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Integrating dynamics into design and motion optimization of a 3-PRR planar parallel manipulator with discrete time transfer matrix method. (English) Zbl 07348358

Summary: This paper presents a novel method of dynamic modeling and design optimization integrated with dynamics for parallel robot manipulators. Firstly, a computationally efficient modeling method, the discrete time transfer matrix method (DT-TMM), is proposed to establish the dynamic model of a 3-PRR planar parallel manipulator (PPM) for the first time. The numerical simulations are performed with both the proposed DT-TMM dynamic modeling and the ADAMS modeling. The applicability and effectiveness of DT-TMM in parallel manipulators are verified by comparing the numerical results. Secondly, the design parameters of the 3-PRR parallel manipulator are optimized using the kinematic performance indices, such as global workspace conditioning index (GWCI), global condition index (GCI), and global gradient index (GGI). Finally, a dynamic performance index, namely, driving force index (DFI), is proposed based on the established dynamic model. The described motion trajectory of the moving platform is placed into the optimized workspace and the initial position is determined to finalize the end-effector trajectory of the parallel manipulator by the further optimization with the integrated kinematic and dynamic performance indices. The novelty of this work includes (1) developing a new dynamic model method with high computation efficiency for parallel robot manipulators using DT-TMM and (2) proposing a new dynamic performance index and integrating the dynamic index into the motion and design optimization of parallel robot manipulators.

MSC:

70E60 Robot dynamics and control of rigid bodies
Full Text: DOI

References:

[1] Zhang, Y.; Dang, Y.; Wu, X., Kinematics and singularity analysis of a novel decoupled translational parallel manipulator, Mechanical Science & Technology for Aerospace Engineering, 27, 4, 622-626 (2010)
[2] Zhang, Q.; Zhang, X.; Liang, J., Dynamic analysis of planar 3-RRR flexible parallel robot, Proceedings of the IEEE International Conference on Robotics & Biomimetics, IEEE
[3] Kim, B. S., Dynamic and kinematic analysis of 6-bar parallel robot, Proceedings of the 2013 44th International Symposium on IEEE
[4] Bogdan, G.; Doina, P.; Calin, V.; Plitea, N., Development of inverse dynamic model for a surgical hybrid parallel robot with equivalent lumped masses, Robotics and Computer-Integrated Manufacturing, 28, 3, 402-415 (2012) · doi:10.1016/j.rcim.2011.11.003
[5] Hay, A. M.; Snyman, J. A., Methodologies for the optimal design of parallel manipulators, International Journal for Numerical Methods in Engineering, 59, 11, 131-152 (2004) · Zbl 1047.70012 · doi:10.1002/nme.871
[6] Zhang, Q.; Mills, J. K.; Cleghorn, W. L.; Jin, J.; Zhao, C., Trajectory tracking and vibration suppression of a 3-PRR parallel manipulator with flexible links, Multibody System Dynamics, 33, 1, 27-60 (2015) · Zbl 1391.70018 · doi:10.1007/s11044-013-9407-2
[7] Liang, D.; Song, Y.; Sun, T.; Jin, X., Rigid-flexible coupling dynamic modeling and investigation of a redundantly actuated parallel manipulator with multiple actuation modes, Journal of Sound and Vibration, 403, 129-151 (2017) · doi:10.1016/j.jsv.2017.05.022
[8] Krauss, R. W., Computationally efficient modeling of flexible robots using the transfer matrix method, Journal of Vibration and Control, 18, 5, 596-608 (2012) · doi:10.1177/1077546311408466
