Dynamic Effect of Beamʹʹs Length and Beamʹʹs Theory on the Flexible Manipulators System

Abstract:In this paper, a comprehensive study is presented on the effect of beamʹs length, shear deformation and beamʹs theory on the dynamic modeling of single-link flexible manipulator. At the first step, Euler-Bernoulli beams theory (EBBT) is adopted. According to this model the effect of shear deformation is neglected. So, this model is only reliable for the case of slender beam. When the beam is short in length direction, shear deformation is an essential factor that may have significant effect on the systemʹs dynamic. Thus in next step the Timoshenko beam theory (TBT) is considered. Here, two types of dynamic models, Euler-Bernoulli and Timoshenko, have been established and used to analyze the dynamic behavior of the system. This model is developed using Gibbs-Applle formulation and assumed mode method. Simulation exercises are performed with bang-bang input torque applied to the joint actuator for a single-link flexible manipulator. To study the effects of length on the dynamic response of the system, the results are evaluated with varying beamʹs length. Finally, a comparative assessment of different beamʹs length and beamʹs theory to the system performance is discussed and represented.