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1、15.费马曲线（有点像螺纹线）kms开思网数学方程：rr = a*a*thetakms开思网圓柱坐标kms开思网方程1: theta=360*t*5kms开思网a=4kms开思网r=a*sqrt(theta*180/pi)kms开思网方程2: theta=360*t*5kms开思网a=4kms开思网r=-a*sqrt(theta*180/pi)kms开思网由于Pro/e只能做连续的曲线，所以只能分两次做kms开思网11.心脏线kms开思网圓柱坐标kms开思网方程：a=10 kms开思网r=a*(1+cos(theta) kms开思网theta=t*360kms开思网kms开思网kms开思网图1
2、1kms开思网kms开思网12.圆内螺旋线kms开思网采用柱座标系 kms开思网方程：theta=t*360 kms开思网r=10+10*sin(6*theta) kms开思网z=2*sin(6*theta)kms开思网kms开思网kms开思网图12kms开思网kms开思网13.正弦曲线kms开思网笛卡尔坐标系 kms开思网方程：x=50*t kms开思网y=10*sin(t*360) kms开思网z=0kms开思网kms开思网kms开思网图13kms开思网kms开思网14.太阳线（这本来是做别的曲线的，结果做错了，就变成这样了）kms开思网kms开思网kms开思网图14kms开思网kms开思
3、网每一页的曲线类型如下：kms开思网第1页：碟形弹簧、葉形线、螺旋线(Helical curve)、蝴蝶曲线和渐开线；kms开思网第2页：螺旋线、对数曲线、球面螺旋线、双弧外摆线和星行线；kms开思网第3页：心脏线、圆内螺旋线、正弦曲线、太阳线和费马曲线（有点像螺纹线）；kms开思网第4页：Talbot 曲线、4叶线、Rhodonea 曲线 、抛物线和螺旋线；kms开思网第5页：三叶线、外摆线、Lissajous 曲线、长短幅圆内旋轮线和长短幅圆外旋轮线；kms开思网第6页：三尖瓣线、概率曲线、箕舌线、阿基米德螺线和对数螺线；kms开思网第7页：蔓叶线、tan曲线、双曲余弦、双曲正弦和双曲正切
4、；kms开思网第8页：一峰三驻点曲线、八字曲线、螺旋曲线、圆和封闭球形环绕曲线；kms开思网第9页：柱坐标螺旋曲线、蛇形曲线、8字形曲线、椭圆曲线和梅花曲线；kms开思网第10页：花曲线、空间感更强的花曲线、螺旋上升的椭圆线、螺旋花曲线和鼓形线；kms开思网第11页：长命锁曲线、簪形线、螺旋上升曲线、蘑菇曲线和8字曲线；kms开思网第12页：梅花曲线、桃形曲线、碟形弹簧、环形二次曲线和蝶线；kms开思网第13页：正弦周弹簧、环形螺旋线、内接弹簧、多变内接式弹簧和柱面正弦波线；kms开思网第14页：ufo（漩涡线）手把曲线、篮子、圆柱齿轮齿廓的渐开线方程和对数螺旋曲线；kms开思网第15页：罩形
5、线、向日葵线、太阳线、塔形螺旋线和花瓣线；kms开思网第16页：双元宝线、阿基米德螺线的变形、渐开线方程、双鱼曲线和蝴蝶结曲线；kms开思网第17页：“两相望”曲线、小蜜蜂、弯月、热带鱼和燕尾剪；kms开思网第18页：天蚕丝、心电图、变化后的星形线、小白兔和大家好；kms开思网第19页：蛇形线、五环、蜘蛛网、次声波和十字渐开线；kms开思网第20页：内五环和蜗轨线；kms开思网kms开思网1.碟形弹簧kms开思网圓柱坐标 kms开思网方程：r = 5 kms开思网theta = t*3600 kms开思网z =(sin(3.5*theta-90)+24*tkms开思网kms开思网kms开思网图
6、1kms开思网kms开思网2.葉形线.kms开思网笛卡儿坐標标kms开思网方程：a=10 kms开思网x=3*a*t/(1+(t3) kms开思网y=3*a*(t2)/(1+(t3)kms开思网kms开思网kms开思网图2kms开思网kms开思网3.螺旋线(Helical curve)kms开思网圆柱坐标（cylindrical） kms开思网方程： r=t kms开思网theta=10+t*(20*360) kms开思网z=t*3kms开思网kms开思网kms开思网图3kms开思网kms开思网4.蝴蝶曲线kms开思网球坐标 kms开思网方程：rho = 8 * t kms开思网theta =
