5自由度船舶靠泊装置运动学及工作空间分析

Kinematics and Workspace Analysis of 5-DOF Ship Berthing Device

为提高船舶靠泊安全系数,减少大型船舶靠泊事故的发生,设计一种以"两转动一平移3-RPU"并联机构为主体结构的5自由度船舶靠泊装置。基于螺旋理论和修正G-K公式,计算出并联机构的自由度;利用齐次位姿变换建立各连杆矢量方程,推导出并联机构位置正反解数学表达式,基于位置反解表达式求出并联机构的雅克比矩阵,并根据雅克比矩阵对3-RPU机构的3类运动学奇异性进行分析;建立机构驱动关节速度与动平台速度之间的关系,对正反解的研究结果进行数值验证,并运用MATLAB对位置和速度反解进行仿真;采用蒙特卡洛法求解并联机构的可达工作空间,运用MATLAB编程绘制出工作空间三维图和截面图,验证了3-RPU并联机构的可行性,为3-RPU并联机构的应用提供理论依据。

In order to improve the safety factor of ship berthing and reduce the occurrence of berthing accidents of large ships, a 5-DOF ship berthing device is designed with the parallel mechanism of two rotation and one translation 3-RPU as the main structure. Based on the screw theory and the modified G-K formula, the degree of freedom of the parallel mechanism is calculated. The vector equation of each linkage is established by using homogeneous pose transformation, and the mathematical expression of positive and negative solution of parallel mechanism position is deduced, the Jacobian matrix of the parallel mechanism is calculated based on the expression of the position inverse solution, and the 3 kinds of kinematic singularities of the 3-RPU mechanism are analyzed according to the Jacobian matrix. The relationship between the velocity of the driving joint and the velocity of the moving platform is established, and the research results of the positive and negative solutions are verified by numerical value, and the position and speed solutions are simulated by MATLAB. The reachable workspace of the parallel mechanism is solved by Monte Carlo method, and the three-dimensional diagram and section diagram of the workspace are drawn by MATLAB programming, the feasibility of the 3-RPU parallel mechanism is verified, which provides a reference for the application of the 3-PRU parallel mechanism for theoretical basis.