Workspace-constrained optimal design of three-degrees-of-freedom parallel manipulators with minimum parasitic motions by integrating interval analysis, region mapping and differential evolution

References

• Alefeld, G., and G. Herzberger. 1983. Introduction to Interval Computations.: Academic Press.
   Google Scholar
• Brest, J., S. Greiner, B. Bošković, M. Mernik, and V. Žumer. 2006. “Self-Adaptive Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems.” IEEE Transactions on Evolutionary Computation 10 (6): 646–657. doi: 10.1109/TEVC.2006.872133
   Web of Science ®Google Scholar
• Carretero, J. A., M. A. Nahon, C. M. Gosselin, and B. Buckham. 1997. “Kinematic Analysis of a Three-DOF Parallel Mechanism for Telescope Applications.” In Proceedings of the 1997 ASME Design Engineering Technical Conference (DETC‘97), Sacramento, CA, September 14–17, 1–8. Paper Number DAC-3981.
   Google Scholar
• Carretero, J. A., M. A. Nahon, and R. P. Podhorodeski. 2000a. “Workspace Analysis and Optimization of a Novel 3-DOF Parallel Manipulator.” International Journal of Robotics and Automation 15 (4): 178–188.
   Google Scholar
• Carretero, J. A., R. P. Podhorodeski, M. A. Nahon, and C. M. Gosselin. 2000b. “Kinematic Analysis and Optimization of a New Three Degree-of-Freedom Spatial Parallel Manipulator.” Journal of Mechanical Design 122 (1): 17–24. doi: 10.1115/1.533542
   Web of Science ®Google Scholar
• Chen, J., B. Xin, Z. Peng, L. Dou, and J. Zhang. 2009. “Optimal Contraction Theorem for Exploration–Exploitation Tradeoff in Search and Optimization.” IEEE Transactions on Systems, Man, and Cybernetics—Part A: Systems and Humans 39 (3): 680–691. doi: 10.1109/TSMCA.2009.2012436
   Web of Science ®Google Scholar
• Coello Coello, C. A. 2002. “Theoretical and Numerical Constraint-Handling Techniques Used With Evolutionary Algorithms: A Survey of the State of the Art.” Computer Methods in Applied Mechanics and Engineering 191 (11–12): 1245–1287. doi: 10.1016/S0045-7825(01)00323-1
   Web of Science ®Google Scholar
• Das, S., and P. N. Suganthan. 2011. “Differential Evolution: A Survey of the State-of-the-Art.” IEEE Transactions on Evolutionary Computation 15 (1): 4–31. doi: 10.1109/TEVC.2010.2059031
   Web of Science ®Google Scholar
• Deb, K. 2000. “An Efficient Constraint Handling Method for Genetic Algorithms.” Computer Methods in Applied Mechanics and Engineering 186 (2–4): 311–338. doi: 10.1016/S0045-7825(99)00389-8
   Web of Science ®Google Scholar
• Elishakoff, I., and Y. Miglis. 2012. “Overestimation-Free Computational Version of Interval Analysis.” International Journal for Computational Methods in Engineering Science and Mechanics 13 (5): 319–328. doi: 10.1080/15502287.2012.683134
   Google Scholar
• Fang, H., and J. P. Merlet. 2005. “Multi-Criteria Optimal Design of Parallel Manipulators Based on Interval Analysis.” Mechanism and Machine Theory 40 (2): 157–171. doi: 10.1016/j.mechmachtheory.2004.07.002
   Web of Science ®Google Scholar
• Feng, C., S. Cong, H. Shan, W. Shang, and Y. Zhang. 2009. “Self-Calibration for Kinematic Parameters of a Redundant Planar Two-Degree-of-Freedom Parallel Manipulator Using Evolutionary Algorithms.” Engineering Optimization 41 (4): 385–398. doi: 10.1080/03052150802582159
   Web of Science ®Google Scholar
• Gough, V. E., and S. G. Whitehall. 1962. “Universal Tyre Test Machine.” In Proceedings of the FISITA Ninth International Technical Congress, May, 117–135. London: The Institution of Mechanical Engineers.
   Google Scholar
• Jaulin, L., and M. Kieffer. 2001. Applied Interval Analysis: With Examples in Parameter and State Estimation, Robust Control and Robotics. Berlin: Springer-Verlag.
   Google Scholar
• Lee, K. M., and D. K. Shah. 1988. “Kinematic Analysis of a 3-Degrees-of-Freedom in-Parallel Actuated Manipulator.” IEEE Journal of Robotics and Automation 4 (3): 354–360. doi: 10.1109/56.796
   Google Scholar
• Li, Q. C., Z. Chen, Q. H. Chen, C. Y. Wu, and Z. Huang. 2010. “Structural Condition for [PP]S Parallel Mechanism Without Parasitic Motion.” Journal of Mechanical Engineering 46 (15): 31–35. doi: 10.3901/JME.2010.15.031
   Google Scholar
• Li, Q. C., and J. M. Hervé. 2010. “1T2R Parallel Mechanisms Without Parasitic Motion.” IEEE Transactions on Robotics 26 (3): 401–410. doi: 10.1109/TRO.2010.2047528
   Web of Science ®Google Scholar
• Merlet, J. P. 2001. “Micro Parallel Robot MIPS for Medical Applications.” In Proceedings of the IEEE International Conference on Emerging Technologies and Factory Automation, Antibes, France, October 15–18, 611–619. Los Alamitos, CA: IEEE Computer Society.
