Stiffness analysis of a planar parallel manipulator with variable platforms

References

• Abdolshah, S., D. Zanotto, G. Rosati, and S. K. Agrawal. 2017. Optimizing stiffness and dexterity of planar adaptive cable-driven parallel robots. Journal of Mechanisms and Robotics 9 (3):031004. doi:10.1115/1.4035681.
   Google Scholar
• Albu-Schaffer, A., O. Eiberger, M. Grebenstein, S. Haddadin, C. Ott, T. Wimbock, S. Wolf, and G. Hirzinger. 2008. Soft robotics: From torque feedback controlled lightweight robots to intrinsically compliant systems. IEEE Robotics and Automation Magazine 15 (3):20–30.
   Web of Science ®Google Scholar
• Bounab, B. 2016. Multi-objective optimal design based kineto-elastostatic performance for the delta parallel mechanism. Robotica 34 (2):258–73. doi:10.1017/S0263574714001416.
   Web of Science ®Google Scholar
• Carbone, G., and M. Ceccarelli. 2010. Comparison of indices for stiffness performance evaluation. Frontiers of Mechanical Engineering in China 5 (3):270–8. doi:10.1007/s11465-010-0023-z.
   Google Scholar
• Chen, G., H. Wang, Z. Lin, and X. Lai. 2015. The principal axes decomposition of spatial stiffness matrices. IEEE Transactions on Robotics 31 (1):191–207. doi:10.1109/TRO.2015.2389415.
   Web of Science ®Google Scholar
• Dai, J. S., and X. Ding. 2006. Compliance analysis of a three-legged rigidly-connected platform device. Journal of Mechanical Design 128 (4):755–64. doi:10.1115/1.2202141.
   Web of Science ®Google Scholar
• Gao, X., Z. Ren, L. Zhai, Q. Jia, and H. Liu. 2019. Two-stage switching hybrid control method based on improved PSO for planar three-link under-actuated manipulator. IEEE Access 7:76263–73. doi:10.1109/ACCESS.2019.2921968.
   Web of Science ®Google Scholar
• Görgülü, İ., and M. İ. C. Dede. 2019. A new stiffness performance index: Volumetric isotropy index. Machines 7 (2):44. doi:10.3390/machines7020044.
   Web of Science ®Google Scholar
• Görgülü, İ., G. Carbone, and M. İ. C. Dede. 2020. Time efficient stiffness model computation for a parallel haptic mechanism via the virtual joint method. Mechanism and Machine Theory 143:103614. doi:10.1016/j.mechmachtheory.2019.103614.
   Web of Science ®Google Scholar
• Gosselin, C. 1990. Stiffness mapping for parallel manipulators. IEEE Transactions on Robotics and Automation 6 (3):377–82. doi:10.1109/70.56657.
   Google Scholar
• Guo, Y., H. Dong, and Y. Ke. 2015. Stiffness-oriented posture optimization in robotic machining applications. Robotics and Computer-Integrated Manufacturing 35:69–76. doi:10.1016/j.rcim.2015.02.006.
   Web of Science ®Google Scholar
• Huang, G., S. Guo, D. Zhang, H. Qu, and H. Tang. 2018. Kinematic analysis and multi-objective optimization of a new reconfigurable parallel mechanism with high stiffness. Robotica 36 (2):187–203. doi:10.1017/S0263574717000236.
   Web of Science ®Google Scholar
• Klimchik, A., A. Pashkevich, and D. Chablat. 2019. Fundamentals of manipulator stiffness modeling using matrix structural analysis. Mechanism and Machine Theory 133:365–94. doi:10.1016/j.mechmachtheory.2018.11.023.
   Web of Science ®Google Scholar
• Klimchik, A., A. Pashkevich, S. Caro, and D. Chablat. 2012. Stiffness matrix of manipulators with passive joints: Computational aspects. IEEE Transactions on Robotics 28 (4):955–8. doi:10.1109/TRO.2012.2187395.
   Web of Science ®Google Scholar
• Klimchik, A., B. Furet, S. Caro, and A. Pashkevich. 2015. Identification of the manipulator stiffness model parameters in industrial environment. Mechanism and Machine Theory 90:1–22. doi:10.1016/j.mechmachtheory.2015.03.002.
   Web of Science ®Google Scholar
• Klimchik, A., D. Chablat, and A. Pashkevich. 2014. Stiffness modeling for perfect and non-perfect parallel manipulators under internal and external loadings. Mechanism and Machine Theory 79:1–28. doi:10.1016/j.mechmachtheory.2014.04.002.
   Web of Science ®Google Scholar
• Koehler, M., A. M. Okamura, and C. Duriez. 2019. Stiffness control of deformable robots using finite element modeling. IEEE Robotics and Automation Letters 4 (2):469–76. doi:10.1109/LRA.2019.2890897.
   Web of Science ®Google Scholar
• Kövecses, J., and S. Ebrahimi. 2009. Parameter analysis and normalization for the dynamics and design of multibody systems. Journal of Computational and Nonlinear Dynamics 4 (3):031008. doi:10.1115/1.3124785.
   Web of Science ®Google Scholar
• Marie, S., E. Courteille, and P. Maurine. 2013. Elasto-geometrical modeling and calibration of robot manipulators: Application to machining and forming applications. Mechanism and Machine Theory 69:13–43. doi:10.1016/j.mechmachtheory.2013.05.003.
   Web of Science ®Google Scholar
• Nguyen-Van, S., K.-W. Gwak, D.-H. Nguyen, S.-G. Lee, and B. H. Kang. 2020. A novel modified analytical method and finite element method for vibration analysis of cable-driven parallel robots. Journal of Mechanical Science and Technology 34 (9):3575–86. doi:10.1007/s12206-020-0809-9.
