Innovative Design of Complex Products

Kinematic Sensitivity Analysis and Dimensional Synthesis of a Redundantly Actuated Parallel Robot for Friction Stir Welding

  • Xinxue Chai ,
  • Ningbin Zhang ,
  • Leiying He ,
  • Qinchuan Li ,
  • Wei Ye
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  • Faculty of Mechanical Engineering and Automation, Zhejiang Sci-Tech University, Hangzhou 310018, China

Received date: 2019-07-20

  Revised date: 2019-11-05

  Online published: 2020-05-18

Supported by

Supported by National Natural Science Foundation of China (Grant Nos. U1713202, 51525504)

Abstract

Friction stir welding (FSW) has been widely applied in many fields as an alternative to traditional fusion welding. Although serial robots can provide the orientation capability required to weld along curved surfaces, they cannot adequately support the huge axial downward forces that FSW generates. Available parallel mechanism architectures, particularly redundantly actuated architectures for FSW, are still very limited. In this paper, a redundantly actuated 2UPR-2RPU parallel robot for FSW is proposed, where U denotes a universal joint, R denotes a revolute joint and P denotes a prismatic pair. First, its semi-symmetric structure is described. Next, inverse kinematics analysis involving an analytical representation of rotational axes is implemented. Velocity analysis is also conducted, which leads to the formation of a Jacobian matrix. Sensitivity performance is evaluated utilizing level set and convex optimization methods, where the local sensitivity indices are unit consistent, coordinate free, and of definite physical significance. Furthermore, global and hierarchical sensitivity indices are proposed for the design process. Finally, dimension synthesis is conducted based on the sensitivity indices and the optimal link parameters of the parallel robot are obtained. In summary, this paper proposes a dimensional synthesis method for a redundantly actuated parallel robot for FSW based on sensitivity indices.

Cite this article

Xinxue Chai , Ningbin Zhang , Leiying He , Qinchuan Li , Wei Ye . Kinematic Sensitivity Analysis and Dimensional Synthesis of a Redundantly Actuated Parallel Robot for Friction Stir Welding[J]. Chinese Journal of Mechanical Engineering, 2020 , 33(1) : 1 -1 . DOI: 10.1186/s10033-019-0427-6

