Although the numerical properties of a step-by-step integration method can be evaluated based on the currently available techniques, there is still lack of a technique for evaluating its capability to capture dynamic loading. In this work, the amplitude error caused by the step discretization error is identified and the correlation between the relative amplitude error and relative step discretization error is analytically established. As a result, it is thoroughly confirmed that the asymptotic constant of the discretization error amplification factor for the displacement response to a cosine loading can be considered as an indicator of the capability to capture dynamic loading for a general step-by-step integration method.

In this paper a model to cover all possible topologies of robot manipulators composed of prismatic and revolute joints is presented. For simplicity, only planar systems are considered, hence to provide plane positioning, systems handled are of three degrees of freedom. The physical model assumes three moving rigid links in articulation with one revolute and one prismatic joint between each link pair, forming a six degrees of freedom open chain linkage. Among each joint pair, one is real and the other fictitious. The real joint is arbitrarily actuated by an externally applied force or torque while the fictitious one is acted upon by an appropriately controlled force or torque as to keep that joint velocity zero, keeping fixed at its initial position. The physical model is accompanied by a mathematical model obtained by Lagrange formulation. This approach is called ‘The method of Fictititous Degrees of Freedom’.