渐开线的公式是
9 |5 N* W6 G' ~! q: ~# Fx=r(cos(theta)+theta*sin(theta))
! H4 D5 t: y8 R) d8 xy=r(sin(theta)-theta*sin(theta)) @# d4 S( T/ |4 T
r - 基圆半径
" A/ y( g2 }2 d5 Atheta - 成形角,弧度值 : s. D5 r, a( k" G7 m, ?3 Q
在不同theta时算出x和y即可。 ( _& E" J$ R. [
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。 % S- n7 T1 ?( M2 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. 2 X4 a, D4 r6 c4 }5 g1 {# A
6 { ]3 i2 i& s: Z(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:")) : K' k! ?# U3 \" i9 R0 P4 O% e4 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))) "" ) ) 5 Q M: f1 x( k, A" B) c, {1 t
(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 "")
) G. R' g, D% R/ W& S(setvar "osmode" os) (command "_undo" "e") (princ) ) |