Quantitative analysis of decoupling and spatial isotropy of a generalised rotation-symmetric 6-DOF Stewart platform

Abstract

The Stewart platform is one of the most frequently studied six-degree-of-freedom (6-DOF) parallel robots. Although it has an uncomplicated architecture, it still poses some remaining research challenges, especially regarding Cartesian stiffness, decoupling, and isotropy. Although it is well established that spatial isotropy is only dependent on the direction vectors of the six links, the diagonal values in the stiffness matrix, and in particular the relationship between the first three elements and the last three elements, are affected by other factors. The methodology proposed in this paper aims at designing decoupled and spatially isotropic Stewart platforms with user-selected values of these diagonal elements. A parametric model of a generalised rotation-symmetric Stewart platform is established and the expression of the corresponding Cartesian stiffness matrix is derived. The approach in this paper is first to find the different cases when the expressions of off-diagonal elements of the Cartesian stiffness matrix are zero and then, within each case, quantitatively derive conditions for decoupling and spatial isotropy. By applying this approach, several novel decoupled and spatially isotropic architectures with three horizontal links were derived.