Path-dependent Multistable Rotational Hinge for Morphing Applications

Exploiting mechanical nonlinearities in compliant structures can be advantageous in unlocking novel structural functionality that can further the advancement of morphing wing design. Examples of these nonlinearities include auxetic meta-material architectures, post-buckling analysis of pre-stressed elements, and bistability of shape-invertible geometries. For instance, thin-walled domes and arch geometries with appropriate curvature have been employed in the literature to design bistable structures that achieve changes in geometry, stiffness, or functionality of a shape-adaptable system. This work explores the design principles of a multistable hinge unit utilizing a discretized arch geometry for morphing applications. The arch is modeled by segmenting it into three high-rigidity sections connected by four compliant hinges, analogous to a four-bar mechanism. An analytical model is formulated based on pseudo-rigid-body modeling principles, in which the rigid sections are modeled as linear springs and the hinges as rotational springs. We demonstrate that the discretized arch model exhibits a multistable response when nonlinear rotational springs with an asymmetric energy potential are introduced. The asymmetry in the rotational spring energy potential drives the rotation of the springs in a specified direction and prevents rotation in the other direction. This creates an additional pathway for locking energy in the system. It is also observed that the system exhibits a path-dependent response to the sequence in which stable states are accessed when an external force is applied to the multistable unit. This behavior results from tailoring the rotational and axial stiffnesses of the system's springs, presenting a means for programming specific state-switching sequences. A physical demonstrator of the multistable arch hinge is manufactured using additive manufacturing, and the path-dependent behavior is characterized numerically and experimentally. Finally, an underactuated morphing rib demonstrator concept is presented using this embeddable multistable hinge unit to achieve camber and chord-wise deformation modes. The load-bearing capability of the presented demonstrator is quantified, and the path-dependent actuation implications are discussed, pointing to the benefits of the proposed underactuated morphing strategy for increasing the energy-saving potential of a compliant morphing structure with multiple programmed stable states.