機械手臂輕量化可以提高機械手臂之靈活性、速度和安全性，同時降低能源成本和機械磨損。隨著科技的進步，對機械手臂輕量化的需求不斷增加，未來有望出現更多創新和突破，使輕量化技術在工業應用中發揮更大的作用。本研究介紹了使用薄殼元素的拓樸最佳化理論，並採用最小化應變能作為目標函數，引入了利用目標剛性對結構進行輕量化的概念，本研究也考慮了重力對拓樸最佳化的影響，最後將使用薄殼元素的拓樸最佳化流程應用於輕量化機械手臂結構的設計。為了驗證所提出最佳化方法的正確性，本研究選擇了兩種不同類型的邊界條件，分別對使用薄殼元素的拓樸最佳化流程進行測試，測試的結構分別為T型板及球殼結構，以上兩個案例可驗證本研究所提出使用薄殼元素的拓樸最佳化流程是否適用於三維空間中的結構建構，以及多方向上的施力，通過比較本研究的結果與其他研究的結果，可評估最佳化方法的效果和最佳化流程的正確性。本研究根據實際的機械手臂應用需求和現有的設計，在拓樸最佳化方法中使用薄殼元素進行設計，且考慮了不同起始體積率對設計結果的影響並進行模擬，通過有限元素分析，可確認設計結果是否符合目標剛性的要求，也討論加入重力考量對拓樸最佳化結果的影響，最後選擇最終體積率最低的結果，進行施力與變形量關係的實驗。通過實驗量測施力與結構變形量之間的關係後，將本研究所設計的拓樸圓管結構與完整圓管進行比較，本研究之設計相對完整圓管減輕約30%的重量，且在輕量化的同時提升6.2%剛性重量比。

Lightweighting of robotic arms can enhance their flexibility, speed, and safety. Recently, the demand for lightweight robotic arms continues to increase, enabling lightweighting technologies to play a greater role in industrial applications. This study introduces the theory of topology optimization using shell elements and adopts the minimization of strain energy as the objective function. The concept of setting a target stiffness to achieve lightweight structures is introduced, and the impact of gravity on topology optimization is considered. The proposed topology optimization process using shell elements is applied to the design of lightweight robotic arm structures. To validate the correctness of the proposed optimization method, two different types of boundary conditions are chosen for testing the topology optimization process using shell elements: a T-shaped plate and a spherical shell structure. These two cases demonstrate the applicability of the proposed topology optimization process using shell elements in three-dimensional space and under multi-directional loading. This study sets the target stiffness for a cylindrical robotic arm ,and then utilizes topology optimization with shell elements to design the structure. Different initial volume fractions' effects on the design results are simulated and evaluated using finite element analysis to ensure satisfaction of the target stiffness requirements. The final design with the lowest volume fraction is selected, and experiments are conducted to measure the relationship between applied forces and deformation. After measuring the force-deformation relationship, the designed topology cylindrical structure is compared with a complete cylindrical structure. The proposed design reduces weight by approximately 30% compared to the complete cylindrical structure, while simultaneously improving the stiffness-to-weight ratio by 6.2%.

[1] YLM公司網頁. https://www.ylm.com.tw/zh-TW/product/YLM_Robot.html
[2] UR 公司網頁. https://www.universal-robots.com/products/ur10-robot/
[3] A. Hentout, M. Aouache, A. Maoudj, and I. Akli, "Human–robot interaction in industrial collaborative robotics: a literature review of the decade 2008–2017," Advanced Robotics, vol. 33, no. 15-16, pp. 764-799, 2019.
[4] D. Kragic, J. Gustafson, H. Karaoguz, P. Jensfelt, and R. Krug, "Interactive, Collaborative Robots: Challenges and Opportunities," in International Joint Conferences on Artificial Intelligence, 2018, pp. 18-25.
[5] F. Vicentini, "Collaborative robotics: a survey," Journal of Mechanical Design, vol. 143, no. 4, 2021.
[6] L. Gualtieri, E. Rauch, and R. Vidoni, "Emerging research fields in safety and ergonomics in industrial collaborative robotics: A systematic literature review," Robotics and Computer-Integrated Manufacturing, vol. 67, p. 101998,2021.
[7] D. F. Braga, S. Tavares, L. F. Da Silva, P. Moreira, and P. M. De Castro, "Advanced design for lightweight structures: Review and prospects," Progress in Aerospace Sciences, vol. 69, pp. 29-39, 2014.
[8] M. Merklein, M. Lechner, T. Schneider, and R. Plettke, "Tailored heat treated profiles-enhancement of the forming limit of aluminum profiles under bending load," in Key Engineering Materials, 2012, vol. 504: Trans Tech Publ, pp.375-380.
[9] H. Hagenah, W. Böhm, T. Breitsprecher, M. Merklein, and S. Wartzack, "Modelling, construction and manufacture of a lightweight robot arm," Procedia CIRP, vol. 12, pp. 211-216, 2013.
[10] C. Pupăză, G. Constantin, and Ș. NEGRILĂ, "Computer aided engineering of industrial robots," Proceedings in Manufacturing Systems, vol. 9, no. 2, pp. 87-92, 2014.
