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Japanese Weaves: Minimum AR Considerations
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Any ring that only passes through two rings of the same wire size must have a minimum aspect ratio of 2 times the wire diameter, or an AR of 2.0. The best example of this is seen in 2 in 1 Chain. This also becomes the minimum AR for the connector rings (the ones which only pass through two other rings) in Japanese 3 in 1, 4 in 1, and 6 in 1.
A single ring which has three rings of the same wire size passing through it has a minimum AR of 2.2, therefore the minimum AR for Japanese 3 in 1 (J3-1) is 2.0 and 2.2.
A single ring passing through four rings of the same wire size requires a minimum AR of 2.4, making the minimum AR for Japanese 4 in 1 (J4-1), and Japanese 6 in 1 Variant (which is techincally 4 in 1 by design), 2.0 and 2.4.
The 6 in 1 Variant sample uses AR of 2.1 and AR of 2.5.
Since 2.4 is the minimum AR for a ring which passes through 4 others of the same size, this makes it the minimum for Japanese 4 in 1 Cube (J4-1C).
Pacman himself is 2.4, the rings in the base have an AR of 2.5.
A single ring which passes through six rings of the same wire size requires a minimum AR of 2.9. Undoubtedly, this causes the minimum AR for Japanese 6 in 1 (J6-1) to be 2.0 and 2.9.
Smaller ring in sample has an AR of 2.1, larger is 2.9.
Any set of two rings of the same size which pass through four rings of the same wire size has a minimum AR of 2.6, making this the minimum AR for the smaller ring of each of the doubled versions of J3-1, J4-1, and J6-1.
Japanese 6 in 2 is doubled J3-1. This weave is seldom seen or used but has AR limits of its own. The sets of two rings passing through six rings of the same wire diameter for this weave requires a minimum AR of 3.3 when 2.6 is used for the smaller rings.
Keeping the AR of the smaller ring at its minimum of 2.6 invokes a mininum AR of 3.8 for the large ring of Japanese 8 in 2.
3.8 also is the minimum AR for Japanese 8 in 2 Cube, albeit, it's very difficult to put together at this AR without mangling the occasional ring.
Japanese 12 in 2 has a minimum AR of 5.2 for the larger rings.
Note: larger ring size in this sample is 0.1 above the minimum AR of 5.3, smaller rings are 2.6's.
in 3 Considerations:
When you move up to tripling rings, the minimum AR relationship becomes more complicated because the middle ring size for both the small and large rings would ideally need to have a slightly smaller inner diameter to cause it not to "float", due to the curve of the inside of the rings.
Multiple Wire Diameters:
When different wire diameters are used for the large and small rings, it becomes more of a matter of inner diameter relationships. It's very common to use smaller wire for the smaller rings, as low AR rings are less common, mostly owing to them being more difficult to manufacture and work with. When you decrease the wire size and maintain the same inner diameter, your AR increases.
This sample is not minimally made, just shown as an example of a smaller wire size used for the smaller rings.
.045" (<18 SWG / 1.14mm) wire, 5/32" (4mm) mandrel (small rings)
.063" (16 SWG / 1.6mm) wire, 1/4" (6.35mm) mandrel (large rings)
It's important to note that ARs are approximate numbers. There is a spectrum of just under 0.1 for any given value, and sometimes what works at the higher end won't work nearing the lower. Rings are not perfect tori either. Minimum ARs are more of a guideline.
With the Japanese weaves, it has been noted that increasing the AR's of the small rings the right amount will lower the minimum AR of the larger rings, if only slightly. I have never tested this theory, but it has been mentioned by others before.
Research for this article caused the mangling of some rings. Sometimes a ring has to take one for the team. Weaving at minimum AR's is not for the meek.
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