Using Bifurcation theory to instruct design of Magneto-Elastic Machines

A major hurdle in designing origami and kirigami based microscale machines is achieving complex functionality with simple sheet designs. We address this problem using magneto-elastic machines: sheets comprised of rigid magnetic panels connected by elastic hinges that fold into equilibrium conformations. To function, such machines need to transform between multiple conformations. Shape transformation is achieved through small variations in the hinge rest angles. These variations, however, typically lead to small conformation changes that are devoid of function. We solve this problem by designing such machines next to bifurcations in the magneto-elastic dynamics, where multiple distinct states are accessible by small changes in the system parameters. The difficulty with this approach is that the higher the order of the bifurcation, the more difficult it is to find magnetic patterns that lead to the corresponding dynamics. To find these rare patterns, we adapt a continuation algorithm that follows bifurcations of growing order along a one dimensional curve in the system's multidimensional phase space. We demonstrate our approach with a macroscopic experiment.