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Title: | 具有彈簧變形與桿件運動方向共線特性之單自由度閉迴路平面靜平衡機構設計 Design of One-DOF Closed-loop Statically Balanced Planar Linkage with Link-Collinear Spring Arrangement |
Authors: | Yung-Yu Kao 高詠育 |
Advisor: | 陳達仁(Dar-Zen Chen) |
Keyword: | 單自由度,閉迴路,平衡,彈簧,桿件運動方向共線, one-DOF,closed-loop,balanced,spring,link-collinear, |
Publication Year : | 2017 |
Degree: | 碩士 |
Abstract: | 本論文提出了具有彈簧變形與桿件運動方向共線特性之單自由度閉迴路平面靜平衡機構設計方法。彈簧變形與桿件運動方向共線可解決彈簧在靜平衡機構中,為了達到特定配置而使用輔助元件所造成的干涉問題。在不使用輔助元件的情況下,連桿機構必需存在滑動對。以四桿機構為基礎,透過桿件向量追蹤各桿件的質心位置,求得機構之重力位能。其中,藉由閉迴路方程式,可將系統的重力位能皆以滑動對向量表示,因此重力位能式即可和彈力位能式一同表示成滑動對向量之函數,總位能方程式即可透過皆以滑動對向量表示的重力與彈力位能式相加而得。總位能式包含滑對動向量之二次項與一次項,根據位能守恆理論,當二次項恆為一常數之必要條件導入時,可推導出四桿機構之滑動對的數量、位置、組態等配置條件;透過係數比較法,可從一次項推導出彈簧之設計參數,包含彈簧常數值、彈簧兩端之接點位置。基於四桿機構之設計方法,進一步討論含有兩個迴路之六桿機構。兩迴路之間存在共同接頭,當共同接頭配置為滑動對時,彈簧同時作用於兩個迴路,此時仍遵守四桿機構之設計原則,但整體系統的彈簧數量可達到最小化。根據四桿機構之設計方法,提出應用於二頭肌阻力訓練裝置之四桿機構設計實例。最後亦提出瓦特型與史蒂芬森型六桿機構設計實例,分別應用於升降機構與支撐機構,驗證本研究之設計概念。 Several methods have been proposed for designing the Statically Balanced Mechanism (SBM) with spring suspension. However, most of them have the problems of interference because the spanning spring arrangement. In this thesis, we proposed a method for designing an one-DOF, closed-loop, planar linkage with link-collinear spring arrangement. The problems of interference which are caused by the spanning-spring arrangement and the use of auxiliary elements can be avoided by the link-collinear spring arrangement. Without using auxiliary elements, the prismatic joint is needed for designing the SBM. The formulation of gravitational energy is obtained by tracking the mass center of each link with link vectors, where the link vectors can be expressed as the prismatic joint vectors by the loop closure equation for the four-link linkage. Thus, the equation of total potential energy can be obtained as the summation of gravitational and elastic energy. For the equation of total potential energy, the quadratic and linear terms of prismatic joint vectors are included. To achieve static balance, the equation of total potential energy needs to remain as a constant value. The numbers, location and configuration of prismatic joints for the four-link SBM are determined by deriving the summation of quadratic terms with the necessary condition; and the stiffness, attachment ends of the springs are determined via the summation of linear terms by comparing coefficients. Based on the design principles of four-link SBM, the six-link SBM which has two independent loops are also discussed. The number of prismatic joints can be reduced by setting the prismatic joint as the common joint which is connected between two independent loops. The application on biceps curl resistance training device is presented as illustrated example for the four-link SBM, and the prototype is fabricated to demonstrate the method of static balance for the various payload. Finally, the applications for Watt and Stephenson type six-link SBM is presented respectively. And the simulated results for the design examples verified the design concept of this thesis. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/67312 |
DOI: | 10.6342/NTU201702512 |
Fulltext Rights: | 有償授權 |
Appears in Collections: | 機械工程學系 |
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File | Size | Format | |
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ntu-106-1.pdf Restricted Access | 3.57 MB | Adobe PDF |
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