漸開線的公式和畫法

阿松

漸開線的公式是

; F4 c5 _' l' a! N

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

, u! B2 P' p# f* B1 n

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,。

) r( n5 ~ X1 G+ l1 D

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.

: g& y9 ~5 C( i; ~8 s

 

3 q: X, U, i: [' R: A

(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 "")

8 w! e8 \$ e" B# ~7 i" g

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

feilong

ding@

zhiqiu

應(yīng)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,。
; W- E. f" s2 t2 L- R是齒輪的基圓,。坐標原點自己點。

liu2da3ye

我要

gb200

原帖由 zhiqiu 發(fā)表 4 R" A3 Q( j. p% T4 p 應(yīng)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(xué)過，也編過幾個復(fù)雜的,。但現(xiàn)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(xué)習探討一下倒是不錯,。在實際應(yīng)用上還是建議使用專業(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的包絡(luò)曲線畫法,，特別是用于校驗矩形花鍵滾刀的齒形設(shè)計，謝謝了,！跪拜了,！
, ~% p- N" Z/ K4 S! shui:   [email protected]

xcy889900

又問：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

venus

原帖由 帶魚 發(fā)表 又問：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

多謝梧桐站友