## 5 Conclusions  
A 6-_P_-RR-R-RR parallel platform with high lateral and longitudinal stiffness is studied in this paper. The platform is mainly intended for use in the precision adjustment systems for third mirror components in a large-caliber telescope system. In the design process, the large load, high precision, and high stiffness indexes are taken as the design objectives of the platform. The platform has small axial dimension, high bearing capacity, high precision, and high stiffness. Different from the traditional parallel mechanism, the leg drive assembly is installed on the base platform surface at an inclination angle of 30\({}^{\circ}\), with low configuration height, which greatly reduces the height of the whole machine, improves the lateral stiffness of the whole machine, and increases the movement stroke of the driving inclined block. The parallel platform adopts offset RR joint with non-intersecting rotating shafts to replace the traditional universal joint, which has a larger bearing capacity and is easier to process and adjust, reducing the risk of interference between joints and other parts in the process of rotation. In this paper, all possible gaps in the structure are eliminated, and the RR-R-RR series kinematic chain is designed with zero gaps and high stiffness. Each revolute joint in the leg series kinematic chain uses a zero-gap dense bead shaft composed of two columns of high-precision large-diameter steel balls rather than the traditional bearing supported rotation joint and is appropriately pre-tightened, thus eliminating the movement gap while increasing the stiffness of the leg kinematic chain. The joint and leg installation datum is designed to improve the assembly precision of the kinematic chain. Different from the common 6-SPS, 6-UCU, and 6-UPS configurations, due to the additional variables introduced by the offset hinge, the traditional kinematic modeling method of parallel mechanism cannot be used to establish the kinematic model of the 6-_P_-RR-R-RR parallel platform. The D-H parameter method is successfully used to establish the complex kinematics mathematical model of the parallel platform, and the correctness of the model is verified via co-simulations. The introduction of the D-H parameter method provides a new solution for the kinematic analysis of complex parallel mechanisms. It lays a foundation for the subsequent analysis of velocity, acceleration, and dynamics. A parallel platform test system that mainly consisted of a test fixture, a simulated load, the grating length gauges, and the display instruments was constructed and motion performance testing was carried out. The static and dynamic stiffness of the platform were then tested to verify the rationality of the proposed design.  
Conceptualization, H.H. and Z.X.; methodology, H.H., Y.Z., and C.H.; software, A.L.; validation, H.H., Y.Z., and H.Z.; formal analysis, H.H.; investigation, Y.Z.; data curation, Y.Z. and H.Z.; writing--original draft preparation, H.H. and Y.Z.; writing--review and editing, Y.Z.; supervision, Z.X.; project administration, H.H. and Z.X.; funding acquisition, H.H. and C.H. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant number 52005478, and the Jilin Scientific and Technological Development Program, grant number 20200404204 YY.  
Not applicable.  
The data presented in this study are available on request form the corresponding author.  
The authors declare no conflict of interest.