Inertia matrix singularity of planar series-chain manipulators

For series chain manipulators whose links are modeled as point masses, there is a multitude of configurations in which the inertia matrix is singular. Intuitively, it is expected that these singular configurations will be complex functions of both mass centers and geometric properties of the links. It is shown that these singularities are purely geometric and can be determined by establishing linear dependence of partial velocities of the mass centers. An iterative method to find these singular configurations by working with the individual link inertia matrices as opposed to the overall inertia matrix of the chain is presented. It is believed that once an analyst is aware that the inertia matrix of a multi-degree-of freedom mechanical system can be singular, a better job of both modeling and interpreting the results of simulation can be done