An Isoparametric Four-Node Beam Element for the Analysis of Planar Robot Manipulators
Abstract Accurate determination of the dynamic response of high speed flexible manipulators requires that the dynamic model incorporates the influence of joint compliances, in addition to faithfully representing the physical characteristics of the links. A finite element model is herein presented for this purpose. The model is based on a 4-node isoparametric Timoshenko beam element to model the structural characteristics of the links including the effects of shear deformation and rotary inertia. It also includes the influence of the rigid body motion and the time derivatives of the elastic deformations of the manipulator on the characteristic matrices of the system, and accounts for the inertia of the drive units and payload and the damping of externally applied dampers. Quasistatic analysis, modal analysis, and linear and nonlinear vibrational responses of a 3-R planar manipulator are determined by solving the appropriate equations of equilibrium. The results of the analysis revealed that the compliance of the joints have a considerable influence on the manipulator response which is manifested by considerable increase in endpoint deflections and substantial decrease in fundamental natural frequency. Nonlinear transient response exhibited a behavior that differs drastically from that obtained when rigid joints are assumed.