When a segment of a flexible link of a flexible robot is currently sliding through a prismatic joint, it is usually assumed that the elastic deformation of the segment equals to zero. This is a kind of time-dependent boundary condition when formulating the dynamics model of a flexible robot consisting of prismatic joints. Hence, the dynamic modeling and especially the inverse dynamic analysis of the flexible robots with the prismatic joints are challenging. In this article, we present a new development of the dynamic modeling method for a generic two-link flexible robot that consists of a prismatic joint and a revolute joint. Moreover, a new bisection method-based algorithm is proposed to analyze the inverse dynamic responses of the flexible robots. Since the bisection method is a rapid converging method in mathematics, the proposed algorithm is effectively applicable to solving the inverse dynamic problem of a flexible robot in a robust manner. Last, the numerical simulation results show the effectiveness and the robustness of the proposed method.

中文翻译：

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柔性机器人动力学建模与逆动力学分析的新进展

当柔性机器人的柔性连杆的一段当前滑动通过棱柱关节时，通常假设该段的弹性变形为零。这是在制定由棱柱关节组成的柔性机器人的动力学模型时的一种瞬态边界条件。因此，具有棱柱关节的柔性机器人的动力学建模，尤其是逆动力学分析具有挑战性。在本文中，我们介绍了通用双连杆柔性机器人的动态建模方法的新发展，该机器人由棱柱关节和旋转关节组成。此外，提出了一种新的基于二分法的算法来分析柔性机器人的逆动态响应。由于二分法在数学上是一种快速收敛的方法，所提出的算法有效地适用于以鲁棒方式解决柔性机器人的逆动力学问题。最后，数值模拟结果表明了该方法的有效性和鲁棒性。