Revisiting miters, spirals, going square, round, and more

I am working on updating my flickr photostream albums, including “all things holding” and will be revisiting posts on this topic over  the next few weeks, possibly adding edits.

There are times in knitting when math becomes a necessity. With online libraries, tools, and fairly intuitive software, drafting angles and shapes is now much easier. I will be teaching a class that includes miters and spirals at a seminar next month, leading me to revisiting the topic. Most published pattern instructions will give starting carriage locations, but shapes may be constructed counter clockwise or clockwise depending on preference. With understanding of how the shapes are formed and stacked, they may in turn be automated (depending on their size and the type of km) using the slip stitch setting. Stitches that are to be knit on each row are programmed as pixels, black squares, or punched holes.

Miter shaping may occur on side or in center of each triangular shape; a minimum of 2 knit rows usually occur at designated spots. Adding more knit rows and playing with angles of triangles will create ruffling effects, other angular shapes, pleats, and more. I have returned to using  Mac Numbers, their shapes and charts to generate most of the images below. Here the colored areas represent knit stitches, white negative (white) spaces stitches in hold. Red lines represent all knit row(s)/ spots for seaming at top and bottom of sequences. Seaming is easiest when done by joining all knit rows. Stitches are always brought into hold opposite the carriage side, returned to work on carriage side. In shaping guide, COL= carriage on left, COR= carriage on right.

knitting each segment

COR                                   COLwedges

Yellow triangle segment: bring all needles out to hold, push them back into work on the carriage side at the determined rate until all needles are back in work. Green triangle segment: with all the needles in work, begin to bring stitches into hold opposite the carriage at the determined rate until all the needles are in hold.

If seaming is desired in miter shaping with resulting eyelets at sides of triangle, the full wedge is split between the top (yellow segment) and the bottom of the piece (green segment). Knitting always starts with at least one or 2 rows of knitting (depending on whether the finished shape is to have a grafted seam.  For the full wedge: * yellow segment, bring all needles out to hold, push them back into work on the carriage side at the determined rate until all needles are back in work. Reverse shaping with green segment: with all the needles in work, begin to bring stitches into hold opposite the carriage at the determined rate until all the needles are in hold. End with knit rows (red line) across all stitches*. Repeat  from * to * for desired number of full segments, end at top with a yellow segment if needed, followed with knit row(s) (red line) before binding off or seaming.

shaping with resulting eyelets at sides of triangle: the final shape COReyelet at sidethe knitting sequence with top/bottom 1/2 triangle segments shown

COR                                   COLfinal at sides

For miter with shaping and resulting eyelets at center of triangle: begin with all knit row(s) (red line) at the start. To shape full wedge: *green segment is worked bringing stitches into hold opposite the carriage at the determined rate until all the needles are in hold. Shaping is next reversed with yellow segment, pushing needles back at the determined rate until all needles are returned to work. End with all knit rows (red line) *. The sides of this miter are all knit rows, an easier place to seam/ graft joins if needed.

shaping with resulting eyelets at center of triangle: the final shape COReyelet at center2the knitting sequence

COR                             COLfinal at center

a tiny test

shaping at side                              shaping at center

400_661

400_662

In the following images the red or blue lines indicate seams or joins

segments composing a square shape 
square_seam
adding squares or rectangles to alter the square
squarextra_seamsadding triangular segments: hexagonpentagon_seamexpanding it with rectangles, shaping at sides
dodecadon extra_seams2shaping at centerhexagon extra_seamsgoing 3D: triangular pocket with point at center 3dmiter

combining shapes: this one is often seen in tams (hats); bottom shaping is on only one side, at the top it occurs on both sides

tam1

tam2adding rectangles or squares to alter shape

tam3

bringing needles out to hold opposite carriage

Spiral stack 1/ green full triangle : knit row (s), *with all the needles in work begin to bring stitches into hold opposite the carriage at the determined rate until all the needles are in hold, end with all knit row(s) (red line).

COR                                   COLspiral stack1 cor

Spiral stack 2yellow full triangle:  knit row (s), *bring all needles out to hold, push them back into work on the carriage side at the determined rate until all needles are back in work, end with all knit row(s) (red line).

