臺灣博碩士論文加值系統

本研究利用拓樸最佳化方法來設計機械利益最大化之自適性撓性夾爪。自適性撓性夾爪為撓性機構的一種，可以適應不同外形、尺寸甚至是不規則形狀之物體，且不會對脆弱與易碎的被夾取物造成損傷。機械利益則是輸出力量與輸入力量的比值，機械利益值越大表示在相同的輸入力量下具有較大的輸出力量，可以承受較大的負載。在拓樸最佳化設計的部分，本研究使用參數化水平集拓樸最佳化方法，此方法以參數化的方式改進了傳統水平集拓樸最佳化方法運算量大的問題，且具有結構邊界較平滑與無灰階元素等優點。本研究以反向機構與夾合機構為例，並分別以機械利益、幾何利益與複合應變能作為撓性機構的目標函數，進行此方法之驗證、比較與討論。本研究並使用了Hinge free方法來避免拓樸最佳化結果產生過細的連接結構，可使結果更為勻稱，並避免應力集中與疲勞破壞。為了加速最佳化流程的收斂速度，本研究提出了一個材料移除方法，在疊代的過程中將靈敏度較低的結構加以移除。在自適性撓性夾爪的設計上，本研究由不同的設計參數與設計方法歸納出五種設計案例，並擬定挑選準則篩選出最合適之自適性撓性夾爪設計後，以3D列印軟性材料的方式進行製作。本研究同時也開發了一個包含了撓性夾爪本體與夾爪致動器之自適性撓性夾爪模組，並將其整合至國產六軸機械手臂，進行不同目標物的夾取實驗。實驗結果顯示本研究所設計的自適性撓性夾爪模組的最大負載為2.5 kg，並可夾取尺寸小於141 mm的未知目標物。此電動撓性夾爪可應用於機器人與自動化產業，並可解決傳統剛性夾取系統無法處理形狀尺寸不固定，且柔軟並容易損傷的目標物之自動化取放問題，有效降低自動化成本並增進生產效能。

This study presents a level set based topology optimization method to design an adaptive compliant gripper with maximum mechanical advantage. The adaptive compliant gripper is a compliant mechanism which can be used in handling of fragile objects with size and shape variations. The mechanical advantage is defined as the ratio of output force to input force. For a same input force condition, a higher mechanical advantage implies a larger output force, which leads to a higher payload for the compliant gripper. A parameterized level set method is used to perform topology optimization, which is with the advantages such as having smoother structural boundaries and a black and white design without gray elements. A hinge free method is used to minimize the de facto hinge problem, and a material removal scheme is proposed to speed up the numerical computation process. The classical benchmark problems in topology optimization literature including inverter mechanism and crunching mechanism are used as the verification examples to demonstrate the effectiveness of the proposed numerical method. The objective functions including mechanical advantage, geometric advantage, and a strain energy based function are used in this study. The proposed method is used to design the compliant gripper. Five analysis cases are performed, and an optimal design is identified according to the design rules and the results from finite element simulation. A compliant gripper module including actuator and 3D printed compliant fingers is prototyped then mounted on a six-axis industrial robot for grasping test. The test results show the developed compliant gripper can grip unknown objects with the size up to 141mm, and the maximum payload is 2.5 kg. The proposed motor-driven compliant gripper can be used to resolve the challenging issue for robotic automation of irregular and fragile objects, as well as to increase the productivity and reduce the cost for industrial automation.