[9] Zhang, X.; Sørensen, R.; Iversen, M. R.; Li, H., Computationally efficient dynamic modeling of robot manipulators with multiple flexible-links using acceleration-based discrete time transfer matrix method, Robotics and Computer-Integrated Manufacturing, 49, 181-193 (2018) · doi:10.1016/j.rcim.2017.06.010
[10] He, B.; Rui, X.; Wang, G., Riccati discrete time transfer matrix method for elastic beam undergoing large overall motion, Multibody System Dynamics, 18, 4, 579-598 (2007) · Zbl 1192.74213 · doi:10.1007/s11044-007-9063-5
[11] Rui, X.; Bestle, D.; Zhang, J.; Zhou, Q., A new version of transfer matrix method for multibody systems, Multibody System Dynamics, 38, 2, 137-156 (2016) · Zbl 1351.70009 · doi:10.1007/s11044-016-9528-5
[12] Rui, X.; Wang, X.; Zhou, Q.; Zhang, J., Transfer matrix method for multibody systems (Rui method) and its applications, Science China Technological Sciences, 62, 5, 712-720 (2019) · doi:10.1007/s11431-018-9425-x
[13] Rui, X.; Wang, G.; Zhang, J., Transfer Matrix Method for Multibody Systems: Theory and Applications (2018), Hoboken, NJ, USA: Wiley, Hoboken, NJ, USA
[14] Rui, X.; Wang, G.; Yun, L., Study on the vibration characteristics of LRMLRS, Journal of Vibration & Shock, 24, 1, 8-12 (2005)
[15] Rong, B.; Rui, X.; Tao, L., Discrete time transfer matrix method for launch dynamics modeling and cosimulation of self-propelled artillery system, Journal of Applied Mechanics, 80, 1 (2013) · doi:10.1115/1.4006869
[16] Rui, X.; Wang, G.; Lu, Y.; Yun, L., Transfer matrix method for linear multibody system, Multibody System Dynamics, 19, 3, 179-207 (2008) · Zbl 1181.70010 · doi:10.1007/s11044-007-9092-0
[17] Krauss, R.; Okasha, M., Discrete-time transfer matrix modeling of flexible robots under feedback control, Proceedings of the American Control Conference (ACC)
[18] Zhang, Q.; Li, C.; Zhang, J., Synchronized motion control and precision positioning compensation of a 3-DOFs macro-micro parallel manipulator fully actuated by piezoelectric actuators, Smart Materials and Structures, 26, 1-15 (2017) · doi:10.1088/1361-665x/aa8b23
[19] Zhou, Z.; Xi, J.; Mechefske, C. K., Modeling of a fully flexible 3PRS manipulator for vibration analysis, Journal of Mechanical Design, 128, 2, 403-412 (2006) · doi:10.1115/1.2167655
[20] Kumar, A.; Waldron, K. J., The workspaces of a mechanical manipulator, Journal of Mechanical Design, 103, 3, 665-672 (1981) · doi:10.1115/1.3254968
[21] Koeppe, R.; Yoshikawa, T., Dynamic manipulability analysis of compliant motion, Proceedings of the IEEE/RSJ International Conference on Intelligent Robots & Systems
[22] Melchiorri, C.; Salisbury, J. K., An algorithm for the control of a hand-arm robotic system, Proceedings of the Fifth International Conference on Advanced Robotics
[23] Gosselin, C.; Angeles, J., A global performance index for the kinematic optimization of robotic manipulators, Journal of Mechanical Design, 113, 3, 220-226 (1991) · doi:10.1115/1.2912772
[24] Stamper, R. E.; Tsai, L.-W.; Walsh, G. C., Optimization of a three DOF translational platform for well-conditioned workspace, Proceedings of the IEEE International Conference on Robotics and Automation
[25] Courteille, E.; Deblaise, D.; Maurine, P., Design optimization of a delta-like parallel robot through global stiffness performance evaluation, Proceedings of the IEEE/RSJ International Conference on Intelligent Robots & Systems
