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Jens Pind Linkage 3 and Variants - Definitions; Differences and Distinguishing Characteristics
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Jens Pind Linkage 3 and Variants - Definitions; Differences and Distinguishing Characteristics
Article © MAIL User: Titus
INTRODUCTION
This article is about a magnificent spiral weave called Jens Pind Linkage (JPL) and its variants. In the following chapters I will explain how regular JPL is constructed, and how the variants are related to the original chain. Also, I will introduce a relatively simple method to distinguish between different JPL variants.
You don't necessarily have to be familiar with the weave(s), but knowing the basics helps a lot. At least a good thing to do before reading further is to take a look at some tutorials about JPL and perhaps make a small length of the chain. One tutorial for weaving JPL can be found here: Jens Pind Linkage 3 (CGI). I will use basic abbreviations of terms like Aspect Ratio (AR) and Inner Diameter (ID) and I assume you know what they mean. If you become puzzled at any point when reading this article, please feel free to ask me for clarifications via e-mail or pm.
Then, on to the topic:
WHAT'S JENS PIND LINKAGE?
JPL can be approached from different angles. Usually it is considered a spiral weave, more specifically a Spiral 4 in 1 chain with the AR of rings set so tight that it won't unwind. A good AR for JPL is (source dependent) around 2,8-3,0.
However, there is a different approach by thinking that instead of spiraling rings, the chain is made of stacked rings (in a sort of Persian way). JPL and its variants are based on three intertwined stacks of rings. Simply put, when you are making a regular JPL chain, every first, fourth, seventh, tenth etc. ring will eventually form one stack. The same is true for every second, fifth, eighth, eleventh etc. and for every third, sixth, ninth, twelfth and so on. A picture will clarify this:
From now on, let's call the blue stack (1. 4. 7. ...) with the letter A. The green stack (2. 5. 8. ...) is called B and the yellow one (3. 6. 9. ...) C.
Now, what defines JPL as JPL, is the orientation of these stacks. How the stacks get to this orientation in the first place, creating JPL, is explained next.
THE IMPORTANCE OF THE FIRST SIX RINGS
Yes, the very first six rings are the most important rings when you are making JPL. That's because they are the rings that define the orientation of the aforementioned stacks for the whole chain. The following rings just elongate the chain. Let's break this down a bit:
The first three rings:
This is what you should have after taking three rings and weaving them properly by the book. Notice the beginning of a spiral to a certain direction? The rings' top halves are coming towards you and the bottom halves are going away from you. This is the regular start of a JPL, but there is another:
On the left we have the same thing as we had in the last picture, and on the right there's the alternative beginning. Notice that the top halves of both pieces are coming towards you.
These two pieces are the beginnings of a left-handed and the right-handed versions of JPL chains, respectively. So, as with some other chains, JPL has a thing called 'handedness'. This is quite important to understand, if you want to identify different chains.
However, at this point all you need to understand is the fact that the first three rings define the chain's handedness. More specifically, the crucial ring is the third ring, because the first two rings can be connected only one single way.
The fourth ring:
The fourth ring isn't particularly interesting, because it doesn't matter if you connect it to the right or wrong "side" of the previous non-connected (first) ring (You will find this out when you rotate the chain 180 degrees). I prefer to keep it in front of the first ring, but in the aforementioned tutorial the fourth ring is woven behind the first ring. This is just a matter of viewpoint.
The fifth ring:
To get actual JPL, this is the ring you want to get right! The orientation of the fifth ring must be just like this or else you'll end up with an asymmetric JPL-look-alike chain, which has different flexibility and stability properties.
The sixth ring:
To maintain the proper JPL continuity, add the last ring as shown. You can now see the beginnings of the aforementioned stacks(highlights).
