Dynamic Modeling and Development of Symbolic Calculation Software for N‐DOF Flexible‐Link Manipulators Incorporating Lumped Mass

Abstract

Considering the complex dynamic modeling of multi-DOF planar flexible manipulators, a general-purpose method for the rigid-flexible coupling dynamic modeling of N-DOF flexible manipulators is proposed in this paper, and symbolic calculation software is developed. The modeling method is based on the Lagrange equation and assumed mode method (AMM). First, the N-DOF flexible manipulator is divided into two parts, which are assumed to be rigid and flexible. On this basis, the rigid part and the flexible part are coupled, and the calculation process of the model is further simplified. Then, the simplest general symbolic expression of the dynamic model of the N-DOF flexible manipulator is obtained with the induction method. According to the modeling method, “symbolic expression computation software for dynamic equations of N-DOF flexible manipulators” is developed using the symbolic calculation software Mathematica. Finally, the dynamic modeling method and the symbolic calculation software are verified by a trajectory tracking experiment with a PD control applied to a 2-DOF flexible manipulator. Compared with the traditional modeling method, the calculation time can be reduced by more than 90% using the modeling method proposed in this paper, which significantly reduces the complexity of the modeling process.

Modal-Decomposition-Dependent State-Space Modeling and Modal Analysis of a Rigid-Flexible, Coupled, Multifreedom Motion System: Theory and Experiment

“…erefore, the system should be treated as a rigid-flexible coupled system [1,5,6]. In highend equipment, the motion system is typically a multiple-input multipleoutput (MIMO) system with multiple degrees of freedom (DOF), and the flexible internal dynamics will produce coupling effects between different motion axes [8,9]. erefore, it is necessary to study the modeling of rigid-flexible, coupled, multi-DOF motion systems.…”