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標題: | 於平面串接型靜平衡機械手臂上具最小跨接空間之彈簧配置 Configurations of Conventional Springs with Minimized Spanning Space on Statically Balanced Planar Articulated Manipulators |
作者: | Wei-Hsiang Wang 王威翔 |
指導教授: | 陳達仁(Dar-Zen Chen) |
關鍵字: | 等效,彈簧,配置,空間,平衡, equivalent,spring,configuration,space,balanced, |
出版年 : | 2018 |
學位: | 碩士 |
摘要: | 本論文提出了在靜態平衡串接型機械手臂上具最小化跨接空間之彈簧配置設計方法。透過將重力位能和彈力位能方程式以剛性矩陣(Stiffness Block Matrix, SBM)表示為機械手臂上任意兩個桿件間的相對位能,並藉此求得在各個關節處重力位能被彈力位能相抵消以達靜態平衡之方程式。根據彈力位能剛性矩陣表示方法,在各關節處皆施加相同量值彈力位能之不同彈簧配置被定義為等效彈簧配置(Equivalent Spring Configuration)。透過將單一個彈簧拆分為具有多個跨越同樣關節數量彈簧之配置,彈力位能可較有效的被利用於抵消重力位能,但能夠減少之跨接空間有限;而透過將單一彈簧拆分為具有多個跨越不同關節數量彈簧之配置,設計上更加自由並能夠更容易地將跨接空間減少。依此便可枚舉出針對不同跨越關節數量彈簧最能有效降低跨接空間之配置調整方式,並歸納出等效彈簧配置之間的變換規則,以施加於具有靜態平衡效果之彈簧配置。最後,以三自由度機械手臂之靜態平衡彈簧配置為示例,計算彈簧跨接面積做為指標,在指定運動軌跡下進行等效配置變換以得跨接空間較小之彈簧配置 This paper proposes a systematic methodology to minimize the spanning space of the tension springs installed on a planar articulated manipulator for statically balancing. The balancing equations for gravitational potential energy compensated by the elastic energy are presented using stiffness block matrix, which reveals the interacting potential energy between any two links of the manipulator. Equivalence of spring is also based on the maintained elastic SBM, assuring the overall spring effectiveness has remained unchanged. The equivalent configurations of a single spring with a different number of joints spanned over are enumerated with or without mounting positions as constraints. The corresponding effects of diminishing the spring spanning space is also discussed. The modification rules between these equivalent configurations thus can be derived and re-arranging methods as a pipeline that leads to minimized overall spanning space on the manipulator can be concluded. An illustrative example of a 3-DOF planar articulated manipulator on designated trajectory is shown. The modifying methods for decreasing spanning space are applied with the actual area contoured by the springs are calculated as index. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/70744 |
DOI: | 10.6342/NTU201801206 |
全文授權: | 有償授權 |
顯示於系所單位: | 機械工程學系 |
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