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<p>In vibration-assisted polishing (VAP), static, kinetostatic, dynamics, and vibration trajectories are extremely important characteristics for compliant mechanisms to generate the vibrating source, but these behaviors lack a systematic modeling theory. This study presents a new XY compliant mechanism design inspired by the grasshopper. The proposed design can provide a wide amplitude amplification by a new self-amplified stroke based on the grasshopper’s legs. The machining qualities of VAP are crucially dependent on the vibrating amplitude, the output force, and the vibration trajectory of the central table. This research is aimed at providing theoretical modeling of the static, kinetostatic, dynamic, and oscillatory trajectories of the suggested structure. The stroke amplification ratio, workspace, stress, and kinetostatic are theoretically formulated by a graphical method and free body diagram. The resonant working frequency of the mechanism is modeled Lagrange’s II method. The dynamic motion and vibration trajectory of the mechanism in two directions are theoretically derived using D’Alembert’s principle. The force ratio between the input and output of the vibrating table is theoretically calculated. The results obtained from the theory closely align with those from the finite element analysis. The results found that the proposed mechanism can work at a wide workspace of 736.6 × 736.6 μm, a large stroke amplification ratio of 4.53, and a high working frequency of 548 Hz. The experimental tests are matched with the theoretical ones. This novel design facilitates a comprehensive design and modeling synthesis for two-dimensional vibrating mechanism for VAP.</p>

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Kinetostatic, dynamic, trajectory modeling for a new grasshopper-inspired 2DOF compliant mechanism for non-resonant vibration-assisted polishing

  • 期刊论文

  • 发表日期：

    2025年5月5日

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  • Hung Van Le,
  • Hieu Giang Le,
  • Thanh-Phong Dao

摘要

In vibration-assisted polishing (VAP), static, kinetostatic, dynamics, and vibration trajectories are extremely important characteristics for compliant mechanisms to generate the vibrating source, but these behaviors lack a systematic modeling theory. This study presents a new XY compliant mechanism design inspired by the grasshopper. The proposed design can provide a wide amplitude amplification by a new self-amplified stroke based on the grasshopper’s legs. The machining qualities of VAP are crucially dependent on the vibrating amplitude, the output force, and the vibration trajectory of the central table. This research is aimed at providing theoretical modeling of the static, kinetostatic, dynamic, and oscillatory trajectories of the suggested structure. The stroke amplification ratio, workspace, stress, and kinetostatic are theoretically formulated by a graphical method and free body diagram. The resonant working frequency of the mechanism is modeled Lagrange’s II method. The dynamic motion and vibration trajectory of the mechanism in two directions are theoretically derived using D’Alembert’s principle. The force ratio between the input and output of the vibrating table is theoretically calculated. The results obtained from the theory closely align with those from the finite element analysis. The results found that the proposed mechanism can work at a wide workspace of 736.6 × 736.6 μm, a large stroke amplification ratio of 4.53, and a high working frequency of 548 Hz. The experimental tests are matched with the theoretical ones. This novel design facilitates a comprehensive design and modeling synthesis for two-dimensional vibrating mechanism for VAP.