PROE曲線常用公式

1、圓柱坐標方程：r = 5theta = t*3600z =(sin(3.5*theta-90)+24*t2.葉形線.笛卡兒坐標標方程：a=10x=3*a*t/(1+(tA3)y=3*a*(tA2)/(1+(tA3)3.螺旋線(Helical curve) 圓柱坐標(cylindrical ) 方程：r=t theta=10+t*(20*360) z=t*34.蝴蝶曲線 球坐標方程：rho = 8 * ttheta = 360 * t * 4phi = -360 * t * 85.漸開線 米用笛卡爾坐標系 方程：r=1an g=360*t s=2*pi*r*t x0=s*cos(a ng) y0

2、=s*s in(ang) x=x0+s*s in(ang) y=y0-s*cos(a ng) z=06螺旋線.笛卡兒坐標方程：x = 4 * cos ( t *(5*360)y = 4 * sin ( t *(5*360)z = 10*t7對數(shù)曲線笛卡爾坐標系方程：z=0x = 10*ty = log(10*t+0.0001)8. 球面螺旋線采用球坐標系方程：rho=4 theta=t*180 phi=t*360*209. 雙弧外擺線卡迪爾坐標方程：1=2.5b=2.5x=3*b*cos(t*360)+l*cos(3*t*360)Y=3*b*sin(t*360)+l*sin(3*t*360)1

3、0. 星行線卡迪爾坐標方程：a=5 x=a*(cos(t*360)A3 y=a*(sin(t*360)A311.心臟線圓柱坐標方程：a=10r=a*(1+cos(theta)theta=t*36012.圓內(nèi)螺旋線 米用柱座標系方程：theta=t*360r=10+10*sin(6*theta)z=2*sin(6*theta)y=10*sin(t*360)z=013.正弦曲線 笛卡爾坐標系14.太陽線這本來是做別的曲線的，結(jié)果做錯了，就變成這樣了方程：x=50*t15.費馬曲線(有點像螺紋線)數(shù)學(xué)方程：r * r = a*a*theta圓柱坐標方程 1: theta=360*t*5a=4r=a*

4、sqrt(theta*180/pi)方程 2: theta=360*t*5a=4r=-a*sqrt(theta*180/pi)由于Pro/e只能做連續(xù)的曲線，所以只能分兩次做16.Talbot 曲線卡笛爾坐標方程：theta=t*360a=1.1b=0.666c=s in( theta)f=1x = (a*a+f*f*c*c)*cos(theta)/ay = (a*a-2*f+f*f*c*c)*si n(theta)/b17.4葉線一個方程做的，沒有復(fù)制18.Rhodonea 曲線采用笛卡爾坐標系方程：theta=t*360*4x=25+(10-6)*cos(theta)+10*cos(10/

5、6-1)*theta)y=25+(10-6)*sin(theta)-6*sin(10/6-1)*theta)19.拋物線笛卡兒坐標方程：x =(4 * t)y =(3 * t) + (5 * t A2)z =0 :20.螺旋線圓柱坐標方程：r = 5theta = t*1800z =(cos(theta-90)+24*t21.三葉線圓柱坐標方程：a=1theta=t*380b=sin(theta) r=a*cos(theta)*(4*b*b-1)22.外擺線迪卡爾坐標方程：theta=t*720*5b=8a=5x=(a+b)*cos(theta)-b*cos(a/b+1)*theta) y=(

6、a+b)*sin(theta)-b*sin(a/b+1)*theta) z=023. Lissajous 曲線 theta=t*360a=1b=1 c=100 n=3 x=a*si n(n *theta+c) y=b*si n(theta)24.長短幅圓內(nèi)旋輪線卡笛爾坐標方程：a=5b=7c=2.2theta=360*t*10x=(a-b)*cos(theta)+c*cos(a/b-1)*theta)y=(a-b)*sin(theta)-c*sin(a/b-1)*theta)25.長短幅圓外旋輪線 卡笛爾坐標方程：theta=t*360*10a=5b=3c=5x=(a+b)*cos(theta

