I am trying to figure out a way to do a concave parabolic grind. Note that I am not trying to do a hollow grind. I want to grind shallow hemispherical (bowl-shaped) depressions with radii ranging from golf ball to cantaloupe sized. So far, I haven't seen any grinding products that would work. I see there are concave cutting wheels for cutting sink holes out of marble and granite, and I saw a mushroom-shaped grinding wheel for snag removal, but it was too small. The closest thing I found were diamond grinding wheels with a slight radius, that cost about $100 for a 6" wheel, but they won't really work for me because the radius of the wheel face doesn't match the wheel diameter, so I would get rounded slots instead of spherical depressions. Does anyone know a good way to do this short of CNC milling?

Milling operation?

It would be good to know what you're planning to grind. Hardened steel is one thing; a block of talc is another.

Getting a hemispherical bit in those sizes will be very pricy!  And take a huge machine to spin/hold it.  Any chance you can forge the dimple and then clean it up?  Fairly easy to turn a tool on a lathe and many a hydraulic press would then imprint it.  As price is no problem. what about EDM?

Lots of ways to do it, but what is the application? It doesn't take a CNC to mill it,but it does make it easier. Can it be chucked in a lathe? There are a few ways to swing a radius with the compound, and radius tools that go in the compound. They can be ground , or lapped in. They can be pressed in. They can be spun in. 

We need more information like; material, condition, thickness, size, use, etc.....

I have seen cutters made from spring, not unlike a big space bit. Find the profile, harden, sharpen and turn slow. Grinders work, but can be dangerous, a fixture helps, but remember the grind stone is wearing away. 

4 hours ago, ThomasPowers said:

Getting a hemispherical bit in those sizes will be very pricy!  And take a huge machine to spin/hold it.  Any chance you can forge the dimple and then clean it up?  Fairly easy to turn a tool on a lathe and many a hydraulic press would then imprint it.  As price is no problem. what about EDM?

I thought about forging the dimples in, but I won't be able to straighten the blade without damaging the dimples. I am trying to make a blackened steel blade that looks like knapped obsidian.

Why can't you straighten it?  Your chunk of firewood used as a hammer not working?  Anyway the sizes you mention are way too large for what you say you want to do and knapped doesn't usually have a dished appearance as much as a troughed one.  I suggest you look at the many makers who do this type of blade ornamentation and then ask the ones who's work you like the best how they do it.  On your own you might try a rather small radius cross peen and make hard strikes close together as you walk down the blade and then wire brush it and go over it with a sisal buff using black compound to smooth the edges some.  Getting boths sides even will be the trick!

Model concoidal fractures, nothing hemispherical about them, they are literally wave patterns in the stone.

Think chasing but study knapped stone or you're just guessing.

Frosty The Lucky.