摘要 i
ABSTRACT ii
致謝 xv
目錄 xvi
表目錄 xx
圖目錄 xxii
符號說明 xxvi
第一章 緒論 1
1-1 自適性撓性夾爪介紹 1
1-2 結構最佳化文獻回顧 4
1-2-1 拓樸最佳化文獻回顧 5
1-2-2 水平集方法拓樸最佳化文獻回顧 7
1-3 研究目的 9
1-4 本文架構 10
第二章 拓樸最佳化理論 11
2-1 前言 11
2-2 傳統水平集拓樸最佳化理論介紹 11
2-2-1 水平集函數原理 13
2-2-2 設計區間、初始水平集函數與有限元素分析 14
2-2-3 形狀導數、迎風差分法與重新初始化 17
2-3 參數化水平集拓樸最佳化理論介紹 19
2-3-1 參數化水平集方法 20
2-3-2 近似重新初始化方法 24
2-3-3 函數 25
2-4 撓性機構拓樸最佳化目標函數 26
2-4-1 機械利益與幾何利益 27
2-4-2 複合應變能目標函數 29
2-4-3 Hinge free方法 30
2-5 法向速度場 32
2-5-1 機械利益之法向速度場 32
2-5-2 幾何利益之法向速度場 36
2-5-3 複合應變能目標函數之法向速度場 37
2-5-4 Hinge free方法之法向速度場 39
2-6 材料移除方法 40
2-6-1 元素靈敏度 41
2-6-2 移除準則 44
2-7 收斂準則 45
2-8 本章小結 45
第三章 撓性機構拓樸最佳化範例 47
3-1 前言 47
3-2 反向機構 47
3-2-1 機械利益最大化 49
3-2-2 幾何利益最大化 53
3-2-3 複合應變能目標函數 57
3-2-4 Hinge free方法 59
3-2-5 材料移除結果 61
3-3 夾合機構 65
3-3-1 機械利益最大化 67
3-3-2 幾何利益最大化 69
3-3-3 複合應變能目標函數 71
3-3-4 Hinge free方法 73
3-3-5 移除材料結果 75
3-4 本章小結 79
第四章 自適性撓性夾爪拓樸最佳化設計 81
4-1 前言 81
4-2 邊界條件 82
4-3 分析案例 87
4-3-1 Hinge free方法 87
4-3-2 更改初始水平集函數之孔洞數量 89
4-3-3 更改初始水平集函數之孔洞分佈與大小 91
4-3-4 調整非設計區間、輸入端與輸出端彈簧常數 92
4-3-5 材料移除方法 96
4-3-6 挑選準則 98
4-3-7 分析案例結果整理 102
4-4 有限元素分析模擬結果 102
4-4-1 空負載模擬 103
4-4-2 夾持圓球模擬 107
4-5 本章小結 110
第五章 自適性撓性夾爪試做與驗證 111
5-1 前言 111
5-2 自適性撓性夾爪實驗結果 112
5-2-1 輸入力量量測實驗 112
5-2-2 輸出位移量測實驗 114
5-2-3 機械利益量測實驗 116
5-3 自適性撓性夾爪模組 119
5-4 系統整合 122
5-5 夾持實驗 125
5-5-1 實際物體夾持實驗 125
5-5-2 夾取範圍與負載實驗 126
5-6 本章小結 130
第六章 結論與建議 131
6-1 結論 131
6-2 建議 132
參考文獻 134

[1]台灣氣立公司網頁 http://www.chelic.com/.
[2]上銀科技網頁 http://www.hiwin.com.tw/.
[3]SCHUNK公司網頁http://de.schunk.com/.
[4]L. L. Howell, S. P. Magleby, B. M. Olsen, and J. Wiley, Handbook of Compliant Mechanisms: Wiley Online Library, 2013.
[5]Y. Li, Topology optimization of compliant mechanisms based on the BESO method, 2014.
[6]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.
[7]SOFTROBOTICS公司網頁http://www.softroboticsinc.com/.
[8]SRT公司網頁http://www.softrobottech.com/.
[9]FESTO公司網頁http://www.festo.com/.
[10]ROBOTIQ公司網頁http://robotiq.com/.
[11]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.
[12]M. P. Bendsøe and O. Sigmund, Topology Optimization: Theory, Methods and Applications. 2003: Springer.
[13]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, in 58th Ilmenau Scientific Colloquium, 2014, vol. 3, pp. 1-12.
[14]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碩士論文, 2016.
[15]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.
[16]M. P. Bendsøe and N. Kikuchi, Generating optimal topologies in structural design using a homogenization method, Computer Methods in Applied Mechanics and Engineering, vol. 71, no. 2, pp. 197-224, 1988.
[17]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.
[18]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.
[19]K. Suzuki and N. Kikuchi, A homogenization method for shape and topology optimization, Computer Methods in Applied Mechanics and Engineering, vol. 93, no. 3, pp. 291-318, 1991.
[20]O. Sigmund, A 99 line topology optimization code written in Matlab, Structural and Multidisciplinary Optimization, vol. 21, no. 2, pp. 120-127, 2001.
[21]D. P. Bertsekas, Nonlinear optimization: Athena Scientific, Belmont, 1999.
[22]X. Huang and M. Xie, Evolutionary Topology Optimization of Continuum Structures: Methods and Applications: John Wiley ＆ Sons, 2010.
[23]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.
[24]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.
[25]R. Ansola, E. Veguería, A. Maturana, and J. Canales, 3D compliant mechanisms synthesis by a finite element addition procedure, Finite Elements in Analysis and Design, vol. 46, no. 9, pp. 760-769, 2010.
[26]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.
[27]B. Zhu, X. Zhang, N. Wang, and S. Fatikow, Topology optimization of hinge-free compliant mechanisms using level set methods, Engineering Optimization, vol. 46, no. 5, pp. 580-605, 2014.
