本研究利用三維撓性機構拓樸最佳化方法來設計氣動軟性致動器，藉由多個軟性致動器的組合來設計二指式及三指式的氣動軟性夾爪。致動器採用矽膠軟性材料，並以模具成型加工製作。在氣動軟性致動器之三維拓樸最佳化流程中，採用交互位能最大化為目標函數。為了更精確的描述氣動軟性致動器之彎曲能力，本研究提出一個雙輸出端邊界條件，以致動器指節中央固定、兩端輸出方式來進行拓樸最佳化設計，其獲得之致動器彎曲能力較以一端固定、另一端輸出之邊界條件佳。氣囊部分設定為非設計區間，經過調整氣囊之尺寸、厚度及間距來獲得較佳之彎曲能力。另外，考量製造可行性及致動器彎曲能力，定義共六項篩選準則，依準則挑選出一組最佳的結果來進行夾爪試作。本研究進行致動器之空負載彎曲能力測試、推力測試與二指式氣動夾爪及三指式氣動夾爪之夾取範圍測試、最大負載重量測試與實物夾取測試。由實驗結果顯示，致動器在輸入壓力為60 kPa時，其彎曲角度為117度，較市售SRT致動器高172%；致動器在輸入壓力為80 kPa時，其指尖點推力為9.16 N，平均推力相較市售SRT致動器高78%；二指式夾爪於壓力80 kPa時，最大負載重量為2.7 kg，平均負載重量較市售SRT二指式夾爪高44%；三指式夾爪於壓力80 kPa時，最大負載重量為5.1 kg，平均負載重量較市售SRT三指式夾爪高140%。且夾爪可夾取形狀、尺寸不同之目標物，且夾取脆弱易碎之目標物時，不會造成目標物損傷。

　This study presents a 3D topology optimization method to design the soft pneumatic actuator. Two-finger and three-finger gripper are designed by combination of multiple soft actuators which are made of soft silicone material through the molding process. The maximization of mutual potential energy (MPE) is used as the objective function in the 3D topology optimization process to design the soft pneumatic actuator. In order to express the bending ability of the soft pneumatic actuator, this study proposes a dual-output port boundary condition that one segment of the actuator is fixed at the center and the two output ports are at two free ends. The bending ability of the device designed by the proposed boundary condition is better than the general boundary condition that one end is fixed and the output port is at the other end. The air chamber is the non-design domain in the topology optimization, and its size, thickness and spacing are design parameters. In addition, by considering the feasibility of manufacturing, and the bending ability of the actuator, six criteria are defined to select the best design for prototype. In this study, the bending test of the actuator, grasping-range test, payload test and grasping test of the two-finger and three-finger gripper are performed. The experimental results show that when the input pressure of the actuator is 60 kPa, its bending angle is 117 degrees, which is 172% higher than that of the commercial SRT actuator. When the pressure of the two-finger gripper is 80 kPa, the maximum payload is 2.7 kg; the averaged payload is 44% higher than that of the commercial SRT two-finger gripper. When the pressure of the three-finger gripper is 80 kPa, the maximum payload is 5.1 kg, and the averaged payload is 140% higher than the commercial SRT three-finger gripper. The test results show that the developed grippers can be used to grasp size-varied delicate objects without causing damage to the objects.

[1] FESTO公司網頁. https://www.festo.com/tw/zh/e/about-festo-id_3847/.
[2] ROBOTIQ公司網頁. https://robotiq.com/.
[3] TOYO公司網頁. https://www.toyorobot.com/.
[4] Softrobotics公司網頁https://www.softroboticsinc.com/.
[5] L. L. Howell, "Compliant mechanisms," 21st Century Kinematics：Springer, pp. 160-167, 2013.
[6] SRT公司網頁. http://en.softrobottech.com/.
[7] SoftGripping公司網頁. https://soft-gripping.com/.
[8] EMPIRE-ROBOTICS公司網頁. https://www.empirerobotics.com/.
