漸開(kāi)線的公式和畫(huà)法

阿松

漸開(kāi)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

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theta - 成形角，弧度值

在不同theta時(shí)算出x和y即可。

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我用Autolisp做了個(gè)程序，希望對(duì)大家有用。歡迎大家討論。這里用的極坐標(biāo)。

;*************************************************************************************
;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:"))

(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))) ""
  )
)

(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 "")

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

feilong

ding@
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zhiqiu

應(yīng)該是y=r(sin(theta)-theta*cos(theta))，請(qǐng)問(wèn)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(biāo)準(zhǔn)為20度）？坐標(biāo)原點(diǎn)在哪？

阿松

你看的仔細(xì)。是寫(xiě)錯(cuò)了。
是齒輪的基圓。坐標(biāo)原點(diǎn)自己點(diǎn)。

liu2da3ye

我要

gb200

原帖由 zhiqiu 發(fā)表 應(yīng)該是y=r(sin(theta)-theta*cos(theta))，請(qǐng)問(wèn)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(biāo)準(zhǔn)為20度）？坐標(biāo)原點(diǎn)在哪？

j, g* ?8 F* E2 K: X9 d

呵呵！看的仔細(xì)！強(qiáng)！雖然三年以前學(xué)過(guò)，也編過(guò)幾個(gè)復(fù)雜的。但現(xiàn)在還是看不懂了。沒(méi)精力去搞這個(gè)。感覺(jué)auto cad 在這方面不是很強(qiáng)。學(xué)習(xí)探討一下倒是不錯(cuò)。在實(shí)際應(yīng)用上還是建議使用專(zhuān)業(yè)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(shí)的包絡(luò)曲線畫(huà)法，特別是用于校驗(yàn)矩形花鍵滾刀的齒形設(shè)計(jì)，謝謝了！跪拜了！
hui:   xcy889900@163.com

xcy889900

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

原帖由 帶魚(yú) 發(fā)表 5 K$ k! K3 _1 C+ s5 @8 Q 又問(wèn)：樓主，是否能找到《工具技術(shù)》1998年05期刊“修緣插齒刀齒形技術(shù)方法”急用！謝謝

和你說(shuō)的不是完全一樣，但是《工具技術(shù)》1998年05期的文章也只有這篇了。

阿松

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