Simplified dynamic characteristic analysis method for parallel manipulators with flexure hinges

To acquire precise high-resolution cryo-electron tomography data from transmission electron microscopy, a parallel manipulator (PM) with flexure hinges is often used to support and manipulate the samples. The precision and stability of the PM’s motion are intricately associated with its dynamic characteristics. Thus, it is essential to predict and enhance the PM’s dynamic characteristics during the initial design phase. To achieve this goal, a simplified dynamic characteristic analysis method (SDCAM) for PMs is developed. This method is based on the mass–spring model and accounts for only the mass of the mobile platform and the stiffness of the legs. A typical 6-PSS PM is employed as a case study to evaluate the proposed method. Analysis of the associated stiffness, mass, and frequency matrices allows us to derive the natural frequencies and modal shapes of the PM. The validity of the proposed SDCAM is confirmed through comparisons with the finite element method and the substructure synthesis method. Finally, using the average and population standard deviation of the first six-order natural frequencies of the PM as evaluation criteria, a hybrid optimization algorithm based on the multi-island genetic algorithm and sequential quadratic programming is adopted to optimize the configuration parameters and improve the PM’s dynamic characteristics. The impact of load on dynamic characteristics and optimization is explored based on practical application scenarios of the PM. We find that the SDCAM can be used to estimate the natural frequencies of PMs with flexure hinges, and the hybrid optimization algorithm in conjunction with the SDCAM effectively enhances the dynamic characteristics of PMs, thus providing important guidance for early-stage design.