Thursday, February 28, 2013

Wire bending jig for zip crochet

This is typical of the jigs I have used. The dowel pins have a diameter about 7x that of the wire. The spacing between the two lower pins is about 1.7x the wire diameter. The altitude of the triangle connecting the centers of the pins is about 14 wire diameters.

Bending 8 gauge AWG copper wire.

A walking chain stitch being assembled.

Zip crochet: splices

A zip crochet splice.

The chain (the horse's path) must splice to itself at the completion of the work. This is easily accomplished by overlapping a few links. If the wire is cut just past a bend, that bend can be bent further to seize some portion of the other end of the chain.

A half-completed splice.

Tuesday, February 26, 2013

Bent-wire crochet: remounts

Where a clown remounts the horse, or, in plain speech, at the base of a crochet stitch, the left/right rhythm of the chain needs to be maintained. The approach diagrammed above seems to be the most practical. The reach, the first part of the crochet stitch (the angled red line in the diagram,) determines the path of the returning chain stitches. The reach needs to be angled backwards so that at least one of the fully completed links of the chain can be engaged. In the finished fabric this three-way join will be deformed into a nearly equiangular 'Y.'

Beginning of a remount in bent-wire crochet.

Bent-wire crochet: dismounts

Dismounts are the places where a clown gets down off the horse, or, in plain speech, the places where crochet stitches attach to a previously completed part of the chain. Dismounts allow more freedom than remounts because the clown does not need to be completely in-stride with the horse. The easiest possibilities are aligning the reach (the straight run of wire that the clown straddles, indicated in red in the figure above) with a protrusion of the chain on the far side (see the left side of the figure) or aligning with a protrusion on the near side (see the right side of the figure above.) Aligning with the far side seems easier.

The dismounts are necessarily enantiomorphic. For example, if a clown dismounting on the right side of the horse starts on his right foot, then a clown dismounting on the left side of the horse starts on his left foot. Just as for remounts, there will be an even number of horse steps between dismounts to the same side, and an odd number of horse steps between dismounts to opposite sides.

Setting up a dismount to the left.

Beginning a dismount to the left that is aligned with a far-side protrusion.

Monday, February 25, 2013

More dances with hooves: a correction

Thinking about it some more, the previous post understates the constraints on the coordination of the clown paths with the horse's path, and so comes to the wrong conclusion.

The clowns actually need to remount fully in step with the horse. This is simply because the clown's chain transmutes into a continuation of the horse's chain at the join. (As a practical matter of crochet, we have more freedom in how we do the dismount, but we'll see that that cannot save the day.)

Because our ambition is to make the work truly ambidextrous and optimally strong, all remounts must be made the same way; for example, remounts from the left side of the horse must be a mirror image of a remounts from the right side of the horse. For any two remounts on the same side to be done the same way, we need them to be separated by an even number of horse steps. But on the other hand, for any two remounts from different sides to be done the same way (that is, they must be mirror images of each other,) they must be separated by an odd number of horse steps. As there is no number that is both even and odd, in walking crochet there is no way that all edges can be of equal length.

Friday, February 22, 2013

Ambidextrous crochet: the parable of the two-legged horse

There is something sad in the 21st century about doing one right-handed stitch after the other. This post looks at what happens in crochet when the ambidextrous walking stitch is substituted for the chain stitch.
Imagine a two-legged horse that walks around in a closed circuit on a small, dusty planet. Its path, however serpentine it might be, never crosses over itself. The second time around the circuit, and all later times around it, the horse steps exactly in its own hoof prints.
Imagine also, there are clowns on the planet that like to ride horseback. This particular time around the horse's circuit, at a point in time and space we call START, all the clowns are astride the horse's back.
When afoot, clowns never cross over their own tracks, the horse's tracks, or anyone else's tracks. Clearly then, it matters to each clown which side of the horse he dismounts from, since that limits where he can walk. One at a time, at their own whim, clowns dismount from whichever side of the horse they choose, and wisely waddle over to some future point on the horse's route (which is to say, they never go to a point on the circuit that the horse has already passed since START.) There they wait to remount the horse. (A little thought will convince you that a clown that dismounts on the horse's right must also remount on its right—assuming the little planet is a topological sphere—and likewise for the left; this is a consequence of the Jordan Curve Theorem.) 
When the horse reaches START again, we find all the clowns have remounted the horse.

The footprints left in the little planet's dust represent one way an article that is a topological sphere can be crocheted in walking stitches--and this is about how the stitches will look. The horse's tracks are the plain walking stitches, the clowns' tracks are crochet stitches with walking stitches inside (rather than the chain stitches of the traditional technique.)  Of course, since a crocheter can only work in one place at a time, the clown tracks will actually be made by waiting till the point where the clown remounts the horse, making a straight run to where he dismounts, turning and chaining back astride the straight run.

