Kinematic Analysis and Performance Test of a 6-DOF Parallel Platform with Dense Ball Shafting as a Revolute Joint

Abstract

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.

Workspace analysis of axial offset joint based on parameterization

“…The workspace comparison method is similar to that used in the previous section for the 6-U C U PM. Firstly, the inverse kinematics solution of the 6- P -RR-R-RR PM with offset joints needs to be obtained, which can be referenced in the literature [12]. And the 3D model of the 6- P -RR-R-RR PM with offset joints can be found in Fig.…”

“…Since the mechanical properties of the offset joint were calculated through experiments, theoretical analyses, and CAD simulations, the PM using offset joints has had many applications, such as bone-surgery operation [11] and large-diameter telescopes precisely adjustment [12], because of its greater precision, workspace, and carrying capacity. Hu and Lu [13] and Ji and Wu [14] proposed a three-degrees-of-freedom (3-DOF) PM with offset joints and analyzed the PM’s kinematics, singularity, and workspace.…”

Direct and Inverse Cinematic Resolution Calculation using Denavit-Hartenberg Algorithm and Geometric Method for Robot with 5 DOF

“…All the algorithms aim to find an optimal design for local search optimization having as input the system a kinematic structure. Han et al, 2021 [12], implemented offset RR joints that offer high levels of precision, in areas of load to size ratios very high values and equally high offerings in regards to stiffness. All the features mentioned aimed to be used in the development of a parallel platform.…”

“…To obtain theta 1, each variable was solved using trigonometric relations of a right triangle as shown in (11), (12) and (13).…”

Inverse dynamics analysis of a 6-RR-RP-RR parallel manipulator with offset universal joints

“…Algorithms based on joint constraints [6, 7] have attempted to establish the displacement kinematics of a 6-RR- C -RR PM with RR–joints (where C denotes a cylindrical joint whose translational degree of freedom (DOF) is actuated). Additionally, the displacement kinematics of a 6- P -RR-R-RR PM have been studied using both the joint-constraint algorithm and the Denavit–Hartenberg (D–H) parameters [8, 9], with numerical solutions obtained. The displacement kinematics of a 6-RR- RP -RR PM (see Fig.…”