Abstract:

This study introduces a versatile trapezoidal X-mechanism with three degrees-of-freedom (DOFs) to enable practical nonlinear manipulation using standard mechanical components. When integrated springs and rods are arranged in a trapezoidal configuration, the mechanism exhibits rich nonlinear characteristics along multiple directions and can be flexibly configured into trapezoidal, quadrilateral, or triangular forms, encompassing the known X-shaped variants in the literature. Compared with classic single-DOF X-structures, the proposed design offers superior versatility, compactness, and a self-contained spring-rod architecture without additional connections, while achieving comparable nonlinear dynamics. Analytical modeling, numerical simulations, and experimental validations demonstrate that the trapezoidal X-mechanism can be readily implemented with common spring-slider units, eliminating the need for custom rod fabrication. The structure enables tunable stiffness profiles, including positive, quasi-zero, zero, and negative stiffnesses across multiple directions, providing an expanded and adjustable quasi-zero stiffness (QZS) range. These features enhance the practicality and flexibility of engineering applications for noise, vibration, and stability control, offering a robust framework for designing nonlinear systems using widely available components.

Key words: trapezoidal X-mechanism, nonlinear stiffness, quasi-zero stiffness (QZS), negative stiffness, multi-degree-of-freedom (MDOF) mechanism