Abstract
Polishing is a kind of finishing process that can effectively reduce the surface defects and improve the form accuracy. This paper presents a novel hybrid machine with 6 degrees of freedom (DOF) serial-parallel topological structure used as an ultra-precision polishing equipment which is composed of a 3-DOF parallel robot, a 2-DOF serial robot and a turntable providing a redundant DOF. Due to the complexity of structure, stiffness performance evaluation of the parallel robot becomes a challenge. As a result, a theoretical model of the parallel robot based on the virtual work principle and the deformation superposition principle is formulated for analyzing the stiffness performance. With the developed model, a multi-objective dimensional optimization method is developed to maximize both the workspace volume and the global stiffness performance of the parallel robot. Artificial intelligence approach based on genetic algorithms is implemented to obtain an optimal combination of structural parameters. The effectiveness of this method is validated by simulation and the parallel robot with optimized structural parameters has a workspace with higher stiffness performance, hence justifies its suitability for high precision polishing.
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References
Cheung, C. F., Kong, L. B., Ho, L. T., and To, S., “Modelling and Simulation of Structure Surface Generation Using Computer Controlled Ultra-Precision Polishing,” Precision Engineering, Vol. 35, No. 4, pp. 574–590, 2011.
Lin, W., Xu, P., Li, B., and Yang, X., “Path Planning of Mechanical Polishing Process for Freeform Surface with a Small Polishing Tool,” Robotics and Biomimetics, Vol. 1, No. 1, pp. 24, 2014.
Kumar, S., Jain, V. K., and Sidpara, A., “Nanofinishing of Freeform Surfaces (Knee Joint Implant) by Rotational-Magnetorheological Abrasive Flow Finishing (R-MRAFF) Process,” Precision Engineering, Vol. 42, pp. 165–178, 2015.
Allen, Y. Y., Hezlep, M., and Pol, T., “A Computer Controlled Optical Pin Polishing Machine,” Journal of Materials Processing Technology, Vol. 146, No. 2, pp. 156–162, 2004.
Kurita, T. and Hattori, M., “Development of New-Concept Desk Top Size Machine Tool,” International Journal of Machine Tools and Manufacture, Vol. 45, No. 7, pp. 959–965, 2005.
Cheng, H.-B., Feng, Z.-J., Cheng, K., and Wang, Y.-W., “Design of a Six-Axis High Precision Machine Tool and Its Application in Machining Aspherical Optical Mirrors,” International Journal of Machine Tools and Manufacture, Vol. 45, No. 9, pp. 1085–1094, 2005.
Zhao, J., Zhan, J., Jin, R., and Tao, M., “An Oblique Ultrasonic Polishing Method by Robot for Free-Form Surfaces,” International Journal of Machine Tools and Manufacture, Vol. 40, No. 6, pp. 795–808, 2000.
Basanez, L. and Rosell, J., “Robotic Polishing Systems,” IEEE Robotics & Automation Magazine, Vol. 12, No. 3, pp. 35–43, 2005.
Feng-yun, L. and Tian-sheng, L., “Development of a Robot System for Complex Surfaces Polishing Based on CL Data,” The International Journal of Advanced Manufacturing Technology, Vol. 26, Nos. 9-10, pp. 1132–1137, 2005.
Márquez, J. J., Pérez, J. M., Rıos, J., and Vizán, A., “Process Modeling for Robotic Polishing,” Journal of Materials Processing Technology, Vol. 159, No. 1, pp. 69–82, 2005.
Weck, M. and Staimer, D., “Parallel Kinematic Machine Tools-Current State and Future Potentials,” CIRP Annals-Manufacturing Technology, Vol. 51, No. 2, pp. 671–683, 2002.
Lin, W., Li, B., Yang, X., and Zhang, D., “Modelling and Control of inverse Dynamics for a 5-DOF Parallel Kinematic Polishing Machine,” International Journal of Advanced Robotic Systems, Vol. 10, No. 8, pp. 314, 2013.
Kanaan, D., Wenger, P., and Chablat, D., “Kinematic Analysis of a Serial-Parallel Machine Tool: The Verne Machine,” Mechanism and Machine Theory, Vol. 44, No. 2, pp. 487–498, 2009.
Zhang, J., Zhao, Y., and Jin, Y., “Kinetostatic-Model-Based Stiffness Analysis of Exechon PKM,” Robotics and Computer-Integrated Manufacturing, Vol. 37, pp. 208–220, 2016.
Cheng, G., Xu, P., Yang, D., and Liu, H., “Stiffness Analysis of a 3CPS Parallel Manipulator for Mirror Active Adjusting Platform in Segmented Telescope,” Robotics and Computer-Integrated Manufacturing, Vol. 29, No. 5, pp. 302–311, 2013.
Xiao, S., Li, Y., and Meng, Q., “Mobility Analysis of a 3-PUU Flexure-Based Manipulator Based on Screw Theory and Compliance Matrix Method,” International Journal of Precision Engineering and Manufacturing, Vol. 14, No. 8, pp. 1345–1353, 2013.
Klimchik, A., Chablat, D., and Pashkevich, A., “Stiffness Modeling for Perfect and Non-Perfect Parallel Manipulators Under Internal and External Loadings,” Mechanism and Machine Theory, Vol. 79, pp. 1–28, 2014.
Yan, S., Ong, S. K., and Nee, A. Y. C., “Stiffness Analysis of Parallelogram-Type Parallel Manipulators Using a Strain Energy Method,” Robotics and Computer-Integrated Manufacturing, Vol. 37, pp. 13–22, 2016.
Li, Y. and Xu, Q., “Stiffness Analysis for a 3-PUU Parallel Kinematic Machine,” Mechanism and Machine Theory, Vol. 43, No. 2, pp. 186–200, 2008.
