Experimental and analytical evaluation of tool path error using computer integrated nonlinear kinematical modeling for a 4DOF parallel milling machine

References

• Akhbari, S., A. G. Alamdari, and M. Mahboubkhah. 2019. “Circular Motion Analysis for a Novel 4-DOF Parallel Kinematic Machine.” Journal of the Brazilian Society of Mechanical Sciences and Engineering 41 (5): 215. doi:https://doi.org/10.1007/s40430-019-1716-9.
   Google Scholar
• Akhbari, S., A. Z. Jond, and M. Mahboubkhah. 2018. “Kinematic and Workspace Analyses of a Novel 4-dof Parallel Mechanism.” Paper Presented at the 2018 6th RSI International Conference on Robotics and Mechatronics (Icrom) 23-25 (Oct): 2018.
   Google Scholar
• Akhbari, S., M. Mahboubkhah, and A. Gadimzadeh. 2019. “Linear Motion Analysis for a Novel 4-DOF Parallel Kinematic Machine.” Journal of the Brazilian Society of Mechanical Sciences and Engineering 41 (10): 428. doi:https://doi.org/10.1007/s40430-019-1927-0.
   Google Scholar
• Barari, A., H. A. ElMaraghy, and P. Orban. 2009. “NURBS Representation of Actual Machined Surfaces.” International Journal of Computer Integrated Manufacturing 22 (5): 395–410. doi:https://doi.org/10.1080/09511920802392730.
   Web of Science ®Google Scholar
• Bates, D. M., and D. G. Watts. 1980. “Relative Curvature Measures of Nonlinearity.” Journal of the Royal Statistical Society. Series B (Methodological) 42 (1): 1–25
   Google Scholar
• Bates, D. M., and D. G. Watts. 1988. Nonlinear Regression Analysis and Its Applications. Vol. 2. Wiley, New York: Wiley Online Library.
   Google Scholar
• Briot, S., and I. A. Bonev. 2010. “Pantopteron-4: A New 3T1R Decoupled Parallel Manipulator for Pick-and-place Applications.” Mechanism and Machine Theory 45 (5): 707–721. doi:https://doi.org/10.1016/j.mechmachtheory.2009.07.007.
   Google Scholar
• Briot, S., V. Arakelian, and G. Sylvain. 2008. “Design and Prototyping of a Partially Decoupled 4-DOF 3T1R Parallel Manipulator with High-load Carrying Capacity.” Journal of Mechanical Design 130 (12): 122303. doi:https://doi.org/10.1115/1.2991137.
   Google Scholar
• Chalak Qazani, M., S. Pedrammehr, A. Rahmani, M. Shahryari, A. K. S. Rajab, and M. M. Ettefagh. 2014. “An experimental study on motion error of hexarot parallel manipulator.” The International Journal of Advanced Manufacturing Technology 72 (9–12):1361–76. doi:https://doi.org/10.1007/s00170-014-5685-y.
   Google Scholar
• Chalak Qazani, M., S. Pedrammehr, and M. J. Nategh. 2014. “A Study on Motion of Machine Tools’ Hexapod Table on Freeform Surfaces with Circular Interpolation.” The International Journal of Advanced Manufacturing Technology:1–9. doi:https://doi.org/10.1007/s00170-014-6264-y.
   Google Scholar
• Choi, H.-B., A. Konno, and M. Uchiyama. 2009. “Closed-form Forward Kinematics Solutions of a 4-DOF Parallel Robot.” International Journal of Control, Automation, and Systems 7 (5): 858. doi:https://doi.org/10.1007/s12555-009-0520-1.
   Google Scholar
• Choi, H.-B., O. Company, F. Pierrot, A. Konno, T. Shibukawa, and M. Uchiyama. 2003. “Design and Control of a Novel 4-DOFs Parallel Robot H4. Paper Presented at the Robotics and Automation, 2003.” Proceedings of2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422). Taipei, Taiwan: IEEE International Conference.
   Google Scholar
• Cui, H., Z. Zhu, Z. Gan, and T. Brogardh. 2005. “Kinematic Analysis and Error Modeling of TAU Parallel Robot.” Robotics and Computer-Integrated Manufacturing 21 (6): 497–505. doi:https://doi.org/10.1016/j.rcim.2004.07.018.
   Google Scholar
• Demailly, J.-P. 1997. Complex Analytic and Differential Geometry. Grenoble, France: University of Grenoble.
   Google Scholar
• Dong, G., T. Sun, Y. Song, H. Gao, and B. Lian. 2014. “Mobility Analysis and Kinematic Synthesis of a Novel 4-DoF Parallel Manipulator.” Robotica 34 (5): 1010–1025. doi:https://doi.org/10.1017/S0263574714002021.
