Thanks for the explanation, Ed. I know axe guys talked about this a lot, saying the axe should be "center balanced"; i.e., the weight of the cutting edge and poll should line up with the center of the handle, or it will want to twist in your grip when swung. When I finally obtained a big HI khukri, these concepts became immediately obvious in use. It has a lot of weight out there on the blade which drops below the centerline from the handle.
But I think it may also be worth pointing out that you'd want to do it differently depending on whether you want to cut with just the tip area, or further down the blade.
Let me define a convex blade as a bellied blade and a concave blade as a hooked blade.
If ya don't mind, I'll use a saber and sickle when talking about your ideas of a convex or concave blade, respectively.
With my khukri, if I chopped about halfway down the blade in the deep part of the curve (using the portion of the edge shaped like a sickle), the weight further out below the edge would help carry it forward in the cut and keep things aligned. However, if I tried chopping near the tip,
the opposite effect happened. Now, the blade was acting like the "positive rake" you mentioned with a bicycle. Now, the mass was way behind the edge, and the blade wanted to twist severely.
And, as mentioned above, the mass distribution matters not just on impact, but when you start the swing, too. If the mass is below the centerline from your grip, ("forward rake", or sickel) it will want to twist in your hand a bit during the swing, making it harder to get the cut aligned to begin with. With a saber type blade, with the mass lagging behind your hand ("negative rake"), it will want to stay more in line with a straight swing, but can still cause problems with a curving swing.
Also, it's not just the mass, but the geometry involved. With the edge further below the centerline like a sickle, it forms a longer lever against your grip. And since it's actually leading ahead of the grip, can cause more twising. With a saber shape, even if the edge is the same distance from the centerline, now it's behind your grip, and will want to stay aligned better- "negative rake". This can have just as much effect as the mass.
So, if I'm understanding you correctly, I pretty much agree with your ideas. But I still think it really depends on whether you want to use the belly or the tip for more of your cutting.
Rotation balance can be achieved with a false edge or a fuller which lightens the spine of the knife moving the balance point forward toward the edge.
Perhaps the best compromise between the two would be a straight symmetrical double edged blade like a European sword or dagger.