7、 360 * t * 4 kms开思网phi = -360 * t * 8kms开思网kms开思网kms开思网图4kms开思网kms开思网5.渐开线kms开思网采用笛卡尔坐标系kms开思网方程：r=1 kms开思网ang=360*t kms开思网s=2*pi*r*t kms开思网x0=s*cos(ang) kms开思网y0=s*sin(ang) kms开思网x=x0+s*sin(ang) kms开思网y=y0-s*cos(ang) kms开思网z=0kms开思网kms开思网kms开思网图5kms开思网6.螺旋线.kms开思网笛卡儿坐标 kms开思网方程：x = 4 * cos ( t *(5*
8、360) kms开思网y = 4 * sin ( t *(5*360) kms开思网z = 10*tkms开思网kms开思网kms开思网图6kms开思网kms开思网7.对数曲线kms开思网笛卡尔坐标系 kms开思网方程：z=0 kms开思网x = 10*t kms开思网y = log(10*t+0.0001)kms开思网kms开思网kms开思网图7kms开思网kms开思网8.球面螺旋线kms开思网采用球坐标系kms开思网方程：rho=4 kms开思网theta=t*180 kms开思网phi=t*360*20kms开思网kms开思网kms开思网图8kms开思网kms开思网9.双弧外摆线kms开
9、思网卡迪尔坐标 kms开思网方程： l=2.5 kms开思网b=2.5 kms开思网x=3*b*cos(t*360)+l*cos(3*t*360) kms开思网Y=3*b*sin(t*360)+l*sin(3*t*360)kms开思网kms开思网kms开思网图9kms开思网kms开思网10.星行线kms开思网卡迪尔坐标 kms开思网方程：a=5 kms开思网x=a*(cos(t*360)3 kms开思网y=a*(sin(t*360)3kms开思网kms开思网16.Talbot 曲线kms开思网卡笛尔坐标kms开思网方程：theta=t*360kms开思网a=1.1kms开思网b=0.666km
10、s开思网c=sin(theta)kms开思网f=1kms开思网x = (a*a+f*f*c*c)*cos(theta)/akms开思网y = (a*a-2*f+f*f*c*c)*sin(theta)/bkms开思网kms开思网kms开思网图16kms开思网kms开思网17.4叶线（一个方程做的，没有复制）kms开思网kms开思网kms开思网图17kms开思网kms开思网18.Rhodonea 曲线 kms开思网采用笛卡尔坐标系 kms开思网方程：theta=t*360*4 kms开思网x=25+(10-6)*cos(theta)+10*cos(10/6-1)*theta) kms开思网y=25
11、+(10-6)*sin(theta)-6*sin(10/6-1)*theta)kms开思网kms开思网kms开思网图18kms开思网kms开思网19. 抛物线 kms开思网笛卡儿坐标kms开思网方程：x =(4 * t) kms开思网y =(3 * t) + (5 * t 2) kms开思网z =0kms开思网kms开思网kms开思网图19kms开思网kms开思网20.螺旋线kms开思网圓柱坐标kms开思网方程：r = 5 kms开思网theta = t*1800 kms开思网z =(cos(theta-90)+24*tkms开思网kms开思网kms开思网21.三叶线kms开思网圆柱坐标kms
12、开思网方程：a=1kms开思网theta=t*380kms开思网b=sin(theta)kms开思网r=a*cos(theta)*(4*b*b-1)kms开思网kms开思网kms开思网图21kms开思网22.外摆线kms开思网迪卡尔坐标kms开思网方程：theta=t*720*5kms开思网b=8kms开思网a=5kms开思网x=(a+b)*cos(theta)-b*cos(a/b+1)*theta)kms开思网y=(a+b)*sin(theta)-b*sin(a/b+1)*theta)kms开思网z=0kms开思网kms开思网kms开思网图22kms开思网kms开思网23. Lissajou