We don't need a sphere to draw the diagram on. If we imagine the small planet is covered with a rubber skin, we can pick someplace where nobody happened to step, cut a small round hole there, and stretch the perimeter of the hole until the rubber skin pulls flat (this gives us a Schlegel diagram.) Now, spotting the hoofprints of the horse, we can stretch the rubber skin still more until the horse's circuit becomes a circle. (Notice that none of the paths crossed on the planet, and none will cross after all this stretching.) So our diagram of footprints and hoofprints can always be simplified to circular horse path  connected by inner and/or outer chords of non-crossing clown paths.

One constraint needs to be added to the story. In the interest of the strength of the fabric, walking stitches should engage each other as fully as possible wherever they meet: preferably they will engage at two footsteps, not just one. In terms of the fable, a clowns first two steps after dismounting, and last two steps before remounting, should superimpose on horse steps. That creates a phasing constraint between horse steps and clown steps that is easier to draw than put in words (see the diagram above.)

A natural question is whether this constraint interferes with other constraints we may wish to impose, such as equal path lengths. If path lengths are even, it does not.

Thursday, February 21, 2013

Bent-wire crochet: the crochet stitches

"The Captain, in a wig, generally sat in a corner chair with arms to it, never doing anything that ever I saw. He was old and getting frail, eighty-five or eighty-six, I believe. Sometimes when he was not well he wore a plaid cloak, and a nightcap, red or white, made by his industrious wife in a stitch she called shepherd's knitting; it was done with a little hook which she manufactured for herself out of the tooth of an old tortoise-shell comb, and she used to go on looping her homespun wool as quick as fingers could move, making not only caps, but drawers and waistcoats for winter wear for the old husband she took such care of." 
—Elizabeth Grant, Memoirs of a Highland Lady, a recollection from 1812/13. 

"Crochet—so called from the French name of the instrument wherewith it is worked—though long known and practiced in Scotland, in its simplest form, under the name Shepherd's knitting, did not attract particular attention until within the last seven years. Since that time it has been brought to great perfection, and has obtained the preference over all other ornamental works of a similar nature." 
—Frances Lambert, "Handbook of Needlework," 1846.

Crochet was revolutionized in the first half of the nineteenth century by the introduction of new stitches and new hooks suited to making them. The earlier, more basic technique (it is variously called slip stitch or bosnian crochet, shepherd's or shepherd's crook knitting) is simply chain stitches worked through each other. Articles of shepherd's crook knitting can be country-charming to our eyes today, but they held little consumer appeal in a time when everyday life was a bit too country. Shepherd's crook knitting remained a stay-at-home Cinderella, a craft practiced only in scattered maritime communities of Europe.

A traditional hook for shepherd's crook knitting (a.k.a., slip stitch crochet.) Image from String Geekery.

Even in shepherd's crook knitting, you can put a stitch absolutely anywhere you please (it seems crochet's real desire is to make a cobweb, not a fabric,) but that will just leave you with a long, loose, unconsolidated stitch. The nineteenth-century innovation was a simple way to make a stitch reach out a long way, but work back to where it started in a series of chain stitches, chain stitches that were made all the tighter by a helical overwrap of yarn—the very yarn of the original reach.

Now, for the first time, a seamless article could be made with any desired degree of rigidity, security from unravelling, and structural ornamentation. The killer app turned out to be purses. With in a few years the old way of making coin purses, spool knitting, was out, and crochet was in. As the preferred wrapper of money, articles of crochet were now to be found in every bank and city street, and aboard every Grand Tour. Cinderella never missed another ball.

Around 1840, when the new technique was coming over in a wave, the British called it crochet ("hook"in French) because the news was coming from France, but we now know that the first crochet patterns had been published in Sweden twenty years earlier. The Swedes are the only people who did not name crochet for its remarkable hook, so it is plausible that their ancestors made the innovations of crochet's finger-worked era as well. (A plausible reason why it is only scattered maritime communities in Europe that know how to do shepherd's crook knitting is the Vikings.)

The technique of the new stitches, called, single, double, treble, etc., crochets, involves the wrapping of extra turns of yarn, or yarn-overs, on the shaft of the crochet hook at certain stages in the making of the stitch. Since a hook shaped like a shepherd's crook cannot very well store on its shaft extra turns of a suitable diameter for its hook to later pull through, the new stitches required redesigned hooks as well: modern crochet hooks are more cylindrical and less aggressively hooked.

A challenge in bent-wire crochet is to make these crochets, these out-and-back stitches, with the same assembly technique used for the chain stitch. My approach has been to make the reach out to the point of attachment with straight wire, then turn, and work a chain back that straddles the reach (rather than being helically wrapped by it as in the traditional technique.) The sculpture in the image below displays an approximately 13-tuple crochet stitch worked in this technique (in this case, there's nothing attached at the far end of the crochet stitch—not something you could do in yarn.)

Interaction. Galvanized steel wire.

