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Easy Spherical Sphere Example
Article © MAIL User: Inventor

Rings Used: 14 ga. 3/8" aluminum or bronze
Ring Count: 172
Pliers Used: two flat-nose plus one curved needle-nose for tight spots



Image: sphereexample1.jpg

An Easy Sphere

Walk with me on a little chainmaille journey and I'll show you how to make an easy spherical sphere like those shown in the above photo. These spheres were difficult for me to design yet they are easy to weave and they only require 172 rings. Mind you, they are slowly and carefully woven in tight spaces, but yes only 172 of them to make a very pleasing little spherical sphere.

In fact, to make it as easy and fun as possible, I hereby banish all mathematics from this article! Away trigonometry, away calculus, away wicked cosine function - there shall be none of that stuff of wizards and conjurers in this article! Of course, the tricky business of designing your own spheres in different sizes and weaves involves plenty-o-math, but we are not concerned with that at all in this article. (The mathemagically gifted may wish to see Spherical Spheres -- Ed.)


The Table

In place of all the mathematics is a small, gentle little table of numbers, shown below.

row | pairs
-----------
0 | 18
1 | 16
2 | 12
3 | 6

The table tells us exactly how many ring pairs to weave on each row to make a very round and rigid, self-supporting little sphere. We're showing ring pairs instead of single rings in the table because our weave of choice is Kingsmaille (European 8 in 2), which is simply European 4 in 1 with every ring position doubled.


Weaving the Equator

Let's begin by weaving the equator of the sphere and the two surrounding rows all at once. We are going to start by making ordinary Kingsmaille from scratch. Take some 14 ga. 3/8" aluminum rings. I also use bronze rings, but these require greater hand strength and more finagling in tight spots. For your first sphere I suggest aluminum, which is plenty challenging when you get to the tighter rings. I suppose that copper would work also but I have not tried copper.

Close eight rings and put them on a single open ring. Close it, then add another open ring through the eight rings and close it. The result is shown below.

Image: sphereexample2.jpg

Now close four rings and put them on an open ring, then weave them into the four rightmost rings of the previous photo. Then double the central ring as per Kingsmaille style. If you have any trouble with this, see a tutorial on Kingsmaille weaving.

Image: sphereexample3.jpg

Continue to add Kingsmaille sections until you have 17 pairs on the equator and 18 pairs on the adjacent rows, as shown below. This will seem to be too long of a piece, but remember that the circumference of the equator is pi times the diameter, so the piece must be over three times as long as your mind thinks it will be. Dangit, pi snuck into the article and I said there would be no math! Sneaky pi...

Image: sphereexample4.jpg

Now add two rings to the equator in such a way that you close both ends together. You will end up with a sort of miniature Kingsmaille bracelet, as shown below.

Image: sphereexample5.jpg

Next use your hands to smoosh and twist and rotate the equator around like a car tire. This is not only therapeutic after doing all that weaving but it also helps the rings to equalize their positions and settle into place. Enjoy your smooshing, you deserve it!

Removing Rings

OK, let's look back at that table. We see that row 0 has 18 ring pairs, which your equator does have. However rows 1, which are on either side of the equator, require only 16 ring pairs. What we will do now to reduce rows 1 down to 16 ring pairs is to remove two ring pairs from rows 1.

Now there is a particular way that we must remove these rings. We will be forming reductions as is commonly done in chainmaille, but they are special kingsmaille tight-weave reductions. What we do is at each location where we would like to remove a pair of rings, we remove one ring from two adjacent pairs. Note that this is different from just removing a pair of rings. See the photo below for an example of the first ring pair removed. The reduction is marked with a bread tie wrap.

Image: sphereexample6.jpg

It is important to make our reductions in this distributed way because the following row will get too tight to weave if we don't. Now count out your rings and remove another pair exactly opposite of the first pair that you removed. Save the rings to reuse them because we said we only want to use 172 rings, right?

Up next is another little trick of the spherical sphere which helps to keep the equator from getting all twisty and tangley. The row 1 we just removed those two pairs of rings from we will call the northern hemisphere row 1. The trick is that we will leave the rings unremoved from the southern hemisphere row 1 until we complete the northern hemisphere row 2. By not removing those rings until we have to, we help keep the equator held in proper shape until the northern hemisphere row 2 is in place to do the job. Believe me, this little delayed-action trick prevents a tangled mess of rings, especially if you ever find yourself weaving single-ringed European spheres such as a European 6 in 1 sphere.

