Dynamics of Slender Single-Link Flexible Robotic Manipulator Based on Timoshenko Beam Theory

Abstract

It is well known that irrespective of the joint signature, namely serial or articulated, a single-link manipulator has a great application in the field of robotics. For the study of dynamics of single-link manipulators, the conjugate problem is studied based on Timoshenko beam theory. Governing differential equations and the boundary conditions are usually considered as exact and the formulation leads to an eigenvalue problem where the elements of the matrices are in exact form. In view of the above, this chapter investigates the said problem in particular for a single-link semi-compliant flexible robotic manipulator. After the successful modelling of the single-link manipulator, with Timoshenko beam theory, the model has been compared with the existing calculation of an undamped Euler–Bernoulli cantilever beam as well, taking tip mass to be zero. The study extends further by taking tip mass to be non-zero and the results are compared with mass-loaded clamped-free Timoshenko beam. These comparisons are found to be in good agreement.