[26] Kurazume, R.; Hasegawa, T., A new index of serial-link manipulator performance combining dynamic manipulability and manipulating force ellipsoids, IEEE Transactions on Robotics, 22, 5, 1022-1028 (2006) · doi:10.1109/tro.2006.878949
[27] Rezania, V.; Ebrahimi, S., Dexterity characterization of the RPR parallel manipulator based on the local and global condition indices, Journal of Mechanical Science and Technology, 31, 1, 335-344 (2017) · doi:10.1007/s12206-016-1237-8
[28] Bi, S.; Zhuang, Z.; Xia, T., Multi-objective optimization for a humanoid robot walking on slopes, Proceedings of the International Conference on Machine Learning & Cybernetics
[29] Luo, J.; Wang, D.; Xing, Z., Multi-objective optimal kinematic design of 3-TPS/TP parallel robot manipulator, Advanced Engineering Forum, 2012, 2-3, 324-329 (2012)
[30] Gallardo-Alvarado, J.; Tinajero-Campos, J. H., A parallel manipulator with planar configurable platform and three end-effectors, Mathematical Problems in Engineering, 2019 (2019) · Zbl 1435.70024 · doi:10.1155/2019/7972837
[31] Mo, J.; Qiu, Z.; Zeng, L.; Zhang, X.-M., A new calibration method for a directly driven 3PRR positioning system, Journal of Intelligent & Robotic Systems, 85, 3-4, 613-631 (2017) · doi:10.1007/s10846-016-0403-7
[32] Chandra, R.; Zhang, M.; Mengjie, L., Solving the forward kinematics of the 3RPR planar parallel manipulator using a hybrid meta-heuristic paradigm, Proceedings of the International Symposium on Computational Intelligence in Robotics and Automation
[33] Baron, L.; Angeles, J., The direct kinematics of parallel manipulators under joint-sensor redundancy, IEEE Transactions on Robotics and Automation, 16, 1, 12-19 (2000) · doi:10.1109/70.833183
[34] Chen, G.; Rui, X.; Abbas, L. K.; Wang, G.; Yang, F.; Zhu, W., A novel method for the dynamic modeling of Stewart parallel mechanism, Mechanism and Machine Theory, 126, 8, 397-412 (2018) · doi:10.1016/j.mechmachtheory.2018.04.024
[35] Macho, E.; Altuzarra, O.; Amezua, E.; Hernandez, A., Obtaining configuration space and singularity maps for parallel manipulators, Mechanism and Machine Theory, 44, 11, 2110-2125 (2009) · Zbl 1247.70015 · doi:10.1016/j.mechmachtheory.2009.06.003
[36] Bonev, I. A.; Ryu, J., A geometrical method for computing the constant-orientation workspace of 6-PRRS parallel manipulators, Mechanism and Machine Theory, 36, 1, 1-13 (2001) · Zbl 1140.70312 · doi:10.1016/s0094-114x(00)00031-8
[37] Monsarrat, B.; Gosselin, C. M., Workspace analysis and optimal design of a 3-leg 6-DOF parallel platform mechanism, IEEE Transactions on Robotics and Automation, 19, 6, 954-966 (2003) · doi:10.1109/tra.2003.819603
[38] Pham, C. B.; Yeo, S. H.; Yang, G., Workspace analysis and optimal design of cable-driven planar parallel manipulators, Proceedings of the IEEE Conference on Robotics, Automation and Mechatronics
[39] Ebrahimi, I.; Carretero, J. A.; Boudreau, R., 3-PRRR redundant planar parallel manipulator: inverse displacement, workspace and singularity analyses, Mechanism and Machine Theory, 42, 8, 1007-1016 (2007) · Zbl 1129.70005 · doi:10.1016/j.mechmachtheory.2006.07.006
[40] Brisan, C.; Csiszar, A., Computation and analysis of the workspace of a reconfigurable parallel robotic system, Mechanism and Machine Theory, 46, 11, 1647-1668 (2011) · doi:10.1016/j.mechmachtheory.2011.06.014
[41] Wang, J.; Wu, J.; Li, T.; Liu, X., Workspace and singularity analysis of a 3-DOF planar parallel manipulator with actuation redundancy, Robotica, 27, 1, 51-57 (2009) · doi:10.1017/s0263574708004517
