Nonlinear Dynamic Analysis of a Spatial Mobile Flexible Robot

Using some agent variables, the general structure of the dynamic model of a spatial mobile robot with N flexible links and N revolute joints that is a set of 5N+6 nonlinear coupled partial differential equations along with boundary conditions, has been presented. Non-conservative forces and moments have been neglected. While being considered, the general structure of the dynamic model is not changed. The base of the robot is a six-DoF rigid body in space and each link, as an Euler-Bernoulli beam, has whole elastic spatial degrees of freedom; i.e., tension compression, torsion and two spatial bendings. The links are made from a linearly elastic isotropic material and are dynamically modeled much more accurately than that of a nonlinear 3D Euler-Bernoulli beam. That is, the elastic orientation of cross-sectional frame of each link is considerable. Moreover, when the elastic orientation of the cross-section is neglected, the dynamic model of each link remains more accurate than that of a nonlinear 3D Euler-Bernoulli beam. These findings have promoted the conventional nonlinear 2D and 3D Euler-Bernoulli beam theory within which the elastic orientation of the cross-sectional frame is actually negligible. So far, Leonhard Euler (1707-1783 A.D.) has had a significant role in beam's vibrational analysis and column's stability. Euler-Bernoulli beam is the most rigid model for the beams within which the cross-section remains plane according to the Bernoulli's (1700-1782 A.D.) hypothesis. The deficiencies in the formulation of the nonlinear 2d and 3d Euler-Bernoulli beam theories had not been considered before in several the references. This issue has considerable engineering and educational applications.