Z4型冗余驱动并联操作器的驱动特性研究

doi:10.3901/JME.2024.07.066

摘要/Abstract

摘要： 并联操作器作为串-并联式混联加工装备的核心模块，其驱动特性对系统性能至关重要。以Z4型冗余驱动并联操作器为研究对象，提出一类驱动特性评价指标，并基于该类指标对其进行任务空间优选和伺服扭矩参数预估。首先，采用封闭矢量法求解操作器的运动学逆解，并构建无量纲雅可比矩阵以评估其运动学各向同性。其次，运用Lagrange法建立操作器的刚体动力学模型，并基于最小二范数法进行驱动力分配。接着，选取末端刀尖点为参考点，定义加速度、速度和动态切削力的驱动各向同性指标和驱动扭矩指标。最后，基于所提指标，搜索综合性能良好的任务空间，确定伺服扭矩参数，并通过实验验证所选电机满足使用要求。

关键词: 并联操作器, 动力学建模, 各向同性, 驱动扭矩

Abstract: As the core module of serial-parallel hybrid machining equipment, the driving characteristics of parallel manipulators are crucial to overall system performance. A set of index is proposed to evaluate the driving characteristics of a Z4 redundantly actuated parallel manipulators. Based on the proposed indices, the task workspace is optimized and the servo torques are predicted. First, the inverse kinematics of a Z4 parallel manipulator is derived with closed-loop vector method to construct a nondimensional Jacobian matrix, which is used to evaluate kinematic isotropy. Second, a rigid-body dynamic model is established by using Lagrange method, based on which a minimum 2-norm is formulated to allocate driving forces between different limbs. By selecting the tooltip as a reference point, a set of isotropy index is defined in terms of acceleration, velocity, and dynamic cutting force as well as driving torque. Finally, the optimum task workspace and servo torques are determined based on the proposed indices. A simple experimental test is carried out to validate the selected servo-motors meet the serving requirements.

Key words: parallel manipulator, dynamics modeling, isotropy, driving torque

中图分类号:

TP24

张俊, 吴成阳, 方汉良, 孙载超, 王凯龙, 汤腾飞. Z4型冗余驱动并联操作器的驱动特性研究[J]. 机械工程学报, 2024, 60(7): 66-78.

ZHANG Jun, WU Chengyang, FANG Hanliang, SUN Zaichao, WANG Kailong, TANG Tengfei. Investigation on Driving Characteristics of a Z4 Redundantly Actuated Parallel Manipulator[J]. Journal of Mechanical Engineering, 2024, 60(7): 66-78.

