This was the link I used and the basics were really easy to understand (except for that whole laying flat thing).
I've done the same technique, when making grass, fiber, rag or coiled fabric baskets. What I did was just add another stitch every 4 or 5 stitches all around the whole thing whenever I wanted to increase OR, do the regular stitch for 3 or 4 rows, then do 2 stitches in a hole every other stitch for one round, then go back again to one stitch per hole for 3 or 4 rounds (It's kind of like crocheting a hat with a flat brim or a flat doily). You'll need to mark where each new round starts with a bright piece of yarn or a safety pin. This way you'll know when to start or stop increasing... You said "I've found, there is nothing that tells me how to make it lay flat without making the outer stitches huge. How do I make it flat and keep the stitch continuity?" My answer would be to do 2 or 3 regular stitches instead of one huge one. (It looks like the blue rug in the picture is a bit "floppy" around the edges)
Getting your rug to lay flat is the problem with nearly ALL rag rugs. I had the very same problem with the first one I made & also with crocheted rugs or even crotched blankets that I've crocheted in the round. It's really all about getting the right amount of tension & fabric around each successive round. When it comes right down to it, you either end up with to little on the edges & end up with a bow shaped rug, or to much fabric or yarn on the edges & end up with a rippled effect.
As you are making your rug, you have to be VERY careful & check out the lay of the rug EACH time you go around. Just lay it on a flat floor & see how it's going. You may have to add more fabric (or more crochet stitches if you're crocheting it) or less.
As far as fixing one that's all ready completed, the only thing you can do is either dampen it then set something heavy on it until it's dry. You'll need to put a large garbage bag that's been cut open (to increase the size) or some kind of plastic tarp on the floor, then above the rug to prevent damage to your floor. Set something heavy on it until it's totally dry. You may be able to get by with just spraying a bit of water on it, but I think you'll have to completely wet it, then leave it to dry as you would when setting your hair.
If it was made of wool, you could block it with pins & then steam it with an iron. These may force it down. But, this technique won't work if your fabric is polyester or not a "natural" fiber. When it comes right down to it, if your finished rug is not laying flat you'll probably have to rip some of it out & start over again. Before you do something that drastic, why don't you take a look at some of the sites below & see what info you can get out of them. I believe the top URL is what you are looking for, but also, click on the second URL, then look to the left on that URL & you'll see a whole list of rug info you can click on. Also, click on the "Amish Knot" on that same site.
HERE ARE SOME RAG RUG DIRECTIONS:
TOOTHBRUSH RAG RUGS:
BRAIDING & SEWING RAG RUGS:
LINKS FOR HOW TO MAKE COILED FABRIC BASKETS:
I have made quite a few crochet rugs from rags and the way I done it is lay the rug down quite often to see if it is staying flat. When ever it looks like it is going to start turning up I crochet a extra crochet stitch in the same hole. That will make the curved areas lay flat. Probably several extra stitches in every round. A time or two when I had a bowl I would wet the rug and lay it down, patting it down till it lays flat, and then let it dry that way.
If you are trying to make a round rug you have to increase the amount of stitches at the ends. When you go around the end of the rug put two stitches in every other stitch until you get back to the long sides. It is much easier to do a square or an oblong rug rather than a round or an oval rug.
You might try steam ironing it. Mist lightly with water, then
place a towel underneath and iron it directly on the floor.
I had the same issue on mine I made from old flannel plaid sheets i used. It turned out wonderful but wants to rise up in the center much like a bowl with sides. I laid a heavy item on it for days and it helped some by still not completely flat. I hope someone post the fix it answer on your request.
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