# The Ideal Sleeve Cap

by on February 8, 2013

bodice muslin

I apologize for not visiting blogs/forums but I’ve been obsessed with the sleeve cap problem.

For those who care about the Math, I’ve updated the previous post with some findings regarding the origin of French Curves/vary form rules.

We may have a solution to obtaining the sleeve cap shape that fits a modified armhole, but it needs testing.

The jacket pattern has a new armhole. Here’s how I got the front scoop.

I may have scooped too much. I don’t want my sleeve sticking straight out of my boob!

Here’s the back scoop. It didn’t change much at all.

Here’s the new armhole shape.

Now that I’ve convinced myself that the vary form rule behaves like a quadratic Bézier curve, it helps me in adjusting. The start and stop points of the curve are the anchor points. As you move the curve around between those points there are actually two other invisible control points at work. These four points form a polygon that acts like a little house for the curve. The curve is stuck in there and can’t come outside and play. As the curve deepens what’s happening is that one of the invisible control points is acting like a magnet pulling the curve toward it to get that deeper shape. As it pulls, the rest of the polygon flattens out so the curve has to flatten out too because it is stuck in the polygon house.

I used the method I wrote about in the last post to make a new sleeve cap draft but I don’t like it.

What I really want is the ideal shape that exactly fits my new armhole.

Before I sew the sleeve muslin to the bodice muslin I’d like to try out a technique Martin and I dreamed up for getting the ideal sleeve cap shape and mark those points on the muslin. That way I can compare the ideal points to my above draft and see how they differ.

The idea is to model your ideal cone sleeve position in 3 space and measure the lines from the centerpoint of the cuff ring in 3D to the points along the new armhole in 3D. This should produce the ideal sleeve cap shape. We’re going to try it. It might take some time to make this happen but hopefully I’ll have the muslin up and can share photos sometime this weekend.

We’ll use the the pythagorean theorem to calculate this x, y, z point in 3 space:

L = sqrt (x2 + y2 + z2)

where L is the length of the sleeve cone.

Here’s the steps we envision:

1. Adjust the armhole pattern as needed and construct a muslin bodice with the new armhole. Place it on the dress form, making sure that the top shoulder seam and side seam are correctly aligned.
2. Roll up some poster paper into a cone shape and insert the arm into the cone. Make sure the cone edge makes contact with the body at every point, but does not bend. Adjust the paper cone as needed to make this happen.
3. Draw a ring on the paper cone approximately where the cuff would be, and mark the side center and back center points of the cuff ring.
4. Measure the length of the sleeve cone. This is L.
5. Move the arm forward and back to guesstimate the approximate arc of arm swing and settle the arm, not perfectly at rest, but a little forward and outward. I think this is the anatomically correct position based on reading pages 163-169 of The Entrepreneur’s Guide to Sewn Product Manufacturing by Kathleen Fasanella, although she says human arms hang forward and down, not a little outward. I think there’s also a slight outward rotation. Readjust the arm cone as needed so it’s still making contact with the body along the edge, then tape the paper sleeve cone closed.
6. Measure the distance from the side plane of the body to the center side of the cuff ring in the same plane, and to get the outward rotation, measure the distance from the side plane of the body out to the center back of the cuff ring. The first distance is the forward rotation and the second distance is the outward rotation.
7. Solve y = sqrt( L2 – x2 – z2) to get the correct y coordinate. Now we have the ideal position of the center of the sleeve cuff in space.
8. Place a candlestick with wax candle at the center of a surface whose center is y inches vertically down and x inches horizontally out (chair plus some books?) from the center point of the armhole. Measure z inches up from the base of the candlestick and mark the wax candle at that distance. Using a knife, slice off the top of the candle at the mark then place it back in the holder in the same x,y position with respect to the armhole center point. The wick now represents the ideal sleeve cuff center x,y,z point in 3D.
9. Measure from the wick of the candle to several points at fixed distances, say 1/2 inch (or maybe less), along the armhole edge to get the different lengths and write these down, in order as you move along the armhole edge from front to back side seam. Make sure to also get (and note) the shoulder seam distance.
10. Using a 2D draft sleeve pattern piece with extra room at the top, measure from the center point of the cuff up to sleeve cap and mark each of the distances from #9 along the same fixed 1/2 inch (or less) distances along the edge to get the ideal sleeve cap shape. This shape has no ease so you to add that in if needed but you probably won’t need much.

