为提高海上波浪补偿条件下的承载能力，本文在3-RCU并联机构中引入承重UCU分支，构建3-RCU/UCU型并联机构。在分析各机构运动学的基础上，运用凯恩方程建立以任务空间矢量为输入，关节空间驱动力为输出的动力学模型。根据分支绕轴线方向的惯量显著小于垂直轴线方向惯量这一情况，忽略绕自身轴线的旋转运动，从而在不影响建模精度的前提下显著降低了计算量。随后进行数值求解并与Adams模型结果对比，验证了本文模型准确性。分析动力学模型计算效率，结果表明本文所提建模方法有效降低了模型的计算量，使其适合用于基于动力学模型的运动控制策略设计。
In order to improve the load-bearing capacity of wave compensation, a UCU branch was inducted into the 3-RCU mechanism to construct 3-RCU/UCU parallel manipulator. Firstly, a dynamic model whose input and output were the task space vector and joint space driving force was established by Kane equation. Secondly, according to the property that the driving branches’ inertia around their axes were much less than the rotation inertia around which was vertical to their axes, the dynamic model was simplified by neglecting the rotation around its axis. This simplification reduced the calculations without compromising model accuracy. Then the accuracy of the dynamic model and the effectiveness of the proposed modeling method were validated by comparing the numerical simulation results with those from an Adams model. Finally, the computational efficiency of the dynamic model was analyzed. The analysis results showed that the proposed modeling method could reduce computational complexity effectively, which was suitable for the design of motion control strategy based on the dynamic model.
2025,47(15): 65-71 收稿日期：2024-11-4
DOI：10.3404/j.issn.1672-7649.2025.15.011
分类号：U661.3；TH113
基金项目：国家自然科学基金资助项目（51979117）
作者简介：丁文柯(1999-),男,硕士研究生,研究方向为多体动力学、运动控制
参考文献：
[1] 刘彩云. 船舶动力定位辅助锚泊系统控制方法研究[D]. 哈尔滨: 哈尔滨工程大学, 2020.
[2] 高潇阳. 基于自适应动态规划的船舶动力定位优化控制研究[D]. 大连: 大连海事大学, 2021.
[3] LIU Z, WU J, WANG D. An engineering-oriented motion accuracy fluctuation suppression method of a hybrid spray-painting robot considering dynamics[J]. Mechanism and Machine Theory, 2019, 131: 62-74.
[4] 张彦方. 海上风电登靠步桥发展与关键技术研究综述[J]. 中国舰船研究, 2024, 19(4): 48-58.
ZHANG Y F. Overview of offshore wind power gangway development and key technologies[J]. Chinese Journal of Ship Research, 2024, 19(4): 48-58.
[5] JAOUEN F, VAN DEN BERG J, VAN DER SCHAAF H, et al. How does barge-master compensate for the barge motions: Experimental and numerical study[C]//International Conference on Offshore Mechanics and Arctic Engineering, Rio de Janeiro, Brazil, ASME, 2012: Volume 1: Offshore Technology. 2012.
[6] 李玉昆. 3-UPS/S并联稳定平台的性能分析与稳定补偿实验研究[D]. 秦皇岛: 燕山大学, 2018.
[7] LIU W, DU J, LI J, et al. Stabilization control of 3-DOF parallel vessel-borne platform with dynamic uncertainties and unknown disturbances[J]. Applied Ocean Research, 2022, 126: 103271.
[8] CAI Y, ZHENG S, LIU W, et al. Sliding-mode control of ship-mounted Stewart platforms for wave compensation using velocity feedforward[J]. Ocean Engineering, 2021, 236: 109477.
[9] YANG C, HAN J, ZHENG S, et al. Dynamic modeling and computational efficiency analysis for a spatial 6-DOF parallel motion system[J]. Nonlinear Dynamics, 2012, 67: 1007-1022.
[10] WU J, WANG L, YOU Z. A new method for optimum design of parallel manipulator based on kinematics and dynamics[J]. Nonlinear Dynamics, 2010, 61: 717-727.
[11] DASGUPTA B, CHOUDHURY P. A general strategy based on the Newton–Euler approach for the dynamic formulation of parallel manipulators[J]. Mechanism and Machine Theory, 1999, 34(6): 801-824.
[12] WANG W, WANG N, WU X. Kinematics and dynamics analysis of a six-degree of freedom parallel manipulator[J]. International Journal of Advanced Robotic Systems, 2022, 19(5): 1-13
[13] WU P, XIONG H, KONG J. Dynamic analysis of 6-SPS parallel mechanism[J]. International Journal of Mechanics and Materials in Design, 2012, 8: 121-128.
[14] YANG C, HUANG Q, HAN J. Decoupling control for spatial six-degree-of-freedom electro-hydraulic parallel robot[J]. Robotics and Computer-Integrated Manufacturing, 2012, 28(1): 14-23.
[15] WU J, GAO Y, ZHANG B, et al. Workspace and dynamic performance evaluation of the parallel manipulators in a spray-painting equipment[J]. Robotics and Computer-Integrated Manufacturing, 2017, 44: 199-207.
[16] HE L, LI Q, ZHU X, et al. Kinematic calibration of a three degrees-of-freedom parallel manipulator with a laser tracker[J]. Journal of Dynamic Systems, Measurement, and Control, 2019, 141(3): 031009.
[17] 王晓明, 徐振邦, 王兵, 等. 基础激励下6-UHP并联平台的动力学建模与仿真[J]. 机器人, 2016, 38(6): 687-695.
WANG X M, XU ZH B, WANG B, et al. Dynamic modeling and simulation of a 6-UHP parallel platform under base excitation[J]. Robot, 2016, 38(6): 687-695.
[18] 刘国军. 六自由度运动模拟平台的分析及结构参数的优化[D]. 哈尔滨: 哈尔滨工业大学, 2014.