参考文献

[1] LU Yi,DAI Zhuohong,YE Nijia. Stiffness analysis of parallel manipulators with linear limbs by considering inertial wrench of moving links and constrained wrench[J]. Robotics and Computer-Integrated Manufacturing,2017,46:58-67.
[2] WU Jun,WANG Jinsong,WANG Liping,et al. Dynamics and control of a planar 3-DOF parallel manipulator with actuation redundancy[J]. Mechanism and Machine Theory,2009,44(4):835-849.
[3] WAHL J. Articulated tool head:Germany,WO2000025976A2[P]. 2001-05-11.
[4] DONG Chenglin,LIU Haitao,HUANG Tian,et al. A screw theory-based semi-analytical approach for elastodynamics of the tricept robot[J]. Journal of Mechanisms and Robotics-Transactions of the ASME,2019,11(3):031005.
[5] NEUMANN K E. Robot:US, 4732525[P]. 1988-03-22
[6] FANG Hanliang,TANG Tengfei,HE Zhen,et al. A novel hybrid machine tool integrating a symmetrical redundantly actuated parallel mechanism:Design,kinematics,prototype and experiment[J]. Mechanism and Machine Theory,2022,176:105013.
[7] THOMAS M J,JOY M L,SUDHEER A P. Kinematic and dynamic analysis of a 3-PRUS spatial parallel manipulator[J]. Chinese Journal of Mechanical Engineering,2020,33(1):1-17.
[8] LI Yanbiao,ZHENG Hang,CHEN Bo,et al. Dynamic modeling and analysis of 5-PSS/UPU parallel mechanism with elastically active branched chains[J]. Chinese Journal of Mechanical Engineering,2020,33(1):1-12.
[9] LIU Xiaofei,YAO Jiantao,XU Yundou,et al. Research of driving force coordination mechanism in parallel manipulator with actuation redundancy and its performance evaluation[J]. Nonlinear Dynamics,2017,90(2):983-998.
[10] 柴馨雪,杨泳,徐灵敏,等. 2-UPR-RPU并联机器人的动力学建模与性能分析[J]. 机械工程学报,2020,56(13):110-119. CHAI Xinxue,YANG Yong,XU Lingmin,et al. Dynamic modeling and performance analysis of a 2-UPR-RPU parallel manipulator[J]. Journal of Mechanical Engineering,2020,56(13):110-119.
[11] 李研彪,郑航,孙鹏,等. 考虑关节摩擦的5-PSS/UPU并联机构动力学建模及耦合特性分析[J]. 机械工程学报,2019,55(3):43-52. LI Yanbiao,ZHENG Hang,SUN Peng,et al. Dynamic modeling with joint friction and research on the inertia coupling property of a 5-PSS/UPU parallel manipulator[J]. Journal of Mechanical Engineering,2019,55(3):43-52.
[12] 李永泉,郭雨,张阳,等. 基于牛顿欧拉法的一种空间被动过约束并联机构动力学建模方法[J]. 机械工程学报,2020,56(11):48-57. LI Yongquan,GUO Yu,ZHANG Yang,et al. Dynamic modeling method of spatial passive over-constrained parallel mechanism based on newton euler method[J]. Journal of Mechanical Engineering,2020,56(11):48-57.
[13] ABDELLATIF H,HEIMANN B. Computational efficient inverse dynamics of 6-DOF fully parallel manipulators by using the Lagrangian formalism[J]. Mechanism and Machine Theory,2009,44(1):192-207.
[14] 牛雪梅,高国琴,刘辛军,等. 新型驱动冗余并联机构动力学建模及简化分析[J]. 机械工程学报,2014,50(19):41-49. NIU Xuemei,GAO Guoqin,LIU Xinjun,et al. Dynamic formulation and simplified model of a novel 3-DOF parallel mechanism with actuation redundancy[J]. Journal of Mechanical Engineering,2014,50(19):41-49.
[15] ASADA H. A geometrical representation of manipulator dynamics and its application to arm design[J]. Journal of Dynamic Systems Measurement and Control,1983,105(3):131-142.
[16] SHAO Zhufeng,TANG Xiaoqiang,XU Chen,et al. Research on the inertia matching of the Stewart parallel manipulator[J]. Robotics and Computer Integrated Manufacturing,2012,28(6):649-659.
[17] 王冬,吴军,王立平,等. 3-PRS并联机器人惯量耦合特性研究[J]. 力学学报,2016,48(4):804-812. WANG Dong,WU Jun,WANG Liping,et al. Research on the inertia coupling property of a 3-PRS parallel robot[J]. Chinese Journal of Theoretical and Applied Mechanics,2016,48(4):804-812.
[18] 赵庆,王攀峰,黄田. 考虑链间耦合的高速并联机器人惯性参数预估方法[J]. 天津大学学报,2017,50(8):868-876. ZHAO Qing,WANG Panfeng,HUANG Tian. An inertia parameter estimation method for high-speed parallel robots by considering inter-chain coupling[J]. Journal of Tianjin University,2017,50(8):868-876.
[19] YOSHIKAWA T. Dynamic manipulability of robot manipulators[C]//Proceedings of the 1985 IEEE International Conference on Robotics and Automation,1985:1033-1038.
[20] YOSHIKAWA T. Translational and rotational manipulability of robotic manipulators[C]//American Control Conference,1990:228-233.
[21] BOWLING A,KHATIB O. The dynamic capability equations:A new tool for analyzing robotic manipulator performance[J]. IEEE Transactions on Robotics,2005,21(1):115-123.
[22] LI Yuwen,WANG Jinsong,LIU Xinjun,et al. Dynamic performance comparison and counterweight optimization of two 3-DOF parallel manipulators for a new hybrid machine tool[J]. Mechanism and Machine Theory,2010,45(11):1668-1680.
[23] WU Jun,ZHANG Binbin,WANG Liping. A measure for evaluation of maximum acceleration of redundant and nonredundant parallel manipulators[J]. Journal of Mechanisms and Robotics,2016,8(2):021001.
[24] CHONG Zenghui,XIE Fugui,LIU Xinjun,et al. Evaluation of dynamic isotropy and coupling acceleration capacity for a parallel manipulator with mixed DoFs[J]. Mechanism and Machine Theory:Dynamics of Machine Systems Gears and Power Trandmissions Robots and Manipulator Systems Computer-Aided Design Methods,2021,163(6):104382.
[25] GOSSELIN C M,ANGELES J. A global performance index for the kinematic optimization of robotic manipulators[J]. ASME Journal of Mechanical Design,1991,113(3):220-226.
[26] 董成林,刘海涛,黄田. 含冗余驱动支链4-UPS&UP并联机构的运动学性能分析[J]. 机械工程学报,2016,52(5):124-129. DONG Chengling,LIU Haitao,HUANG Tian. Kinematic performance analysis of redundantly actuated 4-UPS&UP parallel manipulator[J]. Journal of Mechanical Engineering,2016,52(5):124-129.
[27] DUAN Zhenjing,LI Changhe,DING Wenfeng,et al. Milling force model for aviation aluminum alloy:Academic insight and perspective analysis[J]. Chinese Journal of Mechanical Engineering,2021,34(1):1-35.
[28] WOJCIECHOWSKI S,MATUSZAK M,POWALKA B,et al. Prediction of cutting forces during micro end milling considering chip thickness accumulation[J]. International Journal of Machine Tools and Manufacture,2019,147:103466.
[29] 刘晓飞. 冗余驱动并联机构动力学分析与控制策略研究[D]. 秦皇岛:燕山大学,2017. LIU Xiaofei. Dynamic analysis and control strategy research of redundantly actuated parallel manipulator[D]. Qinhuangdao:Yanshan University,2017.
[30] 张俊,鲍雨菲,方汉良,等. 新型5轴混联加工单元的后置处理算法[J]. 机械工程学报,2023,59(1):298-308. ZHANG Jun,BAO Yufei,FANG Hanliang,et al. Post-processing algorithm of a novel five-axis hybrid kinematic machining unit[J]. Journal of Mechanical Engineering,2023,59(1):298-308.