漸開線的公式和畫法

阿松

漸開線的公式是

x=r(cos(theta)+theta*sin(theta))

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y=r(sin(theta)-theta*sin(theta))

r - 基圓半徑

theta - 成形角，弧度值

在不同theta時算出x和y即可。

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我用Autolisp做了個程序，希望對大家有用。歡迎大家討論。這里用的極坐標。

;*************************************************************************************
;This program is to draw a involute in AutoCAD, anyone can use it freely without permission.
;Take the risk youself, suggest you to open a new drawing and run this program first, then
;copy it to your drawing.
;Chen Xiangsong
;
;Distance Offset: means when you draw a curve rather than a standard involute.
;   it starts to draw the curve not from the base circle.
;   it is curtate or prolate involute. it is useful as you draw gear root.
;   standard involute, enter 0
;
;Radius of Base Circle: You have to know the meaning, or the program is useless to you
;
;Angle to go:  means the length of involute you want. in degrees. it is not pressure
;   angle, it is the pressure angle add involute Phi.
;
;Accurancy:  the density of points you want on the curve, the smaller the more accurate.
;   but will slow down your pc's speed. I normally enter 0.01
;
;Center of Curve: LEASE PICK A POINT ON THE SCREEN RANDOMLY, IT IS VERY IMPORTANT.
;   DON'T PICK A SPECIAL POINT. That's the disadvantage of my program.

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(defun c:involute ()
(command "_undo" "be")
(setq os (getvar "osmode"))
(setvar "osmode" 0)
(setq q 0)
(setq f 0)
(setq h (getreal "\nDistance Offset:"))
(setq r (getreal "\nRadius of Base Circle:"))
(setq t (getreal "\nAngle to go:"))
(setq n (getreal "\nAccurancy:"))
(setq cent (getpoint "\nCenter of Curve:"))

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(if (= h 0)  (command "pline"  (list (+ 0       (car cent)) (cadr cent))
     (list (+ (/ r 2) (car cent)) (cadr cent)) ""
  )
  (command "pline" (setq trimpoint (list (+ h r (car cent)) ((if (> h 0) - +) (cadr cent) (/ r 1))))
     (list (+ h r (car cent)) ((if (> h 0) - +) (cadr cent) (/ r 2))) ""
  )
)

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(while (< f (* t (/ pi 180)))
 (setq a (atan (* r f) (+ r h)))
 (setq ri (/ (+ r h) (cos a)))
 (setq q (- f a))
 (setq pt0 (polar cent q ri))
 (command "pline" "" pt0 "")
 (setq f (+ f n))
)
(command "pedit" (entlast) "j" "all" "" "f" "")
(command "circle" cent r)
(setq bs (entlast))
(command "line" cent (list (+ 1 r h (car cent)) (cadr cent)) "")
(setq lt (entlast))
(if (= h 0) (command "trim" bs "" cent "")
  (command "trim" lt "" trimpoint "")
)
(command "erase" lt "")

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(setvar "osmode" os)
(command "_undo" "e")
(princ)
)

feilong

ding@

zhiqiu

應該是y=r(sin(theta)-theta*cos(theta))，請問基圓是不是齒輪的基圓（就是齒輪分度圓半徑與cosα的乘積，α是齒輪壓力角，標準為20度）？坐標原點在哪？

阿松

你看的仔細。是寫錯了。
* ^" ], H1 b0 a7 L: b) o是齒輪的基圓。坐標原點自己點。

liu2da3ye

我要

gb200

原帖由 zhiqiu 發表 應該是y=r(sin(theta)-theta*cos(theta))，請問基圓是不是齒輪的基圓（就是齒輪分度圓半徑與cosα的乘積，α是齒輪壓力角，標準為20度）？坐標原點在哪？

呵呵！看的仔細！強！雖然三年以前學過，也編過幾個復雜的。但現在還是看不懂了。沒精力去搞這個。感覺auto cad 在這方面不是很強。學習探討一下倒是不錯。在實際應用上還是建議使用專業的三維制圖軟件。

xcy889900

各位老大，我想知道齒輪刀具與被切齒輪嚙合時的包絡曲線畫法，特別是用于校驗矩形花鍵滾刀的齒形設計，謝謝了！跪拜了！
hui:   xcy889900@163.com

xcy889900

又問：樓主，是否能找到《工具技術》1998年05期刊“修緣插齒刀齒形技術方法”急用！謝謝

venus

原帖由 帶魚 發表 ! R. U! X2 V' X4 J0 [' b' P 又問：樓主，是否能找到《工具技術》1998年05期刊“修緣插齒刀齒形技術方法”急用！謝謝

和你說的不是完全一樣，但是《工具技術》1998年05期的文章也只有這篇了。

阿松

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