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<p>For the theoretical model of multi-stage amplification mechanisms, two main deficiencies exist. On the one hand, when analyzing flexure hinges, the Euler–Bernoulli beam theory is typically adopted, which ignores the influence of shear deformation on hinge flexibility. On the other hand, the coupling effect between the bending and axial flexibility of flexure beams is neglected. These two factors together result in a significant discrepancy between the theoretically calculated magnification and experimental results. To address this issue, this paper proposes a precise mechanical modeling method based on the flexibility matrix. First, the flexibility matrix of flexure hinges considering the shear effect is derived using the Timoshenko beam theory. Then, for the flexure beams connecting the 1st and 2nd stages as well as the 2nd and 3rd stages of the mechanism, a comprehensive beam element model is established that accounts for axial, bending, and shear deformations simultaneously. Finally, finite element simulation and experimental results are presented to verify the rationality and accuracy of the proposed theoretical model.</p>

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Modeling and design of a large-stroke three-stage amplification microgripper based on flexibility matrix method

  • 期刊论文

  • 发表日期：

    2026年8月3日

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  • Xiaodong Chen,
  • Zhengyang Zhang,
  • Huifeng Tan,
  • Fengjie Tian

摘要

For the theoretical model of multi-stage amplification mechanisms, two main deficiencies exist. On the one hand, when analyzing flexure hinges, the Euler–Bernoulli beam theory is typically adopted, which ignores the influence of shear deformation on hinge flexibility. On the other hand, the coupling effect between the bending and axial flexibility of flexure beams is neglected. These two factors together result in a significant discrepancy between the theoretically calculated magnification and experimental results. To address this issue, this paper proposes a precise mechanical modeling method based on the flexibility matrix. First, the flexibility matrix of flexure hinges considering the shear effect is derived using the Timoshenko beam theory. Then, for the flexure beams connecting the 1st and 2nd stages as well as the 2nd and 3rd stages of the mechanism, a comprehensive beam element model is established that accounts for axial, bending, and shear deformations simultaneously. Finally, finite element simulation and experimental results are presented to verify the rationality and accuracy of the proposed theoretical model.