On the Design Synthesis of Multistable Equilibrium Systems

Abstract

Multistable equilibrium (MSE) systems are a type of adaptable system that can have multiple mechanical configurations requiring no power to maintain the stable configurations. Thus, power is only needed to move among the stable states, and each stable configuration represents a level of adaptability. Since stable equilibrium configurations can be defined by potential energy minima, we base the design of MSE systems on shaping the potential energy curve at desired equilibrium configurations. This view allows one to construct a performance space defined by how well candidate systems meet a desired potential energy curve. By using a Monte Carlo mapping to link the performance space to the design space in tandem with stochastic optimization methods, the designer determines whether or not a certain system topology can be designed as a MSE system. Qualitative and quantitative mapping procedures enable the designer to decide whether or not the desired design lies near the center or periphery of a performance space. This dictates how the optimization is to be executed which in turn informs the designer as to whether or not a feasible limit in the system performance has indeed been reached.