Rotating and Length-Varying Flexible Manipulators (RLVFMs) benefit from the ability to transform their length to adapt to complex and demanding workspaces but suffer from increased complexity in nonlinear dynamical characteristics and thus difficulties in modeling. To provide an in-depth understanding of the RLVFMs, this paper proposes a novel dynamical modeling approach for the RLVFMs, called the Parametric Global Modal Method (PGMM), and presents a framework to study their nonlinear responses. It is capable of addressing time-varying boundary conditions and describing the elastic deformation of all flexible components with only one set of modal coordinates. A low-dimensional dynamical model of a RLVFM is developed. The natural characteristic results obtained from the models developed by the PGMM and the finite element method (FEM) are compared for verifications of the PGMM. Via a convergence analysis of responses, the high precision of the model developed by the PGMM is verified to be achieved by using only the first two modes. On this basis, the dynamic responses and computational efficiency of the low-dimensional model are validated through experiments and finite element method (FEM) simulations. Moreover, the responses of the RLVFM under operations of rapid maneuvering are studied and a potential vibration control strategy for the RLVFM is preliminarily demonstrated. This work provides a new way of developing advanced dynamical modeling methods of reconfigurable and deformable multi-component mechanisms for their dynamical design, response analysis, and system control.

中文翻译：

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用于旋转和长变柔性操纵器动力学建模和响应分析的参数化全局模态方法


旋转和长度变化柔性操纵器 （RLVFM） 受益于变换其长度以适应复杂和苛刻的工作空间的能力，但非线性动力学特性的复杂性增加，因此建模困难。为了更深入地理解 RLVFM，本文提出了一种新的 RLVFM 动力学建模方法，称为参数全局模态法 （PGMM），并提出了一个研究其非线性响应的框架。它能够解决时变边界条件，并仅使用一组模态坐标描述所有柔性组件的弹性变形。开发了 RLVFM 的低维动力学模型。比较了从 PGMM 和有限元方法 （FEM） 开发的模型获得的自然特性结果，以验证 PGMM。通过响应的收敛分析，验证了仅使用前两种模式即可实现 PGMM 开发的模型的高精度。在此基础上，通过实验和有限元法 （FEM） 仿真验证了低维模型的动力学响应和计算效率。此外，研究了 RLVFM 在快速机动操作下的响应，并初步展示了 RLVFM 的潜在振动控制策略。这项工作为开发可重构和可变形多组件机构的高级动力学建模方法提供了一种新方法，用于其动力学设计、响应分析和系统控制。