[9] H. Zhang, A. S. Kumar, J. Y. H. Fuh, and M. Y. Wang, "Design and development of a topology-optimized three-dimensional printed soft gripper," Soft Robotics, vol. 5, no. 5, pp. 650-661, 2018.
[10] PIAB公司網頁. https://www.piab.com/.
[11] M. T. Tolley, R. F. Shepherd, B. Mosadegh, R. J. Wood, and G. M. Whitesides, "Resilient, Untethered Soft Robot," U.S. Patent No. 10689044, 2015.
[12] J. A. Lessing, R. Knopf, K. Alcedo, D. V. Harburg, and S. P. Singh, "Soft Robotic Grippers for Cluttered Grasping Environments, High Acceleration Movements, Food Manipulation, and Automated Storage and Retrieval Systems," U.S. Patent No. 32455986, 2017.
[13] K. C. Galloway, R. J. Wood, and K. Becker, "Soft Robotic Actuators and Grippers," U.S. Patent No. 10780591, 2019.
[14] 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.
[15] L. L. Howell, S. P. Magleby, B. M. Olsen, and J. Wiley, Handbook of compliant mechanisms. Wiley Online Library. 2013.
[16] O. Sigmund, "Topology optimization: a tool for the tailoring of structures and materials," Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, vol. 358, no. 1765, pp. 211-227, 2000.
[17] A. Milojević, S. Linß, L. Zentner, N. T. Pavlović, N. D. Pavlović, T. Petrović, M. Milošević, and M. Tomić, "Optimal design of adaptive compliant mechanisms with inherent actuators comparing discrete structures with continuum structures incorporating flexure hinges," Proceedings of the 58th IWK, Ilmenau Scientific Colloquium, Technische Universität Ilmenau, 2014.
[18] 邱震華, 拓樸與尺寸最佳化於自適性撓性夾爪機械利益最大化設計之研究, 國立成功大學機械工程學系碩士學位論文. 2016.
[19] S. Nishiwaki, M. I. Frecker, S. Min, and N. Kikuchi, "Topology optimization of compliant mechanisms using the homogenization method," International Journal for Numerical Methods in Engineering, vol. 42, no. 3, pp. 535-559, 1998.
[20] M. P. Bendsøe and O. Sigmund, "Material interpolation schemes in topology optimization," Archive of Applied Mechanics, vol. 69, no. 9-10, pp. 635-654, 1999.
[21] M. Y. Wang, S. Chen, X. Wang, and Y. Mei, "Design of multimaterial compliant mechanisms using level-set methods," Journal of mechanical design, vol. 127, no. 5, pp. 941-956, 2005.
[22] M. Y. Wang, X. Wang, and D. Guo, "A level set method for structural topology optimization," Computer Methods in Applied Mechanics and Engineering, vol. 192, no. 1-2, pp. 227-246, 2003.
[23] 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.
[24] B. S. Lazarov and O. Sigmund, "Filters in topology optimization based on Helmholtz‐type differential equations," International Journal for Numerical Methods in Engineering, vol. 86, no. 6, pp. 765-781, 2011.
[25] O. Sigmund, "On the design of compliant mechanisms using topology optimization," Journal of Structural Mechanics, vol. 25, no. 4, pp. 493-524, 1997.
[26] X. Huang and M. Xie, Evolutionary Topology Optimization of Continuum Structures: Methods and Applications. John Wiley & Sons. 2010.
[27] O. Sigmund, "A 99 line topology optimization code written in Matlab," Structural and multidisciplinary optimization, vol. 21, no. 2, pp. 120-127, 2001.
[28] 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.
[29] M. Y. Wang, "Mechanical and geometric advantages in compliant mechanism optimization," Frontiers of Mechanical Engineering in China, vol. 4, no. 3, pp. 229-241, 2009.
[30] S. Chen and M. Y. Wang, "Designing distributed compliant mechanisms with characteristic stiffness," Proceedings of the International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2007.
