Dynamic analysis of spatial parallel manipulator with rigid and flexible couplings

Abstract

The dynamics of spatial parallel manipulator with rigid and flexible links is explored. Firstly, a spatial beam element model for finite element analysis is established. Then, the differential equation of motion of beam element is derived based on finite element method. The kinematic constraints of parallel manipulator with rigid and flexible links are obtained by analyzing the motive parameters of moving platform and the relationships of movements of kinematic chains, and the overall kinetic equation of the parallel mechanism with rigid and flexible links is derived by assembling the differential equations of motion of components. On the basis of abovementioned analyses, the dynamic mechanical analysis of the spatial parallel manipulator with rigid and flexible links is conducted. After obtaining the method for force analysis and expressions for the calculation of dynamic stress of flexible components, the dynamic analysis and simulation of spatial parallel manipulator with rigid and flexible links is performed. The result shows that because of the elastic deformation of flexible components in the parallel mechanism with rigid and flexible links, the force on each component in the mechanism fluctuates sharply, and the change of normal stress at the root of drive components is also remarkable. This study provides references for further studies on the dynamic characteristics of parallel mechanisms with rigid and flexible links and for the optimization of the design of the mechanism.

Keywords

rigid and flexible couplings / parallel mechanism / finite element / force analysis / dynamic stress

References

[1] LiuS-z, YuY-q, SiG-n, YangJ-x, SuL-ying. Kinematic and dynamic analysis of a three-degree-of-freedom parallel manipulator [J]. Journal of Mechanical Engineering, 2009, 45(8): 11-17

[2] ZhangK-t, FangY-f, GuoSheng. Design analyses of a novel 3-DOF parallel mechanism [J]. Journal of Mechanical Engineering, 2009, 45(1): 68-72

[3] GanD-m, LiaoQ-z, DaiJ S, WeiS-m, SeneviratneL D. Forward displacement analysis of the general 6–6 Stewart mechanism using Gröbner bases [J]. Mechanism and Machine Theory, 2009, 44(9): 1640-1647

[4] LiuS-z, ZhuZ-c, SunZ-p, CaoG-hua. Kinematics and dynamics analysis of a three-degree-of-freedom parallel manipulator [J]. Journal of Central South University, 2014, 21(7): 2660-2666

[5] LiuS-z, ZhuZ-c, YuY-q, LiuC-s, ZhangL-jie. Frequency analysis of a spatial rigid-flexible coupling parallel manipulator [J]. Journal of Mechanical Engineering, 2011, 47(23): 39-48

[6] LiuS-z, YuY-q, ZhuZ-c, SuL-y, LiuQ-bo. Dynamic modeling and analysis of a 3-RRS parallel manipulator with flexible links [J]. Journal of Central South University of Technology, 2010, 45(4): 12-15

[7] ZhangJ, ZhaoY-qin. Elastodynamic modeling and joint reaction prediction for 3-PRS PKM [J]. Journal of Central South University, 2015, 22(8): 2971-2979

[8] ZhangQ, Mills JamesK, Cleghorn WilliamL, JinJ-m, SunZ-jun. Dynamic model and input shaping control of a flexible link parallel manipulator considering the exact boundary conditions [J]. Robotica, 2015, 33(6): 1201-1230

[9] ChenZ-s, KongM-x, JiC, LiuMing. An efficient dynamic modelling approach for high-speed planar parallel manipulator with flexible links [J]. Proceedings of the Institution of Mechanical Engineers Part C-Journal of Mechanical Engineering Science, 2015, 229(4): 663-678

[10] DuZ-j, ShiR-c, DongWei. Kinematics modeling of a 6-PSS parallel mechanism with wide-range flexure hinges [J]. Journal of Central South University, 2012, 19(9): 2482-2487

[11] WangX-y, MillsJ K. Dynamic modeling of a flexible-link planar parallel platform using a sub-structuring approach [J]. Mechanism and Machine Theory, 2006, 41(6): 671-687

[12] FattahA, AngelesJ, MisraA K. Dynamics of a 3-DOF spatial parallel manipulator with flexible links [C]// IEEE International Conference on Robotics and Automation. Nagoya, Piscataway: IEEE, 1995, 3(1): 627-632

[13] FattahA, MisraA K, AngelesJDynamics of a flexible-link planar parallel manipulator in cartesian space [C]// ASME, Design Engineering Division, 20th Design Automation Conference, 1994483-490

[14] PirasG, CleghornW L, MillsJ K. Dynamic finite-element analysis of a planar high-speed, high-precision parallel manipulator with flexible links [J]. Mechanism and Machine Theory, 2005, 40(7): 849-862

[15] LiuS-zengDynamics of 3-DOF spatial flexible parallel robots [D], 2009BeijingBeijing University of Technology

[16] ZhaoY-j, GaoF, DongX-j, ZhaoX-chao. Elastodynamic characteristics comparison of the 8-PSS redundant parallel manipulator and its non-redundant counterpart—the 6-PSS parallel manipulator [J]. Mechanism and Machine Theory, 2010, 45(2): 291-303