The design of spatial compliant mechanisms with distributed multi-stability based on post-buckled cylindrical compliant beams

Multi-stable compliant mechanisms (MSCMs) feature multiple stable structural configurations. The majority of MSCMs can only transfer from one stable configuration to another via a single transferring path in a fixed sequence, which is defined as hierarchical multi-stability. This study introduces the distributed concept from the computing science to the field of MSCMs. The compliant mechanism with distributed multi-stability has a group of stable states which are mutually connected by a network of stable-state-transferring paths. It can transfer from one stable state to the targeted one via multiple paths. A general structural method is proposed to construct the spatial compliant mechanisms with distributed multi-stability based on the interaction of post-buckled cylindrical compliant beams. The beams are spatially arranged to align the lines that connect the vertex and the center point of five convex regular polyhedrons. A series of distributed multi-stability, i.e. octa-stability (conditional), hexa-stability, octa-stability, dodeca-stability, and icosa-stability, can be obtained. The distributed hexa-stability is focused and demonstrated in this research as a case study. A sequential preloading method is proposed for equivalent axial displacement preloading on the compliant beams in both finite element analysis (FEA) simulations and prototype operations. As a case study, the distributed hexa-stability is verified by the strain energy distribution scatter graph drawn based on the FEA simulations. The six stable states are equivalent and have identical rotational angles observing from the direction perpendicular to each surface of the outer cubic frame. A prototype of the hexa-stable compliant mechanism is fabricated using 3D printers in the assembling manner. The distributed hexa-stability is further observed, measured, and experimentally verified using a Vicon camera system. The application of the hexa-stable compliant mechanism used as a multi-directional optical reflector is demonstrated. Extending the geometric configurations from regular polyhedrons to semi-regular polyhedrons and regular prisms, the capability of the proposed structural concept to construct multi-stability is investigated. The series of MSCMs with distributed multi-stability can be used as multi-base logical units for advanced mechanical computing. Further application fields include precision platform, vibrational energy harvesting, space exploration, metamaterials, and adjustable mirror mounts in photonics.