[11] M. Bugday and M. Karali, "Design optimization of industrial robot arm to minimize redundant weight," Engineering Science and Technology, an International Journal, vol. 22, no. 1, pp. 346-352, 2019.
[12] R. Bischoff et al., "The KUKA-DLR Lightweight Robot arm-a new referenceplatform for robotics research and manufacturing," in ISR 2010 (41stinternational symposium on robotics) and ROBOTIK 2010 (6th German conference on robotics), 2010: VDE, pp. 1-8.
[13] M. Kleiner, M. Geiger, and A. Klaus, "Manufacturing of lightweight 80 components by metal forming," CIRP annals, vol. 52, no. 2, pp. 521-542, 2003.
[14] M. Cong, T. Wang, and C. S. Zhang, "A study of topology optimization design for the wafer handling robot arm," in Materials Science Forum, 2009, vol.626: Trans Tech Publ, pp. 471-476.
[15] X. Wang, D. Zhang, C. Zhao, P. Zhang, Y. Zhang, and Y. Cai, "Optimal designof lightweight serial robots by integrating topology optimization andparametric system optimization," Mechanism and Machine Theory, vol. 132,pp. 48-65, 2019.
[16] G. L. Srinivas and A. Javed, "Topology optimization of rigid-links for industrial manipulator considering dynamic loading conditions," Mechanism and Machine Theory, vol. 153, p. 103979, 2020.
[17] A. Javed, "Topology Optimization of KUKA KR16 Industrial Robot Using Equivalent Static Load Method," in 2021 IEEE International IOT,Electronics and Mechatronics Conference (IEMTRONICS), 2021: IEEE, pp. 1-6.
[18] M. G. Alkalla and M. A. Fanni, "Integrated structure/control design of highspeed flexible robot arms using topology optimization," Mechanics Based
Design of Structures and Machines, vol. 49, no. 3, pp. 381-402, 2021.
[19] M. Cavazzuti, A. Baldini, E. Bertocchi, D. Costi, E. Torricelli, and P. Moruzzi, "High performance automotive chassis design: a topology optimization based approach," Structural and Multidisciplinary Optimization, vol. 44, pp. 45-56,2011.
[20] J.-H. Zhu, W.-H. Zhang, and L. Xia, "Topology optimization in aircraft and aerospace structures design," Archives of Computational Methods in Engineering, vol. 23, pp. 595-622, 2016.
[21] O. Sigmund, "On the design of compliant mechanisms using topology optimization," Journal of Structural Mechanics, vol. 25, no. 4, pp. 493-524, 1997.
[22] S. Perai, "Methodology of compliant mechanisms and its current developments in applications: a review," American Journal of Applied Sciences, vol. 4, no. 3, pp. 160-167, 2007.
[23] B. Zhu et al., "Design of compliant mechanisms using continuum topology optimization: A review," Mechanism and Machine Theory, vol. 143, p. 103622, 2020.
[24] N. P. Van Dijk, K. Maute, M. Langelaar, and F. Van Keulen, "Level-set methods for structural topology optimization: a review," Structural and Multidisciplinary Optimization, vol. 48, pp. 437-472, 2013.
[25] M. P. Bendsøe and N. Kikuchi, "Generating optimal topologies in structural 81design using a homogenization method," Computer methods in applied mechanics and engineering, vol. 71, no. 2, pp. 197-224, 1988.
[26] M. P. Bendsøe and O. Sigmund, "Material interpolation schemes in topology optimization," Archive of applied mechanics, vol. 69, pp. 635-654, 1999.
[27] X. Huang and M. Xie, Evolutionary topology optimization of continuum structures: methods and applications. John Wiley & Sons, 2010.
[28] G. Allaire, F. Jouve, and A.-M. Toader, "Structural optimization using sensitivity analysis and a level-set method," Journal of computational physics, vol. 194, no. 1, pp. 363-393, 2004.
[29] O. Sigmund, "Design of material structures using topology optimization," Technical University of Denmark Lyngby, 1994.
[30] J. K. Guest, J. H. Prévost, and T. Belytschko, "Achieving minimum length scale in topology optimization using nodal design variables and projection functions," International journal for numerical methods in engineering, vol. 61, no. 2, pp. 238-254, 2004.
[31] O. Sigmund, "Morphology-based black and white filters for topology optimization," Structural and Multidisciplinary Optimization, vol. 33, pp. 401- 424, 2007.
[32] S. Xu, Y. Cai, and G. Cheng, "Volume preserving nonlinear density filter based on heaviside functions," Structural and Multidisciplinary Optimization, vol. 41, pp. 495-505, 2010.
[33] F. Wang, B. S. Lazarov, and O. Sigmund, "On projection methods, convergence and robust formulations in topology optimization," Structural and multidisciplinary optimization, vol. 43, pp. 767-784, 2011.
[34] R. Ansola, J. Canales, J. A. Tarrago, and J. Rasmussen, "An integrated approach for shape and topology optimization of shell structures," Computers & structures, vol. 80, no. 5-6, pp. 449-458, 2002.
