Back to that pie: a bit of holding

Holding/ short rowing is used to knit each wedge. The basic rule for holding is followed: stitches are brought into work on the carriage side, and into hold opposite the carriage to avoid floats. The greater the number of sections, for either the full circle or a donut, the smoother the curves at the outer circumference, as can be imagined in the form below, which divided into more sections than those 5 in our original calculation.

The “pie slices” begin and end on open stitches, ultimately requiring a join where the radii meet, using whatever method is preferred by the knitter. Assuming the knit carriage is on left and set for hold in the diagrams below, if all stitches are brought into hold except 1 on the carriage side (or number required by calculations for the individual piece), 2 rows are knit, and action is repeated until all needles are in work, the following shape starts to fill in and a miter with pointed edges is created.

If all the needles are in work, and one begins to bring them into hold opposite the carriage, one begins to fill in the shape creating the form below, and a spiral is created, with circumference edges more rounded.

Like shapes may be stacked sequentially. If shaping at the top of the initial triangle wedge is reversed however,  the following begins to occur.

Knit rows in between the triangles begin to create larger holes in center of pie, and a donut occurs. The donut center can be varied, the knit rows between triangles increased to suit. The illustration below shows some of the variables. The plain knit rows are another factor in smoothing that outer circumference.

Oh the math! “magic formula”

There are many knitting programs that will perform the necessary calculations, as well as a variety of knit calculators. The diophantine formula is the basis for what is know to some knitters as the “magic formula”. In the early 1980s Alles Hutchinson authored a small book on the subject. There is a bit of personal leeway in the results, and the formula may be used in calculating even complex shapes with the proviso that one has the patience to break such shapes into series of simpler ones.

There are many online resources for information and calculators to sort out the math, including a triangle calculator

Using the gauge to match the previous post of 4S and 6R per inch the calculation for the pie divided into five triangles  breaks down into the web calculator result pictured below:

The longhand method for same calculation which follows and also translates to: bring into hold 2 stitches for 4 times, 1 stitch for 80 times. Stitches in shaping are proofed as above: 88 stitches shaped over 84 rows.


Knitting math and pies

Math is non always fun, and is downright dreaded by some. One instance in knitting wherein basic calculations are required is in obtaining stitch and row gauges. I have known one hand knitter who would purchase yarn (not necessarily the one used in pattern), knit happily away, and try the finished product on everyone she knew until she found an accommodating body shape and size. If the large number of family and friends did not oblige, sweaters were stored until such a correct body appeared. Predictable results require careful measurements and some basic formula calculations.

Using home knitting machines to produce circular forms one resorts to breaking down the round object into pie wedges, which in turn are knit as triangles with straight line outer edges. The outer final circumference curve is controlled in a number of ways, one is by creating a far greater number of pie slices. For this exercise I will work with 5 segments. 

There are some math constants. One example: to find the circumference of a circle its diameter is multiplied by pi = 3.14. If the diameter of our knit is 44 inches, its circumference will measure 44 X 3.14 = 138.16 inches. Using the rule of 5 or less than 5, this measurement is rounded to 138 inches.

The radius becomes the width of the pie wedge. In this instance, it would measure 22 inches. Let us assume our gauge is 4 stitches and 6 rows per inch. The radius is converted to stitches: 22 X 4 = 88 sts. The circumference becomes rows:  138 X 6 = 828 rs.  If subdivided into 5 slices, each slice would be composed of 166 rows.

To knit the pie slice, short row are used ; since they happen every 2 rows, our row number for outer edge is divided by 2, yielding the total of now 83, which in this exercise I will round off to the even # 84.

To mesh or not to mesh 4

The following illustrate some of the process involved in planning out fabric akin to the one in the previous post. Black borders outline blocks of 6 stitches/rows,  reflect markings on blank Brother card. In option A: motif is planned and drawn. In this instance it is colored in in green (1), the area it covers will ultimately remain unpunched on card or blank on mylar.   Graph paper may be used to work this out, knit design software, or as in this case, an excel spreadsheet.  A grid is created  with every other square blacked out or colored in (2). Motif is super- imposed on grid (3). Repeat is expanded adding 2 blank rows above each design row (4). Rust squares represent punched holes in card or black squares in mylar.

Option A

Option B: the same motif is lengthened X3 (5). Lace mesh base is drawn out (6). Elongated motif is then superimposed on mesh (7). Electronic patterning on 910 allows for minimal drawing using all black squares, in turn making it necessary to color reverse for lace. Two separate motifs are used, method for programming such repeats is in 910 manual. However,  there are considerations for needle position and pattern selector placement for  this “shortcut” to work properly, the steps are described by Kathleen Kinder and others. I prefer to work with what I “see” in terms of punched holes or squares, this is the method used to develop my previous flower motif swatch. The short supply of mylars may also be a consideration in using them or not for such large, and perhaps limited use design repeats. If interface cables and software are available, other options abound.

