This paper presents a novel and scalable screw-theoretic multibody synthesis framework for PDE-based dynamic modeling of serial robotic manipulators with an arbitrary number of flexible links in three-dimensional space. The proposed approach systematically constructs screw-theoretic PDE models for individual flexible links and rigorously enforces holonomic joint constraints through interaction forces. The dynamics of each link are formulated using a set of dual screws expressed in body-fixed coordinates: one describing the motion of the body-fixed frame relative to the inertial frame, a second relating the body-fixed frame to the undeformed configuration, and a third capturing elastic deformations. By expressing the system energy and applying variational principles, the governing dynamics of each link had been previously derived in a unified manner. Synthesizing the individual link models yields an infinitely scalable multibody representation capable of capturing both local (subsystem-level) and global (system-level) dynamics. The framework explicitly recovers all dynamic states, including the motion of each body-fixed frame and the distributed deformation fields of the flexible links. For computational tractability and mathematical rigor, the resulting governing equations are formulated as a semi-explicit index-1 differential-algebraic system. Furthermore, by applying separation of variables, the PDE model is recast as an abstract Cauchy problem, and well-posedness of the resulting system is established.

翻译：本文提出了一种新颖且可扩展的螺旋理论多体综合框架，用于对三维空间中具有任意数量柔性连杆的串联机器人操作臂进行基于偏微分方程（PDE）的动力学建模。该方法系统地构建了单个柔性连杆的螺旋理论PDE模型，并通过相互作用力严格施加完整约束。每个连杆的动力学使用一组以物体固定坐标表示的对偶螺旋进行公式化：其中一个描述物体固定系相对于惯性系的运动，第二个将物体固定系与未变形构型相关联，第三个捕捉弹性变形。通过表达系统能量并应用变分原理，先前已以统一的方式推导出每个连杆的支配动力学方程。综合各连杆模型可得到无限可扩展的多体表示，该表示能够同时捕捉局部（子系统级）和全局（系统级）的动力学行为。该框架明确恢复了所有动力学状态，包括每个物体固定系的运动以及柔性连杆的分布变形场。为确保计算可行性与数学严谨性，所得支配方程被表述为一个半显式指标-1微分代数系统。此外，通过应用分离变量法，将PDE模型重新表述为抽象柯西问题，并证明了所得系统的适定性。