[35] C. Jog, "Higher-order shell elements based on a Cosserat model, and their use in the topology design of structures," Computer Methods in Applied Mechanics and Engineering, vol. 193, no. 23-26, pp. 2191-2220, 2004.
[36] B. Hassani, S. M. Tavakkoli, and H. Ghasemnejad, "Simultaneous shape and topology optimization of shell structures," Structural and Multidisciplinary Optimization, vol. 48, pp. 221-233, 2013.
[37] S. Y. Kim, C. K. Mechefske, and I. Y. Kim, "Optimal damping layout in a shell structure using topology optimization," Journal of Sound and Vibration, vol. 332, no. 12, pp. 2873-2883, 2013.
[38] P. Kang and S.-K. Youn, "Isogeometric topology optimization of shell structures using trimmed NURBS surfaces," Finite Elements in Analysis and 82 Design, vol. 120, pp. 18-40, 2016.
[39] S. Goo, S. Wang, J. Hyun, and J. Jung, "Topology optimization of thin plate structures with bending stress constraints," Computers & Structures, vol. 175, pp. 134-143, 2016.
[40] G. Angelucci, S. M. Spence, and F. Mollaioli, "An integrated topology optimization framework for three‐dimensional domains using shell elements," The Structural Design of Tall and Special Buildings, vol. 30, no. 1, p. e1817, 2021.
[41] X. Meng, Y. Xiong, Y. M. Xie, Y. Sun, and Z.-L. Zhao, "Shape–thickness– topology coupled optimization of free-form shells," Automation in Construction, vol. 142, p. 104476, 2022.
[42] T. Ho-Nguyen-Tan and H.-G. Kim, "Level set-based topology optimization for compliance and stress minimization of shell structures using trimmed quadrilateral shell meshes," Computers & Structures, vol. 259, p. 106695, 2022.
[43] D. Benson, Y. Bazilevs, M.-C. Hsu, and T. Hughes, "Isogeometric shel analysis: the Reissner–Mindlin shell," Computer Methods in Applied Mechanics and Engineering, vol. 199, no. 5-8, pp. 276-289, 2010.
[44] J. Kiendl, K.-U. Bletzinger, J. Linhard, and R. Wüchner, "Isogeometric shell analysis with Kirchhoff–Love elements," Computer methods in applied mechanics and engineering, vol. 198, no. 49-52, pp. 3902-3914, 2009.
[45] G. Kulikov and S. Plotnikova, "Simple and effective elements based upon Timoshenko–Mindlin shell theory," Computer Methods in Applied Mechanics and Engineering, vol. 191, no. 11-12, pp. 1173-1187, 2002.
[46] C. Wang, P. Hu, and Y. Xia, "A 4-node quasi-conforming Reissner–Mindlin shell element by using Timoshenko's beam function," Finite Elements in Analysis and Design, vol. 61, pp. 12-22, 2012.
[47] E. Andreassen, A. Clausen, M. Schevenels, B. S. Lazarov, and O. Sigmund, "Efficient topology optimization in MATLAB using 88 lines of code," Structural and Multidisciplinary Optimization, vol. 43, pp. 1-16, 2011.
[48] T. E. Bruns and D. A. Tortorelli, "An element removal and reintroduction strategy for the topology optimization of structures and compliant mechanisms," International journal for numerical methods in engineering, vol.57, no. 10, pp. 1413-1430, 2003.
[49] A. Diaz and O. Sigmund, "Checkerboard patterns in layout optimization,"Structural optimization, vol. 10, pp. 40-45, 1995.
[50] O. Sigmund and J. Petersson, "Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh83 dependencies and local minima," Structural optimization, vol. 16, pp. 68-75,1998.
[51] J. E. K. Hersbøll, "3D Topology Optimization with Fatigue Constraints," Department of Mechanical and Manufacturing Engineering, Aalborg University, master thesis, 2018.
[52] O. Sigmund, "On the usefulness of non-gradient approaches in topology optimization," Structural and Multidisciplinary Optimization, vol. 43, pp. 589-596, 2011.
[53] J. Wu, A. Clausen, and O. Sigmund, "Minimum compliance topology optimization of shell–infill composites for additive manufacturing," Computer Methods in Applied Mechanics and Engineering, vol. 326, pp. 358-375, 2017.
[54] B. Zheng, C.-j. Chang, and H. C. Gea, "Topology optimization considering body forces," International Journal for Simulation and Multidisciplinary Design Optimization, vol. 3, no. 1, pp. 316-320, 2009.
[55] K. Svanberg, "The method of moving asymptotes—a new method for structural optimization," International journal for numerical methods in engineering, vol. 24, no. 2, pp. 359-373, 1987.
[56] K. Svanberg, "MMA and GCMMA-two methods for nonlinear optimization," vol, vol. 1, pp. 1-15, 2007.
[57] H. Lin, A. Xu, A. Misra, and R. Zhao, "An ANSYS APDL code for topology optimization of structures with multi-constraints using the BESO method with dynamic evolution rate (DER-BESO)," Structural and Multidisciplinary Optimization, vol. 62, pp. 2229-2254, 2020.
[58] SOCO 公司網頁. https://www.soco.com.tw/product.php?lang=tw