[31] Z. Luo, L. Tong, M. Y. Wang, and S. Wang, "Shape and topology optimization of compliant mechanisms using a parameterization level set method," Journal of Computational Physics, vol. 227, no. 1, pp. 680-705, 2007.
[32] M. Frecker, G. Ananthasuresh, S. Nishiwaki, N. Kikuchi, and S. Kota, "Topological synthesis of compliant mechanisms using multi-criteria optimization," ASME Journal of Mechanical Design, vol. 119, no. 2, pp. 238-245, 1997.
[33] B. Zhu, X. Zhang, H. Zhang, J. Liang, H. Zang, H. Li, and R. Wang, "Design of compliant mechanisms using continuum topology optimization: A review," Mechanism and Machine Theory, vol. 143, 2020.
[34] J. Shintake, V. Cacucciolo, D. Floreano, and H. Shea, "Soft robotic grippers," Advanced Materials, vol. 30, no. 29, 2018.
[35] R. F. Shepherd, F. Ilievski, W. Choi, S. A. Morin, A. A. Stokes, A. D. Mazzeo, X. Chen, M. Wang, and G. M. Whitesides, "Multigait soft robot," Proceedings of the national academy of sciences, 2011.
[36] J. Fras and K. Althoefer, "Soft biomimetic prosthetic hand: Design, manufacturing and preliminary examination," Proceedings of 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2018.
[37] P. Paoletti, G. Jones, and L. Mahadevan, "Grasping with a soft glove: intrinsic impedance control in pneumatic actuators," Journal of the Royal Society Interface, vol. 14, no. 128, 2017.
[38] E. M. de Souza and E. C. N. Silva, "Topology optimization applied to the design of actuators driven by pressure loads," Structural and Multidisciplinary Optimization, pp. 1-24, 2020.
[39] K. Suzumori, S. Iikura, and H. Tanaka, "Development of flexible microactuator and its applications to robotic mechanisms," Proceedings of the 1991 IEEE International Conference on Robotics and Automation, 1991.
[40] F. Ilievski, A. D. Mazzeo, R. F. Shepherd, X. Chen, and G. M. Whitesides, "Soft robotics for chemists," Angewandte Chemie, vol. 123, no. 8, pp. 1930-1935, 2011.
[41] K. Liu and A. Tovar, "An efficient 3D topology optimization code written in Matlab," Structural and Multidisciplinary Optimization, vol. 50, no. 6, pp. 1175-1196, 2014.
[42] O. Sigmund, "Morphology-based black and white filters for topology optimization," Structural and Multidisciplinary Optimization, vol. 33, no. 4-5, pp. 401-424, 2007.
[43] R. T. Shield and W. Prager, "Optimal structural design for given deflection," Zeitschrift für angewandte Mathematik und Physik ZAMP, vol. 21, no. 4, pp.
513-523, 1970.
[44] M. P. Bendsoe and O. Sigmund, Topology optimization: theory, methods, and applications. Springer Science & Business Media. 2013.
[45] 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.
[46] J.-i. Koga, J. Koga, and S. Homma, "Checkerboard Problem to Topology Optimization of Continuum Structures," Computational Engineering, Finance, and Science, 2013.
[47] F. Wang, B. S. Lazarov, and O. Sigmund, "On projection methods, convergence and robust formulations in topology optimization," Structural and Multidisciplinary Optimization, vol. 43, no. 6, pp. 767-784, 2011.
[48] T. E. Bruns and D. A. Tortorelli, "Topology optimization of non-linear elastic structures and compliant mechanisms," Computer Methods in Applied Mechanics and Engineering, vol. 190, no. 26-27, pp. 3443-3459, 2001.
[49] K. Svanberg, "MMA and GCMMA-two methods for nonlinear optimization," Technical report, 2007.
[50] Smooth-on公司網頁. https://www.smooth-on.com/products/dragon-skin-30/.
