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Theo Jansen 步行機構動力學分析

圖 6-5 為 Theo Jansen 步行機構,其中R1X、R1Y、R2、R3、R4、R5、R6、R7、 R8、R9和R10分別為其各桿件之桿長,三接頭桿OCD 中O = 𝛼,三接頭桿 EFG 中

F =,𝜃3、𝜃4、𝜃5、𝜃6、𝜃7和𝜃8為其致動接頭的旋轉角度,𝜃2為輸入角(輸入變 數),G 點座標(XG, YG)為步行軌跡(輸出變數),設定一 XY 座標,以固定樞軸 O 為原點。Theo Jansen 步行機構之各項參數如表 6-4 所示。

圖 6-5 Theo Jansen 步行機構

表 6-4 Theo Jansen 步行機構之各項參數

其中Ri為桿件i 之長度,aGi為桿件i 之質心加速度,𝑟mi為桿件i 轉軸至其質心 之距離。將Theo Jansen 步行機構進行模組化拆解,如圖 6-6,且將桿件 7 之 F 點 假想為固定樞軸。桿件4 與桿件 7 之質心分別位於 α 及  之角平分線上。

圖 6-6 Theo Jansen 模組化拆解

首先先計算各桿件所受到的慣性力FGi = −miaGi: FG2 = −m2aG2 = 0.75N(190°) FG3 = −m3aG3 = 0.396N(198.2°)

FG4 = −m4aG4 = 0.408N(227°) FG5 = −m5aG5 = 0.258N(27.8°) FG6 = −m6aG6 = 0.51N(181.4°) FG7 = −m7aG7 = 0.428N(144.5°)

FG8 = −m8aG8 = 0.071N(31°)

計算桿件所受的慣性矩TGi= −IGiαi

圖 6-7 Theo Jansen 步行機構慣性力等效偏移

表 6-5 Li 與hi 之數值

h4 −10.26 mm L5 28.79 mm

h7 −19.44 mm L6 14.57 mm

L3 33.29 mm L7 13.69 mm

L4 10.93 mm L8 22.2 mm

求得各項所需參數後,可開始進行模組化力學分析,首先分析由桿件7 及桿件 8

組成的RR 機械手臂,將偏移後的慣性力FG7及FG8視為外力P 與 Q,並將 F 點假想 為此機械手臂之固定樞軸,代入副函式:

[F87t, F87n, F48x, F48y, F67x, F67y]

= ForceRR(F , F , 0,0, R , R , L , L , h , 0, θ , θ , 31,144.5)

可得到

可得到

可得到

結論

樣只需重複套用個基礎模組及可求得大部分平面連桿機構之動力學分析。

5. 本論文所提出的模組化方法之主要缺點在於,建立三個基礎模組可分析大部 分之平面連桿機構,但仍然有少部分連桿機構無法套用此三種模組,例如含 有Assur group 3 之機構。往後仍需建立其他基礎模組並盡量簡化其計算過 程,以最少之基礎模組完成連桿機構之力學分析。

根據本論文之研究,在處理連桿機構之力學問題時,套用模組的方法有一定的 規則可循,因此有將其程式化之可能,利用電腦輔助分析套用模組的順序為本研究 未來可能可以延伸的方向。

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