Efficient formulations for the manipulator inertia matrix in terms of minimal linear combinations of inertia parameters

This article summarizes four formulations of the composite body method for the inertia matrix of a manipulator in the earlier works and presents a new formulation. These five formulations all use the first moments and the inertia tensors of composite bodies about the origin of the local frame. This paper also presents an algorithm for computing these first moments and inertia tensors. This algorithm utilizes a set of minimal linear combinations of inertia parameters instead of the natural inertia parameters, so that a number of redundant computations are saved. It is found that the new algorithm for the first moments and the inertia tensors of composite bodies is computationally superior to the others in the literature. On the other hand, two among the five formulations for the inertia matrix are more efficient than the other three as well as the others in the literature. The new formulation is one of these two most efficient formulations, and is specially adequate to a manipulator with some translational joints. Q 1999 John Wiley & Sons, Inc.