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Task-based torque minimization of a 3-PṞR spherical parallel manipulator

Published online by Cambridge University Press:  07 June 2021

Soheil Zarkandi Open the ORCID record for Soheil Zarkandi [Opens in a new window]
Soheil Zarkandi*
Affiliation:
Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran
*
Email: zarkandi@gmail.com
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Abstract

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A comprehensive dynamic modeling and actuator torque minimization of a new symmetrical three-degree-of-freedom (3-DOF) 3-PṞR spherical parallel manipulator (SPM) is presented. Three actuating systems, each of which composed of an electromotor, a gearbox and a double Rzeppa-type driveshaft, produce input torques of the manipulator. Kinematics of the 3-PṞR SPM was recently studied by the author (Zarkandi, Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 2020, https://doi.org/10.1177%2F0954406220938806). In this paper, a closed-form dynamic equation of the manipulator is derived with the Newton–Euler approach. Then, an optimization problem with kinematic and dynamic constraints is presented to minimize torques of the actuators for implementing a given task. The results are also verified by the SimMechanics model of the manipulator.

Keywords

spherical parallel manipulatordynamic modelingNewton-Euler methodSimMechanicsRzeppa jointTorque minimizationdynamic dexterity

Information

Type
Article
Information
Robotica , Volume 40 , Issue 3 , March 2022 , pp. 475 - 504
Copyright
© The Author(s), 2021. Published by Cambridge University Press

