There is increased demand for high spatial resolution in domestic and international nano-imaging experimental stations utilizing synchrotron radiation. Nano or nanoradian level positioning accuracy and stability are necessary for focusing mirrors or monochromators on the beamlines.

This study aims to design and optimize a redundant parallel flexible hinge rotating device to meet this demand.

First of all, the kinematics of the flexible mechanism were initially analyzed, and the virtual displacement principle was employed to derive the overall static rotational stiffness of the mechanism. Then, the characteristics of the mechanism, as well as the impact of hinge parameters on stiffness, were investigated. Subsequently, the dynamic model of the mechanism was built by employing the Lagrange equation, and the natural frequency in the motion direction was deduced. Finally, an optimization model was developed for the static and dynamic dual purpose mechanism design, solved through a genetic algorithm accounting for nonlinear constraints. In addition, the first four resonance frequencies and vibration modes of the flexible mechanism were examined using a finite element method for modal analysis followed by the creation and assembly of a high-precision flexible hinge mechanism along with a rotary adjustment device for experimental testing.

Test results indicate that the flexible angular displacement adjustment mechanism achieves a rotation angle of 0.668° and bidirectional repeatability of ±8.91 nrad during fine-tuning. In addition, the angle resolution of 15 nrad and stability of 2.72 nrad (root mean square value) are achieved over a 30 min test in the frequency range of 1~500 Hz. The first natural frequency of the mechanism is approximately 295 Hz, which aligns with the theoretical calculations and finite element analysis results.

The effectiveness and reliability of the optimized flexible mechanism in achieving nanoradian level high-precision angular displacement adjustment is confirmed by this study.