具有解析解的1T2R重载并联稳定平台运动学及动力学建模

doi:10.12382/bgxb.2023.1168

摘要/Abstract

摘要：

针对一移两转舰船重载并联稳定平台普遍存在伴随运动、不利于求解运动学解析解且增加控制系统难度的问题,提出一种去除绕z轴伴随转动、具有解析解的1T2R变异3UPS-PUU-2SS并联稳定平台机构。通过分析空间约束支链的运动特性,证明了该机构没有绕z轴的转动。采用空间闭环矢量方程法,建立约束方程组和运动学模型,进而求得伴随移动和逆运动学解析解。通过快速极坐标搜索法绘制该机构的可达工作空间,并通过雅可比矩阵条件数分析该工作空间的灵巧度;基于虚功原理建立该机构的动力学模型,通过5次多项式插值法进行数值求解,绘制驱动力理论曲线并与动力学仿真曲线进行对比。理论与仿真结果表明:可达工作空间可以满足某舰船四级海况下的运动补偿要求,其全局灵巧度大于0.32,动力学模型的理论与仿真结果最大误差在1.42%以内,验证了动力学模型的准确性;该并联机构运动学与动力学性能良好,为其实际应用提供了理论基础。

关键词: 稳定平台, 伴随运动, 解析解, 运动学, 动力学

Abstract:

In order to solve the parasitic motion of the heavy-load parallel stabilized platform of one translation and two rotations ship, which is not conducive to solving the analytical solution of kinematics and increases the difficulty of control system, a platform mechanism of 1T2R variant 3UPS-PUU-2SS parallel stabilized platform with analytical solution is proposed to remove the accompanying rotation around z-axis. By analyzing the motion characteristics of the spatially constrained branched chain, it is proved that the parallel platform does not rotate around z-axis. The spatial closed-loop vector equation method is used to establish the constraining equations and kinematic models, and then the analytical solutions of parasitic motion and inverse kinematics are obtained. The reachable workspace of the parallel platform is plotted by the fast polar coordinate search method, and the dexterity of the workspace is analyzed by the Jacobian matrix conditional number. A dynamic model of the parallel platform is established based on the virtual work principle, and the numerical solution is carried out by the 5-order polynomial interpolation method, and the theoretical curve of driving force is drawn, which is compared with the dynamic simulation curve of the finite element analysis software. The theoretical and simulated results show that the achievable workspace can meet the motion compensation requirements of a ship in the fourth-level sea state, its global dexterity is greater than 0.32, and the maximum error between the theoretical and simulated results of the dynamic model is within 1.42%, which verifies the accuracy of the dynamic model.

Key words: stabilized platform, parasitic motion, analytical solution, kinematics, dynamics

中图分类号:

TH112

强红宾, 杜亮亮, 康绍鹏, 刘凯磊, 周岭, 曾水生. 具有解析解的1T2R重载并联稳定平台运动学及动力学建模[J]. 兵工学报, 2024, 45(11): 3959-3969.

QIANG Hongbin, DU Liangliang, KANG Shaopeng, LIU Kailei, ZHOU Ling, ZENG Shuisheng. Kinematics and Dynamics Modeling of 1T2R Heavy-load Parallel Stabilized Platform with Analytical Solution[J]. Acta Armamentarii, 2024, 45(11): 3959-3969.

图/表 13

图1 稳定平台的三维模型

Fig.1 3D model of the stabilized platform

图2 变异3UPS-PUU-2SS并联平台简图

Fig.2 Schematic diagram of theparallel platform of variant 3UPS-PUU-2SS

图3 变异PUU机构

Fig.3 Mutated PUU institutions

图4 动平台位姿变化

Fig.4 Pose change of moving platform

图5 可达工作空间

Fig.5 Reachable workspace

图6 LCI分布

Fig.6 Distribution of dexterity indicators

图7 稳定平台第i条驱动支链的位置和尺寸参数

Fig.7 The position and size parameters of stabilizing the ith driving branch chain of the platform

表1 稳定平台质量属性

Table 1 Quality attributes of stabilized platform

运动杆件名称	质量/kg
动平台负载(飞机)	95563.3252
动平台质量	4700.7841
驱动支链缸筒	196.9004
驱动支链缸杆	124.9865
第1约束杆	130.0745
第2约束杆	161.7952
第3约束杆	130.0745

图8 驱动杆1的仿真与理论驱动力曲线对比

Fig.8 Comparison of the simulated and theoretical driving force curves of the driving rod 1

图9 驱动杆2的仿真与理论驱动力曲线对比

Fig.9 Comparison of the simulated and theoretical driving force curves of the driving rod 2

