Configuration Bifurcation Characteristics of the Semi-Regular Hexagon Gough-Stewart Parallel Manipulator

Type-II singularities exist in parallel manipulators commonly. At this kind of singularities, the end-effector is locally movable and uncertain even when all the actuate joints are located. In order to explore a possible approach to obtain the concrete output of the mobile platform at the very small vicinity (germ space) of the singular point, in this paper, the configuration bifurcation characteristics at the germ space have been investigated. At first, the type-II singularity has been identified with Golubitsky-Schaeffer normal form. The result shows that the type-II singular points belong to the turning points. Then, the configuration bifurcation equation is reduced into one dimensional form. Based on this one dimensional equation, the unperturbed and perturbed configuration bifurcation behaviors at the germ space of the turning point have been analyzed. It is found that all configuration branches converged in the same singular point in the unperturbed system can be separated in the perturbed system. This discovery has presented a possible approach to control the parallel manipulator passing through the singular point with a desired configuration.