Back in 1974, a guy named James Dyson had a plan to reinvent the wheelbarrow: He replaced its wheels with a single ball, allowing the whole thing to pivot with ease. Almost four decades later, Dyson's namesake appliance company is repeating the trick with vacuum cleaners. In the new Dyson DC40 Multi Floor vacuum, the ball is now also the engine—more than 110 pieces of machinery, circuitry, and filters are stuffed inside, powering a light, easy-to-maneuver device. Dyson opened its notebooks, showing us how 70 engineers designed the new sucker.
 In 2005, the company released a trial balloon—its first ball-based vacuum. Then it monitored feedback, learning the next generation had to be lighter and slimmer. "We had to figure out how to strip away components, putting more in the ball and fewer on the body," Dyson (the man) says.
 Dyson's designers built more than 5,000 prototypes, using such household tools as foam and cardboard. The goal: focus on form and feel, before dealing with mechanics.
 The company worked with Oxford University's Gait Lab to watch how people move with a Dyson ball vacuum, then made sketches like these to visualize the range of motion their machine needs.
 To make sure the final product could stand up to the rigors of daily use, the company put the prototypes through a gauntlet of extreme tests, including a Sisyphean run of more than 800 miles on a treadmill-like turntable rig.
 The final challenge: fitting mechanics inside a ball. "If we had set out to design a vacuum that rode on a cube, we'd have had an easier time," Dyson says. The team solved the problem by thinking of it like a 3-D jigsaw puzzle: Everything fits snugly, odd shapes and all. ($500, dyson.com)
A version of this article appeared in the July/August 2012 issue of Fast Company magazine.