[51] CNS 3553:2016 硫化或熱塑性橡膠－拉伸應力－應變性質之測定, 中華民國國家標準, 2016.
[52] H. Li, J. Yao, P. Zhou, X. Chen, Y. Xu, and Y. Zhao, "High-force soft pneumatic actuators based on novel casting method for robotic applications," Sensors and Actuators A: Physical, vol. 306, 2020.
[53] K. C. Galloway, K. P. Becker, B. Phillips, J. Kirby, S. Licht, D. Tchernov, R. J. Wood, and D. F. Gruber, "Soft robotic grippers for biological sampling on deep reefs," Soft Robotics, vol. 3, no. 1, pp. 23-33, 2016.
[54] P. Polygerinos, S. Lyne, Z. Wang, L. F. Nicolini, B. Mosadegh, G. M. Whitesides, and C. J. Walsh, "Towards a soft pneumatic glove for hand rehabilitation," Proceeding of the 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2013.
[55] S. Terryn, J. Brancart, D. Lefeber, G. Van Assche, and B. Vanderborght, "Self-healing soft pneumatic robots," Science Robotics, vol. 2, no. 9, 2017.
[56] H. K. Yap, H. Y. Ng, and C.-H. Yeow, "High-force soft printable pneumatics for soft robotic applications," Soft Robotics, vol. 3, no. 3, pp. 144-158, 2016.
[57] ImageJ公司網頁. https://imagej.net/Welcome.
[58] Y. Elsayed, A. Vincensi, C. Lekakou, T. Geng, C. M. Saaj, T. Ranzani, M. Cianchetti, and A. Menciassi, "Finite element analysis and design optimization
of a pneumatically actuating silicone module for robotic surgery applications," Soft Robotics, vol. 1, no. 4, pp. 255-262, 2014.
[59] M. Luo, M. Agheli, and C. D. Onal, "Theoretical modeling and experimental analysis of a pressure-operated soft robotic snake," Soft Robotics, vol. 1, no. 2, pp. 136-146, 2014.
[60] H. K. Yap, J. C. H. Goh, and R. C. H. Yeow, "Design and characterization of soft actuator for hand rehabilitation application," Proceeding of the 6th European conference of the International Federation for Medical and Biological Engineering, 2015.
[61] 允統財公司. https://yttpump.com.tw/product-43.html.
[62] J. H. Low, W. W. Lee, P. M. Khin, N. V. Thakor, S. L. Kukreja, H. L. Ren, and C. H. Yeow, "Hybrid tele-manipulation system using a sensorized 3-D-printed soft robotic gripper and a soft fabric-based haptic glove," IEEE Robotics and Automation Letters, vol. 2, no. 2, pp. 880-887, 2017.
[63] G. Miron, B. Bédard, and J.-S. Plante, "Sleeved bending actuators for soft grippers: A durable solution for high force-to-weight applications," Actuators, vol. 7, no. 3, 2018.
[64] W. Park, S. Seo, and J. Bae, "A hybrid gripper with soft material and rigid structures," IEEE Robotics and Automation Letters, vol. 4, no. 1, pp. 65-72, 2018.
[65] Z. Wang, Y. Torigoe, and S. Hirai, "A prestressed soft gripper: design, modeling, fabrication, and tests for food handling," IEEE Robotics and Automation Letters, vol. 2, no. 4, pp. 1909-1916, 2017.
[66] P. M. Khin, H. K. Yap, M. H. Ang, and C.-H. Yeow, "Fabric-based actuator modules for building soft pneumatic structures with high payload-to-weight ratio," Proceeding of the 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2017.
[67] H. Zhang, A. S. Kumar, F. Chen, J. Y. Fuh, and M. Y. Wang, "Topology optimized multimaterial soft fingers for applications on grippers, rehabilitation, and artificial hands," IEEE/ASME Transactions on Mechatronics, vol. 24, no. 1, pp. 120-131, 2018.