   Google Scholar
• Gallardo-Alvarado, J., M. A. García-Murillo, N. Islam, and M. H. Abedinnasab. 2017. “Kinematics of the 4-RUU Parallel Manipulator Generator of the Schönflies Motion by Means of Screw Theory.” Journal of Mechanical Science and Technology 31 (10): 4925–4932. doi:https://doi.org/10.1007/s12206-017-0941-3.
   Google Scholar
• Gogu, G. 2007. “Structural Synthesis of Fully-isotropic Parallel Robots with Schönflies Motions via Theory of Linear Transformations and Evolutionary Morphology.” European Journal of Mechanics - A/Solids 26 (2): 242–269. doi:https://doi.org/10.1016/j.euromechsol.2006.06.001.
   Google Scholar
• Guo, S., Y. Wei, Q. Haibo, D. Zhang, and Y. Fang. 2014. “A Serial of Novel Four Degrees of Freedom Parallel Mechanisms with Large Rotational Workspace.” Robotica 34 (4): 764–776. doi:https://doi.org/10.1017/S0263574714001842.
   Google Scholar
• Hee-Byoung, C., A. Konno, and M. Uchiyama. 2003. “Closed-form Solutions for the Forward Kinematics of a 4-DOFs Parallel Robot H4. Paper Presented at the Intelligent Robots and Systems, 2003. (IROS 2003).” Proceedings of 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003) (Cat. No.03CH37453), 27–31 October 2003. Las Vegas, NV, USA.
   Google Scholar
• Jean-Pierre, M. 2012. Parallel Robots. Vol. 74. The Netherlands: Springer Science & Business Media.
   Google Scholar
• Karimi, D., and M. J. Nategh. 2011. “A Statistical Approach to the Forward Kinematics Nonlinearity Analysis of Gough-Stewart Mechanism.” Journal of Applied Mathematics. Article ID: 393072.
   Google Scholar
• Karimi, D., and M. J. Nategh. 2014. “Development of a Novel Adaptive Nonuniform Rational Basis Spline Interpolator with Limited Kinematic Error for Hexapod Machine Tools.” Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 228 (3): 319–327. doi:https://doi.org/10.1177/0954405413493268.
   Google Scholar
• Karimi, D., and M. J. Nategh. 2015. “Contour Maps for Developing Optimal Toolpath and Workpiece Setup in Hexapod Machine Tools by considering the Kinematics Nonlinearity.” Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture230 (9): 1572-1583. 0954405415592123.
   Google Scholar
• Kui-Jing, Z., G. Jian-she, and Z. Yong-Sheng. 2005. “Path Control Algorithms of a Novel 5-DOF Parallel Machine Tool.” Paper presented at the Mechatronics and Automation, 2005 IEEE International Conference, 2005. Niagara Falls, ON, Canada.
   Google Scholar
• Lee, C.-C., and J. M. Hervé. 2011. ““Isoconstrained Parallel Generators of Schoenflies Motion.”.” Journal of Mechanisms and Robotics 3 (2): 021006–10. doi:https://doi.org/10.1115/1.4003690.
   Google Scholar
• Li, Z. 2000. “Reconfiguration and Tool Path Planning of Hexapod Machine Tools.”
   Google Scholar
• Liu, S., T. Huang, J. Mei, X. Zhao, P. Wang, and D. G. Chetwynd. 2012. “Optimal Design of a 4-DOF SCARA Type Parallel Robot Using Dynamic Performance Indices and Angular Constraints.” Journal of Mechanisms and Robotics 4 (3): 031005–10. doi:https://doi.org/10.1115/1.4006743.
   Google Scholar
• Lu, Y., and H. Bo. 2007. “Analyzing Kinematics and Solving Active/constrained Forces of a 3SPU+UPR Parallel Manipulator.” Mechanism and Machine Theory 42 (10): 1298–1313. doi:https://doi.org/10.1016/j.mechmachtheory.2006.11.002.
   Web of Science ®Google Scholar
• Lu, Y., Y. Shi, Z. Huang, Y. Jianping, L. Shihua, and X. Tian. 2009. “Kinematics/statics of a 4-DOF Over-constrained Parallel Manipulator with 3 Legs.” Mechanism and Machine Theory 44 (8): 1497–1506. doi:https://doi.org/10.1016/j.mechmachtheory.2008.12.001.
   Google Scholar
• Mahboubkhah, M., and A. Barari. 2019. “Design and Development of a Novel 4-DOF Parallel Kinematic Coordinate Measuring Machine (CMM).” International Journal of Computer Integrated Manufacturing 1–11. doi:https://doi.org/10.1080/0951192X.2019.1610576.
