A new composite body method for manipulator dynamics

This article presents a new composite body method for numerically forming the inertia matrix and the bias vector of manipulators, which is more efficient than the other two existing types of composite body methods. The main discrepancy of this one from the existing ones is that all points in a manipulator are observed from the origin of the base frame and the distances are all measured from this origin. The required computations of the present method for the inertia matrix and the bias vector of a manipulator with n rotational joints are (10.5n2 + 38.5n - 85)M + (6n2 + 39n - 70)A and (12.5n2 + 5.5n + 3)M + (9n2 + n)A, respectively, where “M” denotes multiplications, “A” does additions. In numerically forming the inertia matrix, the present method is more efficient than other methods in the literature for a manipulator with five or more joints; whereas this method is also superior to the recursive Newton-Euler formulation in computing the bias vector for a manipulator with six or less joints.