現今大多數產業都已逐漸邁入科技化與自動化，過往於機構設計中運動及力學生成常用的試誤法與經驗法，此類緩慢的開發流程在目前情況下已不符效益。因此採用電腦輔助工程對機構進行設計，可更快速的求得所需的機構參數，降低產品開發週期，是目前的趨勢。為了解決上述之問題並降低產品開發週期，本研究主要應用幾何約束編程法(Geometric Constraint Programming, GCP)進行機構分析及尺寸合成，此方法利用現有的參數化設計軟體，如Solidworks、Creo等，在草圖模式下可給定各種約束條件，以此來設計機構尺寸使其符合設計需求。本研究提出一種於GCP中解決力生成問題的方法，並透過三種設計實例演示，其一為甩鍋機構的運動生成及動平衡，藉由分析人員操作炒鍋數據，使用GCP設計桿件尺寸及動平衡，並由Solidworks Motion進行模擬驗證。其二為壓罐機機構的力合成及動平衡，使用GCP方法生成機構尺寸及需求輸入扭矩，藉由Solidworks Motion進行模擬驗證，可得輸入扭矩誤差為0.5%，驗證此力生成機構的可行性。其三為可變負載划船機構的力合成，透過GCP方法設計一符合可變負載條件的連桿尺寸，並使用ADAMS進行模擬驗證，此機構與設計目標最大誤差僅2.15%。

With the advancement of technology and automation in most industries, the trial-and-error and empirical method people used to adopt in the past have become ineffective in the process of designing motion and force generation in mechanism. With a view to maximizing the overall cost effectiveness and increasing the company’s profits, using computer-aided mechanism design has become an evolving trend. In doing so, engineers can efficiently and quickly obtain the needed mechanism parameter, thereby shortening the product development cycle.
In order to reduce the development cycle time, this study applies Geometric Constraint Programming (GCP) in mechanism analysis and dimensional synthesis. By means of the present parameter design software such as Solidworks and Creo, constraint conditions can be added in sketch model to satisfy the requirements of the mechanism dimension. This study will demonstrate three types of design examples to offer the solution to force generation problem. The first type is the motion generation of operating wok mchanism and dynamic balancing. By analyzing the collected data from operating wok, GCP is used to design rod dimension and dynamic balancing. And then Solidworks Motion will be used to simulated and further verify operating wok mchanism. The second one is the force generation of crusher mechanism and dynamic balancing. It uses GCP to generate mechanism dimension and then input torque in accordance with its requirements. With the simulation of Solidworks Motion, the data error of the input torque is 0.5% to confirm the possibility of the force generation mechanism. The third is the force generation of variable resistance rowing mechanism. With GCP, the linkage dimension is designed to meet the condition of variable resistance and is further simulated and tested via ADAMS. The biggest data error is only 2.15% compared to the design goal.

[1] 林祺堡, "遺傳演算法應用於史帝芬森三型沖床之尺寸合成," 碩士, 機械工程學系所, 國立中興大學, 台中市, 2016.
[2] 鍾學典, "新型混合差分演算法應用於平面連桿機構之最佳化尺寸合成," 碩士, 機械與精密工程研究所, 國立高雄應用科技大學, 高雄市, 2011.
[3] 李威廷, "演化型演算法應用於五連桿路徑產生機構之最佳化尺寸合成," 碩士, 機械與精密工程研究所, 國立高雄應用科技大學, 高雄市, 2011.
[4] 許剛錦, "平面路徑產生機構之混合粒子群最佳化尺寸合成," 碩士, 機械與精密工程研究所, 國立高雄應用科技大學, 高雄市, 2010.
[5] 謝東霖, "演化型演算法應用於四連桿路徑產生機構與六連桿義肢膝關節機構之最佳化尺寸合成," 碩士, 機械與精密工程研究所, 國立高雄應用科技大學, 高雄市, 2014.
[6] 尤葦忱, "五種最佳化方法應用於機械零件設計與路徑產生機構尺寸合成之有效性研究," 碩士, 機械工程系, 國立高雄應用科技大學, 高雄市, 2018.
[7] 王秋閔, "修正螢火蟲演算法於路徑產生機構之最佳化尺寸合成," 碩士, 機械工程學系, 國立成功大學, 台南市, 2018.
[8] 張栢, "瓦特II型六連桿步行機構之最佳化尺寸合成及運動靜力分析," 碩士, 機械工程系, 國立高雄應用科技大學, 高雄市, 2018.
[9] 陳妍綺, "多目標修正螢火蟲演算法於路徑產生機構之最佳化尺寸合成," 碩士, 機械工程學系, 國立成功大學, 台南市, 2019.
[10] W. Lin, K. Hsiao, "A new differential evolution algorithm with a combined mutation strategy for optimum synthesis of path-generating four-bar mechanisms," Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, vol. 231, no. 14, pp. 2690-2705, 2017.
