Parametric damped vibrations of Gough–Stewart platforms for symmetric configurations

• A parametric model for the damped vibrations of GSPs is developed.
• The Jacobian, stiffness and damping matrices are parametrically formulated.
• Well-structured equations of eigenvectors and damped eigenfrequencies are presented.
• Decoupled vibrations are analytically investigated.
• The developed parametric model in this paper can be directly used to optimize GSPs.

Modal behavior of a Gough–Stewart Platform (GSP) is sensitive to several variables related to its inertia, damping and stiffness as well as its complex 3-D geometry. To optimize its dynamical performance, due to the complications of this system, it is crucial to have the equations parametrically at the neutral configuration. However, in the literature, no complete parametric solution to this problem is presented. In this paper, we establish a fully-parametric and closed-form model for the damped vibrations of GSPs. In particular, this analytical model can be used in order to design, optimize and control GSPs in high-precision/bandwidth applications. Parametric expressions of the damped eigenfrequencies and the corresponding eigenvectors as well as the Jacobian, stiffness and damping matrices are developed. Interestingly, despite the complexity of the system, it is shown how well-structured algebraic expressions are obtained using the Cartesian-space approach. Having analytically studied the eigenvectors, the conditions for decoupled vibrations are also analytically formulated. Finally, using a reference GSP, the sensitivity of the damped eigenfrequencies to stiffness and damping variations are investigated accompanied by a cross-check with an ABAQUS® simulation.

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