Weaving Rows 2

So we removed our two ring pairs from the northern hemisphere row 1 and now we're ready to weave the northern hemisphere row 2 on top of it. We will be going ORAAT (One Ring At A Time) from here on out, that is just the nature of spherical spheres. First let's return to our simple table and look at the entry for row 2. It is 12-pairs and we are adding it on top of a 16-pair row, so there will be four reductions.

Take four bread-ties and mark the positions of four equally-spaced reductions in such a way that they are as far apart from the existing two reductions as possible. In simpler terms, we want to space the reductions evenly. Also, the last thing we want is for a reduction to line up with a reduction from the previous row, because that propagates errors in spherical shape and can lead to a portion of the sphere that either gets spaced too far to weave or creates an egg shape.

Now add all of your rings for the northern hemisphere row 2 (reusing the removed ones) and you will end up with something just like the photo below.

Image: sphereexample7.jpg

Since the northern hemisphere row 2 is done, we can now weave the southern hemisphere row 2. We begin by removing the ring pairs as before. I have made this sphere with the reductions of rows 1 aligned, and it turns out a little bit rectangular or pointy at the equator, so I recommend removing the southern hemisphere row 1 pairs at 90 degrees from the northern hemisphere row 1 removed pairs. This makes the sphere rounder. Note that because our 18 rings are not divisible by four, there will be a slight rotation, not exactly 90 degrees. Just pretend the reductions repel each other and space them out as symmetrically as you can.

Repeat the process of weaving the northern hemisphere row 2 on the southern hemisphere row 2, and you will have a donut-shaped object as shown below. (note: is this a good tire for a sculpture car?)

Image: sphereexample8.jpg


Break Time

Whew, that was some tricky weaving. The good news is that we are almost done now and bonus: there is no bad news! Remember how we smooshed and rolled the equator after finishing it? Now it's time for another smooshing session. Roll it, twist it, juggle it, shake it, whatever. Let those rings relax into a minimum energy state so that everything will be all symmetrical and equalized. Actually the reductions sort of make it a little bit wavy when the rings are relaxed, but the row 3 rings will pull that tight into a spherical sphere shape. There, wasn't that fun? Now on to the final rows, rows 3.


Weaving Rows 3

The special thing about the last row is that we don't weave it with doubled Kingsmaille rings, but instead we weave it with single rings. This is because of the rapidly reduced number of ring pairs from rows 2 (12 pairs) to rows 3 (6 pairs). In fact, every other ring pair is a reduction or in other words it's *all* reductions! So we take our 6 pairs of rings, which is obviously 12 single rings, and weave them into place at the 12 positions of rows 2.

One thing to note for row 3 is that this is the tightest, most difficult row to weave. One trick to help with that is to open the rings w-a-y wide, like almost to 90 degrees so that their gaps can span large distances, especially when weaving on top of reductions. Another trick is to start weaving at such a location that the very final ring of each row 3 is through two full pairs, not a reduction and a full pair. This is because the final rings are the most difficult and the very last ring is the most difficult ring of the whole project. Ain't them the breaks?

It is also useful to sometimes close rings in two steps: begin by squeezing the ring closed with the jaws of your curved needle-nose pliers using just one pliers to get it close to being closed, then finish with two pliers as usual. I know, it sounds like a struggle. It is. With perseverance and taking breaks to calm your nerves and let your hands rest, you will be able to wrestle those final rings in place and they will all hold together in a snug, tight little spherical sphere shape.

We do this for the northern hemisphere and then the southern hemisphere, and guess what? We're done! There is no need to add a special closing ring at the north and south poles because the weave is tight enough to hold them in place. Naturally we will want to do a final smooshing to settle everything in place and to enjoy the feeling of our nice round sphere in our hands. The completed sphere is shown below.

Image: sphereexample9.jpg

And here is a bronze one that i made, shown below.

Image: sphereexample10.jpg


Conclusion

Although creating spherical spheres requires a healthy dose of trigonometry and other math, we can avoid all that by using a pre-calculated table of numbers. This table tells us how many rings to put on each row so that the sphere turns out nice and round. There are a few tricks along the way, but weaving this sphere is basically a simple process that any chainmaille weaver with intermediate skills can accomplish.

I wish you the very best in your chainmaille adventures - have fun and enjoy the moment!

Original URL: http://www.mailleartisans.org/articles/articledisplay.php?key=509