Nonlinear rotational stiffness manipulation via a versatile rotational X-mechanism

Rotational vibration plays a crucial role in industrial sectors, impacting structural stability, vibration control, and energy efficiency. To meet these goals, it is essential to fine-tune the rotational stiffness of structures or materials. However, developing effective and cost-efficient adjustable rotational stiffness systems has been challenging due to unpredictable nonlinear behaviors, complex requirements, and manufacturing difficulties. This study introduces an easy-to-implement method for manipulating rotational stiffness using a compact and versatile rotational X-mechanism. This innovative approach allows systems to achieve a wide range of desired stiffness levels (positive, negative, zero, quasi-zero, and multi-stable equilibria), with the nonlinearity of these systems being fully controllable and predictable through straightforward and reliable mathematical modeling. The method offers exceptional adjustability, easily implemented through various simple mechanisms in practical mechanical designs. Two application prototypes featuring the X-mechanism are highlighted: a 1-DoF rotational platform and a 2-DoF rotational platform. The results demonstrate that both structures exhibit a broad range of desired nonlinear rotational stiffness and outstanding ultra-low-frequency vibration isolation performance. This new approach showcases the effectiveness and immense potential of leveraging nonlinearities with a rotational X-mechanism in diverse engineering applications. © 2025 The Authors