Vibration Analysis of Multilink Manipulators Based on Timoshenko Beam Theory

Abstract

Timoshenko's theory is adopted in order to accurately describe the freely vibrating dynamics of a multilink flexible manipulator. It is herein presented an analytical modelling strategy that extends previous works through a more refined model which accounts for elastic complicating effects along with lumped inertial loads which are typically mounted on joints of manipulators; in this regard, more accurate results are provided. The eigenproblem is presented from an analytical point of view through a matrix formulation, thus providing an essentially closed formula. Apart from the limitations of the implementing calculator, the formulation can take into account an arbitrary number of links in an arbitrary settled configuration, thus allowing relevant analytical analysis and avoiding the need to recur to nonimmediate numerical schemes. Once the analytical model is introduced, solutions are compared to both those achieved by previous models and those obtained by a finite elements method.

Nonlinear modelling and dynamics of spatial multi-link rigid-flexible manipulator with moving platform

“…Matrix representation for joint and deflection motion has been used and deflection transformations have been expressed in terms of summation of mode shapes with a further comparison of the presented formulation with the earlier reported rigid link cases. Timoshenko beam model has been adopted by [8] to accurately model the dynamics of freely vibrating multi-link flexible manipulator incorporating the elastically complicated effects along with the inertia loads typically mounted on the joints of the manipulator. The influences of the slenderness ratio and the angular configuration of the manipulator on the natural frequencies have been investigated.…”

Modal Analysis of 3-RRR SPM Model

“…Patel and George presented survey on [1] parallel manipulators applications concluded that a continued and incessant effort by researchers will lead to an increased capability and effectiveness of various parallel robotics et al [2] presented a novel approach of workspace modeling with Euler parameters is proposed for a special class of spherical parallel manipulators with symmetrical structure [3] presented a multi-objective optimization problem is formulated to optimize the structural and geometric parameters of the spherical parallel manipulator. Castri and Messina [4] described the freely vibrating dynamics of multi-link flexible manipulator adopting Timoshenko's theory. Rong et al [5] reported a stiffness and modal analysis of precision parallel manipulator with flexure hinges.…”