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漸開線的公式是 ! Z) u% `1 `1 `% l
x=r(cos(theta)+theta*sin(theta))
1 V- {1 B1 i. ~( I+ fy=r(sin(theta)-theta*sin(theta)) * L7 Z! D3 ?6 w3 d# w' r3 ^4 D
r - 基圓半徑 6 }4 S" @; t8 L- J7 W
theta - 成形角，弧度值 7 x) l+ Y& L# W2 k, P, e
在不同theta時算出x和y即可。
3 y3 ~$ N0 ]* j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。 ; n3 |3 A/ n7 X. J4 |! H
;*************************************************************************************
;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.
9 w. V* o& z; E! B& M W
5 x7 y1 ~% g5 |) f X0 d9 J(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:"))
' {+ a) t9 x$ A- z8 `. H7 P; z(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))) ""
)
)
4 l$ L1 b" w$ X3 e* w! e A- `(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 "")
& }+ E$ B( w( k% j+ f(setvar "osmode" os)
(command "_undo" "e")
(princ)
) | 
發表于 2006-3-28 19:30:57
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