Dynamic Modeling of the Ball-on-Flexible Beam Using Euler-Lagrangian Formulation

Nonprehensile manipulation involves moving objects without physical grasping using methods such as rolling, sliding, pushing, and throwing. In the context of rolling manipulation, a novel nonconventional type manipulator, referred to as the ball-on-flexible beam system, is presented in this paper. A flexible beam with multiple linear actuating rods attached to the underside of it can be controlled to move an overlying ball using rolling manipulation. Since the absence of physical grasping in nonprehensile manipulation often requires taking into account the dynamics of the system, we focus on the derivation of the dynamic model of the ball-on-flexible beam in this paper. The dynamic model is derived using the Euler-Lagrangian formulation. In the calculation of the kinetic and potential energies of the beam and the ball, the deflection of the flexible beam is taken into account based on the Euler-Bernoulli beam theory. The accuracy of the derived model is verified through a finite element analysis (FEA) case study.