The new-generation X-ray light sources based on accelerators, Diffraction-limited Storage Rings (DLSRs) , and X-ray Free-electron Lasers ( XFELs) , have excellent properties such as high brightness, high coherence, and high collimation, which has enhanced important opportunities for scientific research and technological development. In the meantime, that brings a lot of challenges on the photon beam manipulation as well, the performance demand of optical components have been greatly improved , and at the same time, the attitude adjustment accuracy of optical components has generally entered the "micro/nano" range, such as the resolution of linear motion and angular rotation of optical components are supposed to reach a level of sub-nanometre and nanoradian. In the construction of the beamline, the monochromator is one of the core equipment to guarantee the optical performance of the beamline. In order to meet requirements of high stability and motion precision of beamline optics, for crystal monochromators in the new-generation light sources, a mechanism with a nano-radian angular resolution, driven by piezoelectric nano-displacement stages was developed. An optimized slider-crank mechanism is adopted for a large angle range of tens of degrees, so that a broader energy range can be covered with relatively big Bragg diffraction angles. This paper presents the main design parameters of the offset slider-crank mechanism for crystal monochromators according to the demand of energy range, the energy resolution and the required linear transmission ratio of X-ray crystal monochromator. By establishing a geometrical model of the slider-crank mechanism , it turns out that the transmission ratio between the linear displacement and the Sine of the Bragg angle depends solely on the crank rod length. Therefore, the length of crank rod can be determined according to the transmission ratio. At the same time, an optimized model of the offset slider-crank mechanism parameters is established in this paper, and the length of the connecting rod was determined according to achieving a high-precision linear transmission ratio in a large angle range. Finally, the precise angular displacement monitoring was carried out using a high-precision non-contact Fabry-Perot laser interferometer. The measurement errors of the high-precision angle measurement method are analyzed and it is found that the measurement errors can be ignored in the extremely small measurement range within an incremental step. The final results show that an angular resolution of 31.2 nrad can be achieved with a good linear relation of transmission, and the angular stability is better than 16 nrad within 800 seconds. The design of this mechanism has a great convenience for crystal' S adjustment of X-Ray monochromators, and it is conducive to techniques studies on an angular stability of nanoradians.
