This paper presents a research into the progress of modeling of N-viscoelastic robotic manipulators. The governing equations of the system is obtained by using Gibbs-Appell (G-A) formulation and Assumed Mode Method (AMM). When the beam is short in length direction, shear deformation is a factor that may have substantial effects on the dynamics of the system. So, in modeling the assumption of Timoshenko Beam Theory (TBT) and its associated mode shapes has been considered. Although considering the effects of damping in continuous systems makes the formulations more complex, two important damping mechanisms, namely, Kelvin-Voigt damping as internal damping and the viscous air damping as external damping have been considered. Finally, to validate the proposed formulation a comparative assessment between the results achieved from experiment and simulation is presented in time domain.

Keywords: Timoshenko, Kelvin-Voigt, Air Damping, Gibbs-Appell, Experimental Setup

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