13、s 曲线kms开思网theta=t*360kms开思网a=1kms开思网b=1kms开思网c=100kms开思网n=3kms开思网x=a*sin(n*theta+c)kms开思网y=b*sin(theta)kms开思网kms开思网kms开思网图23kms开思网kms开思网24.长短幅圆内旋轮线kms开思网卡笛尔坐标kms开思网方程：a=5kms开思网b=7kms开思网c=2.2kms开思网theta=360*t*10kms开思网x=(a-b)*cos(theta)+c*cos(a/b-1)*theta)kms开思网y=(a-b)*sin(theta)-c*sin(a/b-1)*theta)km
14、s开思网kms开思网kms开思网图24kms开思网kms开思网25.长短幅圆外旋轮线kms开思网卡笛尔坐标kms开思网方程：theta=t*360*10kms开思网a=5kms开思网b=3kms开思网c=5kms开思网x=(a+b)*cos(theta)-c*cos(a/b+1)*theta)kms开思网y=(a+b)*sin(theta)-c*sin(a/b+1)*theta)kms开思网26. 三尖瓣线kms开思网a=10kms开思网x = a*(2*cos(t*360)+cos(2*t*360)kms开思网y = a*(2*sin(t*360)-sin(2*t*360)kms开思网kms
15、开思网kms开思网图26kms开思网kms开思网27.概率曲线！kms开思网方程：kms开思网笛卡儿坐标kms开思网x = t*10-5kms开思网y = exp(0-x2)kms开思网kms开思网kms开思网图27kms开思网kms开思网28.箕舌线kms开思网笛卡儿坐标系kms开思网a = 1kms开思网x = -5 + t*10kms开思网y = 8*a3/(x2+4*a2)kms开思网kms开思网kms开思网图28kms开思网kms开思网29.阿基米德螺线kms开思网柱坐标kms开思网a=100kms开思网theta = t*400kms开思网r = a*thetakms开思网kms开
16、思网kms开思网图29kms开思网kms开思网30.对数螺线kms开思网柱坐标kms开思网theta = t*360*2.2kms开思网a = 0.005kms开思网r = exp(a*theta)kms开思网31.蔓叶线kms开思网笛卡儿坐标系kms开思网a=10kms开思网y=t*100-50kms开思网solvekms开思网x3 = y2*(2*a-x)kms开思网for xkms开思网kms开思网kms开思网图31kms开思网kms开思网32.tan曲线kms开思网笛卡儿坐标系kms开思网x = t*8.5 -4.25kms开思网y = tan(x*20)kms开思网kms开思网kms
17、开思网图32kms开思网kms开思网33.双曲余弦kms开思网x = 6*t-3kms开思网y = (exp(x)+exp(0-x)/2kms开思网kms开思网kms开思网图33kms开思网kms开思网34.双曲正弦kms开思网x = 6*t-3kms开思网y = (exp(x)-exp(0-x)/2kms开思网kms开思网kms开思网图34kms开思网kms开思网35.双曲正切kms开思网x = 6*t-3kms开思网y = (exp(x)-exp(0-x)/(exp(x)+exp(0-x)kms开思网kms开思网36.一峰三驻点曲线kms开思网x = 3*t-1.5kms开思网y=(x2-
18、1)3+1kms开思网kms开思网kms开思网图36kms开思网kms开思网37.八字曲线kms开思网x = 2 * cos ( t *(2*180) kms开思网y = 2 * sin ( t *(5*360) kms开思网z = 0kms开思网kms开思网kms开思网图37kms开思网kms开思网38.螺旋曲线kms开思网r=t*(10*180)+1kms开思网theta=10+t*(20*180)kms开思网z=tkms开思网kms开思网kms开思网图38kms开思网kms开思网39.圆kms开思网x = cos ( t *(5*180) kms开思网y = sin ( t *(5*18
19、0) kms开思网z = 0kms开思网kms开思网kms开思网图39kms开思网kms开思网40.封闭球形环绕曲线kms开思网rho=2kms开思网theta=360*tkms开思网phi=t*360*10kms开思网41.柱坐标螺旋曲线kms开思网x = 100*t * cos ( t *(5*180) kms开思网y = 100*t * sin ( t *(5*180) kms开思网z = 0kms开思网kms开思网kms开思网图41kms开思网42.蛇形曲线kms开思网x = 2 * cos ( (t+1) *(2*180) kms开思网y = 2 * sin ( t *(5*360)
