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標題: | 彈性樑–滑塊機構的變形與穩定性分析 Deformation and Stability of an Elastica-Slider Device |
作者: | Yi-Hsiang Su 蘇以翔 |
指導教授: | 陳振山(Jen-San Chen) |
關鍵字: | 彈性樑,雙穩態,穩定性,小變形理論, Elastica,bistable,stability,small-deformation theorem, |
出版年 : | 2011 |
學位: | 碩士 |
摘要: | 本文研究一個由彈性樑與滑塊組成的撓性機構。此機構可藉由旋轉彈性樑使滑塊產生平移運動,反之亦可藉著移動滑塊來使樑旋轉。此機構可作為雙平衡裝置,靈感來自於滑塊-曲柄機構。利用射線法求得彈性樑的一系列變形,再用微擾法分析各個變形的穩定性。我們考慮兩種負載裝置:控制力量與控制位移。此機構的穩定性隨負載裝置而不同,當端點彎矩或角度到達臨界點時會發生折斷式挫曲,由原先的變形跳至另一穩定的變形。我們可得知挫曲發生時控制力量的臨界彎矩以及控制位移的臨界角。只要初始角度不為零,此機構就維持雙向穩定的特性。在初始角度小的情況下,可利用小變形理論將臨界彎矩及臨界角用函數表示。初始角度為15度以內,利用小變形理論所求得的臨界彎舉與臨界角與樑理論所求得的解相當的近似。最後設計一個控制彎矩的實驗裝置,考慮實驗儀器的幾何形狀,理論與實驗值相當符合。 This paper studies a compliant mechanism composed of an elastica and a slider. This assembly transmits a rotating motion to a translational one, or vice versa. It can also be used as a bistable device. The design is inspired by the well known slider-and-crank linkage. The deformation sequence of the assembly is first analyzed with shooting method. A vibration method is then employed to analyze the stability of the deformations. Two different loading mechanisms are studied, one is load control and the other is displacement control. The stability of the assembly depends on which control mechanism is adopted. As the end moment or the end angle reaches a critical value, snapping will occur. The critical end moment for load control and critical end angle for displacement control are thus identified. It is found that bistable configurations always exist as long as the initial angle is not zero. In the special case when the initial angle is small, a small-deformation theory is developed and the critical end moment and critical end angle can be expressed in closed forms. The critical end moment and critical end angle predicted from small-deformation theory agree with the elastica theory very well when the initial angle is smaller than . Finally, a load-control experimental set-up is constructed to verify the design concept. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/23700 |
全文授權: | 未授權 |
顯示於系所單位: | 機械工程學系 |
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