COR                                   COLfull stack 2

3D spiral 3Dspiral

If the object is to construct a circular shape, the greater the number of panels, the smoother the outer edge of the piece . Some of the pie-bilities: so many pies

In all instances above the radius and therefore 2 sides of each wedge remain equal in size, and therefore are composed of the same number of stitches. The triangle knit to achieve these shapes are isosceles triangles, where 2 of 3 sides are equal in length and in this case, number of stitches. The 2 equal sides are usually referred as legs, the remaining one as the base. The 2 base angles are equal as well. The remaining angle is the vertex one. In knitting, this will be the pivot point for the wedges, the center point of the “pie” shape. In the illustrations below the vertex angles are marked by blue dots. Its angle value is the first represented in the numbers immediately below each shape, with the other 2 numbers indicating the remaining, equal 2 angles. The sum of all 3 should equal 180 degrees.all anglesTaking it to a shape: octagon (half the total # of wedges shown). In colored shapes spiral, stacking equal triangles is shown on left; full triangle, divided into 2 segment shaping for miter on right.octagon col

Oh, yes, the math! The desired shape may be drawn to scale using any number of tools. Wedges may in turn be shaped following the scale drawing on any charting device such as knit-leaders, or stitches and rows required may be calculated on actual full drawing measurements. In knitting, the equal sides (AC, AB) of the triangles are formed by stitches, the height of the triangle (CB) by rows. If finished size matters, accurate gauge is required. One approach to calculating the base (CB) is to think of the whole shape as a complete circle, in this case divided into 8 “pie” wedges, with congruent sides (radius) measuring 10 inches each. To find the circumference of the circle, multiply the diameter (20) inches by pi 3.14 = the total in this case, of 62.8, rounded off to 63. Divide that number by the number of sections (8) = 7.85, rounded off to 8 inches (rows). If stitch gauge is 6 stitches and 8 rows per inch, each triangle would be 60 stitches wide, 64 rows high. Holding happens every other row, opposite the carriage, so total number of rows is divided by 2 = 32 for knitting a spiral. The stitches are distributed along one edge over the total 64 rows in height. The goal is to reduce shape down to the next to last group, followed by two rows knit over all the stitches at the end of each section. This will cause a small hole at the center of each completed pie due to extra rows knit. For a miter 2 triangular shapes are required for each wedge, so holding sequences are recalculated with shaping now occurring over 16 rows for knitting a miter. screenshot_09 color

An online calculator is available to help calculate the number of stitches brought into hold opposite the carriage or into work on carriage side, sequence preference should be tested on swatches where gauge is significant

  spiral screenshot_02miter Miter online

Magic formula (X represents times)magic formula

In the photo below I chose to start with all the needles out to hold,  pushing them back into work across the knit for the spiral. For the miter again, I began with all needles in hold, pushing back the required needles into work; for the top half of each wedge needles were returned to hold opposite the carriage at the same rate, forming the upper half of the “pie slice”. The swatch is not worked at the same rate as shapes calculated above. It is shown on its purl side with color changes to highlight the intersections where wedges begin to repeat. The yarns used are random acrylics, in different weights. photo miter spiral

A previous post on short row knitting from with links to other online sources http://alessandrina.com/2013/12/18/holding-stitches-short-rows/. A category search in my blog roll for miters and spirals will link to blog posts including pies: http://alessandrina.com/2011/06/18/knitting-math-and-pies1/  http://alessandrina.com/2011/06/22/back-to-that-pie-a-bit-of-holding/  breaking and mixing up pie wedges: http://alessandrina.com/2014/07/21/miters-and-spirals-visualizing-charting-and-more-3/ . A garter bar short row trim:  http://alessandrina.com/2013/02/28/garter-bar-short-row-trim/. Charting shapes: using Gimp and Mac Numbers: http://alessandrina.com/2014/07/14/miters-and-spirals-visualizing-charting-and-more-1/  . Executable charts, shapes, automating with slip stitch: http://alessandrina.com/2014/02/24/holdingshort-rows-hand-tech-to-chart-to-automating-with-slip-stitch-1/  http://alessandrina.com/2014/02/20/wisteria-cousin-revisited-holding-using-slip-stitch/  http://alessandrina.com/2013/01/21/automating-pleating/ http://alessandrina.com/2013/12/28/short-rows_-balls-tams-3d-rounds/  http://alessandrina.com/2015/09/07/a-tale-of-2-donuts/ http://alessandrina.com/2011/03/29/lace-meets-hold-and-goes-round/  http://alessandrina.com/2011/03/29/the-doilies/

Hand knit “dragon scales”

detail of half fisherman machine knit version of stitch500_606

My last experiments led to a search for possible hand knit “scale” version. Similar shapes may be achieved through holding, but here the effect is created through use of increases and decreases. The test for the repeat was knit in a 4 ply acrylic. As with the machine knit version, the pockets become more pronounced as the fabric relaxes, without any blocking. Garter stitch was used in the first sample, for both texture and speed. Everyone has their preferred methods for increasing (M1) or decreasing/ combining 3 stitches into one. I tried picking up from row below or casting on single stitches (#1), but found the least noticeable methods to my eye, using this yarn and stitch type, were simply to knit in front and back of the stitch (#3) where an increase was required, and to knit 3 together (#2) for the decreases.

numbered_636the reverse structure curves in a similar way to the machine knit 500_637

