On the positive definiteness and uniform boundedness of the inertia matrix of robot manipulators

In this paper we give a new alternative proof for the positive definiteness of the inertia matrix of robot manipulators and give an explicit uniform bound for its determinant. This in turn shows that the inertia matrix can not be arbitrarily singular and that its minimum eigenvalue is uniformly bounded if all its eigenvalues are bounded. Hence, we completely characterize the class of robot manipulators with bounded inertia matrix and show that it includes manipulators with nontrivial joint configurations. For manipulators of this class, we give easily computable uniform bounds for the minimum and maximum eigenvalues of the inertia matrix