   Google Scholar
• Merlet, J. P. 2002. “Still a Long Way to Go on the Road for Parallel Mechanisms.” Keynote Speech Presented at the ASME 2002 International Design Engineering Technical Conference and Computers and Information in Engineering Conference, Montréal, Quebec, Canada, September 29–October 2.
   Google Scholar
• Miguel, G. V. C., A. C. V. Carlos, A. G. Jaime, and A. P. F. Edgar. 2010. “Differential Evolution Techniques for the Structure-Control Design of a Five-Bar Parallel Robot.” Engineering Optimization 42 (6): 535–565. doi: 10.1080/03052150903325557
   Web of Science ®Google Scholar
• Moore, Ramón E.. 1979. Methods and Applications of Interval Analysis. Vol. 2 of SIAM Studies in Applied Mathematics. Philadelphia, PA: SIAM.
   Google Scholar
• Nahon, M., R. Ricard, and C. M. Gosselin. 1995. “A Comparison of Flight Simulator Motion-Base Architectures.” In Proceedings of the CEAS Symposium on Simulation Technology, Delft, The Netherlands, November, 1–16.
   Google Scholar
• Pond, G., and J. A. Carretero. 2009. “Architecture Optimisation of Three 3-PRS Variants for Parallel Kinematic Machining.” Robotics and Computer-Integrated Manufacturing 25 (1): 64–72. doi: 10.1016/j.rcim.2007.09.002
   Google Scholar
• Price, Kenneth, Rainer M. Storn, and Jouni A. Lampinen. 2005. Differential Evolution: A Practical Approach to Global Optimization. Natural Computing Series, edited by G. Rozenberg, T. Bäck, A. E. Eiben, J. N. Kok, and H. P. Spaink, 1st ed. New York: Springer-Verlag.
   Google Scholar
• Qin, A. K., V. L. Huang, and P. N. Suganthan. 2009. “Differential Evolution Algorithm with Strategy Adaptation for Global Numerical Optimization.” IEEE Transactions on Evolutionary Computation 13 (2): 398–417. doi: 10.1109/TEVC.2008.927706
   Web of Science ®Google Scholar
• Qu, H. B., Y. F. Fang, and S. Guo. 2012. “Parasitic Rotation Evaluation and Avoidance of 3-UPU Parallel Mechanism.” Frontiers of Mechanical Engineering 7 (2): 210–218. doi: 10.1007/s11465-012-0317-4
   Google Scholar
• Rahnamayan, S., H. R. Tizhoosh, and M. M. A. Salama. 2008. “Opposition-Based Differential Evolution.” IEEE Transactions on Evolutionary Computation 12 (1): 64–79. doi: 10.1109/TEVC.2007.894200
   Web of Science ®Google Scholar
• Runarsson, T. P., and X. Yao. 2000. “Stochastic Ranking for Constrained Evolutionary Optimization.” IEEE Transactions on Evolutionary Computation 4 (3): 284–294. doi: 10.1109/4235.873238
   Web of Science ®Google Scholar
• Stewart, D. 1965. “A Platform with Six Degrees of Freedom.” Proceedings of the Institution of Mechanical Engineers 180 (1): 371–386. doi: 10.1243/PIME_PROC_1965_180_029_02
   Google Scholar
• Storn, R., and K. Price. 1997. “Differential Evolution—a Simple and Efficient Heuristic for Global Optimization Over Continuous Spaces.” Journal of Global Optimization 11 (4): 341–359. doi: 10.1023/A:1008202821328
   Web of Science ®Google Scholar
• Tahmasebi, F., and L. W. Tsai. 1995. “On the Stiffness of a Novel Six-Degree-Freedom Parallel Minimanipulator.” Journal of Robotic Systems 12 (12): 845–856. doi: 10.1002/rob.4620121208
   Google Scholar
• Tang, X. Y., and I. M. Chen. 2006. “A Large-Displacement 3-DOF Flexure Parallel Mechanism with Decoupled Kinematics Structure.” In Proceedings of the 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems, Beijing, PR China, October 9–15, 1668–1673. Los Alamitos, CA: IEEE Computer Society.
   Google Scholar
• Tsai, M. S., T. N. Shiau, Y. J. Tsai, and T. H. Chang. 2002. “Direct Kinematic Analysis of a 3-PRS Parallel Manipulator.” Mechanism and Machine Theory 38 (1): 71–83. doi: 10.1016/S0094-114X(02)00069-1
   Google Scholar
• Xu, Q. S., and Y. M. Li. 2008. “Design of a Partially Decoupled High Precision XYZ Compliant Parallel Micromanipulator.” In Proceedings of the 3rd IEEE International Conference on Nano/Micro Engineered and Molecular Systems (NEMS 2008), Sanya, PR China, January 6–9, 13–18. Los Alamitos, CA: IEEE Computer Society.
   Google Scholar