ProENGINEER方程曲線講課教案

1、Good is good, but better carries it.精益求精，善益求善。ProENGINEER方程曲線-方程曲線1.碟形彈簧圓柱坐標(biāo)方程：r=5theta=t*3600z=(sin(3.5*theta-90)+24*t2.葉形線.笛卡兒坐標(biāo)標(biāo)方程：a=10 x=3*a*t/(1+(t3)y=3*a*(t2)/(1+(t3)3.螺旋線(Helicalcurve)圓柱坐標(biāo)（cylindrical）方程：r=ttheta=10+t*(20*360)z=t*34.蝴蝶曲線球坐標(biāo)方程：rho=8*ttheta=360*t*4phi=-360*t*85.漸開線采用笛卡爾坐標(biāo)系方程：r=

2、1ang=360*ts=2*pi*r*tx0=s*cos(ang)y0=s*sin(ang)x=x0+s*sin(ang)y=y0-s*cos(ang)z=06.螺旋線.笛卡兒坐標(biāo)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(biāo)系方程：z=0 x=10*ty=log(10*t+0.0001)8.球面螺旋線采用球坐標(biāo)系方程：rho=4theta=t*180phi=t*360*209.雙弧外擺線卡迪爾坐標(biāo)方程：l=2.5b=2.5x=3*b*cos(t*360)+l*cos(3*t*360)Y=3*b*sin(t*360)+l*sin(3

3、*t*360)10.星行線卡迪爾坐標(biāo)方程：a=5x=a*(cos(t*360)3y=a*(sin(t*360)311.心臟線圓柱坐標(biāo)方程：a=10r=a*(1+cos(theta)theta=t*36012.圓內(nèi)螺旋線采用柱座標(biāo)系方程：theta=t*360r=10+10*sin(6*theta)z=2*sin(6*theta)13.正弦曲線笛卡爾坐標(biāo)系方程：x=50*ty=10*sin(t*360)z=015.費(fèi)馬曲線（有點(diǎn)像螺紋線）數(shù)學(xué)方程：rr=a*a*theta圓柱坐標(biāo)方程1:theta=360*t*5a=4r=a*sqrt(theta*180/pi)方程2:theta=360*t*5

4、a=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(biāo)方程：theta=t*360a=1.1b=0.666c=sin(theta)f=1x=(a*a+f*f*c*c)*cos(theta)/ay=(a*a-2*f+f*f*c*c)*sin(theta)/b18.Rhodonea曲線采用笛卡爾坐標(biāo)系方程：theta=t*360*4x=25+(10-6)*cos(theta)+10*cos(10/6-1)*theta)y=25+(10-6)*sin(theta)-6*sin(10/6-1)*theta)19.拋物線笛卡兒

5、坐標(biāo)方程：x=(4*t)y=(3*t)+(5*t2)z=020.螺旋線圓柱坐標(biāo)方程：r=5theta=t*1800z=(cos(theta-90)+24*t21.三葉線圓柱坐標(biāo)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(biāo)方程：theta=t*720*5b=8a=5x=(a+b)*cos(theta)-b*cos(a/b+1)*theta)y=(a+b)*sin(theta)-b*sin(a/b+1)*theta)z=023.Lissajous曲線theta=t*360a=1b=1c=100n=3x=a*sin(

6、n*theta+c)y=b*sin(theta)24.長短幅圓內(nèi)旋輪線卡笛爾坐標(biāo)方程：a=5b=7c=2.2theta=360*t*10 x=(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(biāo)方程：theta=t*360*10a=5b=3c=5x=(a+b)*cos(theta)-c*cos(a/b+1)*theta)y=(a+b)*sin(theta)-c*sin(a/b+1)*theta)26.三尖瓣線a=10 x=a*(2*cos(t*360)+cos(2*t

7、*360)y=a*(2*sin(t*360)-sin(2*t*360)27.概率曲線！方程：笛卡兒坐標(biāo)x=t*10-5y=exp(0-x2)28.箕舌線笛卡兒坐標(biāo)系a=1x=-5+t*10y=8*a3/(x2+4*a2)29.阿基米德螺線柱坐標(biāo)a=100theta=t*400r=a*theta30.對數(shù)螺線柱坐標(biāo)theta=t*360*2.2a=0.005r=exp(a*theta)31.蔓葉線笛卡兒坐標(biāo)系a=10y=t*100-50solvex3=y2*(2*a-x)forx32.tan曲線笛卡兒坐標(biāo)系x=t*8.5-4.25y=tan(x*20)33.雙曲余弦x=6*t-3y=(exp(x

8、)+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(0-x)/(exp(x)+exp(0-x)36.一峰三駐點(diǎn)曲線x=3*t-1.5y=(x2-1)3+137.八字曲線x=2*cos(t*(2*180)y=2*sin(t*(5*360)z=038.螺旋曲線r=t*(10*180)+1theta=10+t*(20*180)z=t39.圓x=cos(t*(5*180)y=sin(t*(5*180)z=040.封閉球形環(huán)繞曲線rho=2theta=360*tphi=t*360*1041.柱坐標(biāo)螺旋曲線x=

9、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*(5*360)z=t*(t+1)43.8字形曲線柱坐標(biāo)theta=t*360r=10+(8*sin(theta)244.橢圓曲線笛卡爾坐標(biāo)系a=10b=20theta=t*360 x=a*cos(theta)y=b*sin(theta)45.梅花曲線柱坐標(biāo)theta=t*360r=10+(3*sin(theta*2.5)246.另一個花曲線theta=t*360r=10-(3*sin(theta*3)2z=4*sin(theta*3)2

