AUTOCAD作图求助

gaogl168

现有一个问题，想用CAD作图求出来，可是本人水平太差，想不出来，在这请教各位大侠了！问题如下，已知弦的长度和弦所对圆弧的长度，如何在CAD里面通过作图求出圆的直径？见附件，直线长度知道，弧长知道，求半径。补充一点，条件是我们只知道直线长度和弧长。附件图形只是示意，不代表直线和圆弧已经连接到一块了，如果是那样的话，就太简单了，岂不是直接捕捉圆心也就出来了

drc2000

此问题没有精确的计算公式.但是若弦长和弧长相差不大时,有个近似的公式:
d=√(c^3/(c-a)/6),
(其中d是圆的直径,c是弧长,a是弦长)
若要较精确的数值,请给出具体数值来吧,我可以帮你算算.

chenjun_nj

设m为弦长、n为弧长，R为半径（待求）；
设圆心角为α，那么n=αR，即α=n/R；
又m=2R.sin(α/2)
即m=2R.sin(n/(2R))
用叠代法就可以求出R的数值解。
建议在excel中求。

qjchen

:) 此题确实是得用数值解法了

根据chenjun兄的解法，采用以前的二分法lisp编了一段LISP，不过最后是画出圆而没有画出弧

2. 
   
3. ;;; By qjchen@gmail.com
   
4. ;;; The main code mainly from the MIT book "Structure and interpretaion of computer programs"
   
5. ;;; judge whether the initial range is suitable
   
6. (defun halfsolve (f a b / a-value b-value)
   
7.   (setq        a-value        ((eval f) a)
   
8.         b-value        ((eval f) b)
   
9.   )
   
10.   
    
11.   (cond
    
12.     ((and (< a-value 0) (> b-value 0)) (searchhalf f a b))
    
13.     ((and (> a-value 0) (< b-value 0)) (searchhalf f b a))
    
14.     ((= a-value 0) a)
    
15.     ((= b-value 0) b)
    
16.     (T (prompt "The Values maybe not between a and b"))
    
17.   )
    
18. )
    
19. 
    
20. ;;core code of dichotomy
    
21. (defun searchhalf (f neg-point pos-point / test-value midpoint)
    
22.   (setq midpoint (/ (+ neg-point pos-point) 2))
    
23.   (cond
    
24.     ((close-enough? neg-point pos-point) midpoint)
    
25.     (T
    
26.      (setq test-value ((eval f) midpoint))
    
27.      (cond
    
28.        ((> test-value 0) (searchhalf f neg-point midpoint))
    
29.        ((< test-value 0) (searchhalf f midpoint pos-point))
    
30.        (T midpoint)
    
31.      )
    
32.     )
    
33.   )
    
34. )
    
35. 
    
36. ;;judge small enough
    
37. (defun close-enough? (x y)
    
38.   (< (abs (- x y)) 1e-10)
    
39. )
    
40. 
    
41. ;; The equation to be solve, -x^3+2x+3=0
    
42. ;;  2*x*sin(arcl/2/x)-linel
    
43. (defun myfuntosolve (x)
    
44.   (- (* x 2.0 (sin (/ arclength 2. x))) linelength)
    
45. )
    
46. 
    
47. ;;Main function by qjchen@gmail.com
    
48. (defun c:t( / a ang arclength d linelength p1 r)
    
49.   (setq a (vlax-ename->vla-object (car (entsel "\n Please select a line"))) arclength (getreal "\n Arc Length"))
    
50.   (setq linelength (Vlax-get  a 'length))
    
51.   (if (> arclength linelength)
    
52.     (progn (princ (rtos (setq r (halfsolve myfuntosolve (/ linelength 2.0) (/ linelength 0.01))) 2 14))
    
53.            (setq P1 (Vlax-get  a 'StartPoint)
    
54.                  ang (Vlax-get  a 'Angle)
    
55.                  d (sqrt (- (* r r) (* linelength linelength 0.25))))
    
56.            (command "circle" (polar (polar P1 ang (* 0.5 linelength)) (+ ang (* 0.5 pi)) d) r)
    
57.            (command "circle" (polar (polar P1 ang (* 0.5 linelength)) (+ ang (* 0.5 pi)) (- d)) r)
    
58.     )
    
59.     (princ "the Arc length is too small")
    
60.   )
    
61.   (princ)
    
62. )
    

<br /> ;;; By qjchen@gmail.com<br /> ;;; The main code mainly from the MIT book "Structure and interpretaion of computer programs"<br /> ;;; judge whether the initial range is suitable<br /> (defun halfsolve (f a b / a-value b-value)<br />   (setq        a-value        ((eval f) a)<br />         b-value        ((eval f) b)<br />   )<br />   <br />   (cond<br />     ((and (< a-value 0) (> b-value 0)) (searchhalf f a b))<br />     ((and (> a-value 0) (< b-value 0)) (searchhalf f b a))<br />     ((= a-value 0) a)<br />     ((= b-value 0) b)<br />     (T (prompt "The Values maybe not between a and b"))<br />   )<br /> )<br /> <br /> ;;core code of dichotomy<br /> (defun searchhalf (f neg-point pos-point / test-value midpoint)<br />   (setq midpoint (/ (+ neg-point pos-point) 2))<br />   (cond<br />     ((close-enough? neg-point pos-point) midpoint)<br />     (T<br />      (setq test-value ((eval f) midpoint))<br />      (cond<br />        ((> test-value 0) (searchhalf f neg-point midpoint))<br />        ((< test-value 0) (searchhalf f midpoint pos-point))<br />        (T midpoint)<br />      )<br />     )<br />   )<br /> )<br /> <br /> ;;judge small enough<br /> (defun close-enough? (x y)<br />   (< (abs (- x y)) 1e-10)<br /> )<br /> <br /> ;; The equation to be solve, -x^3+2x+3=0<br /> ;;  2*x*sin(arcl/2/x)-linel<br /> (defun myfuntosolve (x)<br />   (- (* x 2.0 (sin (/ arclength 2. x))) linelength)<br /> )<br /> <br /> ;;Main function by qjchen@gmail.com<br /> (defun c:t( / a ang arclength d linelength p1 r)<br />   (setq a (vlax-ename->vla-object (car (entsel "\n Please select a line"))) arclength (getreal "\n Arc Length"))<br />   (setq linelength (Vlax-get  a 'length))<br />   (if (> arclength linelength)<br />     (progn (princ (rtos (setq r (halfsolve myfuntosolve (/ linelength 2.0) (/ linelength 0.01))) 2 14))<br />            (setq P1 (Vlax-get  a 'StartPoint)<br />                  ang (Vlax-get  a 'Angle)<br />                  d (sqrt (- (* r r) (* linelength linelength 0.25))))<br />            (command "circle" (polar (polar P1 ang (* 0.5 linelength)) (+ ang (* 0.5 pi)) d) r)<br />            (command "circle" (polar (polar P1 ang (* 0.5 linelength)) (+ ang (* 0.5 pi)) (- d)) r)<br />     )<br />     (princ "the Arc length is too small")<br />   )<br />   (princ)<br /> )<br />

gaogl168

这里真是高手如云！在一次计算盘梯的时候，最后归纳为这样一个问题！
在此非常感谢楼上各位不仅给出了思路，还给出了程序！非常感谢！

preschool

很诧异，就在原弧线上再任意画两条弦，然后分别做出中垂线，得到两垂线交点便是圆心了。