Programmable Multistable Mechanisms: Design, modeling, characterization and applications

Multistable Mechanisms are mechanical devices having more than one stable state. Since these mechanisms can maintain different deformations with zero force, they are advantageous for low power environments such as wristwatches and medical devices. In this thesis, I introduce programmable multistable mechanisms (PMMs), a new family of multistable mechanisms where the number, position, and stiffness of stable states can be controlled by programming inputs modifying the boundary conditions. PMMs can be synthesized by combining bistable mechanisms. This method was used to produce the T-mechanism, a PMM consisting of two double parallelogram mechanisms (DPMs) connected orthogonally where each DPM consists of two parallel beams connected centrally by a rigid block and axially loaded by programming input. An analytical model based on Euler-Bernoulli beam theory was derived to describe qualitatively the stability behaviour of the T-mechanism. The model approximates the mechanism's stiffness by a sixth order polynomial from which the reaction force and strain energy expressions can be estimated. These explicit formulas provide analytical expressions for the number, position, and stiffness of stable and unstable states as functions of the programming inputs. The qualitative stability behavior was represented by the programming diagram, bifurcation diagrams and stiffness maps relating the number, position and stiffness of stable states with the programming inputs. In addition, I showed that PMMs have zero stiffness regions functioning as constant-force multistable mechanisms. Numerical simulations validated these results. Experimental measurements were conducted on the T-mechanism prototype manufactured using electro-discharge machining. An experimental setup was built to measure the reaction force of the mechanism for different programming inputs. I verified the possible configurations of the T-mechanism including monostability bistability, tristability, quadrastability, zero stiffness regions, validating my analytical and numerical models. Compared to classical multistable mechanisms which are displaced between their stable states by imposing a direct displacement, PMMs can be displaced by modifying mechanism strain energy. This property increases the repeatability of the mechanism as the released energy is independent of the driving parameters, which can be advantageous for mechanical watches and medical devices. Accurate timekeepers require oscillators having repeatable period independent of their energy source. However, the balance wheel spiral spring oscillator used in all mechanical watches, suffers from isochronism defect, i.e., its oscillation period depends on its amplitude. I addressed this problem by introducing novel detached constant force escapements for mechanical wristwatches based on PMMs. In the medical domain, I applied PMMs to construct a retinal vein cannulation needle for the treatment of retinal vein occlusion. PMMs based needle