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<p>Compliant joints are widely used in precision positioning stages due to their nearly zero friction. A two-dimensional rigid-flexible coupling positioning stage (2D-RFCPS) containing multiple compliant joints is proposed to compensate for positioning errors caused by nonlinear friction, achieving long-stroke ultra-precision positioning. The kinetic and strain energies of the moving stages in the 2D-RFCPS are calculated based on the floating frame approach and the finite element method, respectively. These are used to establish the dynamic model of the 2D-RFCPS using the Lagrangian equation, revealing vibration coupling effects between the moving stages across six spatial directions. The accuracy of the dynamic model is validated through two comparative experiments. First, simulations under constant and harmonic forces are conducted using MATLAB and ADAMS, with the maximum root-mean-square error (RMSE) between the MATLAB and ADAMS results in displacement and velocity are 6.86E-4m and 2.9E-3m/s, respectively. Second, active disturbance rejection control (ADRC) algorithm is applied for point-to-point motion simulations and physical experiments, resulting in RMSE values of 8.80E-6m and 1.74E-4m/s in displacement and velocity, respectively. Additionally, the effectiveness of the dynamic model is demonstrated through vibration coupling analysis between the X-Tab and Y-Tab across six spatial directions. Notably, the Y-Tab rotation around the Z-axis is significantly influenced by the eccentric inertial torque, with the rotation amplitude increasing by 177.7% at the eccentric position.</p>

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Research on vibration coupling effect of two-dimensional rigid-flexible coupling positioning stage with compliant joints

  • 期刊论文

  • 发表日期：

    2026年1月9日

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  • Chi Zhang,
  • Zhijun Yang,
  • Guanxin Huang

摘要

Compliant joints are widely used in precision positioning stages due to their nearly zero friction. A two-dimensional rigid-flexible coupling positioning stage (2D-RFCPS) containing multiple compliant joints is proposed to compensate for positioning errors caused by nonlinear friction, achieving long-stroke ultra-precision positioning. The kinetic and strain energies of the moving stages in the 2D-RFCPS are calculated based on the floating frame approach and the finite element method, respectively. These are used to establish the dynamic model of the 2D-RFCPS using the Lagrangian equation, revealing vibration coupling effects between the moving stages across six spatial directions. The accuracy of the dynamic model is validated through two comparative experiments. First, simulations under constant and harmonic forces are conducted using MATLAB and ADAMS, with the maximum root-mean-square error (RMSE) between the MATLAB and ADAMS results in displacement and velocity are 6.86E-4m and 2.9E-3m/s, respectively. Second, active disturbance rejection control (ADRC) algorithm is applied for point-to-point motion simulations and physical experiments, resulting in RMSE values of 8.80E-6m and 1.74E-4m/s in displacement and velocity, respectively. Additionally, the effectiveness of the dynamic model is demonstrated through vibration coupling analysis between the X-Tab and Y-Tab across six spatial directions. Notably, the Y-Tab rotation around the Z-axis is significantly influenced by the eccentric inertial torque, with the rotation amplitude increasing by 177.7% at the eccentric position.