500 m口径球面射电望远镜（FAST）采用索驱动并联机器人与Stewart平台组合实现馈源在百米工作空间内的毫米高定位精度。该文提出了该类刚柔结合机构的动力学建模方法，分别对绳索和Stewart平台进行精确建模，通过两级机构模型的联立对中间结构的Newton-Euler方程迭代来求解系统的振动，探讨系统耦合振动的本质，从原理上说明了Stewart平台补偿误差对系统造成的具体影响并以数值形式表达。研究结果为FAST提高观测精度提供了必要条件，也为这类刚柔结合机构的控制算法提供了重要理论基础。
Five-hundred-meter aperture spherical radio telescope (FAST) uses a cable-driven parallel robot with a Stewart platform for precision positioning at the millimeter level. This paper presents a dynamic modeling method for this type of rigid-flexible mechanism which accurately models the cable and the Stewart platform and eliminates system vibrations by iterating the Newton-Euler equations of the intermediate structure between the two models. The nature of the coupled system vibrations is also analyzed to explain the impact of the Stewart platform's error compensation on the system motion with the error composition modeled numerically. This research will improve the FAST observation accuracy and provides a theoretical basis for control algorithms for this type of rigid-flexible mechanisms.
[1] NAN R D. Five-hundred-meter aperture spherical radio telescope (FAST)[J]. Science in China Series G:Physics, Mechanics & Astronomy, 2006, 49(2):129-148.
[2] JIANG P, YUE Y L, GAN H Q, et al. Commissioning progress of the FAST[J]. Science China Physics, Mechanics & Astronomy, 2019, 62(5):959502.
[3] JIANG P, TANG N Y, HOU L G, et al. The fundamental performance of FAST with 19-beam receiver at L band[J]. Research in Astronomy and Astrophysics, 2020, 20(5):64.
[4] QIAN L, YAO R, SUN J H, et al. FAST:Its scientific achievements and prospects[J]. The Innovation, 2020, 1(3):100053.
[5] QIU Y Y, DUAN B Y, WEI Q, et al. Elimination of force singularity of the cable and cabin structure for the next generation large radio telescope[J]. Mechatronics, 2002, 12(7):905-918.
[6] LU Y J, ZHU W B, REN G X. Feedback control of a cable-driven Gough-Stewart platform[J]. IEEE Transactions on Robotics, 2006, 22(1):198-202.
[7] REN G X, ZHU W B, ZHANG H, et al. Test study of the feed-support system for a large radio telescope[C]//IUTAM Symposium on Mechanics and Reliability of Actuating Materials. Beijing, China:Springer, 2006:261-270.
[8] SUN J H, NAN R D, ZHU W B, et al. Simulation model of FAST focus cabin for pointing accuracy analysis[C]//Proceedings Volume 7017, Modeling, Systems Engineering, and Project Management for Astronomy III. Marseille, France:SPIE, 2008:70171L.
[9] DUAN X C, MI J W, ZHAO Z. Vibration isolation and trajectory following control of a cable suspended Stewart platform[J]. Machines, 2016, 4(4):20.
[10] 汤奥斐, 李言, 仇原鹰, 等. 大跨度柔索驱动并联机构逆动力学研究[J]. 机械科学与技术, 2010, 29(4):435-440. TANG A F, LI Y, QIU Y Y, et al. Inverse dynamics of a long-span wire driven parallel robot[J]. Mechanical Science and Technology for Aerospace Engineering, 2010, 29(4):435-440. (in Chinese)
[11] SHAO Z F, TANG X Q, WANG L P, et al. Dynamic modeling and wind vibration control of the feed support system in FAST[J]. Nonlinear Dynamics, 2012, 67(2):965-985.
[12] IRVINE H M. Cable structures[M]. Cambridge:MIT Press, 1981.
[13] DASGUPTA B, MRUTHYUNJAYA T S. A Newton-Euler formulation for the inverse dynamics of the Stewart platform manipulator[J]. Mechanism and Machine Theory, 1998, 33(8):1135-1152.
[14] 何兆麒, 薛冬新, 张娟, 等. 一种改进的Stewart平台Newton-Euler动力学模型[J]. 振动与冲击, 2018, 37(9):221-229. HE Z Q, XUE D X, ZHANG J, et al. Improved Newton-Euler dynamic models for a Stewart platform[J]. Journal of Vibration and Shock, 2018, 37(9):221-229. (in Chinese)