The number of stitches remains constant on each row knit; the chart reflect side panels (A, C).The central 18 stitches (B) that may be repeated multiple times to achieve the desired width. The border stitches added may be any number, are also knit on every row.

screenshot_06scale_symbols

The fabric changes dramatically when every other row is purled. This swatch was knit with a single stitch garter stitch border, and I experimented with increases and decreases. The M1 sts were created by picking a loop up knitwise from the row below for the increase. The slight shift in the pattern center where decreases and increases meet helps define a point on the “scale” shape. The same yarn and needle size were used as in the above sample. A softer, thinner yarn knit using smaller needle size would benefit either variation. To my eye, the all garter stitch version was more successful and pleasing.

knit as “outside”, default shapeknit frontits reverse500_643purl as “right side” after poking scales out 500_639its reverse

500_646

for a less pronounced, “scaly” relative using lace in its design please see http://alessandrina.com/2015/01/09/a-swatch-experiment/     http://alessandrina.com/2015/03/28/machine-knit-dragon-scales-update/

Vertical racking 3: automating half fisherman in pattern (2)

Working with the half fisherman racking discussed in the last post, here is an approach to interpreting the fabric seen below for knitting on a Brother model knitting machine500_557For the sample chart I chose a 12 stitch repeat, making it executable on any knitting machine. The ribber is set to half pitch. An often overlooked clue as to what is happening or is about to, is found in the arrows just below the racking position indicator. With the latter at 5, the red triangle appears pointing to L. As the bed is racked to position 4, the red arrow now points to the letter R. This is a simple racking pattern involving only the 2 positions, either to R or L

pitch_rack

Once on position 4, the red arrow indicates the direction in which the bed was racked on the last move (R), the “empty” arrow the direction for the next move (L), bringing position back to 5. More complex patterns require a bit more planning and tracking to avoid errors.

rack2

Racking patterns in books often recommend beginning fabric with the setting on 5, or the center position for the machine in question.  Doing so allows for balanced edges in patterns that swing by multiple positions in both directions. In this instance, for the sake of avoiding mistakes in as many ways as possible, I would start the pattern on racking position 10. Racking cannot go any further to the right, so no chance for example of racking to 6 rather than 4 in the knitting because of inattention. Having a “cheat sheet” with row numbers where no racking occurs, and position of the carriage to R or L at their start and or after knitting is also helpful. I had to lower the tension on both beds considerably to avoid forming loops that in turn got hung up on gate pegs. Especially at the start make certain that the comb and weights drop properly. Using KCI will insure that the first and last stitch on the main bed are always knit. In the patterning used on the Passap back bed (previous post), the groups of needles in each half of the repeat will change to the alternate position with each pass of the lock. On the rows where the back lock is changed to N, selection continues in pattern, but no tucking occurs. In this chart the pattern is maintained continuous throughout, while blank “remaining” squares are filled in on rows where no tucking or racking occurs = N, every needle knits. In Brother machines both tuck buttons are pushed in. Selected needles knit, non selected tuck across the row. 

new program 2symbols

I tested the pattern approach on my 910, with a 38 row, 20 stitch repeat in a random acrylic. I had some issue with some needles not selecting properly, for whatever reason. The repeat was not planned so a full 10 stitches were at each side of the knit, resulting in the difference on the right side of the swatch photo from its left.

larger repeat

half the repeat with color change on single plain knit row (use of color changer only possible with even row change sequences), top stripe of swatch in plain rib

half repeatN1

1rowN1_584

back to scales and knitting them

Overall,  wider repeats and thicker yarns gave me harder to knit fabric, with less noticeable pockets and lack of stretch and “bounce”;  ultimately I went back to a 6X6, 12 stitch 2 row sequences illustrated in the chart above. The thinner yarn needs to be with a bit of stretch, and enough strength not to break when ribbed and racked at the tightest possible tension. This is a fabric that requires concentration, having as many clues as possible to help stay on track is useful. If errors are made close enough to the all knit row, it is possible to unravel carefully to that point, and continue on. Mylars or punchcards may be marked to reflect racking position. Here the mark on the right = 10, the one on the left = 9. Marks take into consideration that the card reader’ design row and knitter’s eye level row views are not the same.

mylar_marks

A row cheat sheet can help track carriage location for all knit rows. Pictured below is part of mine. Wording for clues or description of sequences should make sense to the person knitting, not necessarily follow a specific formula.

screenshot_34

some of what “did not work”, including a very long swatch with a confused pattern due to creative operator error

500_591a finished piece with yarn ends not yet woven in500_590

The fabric is tugged lengthwise, left unblocked, and pockets may pop on either side of it, with the majority on one side of the knit as opposed to the other

the start of a series in varied colors and fibers500_604