## 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:

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

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:

Thusly:

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

In OpenSCAD, that goes a little something like this:

```DentDepth = HandleThick/4;
DentDia = 15.0;
```

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

```for (i=[-1,1]) {
```

`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:

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:

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

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…