Here's a hint that helped me understand much of the mystery of phone cord kinks:
Notice how in bhouston's image above the coil on the left of the kink has opposite spin as the coil on the right. With this kind of kink there is no solution but to completely re-coil one of the sides.
I think you could "fold" the whole cable back on itself at that point. Instead of unwinding around the axis of the helix, unwind around an axis at a right-angle.
No, dual is correct. There's no local way to unkink the phone cable in that image. Just notice that the orientation (whether a cord spirals clockwise or counterclockwise as you travel along it) doesn't change in a properly unkinked cord, but the left and right side of the cord in the photograph have opposite orientations. Whatever manipulation you do locally around the kink (even if it involves rotating the whole rest of the cord around rigidly) won't change the orientation of either side.
A corollary to this is that the kink in the picture wasn't created locally, and is not the kind of kink you accidentally create. Though you can create a stretch of mis-oriented cord by trying to fix what starts as a local kink, but that requires fiddling with that entire section of cord.
Chirality refers to the type of twist. While the side of the cord that is inner or outer will stay the same, but if you're looking from one end toward the other, the cord will approach you in a clockwise or counter clockwise circles. Possibly clearer, if you imagine screws[1] that are turned clockwise or counter clockwise to drive into a hole.
A kink where the chirality is different on each side is different than a kink where it remains the same on each side. It is possible to create a disturbance where the chirality or twisitng remains the same on both side of the disturbance.
Here is a drawing of how to create a disturbance in a telephone cord.[2] And, here is another drawing where two rigid rods have a flexible connector.[3] In these cases the chirality is the same on both sides, so you could just undo the loop.
However, in the photograph that was posted, the chirality has changed[1]. So, you would have to straighten and recoil one of the sides to match the other's chirality.
That was my first thought on seeing the second picture, but that's not what's being discussed:
'The shape that Bertoldi and colleagues at SEAS unexpectedly encountered is a hemihelix with _multiple_ “perversions.”'
[...]
'there is a critical value of the aspect ratio at which the resulting shape transitions from a helix to a hemihelix with _periodic reversals_ of chirality'.
A phone cord may have multiple reversals, but they almost certainly won't be periodic.
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[ 3.0 ms ] story [ 47.9 ms ] threadhttp://i.imgur.com/AS7UI.jpg
:)
A corollary to this is that the kink in the picture wasn't created locally, and is not the kind of kink you accidentally create. Though you can create a stretch of mis-oriented cord by trying to fix what starts as a local kink, but that requires fiddling with that entire section of cord.
A kink where the chirality is different on each side is different than a kink where it remains the same on each side. It is possible to create a disturbance where the chirality or twisitng remains the same on both side of the disturbance.
Here is a drawing of how to create a disturbance in a telephone cord.[2] And, here is another drawing where two rigid rods have a flexible connector.[3] In these cases the chirality is the same on both sides, so you could just undo the loop.
However, in the photograph that was posted, the chirality has changed[1]. So, you would have to straighten and recoil one of the sides to match the other's chirality.
[1] Screws http://imgur.com/VbBWL7F
[2] Cords http://imgur.com/yJWrAIt
[3] Rods http://imgur.com/Qytn8o1
'The shape that Bertoldi and colleagues at SEAS unexpectedly encountered is a hemihelix with _multiple_ “perversions.”' [...] 'there is a critical value of the aspect ratio at which the resulting shape transitions from a helix to a hemihelix with _periodic reversals_ of chirality'.
A phone cord may have multiple reversals, but they almost certainly won't be periodic.