References

[1] W M Thomas. Friction stir butt welding: International Patent Application No. PCT/GB92/02203, 1991.
[2] P L Threadgill, A J Leonard, H R Shercliff, et al. Friction stir welding of aluminium alloys. International Materials Reviews, 2009, 54(2): 49–93.
[3] R Nandan, T DebRoy, H K D H Bhadeshia. Recent advances in friction-stir welding-process, weldment structure and properties. Progress in Materials Science, 2008, 53(6): 980–1023.
[4] M Soron, I Kalaykov. A robot prototype for friction stir welding. Proceedings of the IEEE Conference on Robotics, Automation and Mechatronics, Bangkok, Thailand, June 1–3, 2006: 1–5.
[5] A V Strombeck, C Schilling, J D Santos. Robotic friction stir welding-tool technology and applications. Biuletyn Instytutu Spawalnictwa, 2001, 45(6): 49–52.
[6] A P Manogaran, G Racineux, J Y Hascoet. Measurement and comparison of force effort during friction stir welding in a parallel kinematic 5-axis milling machine. Proceedings of the ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis, Nantes, France, July 2–4, 2012: 115–121.
[7] J Shi, Y H Wang, G Zhang, et al. Optimal design of 3-DOF PKM module for friction stir welding. International Journal of Advanced Manufacturing Technology, 2013, 66(9–12): 1879–1889.
[8] Q C Li, W F Wu, J N Xiang, et al. A hybrid robot for friction stir welding. Proceedings of the Institution of Mechanical Engineers Part C-Journal of Mechanical Engineering Science, 2015, 229(14): 2639–2650.
[9] C Z Wang, Y F Fang, S Guo, et al. Design and kinematical performance analysis of a 3-RUS/RRR redundantly actuated parallel mechanism for ankle rehabilitation. Journal of Mechanisms and Robotics, 2013, 5(4): 041003.
[10] C Z Wang, Y F Fang, S Guo. Multi-objective optimization of a parallel ankle rehabilitation robot using modified differential evolution algorithm. Chinese Journal of Mechanical Engineering, 2015, 28(4): 702–715.
[11] H B Qu, Y F Fang, S Guo. Structural synthesis of a class of 3-DOF wrist mechanisms with redundantly-actuated closed-loop units. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2016, 230(2): 276–290.
[12] J Wu, B B Zhang, L P Wang. Optimum design and performance comparison of a redundantly actuated solar tracker and its nonredundant counterpart. Solar Energy, 2016, 127: 36–47.
[13] L P Wang, B B Zhang, J Wu. Optimum design of a 4-PSS-PU redundant parallel manipulator based on kinematics and dynamics. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2016, 230(13): 2273–2284.
[14] J Wu, B B Zhang, L P Wang. A measure for evaluation of maximum acceleration of redundant and nonredundant parallel manipulators, Journal of Mechanisms and Robotics, 2016, 8(2): 021001.
[15] J Wu, T M Li, B Q Xu. Force optimization of planar 2-DOF parallel manipulators with actuation redundancy considering deformation. Proceedings of Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science, 2013, 227(6): 1371–1377.
[16] F G Xie, X J Liu, Y H Zhou. Optimization of a redundantly actuated parallel kinematic mechanism for a 5-degree-of-freedom hybrid machine tool. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 2014, 228(12): 1630–1641.
[17] J Kim, F C Park, S J Ryu, et al. Design and analysis of a redundantly actuated parallel mechanism for rapid machining. IEEE Transactions on Robotics and Automation, 2001, 17(4): 423–434.
[18] S H Kim, D Jeon, H P Shin, et al. Design and analysis of decoupled parallel mechanism with redundant actuator. International Journal of Precision Engineering and Manufacturing, 2009, 10(4): 93–99.
[19] H Shin, S C Lee, W In, et al. Kinematic optimization of a redundantly actuated parallel mechanism for maximizing stiffness and workspace using Taguchi method. Journal of Computational and Nonlinear Dynamics, 2011, 6(1): 011017.
[20] S Jin, J Kim, T Seo. Optimization of a redundantly actuated 5R symmetrical parallel mechanism based on structural stiffness. Robotica, 2015, 33(9): 1973–1983.
[21] H Saafi, M A Laribi, S Zeghloul. Redundantly actuated 3-RRR spherical parallel manipulator used as a haptic device: improving dexterity and eliminating singularity. Robotica, 2015, 33(5): 1113–1130.
[22] H Wang, L Y Kong, G L Chen, et al. Design of an actuation device with the capability of automatically distributing external load based on stability theorems. Journal of Mechanical Design, 2015, 137(8): 085001.
[23] J H Choi, T W Seo, J W Lee. Torque distribution optimization of redundantly actuated planar parallel mechanisms based on a null-space solution. Robotica, 2014, 32(7): 1125–1134.
