Uniform modal frequencies and damping in multi-legged Stewart platforms

Abstract

This paper presents the design of a novel two-radii Gough–Stewart platform (TRGSP) for multi-axis vibration isolation with an arbitrary number of legs, capable of achieving uniform natural frequencies and damping across the first six degrees of freedom (DOF). Conventional single-radii Gough–Stewart platforms cannot achieve such uniform modal characteristics, limiting their effectiveness in six DOF isolation. The proposed TRGSP is dynamically isotropic with complete modal decoupling and enabling representation as six independent single-input–single-output dynamical systems, thereby simplifying damper tuning and controller design. For the first time, a general closed-form analytical framework is developed for dynamically isotropic TRGSPs with more than six legs, and all design variables are derived using a novel geometry-based approach that reduces the 3D dynamic isotropy problem to a 2D triangular geometry problem An innovative, cost-effective transitional design strategy is further proposed to upgrade existing platforms by adding legs to accommodate increased payloads while preserving dynamic isotropy. Under stated modeling assumptions, the analytical results are validated numerically through finite element method (FEM) simulations for multiple leg configurations and further confirmed experimentally using a 6-leg dynamically isotropic TRGSP prototype developed for spacecraft micro-vibration isolation. The framework provides a practical solution for next-generation multi-axis vibration isolation systems for use in spacecraft and precision applications. © 2026