Draft
Alternating German Twisted Cast On
The German twisted cast on alternated for a rib edge with extra stretch.
7 min videoGood for ribbing, sock cuffs
This is the German twisted cast on, also called the Old Norwegian cast on, worked so that it alternates a knit stitch and a purl stitch. That makes it a natural start for ribbing: knit, purl, knit, purl for one by one, or two and two for two by two.
The first row has a twist in it that gives the edge durability, and it still has enough stretch for a ribbed cuff. It is a good choice for a sweater cuff, the hem of a hat, or the cuff of a mitt or sock.
The knit stitch is the same as the plain German twisted cast on. The purl stitch is the mirror of it and the hardest part, so the video shows it several times.

1 Set up the slingshot
Twist the yarn around the needle to anchor it, then take up the slingshot hold. The tail runs around your thumb and the working yarn over your index finger, with both ends held in your other fingers.

2 Go under both thumb strands
The first stitch is a knit stitch. Bring the needle under both strands on your thumb together, then come back through the center loop, the one between the two strands.

3 Over the finger strand and out
Swing the needle around the outside and over the center strand on your index finger to pick it up. Then bring it out through the loop on your thumb, through the little triangle the strands make.

4 Release the thumb and tighten
Drop the loop off your thumb and tighten the stitch down. That is one knit stitch.

5 Now reverse it for a purl
Come around the outside and pick up both strands on your index finger from underneath. Go over the top of the center strand and back through the middle, between the two strands.

6 Pick up the inside thumb strand
Come around the outside and over the top, then catch the inside strand that runs around your thumb.

7 Back out through the finger loop
Now the needle has to come through the loop on your index finger. The easy way is to pull the needle back out toward you, so the loop opens up, then push it through the middle. The needle is now outside the loop.

8 Release the finger and tighten
Let the loop drop off your index finger and tighten the stitch down. That is one purl stitch. The purl is the hard part, so go slowly the first few times.

9 Then keep alternating
Knit, purl, knit, purl, and the cast on lines up with one by one ribbing. For two by two ribbing, do two purls in a row, then two knits. The edge has a twist along the first row that gives it strength, but it still stretches as much as the ribbing needs.