|Abstract: ||摘要:本研究的目的是利用連續法(亦稱同倫法)解 球面四連桿路徑產生機構之合成問題.用連續 法解機構的尺寸合成問題能獲得全部的解,提 供設計者所有符合運動條件的機構.連續法近 來被引用在解平面機構之合成問題,包括路徑 產生□函數產生以及運動產生等問題,得到令 人滿意的結果.此法不同於牛頓法等局部數值 分析法,對初始值(Initial guess)之要求不需要嚴 格,同樣能獲得收歛,並且解出所有答案;為一種 全面性收歛的數值方法.球面路徑產生機構的 設計方程式為一高度非線性之方程式系統,過 去的研究都限於五個精確點(Precision point)以下. 鑑於連續法在平面機構合成的成效,我們認為 應用連續法解球面路徑產生機構的合成能得到 相當的突破.本研究將先對球面四連桿之四及 五精確點的路徑合成作探討,並與過去的研究 結果相比較,以便確立程式的有效性;然後再研 究九個精確點的路徑合成問題.所有解得之機 構將先檢查是否有Order defect或Branch defect,最後 再根據機構之可轉性分類.|
Abstract:The objective of this research is to synthesis spherical four-bar path generators using continuation method (also known as homotopy method). By continuation method, we may obtain all the solutions to the dimension synthesis problem, and provide mechanism designers with all possible choices which meet the kinematic specifications. Continuation method has been applied successfully in the synthesis of planar mechanisms recently, including problems of path-generation, function-generation, and rigid-body guidance of four-bar and six-bar mechanisms. In contrast to other local numerical schemes such as Newton-Ralphson method and Powell method which are sensitive to initial guess, continuation method is a global convergence method that guarantee to find all solutions to the problems. Due to the effectiveness of continuation method applying in the synthesis of planar mechanisms, we believe that such method will breakthrough in the synthesis of spherical mechanisms. In this research, the problems with four and five precision points will be solved and compared with previous results. We use the principles of inversion and poles to derive the design equations. The method was extended from planar geometry. Equations derived from such method are simple and effective. More importantly, the total degree of the system design equations is lower than other methods, so that continuation method can be applied effectively. The derived mechanisms will be classified by their rotatability, and mechanisms with branch defect and order defect will be excluded.