基于拉格朗日的冗余驱动并联机构刚体动力学建模

针对4-UPS-RPU 4自由度冗余驱动并联机构的刚体动力学建模问题,基于拉格朗日方程建立冗余驱动并联机构动力学模型。首先,推导出4-UPS-RPU冗余驱动并联机构系统的动能表达式、势能表达式和作用于并联机构非保守力的等效广义力;然后,应用拉格朗日法建立4-UPS-RPU冗余驱动并联机构的动力学模型,为并联机构驱动力的求解以及整个机构的动力学分析奠定基础;最后结合算例,采用Matlab编程对动力学模型进行数值计算并绘制了机构驱动杆驱动力变化曲线,将上述分析结果与ADAMS虚拟仿真结果对比验证了所建动力学模型的正确性。研究不仅为4-UPS-RPU 4自由度冗余驱动并联机构动力学优化设计和控制等后续研究提供了理论依据,也为其他冗余驱动并联机构的动力学建模提供了可行的方法。

Rigid Dynamics Modeling of Redundant Actuation Parallel Mechanism Based on Lagrange Method

To realize the rigid dynamics modeling of a novel 4-UPS (universal joints-prismatic pairs-spherical joints)-RPU (revolution joints-prismatic pairs-universal joints) spatial 4-degree of freedom redundant actuation parallel mechanism, the Lagrange method was adopted. Firstly, the expression of kinetic energy and potential energy of 4-UPS-RPU redundant actuation parallel mechanism were educed, and the equivalent generalized force of non conservative force was analyzed. Secondly, the dynamics model of 4-UPS-RPU redundant actuation parallel mechanism was established by the Lagrange method, which was the foundation of the solution of driving force and dynamic analysis. Finally, the driving forces of 4-UPS-RPU spatial 4-degree of freedom redundant actuation parallel mechanism were solved by theoretical calculation and virtual simulation combined with examples, respectively. The numerical results obtained by solving the dynamics model of the 4-UPS-RPU parallel mechanism by Matlab were in agreement well with the virtual simulation results by ADAMS. The results can provide theoretical basis for dynamic optimization design and control of 4-UPS-RPU parallel mechanism, and also suggest a way of thinking about rigid body dynamics modeling for other redundant actuation spatial parallel mechanism.