Kinematic and dynamic modeling of viscoelastic robotic manipulators using Timoshenko beam theory: theory and experiment

This paper presents an investigation into the development of modeling of n -viscoelastic robotic manipulators. The dynamic model of the system is derived using Gibbs-Appell formulation and assumed mode method. When the beam is short in length direction, shear deformation is a factor that may have significant effects on system dynamic. So, in modeling, the assumption of Timoshenko beam theory and associated mode shapes has been considered. Although including the effect of damping in continuous systems makes the formulations more complicated, two important damping mechanisms, namely, Kelvin-Voigt damping as internal damping and the viscous air damping as external damping have been considered. Based on derived formulation, a non-linear recursive algorithm is developed for deriving the inverse dynamic equation of motion, systematically. The performance of the proposed algorithm was assessed in terms of the required mathematical operations for deriving the kinematic and dynamic equations of the mechanical system. Finally, to validate the proposed formulation, a comparative assessment between the results achieved from experiment and simulation is presented in time and frequency domains.