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標題: | 分支型態之鉸接式靜平衡平面機構之設計 Design of Branch Type Articulated Statically Balanced Planar Mechanism |
作者: | Liang-Chun Chou 周良駿 |
指導教授: | 陳達仁 |
關鍵字: | 靜平衡,彈簧平衡,分支,剛性矩陣,零自由長度彈簧, statically balanced,spring balance,branch,stiffness block matrix,zero-free-length spring, |
出版年 : | 2014 |
學位: | 碩士 |
摘要: | 本論文提出一種分支型態之鉸接式靜平衡平面機構之設計。藉由安裝彈簧於機構之桿件特定位置上,使其彈力位能隨著桿件運動增減,進而使系統重力位能及彈力位能總合為一定值,該平面機構能夠平衡自身桿件在改變其位置時重力位能的改變,使系統在任何位置皆能夠達到靜平衡。基於此概念,首先定義分支型態之平面機構並予以分類,分支型態平面機構包含原來機構主幹部分(Main Part),以及分支部分(Branch Part),在定義分支型態平面機構之重力位能時,給予主幹與分支之重疊部分桿件一個質量比例常數,定義該桿件之質量分屬於主幹以及各分支部份之比例。接著利用剛性矩陣(Stiffness Block Matrix)分別表示主幹部分以及分支部份之重力位能,以及系統之彈力位能。將表示重力位能及彈力位能的剛性矩陣結合,即能夠清楚表示各桿件之間重力位能及彈力位能之效應。分支型態平面機構之靜平衡將拆成兩個部分討論,分別為主幹部分以及分支部分,視分支數目之多寡,可得兩個或兩個以上之剛性矩陣。令所有剛性矩陣除了主對角線上元素之外的元素為零矩陣可分別得設計方程式。根據特定的彈簧安裝角度以及設計方程式之間的交互關係,整理可得最佳設計方程式,透過最佳設計方程式可以確認彈簧常數以及安裝位置進而使系統達到靜平衡。接著提出兩個設計範例,分別為三自由度和五個自由度的分支型態平面機構,在合適的範圍分別設定各桿件質量、長度及相關參數,代入最佳設計方程式,選定合適的彈簧常數並決定彈簧安裝位置,使系統達到靜平衡。最後,根據設計理論使用ADAMS建立模型,並代入相關設計參數,驗證本研究之設計概念。 This thesis addresses a design of branch type articulated statically balanced planar mechanism. Statically balanced mechanism is capable of self-sustaining the change of gravitational potential energy of the system at any configuration. By installing springs at particular places of linkages, total potential energy of system remains constant, keeping the system statically balanced. Branch type mechanism is divided into two parts to discuss, main part and branch part. The gravitational potential energy of the superposition of main part and branch part contains a mass ratio parameter. Mass ratio parameter indicates that the mass of the overlapped link belongs to main part or branch part. With stiffness block matrix, the gravitational potential energy and elastic potential energy of both main part and branch part can be described clearly. Based on the number of branches, there are two or more stiffness block matrices of the system. By letting the off-diagonal entries of the stiffness block matrices be zero matrices, the design equations of both main part and branch part are derived. The system can be statically balanced by selecting the constants and installation configurations of springs with the design equations. Illustration of the methodology are demonstrated by a 3-DOF branch type statically balanced planar mechanism which contains 2-DOF main part and 1-DOF branch part, and a 5-DOF branch type statically balanced planar mechanism which contains 3-DOF main part and 2-DOF branch part Final, the simulation models are built in ADAMS to verify the design concept of this study. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/57524 |
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顯示於系所單位: | 機械工程學系 |
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