Category: Circles and Squares

Knitting math and pies

Math is not 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 a 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 rows 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.

Approaching “circular knits” on the machine: a series

Circular sweaters and vests have been in the pattern marketplace for a while, and there are very few online resources for purchasing patterns for machine knitting. My first attempt at one such pattern was a hand-knit for my granddaughter. It began on long circulars and was worked from the outer diameter, with stitches decreased at intervals, eventually bound off at the center. Most adult sweaters and vests both in HK and crochet are worked from the center out. A common diagram for such sweaters regardless of approach is seen below, a vest could result by simply omitting the sleeves.

Diagram A

Placement and shapes of sleeves are crucial to fit. A straight sleeve top as seen in dropped shoulder sweaters can result in the sleeve opening occurring on the arm inches below the shoulder, making the top of the circle that forms the collar flop around, and the sweater is hard to keep on (the result in my hand knit). Better shoulder fit and having a cap at the top of the sleeve, whether traditional or raglan and adjusting back garment width can achieve stability. In large sizes created by simply making the circle larger, the fit becomes very different in the front, and there are other, better ways to achieve a similar look. Calculations involved in planning these garments share common methods with “doilies”, shawls, ruffles, and more.

In hand knit/crochet another approach is to knit a square/rectangle variant, which can begin and end in open stitches. This piece is folded in half, circulars are used to pick up all the open stitches which now become the inner diameter of a circle, and increases are made regularly, evenly across the rows at intervals to achieve the desired outer diameter. The opening created by the folded fabric becomes the armhole, which may have to be partially stitched closed upon completion of the piece depending on size requirements.

Diagram B: red line represents fold

On the home knitting machines evenly spaced increases and decreases are possible but not practical, requiring removal of the kniting whether on garter bar or ravel cord, with rehanging of all the stitches after adjusting the number of needles in use. Patterning can continue if this is done on plain knit rows, and design shifts are taken into consideration. Though circular knits can be achieved using a ribber, there are distinct differences in tension between the two beds in Japanese machines, not so in Passap knitting. Here again, increasing/decreasing evenly across rows impractical if not impossible. Increases along the outer edges of the knit are easy, but the result is a series of triangles meeting and pointing down from the garment on that edge, a common sight in the marketplace at the moment, but not so good if a circle is the desired shape. One approach on the machine can be seen in the diagram below. The central shape is shared with the above diagram, but the circle is broken up so the garment becomes a flat construct. “Extra” smaller rectangles on the side represent a possible longer cap sleeve. Here the whole piece would be folded in half and seamed. If the center shape has straight sides adjustments can be made in seaming for the desired armhole measurement. The remaining problem: how to get that outer “diameter” created by the bottom and top of the piece to approach the width needed without increases and decreases across rows. With this approach the seams that bring the top and bottom sections together will move toward the front of the garment, so the joining method and its visibility is a consideration.

Diagram C

Doilies: Lace meets hold and goes round

This post was written originally in 2011, in one of my lace “phases”, with test swatches knit on a 910 using a mylar sheet or on my 892E Andare Brother punchcard machine. Early on many of the posts were used to record what I had made, sometimes providing the repeats, but not usually step by step instructions. The shares were intended for anyone with previous experience who might want to create their own version of such fabrics. Now in 2020, my swatches are usually knit with download cables img2track on a 930 or less frequently on a 910 using ayab, via an iMac. In revisiting those early posts I sometimes find myself wondering about the content and how their fabrics were achieved. At the time, as now, I tried to respect copyrights. Since then many machine knitting publications are now downloadable for free online and I began to include information from them, and when possible, links to the source.

