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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2021, Vol. 55 Issue (5): 810-822    DOI: 10.3785/j.issn.1008-973X.2021.05.002
    
Design and modeling of wire-driven rigid-flexible parallel mechanism for wave compensation
Yuan CHEN(),Deng-hui GUO,Li-xia TIAN
School of Mechanical and Electrical Engineering, Shan Dong University, Weihai 264209, China
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Abstract  

A rigid-flexible hybrid drive active parallel mechanism for wave compensation was proposed in order to reduce the damage caused by wind and waves in the transport of container goods at sea. The mathematical model of positional inverse solution was established based on the matrix rotation principle and the geometric closure method of the dynamic platform of rigid-flexible hybrid parallel mechanism. The mathematical model of the positional forward solution was constructed by using spatial geometry. The second order effect matrix of acceleration and velocity Jacobian was established by using the derivation rule to obtain the positional inverse solution. The system stiffness matrix was derived on the basis that the rope is a flexible variable body, and the factors affecting the system stiffness and the principle of increasing the system stiffness were explored. In addition, the kinematics and system stiffness values were verified by numerical simulation, and the input and output data errors of the inverse and positive solutions were not more than 2.25% of the actual errors. Results showed that the theoretical simulation curve and the prototype simulation curve coincided, and the error was not more than 7.4%, which verified the correctness of the kinematics model. The influence of stiffness factors on the stiffness of system was found according to the stiffness matrix. Finally, the parallel mechanism of the rope-driven rigid-flexible hybrid wave compensation was experimentally verified, and the compensation effect of the mechanism was more than 90%. Results provide theoretical support for the motion and the mechanism design of rigid-flexible hybrid active parallel mechanism for wave compensation.

Key words： spiral theory      active wave compensation      rigid-flexible hybrid parallel mechanism      kinematics      stiffness of flexible bod     
Received: 08 May 2020      Published: 10 June 2021
CLC:  TP 242.2  
Fund:  国家自然科学基金资助项目（52075293）；中央高校基本科研业务费专项资金资助项目（2019ZRJC006）；山东省重大创新工程资助项目（2017CXGC0923）；山东省自然科学基金资助项目（ZR2019MEE019）
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Yuan CHEN
Deng-hui GUO
Li-xia TIAN
Cite this article:

Yuan CHEN,Deng-hui GUO,Li-xia TIAN. Design and modeling of wire-driven rigid-flexible parallel mechanism for wave compensation. Journal of ZheJiang University (Engineering Science), 2021, 55(5): 810-822.

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http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2021.05.002     OR     http://www.zjujournals.com/eng/Y2021/V55/I5/810


绳牵引刚柔式波浪补偿并联机构的设计与建模

为了减少海上集装箱货物运输中风浪造成的损坏，提出刚柔混合驱动主动式波浪补偿并联机构. 基于刚柔混合并联机构的动定平台的矩阵旋转原理和几何封闭法建立位置逆解数学模型；利用空间几何原理构建机构位置正解数学模型；利用求导法则对位置逆解进行求导，建立速度雅可比矩阵与加速度的二阶影响矩阵；基于绳子是柔性变形体推导出系统刚度矩阵，探究影响系统刚度的因素和增加系统刚度的原则. 利用数值模拟仿真对运动学和系统刚度进行验证，结果表明位置正逆解的输入输出误差不超过实际误差的2.25%；发现理论仿真曲线和样机仿真曲线较吻合，误差不超过7.4%，验证了运动学模型的正确性；根据刚度矩阵发现刚度影响因素对系统刚度的影响规律. 通过对绳驱动刚柔混合驱动波浪补偿并联机构的实验验证，发现该机构的补偿效果均高于90%. 证明研究结果为刚柔混合主动式波浪补偿并联机构的运动和机构设计提供了理论支持.


关键词： 螺旋理论,  主动式波浪补偿,  刚柔混合式并联机构,  运动学,  柔性体刚度 
Fig.1 Schematic diagram of rigid-flexible hybrid active parallel mechanism for wave compensation
Fig.2 Compensation effect diagram of compensation mechanism
Fig.3 Schematic diagram and coordinate system of rigid-flexible hybrid active parallel mechanism for wave compensation
Fig.4 Branched-chain coordinate system of parallel mechanism for wave compensation
序号 ${{{P}}_0}$/mm ${}_{{P}}^{{O}}{{R}}$ 绳长符号 计算绳长/mm 输入绳长/mm 绳长误差/mm
实例1 $\left[ {\begin{array}{*{20}{c}} { - 0.64} \\ { - 1.54} \\ {47.37} \end{array}} \right]$ $\left[ {\begin{array}{*{20}{c}} {0.351}&{0.813}&{0.525} \\ { - 0.876}&0&{0.318} \\ {0.397\;9}&{ - 0.573}&{0.600} \end{array}} \right]$ L1 78.574 80 1.426
L2 97.756 100 2.243
L3 98.379 100 1.621
实例2 $\left[ {\begin{array}{*{20}{c}} {5.790} \\ { - 4.222} \\ {47.370} \end{array}} \right]$ $\left[ {\begin{array}{*{20}{c}} {0.291}&{0.993}&{ - 0.273} \\ { - 0.769}&{0}&{ - 0.399} \\ { - 0.447}&{0.027}&{0.859} \end{array}} \right]$ L1 118.124 120 1.876
L2 131.358 130 1.358
L3 78.279 80 1.721
Tab.1 Comparison between calculated with given rope lengths
Fig.5 Rope variation vector and unit vector under small displacement
参数 数值
固定平台的直径×厚度/mm 100×20
动平台的直径×厚度/mm 50×10
支链长度×导程/mm 70×600
支链刚度系数/(N·m?1) 200
绳索截面面积/mm2 0.83
绳索弹性模量/GPa 70.5
Tab.2 Parameters of rigid-flexible hybrid parallel mechanism
Fig.6 Change in length of rope
Fig.7 Change in rope velocity when angle α and angle β change with time according to predetermined trajectory
Fig.8 Change in rope acceleration when angle α and angle β change with time according to predetermined trajectory
Fig.9 Change in system stiffness when dynamic platform rotates around X axis
Fig.10 Changes in system stiffness when height changes in Z direction
Fig.11 Effect of rope preload on overall stiffness of system
Fig.12 Experimental prototype of wire-driven rigid-flexible parallel mechanism for wave compensation
Fig.13 PID control block of control system
Fig.14 Compensation motion of end effector position and attitude
Fig.15 Motion curve of end effector of supply ship and compensation mechanism
Fig.16 Change curve of rope tension during swing in X direction
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