I have an idea for a crank design. I doubt it's new or original, and might not even be possible or even more efficient, but it's in my mind and I thought I'd burden your time with it.
When cranks go in a circle, I can't help but think that there is only a short amount of distance around the circle in which much force is being applied. The rest is lateral movement, right? For example: When one pedal is down and the other is up, then the top pedal must be pushed forward while the lower pedal pushed backward. It seems like wasted time and energy to do that.
So, what if pedals only went straight down and straight up, so that the full weight and pressure from the rider is put on one of the pedals at all times?
I sketched a rough diagram (not accounting for gearing) that shows the general idea. And the entire shaft could be rotated somewhat for standing, sitting, etc. (angle).
Keep in mind that in this diagram, I only drew one pedal. This is the right side of the bike. The other pedal is on the other side at the opposing point in the chain (so that the pedals are always half-way around the "circle" from each other).
On another note: Why hasn't anyone designed a bike in which it is driven by rowing, as in a boat (only you obviously face forward instead of backward, as is common in a rowboat).
I wonder if that would be a good way to build upper body strength while providing transportation.