In this work, a systematic approach is presented for the development of dynamic equations of motion of a robot manipulator with mechanical flexibility. A simple structural lightweight rotating manipulator with joint elastic flexibility is considered for the mechanical flexibility study. The complexity of mathematical equations involved in mechanical flexibility is analyzed. The analytical approach helps the design for controls of flexible manipulator. A set of decoupled dynamic equations are derived incorporating both the structural and joint flexibility. The dynamic equations are compared with a detailed model, and the results are showing that equations are accurate for small joints. Also the results from the simulation show that in a flexible joint system, there is no rigid mode.

中文翻译：

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拉格朗日法的机械臂机械臂数值分析

在这项工作中，提出了一种系统的方法来开发具有机械灵活性的机器人机械手的动态运动方程。对于机械柔韧性研究，考虑了具有关节弹性柔韧性的简单结构的轻型旋转机械手。分析了涉及机械柔韧性的数学方程的复杂性。分析方法有助于设计柔性机械手的控件。导出了一组解耦的动力学方程，其中包含了结构和关节的灵活性。将动力学方程与详细模型进行了比较，结果表明该方程对于小节理是准确的。仿真结果还表明，在柔性接头系统中，没有刚性模式。