(Originally published on March 13th, 2018 at https://aerospace.illinois.edu)

When designing mechanisms that move and work together, the variables may seem unlimited. But in fact, there is likely a design that optimizes the efficiency of the mechanism, like finding the sweet spot for the fulcrum on a pair of plyers to get maximum force. Kai James, professor in the Department of Aerospace Engineering at the University of Illinois, is working to design a computer algorithm to find that point of greatest efficiency. And, he is using the science to attract more underserved students to STEM.

Topology optimized multi-body gripper mechanism

James’ project was recently funded through the National Science Foundation Faculty Early Career Development (CAREER) Program. Proposals that are selected are from a single early-career investigator that include research and education activities that are integrated, innovative, and ambitious.

“I want to create a framework where algorithms could, starting with the black box, generate an entire design concept for compound machines that contain multiple components,” James says. “In addition to optimizing the structure of each component—it’s shape, geometry, and material layout—the algorithm can also optimize the connectivity between the components. So the algorithm, for example, will tell us where a hinge should be placed to maximize mechanical advantage”

James explains that the algorithm will generate a series of numbers, resulting in a mathematical description of the design. After it is interpreted, a corresponding computer aided design file, or CAD, is created that contains a 3D representation of the design.

“What’s new about this project is that the types of algorithms we’re using have previously only been applied to the designs of structures—meaning that the system you’re creating contains a single part,” James says. “It moves, but all of the motion is purely due to elastic deflection—bending, twisting, and basically straining the material.

“In the real world, mechanisms have multiple components. Motion isn’t due to elasticity, but rather through what’s called *rigid body motion*. In a pair of plyers, for example, the two lever arms are undergoing rigid body motion. There may be some elastic compliance, but we’re not relying on that compliance to generate the transfer of force from the input to the output. If you apply force of 100 Newtons at the input, we want to maximize the output force at the jaws of the particular device. In this case, because of the geometry and where the fulcrum is placed, we’ll get a mechanical advantage magnification of this force by about 10 times. The output will be 10 times stronger than the input force.”

In order to generate the design, James says the algorithm has to know how the design behaves mathematically.

“Within the algorithm there will be a module that simulates the mechanical response of the system. And it will do that repeatedly,” James says. “You start out with an initial baseline, a guess, for what we think the design should look like. The algorithm will determine how good the design is and where the design can be improved. It will iteratively generate new designs, test the design, and then systematically modify it. It’s all automated. We tell it what an optimal design should be, what criteria needs to be satisfied, and the algorithm searches the virtual space of potential designs to determine how effective the current design is, then it determines how sensitive that effectiveness is to small changes in the design. This is called sensitivity analysis. It’s a form of calculus.”

What does this have to do with aerospace? James says aerospace engineers may want to describe the efficiency or the performance of a mechanism such as drag in the case of an aircraft design.

“We have an algorithm that evaluates drag as a function of the design features,” James says. “They are represented mathematically as a set of parameters. The algorithm has to know the physics of the system that you’re trying to design, then it can evaluate the design, perform a sensitivity analysis. Based on those sensitivities, it will determine how it should update the design to improve it. And those improvements will happen incrementally. We perform that successively until the algorithm converges to a design that satisfies our optimality criteria. Once you have that, that’s the best possible design or at the very least, a mathematical optimum within the design space that you’ve provided for the algorithm to search.”

James says, this level of physics is what a first-year graduate student would likely understand, but the science will be modified to be accessible to undergraduate students.

The $500,000 NSF funding will make possible a series of workshops every other week, beginning in August, 2018 and run through 2023. The workshops will be less formal than an actual course.

Undergraduate students who participate in the workshops don’t need to be majoring in math or science or even engineering. James will work with the university Office of Minority Student Affairs to market the program to attract students who wouldn’t normally gravitate toward STEM disciplines, that is, science, technology, engineering, and math. The outcome of the workshops will be activities for K-12 visitors to the Engineering Open House at the University of Illinois the following spring.

Rather than being theoretical, the information students receive will be focused on applications, taking a high-level look at optimal design. “It will look at some new breakthroughs in the research community to whet the students’ appetite for STEM,” James says. “There will be some technical instruction as well. They’ll learn to understand some of the mathematics that govern these algorithms and design strategies.”