7、)-c*cos(a/b+1)*theta) y=(a+b)*si n(theta)-c*s in (a/b+1)*theta)26.三尖瓣線a=10x = a*(2*cos(t*360)+cos(2*t*360) y = a*(2*si n(t*360)-si n(2*t*360)27.概率曲線！方程：笛卡兒坐標x = t*10-5y = exp(0-xA2)28.箕舌線笛卡兒坐標系a = 1x = -5 + t*10y = 8*aA3/(xA2+4*aA2)29.阿基米德螺線 柱坐標a=100theta = t*400r = a*theta30.對數(shù)螺線柱坐標theta = t*360*2.

8、2 a = 0.005r = exp(a*theta)31.蔓葉線笛卡兒坐標系a=10 y=t*100-50 solvexA3 = yA2*(2*a-x)for x32.tan曲線笛卡兒坐標系x = t*8.5-4.25y = tan(x*20)33.雙曲余弦x = 6*t-3y = (exp(x)+exp(0-x)/234.雙曲正弦x = 6*t-3y = (exp(x)-exp(0-x)/235.雙曲正切x = 6*t-3y = (exp(x)-exp(O-x)/(exp(x)+exp(O-x)36. 一峰三駐點曲線x = 3*t-1.5 y=(xA2-1)A3+10z37.八字曲線x =

9、 2 * cos ( t *(2*180)y = 2 * sin ( t *(5*360)38.螺旋曲線r=t*(10*180)+1 theta=10+t*(20*180) z=t39圓x = cos ( t *(5*180)y = si n ( t *(5*180)z = 040.封閉球形環(huán)繞曲線rho=2theta=360*tphi=t*360*1041.柱坐標螺旋曲線x = 100*t * cos ( t *(5*180)y = 100*t * sin ( t *(5*180)z = 042.蛇形曲線x = 2 * cos ( (t+1)*(2*180)y = 2 * sin ( t *

10、(5*360)z = t*(t+1)43.8字形曲線柱坐標theta = t*360r=10+(8*si n( theta)A244橢圓曲線 笛卡爾坐標系a = 10b = 20theta = t*360x = a*cos(theta) y = b*s in( theta)45.梅花曲線柱坐標theta = t*360r=10+(3*s in (theta*2.5)F246另一個花曲線theta = t*360r=10-(3*si n(theta*3)A2z=4*si n(theta*3)A247.改一下就成為空間感更強的花曲線了;)theta = t*360r=10-(3*sin(theta

11、*3)F2z=(r*sin(theta*3)F248.螺旋上升的橢圓線a = 10b = 20theta = t*360*3x = a*cos(theta) y = b*s in( theta) z=t*1249甚至這種螺旋花曲線 theta = t*360*4r=10+(3*si n(theta*2.5)A2z = t*1650鼓形線笛卡爾方程r=5+3.3*si n(t*180)+t theta=t*360*10 z=t*1051長命鎖曲線笛卡爾方程：a=1*t*359.5b=q2*t*360c=q3*t*360rr仁w1rr2=w2rr3=w3x=rr1*cos(a)+rr2*cos(b

12、)+rr3*cos(c)y=rr1*sin(a)+rr2*sin(b)+rr3*sin(c)51長命鎖曲線笛卡爾方程：a=1*t*359.5b=q2*t*360c=q3*t*360rr仁w1rr2=w2rr3=w3x=rr1*cos(a)+rr2*cos(b)+rr3*cos(c)y=rr1*sin(a)+rr2*sin(b)+rr3*sin(c)圖5152簪形線球坐標方程：rho=200*ttheta=900*tphi=t*90*1053.螺旋上升曲線r=tA10theta=tA3*360*6*3+tA3*360*3*3z=tA3*(t+1)54.蘑菇曲線rho=tA3+t*(t+1) th