There, the defining part is over and the rest should be nothing more than elongating your chain with the fact in mind, that the added ring goes on the proper stack and it has the correct lean. In other words, don't put the ring to the wrong side of the stack (it will cause a distortion in the chain). If everything goes right, with these instructions and the help of tutorials, you should end up with something like this:
THE TWISTSTEP METHOD - IDENTIFYING YOUR JPL CHAINS
Some time ago I came up with this method to help me identify my messed up JPL chains. At the same time I happened to find some JPL variants and gained a much better insight to this particular group of chains. I hope the Twiststep method will be of assistance to you as much as it has been for me.
The method is a versatile tool in identifying as well as quality-checking your 4-in-1 JPL chains. It's based on checking each and every non-connecting ring pairs' orientation while rotating the chain in a proper direction. The ring pairs' orientations will be written down, and the result will be a unique orientation pattern for each JPL variant chain. The method can be used to identify the weave of both right- and left-handed chains (it won't identify the handedness, necessarily).
The method contains 6 steps, the final 2 of which are repeating (marked with an asterisk *):
1. Start from the end ring
2. Identify the handedness
3. Check the first non-connecting ring
4. Twiststep
5. Check the non-connecting ring (*)
6. Twiststep (*)
At first this might feel a bit confusing and complicated, but once you get the hang of it, it's really simple. Now, let's get our hands on our mystery piece. I suggest (for the sake of clarity when learning this) you use left-handed regular JPL like the piece shown in the pics above. I'll be doing the same:
1. Start from the end ring
Take your chain and grab it from either end. Hold the first ring of the chain between your fingers in a vertical position as shown in the picture. You should be looking straight through the first ring.
2. Identify the handedness
The idea behind this phase is the same as above (The first three rings). To see if your chain is left- or right handed, look how the spiral starts. If you hold the left end of the chain and the rings' upper halves come towards you, you have a left-handed chain. Contrariwise, if the rings' upper halves go away from you, you have a right-handed chain. However, if you hold the right end of the chain and the rings' top halves come towards you, it's a right-handed chain. If they go away, it's a left-handed one. Logical or not, this is just my definition.
Notice how the *upper halves* and the end you are holding affect each other?
Left end, coming towards - left-handed
Right end, coming towards - right handed
Left end, going away - right handed
Right end, going away - left handed
My sample piece is left-handed, because I hold the left end and the highlighted The second and third rings' upper halves come towards me.
This might not be the clearest way to see the handedness, and it's not entirely necessary to know it, especially when you are more familiar with the method. It is, however, a thing to know about your chain and the information helps in the fourth step when learning the method.
3. Check the first non-connecting ring
While still holding the first ring in the same position as before, you can notice that the rest of the stack A runs in the same vertical position as the first ring. The idea behind this phase is to see if the next non-connecting (the fourth ring, highlighted in the pic) ring is *in front* or *behind* the ring you're holding at the moment. The example shows it's clearly in front of the first ring, so we'll take a piece of paper and note, for example F (Front). In case it would have been behind, the letter could have been B (Behind). Naturally, you can use any characters you like, but in this article I'll be using these two.
4. Twiststep
The name of this phase tells what you'll do: You will turn the chain one step to the proper direction so that you'll end up with holding the second ring (the first ring in stack B) in the same position as you held the first ring before. The proper direction is the direction your chain twists more naturally as you hold it. In other words, the smallest twist (in degrees) you need to make to get the second ring to the vertical position, is the proper direction. An example:
By twisting my chain roughly 30 degrees clockwise (the same direction you tighten a screw, arrow in the picture), I'm able to get the second ring vertically between my fingers. If I'd twisted the chain anti-clockwise (direction to loosen a screw), I'd need 60 degrees to do the same; thus the clockwise direction is the natural, proper direction. So, remember to twist the chain as little as possible with each step.
How knowing the handedness helps, then? Simply put: The proper direction for the left-handed chain is clockwise and for the right-handed chain it's anti-clockwise. This is true no matter in which hand you're holding the end of the chain.
So, I twist the chain clockwise one step and hold the first ring in stack B.
5. Checking the non-connecting ring (*)
Similarly as in phase number 3, examine the orientation of the non-connecting ring (the second stack B ring) and mark it using the appropriate character.
