The analysis presented in this work confirms that optimizing the diameter ratio and wrap angle is crucial for tailoring the auxetic properties of HAYs. A higher diameter ratio enhances the auxetic effect, making the material more responsive to axial strain with sustained lateral expansion. Conversely, a lower wrap angle improves the initial auxetic response but limits the range of strain over which this response is maintained. These insights are critical for designing materials with desired mechanical properties, particularly in applications requiring specific auxetic behavior within a defined range of strain.

Model 3, introduced in this work, generally provides a reasonable approximation of the contact pressure behavior as a function of axial strain, especially at low strains. However, as strain increases, the limitations of Model 3 become apparent due to its simplified assumptions. The discrepancies observed between the theoretical models and simulation results suggest that further refinement or calibration might be needed to improve their accuracy, particularly in predicting the exact magnitude of contact pressure under different loading conditions.

Overall, this work contributes valuable insights into the design of auxetic materials, offering guidelines for optimizing HAYs' performance while minimizing adverse effects like engulfment. Future work should include experimental validation to fully bridge the gap between theory, simulation, and real-world application, ensuring that the theoretical advancements can be reliably applied in practice.

Metamaterials are tessellated structures that introduce unique properties to motion system applications. The research on behaviour changes caused by this tessellation remains limited. This paper outlines the change in behaviour from a compliant unit cell to a metamaterial motion system, regarding linear stiffness, range of motion (RoM) and crosstalk. These properties are achieved through the analysis of series and parallel configurations, as well as scaling variations. The concept of an ideal shear cell is presented, describing desired motion system characteristics. Roberts mechanism approximates the ideal shear cell, bringing embodiment for finite element analysis and experimental validation. Results indicate that parallel configurations increase stiffness, while series arrangements reduce it, with RoM and crosstalk displaying opposing trends. Additionally, variations in flexure thickness introduce a trade-off between stiffness and range of motion. Different scaling strategies affect overall stiffness with minimal impact on RoM and crosstalk. While the main findings do not indicate inherent performance benefits to compliant mechanisms. This research contributes valuable insights into the design and performance of metamaterial-based motion systems, providing a foundational framework for future studies and applications.