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James Madison University

Title: M3:Optimal steps: What makes a good leg?

Director: Roger Thelwell


Dates of Program: June 17 -July 26, 2013


The primary research question for this project is “What makes a leg a good one?” There are many interesting mathematical questions buried in the question of mechanical leg design and walking. M3 mathematicians propose to do the following:

  • Looks at current designs of legs used by walking robots.
  • Build several legs and physically measure effort.
  • Explore various models of effort, and compare them to measurement.
  • Model realistic measure of effort.
  • Consider geometry of leg motion.
  • Optimize various geometries and build prototypes for measurement.
  • Consider the above questions when designing functioning legs for a walking robot.

As the participants gain intuition about leg design by building and playing with a variety of them, the quantities that will show up in the mathematics will have more meaning. There is a lot of theoretical and numerical work that is required to understand the question of leg design. Preliminary work by the previous REU students has suggested some of the quantities that need to be optimized, but the models that the students will explore this summer will provide many more possible quantities to be considered in a mechanical leg system. And since a mechanical system isn’t restricted to biological mimicry, there might be two, or four, or even two hundred legs.

Student Researchers Supported by MAA:

Traymon Beavers
Mikias Kidane
Luis Parada
Lisha White
Jojo Yirrah

Program Contact:

Bill Hawkins

Support for NREUP is provided by the National Science Foundation's Division of Mathematical Sciences and the National Security Agency.