My non-connecting ring is (B)ehind the ring I'm holding.
6. Twiststep (*)
Let's twist again (like we did last summer -- Ed). The shortest twist you need to make to get a hold of the first stack C ring, is the thing. My chain twists clockwise. Highlighted in the picture is the non-connecting ring you need to check.
From now on, repeat phases 5. and 6. and move on through your chain. Mark the orientations until you get a clear repeating pattern.
I repeated the phases and got a pattern like this: FBFBFBFBF...
I identified the chain as regular JPL, using the following list of patterns:
TWISTSTEP PATTERNS and JPL VARIANTS
The patterns you get are unique to each JPL variant. They also tell you if there's a mistake somewhere in the chain (if the pattern isn't repeating itself). The following chapters are based on results I got when creating the method and applying it to finding new weaves (discussion and pictures here ). NOTE! The patterns aren't absolute, because the "starting" orientation as well as the handedness of the chain will change the sequence you'll write down. More importantly, you should find a trend how different Backs and Fronts change (look for a repeating pattern). Also, if you twist the chain to the "wrong" direction, the patterns won't match the chain as follows.
- Regular Jens Pind Linkage = JPL for short -
Pattern: ...FBFBFBFBF...
Repeating part: FB (Actually FBFBFB)
Because regular JPL is symmetrical and the simplest of JPL variants, the pattern is the easiest to recognize as well.
- Asymmetric or alternate "mistake" JPL = AJPL for short -
Pattern: ...FFFBBBFFFBBBFFF...
Repeating part: FFFBBB
The AJPL pattern is interesting compared to the regular JPL pattern. You can see that the difference between these two is the second, fifth, eight etc. character (because the orientation of the fifth ring!). One small change in ring orientation creates two dramatically different patterns.
- Single Oscillating JPL = 1-O-JPL for short -
Pattern: ...FBFFFBFBFFFBFBFFFB...
Repeating part: FBFFFB (Or FFFBFB)
1-O-JPL is the thing I got first after I had sorted out the JPL and AJPL patterns. I changed one character in the JPL pattern, made a sample piece using that pattern and ended up with this. One stack "oscillates" meaning the bending and stability properties are radically different from normal JPL. This chain is very AR sensitive (AR around 2,8-2,9).
- Single Oscillating AJPL = 1-O-AJPL for short -
Pattern: ...FFFFBBFFFFBBFFFFBB...
Repeating part: FFFFBB (Or FBBFFF)
I was able to make this chain from my sample 1,2mm BA 3,5mm ID rings (AR ~2,95 with springback, used also in this article) and it was relatively stable. It bends a bit better than the 1-O-JPL counterpart so it could be used in practice. However, further stability tests might be needed considering longer periods of use.
- Triple Oscillating JPL = 3-O-JPL for short -
Pattern: ...FBFFBFFBF...
Repeating part: FBF (Actually FBFFBF)
This one I was only able to make from lock washers. The triple oscillation makes the weave very unstable when made from round wire, but I'd presume the possible AR would be less than 2,9 IF it can be made from round wire at all. However, I'm pretty fond of this chain for some reason.
- Triple Oscillating AJPL = 3-O-AJPL for short -
Pattern: ...FFFFFFFFF...
Repeating part: F (Actually FFFFFF)
This one is only theoretical chain with a very clean twiststep pattern. I wasn't even able to make it from my washers. However, I tried different ring/material/ID combinations (round wire) and got an estimate of AR 3,15 that MIGHT be good for 3-O-AJPL. Further studies required...
FINISHING WORDS
The field of JPL and its variants is far from clear. Most likely because regular Jens Pind Linkage happens to be the most popular and practical JPL chain out there, for now. Further research could be done based on these aspects I have presented in this article, or someone could take defining JPL to a totally different direction. I truly hope reading this brings you closer to this great family of chains and helps you understand it more.
If you notice any flaws, typos or just would like to comment this article, please feel free to PM or e-mail me. Also questions and discussion are greatly accepted.
