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浙江大学学报(工学版)
浙江大学学报(工学版)  2021, Vol. 55 Issue (5): 810-822    DOI: 10.3785/j.issn.1008-973X.2021.05.002
机械工程     
绳牵引刚柔式波浪补偿并联机构的设计与建模
陈原(),郭登辉,田丽霞
山东大学 机电与信息工程学院，山东 威海 264209
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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摘要：

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    
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
收稿日期: 2020-05-08 出版日期: 2021-06-10
CLC:  TP 242.2  
基金资助: 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）
作者简介: 陈原（1976—），男，教授，博导，从事机器人机构学研究. orcid.org/0000-0003-1611-1023. E-mail： cyzghysy@sdu.edu.cn
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陈原
郭登辉
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引用本文:

陈原,郭登辉,田丽霞. 绳牵引刚柔式波浪补偿并联机构的设计与建模[J]. 浙江大学学报(工学版), 2021, 55(5): 810-822.

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.

链接本文:

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

图 1  刚柔混合主动式波浪补偿并联机构原理图
图 2  补偿机构整体补偿效果图
图 3  刚柔混合主动式波浪补偿并联机构简图及其坐标系
图 4  波浪补偿并联机构的支链坐标系
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
表 1  计算绳长与给定绳长的对比
图 5  无穷小位移下绳子变化向量和单位向量
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
表 2  刚柔混合并联机构参数
图 6  绳子长度的变化
图 7  α、β按照预定轨迹随时间变化时绳子速度与时间的关系
图 8  α、β按照预定轨迹随时间变化时绳子加速度与时间的关系
图 9  动平台绕X轴旋转时系统刚度的变化
图 10  Z方向高度变化时系统刚度的变化
图 11  绳子预紧力对系统整体刚度的影响
图 12  绳牵引刚柔混合波浪补偿并联机构实验样机
图 13  控制系统PID控制框图
图 14  末端执行器位姿补偿运动
图 15  补给船舶与补偿机构末端执行器的运动曲线
图 16  横摇时绳索拉力的变化
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