I never saw these shaped sleeve heads in the USA, but we in Europe can choose if we want to use the straight ones or the shaped ones. I prefer to use these shaped ones, but the sewing technigue is the same.
The shape of the sleeve head mimics the shape of the sleeve cap, and the purpose is to support the sleeve cap in custom made garments like jackets and coats. The sleeve head fills out the gap between the arm and the sleeve top and it helps to have a nice roll line in a high cap sleeve plus it also prevents to show the seam allowance from the right side.
The sleeve heads are sewn at the armhole after the sleeve is sewn in at the armhole. You can see that the left and right side of the sleeve heads are different in length and shape.
If you fold the sleeve head at the shoulder notch (small slit) you will notice that one part is longer and has a more angled shape at the end, the longer length needs to be attached at the back side armhole.
The shorter length is going towards the front side armhole.This is due to the shape of the armhole, in a well drafted pattern the armhole at the back is always longer in length than the front armhole.
I made a jacket using a gorgeous silk Tussah medium weigth fabric that I ordered from Melody at http://www.fashionistafabrics.com (now sold out) and used the larger thicker sleeve heads, which you can see at the previous picture.
I fused all the pattern parts with a thin stretch fusible interfacing to add some support and to keep the ravelling at the cut edges to a minimum.
Pin the sleeve head shoulder notch matching the shoulder seam and pin towards the back and from the notch towards the front armhole with the edges matching from sleeve, armhole and sleeve heads.
You can sew the sleeve heads into the armhole while you are removing the pins or you could baste the sleeve heads in first, which I did here for an example. I used orange basting thread and basted over the stitching line from the set in sleeves
Sewing the sleeve heads in with the sewing machine a hairline away (inside the seam allowance) from the previous stitching line (sleeve inset)
The sleeve head is not visible because it lays on the machine bed so I can see the previous stitching line from the sleeve inset which is my marking.
I sewed the sleeve heads with a 3 mm stitch length, which is a bit larger than the usual 2,5 mm stitch length which I used to sew the jacket.
Remove the basting thread, add shoulder pads.( The seam allowances are heading towards the sleeve of course)