- Antti Tiihonen, Titus -
This article is about a magnificent spiral weave called Jens Pind Linkage (JPL) and its variants. In the following chapters I will explain how regular JPL is constructed, and how the variants are related to the original chain. Also, I will introduce a relatively simple method to distinguish between different JPL variants.
You don't necessarily have to be familiar with the weave(s), but knowing the basics helps a lot. At least a good thing to do before reading further is to take a look at some tutorials about JPL and perhaps make a small length of the chain. One tutorial for weaving JPL can be found here: Jens Pind Linkage 3 (CGI). I will use basic abbreviations of terms like Aspect Ratio (AR) and Inner Diameter (ID) and I assume you know what they mean. If you become puzzled at any point when reading this article, please feel free to ask me for clarifications via e-mail or pm.
Then, on to the topic:
WHAT'S JENS PIND LINKAGE?
JPL can be approached from different angles. Usually it is considered a spiral weave, more specifically a Spiral 4 in 1 chain with the AR of rings set so tight that it won't unwind. A good AR for JPL is (source dependent) around 2,8-3,0.
However, there is a different approach by thinking that instead of spiraling rings, the chain is made of stacked rings (in a sort of Persian way). JPL and its variants are based on three intertwined stacks of rings. Simply put, when you are making a regular JPL chain, every first, fourth, seventh, tenth etc. ring will eventually form one stack. The same is true for every second, fifth, eighth, eleventh etc. and for every third, sixth, ninth, twelfth and so on. A picture will clarify this:
From now on, let's call the blue stack (1. 4. 7. ...) with the letter A. The green stack (2. 5. 8. ...) is called B and the yellow one (3. 6. 9. ...) C.
Now, what defines JPL as JPL, is the orientation of these stacks. How the stacks get to this orientation in the first place, creating JPL, is explained next.
THE IMPORTANCE OF THE FIRST SIX RINGS
Yes, the very first six rings are the most important rings when you are making JPL. That's because they are the rings that define the orientation of the aforementioned stacks for the whole chain. The following rings just elongate the chain. Let's break this down a bit:
The first three rings:
This is what you should have after taking three rings and weaving them properly by the book. Notice the beginning of a spiral to a certain direction? The rings' top halves are coming towards you and the bottom halves are going away from you. This is the regular start of a JPL, but there is another:
On the left we have the same thing as we had in the last picture, and on the right there's the alternative beginning. Notice that the top halves of both pieces are coming towards you.
These two pieces are the beginnings of a left-handed and the right-handed versions of JPL chains, respectively. So, as with some other chains, JPL has a thing called 'handedness'. This is quite important to understand, if you want to identify different chains.
However, at this point all you need to understand is the fact that the first three rings define the chain's handedness. More specifically, the crucial ring is the third ring, because the first two rings can be connected only one single way.
The fourth ring:
The fourth ring isn't particularly interesting, because it doesn't matter if you connect it to the right or wrong "side" of the previous non-connected (first) ring (You will find this out when you rotate the chain 180 degrees). I prefer to keep it in front of the first ring, but in the aforementioned tutorial the fourth ring is woven behind the first ring. This is just a matter of viewpoint.
The fifth ring:
To get actual JPL, this is the ring you want to get right! The orientation of the fifth ring must be just like this or else you'll end up with an asymmetric JPL-look-alike chain, which has different flexibility and stability properties.
The sixth ring:
To maintain the proper JPL continuity, add the last ring as shown. You can now see the beginnings of the aforementioned stacks(highlights).
There, the defining part is over and the rest should be nothing more than elongating your chain with the fact in mind, that the added ring goes on the proper stack and it has the correct lean. In other words, don't put the ring to the wrong side of the stack (it will cause a distortion in the chain). If everything goes right, with these instructions and the help of tutorials, you should end up with something like this:
THE TWISTSTEP METHOD - IDENTIFYING YOUR JPL CHAINS
Some time ago I came up with this method to help me identify my messed up JPL chains. At the same time I happened to find some JPL variants and gained a much better insight to this particular group of chains. I hope the Twiststep method will be of assistance to you as much as it has been for me.
