GeoBurst creates ZEST for MATHEMATICS by doing hands-on mathematical activities with kids. Check out our website and see what this emerging not-for-profit is up to!
I believe in the intrinsic value of mathematics, and most especially geometry and symmetry. Learning to appreciate math for what it is will reduce our aversion to it when we actually need to use some.
Learning objective: Students will learn about two of the 5 platonic solids, the icosahedron and the dodecahedron. They are both visible in this structure because their dual relationship is highlighted here. The tensegrity ball is neither the icosahedron nor the dodecahedron, yet it is also both. Students will also learn about the principle of tensegrity, and this activity can be partnered with the building of a smaller tensegrity such as the ones on GeoBurst. Students will also learn about knots.
Learning Keywords: 3D geometry, Icosahedron, dodecahedron, platonic solids, dual solids, tensegrity, symmetry (and symmetry groups), triangles, pentagons, engineering, structures, building materials, knots... etc :)
A little background: I first built a small model last year after seeing George Hart's post on Make. I also had these 1/2-1 inch diameter 8-foot bamboo poles, lying around for a project like this, but the giant tensegrity ball idea went into limbo because I didn't know how to reliably attach the ropes to the ends of the poles. You can't just notch bamboo, because it will split to pieces, and I didn't want to buy fasteners for 60 ends of poles.
The answer lay in knots, and this is what my instructable is about. Good, non-slipping, easy and fast knots. Tying the knots for this project took nearly 35 man hours, for which I had help from three friends. Veronika Irvine, Eric Davies, and Charles Campbell. The rest of the time was spent rolling the ball around at the park!
Let us start with a video of the end result.
Step 1: Materials and Build Summary
- 1/2" to 1" thick bamboo poles, 8 feet long, 30 of them
- At most 100 meters of paracord
- At most 500 feet of 3/8" thick yellow polyrope
- Duct tape (better than tarp tape I used)
- propane torch
- efficient rope cutting knives
- time and patience
Each pole and 11 foot piece of poly rope are paired up and attached at the ends. The poly rope pulls inwards, toward the middle of the pole, so the paracord is used to prevent the attachment points from slipping.
Warning: Knot lingo is approaching. If you don't know these names, just skim over them and I'll explain later.
At each end of each pole, a piece of paracord is tied on with a rolling hitch and a jug knot, and the poly rope ends are tied to the handles of these jug knots, with half hitches.
The Rolling Hitch tightens when you put a load on it that is parallel to the pole. This prevents the whole knot from sliding toward the middle.
The Jug Knot is used for carrying jugs because it provides a nice little handle. We use then handle to tie the poly rope into. This knot takes a long time to initially adjust, so I am debating whether I recommend using it, but it does work very well once it is on.
Go to http://geoburst.ca/craft_articles/random_canvas_details.html to see how I made the print on the wall in the picture.
Step 2: Tie a SINGLE Jug Knot
I'll borrow from wikipedia, since there are great instructions there.
The knot is begun by making a bight in a piece of rope and folding the bight back on itself to make two separated loops that are mirror images of each other. Lay one loop on top of the other so that they overlap slightly and create a cat's eye shaped hole above a triangular shaped hole between the two loops. Make a bird's beak with your index and thumb and weave them down through the loop, up through the cat's eye and down through the bottom loop, bunching the coils of rope against your fingers. Pinch the section of rope that was the bottom of the triangle and flip the coils over the pinched section. The flip may take a little practice, but the pinched section should become a short bight hanging off a circular shaped knot.
Step 3: "Dress" the Jug Knot on the Pole
Tie the 5cm end to the long end behind the jug knot with a surgeons knot (or sheet bend?). I have not perfected this part, because I know that a surgeon's knot can "capsize", but it does seem to be working so far.
Step 4: Tie the Rolling Hitch
Once again, best to pull knot tying instructions from a wikipedia.
- Start with a turn around the object. Bring the working end towards the direction of pull and between the standing part and the object.
- Make another wrap around the object, completing a round turn. The wraps of the round turn should progress towards the desired direction of pull. Bring the working end out over the standing part away from the direction of pull.
