Flat grind:
the angle of the two sides form the primary bevel. The more acute the angle the sharper. (But remember, too sharp and it chips easily).The angle will range from less than 8 degrees for a scalpel, 8-10 for a thin fillet knife, 12-16 for working knives,20-25 for a hawk or an axe. The secondary bevel is the angle that you grind the actual cutting edge to. It can be as low as the primary bevel (called a full flat grind) and up to 35 degrees for an axe. To make a flat grind is pretty simple. File by hand or grind on a platen. Shape both sides till they almost meet at the edge.
Hollow grind:
The hollow on each side is calculated so it will remove a lot of the steel from the blade sides, making a lighter blade and giving a shallower primary angle. The grind is formed with a contact wheel . The diameter of the wheel determines how far up the blade edge the hollow grind goes. Wheels from 6" to 24" are used, but most makers use 8-16" wheels. While there are several jigs and devises to hollow grind a blade on, almost everyone just uses their hands and watches the hollow form. It takes practice, but becomes second nature after a while. The secondary bevel is usually a bit more acute on a hollow grind. Hollow grinds are cutters and are popular for hunting knives, skinners, razors,and blades that require a strong spine and a thin edge.
Convex grind:
The convex grind is referred to as an Appleseed grind (the Japanese name for it) because the cross section looks like an apple seed. It gives a lot of blade mass, strong edge, and good cleaving ability (due to the wedging effect of the fatter area right behind the edge). This is the grind for swords, choppers, camp knives, cleavers, and any knife that you want a tough but sharp edge.Basically there is no secondary bevel. The blade is done on a slack belt and just rounds on down to a sharp edge. A very small secondary bevel is usually added to strengthen the edge. These blades are not great slicers (as in flat and hollow grinds), but will outlast every other edge shape when hard work is done.
Stacy