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Making Finger Grip Dents: The Chord Equation

The handle of that quilting circle template has a pair of finger grip dents, which, while they aren’t strictly necessary, seemed like a nice touch:

Quilting circle template - solid model

Quilting circle template – solid model

They’re the result of subtracting a pair of spheres from the flat handle:

Quilting circle template - handle dent spheres - solid model

Quilting circle template – handle dent spheres – solid model

Given:

  • m = the depth of the dent
  • c = its diameter on the surface of the handle

There’s an easy way to compute R = the radius of the sphere that excavates the dent:

Circle chord vs depth sketch

Circle chord vs depth sketch

Thusly:

R = (m2 + c2/4) / (2 m)

In OpenSCAD, that goes a little something like this:

DentDepth = HandleThick/4;
DentDia = 15.0;
DentSphereRadius = (pow(DentDepth,2) + pow(DentDia,2)/4)/(2*DentDepth);

Then generate the sphere (well, two spheres, one for each dent) and offset it to scoop out the dent:

for (i=[-1,1]) {
	translate([i*(DentSphereRadius + HandleThick/2 - DentDepth),0,StringHeight])
		sphere(r=DentSphereRadius);

HandleThick controls exactly what you’d expect. StringHeight sets the location of the hole punched through the handle for a string, which is also the center of the dents.

The spheres have many facets, but only a few show up in the dent. I like the way the model looks, even if the facets don’t come through clearly in the plastic:

Quilting circle template - handle dent closeup - solid model

Quilting circle template – handle dent closeup – solid model

It Just Works and the exact math produces a better result than by-guess-and-by-gosh positioning.

The sphere radius will come out crazy large for very shallow dents. Here’s the helmet plate for my Bicycle Helmet Mirror Mount, which has an indentation (roughly) matching the curve on the side of my bike helmet:

Helmet mirror mount - plate

Helmet mirror mount – plate

Here’s the sphere that makes the dent, at a somewhat different zoom scale:

Helmet mirror mount - plate with sphere

Helmet mirror mount – plate with sphere

Don’t worry: trust the math, because It Just Works.

You find equations like that in Thomas Glover’s invaluable Pocket Ref. If you don’t have a copy, fix that problem right now; I don’t get a cut from the purchase, but you’ll decide you owe me anyway. Small, unmarked bills. Lots and lots of small unmarked bills…

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  1. #1 by smellsofbikes on 2013-08-02 - 12:28

    I’ve been hitting “tell the publisher I’d like to read this book on Kindle” for about three years now, because then I’d have a non-greasy, non-beat-up, semi-searchable version out in the shop.

    • #2 by Ed on 2013-08-02 - 14:02

      I can’t imagine how they’d do the formatting for an e-book, though: the diagrams and tables are everything. I don’t want to scroll a peephole around on the page, which is how I’m afraid it would work even though a Kindle Fire’s screen is bigger than the book (it’s lower resolution than paper, so the pix would be either much bigger or much grittier).

      But, yeah, I want one in my pocket, too, along with all the datasheets I already carry!

  2. #3 by Frans on 2013-08-13 - 03:37

    This one can be useful too: http://en.wikipedia.org/wiki/BINAS