[42] Chen, C.-T.; Chi, H.-W., Singularity-free trajectory planning of platform-type parallel manipulators for minimum actuating effort and reactions, Robotica, 26, 3, 371-384 (2008) · doi:10.1017/s0263574707004043
[43] Sefrioui, J.; Gosselin, C. M., Singularity analysis and representation of planar parallel manipulators, Robotics and Autonomous Systems, 10, 4, 209-224 (1992) · doi:10.1016/0921-8890(92)90001-f
[44] Mo, J.; Zhang, X.; Qiu, Z., Control strategy research on avoid and escape the singular area of the 3PRR parallel platform based on SEM environment, Journal of Mechanical Engineering, 51, 23, 1-11 (2015) · doi:10.3901/jme.2015.23.001
[45] Kucuk, S.; Bingul, Z., Comparative study of performance indices for fundamental robot manipulators, Robotics and Autonomous Systems, 54, 7, 567-573 (2006) · doi:10.1016/j.robot.2006.04.002
[46] Enferadi, J.; Nikrooz, R., The performance indices optimization of a symmetrical fully spherical parallel mechanism for dimensional synthesis, Journal of Intelligent & Robotic Systems, 90, 3-4, 305-321 (2018) · doi:10.1007/s10846-017-0675-6
[47] Gosselin, C.; Angeles, J., The optimum kinematic design of a planar three-degree-of-freedom parallel manipulator, Journal of Mechanisms, Transmissions, and Automation in Design, 110, 1, 35-41 (1988) · doi:10.1115/1.3258901
[48] Gosselin, C. M.; Lavoie, E., On the kinematic design of spherical three-degree-of- freedom parallel manipulators, The International Journal of Robotics Research, 12, 4, 394-402 (1993) · doi:10.1177/027836499301200406
[49] Kurtz, R.; Hayward, V., Multiple-goal kinematic optimization of a parallel spherical mechanism with actuator redundancy, IEEE Transactions on Robotics and Automation, 8, 5, 644-651 (1992) · doi:10.1109/70.163788
[50] Boschetti, G.; Rosa, R.; Trevisani, A., Optimal robot positioning using task-dependent and direction-selective performance indexes: general definitions and application to a parallel robot, Robotics and Computer-Integrated Manufacturing, 29, 2, 431-443 (2013) · doi:10.1016/j.rcim.2012.09.013
[51] Kucuk, S.; Bingul, Z., Robot workspace optimization based on a novel local and global performance indices, Proceedings of the IEEE International Symposium on Industrial Electronics
[52] Laramolina, F. A.; Rosario, J. M.; Dumur, D., Multi-objective design of parallel manipulator using global indices, The Open Mechanical Engineering Journal, 4, 1, 37-47 (2010) · doi:10.2174/1874155x01004010037
[53] Tian, H.; Liu, S.; Mei, J.; Chetwynd, D. G., Optimal design of a 2-DOF pick-and-place parallel robot using dynamic performance indices and angular constraints, Mechanism & Machine Theory, 70, 6, 246-253 (2013) · doi:10.1016/j.mechmachtheory.2013.07.014
[54] Zhang, S.; Kong, L., Analysis on kinematics and dynamics performance indices for 6-PUS parallel robot mechanism, China Mechanical Engineering, 15, 20, 501-506 (2004)
[55] Xie, Z.; Xie, F.; Liu, X.; Wang, J.; Shen, X., Parameter optimization for the driving system of a 5 degrees of-freedom parallel machining robot with planar kinematic chains, Journal of Mechanisms and Robotics, 11, 4 (2019) · doi:10.1115/1.4043291
[56] Wu, J.; Wang, J.; You, Z., An overview of dynamic parameter identification of robots, Robotics and Computer-Integrated Manufacturing, 26, 5, 414-419 (2010) · doi:10.1016/j.rcim.2010.03.013
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