13、eta=t*360 phi=tA2*360*20*2055. 8字曲線a=1b=1x=3*b*cos(t*360)+a*cos(3*t*360)Y=b*si n(t*360)+a*si n(3*t*360)56.梅花曲線theta=t*360 r=100+50*cos(5*theta) z=2*cos(5*theta)57.桃形曲線rho=tA3+t*(t+1)theta=t*360phi=tA2*360*10*1058.名稱：碟形彈簧 建立環(huán)境:pro/e 圓柱坐r = 5 theta = t*3600z =(si n(3.5*theta-90)+2459.環(huán)形二次曲線笛卡兒方程：x=50*

14、cos(t*360)y=50*sin(t*360)z=10*cos(t*360*8)60蝶線球坐標：rho=4*si n(t*360)+6*cos(t*360A2)theta=t*360phi=log(1+t*360)*t*36061.正弦周彈簧笛卡爾：ang1=t*360ang2=t*360*20x=ang1*2*pi/360 y=sin(ang1)*5+cos(ang2)z=sin(ang2)62.環(huán)形螺旋線x= ( 50+10*sin(t*360*15)*cos(t*360)y=(50+10*sin(t*360*15)*sin(t*360)z=10*cos(t*360*5)63.內(nèi)接彈簧

15、x=2*cos(t*360*10)+cos(t*180*10) y=2*si n( t*360*10)+si n(t*180*10) z=t*664.多變內(nèi)接式彈簧x=3*cos(t*360*8)-1.5*cos(t*480*8)y=3*sin(t*360*8)-1.5*sin(t*480*8)z=t*865.柱面正弦波線柱坐標：方程r=30theta=t*360z=5*si n(5*theta-90)66. ufo 漩渦線球坐標：rho=t*20A2theta=t*log(30)*60phi=t*720067. 手把曲線 thta0=t*360 thta1=t*360*6 r0=400 r1

16、=40 r=r0+r1*cos(thta1) x=r*cos(thta0) y=r1*sin(thta1) z=068. 籃子圓柱坐標r=5+0.3*si n(t*180)+t theta=t*360*30 z=t*569. 圓柱齒輪齒廓的漸開線方程：afa=60*tx=10*cos(afa)+pi*10*afa/180*sin(afa)x=10*sin(afa)-pi*10*afa/180*cos(afa)z=0注：afa為壓力角，取值范圍是0到60 , 10為基圓半徑。70.對數(shù)螺旋曲線柱坐標：r=sqrt(theta) theta=t*360*30 z=071.罩形線球坐標：rho=4

17、theta=t*60 phi=t*360*1072.向日葵線theta=t*360r=30+10*sin(theta*30)z=073.太陽線r=1.5*cos(50*theta)+1 theta=t*360z=074塔形螺旋線 r=t*80+50 theta=t*360*10 z=t*8075花瓣線球坐標：rho=t*20 theta=t*360*90 phi=t*360*1076雙元寶線r=sin(t*360*10)+30theta=sin(t*360*15)z=sin(t*3)77阿基米德螺線的變形(自己想得)不知前面有沒有？：what柱坐標下：theta=360*2*(t-0.5)r=

18、10*thetaz=078改正來的漸開線方程r=20ang = t*360x=r*cos(a ng)+2*pi*r*t*si n(ang) y=r*si n(an g)-2*pi*r*t*cos(a ng) z=079雙魚曲線80蝴蝶結(jié)曲線球坐標系rho=30+10*sin(t*360*10) theta=t*180*cos(t*360*10) phi=t*360*30x=200*t*sin (t*3600) y=250*t*cos(t*3600) z=300*t*s in (t*1800)81 兩相望“曲線球坐標系rho=30theta=t*360*cos(t*360*20)phi=t*360*2082小蜜蜂笛卡爾坐標系：x=cos(t*360)+cos(3*t*360)Y=sin(t*360)+sin(5*t*360)83彎月x=cos(t*360)+cos(2*t*360)Y=si n(t*360)*2+si n(t*360)*284熱帶魚 a=