图10 驱动杆3的多体动力学运动分析软件与模拟分析软件驱动力曲线对比

Fig.10 Comparison of the simulated and theoretical driving force curves of the driving rod 3

图11 仿真与理论驱动力误差

Fig.11 Simulated and theoretical driving force errors

图12 仿真与理论驱动力曲线误差百分比

Fig.12 Percentage errors of the simulated and theoretical driving force curves

参考文献 24

[1]	刘晓, 赵铁石, 边辉, 等. 耦合型3自由度并联稳定平台机构动力学分析[J]. 机械工程学报, 2013, 49(1):45-52.
	LIU X, ZHAO T S, BIAN H, et al. Dynamics analysis of a 3-DOF coupling parallel mechanism for stabilized platform[J]. Journal of Mechanical Engineering, 2013, 49(1): 45-52. (in Chinese)
[2]	王力航. 电液伺服驱动3UPS/S并联稳定平台协调控制研究[D]. 秦皇岛: 燕山大学, 2019.
	WANG L H. Research on coordination control of electro-hydraulic servo system in 3UPS/S parallel stabilized platform[D]. Qinhuangdao: Yanshan University, 2019. (in Chinese)
[3]	AMPELMANN D J. Development of the access system for offshore wind turbines[D]. Delft, the Nethland: Doctoral Dissertation of Technische Universiteit Delft, 2010: 1-14.
[4]	王玥玥, 魏延辉, 马天宇, 等. 基于动态权值分配的登乘系统运动规划方法[J]. 华中科技大学学报(自然科学版), 2023, 51(8): 102-108.
	WANG Y Y, WEI Y H, MA T Y, et al. Motion planning method for boarding system based on dynamic weights distribution[J]. Journal of Huazhong University of Science and Technology(Natural Science Edition), 2023, 51(8): 102-108. (in Chinese)
[5]	王生海, 王丙昱, 靳国良, 等. 一种基于液压并联装置的六自由度波浪补偿船载起重机: CN117049395A[P]. (2023-11-14).
	WANG S H, WANG B Y, JIN G L, et al. A six-degree-of-freedom wave-compensated shipborne crane based on hydraulic parallel device: CN117049395A[P]. (2023-11-14). (in Chinese)
[6]	吴彦岐. 基于船舶运动预测的六自由度稳定平台[D]. 哈尔滨: 哈尔滨工业大学, 2022. DOI:10.27061/d.cnki.ghgdu.2022.004780.
	WU Y Q. Six degree of freedom stable platform based on ship motion prediction[D]. Harbin: Harbin Institute of Technology, 2022. DOI:10.27061/d.cnki.ghgdu.2022.004780. (in Chinese)
[7]	Safeway: Walk to work the safe way[EB/OL]. (2024-02-28) [2024-03-14]Van Aalst Marine Compensation Systems official website; http://www.vanaalstmarine.com.
[8]	刘晓, 赵铁石, 高佳伟. 非惯性系下舰载稳定平台动力学建模及特性分析[J]. 机器人, 2014, 36(4):411-418. doi: 10.13973/j.cnki.robot.2014.0411
	LIU X, ZHAO T S, GAO J W. Dynamic modeling and analysis of ship-based stabilizing platform in non-inertial system[J]. Robot, 2014, 36(4):411-418. (in Chinese) doi: 10.13973/j.cnki.robot.2014.0411
[9]	QIANG H B, JIN S, FENG X Y, et al. Model predictive control of a shipborne hydraulic parallel stabilized platform based on ship motion prediction[J]. IEEE Access, 2020, 8: 181880-181892.
[10]	王立栋, 陈原. 绳驱动刚柔混合式波浪运动补偿机构的运动学建模与碰撞干涉检测[J]. 兵工学报, 2020, 41(4):737-749. doi: 10.3969/j.issn.1000-1093.2020.04.013
	WANG L D, CHEN Y. Kinematic modeling and collision interference detection of cable-driven rigid-flexible wave motion compensation mechanism[J]. Acta Armamentarii, 2020, 41(4): 737-749. (in Chinese) doi: 10.3969/j.issn.1000-1093.2020.04.013
[11]	赵延治, 赵飞, 杨建涛, 等. 并联6-RUS卫星相机像移补偿机构建模与分析[J]. 中国机械工程, 2016, 27(3):369-375.
	ZHAO Y Z, ZHAO F, YANG J T, et al. Modelling and analysis of 6-RUS parallel mechanism of image compensation of satellite camera[J]. China Mechanical Engineering, 2016, 27(3):369-375. (in Chinese)
