Joining elastic smoothly for in-the-round application in panties can be difficult, especially with narrow elastic. I have tried zigzagging and three-step zigzag but always find it difficult to maneuver the pieces, especially when they are pinned. This weekend I tried a new idea borrowed from doll clothesmaking - using water-soluble stabiliser as a base when working with fiddly bits.
I place a small piece of stabiliser under the presser foot. Then I sew a few stitches directly on the stabiliser.
I use stitch number 8 on my Bernina. I think of it as a "mock coverstitch" - it ends up looking like two rows of straight stitching with a line of zigzag in between.
With the needle down, I place the overlapped ends of the elastic under the presser foot with the cut edges even with where the stitching will go. Then I stitch over the elastic and back onto the stabiliser on the other side.
I then place the next piece of elastic and sew over it.
This is the result. I don't need pins and the elastic doesn't go all skew.
Finally, I just trim away the extra thread and stabiliser. (Here you can see the stitch more clearly.)
And the final joins are flat and smooth, ready to be applied to the fabric. The small straight stitches prevent the join from pulling apart when the elastic is stretched, while the zigzag part "overlocks" the edges and prevents fraying.