Disturbed Configuration Bifurcation Characteristics of Gough–Stewart Parallel Manipulators at Singular Points

Abstract

In this paper, the disturbed configuration bifurcation characteristics of Gough–Stewart parallel manipulators at singular points are investigated. At first, the expended equation corresponding with the kinematics equation of the manipulator is introduced for eliminating the rank reduction and obtaining all of the theoretical singular points. Then, the assembly configurations at the singular points and the configuration bifurcation characteristics near them have been studied. It is found that the configuration bifurcation characteristics at the singular points belong to the turning point type through the Golubitsky–Schaeffer normal form identification. Next, utilizing the universal unfolding approach, the configuration bifurcation characteristics under the perturbation parameters applied to the extendable legs are analyzed. The investigation reveals that all configuration branches converged in the same singular point in the unperturbed system will be separated in the disturbed system. Based on this discovery, a novel approach for the parallel manipulator to pass through the singular points with a desired configuration is presented. The method presented in this paper can be utilized as the singularity avoidance approach for the parallel manipulators with strict trace and exact orientation control requirements, such as virtual parallel machine tools.