An Analytical Framework for Global Dynamic Modeling of Flexible Variable Topology Mechanisms

Abstract

The coupling of topology transition with flexible deformation and rigid motion presents significant challenges in the dynamic modeling of flexible variable topology mechanisms. Existing dynamics models are mostly special-purpose models for their particular cases and thus struggle to completely depict the general topology transition characteristics. To address this gap, this paper proposes an analytical framework for the global dynamic modeling of flexible variable topology mechanisms, focusing on general cases. Initially, the flexible variable topology mechanisms are rigorously defined by the ordered triples and the general topology transition approaches are presented. A novel concept, the “basic flexible kinematic chain set”, is suggested, which can easily transform into the topology of each submechanism by slightly extending. Based on this concept, basic and conditional constraints are established. The continuous dynamic modeling method for each topology is developed using Jourdain’s principle and the Lagrange multiplier method. Additionally, three classes of constraints related to topology transition are identified, and their equations are formulated, elucidating the topology transition nature. Compatibility equations are proposed to define the new coordinate system for describing the deformation of flexible components after the topology transition. An impact dynamic equation is established to describe abrupt velocity change. Integrating compatibility and impact equations, a discontinuous dynamic modeling method for topology transition is developed. Finally, a flexible variable topology mechanism example is studied, and simulations and experiments are conducted to validate the proposed framework. This analytical framework is general-purpose and efficient, guiding the global dynamic modeling of various flexible variable topology mechanisms and the development of sophisticated control techniques.