Stiffness analysis of a cable-driven parallel robot by adding springs

PDF(1427 KB)

Journal of Vibration and Shock ›› 2017, Vol. 36 ›› Issue (10) : 197-202.

LI Qinghuan DUAN Qingjuan LI Fan DUAN Xuechao

Author information +

History +

Abstract

Stiffness is one of the important design index of robot. It affects the dynamic characteristics of the robot mechanism, and determines the load positioning accuracy of the end effector. Since cables can only pull but not push, the Cable-Driven Parallel Mechanism (CDPM) with n degrees of freedom requires at least n+1 cables to fully constrain the end-effector. However it has been shown that the redundant cable leads to increased costs of actuator and results in the complexity of solving the cable force. When springs are added properly into the CDPM between the end-effecter and the base frame, it constitutes a Cable-Spring Mechanism, which can achieve the same number of actuators with cables to fully constrain the end-effector of the Cable-Spring Mechanism. In this paper, the static model of a planar Cable-Spring Mechanism is established, and the static analysis of the Cable-Spring Mechanism is performed. According to the definition of rigidity, the analytical expressions of stiffness matrix are derived on the basis of the static equilibrium equation of the Cable-Spring Mechanism at the position of a feasible workspace point. The Hessian matrix of active stiffness and passive stiffness matrix are derived. The stiffness effect of the cable-driven mechanism by adding the spring is analyzed. A numerical example, a planar Cable-Spring Mechanism with 3 cables and 1 spring compared with a 4-cable driven mechanism, was verified.

Key words

Cable-spring mechanism / Static stiffness / Stiffness matrix / Hessian matrix

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

LI Qinghuan DUAN Qingjuan LI Fan DUAN Xuechao. Stiffness analysis of a cable-driven parallel robot by adding springs[J]. Journal of Vibration and Shock, 2017, 36(10): 197-202

