A novel mathematical approach for finite element formulation of flexible robot dynamics

Abstract

In conventional finite element–Lagrangian methods, the dynamics model of a flexible robot is usually formulated based on a critical assumption that the kinetic energy of an element is approximately calculated with an integral of mass point energy. Since the energy integral is implicit, the formulation of the dynamics model is also very complex and implicit. Hence, this article develops a new mathematical approach for the dynamic modeling of a general flexible/rigid robot. The proposed method is more comprehensive and efficient in comparison with the previous ones because it no longer requires the calculation of the symbolic integrals and the implicit expressions of the elemental and global mass matrices. Besides, the proposed approach is applicable for both the flexible robots and the hybrid flexible/rigid robots. To validate the proposed method, numerical simulations and experimental results are presented.

Keywords:

• Flexible robots
• flexible/rigid robots
• kinematics of machines
• dynamics of machines
• finite elements method

Additional information

Funding

This work was supported by the Vingroup Innovation Foundation (VINIF) annual research support program under Grant VINIF.2019.DA08.