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Traditional applique is done by turning under the edges of the fabric to be appliqued onto the background fabric before stitching. Or you can satin stitch over the edge of the applique fabric to attach it to the background. Raw edge applique is done by cutting the applique fabric to the exact size of the piece. A double-faced fusible webbing (Steam-A-Seam 2 is one of the brands available) is then ironed onto the back of the applique piece, the paper backing is removed and the applique is then ironed into place. There is no fabric turned under. You can complete a raw edge project with no stitching on the applique.
I am sure that the machine you need is an over locker machine to finish the raw edge. Hope this helps.
you have 2 or more pieces of fabric, one for your background and the other your shape/pattern which you want to attach. you attach it simply by sewing around the edge of the fabric usually with a zig-zag stitch. by doing this you using applique to attach the fabric.
A Baby Lock Serger is a sewing machine sometimes known as an "overlocker". These machines actually trim the edge of the fabric as they stitch giving a professional finish.
If you do not have a serger you can use a zig-zag stitch over the edge of the fabric.
An overlock machine is designed to do this job. However you can do overlock by using the zig zag stitch. When sewing edge of garment bring stitching right to the end to create an overlock stitch.
If you mean the edge of the Aida cloth or linen upon which you are cross stitching, then you can just machine sew a zig zag stitch around the very edge of the cloth. I find this helps keep the Aida cloth threads from continually falling out along the edges. Note: the zigzag stitch doesn't need to be tiny, probably a medium size.
The buttonhole stitch is a loop stitch that reinforces the edge. It is similar to a blanket stitch.
to lock the edge
Optimally, a serger is the best way to finish material that ravels. If you do not have a serger, you can finish the raw edge with a regular zig-zag stitch. If you don't have a zig-zag stitch on your machine, you can simply reinforce your seam with another row of straight stitching.
That would be "hem".
The overcast stitch is a type of hand sewing used on a raw (unfinished) edge to prevent unraveling of the fabric. It is stitched twice over the edge of the fabric to make a zigzag.