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Welcome. If I could have the first slide, please? Contrary to calculations made by some engineers, bees can fly, dolphins can swim, and geckos can even climb up the smoothest surfaces. Now, what I want to do, in the short time I have, is to try to allow each of you to experience the thrill of revealing natures design. I get to do this all the time, and its just incredible. I want to try to share just a little bit of that with you in this presentation. The challenge of looking at natures designs -- and Ill tell you the way that we perceive it, and the way weve used it. The challenge, of course, is to answer this question: what permits this extraordinary performance of animals that allows them basically to go anywhere? And if we could figure that out, how can we implement those designs?

And you can absolutely never, absolutely never, because of history and the inherited plan, start with a clean slate. So, organisms have this important history. Really evolution works more like a tinkerer than an engineer. And this is really important when you begin to look at animals. Instead, we believe you need to be inspired by biology. You need to discover the general principles of nature, and then use these analogies when theyre advantageous. This is a real challenge to do this, because animals, when you start to really look inside them -- how they work -- appear hopelessly complex. Theres no detailed history of the design plans, you cant go look it up anywhere. They have way too many motions for their joints, too many muscles. Even the simplest animal we think of, something like an insect, and they have more neurons and connections than you can imagine.

How can you make sense of this? Well, we believed -- and we hypothesized -- that one way animals could work simply, is if the control of their movements tended to be built into their bodies themselves. What we discovered was that two-, four-, six- and eight-legged animals all produce the same forces on the ground when they move. They all work like this kangaroo, they bounce. And they can be modeled by a spring-mass system that we call the spring mass system because were biomechanists. Its actually a pogo stick. They all produce the pattern of a pogo stick. How is that true? Well, a human, one of your legs works like two legs of a trotting dog, or works like three legs, together as one, of a trotting insect, or four legs as one of a trotting crab. And then they alternate in their propulsion, but the patterns are all the same. Almost every organism weve looked at this way -- youll see next week, Ill give you a hint, therell be an article coming out that says that really big things like T. rex probably couldnt do this, but youll see that next week.

Now, whats interesting is the animals, then -- we said -- bounce along the vertical plane this way, and in our collaborations with Pixar, in "A Bugs Life," we discussed the bipedal nature of the characters of the ants. And we told them, of course, they move in another plane as well. And they asked us this question. They say, "Why model just in the sagittal plane or the vertical plane, when youre telling us these animals are moving in the horizontal plane?" This is a good question. Nobody in biology ever modeled it this way. We took their advice and we modeled the animals moving in the horizontal plane as well. We took their three legs, we collapsed them down as one. We got some of the best mathematicians in the world from Princeton to work on this problem. And we were able to create a model where animals are not only bouncing up and down, but theyre also bouncing side to side at the same time. And many organisms fit this kind of pattern. Now, why is this important to have this model? Because its very interesting. When you take this model and you perturb it, you give it a push, as it bumps into something, it self-stabilizes, with no brain or no reflexes, just by the structure alone. Its a beautiful model. Lets look at the mathematics.

And heres one example thats really exciting. This is a collaboration we have with Stanford. And they developed this new technique, called Shape Deposition Manufacturing.