[11] E. C. Kinzel, J. P. Schmiedeler, G. R. Pennock, "Kinematic synthesis for finitely separated positions using geometric constraint programming," (in English), Journal of Mechanical Design, Article vol. 128, no. 5, pp. 1070-1079, Sep 2006.
[12] E. C. Kinzel, J. P. Schmiedeler, G. R. Pennock, "Function Generation With Finitely-Separated Precision Points Using Geometric Constraint Programming," ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, vol. 2: 30th Annual Mechanisms and Robotics Conference, Parts A and B, pp. 381-390, 2006.
[13] S. S. Ambike, J. P. Schmiedeler, "Application of geometric constraint programming to the kinematic design of three-point hitches," Applied Engineering in Agriculture, vol. 23, no. 1, pp. 13-21, 2007.
[14] Z. Pusnik, "Design of Path Correction for Improved Gait Rehabilitation," 2022.
[15] R. A. Zimmerman, "Planar Linkage Synthesis for Coupler Point Path Guidance Using Poles and Rotation Angles," International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, vol. 46377: American Society of Mechanical Engineers, p. V05BT08A086, 2014.
[16] R. A. Zimmerman, "Planar linkage synthesis for function generation using poles and rotation angles," International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, vol. 57137: American Society of Mechanical Engineers, p. V05BT08A066, 2015.
[17] R. A. Zimmerman, "Planar linkage synthesis for mixed motion, path, and function generation using poles and rotation angles," Journal of Mechanisms and Robotics, vol. 10, no. 2, p. 025004, 2018.
[18] G. N. Sandor, A. G. Ereman, Advanced Mechanism Design：Analysis and Synthesis. Englewood Cliffs, New Jersry: Prentice-Hall, 1984.
[19] J. A. Mirth, "The Application of Geometric Constraint Programming to the Design of Stephenson III Dwell Linkages," ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, vol. Volume 5B: 40th Mechanisms and Robotics Conference, V05BT07A082, 2016.
[20] J. P. Schmiedeler, B. C. Clark, E. C. Kinzel, G. R. Pennock, "Kinematic Synthesis for Infinitesimally and Multiply Separated Positions Using Geometric Constraint Programming," Journal of Mechanical Design, vol. 136, no. 3, 2014.
[21] K.-L. Ting, C. L. Chan, "Reversible Geometric Constraint Programming on Kinematic Analysis and Synthesis of Planar Linkages," ASME 2022 International Mechanical Engineering Congress and Exposition, vol. Volume 4: Biomedical and Biotechnology; Design, Systems, and Complexity, V004T06A001, 2022.
[22] 羅琮棋, 李譯文, 陳立衡, "運用 Solidworks 幾何約束進行單暫停及雙暫停六連桿合成," 第 25 屆全國機構及機器設計學術研討會, 國立中山大學, 2022.
[23] Y. Tong, D. H. Myszka, A. P. Murray, "Four-Bar Linkage Synthesis for a Combination of Motion and Path-Point Generation," ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, vol. Volume 6A: 37th Mechanisms and Robotics Conference, V06AT07A054, 2013.
[24] D. M. Chen, "Interactive dynamic force analysis using constraint-based approach," International Journal on Interactive Design and Manufacturing (IJIDeM), vol. 5, pp. 205-212, 2011.
[25] M. T. Scardina, "Optimal synthesis of force-generating planar four-link mechanisms," Virginia Tech, 1996.
[26] B. T. Rundgren, "Optimal synthesis of force-generating planar four-bar mechanism including dynamic effects," Virginia Tech, 2001.
[27] V. H. Arakelian, M. R. Smith, "Shaking Force and Shaking Moment Balancing of Mechanisms: A Historical Review With New Examples," Journal of Mechanical Design, vol. 127, no. 2, pp. 334-339, 2005.
[28] 蔣君宏, 高等機動學. 美商麥格羅希爾國際股份有限公司, 1997.
[29] B. C. Elliott, G. J. Wilson, G. K. Kerr, "A biomechanical analysis of the sticking region in the bench press," Med Sci Sports Exerc, vol. 21, no. 4, pp. 450-462, 1989.
[30] R. Van Den Tillaar, G. Ettema, "The “sticking period” in a maximum bench press," Journal of sports sciences, vol. 28, no. 5, pp. 529-535, 2010.
[31] D. T. McMaster, J. Cronin, M. McGuigan, "Forms of Variable Resistance Training," Strength & Conditioning Journal, vol. 31, no. 1, 2009.
[32] Y. Lin, Y. Xu, F. Hong, J. Li, W. Ye, M. Korivi, "Effects of Variable-Resistance Training Versus Constant-Resistance Training on Maximum Strength: A Systematic Review and Meta-Analysis," International Journal of Environmental Research and Public Health, vol. 19, no. 14, p. 8559, 2022.