The method is a versatile tool in identifying as well as quality-checking your 4-in-1 JPL chains. It's based on checking each and every non-connecting ring pairs' orientation while rotating the chain in a proper direction. The ring pairs' orientations will be written down, and the result will be a unique orientation pattern for each JPL variant chain. The method can be used to identify the weave of both right- and left-handed chains (it won't identify the handedness, necessarily).
The method contains 6 steps, the final 2 of which are repeating (marked with an asterisk *):
1. Start from the end ring
2. Identify the handedness
3. Check the first non-connecting ring
4. Twiststep
5. Check the non-connecting ring (*)
6. Twiststep (*)
At first this might feel a bit confusing and complicated, but once you get the hang of it, it's really simple. Now, let's get our hands on our mystery piece. I suggest (for the sake of clarity when learning this) you use left-handed regular JPL like the piece shown in the pics above. I'll be doing the same:
1. Start from the end ring
Take your chain and grab it from either end. Hold the first ring of the chain between your fingers in a vertical position as shown in the picture. You should be looking straight through the first ring.
2. Identify the handedness
The idea behind this phase is the same as above (The first three rings). To see if your chain is left- or right handed, look how the spiral starts. If you hold the left end of the chain and the rings' upper halves come towards you, you have a left-handed chain. Contrariwise, if the rings' upper halves go away from you, you have a right-handed chain. However, if you hold the right end of the chain and the rings' top halves come towards you, it's a right-handed chain. If they go away, it's a left-handed one. Logical or not, this is just my definition.
Notice how the *upper halves* and the end you are holding affect each other?
Left end, coming towards - left-handed
Right end, coming towards - right handed
Left end, going away - right handed
Right end, going away - left handed
My sample piece is left-handed, because I hold the left end and the highlighted The second and third rings' upper halves come towards me.
This might not be the clearest way to see the handedness, and it's not entirely necessary to know it, especially when you are more familiar with the method. It is, however, a thing to know about your chain and the information helps in the fourth step when learning the method.
3. Check the first non-connecting ring
While still holding the first ring in the same position as before, you can notice that the rest of the stack A runs in the same vertical position as the first ring. The idea behind this phase is to see if the next non-connecting (the fourth ring, highlighted in the pic) ring is *in front* or *behind* the ring you're holding at the moment. The example shows it's clearly in front of the first ring, so we'll take a piece of paper and note, for example F (Front). In case it would have been behind, the letter could have been B (Behind). Naturally, you can use any characters you like, but in this article I'll be using these two.
4. Twiststep
The name of this phase tells what you'll do: You will turn the chain one step to the proper direction so that you'll end up with holding the second ring (the first ring in stack B) in the same position as you held the first ring before. The proper direction is the direction your chain twists more naturally as you hold it. In other words, the smallest twist (in degrees) you need to make to get the second ring to the vertical position, is the proper direction. An example:
By twisting my chain roughly 30 degrees clockwise (the same direction you tighten a screw, arrow in the picture), I'm able to get the second ring vertically between my fingers. If I'd twisted the chain anti-clockwise (direction to loosen a screw), I'd need 60 degrees to do the same; thus the clockwise direction is the natural, proper direction. So, remember to twist the chain as little as possible with each step.
How knowing the handedness helps, then? Simply put: The proper direction for the left-handed chain is clockwise and for the right-handed chain it's anti-clockwise. This is true no matter in which hand you're holding the end of the chain.
So, I twist the chain clockwise one step and hold the first ring in stack B.
5. Checking the non-connecting ring (*)
Similarly as in phase number 3, examine the orientation of the non-connecting ring (the second stack B ring) and mark it using the appropriate character.
My non-connecting ring is (B)ehind the ring I'm holding.
