Regarding the twisting that happens in the front triangle between the front wheel and the rider, yeah, that can affect handling and stuff, and is one thing I keep wanting to fix on CrazyBike2.
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Note that stiffness does not necessarily equate to frame strength. A frame that can flex in the right way acts as a suspension of sorts to the loads it bears, and a frame that cant' flex is much harder on the anchor points of the loads, such as wheels/dropouts, seatpost mounts, cargo mounts, etc.
Some of the experiments I've done with CrazyBike2 to stiffen things up to prevent flex that derailed the middrive chains ended up causing the frame itself to fail under cargo/rider loads, in a different place than the stiffening. Then more stiffening in those areas was required, and then more in other places, etc etc. :/
It depends on the design of the frame itself, as well as the materials used, but sometimes frame flex is a really good thing.
Another note on flex: I originally intended to heavily stiffen up the SB Cruiser trike frame, laterally, but found that it's flex/twist is a good thing, because it helps as a form of suspension allowing the wheel opposite a bump or hole to stay where it is and toss me and the load (dog, cargo, etc) around less than if it were so stiff that it just tossed the whole back end up and down on those bumps/holes when only one wheel at a time does so presently.
On a fully-suspended vehicle, with good damping and whatnot, it wouldnt' make so much difference--but on one with no or non-full supsension, frame flex could make a big difference between breaking the frame over time or just absorbing some of those shocks.
