Kinematics analysis and performance testing of 6-RR-RP-RR parallel platform with offset RR-hinges based on Denavit-Hartenberg parameter method

Abstract

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.