Analysis of Stewart platform with flexural joints at singular configurations

摘要

A parallel mechanism at a singular configuration gains one or more degrees of freedom instantaneously which makes controllability difficult. At such configurations, it cannot resist externally applied forces and moments acting along certain directions. If the rotary joints in the mechanism are replaced by flexural hinges, the instantaneous gain in the degree of freedom of the mechanism can be effectively arrested and the mechanism can resist externally applied forces and moments. This important idea is first demonstrated on a planar truss with flexural joints at a singular configuration. Subsequently this idea is extended to a Stewart platform mechanism with flexural joints at several singular configurations and shown conclusively that it can resist external forces and moments applied in singular directions except for a moment applied about the vertical direction (Z). This singularity is overcome by the introduction of a seventh flexural jointed leg, connecting the centres of the base and platform in all the configurations and the analysis shows finite leg forces for external moment acting about Z axis including forces and moments about all other axes. This is followed by a parametric analysis considering the stiffness of the flexural joints and their effects on the leg forces. Thus this paper has brought out a method wherein the instantaneous gain in the degrees of freedom of mechanisms at singular configurations can be completely overcome by an appropriate choice of flexural joints in the place of regular joints. This research contribution could significantly influence the configuration and design of parallel mechanisms with flexural joints.