Wednesday, February 20, 2013

Bent-wire crochet: making chains from coils

A left-handed coil starting to form a right-hander's chain stitch.

The sailor's method of making a chain stitch (The Ashley Book of Knots #2868) is tantamount to making the stitch from the turns of a coil, and sometimes it is done this way (#2870.) The handedness of the coil determines the handedness of the chain stitch. Ironically, a left-handed coil yields a right-hander's chain stitch, and a right-handed coil yields a left-hander's chain stitch. The coil unrolls about a third of a turn at each stitch to pass through and extend the chain.

A right-hander's chain stitch made from a left-handed coil.

A walking chain stitch, i.e., a chain of alternating left- and right-handed links, must be made from a coil that is alternately left- and right-handed, that is, a figure-eight coil.

(An easy way to tell the handedness of a coil is the slant of its front side. In a left-handed coil the slant is like the middle of an 'S', in a right-handed coil the slant is like the middle of a 'Z'. A mnemonic is that the pairs L-R and S-Z are each in alphabetical order.)

S and Z: a left-handed coil and a right-handed coil.

Bent-wire crochet: the walking chain stitch

A left-hander's chain stitch.

A right-hander's chain stitch.

Fabric artists learn the role each hand plays in a particular technique, but typically resist learning how to switch those roles, even though this handedness has consequences for the work they can produce. For example, above, the chain stitches typical of left- and right-handed crocheters.

In doing flat work (i.e., when not working in the round, where the same stitch can be repeated endlessly,) the usual stratagem upon coming to the end of a row is to turn the work over to avoid the awkwardness of working the next row in the opposite handedness. The fabric is turned over, even though the texture is coarsened, as only every other row will look the same. In the nineteenth century, crocheters disliked coarse fabric textures as much as they disliked working left-handed, so they would actually cut the yarn in order to do the next row right-handed from the same side!

Today, when computer graphics has forced us to be more sophisticated about surfaces and their description, and emboldened us to be more ambitious in what we attempt in the making of fabrics, this sort of limping is out of date. A modern fabric artist should be able to work their technique both left-handed and right-handed, and as well from either side of the fabric.

In order for a fabric technique itself to be modern, it must be ambidextrous. The only ambidextrous sort of chain stitch I know of is a chain that alternates between left- and right-handed links, what I call a walking chain stitch.

Walking chain stitches.

Monday, February 18, 2013

Bent-wire crochet

Wire crochet is usually formed on a hook, the wire being bent as each stitch is made. Using this traditional technique, it is difficult to precisely or variably size the gauge of the stitches. Also, when heavy steel wire is being worked (as for concrete reinforcement,) the size of the hook and the strength to wield it can be limiting.

Alternatively, in a new technique, crochet stitches can be assembled from machine-formed wire coils. The pre-formed coils precisely set the size of each stitch, and most of the strenuous bending will have already been accomplished by a computer-controlled machine.

A right-hander's chain stitch viewed from the front.

The same chain viewed from the rear.

Crochet, though it often looks complicated, consists solely of the chain stitch and the various ways the chain stitch can be worked through itself. The more modern crochet stitches, i.e., those introduced in the nineteenth century—the treble crochet for example—are actually nothing but a short length of chain stitch worked in a different way. Thus, there is essentially only one kind of stitch that needs to be machine-formed in the coil.

There are two ways to form a chain stitch, one more familiar to sailors (The Ashley Book of Knots #2868), the other more familiar to crocheters. Both are relevant here. The sailor's technique is to form hitches and push them through the chain, the crocheter's technique is to form loops on a hook and pull them through the chain.

Ashley shows the hitches being formed in front of the chain and being pushed down through it. From a crocheter's perspective, this is working from the backside, so Ashley's drawing is a rear view of a chain. But a sailor might just as well form the hitches behind the chain, and push them up through the chain, giving a perfect correspondence with a crocheter's perspective.

 If all the hitches to be made in the sailor's technique are made in advance, the result is a coil of wire that gets pushed through the growing chain one turn at a time.

In crochet, by convention, the front side of the chain stitch is the side that the hook enters from. The appearance of the stitch as viewed from the front will depend on whether the crocheter is left- or right-handed, but it can be fancifully described in both cases (see image of a right-hander's chain stitch above) as looking like a trail left by horseshoes, the crotcheter having progressed in the same direction as the horse.

One link of a chain stitch.

Since the chain stitch is periodic, any way of cutting a chain into lengths one-period long will reveal it to be composed of identical pieces. I find it convenient to imagine segmenting the chain into links that look like horseshoes having a long leg and a short leg. The long leg (the first-formed part of the stitch) is a simple straight run, the short leg (the last-formed part of the stitch) ends in a bend transverse to the plane of the horseshoe. These transverse bends protrude on the back side of the chain like vertebrae on a swimmer's back. That makes it easy to remember how to tell the front of a chain stitch from the back.