Abstract：Human-robot interaction include some safety threats to people or products from the robots due to their stiffness. The characteristics of controllable stiffness for cable-driven parallel robots are studied using a static stiffness analysis and cable tension distribution method. The robot kinematics and statics equations are used for the force analysis with the three-dimensional Hessian matrix of the structural matrix to position differential is deduced by introducing a line vector and a differential transform. Then, the static stiffness model is derived for the relationship between the cable tension and the robot stiffness. The robots stiffness is then controlled by analyzing the cable tension polygon and the cable tension distribution. Simulations show that this method can effectively control the robot stiffness.
YUAN H, COURTEILLE E, DEBLAISE D. Static and dynamic stiffness analyses of cable-driven parallel robots with non-negligible cable mass and elasticity[J]. Mechanism and Machine Theory, 2015, 85:64-81.
[2]
YEO S H, YANG G, LIM W B. Design and analysis of cable-driven manipulators with variable stiffness[J]. Mechanism and Machine Theory, 2013, 69:230-244.
[3]
BRACKBILL E A, MAO Y, AGRAWAL S K, et al. Dynamics and control of a 4-dof wearable cable-driven upper arm exoskeleton[C]//Proceedings of 2009 IEEE International Conference on Robotics and Automation. Kobe, Japan:IEEE Press, 2009:2300-2305.
[4]
KAWAMURA S, KINO H, WON C. High-speed manipulation by using parallel wire-driven robots[J]. Robotica, 2000, 18(1):13-21.
[5]
LANDSBERGER S E. Design and construction of a cable-controlled, parallel link manipulator[D]. Cambridge:Massachusetts Institute of Technology, 1984.
[6]
刘欣, 仇原鹰, 盛英. 风洞试验绳牵引冗余并联机器人的刚度增强与运动控制[J]. 航空学报, 2009, 30(6):1156-1164. LIU X, QIU Y Y, SHENG Y. Stiffness enhancement and motion control of a 6-DOF wire-driven parallel manipulator with redundant actuations for wind tunnels[J]. Acta Aeronautica et Astronautica Sinica, 2009, 30(6):1156-1164. (in Chinese)
[7]
隋春平, 赵明扬. 3自由度并联柔索驱动变刚度操作臂的刚度控制[J]. 机械工程学报, 2006, 42(6):205-210. SUI C P, ZHAO M Y. Statics and stiffness study on a 3-DOF parallel wire driven flexible manipulator[J]. Chinese Journal of Mechanical Engineering, 2006, 42(6):205-210. (in Chinese)
[8]
CHEN S F, KAO I. Geometrical approach to the conservative congruence transformation (CCT) for robotic stiffness control[C]//Proceedings of 2002 IEEE International Conference on Robotics and Automation. Washington, DC, USA:IEEE Press, 2002, 1:544-549.
[9]
ANG M H JR, WANG W, LOH R N K, et al. Passive compliance from robot limbs and its usefulness in robotic automation[J]. Journal of Intelligent and Robotic Systems, 1997, 20(1):1-21.
[10]
PASHKEVICH A, KLIMCHIK A, CHABLAT D. Enhanced stiffness modeling of manipulators with passive joints[J]. Mechanism and Machine Theory, 2011, 46(5):662-679.
[11]
ZARGARBASHI S H H, KHAN W, ANGELES J. The Jacobian condition number as a dexterity index in 6R machining robots[J]. Robotics and Computer-Integrated Manufacturing, 2012, 28(6):694-699.
[12]
杜敬利, 保宏, 崔传贞. 基于等效模型的索牵引并联机器人的刚度分析[J]. 工程力学, 2011, 28(5):194-199. DU J L, BAO H, CUI C Z. Stiffness analysis of cable-driven parallel manipulators using equivalent model[J]. Engineering Mechanics, 2011, 28(5):194-199. (in Chinese)
[13]
杜敬利, 段宝岩, 保宏. 增强索支撑系统扭转刚度的索连接位置优化[J]. 工程力学, 2009, 26(4):252-256. DU J L, DUAN B Y, BAO H. Parametric optimization on cable attachments to maximize twist stiffness of cable-supporting system[J]. Engineering Mechanics, 2009, 26(4):252-256. (in Chinese)
[14]
LIM W B, YEO S H, YANG G L. Optimization of tension distribution for cable-driven manipulators using tension-level Index[J]. IEEE/ASME Transactions on Mechatronics, 2014, 19(2):676-683.
[15]
WANG X G, MA S Y, LIN Q. Hybrid pose/tension control based on stiffness optimization of cable-driven parallel mechanism in wind tunnel test[C]//Proceedings of the 2nd International Conference on Control, Automation and Robotics. Hong Kong, China:IEEE, 2016:75-79.
[16]
姚蕊. 大跨度索并联机构力特性及尺度综合设计研究[D]. 北京:清华大学, 2010. YAO R. Study on tension characteristic and dimensional synthetic design of cable driven parallel manipulators with large span[D]. Beijing:Tsinghua University, 2010. (in Chinese)
[17]
唐乐为, 唐晓强, 汪劲松, 等. 七索并联对接机构作业空间分析及索力优化设计[J]. 机械工程学报, 2012, 48(21):1-7. TANG L W, TANG X Q, WANG J S, et al. Workspace analysis and tension optimization design in docking parallel mechanism driven by seven cables[J]. Journal of Mechanical Engineering, 2012, 48(21):1-7. (in Chinese)
[18]
ZIEGLER G M. Lectures on polytopes[M]. New York:Springer-Verlag, 1993.
2018, Vol. 58 