Gao, Z., Zhang, D., and Ge, Y., “Design Optimization of a Spatial Six Degree-of-Freedom Parallel Manipulator Based on Artificial Intelligence Approaches,” Robotics and Computer-Integrated Manufacturing, Vol. 26, No. 2, pp. 180–189, 2010.
Yao, R., Tang, X., Wang, J., and Huang, P., “Dimensional Optimization Design of the Four-Cable-Driven Parallel Manipulator in Fast,” IEEE/ASME Transactions on Mechatronics, Vol. 15, No. 6, pp. 932–941, 2010.
Hosseini, M. A. and Daniali, H. M., “Cartesian Workspace Optimization of Tricept Parallel Manipulator with Machining Application,” Robotica, Vol. 33, No. 9, pp. 1948–1957, 2015.
Tao, Z. and An, Q., “Interference Analysis and Workspace Optimization of 3-RRR Spherical Parallel Mechanism,” Mechanism and Machine Theory, Vol. 69, pp. 62–72, 2013.
Chi, Z., Zhang, D., Xia, L., and Gao, Z., “Multi-Objective Optimization of Stiffness and Workspace for a Parallel Kinematic Machine,” International Journal of Mechanics and Materials in Design, Vol. 9, No. 3, pp. 281–293, 2013.
Jamwal, P. K., Xie, S., and Aw, K. C., “Kinematic Design Optimization of a Parallel Ankle Rehabilitation Robot Using Modified Genetic Algorithm,” Robotics and Autonomous Systems, Vol. 57, No. 10, pp. 1018–1027, 2009.
Yun, Y. and Li, Y., “Optimal Design of a 3-PUPU Parallel Robot with Compliant Hinges for Micromanipulation in a Cubic Workspace,” Robotics and Computer-Integrated Manufacturing, Vol. 27, No. 6, pp. 977–985, 2011.
Sun, T., Song, Y., Dong, G., Lian, B., and Liu, J., “Optimal Design of a Parallel Mechanism with Three Rotational Degrees of Freedom,” Robotics and Computer-Integrated Manufacturing, Vol. 28, No. 4, pp. 500–508, 2012.
Walker, D. D., Brooks, D., King, A., Freeman, R., Morton, R., et al., “The ‘Precessions’ Tooling for Polishing and Figuring Flat, Spherical and Aspheric Surfaces,” Optics Express, Vol. 11, No. 8, pp. 958–964, 2003.
Portman, V., Shneor, Y., Chapsky, V., and Shapiro, A., “Form-Shaping Function Theory Expansion: Stiffness Model of Multi-Axis Machines,” The International Journal of Advanced Manufacturing Technology, Vol. 76, Nos. 5-8, pp. 1063–1078, 2015.
Wang, M., Liu, H., Huang, T., and Chetwynd, D. G., “Compliance Analysis of a 3-SPR Parallel Mechanism with Consideration of Gravity,” Mechanism and Machine Theory, Vol. 84, pp. 99–112, 2015.
Jin, Y., Bi, Z. M., Liu, H. T., Higgins, C., Price, M., Chen, W. H., and Huang, T., “Kinematic Analysis and Dimensional Synthesis of Exechon Parallel Kinematic Machine for Large Volume Machining,” Journal of Mechanisms and Robotics, Vol. 7, No. 4, Paper No. 041004, 2015.
Kakinuma, Y., Igarashi, K., Katsura, S., and Aoyama, T., “Development of 5-Axis Polishing Machine Capable of Simultaneous Trajectory, Posture, and Force Control,” CIRP Annals-Manufacturing Technology, Vol. 62, No. 1, pp. 379–382, 2013.
Liao, L., Xi, F. J., and Liu, K., “Modeling and Control of Automated Polishing/Deburring Process Using a Dual-Purpose Compliant Toolhead,” International Journal of Machine Tools and Manufacture, Vol. 48, No. 12, pp. 1454–1463, 2008.
Merlet, J.-P., “Parallel Robots,” Springer Science & Business Media, 2012.
Company, O. and Pierrot, F., “Modelling and Design Issues of a 3-Axis Parallel Machine-Tool,” Mechanism and Machine Theory, Vol. 37, No. 11, pp. 1325–1345, 2002.
Cheng, G., Qiu, B.-j., Yang, D.-h., and Liu, H.-g., “Workspace Analysis of 3-CPS Parallel Micro-Manipulator for Mirror Active Adjusting Platform,” Journal of Mechanical Science and Technology, Vol. 27, No. 12, pp. 3805–3816, 2013.
Rao, A. B. K., Saha, S. K., and Rao, P. V. M., “Stiffness Analysis of Hexaslide Machine Tools,” Advanced Robotics, Vol. 19, No. 6, pp. 671–693, 2005.
Chen, J.-S. and Hsu, W.-Y., “Design and Analysis of a Tripod Machine Tool with an Integrated Cartesian Guiding and Metrology Mechanism,” Precision Engineering, Vol. 28, No. 1, pp. 46–57, 2004.
Xu, Q. and Li, Y., “An Investigation on Mobility and Stiffness of a 3-DOF Translational Parallel Manipulator via Screw Theory,” Robotics and Computer-Integrated Manufacturing, Vol. 24, No. 3, pp. 402–414, 2008.
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Xu, P., Li, B., Cheung, CF. et al. Stiffness modeling and optimization of a 3-DOF parallel robot in a serial-parallel polishing machine. Int. J. Precis. Eng. Manuf. 18, 497–507 (2017). https://doi.org/10.1007/s12541-017-0060-1
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DOI: https://doi.org/10.1007/s12541-017-0060-1