   Web of Science ®Google Scholar
• Pashkevich, A., D. Chablat, and P. Wenger. 2009. Stiffness analysis of overconstrained parallel manipulators. Mechanism and Machine Theory 44 (5):966–82. doi:10.1016/j.mechmachtheory.2008.05.017.
   Web of Science ®Google Scholar
• Quintero-Riaza, H. F., L. A. Mejía-Calderón, and M. Díaz-Rodríguez. 2019. Synthesis of planar parallel manipulators including dexterity, force transmission and stiffness index. Mechanics Based Design of Structures and Machines 47 (6):680–702. doi:10.1080/15397734.2019.1615503.
   Web of Science ®Google Scholar
• Raoofian, A., A. Taghvaeipour, and A. Kamali. 2018. On the stiffness analysis of robotic manipulators and calculation of stiffness indices. Mechanism and Machine Theory 130:382–402. doi:10.1016/j.mechmachtheory.2018.08.025.
   Web of Science ®Google Scholar
• Trochimczuk, R., A. Łukaszewicz, T. Mikołajczyk, F. Aggogeri, and A. Borboni. 2019. Finite element method stiffness analysis of a novel telemanipulator for minimally invasive surgery. Simulation 95 (11):1015–25. doi:10.1177/0037549719835920.
   Google Scholar
• Wang, K., Z. Xie, Z. Li, and S. Bai. 2020. Optimum configuration design and sensitivity analysis of the 3-RRR PPMs with a general kinematic model. Mechanics Based Design of Structures and Machines. doi:10.1080/15397734.2020.1766490.
   Web of Science ®Google Scholar
• Wu, G., and P. Zou. 2017. Stiffness analysis and comparison of a biglide parallel grinder with alternative spatial modular parallelograms. Robotica 35 (6):1310–26. doi:10.1017/S0263574716000059.
   Web of Science ®Google Scholar
• Wu, G., S. Bai, and P. Hjørnet. 2016. On the stiffness of three/four degree-of-freedom parallel pick-and-place robots with four identical limbs. Paper presented at the 2016 IEEE International Conference on Robotics and Automation (ICRA), Stockholm, Sweden, May 16–21, 861–6.
   Google Scholar
• Wu, G., S. Bai, J. A. Kepler, and S. Caro. 2012. Error modeling and experimental validation of a planar 3-PPR parallel manipulator with joint clearances. Journal of Mechanisms and Robotics 4 (4):041008. doi:10.1115/1.4007487.
   Google Scholar
• Wu, X. 2019. Performance analysis and optimum design of a redundant planar parallel manipulator. Symmetry 11 (7):908. doi:10.3390/sym11070908.
   Google Scholar
• Wu, X., and S. Bai. 2019. Architectural singularities of parallel mechanisms with prismatic joints due to special designs of platform shapes. Mechanical Sciences 10 (2):449–64. doi:10.5194/ms-10-449-2019.
   Web of Science ®Google Scholar
• Wu, X., and Z. Xie. 2019. Forward kinematics analysis of a novel 3-DOF parallel manipulator. Scientia Iranica. Transaction B, Mechanical Engineering 26 (1):346–57.
   Web of Science ®Google Scholar
• Wu, X., Z. Xie, J. Asbøll Kepler, and S. Bai. 2017. A parametric model of 3-PPR planar parallel manipulators for optimum shape design of platforms. Mechanism and Machine Theory 118:139–53. doi:10.1016/j.mechmachtheory.2017.08.002.
   Web of Science ®Google Scholar
• Yan, S. J., S. K. Ong, and A. Y. C. Nee. 2016. Stiffness analysis of parallelogram-type parallel manipulators using a strain energy method. Robotics and Computer-Integrated Manufacturing 37:13–22. doi:10.1016/j.rcim.2015.05.004.
   Web of Science ®Google Scholar
• Yang, C., Q. Li, and Q. Chen. 2019. Multi-objective optimization of parallel manipulators using a game algorithm. Applied Mathematical Modelling 74:217–43. doi:10.1016/j.apm.2019.04.058.
   Web of Science ®Google Scholar
• Zarkandi, S. 2021. Kinematic analysis and workspace optimization of a novel 4RPSP + PS parallel manipulator. Mechanics Based Design of Structures and Machines 49 (1):131–53. doi:10.1080/15397734.2020.1725564.
   Web of Science ®Google Scholar
• Zhang, D., and B. Wei. 2017. Interactions and optimizations analysis between stiffness and workspace of 3-UPU robotic mechanism. Measurement Science Review 17 (2):83–92. doi:10.1515/msr-2017-0011.
   Web of Science ®Google Scholar
• Zhang, D., and Z. Gao. 2012. Forward kinematics, performance analysis, and multi-objective optimization of a bio-inspired parallel manipulator. Robotics and Computer-Integrated Manufacturing 28 (4):484–92. doi:10.1016/j.rcim.2012.01.003.
   Web of Science ®Google Scholar
• Zhao, C., H. Guo, D. Zhang, R. Liu, B. Li, and Z. Deng. 2020. Stiffness modeling of n(3RRlS) reconfigurable series-parallel manipulators by combining virtual joint method and matrix structural analysis. Mechanism and Machine Theory 152:103960. doi:10.1016/j.mechmachtheory.2020.103960.
   Web of Science ®Google Scholar
• Zou, T., and J. Angeles. 2015. The decoupling of the Cartesian stiffness matrix in the design of microaccelerometers. Multibody System Dynamics 34 (1):1–21. doi:10.1007/s11044-014-9408-9.
   Web of Science ®Google Scholar