Analytic singularity expression for 6-DOF Stewart platform-type parallel manipulators

The analytic expression for the singularities of 6-DOF SPM (Stewart-platform type parallel manipulator) is obtained using the concept of LSM (local structurization method) with extra sensors. The resulting equation, however, does not include sensor values, but is a function of design variables. The equation is basically a third-degree polynomial and it exactly provides singularity information for general SPMs. Several symbolic examples are shown to verify the exactness of the singularity equation by comparing it with the previously reported singularities.