In this paper, the problem of the integrals of normalized quasi-velocities is discussed. Introducing the quasi-velocities known from the robotic literature leads to diagonalization of the manipulator mass matrix in velocity space. It is shown here that, for a two-degree-of-freedom (2-DOF) manipulator, sometimes there exist analytical forms of integrals of normalized quasi-velocities. If the analytical method is not available, then a numerical method is used to calculate integrals of the quasi-velocities. This solution is presented for a 3-DOF three-dimensional DDArm (Direct Drive Arm) robot.