References

[1] 王克义.索牵引骨盆运动控制康复机器人研究[D].哈尔滨：哈尔滨工程大学，2009．
WANG Ke-Yi, Research on the pelvis motion control of the rehabilitation robot [D]. Harbin: Harbin Engineering University, 2009.
[2] HILLER M, FANG S Q, MIELCZAREK S, et al. Design, analysis and realization of tendon-based parallel manipulators [J]. Mechanism and Machine Theory, 2005, 40(4): 429-445.
[3] DIAO X M, MAO. A method of verifying force-closure condition for general wire manipulators with seven wires [J]. Mechanism and Machine Theory, 2007, 42(12): 1563-1576.
[4] Gallina P, Rosati G, Rossi A. 3-DOF wire driven planar haptic interface [J]. Journal of intelligent and Robotic Systems, 2001, 32(1): 23-36.
[5] Surdilovic D, Cojbasic Z. Robust Robot Compliant Motion Control Using Intelligent Adaptive Impedance Approach[C]//Proceedings of the 1999 IEEE Conference on Robotics & Automation, Detroit, Michigan, USA, 1999: 2128-2133.
[6] Surdilovic D, Bernhardt R. String-man a New Wire Robot for Gait Rehabilitation[C]//Proceedings of the 2004 IEEE International Conference on Robotics & Automation, New Orleans, LA, USA 2004: 2031-2036.
[7] Surdilovic D, Radojicic J. Robust Control of Interaction with Haptic Interfaces[C]//Proceedings of the 2007 IEEE International Conference on Robotics and Automation，Roma, Italy, 2007: 3237-3244.
[8] Kawamum S, Choe W, Tanak S, et al. Development of an ultrahigh speed robot FALCON using wire driven system[C]// Proceedings of 1995 IEEE International Conference on Robotics and Automation, Nagoya, Japan, 1995: 215-220.
[9] Sadao K, Hitoshi K, Choe W. High-speed manipulation by using parallel wire-driven robots[J]. Robotica, 2000, 18(1): 13-21.
[10]李辉，朱文白．柔索牵引并联机构的静刚度分析[J]．机械工程学报，2010，46(3)：8-16．
LI Hui, ZHU Wen-Bai. Static stiffness analysis of flexible-cable-driven parallel mechanism[J]. Journal of Mechanical Engineering, 2010, 46(3): 8-16.
[11]保宏，杜敬利，段宝岩．大型射电望远镜馈源支撑系统静刚度分析[J]．机械工程学报，2006，42(7)：119-125．
BAO Hong, DU Jing-Li, DUAN Bao-Yan. Analysis of stiffness of suspended feed system for large radio telescope[J]. Journal of Mechanical Engineering, 2006, 42(7): 119-125.
[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 Jing-Li, BAO Hong, CUI Chuan-Zhen. Stiffness analysis of cable-driven parallel manipulators using equivalent model[J]. Engineering Mechanics, 2011, 28(5): 194-199.
[13] Behzasipour S, Khajepour A. Stiffness of cable-based parallel manipulators with application to stability analysis[J]. Journal of Mechanical Design, 2006, 128(6): 303-310.
[14] Tang X, Tang L, Wang J, et al. Workspace quality analysis and application for a completely restrained 3-Dof planar cable-driven parallel manipulator[J]. Journal of Mechanical Science and Technology, 2013, 27(8): 2391-2399.
[15] 王克义等，平面绳索牵引并联机器人静态刚度[J].哈尔滨工程大学学报，2011, 32(9)：1112-1116.
WANG Ke-Yi, et al. Static stiffness of a plane wire-driven parallel robot[J]. Journal of Harbin Engineering University, 2011, 32(9): 1112-1116.
[16] Ming，M．Kajitani，T．Higuchi．On the design of wire parallel mechanism[J]．International Journal of the Japan Society for Precision Engineering，1995，29(4)：337-342P．
[17] R. Andrew Russell, A robotic system for performing sub-millimetre grasping and manipulation tasks, Robot. Auton. Syst. 13 (3) (1994) 209–218.
[18] Alberto Trevisani, Paolo Gallina, Robert L. Williams II, Cable-direct-driven robot (CDDR) with passive SCARA support: theory and simulation, J. Intell. Robot. Syst. 46 (1) (2006) 73–94.
[19] S.K. Mustafa, S.K. Agrawal, On the force-closure analysis of n-DOF cable-driven open chains based on reciprocal screw theory, IEEE Trans. Robot. 28 (1) (2012) 22–31.
[20] Amir Taghavi, et al., Workspace improvement of two-link cable-driven mechanisms with spring cable, Cable-driven Parallel Robots, Springer, Berlin Heidelberg, 2013. 201–213.
[21] Joachim Von Zitzewitz, et al., Use of passively guided deflection units and energy-storing elements to increase the application range of wire robots, Cable-driven Parallel Robots, Springer, Berlin Heidelberg, 2013. 167–184.
[22] T. Bruckmann, C. Sturm, L. Fehlberg, et al., An energy-efficient wire-based storage and retrieval system, 2013 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM), IEEE, 2013, pp. 631–636.
[23] B. Gao, H. Song, J. Zhao, et al., Inverse kinematics and workspace analysis of a cable-driven parallel robot with a spring spine, Mech. Mach. Theory 76 (2014) 56–69.
[24] Duan Q, Vashista V, Agrawal S K. Effect on wrench-feasible workspace of cable-driven parallel robots by adding springs[J]. Mechanism and Machine Theory, 2015, 86: 201-210.
[25] Duan Q, Jin X, Agrawal S K. Addition of Springs and Its Impact On Cable-Driven Serial Manipulators, The ASME 2014 International Design and Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE 2014), August 17–20, 2014，in Buffalo, NY.
[26]刘欣．两种并联机器人的机构性能分析与运动控制研究[D]．西安：西安电子科技大学，2009．
LIU Xin. Analysis of performances and research on the motion control of the two type of parallel robot[D]. Xidian University, 2009.