[24] H Cheng, Y K Yiu, Z Li. Dynamics and control of redundantly actuated parallel manipulators. IEEE-ASME Transactions on Mechatronics, 2003, 8(4): 483–491.
[25] A Müller. Problems in the control of redundantly actuated parallel manipulators caused by geometric imperfections. Meccanica, 2011, 46(1): 41–49.
[26] A Müller. Consequences of geometric imperfections for the control of redundantly actuated parallel manipulators. IEEE Transactions on Robotics, 2010, 26(1): 21–31.
[27] A Müller. On the terminology and geometric aspects of redundant parallel manipulators. Robotica, 2013, 31(1): 137–147.
[28] H Y Wen, W L Xu, M Cong. Kinematic model and analysis of an actuation redundant parallel robot with higher kinematic pairs for jaw movement. IEEE Transactions on Industrial Electronics, 2015, 62(3): 1590–1598.
[29] Z Gao, D Zhang. Performance analysis, mapping, and multi-objective optimization of a hybrid robotic machine tool. IEEE Transactions on Industrial Electronics, 2015, 62(1): 423–433.
[30] T Yoshikawa. Analysis and control of robot manipulators with redundancy//M Brady, R P Paul. Robotics Research: The First International Symposium. Massachusetts: MIT Press Cambridge, 1984: 735–747.
[31] J Ryu, J Cha. Volumetric error analysis and architecture optimization for accuracy of hexaslide type parallel manipulators. Mechanism and Machine Theory, 2003, 38(3): 227–240.
[32] C Gosselin, J Angeles. The optimum kinematic design of a spherical three-degree-of-freedom parallel manipulator. Journal of Mechanisms, Transmissions, and Automation in Design, 1989, 111(2): 202–207.
[33] J P Merlet. Jacobian, manipulability, condition number and accuracy of parallel robots. Journal of Mechanical Design, 2006, 128(1): 199–206.
[34] E Schwartz, R Manseur, K Doty. Noncommensurate systems in robotics. International Journal of Robot and Automation, 2002, 17(2): 86–92.
[35] J Angeles. The design of isotropic manipulator architectures in the presence of redundancies. The International Journal of Robotics Research, 1992, 11(3): 196–201.
[36] I Mansouri, M Ouali. The power manipulability-A new homogeneous performance index of robot manipulators. Robotics and Computer-Intergrated Manufacturing, 2011, 27(2): 434–449.
[37] G Legnani, D Tosi, I Fassi, et al. The 'point of isotropy' and other properties of serial and parallel manipulators. Mechanism and Machine Theory, 2010, 45(10): 1407–1423.
[38] H T Liu, T Huang, D G Chetwynd. A method to formulate a dimensionally homogeneous Jacobian of parallel manipulators. IEEE Transactions on Robotics, 2011, 27(1): 150–156.
[39] C Han, J Kim, J Kim, et al. Kinematic sensitivity analysis of the 3-UPU parallel mechanism. Mechanism and Machine Theory, 2002, 37(8): 787–798.
[40] S Briot, I A Bonev. Accuracy analysis of 3-DOF planar parallel robots. Mechanism and Machine Theory, 2008, 43(4): 445–458.
[41] J Meng, D J Zhang, Z X Li. Accuracy analysis of parallel manipulators with joint clearance. Journal of Mechanical Design, 2009, 131(1): 011013.
[42] P Cardou, S Bouchard, C Gosselin. Kinematic-sensitivity indices for dimensionally nonhomogeneous Jacobian matrices. IEEE Transactions on Robotics, 2010, 26(1): 166–173.
[43] H Wang, G L Chen, Y Zhao, et al. Output error bound prediction of parallel manipulators based on the level set method. Mechanism and Machine Theory, 2010, 45(8): 1153–1170.
[44] Q C Li, J M Herve. Type synthesis of 3-DOF RPR-equivalent parallel mechanisms. IEEE Transactions on Robotics, 2014, 30(6): 1333–1343.
[45] Q C Li, L M Xu, Q H Chen, et al. New family of RPR-equivalent parallel mechanisms: Design and application. Chinese Journal of Mechanical Engineering, 2017, 30(2): 217–221.
[46] C Yang, Q C Li, Q H Chen. Multi-objective optimization of parallel manipulators using a game algorithm. Applied Mathematical Modelling, 2019, 74: 217–243.
[47] Z Huang, J F Liu, Y W Li. On the degree of freedom-the general formula of the degree of freedom which has been searched for 150 years. Beijing: Science Press, 2011. (in Chinese)
[48] R M Murray, Z X Li, S S Sastry. A mathematical introduction to robotic manipulation. Florida: Chemical Rubber Company Press, 1994.
[49] S Boyd, L Vandenberghe. Convex optimization. Cambridge: Cambridge University Press, 2004.
[50] Q C Li, N B Zhang, F B Wang. New indices for optimal design of redundantly actuated parallel manipulators. Journal of Mechanisms and Robotics, 2017, 9(1): 011007.
[51] L M Xu, X X Chai, Q C Li, et al. Design and experimental investigation of a new 2R1T overconstrained parallel kinematic machine with actuation redundancy. Journal of Mechanisms and Robotics, 2019, 11(3): 031016.
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