## 1 Introduction  
When a large-caliber telescope is in orbit, the relative positional relationships between the optical components may change because of factors including shock vibration, gravity release, temperature changes, and air pressure changes. Changes in the relative pose between the primary scope, the secondary mirror, and the third mirror of the telescope have a major influence on the imaging quality of the optical system, so it is necessary to use a high-precision adjustment mechanism to adjust this pose. The six degrees-of-freedom (6-DOF) configuration is commonly used in parallel adjustment mechanisms because of its high stiffness; examples include the 6-SPS configuration [1, 2], the 6-UCU configuration [3], the 6-UPS configuration [4], and the 6-RUS configuration [5, 6]. When compared with the 6-DOF configuration, configurations with fewer DOFs are easier to control and operate and configurations that have attracted the attention of many researchers include the 3-DOF configurations 3-PPS [7], 3-RPS [8], 2 PRU-UPR [9], 3-TPT [10], 3-UPU [11], the 4-DOF configurations 4-PRRRR [12], 2-RPU and 2-SPS [13], and the 5-DOF configurations 3-PPUR [14] and 4 SPU+UPU [15]. The 6-DOF parallel platform under study in this paper is used to adjust the third mirror poses of large-diameter telescopes precisely. To meet the requirements for high precision, a large load-size ratio and high stiffness, a 6-P-RR-R-RR configuration is used for the platform. To perform preliminary ground verification and meet the practical application needs, research is carried out on the kinematics solution and the stiffness and motion performances. The parallel mechanism was first used in aircraft tire tests [16]. Since then, parallel mechanisms have been used widely in many fields. These practical applications include:motion simulators [17; 18], parallel machine tools [19; 20], a 6-DOF micro vibration simulator [21], and a space optical load isolation system [22]. Most telescope secondary mirror or third mirror adjustment systems use parallel mechanisms, including the Visible and Infrared Survey Telescope for Astronomy (VISTA) secondary mirror system [23], and the Very Large Telescope Survey Telescope (VST) secondary mirror system [24]. In recent years, parallel mechanisms have also increasingly been used in surgical procedures, including spinal surgery [25] and ophthalmic surgery [26]. The kinematics analysis of the parallel mechanism does not involve forces or moments, nor does it study the forces or moments generated by the motion. The analysis mainly studies the mapping relationship between the position, the velocity and the acceleration of the mobile platform and the active joint input of the leg that produces the motion; among these factors, the position research is the main basis. The kinematics problems of parallel mechanisms can be divided into inverse kinematics and forward kinematics, and the forward kinematics problem is much more complex than that of inverse kinematics. Parallel mechanisms for common configurations, such as 6-SPS, 6-UCU, and 6-SPU, have simple structures and their inverse kinematics have analytical solutions [27; 28; 29]. However, with the continuing development of parallel mechanisms, a variety of parallel platforms with new structural forms have emerged and inverse kinematics solutions cannot be obtained for these platforms by analytical methods. There is a specific offset distance between the two spatially perpendicular rotating axes of the offset RR joint, and when additional offset variables are introduced, the kinematics of a parallel mechanism with an offset joint becomes quite complex. [PERSON] and [PERSON] [30] studied an offset 3-UPU parallel mechanism with three translational degrees of freedom, established the inverse kinematics and forward kinematics equations for this mechanism, and demonstrated that the mechanism has two inverse kinematics solutions. Two passive offset Hooke joints were used at both ends of each leg, and the two rotational axes of the offset joints were perpendicular to each other.