This paper presents a novel six-degree-of-freedom (6-DOF) parallel platform that is used as the third mirror adjustment system of a large space telescope. In order to meet the design requirements of high precision, a large load–size ratio, and high stiffness in both the transverse and the vertical directions, the parallel platform is designed to be a 6-P-RR-R-RR structure via use of offset RR-joints. The inverse kinematics problem of the designed platform with offset RR-joints is much more complicated than that of a parallel platform with common universal joints owing to the presence of joint-dependent variables in the former problem. In this study, inverse kinematics of the designed parallel platform is mathematically modeled and the Newton–Raphson numerical iterative computation is performed. The accuracy and effectiveness of the proposed mathematical approach are verified by numerical co-simulations using MATLAB and ADAMS. The initial position of the platform is determined by a precision measuring arm. A test system is constructed, and then inverse kinematics solution, resolutions and adjusting steps accuracies of the platform are tested using grating length gauges. Motion strokes of the parallel mechanism are measured using laser tracker.
In order to compensate the optical system bias, which is caused by the change of elevation angle and thermal gradient during the optical alignment of the telescope, a novel high stiffness micro-nano positioning hexapod platform with flexure hinges is proposed in this paper. The novel flexure hinge has a mechanical limit, and its equivalent model is established and analyzed. In addition, in order to speed up the solution process, a novel simplified inverse kinematic model is developed based on the rigid body kinematic theory. Then, an effective rigid-flexible coupling simulation system is built to verify the correctness and applicability of the inverse kinematic model. Finally, a systematic experimental test method and a statistical-based data analysis theory are proposed. The experimental results show that the resolution and repeatability of translation and rotation and lateral stiffness are as follows: 0.3 mm and 0.5 arc sec, ± 0.5 µm and ±0.5 arc sec, 131.6N
⋅
µm-1 and 133.0N
⋅
µm-1. The proposed hexapod platform can be used to correct the optical system bias of large-aperture telescopes.
To meet the special requirements of the third mirror adjustment system for an optical telescope, a 6-P-RR-R-RR parallel platform using offset RR-joints is designed with high precision, a large load-to-size ratio and high stiffness. In order to improve the adjustment accuracy and the stiffness of the whole mechanism, each rotating joint in the subchain is designed as a zero-gap bead shaft system. When compared with a traditional Hooke joint, the offset RR joint has certain characteristics, including large carrying capacity and easy processing and adjustment, that effectively reduce the risk of interference with the joint during rotation and increase the working space of the entire machine. Because of the additional variables introduced by the offset joints, the kinematics problem becomes much more complicated. Regarding the P-RRRRR series subchain, the kinematics model is established using the Denavit–Hartenberg parameter method and then solved by the numerical iteration method. The stiffness of the parallel platform is analyzed and tested, including static and fundamental frequency. Motion performance testing of the parallel platform is performed.
A six degrees-of-freedom parallel platform in a 6-RR-RP-RR configuration with high accuracy, high stiffness and a large working stroke is studied for application to the sub-mirror adjustment system of a large-aperture telescope. To meet the performance requirements, the parallel platform adopts a self-centering and well-designed offset universal hinge. The two hinge axes of the offset hinge do not intersect but have a specific offset in space, which makes the kinematics more complex than that with a common universal hinge. Therefore, to solve this complex kinematics problem, this paper innovatively introduces the Denavit–Hartenberg (D-H) parameter method that is used for series mechanisms. The method has a simple modeling process, strong applicability and continuity, providing a new tool for the analysis and application of the parallel mechanisms. A kinematics model of the parallel platform can be constructed and solved using a numerical iteration method. The accuracy of the numerical kinematics solution is verified using a co-simulation method. This paper analyses the passive derivative motion and the leg length error is compensated. Finally, test studies of the motion resolution, the repetitive positioning accuracy, the motion stroke, the static stiffness of the legs, and the static stiffness and dynamic stiffness of the entire machine were also carried out to verify the platform’s performance.
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