10、47.改一下就成為空間感更強(qiáng)的花曲線了;)theta=t*360r=10-(3*sin(theta*3)2z=(r*sin(theta*3)247.改一下就成為空間感更強(qiáng)的花曲線了;)theta=t*360r=10-(3*sin(theta*3)2z=(r*sin(theta*3)248.螺旋上升的橢圓線a=10b=20theta=t*360*3x=a*cos(theta)y=b*sin(theta)z=t*1249.甚至這種螺旋花曲線theta=t*360*4r=10+(3*sin(theta*2.5)2z=t*1650鼓形線笛卡爾方程r=5+3.3*sin(t*180)+ttheta=t*

11、360*10z=t*1051長命鎖曲線笛卡爾方程：a=1*t*359.5b=q2*t*360c=q3*t*360rr1=w1rr2=w2rr3=w3x=rr1*cos(a)+rr2*cos(b)+rr3*cos(c)y=rr1*sin(a)+rr2*sin(b)+rr3*sin(c)52簪形線球坐標(biāo)方程：rho=200*ttheta=900*tphi=t*90*1053.螺旋上升曲線r=t10theta=t3*360*6*3+t3*360*3*3z=t3*(t+1)54.蘑菇曲線rho=t3+t*(t+1)theta=t*360phi=t2*360*20*20Rho:表示錨點(diǎn)到二次曲線兩端點(diǎn)的

12、距離與其在二次曲線上投影點(diǎn)到兩端點(diǎn)距離的比值。當(dāng)該值小于1/2時，生成一橢圓或橢圓?。划?dāng)該值等于1/2時，生成一拋物線；當(dāng)該值大于1/2時，則生成一雙曲線。phi:比率55.8字曲線a=1b=1x=3*b*cos(t*360)+a*cos(3*t*360)Y=b*sin(t*360)+a*sin(3*t*360)56.梅花曲線theta=t*360r=100+50*cos(5*theta)z=2*cos(5*theta)57.桃形曲線rho=t3+t*(t+1)theta=t*360phi=t2*360*10*1058.名稱:碟形彈簧建立環(huán)境:pro/e圓柱坐r=5theta=t*3600z=

13、(sin(3.5*theta-90)+2459.環(huán)形二次曲線笛卡兒方程：x=50*cos(t*360)y=50*sin(t*360)z=10*cos(t*360*8)60蝶線球坐標(biāo)：rho=4*sin(t*360)+6*cos(t*3602)theta=t*360phi=log(1+t*360)*t*36061.正弦周彈簧笛卡爾：ang1=t*360ang2=t*360*20 x=ang1*2*pi/360y=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*1

14、5)*sin(t*360)z=10*cos(t*360*5)63.內(nèi)接彈簧x=2*cos(t*360*10)+cos(t*180*10)y=2*sin(t*360*10)+sin(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(biāo)方程r=30theta=t*360z=5*sin(5*theta-90)66.ufo（漩渦線）球坐標(biāo)：rho=t*202theta=t*log(30)*60phi=t*720067.手把曲線thta0=t*

15、360thta1=t*360*6r0=400r1=40r=r0+r1*cos(thta1)x=r*cos(thta0)y=r1*sin(thta1)z=068.籃子圓柱坐標(biāo)r=5+0.3*sin(t*180)+ttheta=t*360*30z=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(biāo)：r=sqrt(theta)theta=t*360*30z=071.罩形

16、線球坐標(biāo):rho=4theta=t*60phi=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)+1theta=t*360z=074塔形螺旋線r=t*80+50theta=t*360*10z=t*8075花瓣線球坐標(biāo)：rho=t*20theta=t*360*90phi=t*360*1075花瓣線球坐標(biāo)：rho=t*20theta=t*360*90phi=t*360*1077阿基米德螺線的變形（自己想得）不知前面有沒有？:what柱坐標(biāo)下：theta=360*2*(t-0.5)r=10*thet

17、az=078改過來的漸開線方程r=20ang=t*360 x=r*cos(ang)+2*pi*r*t*sin(ang)y=r*sin(ang)-2*pi*r*t*cos(ang)z=079雙魚曲線球坐標(biāo)系rho=30+10*sin(t*360*10)theta=t*180*cos(t*360*10)phi=t*360*3080蝴蝶結(jié)曲線x=200*t*sin(t*3600)y=250*t*cos(t*3600)z=300*t*sin(t*1800)81”兩相望“曲線球坐標(biāo)系rho=30theta=t*360*cos(t*360*20)phi=t*360*2082小蜜蜂笛卡爾坐標(biāo)系：x=cos(

18、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=sin(t*360)*2+sin(t*360)*284熱帶魚a=5x=(a*(cos(t*360*3)4)*ty=(a*(sin(t*360*3)4)*t85燕尾剪x=3*cos(t*360*4)y=3*sin(t*360*3)z=t86天蠶絲theta=t*3600r=(cos(360*t*20)*.5*t+1)*t87心電圖圓柱坐標(biāo)系：r=sin(t*360*2)+.2theta=10+t*(6*360)z=t*389小白兔theta=t*360-90r=cos(360*(t/(1+t(6.5)*6*t)*3.5+590大家好theta=t*360+180r=cos(360*t3*6)*2+591蛇形線笛卡爾坐標(biāo)系：x=2*cos(t*360*3)*ty=2*sin(t*360*3)*tz=(sqrt(sqrt(sqrt(t)3*592五環(huán)柱坐標(biāo)：theta=t*360*