2007年6月11日 星期一

機動學第十三次作業

第一題:

現在要設計一組複式齒輪,
其轉速比為125。

首先知道,
轉速比:




正負號代表著平面第一個齒輪和最後一個齒輪轉的方向,
相同為正,
相反為負。

而普通串聯齒輪的轉速比的推導:




然而複式齒輪因為有共軸齒輪,
故應修正如下:




其中分打「'」的為共軸齒輪的第二個齒輪,
在減速的複式齒列中,
即為小齒輪。

主動輪和驅動輪可透過中間許多組齒列,
將所有各組的減速比相乘,
即可得到最終的轉速比。

基本上,
每一組的轉速比以不超過10為基準,
因此125開平方後得到約11.18,
意即需兩組轉速比為11.18齒列作組合。
此設計不適合僅用兩組齒列。

而將125開三次方後得到5,
比10小,
因此我們可以設計三組轉速比為5的齒列來組合,
達到最終的要求。

設三個小齒輪齒數皆為12,
則大齒輪齒數應為 12 × 5 = 60

因此整個組合的齒數順序為12:60;12:60;12:60
轉速比為(60/12)*(60/12)*(60/12)= 125
誤差值為0 %



第二題:

我覺得作業六是我弄比較好的一次作業,
因為這個在算可動度或惰性自由度的時候,
其實有點非常抽像。

而且有些連結度大於1的結,
在不同的狀況下,
有時候又要做一些更動改變。
比如滑塊結有時要轉換成一旋轉結或和一桿的結合,
計算起來才會正確;
但有些狀況卻又不用。

為此,
我花了不少時間,
自己就先畫了很多種各式各樣的組合,
來檢驗並試探如何將複雜的結變換成可較簡單的計算,
以套用至古魯伯公式仍適用。

我發現,
一個連結度大於2的結,
如果連結的桿數在三桿以上時,
為了要計算正確及思考方便,
大多都需要把此結作簡化,
最好可以將之轉化成「桿」和「連結度=1的結」之組合,
像作業六題目一中的滑槽結,
我就異想天開地再增加一個虛擬的滑塊於槽中,
而外面的另兩桿所點應的結就變成了滑塊問題。
(當然也是試了很多次類似情形但不同狀況的畫法,
而得到的驗証。)

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