In-situ adjustable nonlinear passive stiffness using X-shaped mechanisms

A desired structural or material stiffness is critical in many engineering systems for structural stability, vibration control, energy saving and manipulation efficiency. However, passive low-cost high-efficiency in-situ adjustable stiffness systems have not yet been well explored, due to uncertain and unexpected nonlinear behavior within materials and structures, difficulty or limitations in manufacturing or implementation, and various demanding requirements. To address these challenges, we present an efficient stiffness-manipulation method using a flexible and compact X-shaped structure (or mechanism). The resulting nonlinear stiffness systems can be conveniently realized and are capable for achieving various desired stiffness (positive, negative, zero or quasi-zero, multi-stable-equilibria). The inherent nonlinearity of such nonlinear stiffness systems is completely controllable and predictable with simple and reliable mathematical modelling, compared to many other metal materials or foldable mechanisms/structures. Due to the advantages of linkage mechanisms, the X-shaped structure (or mechanism) approach offers superior in-situ adjustability which can be easily achieved via various and simple pre-extension/distance/length/height adjustable mechanisms in practical mechanical designs. The stiffness-manipulation methods demonstrated in this study have also advantages including simplicity and efficiency in manufacturing and assembly, high-quality nonlinearity control and in-situ adjustability, and low-cost part production, without stability issues, manufacturing difficulty and strict material restriction, leading to revolutionary or upgrading technologies to existing engineering systems. Theoretical analysis and experimental validation (or case studies) demonstrate the advantages, effectiveness, and great potential of this new approach for exploiting nonlinearities in various engineering applications.