Theoretical and experimental investigation of viscoelastic serial robotic manipulators with motors at the joints using Timoshenko beam theory and Gibbs–Appell formulation

Abstract

In this article, the mathematical modeling of n-viscoelastic-link robotic manipulators based on the Gibbs–Appell formulation and the assumed mode method is developed. The elastic properties of the links are modeled according to the Timoshenko beam theory and its associated mode shapes. Also the dynamic effects of the motors at the joints are fully taken into consideration. In the mathematical modeling, the effects of torsion, extensional deformation, bending in two directions, structural damping, and viscous air as well as the gravity effects have also been considered. A recursive algorithm based on 4 × 4 transformation matrices has been developed to ease the derivation of motion equations. The mismatch between the high-speed vibrations of flexible robotic arms and the low-speed operation of the software and hardware interface in the computer and the experimental setup is a serious obstacle for the measuring and controlling of such systems. So, to verify the simulation results and the results obtained from the experimental test bed, high-speed digital-to-analog converter components on an electronic interface board are used in conjunction with the National Instrument’s LABVIEW software package.