Influence of strut inertia on the vibrations in initially symmetric Gough–Stewart Platforms—an analytical study

Abstract

Consideration of strut inertia can have significant influence on the modal behavior of a Gough–Stewart Platform (GSP). However, in the literature, the strut inertia has not yet been taken into account in its vibration study with a parametric approach. In this paper, we present a fully parametric approach to formulate the damped vibrations of GSPs taking into account the strut masses and moments of inertia for symmetric configurations. For the first time, a combined 6×6 equivalent inertia matrix (mass matrix), including both the inertia properties of the platform and the struts, is formulated parametrically. Subsequently, the eigenvectors and the damped eigenfrequencies are also parametrically developed in the Cartesian space. Furthermore, the conditions for the decoupled vibrations and the effect of strut inertia on these conditions are analytically investigated. With the aid of a reference GSP, the influence of the strut inertia on its modal behavior is systematically investigated. Accordingly, it is concluded that the parametric equations established in this paper can be directly employed in the analysis, optimization and control of GSPs in any application.