本研究利用拓樸最佳化方法於等力輸出撓性機構之設計，並成功設計出一個等力輸出撓性夾爪。在自動化取放產業中，脆弱目標物的取放是一大挑戰，傳統的剛性夾爪可以藉由額外的感測器取得力量回饋或位置回饋，進而穩定夾取脆弱目標物，但其所需零件多，且造價高昂。相反的，撓性夾爪因其結構特性，在夾持脆弱目標物時較不會造成損傷，且撓性夾爪具備一體成形、製作成本低及無背隙等優點。盡管撓性夾爪擁有上述優點，在夾取脆弱目標物時，其輸出力量的控制也是重點，因此等力輸出撓性夾爪可以最穩定的夾取脆弱目標物。撓性機構在作動時，結構通常為大變形，因此本研究之拓樸最佳化方法使用幾何非線性有限元素法進行結構分析。在非線性有限元素法分析過程中，低密度元素容易有網格大變形問題，本研究於低密度元素中加入超彈性體克服此問題。等力輸出最佳化問題可視為誤差最小化問題，是一個多準則最佳化問題，因此本研究使用移動漸近線方法(Method of Moving Asymptotes)更新設計變數。本研究發展之拓樸最佳化方法在對三種設計邊界進行最佳化後，在目標輸出端皆成功獲得等力輸出。得到最佳化結構後，本研究提出三項分析準則對最佳化結構進行分析，此三項準則分別是非線性有限元素法動態分析、結構最大應力與輸入位移關係，以及灰階元素數量統計。本研究之拓樸最佳化結果於靜態及動態分析中，其目標輸出端輸出力量為等力輸出，且根據最大應力與輸入位移關係可得知，結構在作動過程中，其最大應力皆沒有超過其材料抗拉強度。最後本研究發展出的等力輸出撓性機構拓樸最佳化方法能成功設計出等力輸出撓性機構及等力輸出撓性夾爪，此方法可於後續研究中，針對不同應用環境，設計專屬的等力輸出撓性機構。

This study presents a topology optimization procedure to design compliant mechanisms with constant output force. The constant output force optimization problem can be treated as the error minimization problem, which is a multi-criteria optimization problem. Therefore, this study uses the method of moving asymptotes (MMA) to update the design variables. When a compliant mechanism is actuated, the displacement of the structure is usually large, as a result, geometrically nonlinear finite element method is used for structural analysis. In this study, hyperelastic material is added to low-density elements to overcome mesh distortion problems. The topology optimization method developed in this study can successfully obtain constant output force at the target output port. After the optimization results are identified, dynamic finite element analysis is performed to verify the dynamic response of constant force mechanism. The results show the optimized structures can generate constant output force in both static and dynamic finite element analysis. Furthermore, according to the relationship between the maximum stress and the input displacement, the maximum stress of the structure during the operation is smaller than the tensile strength of the material. Finally, the topology optimization procedure developed in this study can successfully design the compliant constant force mechanisms and the compliant grippers with constant output force.

[1] Guthart, G.S. and J.K. Salisbury. The Intuitive/sup TM/telesurgery system: overview and application. in Robotics and Automation, 2000. Proceedings. ICRA'00. IEEE International Conference on. 2000.
[2] 台灣氣立公司網頁. http://www.chelic.com/.
[3] 上銀科技網頁. http://www.hiwin.com.tw/.
[4] SCHUNK公司網頁. https://schunk.com/tw_en/homepage/.
[5] FESTO公司網頁. https://www.festo.com/cms/zh-tw_tw/index.htm.
[6] 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. 成功大學機械工程學系學位論文, 2016: p. 1-163.
[7] Perai, S., Methodology of compliant mechanisms and its current developments in applications: a review. American Journal of Applied Sciences, 2007. 4(3): p. 160-167.
[8] Li, Y., Topology optimization of compliant mechanisms based on the BESO method. RMIT University, 2014.
[9] Mølhave, K. and O. Hansen, Electro-thermally actuated microgrippers with integrated force-feedback. Journal of Micromechanics and Microengineering, 2005. 15(6): p. 1265.
[10] Beyeler, F., A. Neild, S. Oberti, D.J. Bell, Y. Sun, J. Dual, and B.J. Nelson, Monolithically fabricated microgripper with integrated force sensor for manipulating microobjects and biological cells aligned in an ultrasonic field. Journal of Microelectromechanical Systems, 2007. 16(1): p. 7-15.
[11] Dollar, A.M. and R.D. Howe, A robust compliant grasper via shape deposition manufacturing. IEEE/ASME Transactions on Mechatronics, 2006. 11(2): p. 154-161.
[12] Wang, P. and Q. Xu, Design and modeling of constant-force mechanisms: A survey. Mechanism and Machine Theory, 2018. 119: p. 1-21.