6. Twiststep (*)
Let's twist again (like we did last summer -- Ed). The shortest twist you need to make to get a hold of the first stack C ring, is the thing. My chain twists clockwise. Highlighted in the picture is the non-connecting ring you need to check.
From now on, repeat phases 5. and 6. and move on through your chain. Mark the orientations until you get a clear repeating pattern.
I repeated the phases and got a pattern like this: FBFBFBFBF...
I identified the chain as regular JPL, using the following list of patterns:
TWISTSTEP PATTERNS and JPL VARIANTS
The patterns you get are unique to each JPL variant. They also tell you if there's a mistake somewhere in the chain (if the pattern isn't repeating itself). The following chapters are based on results I got when creating the method and applying it to finding new weaves (discussion and pictures here ). NOTE! The patterns aren't absolute, because the "starting" orientation as well as the handedness of the chain will change the sequence you'll write down. More importantly, you should find a trend how different Backs and Fronts change (look for a repeating pattern). Also, if you twist the chain to the "wrong" direction, the patterns won't match the chain as follows.
- Regular Jens Pind Linkage = JPL for short -
Pattern: ...FBFBFBFBF...
Repeating part: FB (Actually FBFBFB)
Because regular JPL is symmetrical and the simplest of JPL variants, the pattern is the easiest to recognize as well.
- Asymmetric or alternate "mistake" JPL = AJPL for short -
Pattern: ...FFFBBBFFFBBBFFF...
Repeating part: FFFBBB
The AJPL pattern is interesting compared to the regular JPL pattern. You can see that the difference between these two is the second, fifth, eight etc. character (because the orientation of the fifth ring!). One small change in ring orientation creates two dramatically different patterns.
- Single Oscillating JPL = 1-O-JPL for short -
Pattern: ...FBFFFBFBFFFBFBFFFB...
Repeating part: FBFFFB (Or FFFBFB)
1-O-JPL is the thing I got first after I had sorted out the JPL and AJPL patterns. I changed one character in the JPL pattern, made a sample piece using that pattern and ended up with this. One stack "oscillates" meaning the bending and stability properties are radically different from normal JPL. This chain is very AR sensitive (AR around 2,8-2,9).
- Single Oscillating AJPL = 1-O-AJPL for short -
Pattern: ...FFFFBBFFFFBBFFFFBB...
Repeating part: FFFFBB (Or FBBFFF)
I was able to make this chain from my sample 1,2mm BA 3,5mm ID rings (AR ~2,95 with springback, used also in this article) and it was relatively stable. It bends a bit better than the 1-O-JPL counterpart so it could be used in practice. However, further stability tests might be needed considering longer periods of use.
- Triple Oscillating JPL = 3-O-JPL for short -
Pattern: ...FBFFBFFBF...
Repeating part: FBF (Actually FBFFBF)
This one I was only able to make from lock washers. The triple oscillation makes the weave very unstable when made from round wire, but I'd presume the possible AR would be less than 2,9 IF it can be made from round wire at all. However, I'm pretty fond of this chain for some reason.
- Triple Oscillating AJPL = 3-O-AJPL for short -
Pattern: ...FFFFFFFFF...
Repeating part: F (Actually FFFFFF)
This one is only theoretical chain with a very clean twiststep pattern. I wasn't even able to make it from my washers. However, I tried different ring/material/ID combinations (round wire) and got an estimate of AR 3,15 that MIGHT be good for 3-O-AJPL. Further studies required...
FINISHING WORDS
The field of JPL and its variants is far from clear. Most likely because regular Jens Pind Linkage happens to be the most popular and practical JPL chain out there, for now. Further research could be done based on these aspects I have presented in this article, or someone could take defining JPL to a totally different direction. I truly hope reading this brings you closer to this great family of chains and helps you understand it more.
If you notice any flaws, typos or just would like to comment this article, please feel free to PM or e-mail me. Also questions and discussion are greatly accepted.
- Antti Tiihonen, Titus -
Original URL: http://www.mailleartisans.org/articles/articledisplay.php?key=523
