten them in crossing pairs, forming a square around that point.  Then they should be somewhat shorter, since none of them would be an actual half circumference of the ball.

If the struts between the rims are flexible enough to give under your weight when you stand on them on the floor, I don't think you would need fabric around the wheel  - and you could see where you're going.

In defense of my suggestion for halving a buckyball, I beleive that the rim of the wheel would extend beyond the vertexes of the bisected pentagons.  The edges of the hexagons joined to the rim would all be parallel with the struts between the rims.

But Roger's idea is much easier to manage, especially the problem of transporting it to the party.

Good luck, Myo

 

myoarin 

User

 17 Jan 2008 01:30 UTCThu 17 Jan 2008 - 1:30 am UTC 

Hi Happyengineer,

Roger found pictures of your human hamster ball.  Congratulations!  Most effective, and great costume, too.  But I bet it was hot (and inconvenient for replacing fluid).

Oh, the link is on GA Alumni Association on google groups.

Cheers, Myo

http://groups.google.co.uk/group/GAalumni/browse_thread/thread/206295685bb9f364/5db46a745b4596a8#5db46a745b4596a8
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