- Complete with a half hitch, moving around the object in the opposite direction as the first turns, as for a cow hitch.
- Dress by snugging the hitch around the object before applying load.
Tie the rolling hitch as close to the jug knot as possible, in such a way that the loaded piece between the two knots is parallel to the pole (ie comes straight off the rolling hitch and into the jug knot).
Step 5: Cover Rolling Hitch With Duct Tape
Duct tape is what I would have used if I had found any, but instead I used tarp tape. It is a distant second.
Important: Before taping the second rolling hitch on a pole, make sure your jug knot loops are sticking out on the same side of the pole.
Step 6: Debug Steps 2-5 for 1 or 2 Knots... and Repeat.
The numbers below include any knots we've already done.
- Cut 60 lengths of paracord 110cm long. Speed up by folding a 110cm length over on itself as the rope comes quickly off a well secured spool.
- Melt the ends of them using a torch. Wear a respirator.
- Tie 60 jug knots and lay them out on a table.
- Repeat steps 3-5 for each jug knot.
Step 7: Prepare, Tie, and Mark the Polyropes
We prepare 30 lengths of polypropylene rope, and pair each of them up with a pole, permanently fastening one end to a jug knot loop. Finally, we mark off the rope with a thick permanent marker in four places.
Do this with 10 lengths of rope and poles first, and test it. Then do the other 20.
- Cut polyrope into 11 foot lengths. Use a spool and double the rope over to save time. Melt the ends with a torch, and use a respirator.
- Secure a rope to one end of a pole with two half hitches and tighten. You will not need to undo this knot later. Repeat this for all poles.
- Mark the rope at 3 foot intervals, starting with the knot you just made (in case it gets loose). Make thick marks all the way around the rope. Repeat this for all poles.
Step 8: Learn to Tie Poles Together
Tie the clove hitches:
- Make an figure 8 in the rope, with one of the black marks on top of the middle.
- Fold the knot and bring the loops of the 8 together, underneath the mark.
- Slip the end of another pole into the loops, up the point just before the jug knot.
- Turn the new pole so that the jug knot loop is on the same side as the mark on the clove hitch.
- Dress (tighten) the clove hitch, keeping the mark in the middle.
- Repeat this for another pole, at another one of the middle marks on the poly rope.
The key here is to use knots that are secure, fast, and easy to untie. I have tried several different ones, and this setup is by far the most successful. As you are building later, you'll often tie one pole into a polyrope, and leave it open to wait for the next pole, before finishing with the slip knot.
Step 9: Test Structure
The key is regularity. The tensegrity ball consists of pentagons and triangles. You'll want to keep notions like "left over right", or vice versa, in your head. Learn to recognize the look of each pole.
The test structure has one pentagon, surrounded by 5 triangles. Build this as a small dome, with the ropes and jug knot loops above the poles.
- pentagons all go in the same direction. I follow the poles around in clockwise or counter clockwise order, and say "left over right" or "right over left", as the case may be.
- triangles go in the opposite direction of pentagons.
- poly ropes must not wrap around their poles.
When ready, push the outer poles inwards, bracing them on the ground perhaps, and push the pentagon upwards. You are testing to see whether you
- Had long enough poly ropes to tie it together at all,
- have a dome with approximately the right curvature, and fairly tight poly ropes (esp the ones around the pentagon).
Step 10: Plan Assembly
Build most of the ball flat, with the inside up. That is, jug knots and clove hitch marks are all next to the ground, underneath the poles. Poly ropes also go underneath the poles, and ends of poles never go over the poles they are tied into.
The (mostly) flat part, uses up 25 of the poles. The last 5 form a pentagon at the top. You can roll the structure around as needed.
Here is a video where I assemble the Giant Tensegrity Ball using this method at Vancouver Island Mini MakerFaire. Refer to the video in step 1 too.
Step 11: Take Your Tensegrity Ball for a Walk!
Enjoy Mathematics, and learn more about my not-for-profit, math education enrichment initiative, called GeoBurst.