I really hope it works. There’s a little built-in error because our arms consist of two cones, not one, but this should be a pretty close approximation if I hold my arms as straight as possible at the elbows while I’m wearing the paper sleeve cone.

Happy weekend!

Update: Yay! We noodled on this some more and think we’ve eliminated the tedious step #9. After step #8, hold up a transparent plastic coordinate system so it aligns with the body plane at the armhole and so that the origin (0,0) aligns with the center armhole. Note the (x,y) coordinates of control points along the edge of the bodice armhole. Use the Pythagorean theorm distance formula for Euclidean three-space to calculate the distances between the 3D sleeve cuff (x,y,z) point and all of the (x,y) armhole control points (z = 0 for all of these points) and write these lengths down, in order from front to back (including the important shoulder point). Then do step #10.

If you don’t have a transparent plastic coordinate system you can use a ruler to get the (x,y) armhole control points. That’s what we’ll have to do for now because we don’t have one. Let’s see, you might hold up a piece of vellum you can see through and mark the armhole origin (0,0) and control points, then lay it down on a table and do the measuring with a ruler to get the (x,y) points.

Second Update: Please see this post for corrections re: the behavior of French Curves vs. Bézier curves and the latest update re: a solution for obtaining an ideal sleeve cap shape.

K-Line February 8, 2013 at 4:43 pm

OK, Susan, I still have a headache from my sleeve cap work – and it did not have 10 steps of math! :-)
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Susan Partlan February 8, 2013 at 4:55 pm

LOL! I know, but honestly, it’s quicker to do a couple of calculations than it is to tediously measure stuff. And once you have your ideal (x,y,z) point in 3D, you only need to do steps #9 (the modified step #9 that uses a coordinate system) & #10 for the next sleeve cap because the (x,y,z) point retains the info you got in steps 2-8. Of course if you decide that’s not the best position and you want to fiddle with getting another one, you’ll have to do the paper sleeve cone thing all over again to get that point.

Update: actually, you wouldn’t have to do the paper sleeve cone thing over again because you can just fiddle with the (x,y,z) point itself. Does it feel like the position needs to come in a little closer to front of your body? Decrease y a little. Does feel like it’s too far out from the side of your body? Decrease x a little. Does it feel a little too raised upward? Decrease z a little. You can futz with little increments of change until you think you’ve got the ideal (x,y,z) for you and then use it forever, or until your body changes and it needs to be adjusted again.

RoseAG February 8, 2013 at 7:47 pm

At last! A use for the Pythagorean theorem.

Susan Partlan February 8, 2013 at 8:17 pm

Ha ha! Isn’t it cool? Who knew you could dust off your math books and find solutions to sewing problems? I love it :).

Kathy Peck Leeds February 9, 2013 at 4:22 am

Hi Susan,
Math literally panics me – that part of my brain just doesn’t function. But, you seem totally brilliant, and I hope this is the most amazing sleeve cap ever. xo

Susan Partlan February 9, 2013 at 9:52 am

Hi Kathy,
Math used to panic me too. I have a story to tell sometime about what happened to lessen my panic so that I could learn what I wanted to learn. As for the sleeve cap, I’m so excited I can barely stand it but I don’t want to rush. If I construct the bodice poorly or screw up the paper sleeve cone measurements it will throw everything off. Nice and slow…

Kathleen February 9, 2013 at 5:37 pm

Fwiw, I also don’t like the sleeve shape you’re showing. I’ve been doing it so long that I shape them by eye.

You’d probably like some of the Russian pattern books. There’s a lot of equations like yours in them.

Susan Partlan February 9, 2013 at 7:09 pm

I agree, that is one sad sleeve cap. That is so cool there are Russian pattern books with similar equations. We are definitely going to have see if we can get our hands on one of those.

Lord do I wish I could shape sleeves by eye.

Tomorrow hopefully we’ll know whether our little experiment will work.

Amos D. Lynch February 14, 2013 at 2:28 am

Place front armhole of the sleeve on the front armhole of front part at the end and fix with pin. Same way fix for the back armhole part. Adjust extra fabric of sleeve as gathers on shoulder seam and stitch sleeves with body part. There are three types of puff sleeves. First one is puff on shoulder arm only; second one is puff on arm circumference and third one with both side puffs. To see the drafting and cutting method of puff sleeve follow the book “Stitching Made Easy”. To view drafting, cutting on paper and fabric and stitching step by step with colored photos buy online CD on sewing product.
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