Matrix Formulation of Constraint Wrenches for Serial Manipulators

A matrix formulation of the constraint forces and moments, together referred here as the wrenches, for serial manipulators is presented in this paper. The methodology is based on the Newton-Euler dynamic equations of motions of the manipulator at hand. The formulation provides joint forces and moments that are necessary for designing the robot links, as well those required by the joint actuators. The latter information is required in inverse dynamics. The formulation is based on writing the kinematic constraint equations using the Decoupled Natural Orthogonal complement (DeNOC) matrices, introduced elsewhere. The kinematic information in the form of the DeNOC matrices of a serial manipulator is used for the determination of the joint torques and forces, which lead to the development of a uniform analytical tool for control and design.