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旋量理论多体综合框架，用于三维空间中具有任意数量柔性连杆的串联机器人机械臂的偏微分方程动力学建模。所提出的方法系统地为各个柔性连杆构建旋量理论偏微分方程模型，并通过相互作用力严格强制执行完整关节约束。每个连杆的动力学均使用一组在物体固定坐标系中表示的对偶旋量进行表述：一个描述物体固定坐标系相对于惯性坐标系的运动，第二个将物体固定坐标系与未变形构型相关联，第三个则捕捉弹性变形。通过表达系统能量并应用变分原理，每个连杆的控制动力学先前已以统一方式推导得出。综合各个连杆模型可产生一个无限可扩展的多体表示，能够同时捕捉局部（子系统级）和全局（系统级）动力学。该框架显式地恢复了所有动态状态，包括每个物体固定坐标系的运动以及柔性连杆的分布变形场。为了计算的可处理性和数学严谨性，所得控制方程被表述为一个半显式指数-1微分代数系统。此外，通过应用变量分离法，该偏微分方程模型被重构为一个抽象柯西问题，并建立了所得系统的适定性。