An efficient algorithm is presented for the calculation of the inverse kinematic accelerations for a 6 degree-of-freedom manipulator with a spherical wrist. The inverse kinematic calculation is shown to work synergistically with the inverse dynamic calculation, producing kinematic parameters needed in the recursive Newton-Euler dynamics formulation. Additional savings in the dynamics computation are noted for a class of kinematically well-structured manipulators such as spherical-wrist arms and for manipulators with simply-structured inertial parameters.