Performance analysis of 3-PPRU parallel mechanism with a completely/partially/non constant Jacobian matrix
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DOI 10.1007/s12206-020-0918-5
Journal of Mechanical Science and Technology 34 (10) 2020 Original Article DOI 10.1007/s12206-020-0918-5 Keywords: · Parallel mechanism · Partially constant Jacobian matrix · Performance analysis · Screw theory
Performance analysis of 3-PPRU parallel mechanism with a completely/partially/ non constant Jacobian matrix Yachao Cao1, Tie Zhang1, Yanzhi Zhao2,3 and Guangcai Ma1 1
Correspondence to: Tie Zhang [email protected] Yanzhi Zhao [email protected]
School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 2 510640, China, Parallel Robot and Mechatronic System Laboratory, Yanshan University, Qinhuangdao 3 066004, China, Key Laboratory of Advanced Forging and Stamping Technology and Science of Ministry of National Education, Yanshan University, Qinhuangdao 066004, China
Abstract
Citation: Cao, Y., Zhang, T., Zhao, Y., Ma, G. (2020). Performance analysis of 3-PPRU parallel mechanism with a completely/ partially/non constant Jacobian matrix. Journal of Mechanical Science and Technology 34 (10) (2020) 4263~4279. http://doi.org/10.1007/s12206-020-0918-5
Received September 8th, 2019 Revised
February 17th, 2020
Accepted July 28th, 2020 † Recommended by Editor Ja Choon Koo
© The Korean Society of Mechanical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2020
This paper proposes a 3-PPRU parallel mechanism (PM) with a completely/ partially/non constant Jacobian matrix. Based on screw theory and selecting actuating components theory, the reasonability of the actuating input selection is analyzed. By different actuating selection, the Jacobian matrix of the PM can realize completely/partially/non constant. The direct, inverse and combined kinematic singularities of the PM with three different Jacobian matrices are discussed. The velocity, payload and stiffness performance of the PM are discussed and compared. A new index, as auxiliary evaluation index, is proposed first.
1. Introduction It is well known that the Jacobian matrix of parallel mechanisms (PM) plays a significant role in kinematics, singularity, and performance evaluation. The Jacobian is not only an important index to measure kinematics and dynamics performance, but also the basis of performance analysis and evaluation. Scholars have done much research work [1-9] in the last decade based on the Jacobian matrix, including n × n Jacobian matrix [2, 3] of limited-degrees of freedom (DoFs) of PMs, 6×6 Jacobian matrix [1, 4, 8], and dimensionally homogeneous Jacobian matrix for performance analysis [9]. In general, Jacobian matrices of most PMs vary with the pose of the moving platform throughout the workspace. In the process of online motion planning, it is necessary to solve the inverse solution of the PMs in real time, which leads to spending much time on position solution and poor control accuracy. If the Jacobian matrix of the PMs can always keep constant, by comparison, the input-output velocity/force mapping relationship remains invariant all the time, it wi
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