[28]Z. Luo, L. Chen, J. Yang, Y. Zhang, and K. Abdel-Malek, Compliant mechanism design using multi-objective topology optimization scheme of continuum structures, Structural and Multidisciplinary Optimization, vol. 30, no. 2, pp. 142-154, 2005.
[29]T. Buhl, C. B. Pedersen, and O. Sigmund, Stiffness design of geometrically nonlinear structures using topology optimization, Structural and Multidisciplinary Optimization, vol. 19, no. 2, pp. 93-104, 2000.
[30]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.
[31]S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol. 79, no. 1, pp. 12-49, 1988.
[32]J. A. Sethian and A. Wiegmann, Structural boundary design via level set and immersed interface methods, Journal of Computational Physics, vol. 163, no. 2, pp. 489-528, 2000.
[33]J. A. Sethian, Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science: Cambridge university press, 1999.
[34]S. Wang and M. Y. Wang, Radial basis functions and level set method for structural topology optimization, International Journal for Numerical Methods in Engineering, vol. 65, no. 12, pp. 2060-2090, 2006.
[35]Z. Luo, M. Y. Wang, S. Wang, and P. Wei, A level set‐based parameterization method for structural shape and topology optimization, International Journal for Numerical Methods in Engineering, vol. 76, no. 1, pp. 1-26, 2008.
[36]Z. Luo, L. Tong, and Z. Kang, A level set method for structural shape and topology optimization using radial basis functions, Computers ＆ Structures, vol. 87, no. 7-8, pp. 425-434, 2009.
[37]P. Wei, Z. Li, X. Li, and M. Y. Wang, An 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions, Structural and Multidisciplinary Optimization, vol. 58, no. 2, pp. 831-849, 2018.
[38]M. Burger, B. Hackl, and W. Ring, Incorporating topological derivatives into level set methods, Journal of Computational Physics, vol. 194, no. 1, pp. 344-362, 2004.
[39]L. Jackowska-Strumillo, J. Sokolowski, and A. Zochowski, The topological derivative method in shape optimization, in The 38th IEEE Conference on Decision and Control (Cat. No. 99CH36304), 1999, vol. 1, pp. 674-679.
[40]M. Otomori, T. Yamada, K. Izui, and S. Nishiwaki, Matlab code for a level set-based topology optimization method using a reaction diffusion equation, Structural and Multidisciplinary Optimization, vol. 51, no. 5, pp. 1159-1172, 2015.
[41]Q. Xia, T. Shi, and L. Xia, Stable hole nucleation in level set based topology optimization by using the material removal scheme of BESO, Computer Methods in Applied Mechanics and Engineering, vol. 343, pp. 438-452, 2019.
[42]X. Yang, Y. Xei, G. Steven, and O. Querin, Bidirectional evolutionary method for stiffness optimization, AIAA journal, vol. 37, no. 11, pp. 1483-1488, 1999.
[43]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.
[44]A. Krishnakumar and K. Suresh, Hinge-free compliant mechanism design via the topological level-set, Journal of Mechanical Design, vol. 137, no. 3, p. 031406, 2015.
[45]G. Allaire, Shape Optimization by the Homogenization Method: Springer Science ＆ Business Media, 2012.
[46]D. Peng, B. Merriman, S. Osher, H. Zhao, and M. Kang, A PDE-based fast local level set method, Journal of Computational Physics, vol. 155, no. 2, pp. 410-438, 1999.
[47]B. S. Morse, T. S. Yoo, P. Rheingans, D. T. Chen, and K. R. Subramanian, Interpolating implicit surfaces from scattered surface data using compactly supported radial basis functions, in ACM SIGGRAPH 2005 Courses, 2005, p. 78.
[48]X. Xie and M. Mirmehdi, Radial basis function based level set interpolation and evolution for deformable modelling, Image and Vision Computing, vol. 29, no. 2-3, pp. 167-177, 2011.
[49]O. Sigmund, On the design of compliant mechanisms using topology optimization, Journal of Structural Mechanics, vol. 25, no. 4, pp. 493-524, 1997.
[50]S. Wang, K. M. Lim, B. C. Khoo, and M. Wang, An extended level set method for shape and topology optimization, Journal of Computational Physics, vol. 221, no. 1, pp. 395-421, 2007.
[51]M. Y. Wang, The augmented lagrangian method in structural shape and topology optimization with rbf based level set method, in The 4th China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems, 2006.
[52]M. P. Bendsøe and O. Sigmund, Optimization of Structural Topology, Shape, and Material: Springer, 1995.
[53]D. Petković, N. D. Pavlović, S. Shamshirband, and N. Badrul Anuar, Development of a new type of passively adaptive compliant gripper, Industrial Robot: An International Journal, vol. 40, no. 6, pp. 610-623, 2013.