   Google Scholar
• Mahboubkhah, M., S. Akhbari, and A. Barari. 2019. “Self-configuration Machining Capability of a 4-DOF Parallel Kinematic Machine Tool with Nonsingular Workspace for Intelligent Manufacturing Systems.” IFAC-PapersOnLine 52 (10): 288–293. doi:https://doi.org/10.1016/j.ifacol.2019.10.044.
   Google Scholar
• Mathews, J. H., and K. D. Fink. 2004. Numerical Methods Using MATLAB. Vol. 4. NJ: Pearson prentice hall Upper Saddle River.
   Google Scholar
• Pakzad, S., S. Akhbari, and M. Mahboubkhah. 2019. “Kinematic and Dynamic Analyses of a Novel 4-DOF Parallel Mechanism.” Journal of the Brazilian Society of Mechanical Sciences and Engineering 41 (12): 561. doi:https://doi.org/10.1007/s40430-019-2058-3.
   Google Scholar
• Pedrammeh, S., M. R. Chalak Qazani, H. Abdi, and S. Nahavandi. 2016. “Mathematical Modelling of Linear Motion Error for Hexarot Parallel Manipulators.” Applied Mathematical Modelling 40 (2): 942–954. doi:https://doi.org/10.1016/j.apm.2015.07.004.
   Google Scholar
• Pierrot, F., and O. Company. 1999. “H4: A New Family of 4-dof Parallel Robots. Paper Presented at the Advanced Intelligent Mechatronics, 1999.” Proceedings of 1999 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (Cat. No.99TH8399). Atlanta, GA, USA.
   Google Scholar
• Pierrot, F., V. Nabat, O. Company, S. Krut, and P. Poignet. 2009. “Optimal Design of a 4-DOF Parallel Manipulator: From Academia to Industry.” IEEE Transactions on Robotics 25 (2): 213–224. doi:https://doi.org/10.1109/TRO.2008.2011412.
   Web of Science ®Google Scholar
• Qazani, M., R. Chalak, S. Pedrammehr, and M. J. Nategh. 2018. “An Investigation on the Motion Error of Machine Tools’ Hexapod Table.” International Journal of Precision Engineering and Manufacturing 19 (4): 463–471. doi:https://doi.org/10.1007/s12541-018-0056-5.
   Google Scholar
• Quarteroni, A., R. Sacco, and F. Saleri. 2010. Numerical Mathematics. Vol. 37. Springer-Verlag New York, Inc: Springer Science & Business Media.
   Google Scholar
• Rolland, L. 1999. “The Manta and the Kanuk: Novel 4-dof Parallel Mechanisms for Industrial Handling.” Proceedings of ASME Dynamic Systems and Control Division IMECE 99: 14–19.
   Google Scholar
• Seber, G. A. F., and C. J. Wild. 2003. “Nonlinear Regression. 2003” Hoboken: John Wiley & Sons Google Scholar.
   Google Scholar
• Shen, G., Y. Tang, J. Zhao, L. Hao, L. Xiang, and L. Ge. 2016. “Jacobian Free Monotonic Descent Algorithm for Forward Kinematics of Spatial Parallel Manipulator.” Advances in Mechanical Engineering 8 (4): 1687814016645447. doi:https://doi.org/10.1177/1687814016645447.
   Web of Science ®Google Scholar
• Wang, J., Z. Wang, T. Huang, and D. J. Whitehouse. 2002. “Nonlinearity for a Parallel Kinematic Machine Tool and Its Application to Interpolation Accuracy Analysis.” Science in China Series E: Technological Sciences 45 (1): 97–105. doi:https://doi.org/10.1360/02ye9012.
   Google Scholar
• Wang, L. C. T., and C. C. Chen. 1993. “On the Numerical Kinematic Analysis of General Parallel Robotic Manipulators.” IEEE Transactions on Robotics and Automation 9 (3): 272–285. doi:https://doi.org/10.1109/70.240196.
   Google Scholar
• Wang, Y., T. Huang, and C. M. Gosselin. 2004. “Interpolation Error Prediction of a Three-degree Parallel Kinematic Machine.” Journal of Mechanical Design 126 (5): 932–937. doi:https://doi.org/10.1115/1.1767184.
   Google Scholar
• Yang, C.-F., S.-T. Zheng, J. Jin, S.-B. Zhu, and J.-W. Han. 2010. “Forward Kinematics Analysis of Parallel Manipulator Using Modified Global Newton-Raphson Method.” Journal of Central South University of Technology 17 (6): 1264–1270. doi:https://doi.org/10.1007/s11771-010-0630-1.
   Google Scholar
• Yang, S., T. Sun, and T. Huang. 2017. “Type Synthesis of Parallel Mechanisms Having 3T1R Motion with Variable Rotational Axis.” Mechanism and Machine Theory 109 (Supplement C): 220–230. doi:https://doi.org/10.1016/j.mechmachtheory.2016.11.005.
   Google Scholar