Kinematics analysis and validation of 3-PUU parallel mechanism

doi:10.3785/j.issn.1006-754X.2024.03.157

Chinese Journal of Engineering Design

2023, Vol. 30

Issue (6): 763-778 DOI: 10.3785/j.issn.1006-754X.2024.03.157

Modeling, Simulation, Analysis and Decision

Kinematics analysis and validation of 3-PUU parallel mechanism

Mingfang CHEN(

),Liangen HUANG,Yongxia ZHANG,Guoyi YAO

Faculty of Mechanical and Electrical Engineering, Kunming University of Science and Technology, Kunming 650500, China

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Abstract

In order to improve the efficiency and accuracy of the design of parallel mechanisms with few degrees of freedom, the theoretical analysis and experimental research were conducted on a self-designed 3-PUU parallel mechanism. Firstly, the degree of freedom of the parallel mechanism was analyzed by using the screw theory and the modified Kutzbach-Grubler formula. At the same time, the forward and inverse kinematics solutions and Jacobian matrix of the parallel mechanism were solved, and its constraint singularity and kinematic singularity were analyzed based on the Jacobian matrix. Then, the workspace of the parallel mechanism was analyzed by using the limit boundary search method, and the global dexterity was constructed by taking the reciprocal of Jacobian matrix condition number as the local dexterity, so as to analyze the kinematic performance of the parallel mechanism. Next, an ADAMS/Simulink co-simulation model of the parallel mechanism was built. Based on the given motion equation of the moving platform, the simulation curves and error curves of the moving platform position were obtained through simulation. Finally, the experimental platform was built by using the parallel mechanism prototype, PC (personal computer), STM32 microcontroller, servo motor and laser tracker, and the position curves of the moving platform were measured. The results showed that the parallel mechanism had a large reachable workspace and good kinematic performance. By comparing theoretical results with simulation results, it could be concluded that the constructed kinematics model of the parallel mechanism was correct. There were some errors between the measured and theoretical values of the moving platform position, mainly due to the mechanical errors of the parallel mechanism and the insufficient precision of the control system. However, the variation trends of the measured curve and the theoretical curve were basically consistent, which further verified the correctness of the kinematics model of the parallel mechanism. The research results can provide reference for the design of parallel mechanisms with few degrees of freedom.

Key words： 3-PUU parallel mechanism kinematics analysis singularity workspace dexterity ADAMS/Simulink simulation

Received: 25 April 2023 Published: 02 January 2024

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Cite this article:

Mingfang CHEN,Liangen HUANG,Yongxia ZHANG,Guoyi YAO. Kinematics analysis and validation of 3-PUU parallel mechanism. Chinese Journal of Engineering Design, 2023, 30(6): 763-778.

URL:

https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2024.03.157 OR https://www.zjujournals.com/gcsjxb/Y2023/V30/I6/763

3-PUU并联机构的运动学分析与验证

为提升少自由度并联机构设计的效率和准确性，针对自主设计的3-PUU并联机构进行了理论分析和实验研究。首先，利用螺旋理论和修正的Kutzbach-Grubler公式分析了并联机构的自由度；同时，解算了并联机构的运动学正反解和雅可比矩阵，并基于雅可比矩阵分析了其约束奇异和运动奇异。然后，利用极限边界搜索法分析了并联机构的工作空间，并以雅可比矩阵条件数的倒数作为局部灵巧度来构造全局灵巧度，分析了并联机构的运动性能。接着，搭建了并联机构的ADAMS/Simulink联合仿真模型，基于给定的动平台运动方程，通过仿真得到了动平台位置的仿真曲线及误差曲线。最后，利用并联机构样机、PC（personal computer，个人计算机）、STM32单片机、伺服电机及激光跟踪仪搭建了实验平台，并测定了并联机构动平台的位置曲线。结果表明，该并联机构具有较大的可达工作空间且其运动性能较好；通过对比理论结果与仿真结果可知，所构建的并联机构运动学模型正确；动平台位置的实测值与理论值之间存在一定误差，主要原因是并联机构存在机械误差以及控制系统精度不足，但实测曲线与理论曲线的变化趋势基本一致，进一步验证了并联机构运动学模型的正确性。研究结果可为少自由度并联机构的设计提供参考。

关键词： 3-PUU并联机构, 运动学分析, 奇异性, 工作空间, 灵巧度, ADAMS/Simulink仿真

Fig.1 Three-dimensional model of 3-PUU parallel mechanism

Fig.2 Kinematics model of 3-PUU parallel mechanism

Fig.3 Motion spiral of branch chain 1 of 3-PUU parallel mechanism

Fig.4 Reachable workspace of 3-PUU parallel mechanism

Fig.5 Dexterity distribution of 3-PUU parallel mechanism under x_O =0 mm

Fig.6 Dexterity distribution of 3-PUU parallel mechanism under y_O =0 mm

Fig.7 Dexterity distribution of 3-PUU parallel mechanism under z_O =750 mm

Fig.8 Virtual prototype model of 3-PUU parallel mechanism

Fig.9 Simulink simulation model for forward kinematics of 3-PUU parallel mechanism

Fig.10 Input of forward kinematics simulation model of 3-PUU parallel mechanism

Fig.11 Position curve of each slider under given motion trajectory S₁

Fig.12 Position curve of each slider under given motion trajectory S₂

Fig.13 Simulation verification results of position of moving platform corresponding to motion trajectory S₁

Fig.14 Simulation verification results of position of moving platform corresponding to motion trajectory S₂

Fig.15 Simulation verification results of velocity and acceleration of moving platform corresponding to motion trajectory S₁

Fig.16 Simulation verification results of velocity and acceleration of moving platform corresponding to motion trajectory S₂

Fig.17 3-PUU parallel mechanism prototype

Fig.18 Experimental platform of 3-PUU parallel mechanism

Table 1 Partial sampling results of moving platform center position

Fig.19 Experimental verification results of position of moving platform center

Table 2 Partial sampling results of slider position

Fig.20 Experimental verification results of slider position


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