An Analytical Framework for Global Dynamic Modeling of Flexible Variable Topology Mechanisms
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 depic...
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MDPI AG
2024-12-01
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| Online Access: | https://www.mdpi.com/2076-0825/13/12/519 |
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| author | Ruihai Geng Yushu Bian Zhihui Gao Yize Zhao Peng Liu |
| author_facet | Ruihai Geng Yushu Bian Zhihui Gao Yize Zhao Peng Liu |
| author_sort | Ruihai Geng |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-df0ef4f72c534e31b301e5b3183fa0a8 |
| institution | DOAJ |
| issn | 2076-0825 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
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| series | Actuators |
| spelling | doaj-art-df0ef4f72c534e31b301e5b3183fa0a82025-08-20T02:57:08ZengMDPI AGActuators2076-08252024-12-01131251910.3390/act13120519An Analytical Framework for Global Dynamic Modeling of Flexible Variable Topology MechanismsRuihai Geng0Yushu Bian1Zhihui Gao2Yize Zhao3Peng Liu4School of Mechanical Engineering and Automation, Beihang University, No. 37 Xueyuan Lu, Haidian District, Beijing 100191, ChinaSchool of Mechanical Engineering and Automation, Beihang University, No. 37 Xueyuan Lu, Haidian District, Beijing 100191, ChinaSchool of Mechanical Engineering and Automation, Beihang University, No. 37 Xueyuan Lu, Haidian District, Beijing 100191, ChinaSchool of Mechanical Engineering and Automation, Beihang University, No. 37 Xueyuan Lu, Haidian District, Beijing 100191, ChinaSystems Engineering Research Institute, China State Shipbuilding Corporation, No. 1 Fengxian East Road, HaiDian District, Beijing 100191, ChinaThe 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.https://www.mdpi.com/2076-0825/13/12/519flexible variable topology mechanismtopology transitionflexibilitydynamic modelimpact |
| spellingShingle | Ruihai Geng Yushu Bian Zhihui Gao Yize Zhao Peng Liu An Analytical Framework for Global Dynamic Modeling of Flexible Variable Topology Mechanisms Actuators flexible variable topology mechanism topology transition flexibility dynamic model impact |
| title | An Analytical Framework for Global Dynamic Modeling of Flexible Variable Topology Mechanisms |
| title_full | An Analytical Framework for Global Dynamic Modeling of Flexible Variable Topology Mechanisms |
| title_fullStr | An Analytical Framework for Global Dynamic Modeling of Flexible Variable Topology Mechanisms |
| title_full_unstemmed | An Analytical Framework for Global Dynamic Modeling of Flexible Variable Topology Mechanisms |
| title_short | An Analytical Framework for Global Dynamic Modeling of Flexible Variable Topology Mechanisms |
| title_sort | analytical framework for global dynamic modeling of flexible variable topology mechanisms |
| topic | flexible variable topology mechanism topology transition flexibility dynamic model impact |
| url | https://www.mdpi.com/2076-0825/13/12/519 |
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