Inertia Matrix Singularity of Series-Chain Spatial Manipulators With Point Masses

Often, the dynamic behavior of multi-degree-of-freedom mechanical systems such as robots and manipulators is studied by computer simulation. An important step in this simulation is the inversion of inertia matrix of the system. In singular configurations of the inertia matrix, the simulation is prone to large numerical errors. Usually, it is believed that an inertia matrix is always positive definite. In this paper, it is shown that for spatial series-chain manipulators, when the links are modeled as point masses, a multitude of configurations exists when the inertia matrix becomes singular. These singularities arise because point masses lead to incomplete models of the system.