[12]	HU Y L, QIAN Q, LI L J, et al. A method for the kinematic analysis of a novel wave compensation bed for ships based on the 8PSS-UP parallel platform[J]. Ocean Engineering, 2023, 288: 116120.
[13]	房立丰, 刘安心, 杨廷力, 等. 一平移二转动并联稳定平台拓扑结构设计[J]. 农业机械学报, 2012, 43(2):205-210.
	FANG L F, LIU A X, YANG T L, et al. Topology structure design of 1T-2R parallel stable platform[J]. Transactions of the Chinese Society for Agricultural Machinery, 2012, 43(2):205-210. (in Chinese)
[14]	ZHAN Y, TIAN H C, XU J N, et al. A novel three-SPR parallel platform for vessel wave compensation[J]. Journal of Marine Science and Engineering, 2020, 8(12):1013.
[15]	李二伟, 赵铁石, 王唱, 等. 大型重载并联稳定接货平台动力学建模[J]. 农业机械学报, 2018, 49(3):411-417, 346.
	LI E W, ZHAO T S, WANG C, et al. Dynamics of large-scale heavy-burden parallel stabilizing cargo-receiving platform[J]. Transactions of the Chinese Society for Agricultural Machinery, 2018, 49(3):411-417, 346. (in Chinese)
[16]	WANG C, ZHAO T S, ZHANG J H, et al. A novel motion planning algorithm for a three DoF foldable parallel compensation platform based on prediction and B-spline[J]. Ocean Engineering, 2022, 266(3): 112876.
[17]	HU X, LI F R, TANG G. Kinematics analysis of 3UPU_UP coupling parallel platform in the marine environment[J]. IEEE Access, 2020, 8: 158142-158151.
[18]	邱建超, 陈海泉, 仇伟晗, 等. 船载串并混联海上稳定廊桥动力学建模与分析[J]. 中国造船, 2023, 64(1):146-160.
	QIU J C, CHEN H Q, QIU W H, et al. Dynamic modeling and analysis of shipborne series-parallel hybird offshore gangway[J]. Ship Building of China, 2023, 64(1):146-160. (in Chinese)
[19]	NIU A Q, WANG S H, SUN Y Q, et al. Dynamic modeling and analysis of a novel offshore gangway with 3UPU/UP-RRP series-parallel hybrid structure[J]. Ocean Engineering, 2022, 266(5): 113122.
[20]	王力航, 郭菲, 卢文娟, 等. 3UPS/S舰船稳定平台非惯性系动力学建模[J]. 机械工程学报, 2020, 56(1):20-29. doi: 10.3901/JME.2020.01.020
	WANG L H, GUO F, LU W J, et al. Non-inertial system dynamic modeling of 3UPS/S ship stability platform[J]. Journal of Mechanical Engineering, 2020, 56(1):20-29. (in Chinese) doi: 10.3901/JME.2020.01.020
[21]	田文杰, 吕东坡, 张相鹏. 基于性能驱动的船载稳定平台尺度参数优化设计[J]. 机器人, 2023, 45(1):78-88.
	TIAN W J, LÜ D P, ZHANG X P. Performance driven optimal design of dimensional parameters for a shipborne stable platform[J]. Robot, 2023, 45(1): 78-88. (in Chinese)
[22]	李豪杰, 张合, 李珂翔, 等. 考虑铰链间隙的水面并联稳定平台动力学分析[J]. 兵工学报, 2017, 38(1):129-134. doi: 10.3969/j.issn.1000-1093.2017.01.017
	LI H J, ZHANG H, LI K X, et al. Dynamic analysis of offshore parallel stabilized platform in considering joint clearance[J]. Acta Armamentarii, 2017, 38(1):129-134. (in Chinese)
[23]	刘辛军, 汪劲松, 高峰, 等. 并联机器人机构新构型设计的探讨[J]. 中国机械工程, 2001, 12(12):20-23, 4.
	LIU X J, WANG J S, GAO F, et al. On the design of a new parallel robotic mechanism[J]. China Mechanical Engineering, 2001, 12(12):20-23,4. (in Chinese)
[24]	王世杰, 冯伟, 李铁军, 等. 空间2自由度冗余驱动并联机构运动学性能分析[J]. 机械工程学报, 2022, 58(23):18-27. doi: 10.3901/JME.2022.23.018
	WANG S J, FENG W, LI T J, et al. Kinematic performance analysis of spatial 2-DOF redundantly actuated parallel manipulator[J]. Journal of Mechanical Engineering, 2022, 58(23): 18-27. (in Chinese) doi: 10.3901/JME.2022.23.018