Abstract
For the fast and efficient closed-loop real-time feedback control of 6-UPS parallel robot (6-UPS), a novel high efficiency calculation of the workspace is proposed and investigated. As a typical Nearly General Platform (NGP), 6-UPS has good symmetries. The symmetries effectively reduce computational cost and improve computational efficiency in the kinematics, singularity, dynamics, and optimization. To scrupulously demonstrate the symmetries of workspace, a novel algorithm is proposed. The modified Euler angles (T&T angles) are employed to represent the orientation matrix of 6-UPS, the inverse kinematics is analyzed, and the workspace of 6-UPS is obtained using the discretization algorithm. Meanwhile, the symmetries of the total orientation workspace are also proved. Compared with the traditional methods, the total orientation workspace reduces 5/6 computation cost, which means that the corresponding computation efficiency is increased by 6 times. Through theoretical and numerical calculations, the symmetries of the total orientation workspace of 6-UPS are verified. The proof of the symmetries lays a solid foundation for improving the computational efficiency of kinematics, dynamics, and control of 6-UPS.
Highlights
The analysis of workspace is very important for designing and analysis of 6-UPS
This paper focuses on benefits of symmetries in discretization method
The numerical examples are performed in order to validate the correctness and validity of the symmetries of the total orientation workspace of 6-UPS about xb-zb plane structure symmetry
Summary
The analysis of workspace is very important for designing and analysis of 6-UPS. Besides, workspace of 6-UPS is relatively limited with respect to serial robot in similar size [1]. Jingshan Zhao [6] used group theory to prove the 3-dimension reachable workspace of 6-UPS with symmetrical structure possesses corresponding symmetry without the previous precondition. The symmetrical characteristics of total orientation workspace are discussed in this paper. Its parameters possess physical meanings and it is the foundation in the proof of the symmetries This new representation of orientation was firstly proposed by Bonev and Ryu [12]. Bonev [11] analyzes its advantages in 6-UPS, such as the direct geometrical interpretations of three parameters, the close relationship with the motion of CNC machine tool, and the simple and intuitive orientation representation. The symmetries of the total orientation workspace are discovered, proved, and compared with the RPY angles representation method.
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