Optimal solution method for the cable catenary between cable-driven parallel robots
WEI Huiling1, QIU Yuanying2, SHENG Ying2, CHEN Haichu1, LU Qinghua1
1. College of Mechanical and Electrical Engineering, Foshan University, Foshan 528225, China; 2. School of Mechanical-Electrical Engineering, Xidian University, Xi'an 710071, China
Abstract：Accurate dynamic models are difficult to develop for long-span cable-driven parallel robots. This paper presents a reduced dimension optimization method for designing nonlinear cable catenaries. This paper gives the differential equation for the catenary and its boundary conditions. The dimension of the transcendental equation of the catenary model was then reduced according to the boundary conditions with the analytical solution obtained using the substitution method and the Taylor expansion method. Then, the Newton method was used to numerically solve the catenary model to study the range and characteristics of the numerical solution. Finally, the effectiveness of the reduced dimension optimization method are verified by examples. This research provides a theoretical basis for accurate dynamic modeling and real-time motion stability control strategies for cable-driven parallel mechanisms.
[1] JIANG X L, BARNETT E, GOSSELIN C. Periodic trajectory planning beyond the static workspace for six-DOF cable-suspended parallel robots[J]. IEEE Transactions on Robotics, 2018, 34(3):781-793. [2] TANG X Q. An overview of the development for cable-driven parallel manipulator[J]. Advances in Mechanical Engineering, 2014, 6:823028. [3] LIN J Q, WU C Y, CHANG J L. Design and implementation of a multi-degrees-of-freedom cable-driven parallel robot with gripper[J]. International Journal of Advanced Robotic Systems, 2018, 15(5):1-10. [4] LI H, YAO R. Optimal orientation planning and control deviation estimation on FAST cable-driven parallel robot[J]. Advances in Mechanical Engineering, 2014, 6:716097. [5] KUAN J Y, PASCH K, HERR H. A high-performance cable-drive module for the development of wearable devices[J]. IEEE/ASME Transactions on Mechatronics, 2018, 23(3):1238-1248. [6] DOUADI L, SPINELLO D, SARFRAZ W. Planar kinematics analysis of a snake-like robot[J]. Robotica, 2014, 32(5):659-675. [7] XIAO Y W, LIN Q, ZHENG Y Q, et al. Model aerodynamic tests with a wire-driven parallel suspension system in low-speed wind tunnel[J]. Chinese Journal of Aeronautics, 2010, 23:393-400. [8] GOUTTEFARDE M, COLLARD J F, RIEHL N, et al. Geometry selection of a redundantly actuated cable-suspended parallel robot[J]. IEEE Transactions on Robotics, 2015, 31(2):501-510. [9] AFLAKIANA A, SAFARYAZDIB A, MASOULEH M T, et al. Experimental study on the kinematic control of a cable suspended parallel robot for object tracking purpose[J]. Mechatronics, 2018, 50:160-176. [10] ZI B, WANG N, QIAN S, et al. Design, stiffness analysis and experimental study of a cable-driven parallel 3D printer[J]. Mechanism and Machine Theory, 2019, 132:207-222. [11] CONE L L. Skycam:An aerial robotic camera system[J]. Byte, 1985, 10(10):122-124. [12] ALBUS J, BOSTELMAN R, DAGALAKIS N. The NIST robocrane[J]. Journal of Robotic System, 1993, 10(5):709-724. [13] SCALERA L, GALLINA P, SERIANI S. Cable-based robotic crane (CBRC):Design and implementation of overhead traveling cranes based on variable radius drums[J]. IEEE Transactions on Robotics, 2018, 34(2):474-485. [14] TEMPEL P, SCHNELLE F, POTT A. Eberhard, design and programming for cable-driven parallel robots in the german pavilion at the EXPO[J]. Machines, 2015, 3(3):223-241. [15] ZHU W B, NAN R D, REN G. Modeling of a feed support system for FAST[J]. Experimental Astronomy, 2004, 17(1-3):177-184. [16] TANG X Q, CHAI X M, TANG L W, et al. Accuracy synthesis of a multi-level hybrid positioning mechanism for the feed support system in FAST[J]. Robotics and Computer-Integrated Manufacturing, 2014, 30:565-575. [17] KOZAK K, ZHOU Q, WANG J S. Static analysis of cable-driven manipulators with non-negligible cable mass[J]. IEEE Transactions on Robotics. 2006, 22(3):425-433. [18] DUAN B Y. A new design project of the line feed structure for large spherical radio telescope and its nonlinear dynamic analysis[J]. Mechatronics, 1999, 9(1):53-64. [19] DUAN X C, QIU Y Y, BAO H, et al. Real-time motion planning-based vibration control of a macro-micro parallel manipulator system for super antenna[J]. Journal of Vibroengineering, 2014, 16(2):694-703. [20] DU J L, BAO H, CUI C Z, et al. Nonlinear PD control of a long-span cable-supporting manipulator in quasi-static motion[J]. Journal of Dynamic Systems Measurement and Control-Transactions of the ASME, 2012, 134(1):11022-11030. [21] DUAN B Y, QIU Y Y, ZHANG F S, et al. On design and experiment of the feed cable-suspended structure for super antenna[J]. Mechatronics, 2009, 19(4):503-509. [22] YAO R, TANG X Q, WANG J S, et al. Dimensional optimization design of the four-cable-driven parallel manipulator in FAST[J]. IEEE/ASME Transactions on Mechatronics, 2010, 15(6):932-941. [23] SRIDHAR D, WILLIAMS Ⅱ R L. Kinematics and statics including cable sag for large cable-suspended robots[J]. Global Journal of Researches in Engineering, 2017, 17(1):1-19. [24] WEI H L, QIU Y Y, SHENG Y. On the cable pseudo-drag problem of cable-driven parallel camera robots at high speeds[J]. Robotica, 2019, 37(10):1695-1709. [25] IRVINE M. Cable structures[M]. Cambridge:MIT Press, 1981. [26] SHAO Z F, TANG X Q, WANG L, et al. Dynamic modeling and wind vibration control of the feed support system in FAST[J]. Nonlinear Dynamics, 2012, 67(2):965-985. [27] QIU Y Y, DUAN B Y, WEI Q, et al. Optimal distribution of the cable tensions and structural vibration control of the cable-cabin flexible structure[J]. Structural Engineering and Mechanics, 2002, 14(1):39-56. [28] 李辉, 朱文白, 潘高峰. 500m口径球面射电望远镜进舱缆线连接机构的设计及其静力学分析[J]. 机械工程学报, 2010, 46(7):7-15.LI H, ZHU W B, PAN G F. Design of linking mechanisms of cable into focus cabin of five-hundred meters aperture spherical radio telescope and its static analysis[J]. Journal of Mechanical Engineering, 2010, 46(7):7-15. (in Chinese) [29] ZI B, DUAN B Y, DU J L, et al. Dynamic modeling and active control of a cable-suspended parallel robot[J]. Mechatronics, 2008, 18(1):1-12. [30] DU J L, AGRAWAL S K. Dynamic modeling of cable-driven parallel manipulators with distributed mass flexible cables[J]. Journal of Vibration and Acoustics, 2015, 137:1-8. [31] SU Y, QIU Y Y, LIU P. The continuity and real-time performance of the cable tension determining for a suspend cable-driven parallel camera robot[J]. Advanced Robotics, 2015, 29(12):743-752. [32] MERIAM J L, KRAIGE L G. Engineering mechanics:Statics[M]. 7th Edition. Hoboken:Wiley, 2011.
2021, Vol. 61 
