Modeling of Flexible Robotic Systems

This paper presents a theoretical background and an example of extending an elastic line equation from several aspects. Navier equation (based on the known laws of dynamics) should be supplemented with all the forces that are participating in the formation of the bending moment of the considered mode. We analyze the system in which the action of coupling forces (inertial, Coriolis\´, and elasticity forces) exists between the present modes. This yields the difference in the structure of Navier equations for each mode. It is shown that Daniel Bernoulli\´s particular integral is just one component of the total elastic deformation of the tip of any mode to which we have to add a component of the elastic deformation of a stationary regime. The essential relationship between "lumped mass approach" (LMA) and "Euler-Bernoulli Equations" (EBE) approaches is proved