Option B

To mesh or not to mesh 3

Many articles were written in the 1980s in Australia, New Zealand, and Britain, some finding their way to newsletters published in the USA at the time investigating this subject. With the advent of electronics the process became “easier”. Kathleen Kinder author of several books on Machine Knitting covering myriad topics (one whole text on lace), also authored Electonic Knitting: an Introduction for Brother and Knitmaster Knitters (?1989) that investigated the move from punchcard to electronics, including lace techniques that in the instance of “filet look alikes” introduced superimposing designs as a quicker method to achieve such fabrics. The common motifs used were often that of a heart or a rose.

One of the many confusing things in lace, is that the punched holes or mylar squares do not represent actual holes in the final fabric. Alternate rows of holes represent first transfers to left, then transfer to right. Brother and Studio punchcard sets included with purchase of machines both include pre-punched cards suitable for this type of mesh. Numbers sometimes varied with machine model year. Studio No. L-6, Brother No 17J (also 20G etc.) are 2 such samples and are vertical mirrored images of each other. Superimposed motifs constitute blank areas of card. Depending on preference some readjustments may be required after a test swatch to alter placement of some of the mesh holes. My fabric below was knit using the basic faggot lace Brother mesh, the corresponding “card” close to 180 rows in length to achieve the brick repeat.

a portion of the card

sideways view of resulting fabric, knit side facing

To mesh or not to mesh 2

The  amended “square mesh card”; grey areas indicate more tape use on reverse.  In basic analysis knit “squares” consist of blocks of blanks on card 12 squares tall by 3 wide, essentially removing 6 lace transfers  (holes in all over card) in those locations; this could be done with software and planned ahead of punching any holes. Electronics capable of programming 2 different motifs increase ease in drawing out pattersn as well as the possibilities in planning larger repeats and repeat sequences

th corresponding swatch viewed on purl side after a quick steaming

flipped 90 degrees

To mesh or not to mesh 1

A good online grouping of mesh repeats is one place to start exploring this topic. Most proprietary large pattern books from machine knitting companies include at least a few suitable cards/mylar samples. They can be used for “all over” fabrics, borders, striping in mixed bands of varying styles, etc. I am presently interested in pursuing a filet crochet like structure by superimposing knit areas onto lace mesh using “lo tech” punchcards or mylar sheets. Filet crochet is often built on a system of solid squares on the more open “ground”. Emulating this type to begin with, here is a punchcard for use on Brother KM resulting in a “square mesh”

a lazy way to explore how adding solid areas to any pattern card is to mask a portion of the card using tape ie. in this case painter’s tape on the reverse side; this is not the best long term solution, but OK for “testing the waters” and sorting out the final repeats. Here is the resulting card reverse side

the card was extended for a full, alternating blocks repeat: a first run at a swatch result showed that oops! I am not quite there with alternating blocks of 4: no worries, more tape is on hand. Below is my preferred, sideways view of present fabric. There is a difference in ridges/ lines as viewed horizontally, every other is thicker because of location of transferred stitches. Knitting sequence is 4  rows of transfers with lace carriage, followed by 2 rows knit with KH throughout. A good starting point.


Japanese punchcard motifs used in Passap E 6000 machines

How years do fly! In “cleaning up” PDFs I found the following, which is actually composed of saved scans of an article I wrote in 1998 (is it really 2011 now?) in my amiga/commodore computer days. The “series” never did happen, the newsletter has long been out of print. The subject was E6000 knitting from Japanese knitting pattern repeats. Binder1

Large scale mesh, breaking rules

Want such a mesh, without hand techniques or extra steps.
In both slip and tuck every space that has a hole, black square, etc. that brings a needle out to to D position (for some unfathomable reason Brother needle positions go A,B,D,E, poor C got skipped) will actually knit. In slip the non selected needles gets skipped, in tuck the non selected needles will hold a loop until that needle is returned to D position.  Side by side loops are troublesome in any stitch type. That aside, tuck can be employed to sequentially lay down loops in some patterns where the lace carriage ultimately moves to produce side by side empty needles. The usual caution with such fabrics: extension rails must be used. Yarn needs to be “friendly” enough to not break easily, and since stitches travel across a wider gap than in single eyelet lace, tension needs to be looser as well. Small changes can make a big difference, and so can patience. I am saving the failed attempts for future felting experiments.

In the fabric below the lace carriage is set for normal lace, the KH carriage to select pattern (KC) and both tuck buttons are depressed. Each carriage works in sequences of 4 rows throughout. For me this experiment will probably fall in the “now that I’ve done it, broken several rules and have one good result  I am over it” category.

Some observations: top bind off as seen in the swatch below, was tight for the fabric. To maximize width, bind off should be around at least 2 gate pegs, even 3 if needed. This allows for completing the task on the machine without adding more work and incorporating hand techniques. Same is worth considering in tuck fabric: the nature of tuck is to be short and fat, lace wants to open up, so this fabric definitely will want to spread. The top approximate 1/3 of the swatch images show use of the same white yarn, knit in  standard single needle mesh. The size difference in “holes” created with the tuck method is easily seen. The white is a 2/8 wool, the other a 16/2 mystery fiber I usually use as waste yarn. The punchcard itself follows as well.

Next on the to do list: “filet crochet” simulations in machine knitting.

knit side
purl side