There is an excellent online resource for the Bond Machine. Techniques are applicable to other KM models for those who enjoy hand techniques. The round lace tablecloth series provides a number of “doily” charts.
The slip setting in both directions is used on the KH for automatic shaping, end needle selection is canceled. It is critical that carriages be off the machine and on the lace extension rails while the alternate carriage is in use as they both engage the timing belt. The latter can be broken if pulled in opposing directions at the same time.
Comparing a pattern on 2 machines: one of the critical differences when using 2 carriages to select patterns, is that on electronic machines such as the 910 or later models, with each carriage pass the design repeat advances one row. With Brother punchcards, the first pass of the second carriage does not advance the card as it makes its first “trip” from the opposite side, the previous preselection and function are repeated.
When operating the lace carriage on a punchcard machine, one of the critical differences is that the preselection row from left to right made with the lace carriage is performed with the punchcard not locked as usual, but rather, set to advance normally. From:  Any circular knit that is shaped with sideways holding segments will need to be seamed when completed. Taking that into account, at least one row is knit with “doily” yarn from left to right after several rows are knit in waste-yarn before the transfers to create open stitches are begun. It is a personal choice and preference whether upon completion of the required number of segments to join by rehanging open stitches and binding off on the machine or grafting (the method I prefer) with the work off the machine after several rows of waste yarn and dropping the work off the KM.
When 2 carriages are selecting needles from opposite sides, the “rule” as provided in the manual is broken, the card starts in the locked position on one side, is released when it reaches the opposite one, as is standard in knitting other stitch types. In this chart, patterning begins with the locked reader and the LC used for the initial preselection row Beginmomg with the LC on the left, the end needle selection is canceled. The two positions in LCs for both punchcard and electronic KMsBack in 2002 exchanges with a fellow member of an Australian Yahoo Group, OzMKers, led to her final edit of this half punchcard repeat for the test doily. All transfers are in the same direction, to the right
A 24 stitch sample, knit in cotton yarn. The center of the circle needs to be managed as opposed to simply gathering it in order to keep the finished shape flat. It is possible for the lace carriage to transfer while at the same time preselecting every needle to be knit by the next pass of the knit carriage from the opposite side. An expanded view of part of the repeat:  In order to get the repeat working properly, I found I needed to edit out one of the punched holes at the start of each repeat, revised card  The original and the amended start of each segment are shown below, I skipped the extra knit rows numbered 21-23 on the original punchcard with the intention of eliminating extra knit rows at the very center, making the circumference at the closure of the doily smaller. I prefer to start with knit rows, in which case the first preselection row would take place from the right. Note that lace transfer marks are directly on top of the solid lines representing knit stitches     If drawing on the back of mylar for use on the 910, either image may be drawn as is, with the number 1 pattern case “A” selector reverse lever to up position.
Repeat design principles are shared in creating edgings, ruffles, and more.
The amended 24 stitch repeat with all transfers to the right knit on the 930 after a few rows misstart. The download is automatically mirrored. The end needle cancellation setting on the 910 LC for the pattern to work properly with the carriage in use. In turn, this repeat as given was used in 2020 for a pattern test on my 930 for all transfers to the left. Note: here the knit stitch black pixels are followed by a blank row, and the transfer marks occur on design row 3, directly below the next series of all black pixels Depending on the machine model, the .png for the repeat may, in turn, need to be mirrored horizontally.
The preselection row for my test swatch is from right to left, using the knit carriage (KC). All black pixels will preselect needles. When the left side is reached, the KC is set to slip in both directions and will knit all preselected needles on its way back to the right. Subsequently, the slip setting will be performing the function of bringing stitches in and out of hold opposite the carriage. Each carriage pass advances the repeat one row. The lace carriage preselects for transfers from left to right, transfers to left, and preselects for the next knit row as it returns to the left and onto its rail. A 40-stitch adaptation from the Bond site to try A 60-stitch repeat also inspired by the Bond post knit on the 910 using a mylar. Gauge still matters, more than the recommended 16 sections to form a full circle would be required using this particular yarn The electronic repeat as drawn on the mylar,    the 60X66 png   In the post on lace edgings automated with slip stitch on Brother machines written in 2020, I shared a modified version of a punchcard published by Susanna Lewis in “A Machine Knitter’s Guide to Creating Fabrics” (1981), the ultimate resource for punchcard knitting for knitters with any amount of experience. The chart on p 223 was modified by me since I like to start my lace edgings on the widest number of stitches in the pattern. The punchcard repeat on the left below is shown after being reorganized to start with a knit row on the full 24-stitch width. On the right, rows of black pixels are added, for a version of the full repeat to be used on electronic machines. The slip stitches are substitutes for manual holding techniques, used to knit rows that are in turn form increases and decreases to alter the outside edge of the trim. The lace pattern resulting from the transfers changes along with their direction as the outside edge does. This image is for the desired effect on the purl side of the fabric. Again, depending on the electronic model or the download program, it may in turn need to be mirrored. Subsequent posts on knit edgings:
Lace edgings on Brother machines- automated with slip stitch
Lace edgings on Brother machines- automated with slip stitch 2
From automated lace edging patterns to doilies and ruffles 

Trying to coax a rectangle into a square.

Blocking is one of those topics open to endless debate both as to method and necessity. In most of the items I produce using conventional yarns, I restrict it pretty much to washing/pressing/ironing as needed, thus avoiding all those blocking wires, pins, etc. In this instance, however, the wire item is in need of some help in changing into and retaining the desired shape: my partial solution is seen in the photo above.

For the curious: Magnet wire or enameled copper wire is a copper or aluminum wire covered with thin insulation. It is used in the construction of transformers, inductors, motors, headphones, loudspeakers, hard drive head positioners, potentiometers, and electromagnets, among other applications. However, it is not usually magnetic itself. Magnet wire insulating films used (in order of increasing temperature range) include polyurethane, polyamide, polyester, polyester-polyimide, polyamide-polyimide (or amide-imide), and polyimide. Kynar wire is an instance of a color-coated member of these families and is used in my “colored” jewelry items. For knitting on a loom, I prefer 32 gauge or thinner (higher numbers), which can be plied successfully for more drape but are nearly invisible singly; 30 gauge or less(lower numbers) moves into the hand crochet/knit coil domain for me.

I enjoy using materials designed for uses other than those for which they were designed, the inherent challenge, surprises, and problem-solving.