Linking is counted in loops, and it is where the bottleneck goes to hide

A seam made one loop at a time

A linking machine looks nothing like a sewing machine. It has a rotating ring of fine steel points, one point for every stitch it will join. The operator lifts the edge of a knitted panel onto that ring loop by loop, putting one open loop on each point. Only when the whole edge is on the ring does the machine sew across it and release it.

Two things follow from that description, and neither is true of anything on a sewing floor.

The ring is gauge-specific. A ring built at twelve points to the inch is for twelve gauge garments. Put a seven gauge panel on it and you are placing a loop on only every second point, badly. So a factory's linking capacity is not one number. It is a set of rings, and a gauge with no rings has no linking capacity at all, whatever the machine count says.

Time is set by the loop count, not by the seam length. A sewing machine crosses a 30 cm seam in roughly the same time whatever the cloth is. A linker has to place every loop, so the same 30 cm edge takes almost twice as long at twelve gauge as at seven, because there are almost twice as many loops on it.

The arithmetic

KV-2280's linked edges are the two shoulders, the two sleeve heads into the armholes, and the neck rib attachment. Together they are 160 cm, which is 63.0 inches.

• At 7 gauge that edge carries 63.0 multiplied by 7, which is 441 loops.
• At 12 gauge it carries 63.0 multiplied by 12, which is 756 loops.

A trained linker at Rangdhanu places about 62 points a minute on wool at this gauge. She needs a further 4.5 minutes a garment to pick up, position, trim and release.

That is where lesson 1's making-up line came from. Note what it does not do. It does not rise in proportion to the loops, because the handling, the overlocking and the finishing do not care about gauge. Only the placing time moves, and it is the part nobody times.

Which floor is the bottleneck

Rangdhanu has 26 twelve-point linking machines with a trained operator on each, working about 9.5 productive hours a day. That is 14,820 linker-minutes a day.

The bottleneck changes floors when the gauge changes. At seven gauge the knitters are waiting on the linkers. At twelve the linkers are waiting on the knitters, and adding a linker at twelve gauge buys nothing at all.

Courses 5.3 and 5.4 teach line balancing and SMV, the standard minute value of an operation. They still apply, inside each floor. What does not carry across is the assumption underneath them. A sewing line is one sequence, and you rebalance it by moving an operator from a fast operation to a slow one. Knitting and linking are two separate fleets of different machines, needing different skills, sitting in different rooms. You cannot move a knitting mechanic onto a linking ring. The balance between the two floors was fixed by what the factory bought, and it is only correct for one gauge at a time.

Linking capacity is people, not machines

Linking is one of the last operations in the industry that is genuinely fed by hand, and it takes a long time to be good at. At Rangdhanu a new operator places about 34 points a minute in her fourth week, and reaches 62 at around week fourteen.

So the answer to "we are short of linking, buy four more machines" is arithmetic rather than an opinion. Four machines with four new operators each contribute 34 divided by 62 of a trained linker — about 2.2 trained linkers, not four — for the first three months. If the order ships in ten weeks, four new machines are worth two.

That is why the real lever is upstream. Fewer loops. A shoulder joined with a narrow shoulder seam carries fewer loops than a full saddle, where the shoulder piece runs from the neck to the cuff. A neck rib attached at a slightly coarser rib gauge carries fewer. A raglan carries more than a set-in sleeve, because the linked edge is longer. Every one of those is a design decision made by somebody who has never seen a linking ring, and every one of them moves a delivery date.

Why the shoulder is linked even when nothing else is

A linked seam is made from the yarn's own loops, so it stretches as far as the fabric around it and recovers with it. An overlocked seam is held by a sewing thread that does not stretch that far, so it becomes the least extensible line in the garment.

On a sweater neck and shoulder that matters physically rather than aesthetically. The opening has to go over a head, and the seam that will not stretch is the seam that snaps. It is why even a cut-and-sew sweater usually links its shoulders and its neck rib and overlocks everything else. And it is why an inspector who finds an overlocked shoulder on a garment specified as linked has found a functional defect, not a substitution.

Act as a sweater factory's planning manager. A buyer has asked me to change the gauge on a knitted style. I need the full consequence, not just a price. Order facts: buyer [BUYER], PO [NUMBER], style [STYLE], quantity [QTY] pieces, FOB [PRICE], ship date [DATE], size ratio [RATIO]. Current gauge [GAUGE] and proposed gauge [GAUGE]. For each gauge give me: the yarn count and the number of ends the machine takes, the finished garment weight in the size ratio, the yarn price per kilogram, my knitting minutes for the full panel set, my machine-hour rate, my linker minutes a garment, my linking rate, and how many machines I own at that gauge. If I have not given you one of those, ask for it rather than assuming a number. Then do the following. First, build the per-garment cost at both gauges as three lines: yarn, knitting, and making up. Give me the difference per garment and on the order. Second, build the capacity at both gauges as two separate floors, knitting and linking, in pieces a day, and tell me which floor is the binding one at each gauge. Third, convert that into days to complete the order and into machine-days used, and say plainly how many days the change adds or removes. Fourth, tell me whether the ship date still holds. If it does not, price the recovery: full air, part air for the launch quantity only, and a split shipment, each against the sea freight it replaces. Fifth, state the net of the saving and the recovery in one sentence a merchandiser can put in an email. Sixth, list what would make this answer wrong.