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渐开线的公式是
4 o' Q: @ a* m* m6 i8 Bx=r(cos(theta)+theta*sin(theta)) 9 I* O! N) J" l2 H" e+ ^1 h8 X
y=r(sin(theta)-theta*sin(theta)) ' Q5 X0 H$ }* J5 v. Y1 |& S6 }6 K
r - 基圆半径
- `6 x3 t$ w, P( r- ]1 I! Otheta - 成形角，弧度值
! z) E* y9 V: X7 k1 X在不同theta时算出x和y即可。 # s0 j4 a4 J4 M1 C) }9 o
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。
$ `! f) R2 X% e& [' f q;*************************************************************************************
;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.
6 o# y0 z/ s; C8 x* Z6 x + S; \8 [+ ?# o1 V
(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:"))
3 R' j! d7 Y: ~(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))) ""
)
) & I( a1 m& e0 \. ~, K: u
(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 "") . o& j3 }( s! i% j, i
(setvar "osmode" os)
(command "_undo" "e")
(princ)
) | 
发表于 2006-3-28 19:30:57
