Bucknell Mathematics Student Colloquium Series
Thurs, Oct. 26 2023 | Noon-12:50PM | Olin 268
Manipulation of thin flexible objects
Presented by Andy Borum, Assistant Professor of Mathematics, Vassar College
ABSTRACT: The next time you tie your shoes, unravel a charging cable, or twirl a noodle around a fork, think about how this problem could be described mathematically. Here is one possible description (continuing with the noodle example)—given two shapes of a three-dimensional curve, one representing the noodle’s starting shape and one representing the goal shape, how should the curve’s endpoints be moved so that the curve deforms from the starting shape into the goal shape? During this process, we should avoid self-intersections of the curve, since the noodle can’t pass through itself, and ensure that the curve remains in stable equilibrium so that the noodle doesn’t slide off of the fork. These two constraints—avoiding self-intersections and remaining stable—make this problem seem particularly challenging. In this talk, I will describe an example of this problem from robotics—manipulation of a thin flexible cable—and I will show how a careful analysis of the equations describing the cable’s shape leads to a closed-form solution of this problem.
Arrive early for Free Pizza!
