Programmable Multistable Mechanisms: Synthesis and Modeling

Abstract

Compliant mechanisms can be classified according to the number of their stable states and are called multistable mechanisms if they have more than one stable state. We introduce a new family of mechanisms for which the number of stable states is modified by programming inputs. We call such mechanisms programmable multistable mechanisms (PMM). A complete qualitative analysis of a PMM, the T-mechanism, is provided including a description of its multistability as a function of the programming inputs. We give an exhaustive set of diagrams illustrating equilibrium states and their stiffness as one programming input varies while the other is fixed. Constant force behavior is also characterized. Our results use polynomial expressions for the reaction force derived from Euler–Bernoulli beam theory. Qualitative behavior follows from the evaluation of the zeros of the polynomial and its discriminant. These analytical results are validated by numerical finite element method simulations.