Piaggio made various heavy industrial things in Genoa. They made fighter planes used in WW2.
After the war, they were not allowed to make military supplies, so they hired this guy:
https://en.wikipedia.org/wiki/Corradino_D%27Ascanio
He who invented the helicopter to look around and help figure out their next project.
All the roads in Europe were pitted and cars could not navigate them.
D'Ascanio looked at the sheet metal stamping, the left over landing gear (which became the front wheel) and penned the vespa as the world's first monocoque vehicle.
Two things, creating a leg shield allowed for easier saddling-up and by covering all moving parts, he designed it to be friendly for women. Every vespa has a lil hook for holding a purse.
Vespa mean's "wasp" in italian because looking from above, the rear has that shape. Plus they buzz around.