Abstract: In order to investigate the concrete moving behaviors at bifurcation points, based on the homotopy method and the static bifurcation condition, the algorithm, which is capable to detect all the configuration branches and bifurcation points, is constructed. With the aid of the concept of maximum uncontrollable domain, uncontrollable orientation components of manipulators at singular points are analyzed. The study shows that the uncontrollable orientation components have relations with both characteristics of the bifurcation curves of configurations and control precision of input parameters. It is found that increasing the control precision of input parameters will reduce uncontrollable regions of manipulators at singularities. By this way, the controllability of manipulators near by singular points is enhanced.

Key words: Bifurcation, Maximum uncontrollable domain, Parallel manipulator, Singularity