渐开线的公式和画法

阿松

渐开线的公式是

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

, z# T2 k% \& M3 H J: L) {7 i$ Q' x

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

! F i5 Q. z# }5 W5 `: B$ g; N- m

r - 基圆半径

5 ?0 u: _8 }8 I) I1 e3 T' U

theta - 成形角，弧度值

在不同theta时算出x和y即可。

我用Autolisp做了个程序，希望对大家有用。欢迎大家讨论。这里用的极坐标。

;*************************************************************************************
;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.

 

8 I. y! {4 h* n

(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:"))

7 X; R$ ~! y) S* B

(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@

zhiqiu

应该是y=r(sin(theta)-theta*cos(theta))，请问基圆是不是齿轮的基圆（就是齿轮分度圆半径与cosα的乘积，α是齿轮压力角，标准为20度）？坐标原点在哪？

阿松

你看的仔细。是写错了。
2 n1 q+ u! u( Y! x: I' R是齿轮的基圆。坐标原点自己点。

liu2da3ye

我要

gb200

原帖由 zhiqiu 发表 9 a+ w) H2 M g( ` 应该是y=r(sin(theta)-theta*cos(theta))，请问基圆是不是齿轮的基圆（就是齿轮分度圆半径与cosα的乘积，α是齿轮压力角，标准为20度）？坐标原点在哪？

呵呵！看的仔细！强！虽然三年以前学过，也编过几个复杂的。但现在还是看不懂了。没精力去搞这个。感觉auto cad 在这方面不是很强。学习探讨一下倒是不错。在实际应用上还是建议使用专业的三维制图软件。

xcy889900

各位老大，我想知道齿轮刀具与被切齿轮啮合时的包络曲线画法，特别是用于校验矩形花键滚刀的齿形设计，谢谢了！跪拜了！
hui:   xcy889900@163.com

xcy889900

又问：楼主，是否能找到《工具技术》1998年05期刊“修缘插齿刀齿形技术方法”急用！谢谢

venus

原帖由 带鱼 发表 + t% C7 a( e- m4 _ z 又问：楼主，是否能找到《工具技术》1998年05期刊“修缘插齿刀齿形技术方法”急用！谢谢

和你说的不是完全一样，但是《工具技术》1998年05期的文章也只有这篇了。

阿松

多谢梧桐站友