Finite element based dynamical modeling of flexible open-loop manipulators with experimental results

This document presents the dynamic analysis of a two-link flexible open-loop manipulator. Equations of motion based on a hybrid rigid body/finite element model are developed. A unique feature of the equations developed herein is the segregated finite element approach to modeling the separate links of the manipulator. This leads to greater freedom in the selection of element types by eliminating inter-element compatibility requirements at the joints of the manipulator. In developing the equations of motion for this system, the Lagrange equation is separately applied to the rigid body and elastic displacement freedoms of each link. This leads to a coupled set of differential equations involving all the dynamic freedoms of the manipulator. The significance of this approach is that no assumptions about the rigid body motion are made. The resulting equations of motion include not only the standard linear finite element dynamic terms, but also several additional terms. These added terms represent important effects such as coupling between rigid body and elastic motion and nonlinear inertia loading phenomena. The presence of non-standard terms in the formulation precludes the use of standard finite element analysis solution procedures.; Experimental results are presented for verification of the equations of motion developed in this work. Verification of the model is done through comparisons of experimental results with theoretical analysis in modal frequency predictions, forced time responses and free vibrational time responses.; In addition to the main thrust of this work, two additional developments are included. In the first, an inverse kinematic analysis procedure is presented in which the effects of link deformations are included. This is done in order to compensate the joint angles of a manipulator for proper end effector positioning in the presence of link deformations. The second development presented is that of a modified beam finite element which allows for regions of rigidity at either or both of the ends of the beam. This new element is shown to be not only practical but also very effective in reducing the computational burden in the dynamic analysis of systems having both rigid and beam-like flexible sections.