[13] Pedersen, C., N. Fleck, and G. Ananthasuresh, Design of a compliant mechanism to modify an actuator characteristic to deliver a constant output force. Journal of Mechanical Design, 2006. 128(5): p. 1101-1112.
[14] Wang, J.-Y. and C.-C. Lan, A constant-force compliant gripper for handling objects of various sizes. Journal of Mechanical Design, 2014. 136(7): p. 071008.
[15] Liu, Y., Y. Zhang, and Q. Xu, Design and control of a novel compliant constant-force gripper based on buckled fixed-guided beams. IEEE/ASME Transactions on Mechatronics, 2017. 22(1): p. 476-486.
[16] Howell, L.L., S.P. Magleby, and B.M. Olsen, Handbook of compliant mechanisms. 2013: John Wiley & Sons.
[17] Bendsøe, M.P. and O. Sigmund, Topology Optimization-Theory, Methods and Applications. 2003.
[18] Bendsøe, M.P. and O. Sigmund, Material interpolation schemes in topology optimization. Archive of Applied Mechanics, 1999. 69(9-10): p. 635-654.
[19] Bendsøe, M.P. and N. Kikuchi, Generating optimal topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering, 1988. 71(2): p. 197-224.
[20] Huang, X. and M. Xie, Evolutionary topology optimization of continuum structures: methods and applications. 2010: John Wiley & Sons.
[21] Sigmund, O., A 99 line topology optimization code written in Matlab. Structural and Multidisciplinary Optimization, 2001. 21(2): p. 120-127.
[22] Bertsekas, D.P., Nonlinear programming. 1999: Athena scientific Belmont.
[23] Svanberg, K., The method of moving asymptotes—a new method for structural optimization. International Journal for Numerical Methods in Engineering, 1987. 24(2): p. 359-373.
[24] Sigmund, O., On the design of compliant mechanisms using topology optimization. Journal of Structural Mechanics, 1997. 25(4): p. 493-524.
[25] Pedersen, C.B., T. Buhl, and O. Sigmund, Topology synthesis of large‐displacement compliant mechanisms. International Journal for Numerical Methods in Engineering, 2001. 50(12): p. 2683-2705.
[26] Liu, C.-H., G.-F. Huang, C.-H. Chiu, and T.-L. Chen. Topology and size optimization of an adaptive compliant gripper to maximize the geometric advantage. in Advanced Intelligent Mechatronics (AIM), 2016 IEEE International Conference on. 2016.
[27] Liu, C.-H. and C.-H. Chiu. Optimal design of a soft robotic gripper with high mechanical advantage for grasping irregular objects. in Robotics and Automation (ICRA), 2017 IEEE International Conference on. 2017.
[28] Holtzer, B., Topology Optimization of Geometrically Nonlinear Structures. Technische Universiteit Delft, 2017.
[29] Yoon, G.H. and Y.Y. Kim, Element connectivity parameterization for topology optimization of geometrically nonlinear structures. International Journal of Solids and Structures, 2005. 42(7): p. 1983-2009.
[30] van Dijk, N.P., M. Langelaar, and F. van Keulen, Element deformation scaling for robust geometrically nonlinear analyses in topology optimization. Structural and Multidisciplinary Optimization, 2014. 50(4): p. 537-560.
[31] Liu, L., J. Xing, Q. Yang, and Y. Luo, Design of large-displacement compliant mechanisms by topology optimization incorporating modified additive hyperelasticity technique. Mathematical Problems in Engineering, 2017. 2017.
[32] Sigmund, O. and J. Petersson, Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Structural Optimization, 1998. 16(1): p. 68-75.
[33] Wu, C. and J. Arora, Design sensitivity analysis and optimization of nonlinear structuralresponse using incremental procedure. AIAA Journal, 1987. 25(8): p. 1118-1125.
[34] Kepler, J., Sensitivity Analysis: The Direct and Adjoint Method. Universitat Linz, 2010.
[35] Yoon, G.H., J.Y. Noh, and Y. Kim, Topology optimization of geometrically nonlinear structures tracing given load-displacement curves. Journal of Mechanics of Materials and Structures, 2011. 6(1): p. 605-625.
[36] Buhl, T., C.B. Pedersen, and O. Sigmund, Stiffness design of geometrically nonlinear structures using topology optimization. Structural and Multidisciplinary Optimization, 2000. 19(2): p. 93-104.
[37] Olhoff, N., Multicriterion structural optimization via bound formulation and mathematical programming. Structural Optimization, 1989. 1(1): p. 11-17.
[38] Martins, P., R. Natal Jorge, and A. Ferreira, A comparative study of several material models for prediction of hyperelastic properties: application to silicone‐rubber and soft tissues. Strain, 2006. 42(3): p. 135-147.