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# Theoretical walker struts its energy-efficient stuff

### Subjects

Bizarre gait could aid design of prosthetic limbs.

A computer model of an extremely energy-efficient walker could help improve prosthetics. Credit: Mary Evans/Classic Stock/H. Armstrong Roberts

Staggering home from the supermarket laden with bags of shopping, it would be impossible — and more than a little silly — to rock your torso quickly back and forth while swinging your legs in loopy, pendulum-like steps. But if you were able to take a cue from a theoretical walker that does just that, you might save yourself some energy.

So say Andy Ruina, an engineer at Cornell University in Ithaca, and Mario Gomes, a mechanical engineer at the Rochester Institute of Technology, both in New York, whose torso-rocking walker has the most energy-efficient gait of any yet discovered. The model's antics (see video), described in a paper accepted for publication in Physical Review E 1, may act as an inspiration to roboticists whose state-of-the-art walkers require tens of kilowatts to move, or to researchers designing prosthetic limbs or hoping to understand human and animal locomotion.

But the computer-generated walker's methods won't be put into practice any time soon. For a start, Ruina and Gomes's simplified two-dimensional model, designed with two rigid legs and a rigid torso connected by springs, has no friction in its joints. And perhaps more importantly, it can move its swinging leg through the ground as it walks, an abstraction made necessary by its lack of knees. Using those idealizations, Ruina and Gomes found a mathematical solution that described a gait that would not lose any energy when the walker's feet touched the ground and began to take on weight from the other leg. "It's like a wheel that would roll forever," says Ruina. "It's a crazy-looking thing."

The key to the gait's success is that the walker's leg is stationary when it touches down and takes the weight. "It has a perfectly soft landing," says Ruina. He says that it is a big surprise to find that any kind of walker, even a theoretical one, can move without losing energy to collisions with the ground. "It lets you know that there's no fundamental limit on what you can do," he says.

Gomes says that the design was inspired by brachiation, the swinging gait of apes moving hand-over-hand through trees, and by the idea that the apes might improve the efficiency of their movements by timing things so that each hand was near-motionless as it grabbed the next branch.

Inspiration

In 2000, Mariano Garcia, a mechanical engineer at the University of California, Berkeley, and Anindya Chatterjee, a mechanical engineer at Pennsylvania State University in University Park, published a paper showing that a simplified walker with stiff legs and no torso had no gait that did not involve losing some energy when its legs hit the ground. They hypothesized that adding a torso might make a difference2.

Although Ruina says building a robot that copies the walker's gait is impossible, Gomes says has been inspired to build one loosely based on it. One design that he is considering consists of a rimless wheel made up of spokes, with an oscillating weight in the middle that can adjust the speed of each spoke to be near-motionless as it hits the ground and takes the weight. "It just kisses the ground and there's no energy transported," says Gomes.

Ruina and Gomes suggest that the need to minimize energy lost when the feet collide with the ground may explain the pendulum-like gait of women of the Luo people of Kenya, who can walk many miles carrying heavy loads on their heads3.

Springs to mind

Steve Collins, a mechanical engineer who develops prosthetic limbs for amputees at Carnegie Mellon University in Pittsburgh, Pennsylvania, says that although the gait of the theoretical walker is not practical in reality, some of the ideas from it could be useful. "It has some funky dynamics going on," he says. "The idea can be expressed in new designs." Collins says that people with prosthetic feet and legs use on average about 25% more energy when walking than people with natural legs. The large part that the springs in Ruina and Gomes's model play in its energy efficiency underline the value of having the right kind of springs in prosthetics.

Arthur Kuo, a mechanical engineer at the University of Michigan in Ann Arbor, is also interested in the role of a springy torso. He says that the model helps to explain how electricity can be harvested by adding springs to walkers' backpacks with only a small increase in energy cost4. "There are all kinds of tricks you can play that can reduce the losses," he says.

## References

1. Gomes, M. W. & Ruina, A. preprint (2010).

2. Chatterjee, A. & Garcia, M. [journal]Dynam. Stab. Syst.[/journal] 15, 139-157 (2000).

3. Maloiy, G. M. O., Heglund, N. C., Prager, L. M., Cavagna, G. A. & Taylor, C. R. Nature 319, 668-669 (1986).

4. Rome, L. C., Flynn, L., Goldman, E. M. & Yoo, T. D. Science 309, 1725-1728 (2005).

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Reich, E. Theoretical walker struts its energy-efficient stuff. Nature (2011). https://doi.org/10.1038/news.2011.37