Dynamic Modeling of a Flexible-Link Flexible-Joint System with Tip Mass Considering Stiffening Effect

This paper presents the dynamic model of a flexible-link, flexible-joint manipulator system with a considerable stiffening effect of the flexible link. A gripper, along with tip mass, is attached at one end of the flexible link. By employing the extended Hamilton's principle, a nonlinear governing equation of motion is derived along with several boundary constraints. Under the assumption of small deformation in free vibration, a simplified motion equation is deduced to determine the natural frequencies of the mechanical system. Four parameters of the system are selected to carry out the sensitivity study on frequency. The results show that the second frequency mainly depends on the mass of tip payload. Moreover, the third frequency is significantly affected by the moment inertia of tip payload. Regarding the constant angular motion, the finite element method is adopted to analyze the dynamic model by considering the stiffening effect. The frequency results are obtained which show a higher stiffness of the Single Flexible-link Flexible-joint (SFF) system with the angular velocity increasing. The influence of three factors (i.e., payload mass, length of the flexible link, and angular velocity) on the fundamental natural frequencies are discussed, which show instinct characteristics of the flexible manipulator system.