References

Zarkandi, S., “Kinematic analysis and optimal design of a novel 3-PṞR spherical parallel manipulator,” Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. (2020). https://doi.org/10.1177%2F0954406220938806.Google Scholar
Park, S., J. Kim and G. Lee “Optimal trajectory planning considering optimal torque distribution of redundantly actuated parallel mechanism,” Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 232(23), 4410–4419 (2018). doi: 10.1177/0954406217751818.CrossRefGoogle Scholar
Baressi Šegota, S., Anðelić, N., Lorencin, I., Saga, M. and Car, Z., “Path planning optimization of six-degree-of-freedom robotic manipulators using evolutionary algorithms,” Int. J. Adv. Rob. Syst. (2020). doi: 10.1177/1729881420908076.CrossRefGoogle Scholar
Gillawat, A. K. and Nagarsheth, H. J. Human Upper Limb Joint Torque Minimization Using Genetic Algorithm. In: Recent Advances in Mechanical Engineering, Lecture Notes in Mechanical Engineering (H. Kumar and P. Jain, eds.) (Springer, Singapore, 2020). https://doi.org/10.1007/978-981-15-1071-7_6.CrossRefGoogle Scholar
Saafi, H., Laribi, M. A. and Zeghloul, S., “Optimal torque distribution for a redundant 3-RRR spherical parallel manipulator used as a haptic medical device,” Rob. Auto. Syst. 89, 40–50 (2017). https://doi.org/10.1016/j.robot.2016.12.005.CrossRefGoogle Scholar
Yao, J., Gu, W., Feng, Z., Chen, L., Xu, Y. and Zhao, Y., “Dynamic analysis and driving force optimization of a 5-DOF parallel manipulator with redundant actuation,” Rob. Comput. Integr. Manuf. 48, 51–58 (2017). https://doi.org/10.1016/j.rcim.2017.02.006.CrossRefGoogle Scholar
Boudreau, R., Léger, J., Tinaou, H. and Gallant, A., “Dynamic analysis and optimization of a kinematically redundant planar parallel manipulator,” Trans. Canad. Soc. Mech. Eng. 42(1), 20–29 (2018). https://doi.org/10.1139/tcsme-2017-0003.CrossRefGoogle Scholar
Gosselin, C. M. and Wang, J., “Singularity loci of a special class of spherical three-degree-of-freedom parallel mechanisms with revolute actuators,” Int. J. Rob. Res. 21(7), 649–659 (2002). doi: 10.1177/027836402322023231.CrossRefGoogle Scholar
Staicu, S., “Recursive modeling in dynamics of Agile wrist spherical parallel robot,” Rob. Comput. Integr. Manuf. 25(2), 409–416 (2009). https://doi.org/10.1016/j.rcim.2008.02.001.CrossRefGoogle Scholar
Staicu, S., “Dynamics of the spherical 3-UPS/S parallel mechanism with prismatic actuators,” Multibody Syst. Dyn. 22, 115–132 (2009). https://doi.org/10.1007/s11044-009-9150-x.CrossRefGoogle Scholar
Enferadi, J. and Akbarzadeh Tootoonchi, A., “Inverse dynamics analysis of a general spherical star-triangle parallel manipulator using principle of virtual work,” Nonlinear Dyn. 61(3), 419–434 (2010).CrossRefGoogle Scholar
Akbarzadeh, A. and Enferadi, J., “A virtual work based algorithm for solving direct dynamics problem of a 3-RRP spherical parallel manipulator,” J. Intell. Rob. Syst. 63, 25–49 (2011). https://doi.org/10.1007/s10846-010-9469-9.CrossRefGoogle Scholar
Sun, T., Song, Y., Dong, G., Lian, B. and Liu, J., “Optimal design of a parallel mechanism with three rotational degrees of freedom,” Rob. Comput. Integr. Manuf. 28(4), 500–508 (2012). https://doi.org/10.1016/j.rcim.2012.02.002.CrossRefGoogle Scholar
Puglisi, L. J., Saltaren, R. J., Portoles, G. R., Moreno, H., Cardenas, P. F. and Garcia, C., “Design and kinematic analysis of 3PSS-1S wrist for needle insertion guidance,” Rob. Auto. Syst. 61(5), 417–427 (2013).CrossRefGoogle Scholar
Wu, G., Caro, S., Bai, Sh. and Kepler, J. , “Dynamic modeling and design optimization of a 3-DOF spherical parallel manipulator,” Rob. Auto. Syst. 62(10), 1377–1386 (2014).CrossRefGoogle Scholar
Zhaon, Y., Qiu, K., Wang, Sh. and Zhang, Z., “Inverse kinematics and rigid-body dynamics for a three rotational degrees of freedom parallel manipulator,” Rob. Comput. Integr. Manuf. 31, 40–50 (2015). https://doi.org/10.1016/j.rcim.2014.07.002.CrossRefGoogle Scholar
Khoshnoodi, H., Rahmani Hanzaki, A. and Talebi, H. A., Kinematics, “Singularity study and optimization of an innovative spherical parallel manipulator with large workspace,” J. Intell. Rob. Syst. 92, 309–321 (2018). https://doi.org/10.1007/s10846-017-0752-x.CrossRefGoogle Scholar
Wu, G. and Bai, Sh., “Design and kinematic analysis of a 3-RRR spherical parallel manipulator reconfigured with four–bar linkages,” Rob. Comput. Integr. Manuf. 56, 55–65 (2019). https://doi.org/10.1016/j.rcim.2018.08.006.CrossRefGoogle Scholar
Enferadi, J. and Jafari, K., “A Kane’s based algorithm for closed-form dynamic analysis of a new design of a 3RSS-S spherical parallel manipulator,” Multibody Syst. Dyn. 49, 377–394 (2020). https://doi.org/10.1007/s11044-020-09736-y.CrossRefGoogle Scholar
Saafi, H., Amine Laribi, M. and Zeghloul, S., “Forward kinematic model improvement of a spherical parallel manipulator using an extra sensor,” Mech. Mach. Theory 91, 102–119 (2015). https://doi.org/10.1016/j.mechmachtheory.2015.04.006.CrossRefGoogle Scholar
Zarkandi, S., “Kinematic and dynamic modeling of a planar parallel manipulator served as CNC tool holder,” Int. J. Dyn. Control 6(1), 14–28 (2018).CrossRefGoogle Scholar
Pedrammehr, S., Danaei, B., Abdi, H., Masouleh, M. T. and Nahavandi, S., “Dynamic analysis of Hexarot: Axis-symmetric parallel manipulator,” Robotica 36(2), 225–240 (2018). doi: 10.1017/S0263574717000315.CrossRefGoogle Scholar
Zarkandi, S., “Inverse and forward dynamics of a 4RSS+PS parallel manipulator with one infinite rotational motion,” Aust. J. Mech. Eng. (2020). doi: 10.1080/14484846.2020.1714352.CrossRefGoogle Scholar
Altuzarra, O., Zubizarreta, A., Cabanes, I. and Pinto, C., “Dynamics of a four degrees-of-freedom parallel manipulator with parallelogram joints,” Mechatronics 19(8), 1269–1279 (2009). https://doi.org/10.1016/j.mechatronics.2009.08.003.CrossRefGoogle Scholar
Liu, M.-J., Li, C.-X. and Li, C.-N., “Dyamics analysis of the Gough–Stewart Platform manipulator,” IEEE Trans. Rob. Autom. 16(1), 94–98 (2000).CrossRefGoogle Scholar
Gallardo, J., Rico, J. M. and Frisoli, A., “Dynamics of parallel manipulators by means of screw theory,” Mech. Mach. Theory 38(11), 1113–1131 (2003).CrossRefGoogle Scholar
Akbarzadeh, A., Enferadi, J. and Sharifnia, M., “Dynamics analysis of a 3-RRP spherical parallel manipulator using the natural orthogonal complement,” Multibody Sys. Dyn. 29(4), 361–380 (2013).CrossRefGoogle Scholar
Sugimoto, K., “Kinematics and dynamic analysis of parallel manipulator by means of motor algebra,” ASME J. Mech., Trans. Autom. Des. 109(1), 3–7 (1987).CrossRefGoogle Scholar
Zarkandi, S., “A new geometric method for singularity analysis of spherical mechanisms,” Robotica 29(7), 1083–1092 (2011). https://doi.org/10.1017/S0263574711000385.CrossRefGoogle Scholar
Euler angles, Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/w/index.php?title=Euler_angles&oldid=996258926 (accessed January 23, 2021).Google Scholar
Stribeck, R., “The key qualities of sliding and roller bearings,” Zeitschrift des Vereines Seutscher Ingenieure 46(38), 39 (1902).Google Scholar
Tu, X., Zhou, Y. F., Zhao, P. and Cheng, X., “Modeling the static friction in a robot joint by genetically optimized BP neural network,” J. Intell. Rob. Syst. 94, 29–41 (2019), https://doi.org/10.1007/s10846-018-0796-6.CrossRefGoogle Scholar
Yoshikawa, T., “Dynamic Manipulability of Robot Manipulators,” IEEE International Conference on Robotics and Automation (ICRA), vol. 2 (1985) pp. 1033–1038.Google Scholar
Wu, J., Wang, J., Li, T., Wang, L. and Guan, L., “Dynamic dexterity of a planar 2-DOF parallel manipulator in a hybrid machine tool,” Robotica 26(1), 93–98 (2008). doi: 10.1017/S0263574707003621.CrossRefGoogle Scholar
Hu, X., Eberhart, R. C. and Shi, Y., “Engineering optimization with particle swarm,” Proceedings of the 2003 IEEE Swarm Intelligence Symposium, Indianapolis, USA (2003) pp. 53–57. doi: 10.1109/SIS.2003.1202247.CrossRefGoogle Scholar