对一种空间3自由度3-UPU对称并联机构进行动力学分析和联合仿真研究。该并联机构由两个完全相同的平台通过3个同样的UPU支链连接而成,其动、定平台始终关于一个中间平面对称,该机构具有两个转动自由度和一个移动自由度。利用矢量法推导机构各构件的速度与加速度,求解机构各分支的雅可比矩阵,运用虚功原理建立3-UPU并联机构的动力学模型。利用联合仿真技术对该并联机构动力学模型进行验证,通过两个运动算例验证了该动力学建模方法的可行性和有效性,特别是利用该动力学模型分析这个机构在发生定轴转动时的动力学特点,为该机构的进一步研究及实际应用奠定了基础。
The dynamic analysis and co-simulation research of a 3-UPU symmetrical parallel mechanism are studied. This mechanism is comprised of two identical platforms and three UPU branches. The base and moving platform are always symmetrical about a middle plane, and it has two rotational and one translational (2R1T) degrees of freedom (DOFs). Firstly, the velocity and acceleration of all the links are derived, the Jacobian matrices of the legs are solved, and the dynamic model of the mechanism is established by virtual work principle. Then, the dynamic model is verified by the co-simulation method. Two numerical examples are given to demonstrate the feasibility and effectiveness of this dynamic model. Especially, the dynamic characteristic of this mechanism during the fixed-axis rotation is analyzed, which is useful for the further study and practical application.
[1] HUNT K H. Structural kinematics of in-parallel-actuated robot-arms[J]. Journal of Mechanisms Transmissions and Automation in Design, 1983, 105(4):705-712.
[2] 王飞博,陈巧红,武传宇,等. 2-UPR-SPR并联机构尺度综合[J]. 机械工程学报, 2015, 51(21):24-32. WANG Feibo, CHEN Qiaohong, WU Chuanyu, et al. Dimensional synthesis of a 2-UPR-SPR parallel manipulator[J]. Journal of Mechanical Engineering, 2015, 51(21):24-32.
[3] 汪满新, 黄田. 1T2R 3自由度并联机构拓扑结构综合[J]. 机械工程学报, 2015, 51(17):1-7. WANG Manxin, HUANG Tian. Type synthesis of 1T2R 3-DOF parallel mechanism[J]. Journal of Mechanical Engineering, 2015, 51(17):1-7.
[4] 柴馨雪,项济南,李秦川. 2-UPR-RPU并联机构奇异分析[J]. 机械工程学报, 2015, 51(13):144-151. CHAI Xinxue, XIANG Jinan, LI Qinchuan. Singularity analysis of a 2-UPR-RPU parallel mechanism[J]. Journal of Mechanical Engineering, 2015, 51(13):144-151.
[5] LI Qinchuan, XIANG Jinan, CHAI Xinxue, et al. Singularity analysis of a 3-RPS parallel manipulator using geometric algebra[J]. Chinese Journal of Mechanical Engineering, 2015, 28(6):1204-1212.
[6] SHAO Zhufeng, TANG Xiaoqiang, WANG Liping, et al. Atlas based kinematic optimum design of the Stewart parallel manipulator[J]. Chinese Journal of Mechanical Engineering, 2015, 28(1):20-28.
[7] TSAI L W. Solving the inverse dynamics of a Stewart-Gough manipulator by the principle of virtual work[J]. Transactions of the ASME, Journal of Mechanical Design, 2000, 122:3-9.
[8] LONG P, KHALIL W, MARTINET P. Dynamic modeling of parallel robots with flexible platforms[J]. Mechanism and Machine Theory, 2014, 81(11):21-35.
[9] 田浩,余跃庆. 柔顺并联机器人动力学及轨迹跟踪[J]. 机械工程学报, 2016, 52(13):38-46. TIAN Hao, YU Yueqing. Dynamics and trajectory tracking of a compliant parallel robot[J]. Journal of Mechanical Engineering, 2016, 52(13):38-46.
[10] 黄真,陈子明,曹文熬,等. 易于控制的对称两转一移并联机构:中国, CN201210445043.1[P]. 2012-11-09. HUANG Zhen, CHEN Ziming, CAO Wenao, et al. Two rotational and one translational degrees of freedom mechanisms of these symmetrical and easily controlled:China, CN201210445043.1[P]. 2012-11-09.
[11] CARRETERO J A, PODHORODESKI R P, NAHON M A, et al. Kinematic analysis and optimization of a new three degree-of-freedom spatial parallel manipulator[J]. Journal of Mechanical Design, 2000, 122(1):17-24.
[12] 陈子明,张扬,黄坤,等. 一种无伴随运动的对称两转一移并联机构[J]. 机械工程学报, 2016, 52(3):9-17. CHEN Ziming, ZHANG Yang, HUANG Kun, et al. Symmetrical 2R1T parallel mechanism without parasitic motion[J]. Journal of Mechanical Engineering, 2016, 52(3):9-17.
[13] 陈峰华. ADAMS 2012虚拟样机技术[M]. 北京:清华大学出版社, 2013. CHEN Fenghua. The virtual prototyping technology ADAMS 2012[M]. Beijing:Tsinghua University Press, 2013.
[14] BONEV I A,ZLATANOV D,GOSSELIN C M. Advantages of the modified Euler angles in the design and control of PKMs[C]//Parallel Kinematic Machines International Conference, Chemnitz, Germany, 2002:171-188.
[15] 朱照宣,周起钊,殷金生. 理论力学[M]. 北京:北京大学出版社, 1982. ZHU Zhaoxuan, ZHOU Qizhao, YIN Jinsheng. Theoretical mechanics[M]. Beijing:Peking University Press, 1982.