Analytic singularity equation and analysis of six-DOF parallel manipulators using local structurization method

An analytic expression for the singularities of a six-degree of freedom Stewart-platform type parallel manipulator (six-DOF SPM) is obtained using the concept of a local structurization method (LSM) with extra sensors. The resulting equation, however, does not include sensor values. It is only a function of design variables. The equation is basically a third-degree polynomial and it exactly provides singularity information of general SPMs. Several symbolic examples are shown to verify the exactness of the singularity equation by comparing it with previously reported singularities. Some other numerical examples are also shown using the proposed singularity equation