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This isn't directly my area of interest but the physics sure are interesting. I wonder if the space of screw drive shapes can be generated by a computer and evaulated with a fitness function that calculates the weight, profile, strength, contact area, for every given application.

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Torx is a pretty optimized drive [1].

Otherwise, yeah, it would likely be possible. Many vendors have been proposing semi-automatic structural optimization via finite element methods for a while now (for example, [2]). I'd assume it'd be pretty long running though, as its a non-linear contact problem likely needing pretty tight tolerances/meshing.

In the real world though, you're much more likely to want something standard.

[1] http://en.wikipedia.org/wiki/Torx

[2] http://www.altairhyperworks.com/HWTemp3Product.aspx?product_...

This is something that could easily be accomplished with finite element modelling of the stresses on the solids involved. There are a lot of variables though, including the range of torques, the manufacturing tolerances on your screw heads and bits, the hardness of the alloys used, not to mention practical choices like being able to use the same driver for multiple types of screw head.

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