20、 kms开思网z = t*(t+1)kms开思网kms开思网kms开思网图42kms开思网kms开思网43.8字形曲线kms开思网柱坐标kms开思网theta = t*360kms开思网r=10+(8*sin(theta)2kms开思网kms开思网kms开思网图43kms开思网kms开思网44.椭圆曲线kms开思网笛卡尔坐标系kms开思网a = 10kms开思网b = 20kms开思网theta = t*360kms开思网x = a*cos(theta)kms开思网y = b*sin(theta)kms开思网kms开思网kms开思网图44kms开思网kms开思网45.梅花曲线kms开思网柱坐标
21、kms开思网theta = t*360kms开思网r=10+(3*sin(theta*2.5)2kms开思网kms开思网kms开思网46.另一个花曲线kms开思网theta = t*360kms开思网r=10-(3*sin(theta*3)2kms开思网z=4*sin(theta*3)2kms开思网kms开思网kms开思网图46kms开思网kms开思网47.改一下就成为空间感更强的花曲线了;)kms开思网theta = t*360kms开思网r=10-(3*sin(theta*3)2kms开思网z=(r*sin(theta*3)2kms开思网kms开思网kms开思网图47kms开思网kms开思
22、网48.螺旋上升的椭圆线kms开思网a = 10kms开思网b = 20kms开思网theta = t*360*3kms开思网x = a*cos(theta)kms开思网y = b*sin(theta)kms开思网z=t*12kms开思网kms开思网kms开思网图48kms开思网kms开思网49.甚至这种螺旋花曲线kms开思网theta = t*360*4kms开思网r=10+(3*sin(theta*2.5)2kms开思网z = t*16kms开思网kms开思网kms开思网图49kms开思网kms开思网50 鼓形线 kms开思网笛卡尔方程kms开思网r=5+3.3*sin(t*180)+tk
23、ms开思网theta=t*360*10kms开思网z=t*10 kms开思网51 长命锁曲线kms开思网笛卡尔方程：kms开思网a=1*t*359.5kms开思网b=q2*t*360kms开思网c=q3*t*360kms开思网rr1=w1kms开思网rr2=w2kms开思网rr3=w3kms开思网x=rr1*cos(a)+rr2*cos(b)+rr3*cos(c)kms开思网y=rr1*sin(a)+rr2*sin(b)+rr3*sin(c)kms开思网kms开思网kms开思网图51kms开思网kms开思网52 簪形线kms开思网球坐标 kms开思网方程：kms开思网rho=200*tkms开
24、思网theta=900*tkms开思网phi=t*90*10kms开思网kms开思网kms开思网图52kms开思网kms开思网53.螺旋上升曲线kms开思网r=t10kms开思网theta=t3*360*6*3+t3*360*3*3kms开思网z=t3*(t+1)kms开思网kms开思网kms开思网图53kms开思网kms开思网54.蘑菇曲线kms开思网rho=t3+t*(t+1)kms开思网theta=t*360kms开思网phi=t2*360*20*20kms开思网kms开思网kms开思网图54kms开思网kms开思网55. 8字曲线kms开思网a=1kms开思网b=1kms开思网x=3*
25、b*cos(t*360)+a*cos(3*t*360)kms开思网Y=b*sin(t*360)+a*sin(3*t*360)kms开思网kms开思网56.梅花曲线kms开思网theta=t*360kms开思网r=100+50*cos(5*theta)kms开思网z=2*cos(5*theta)kms开思网kms开思网kms开思网图56kms开思网kms开思网57.桃形曲线kms开思网rho=t3+t*(t+1)kms开思网theta=t*360kms开思网phi=t2*360*10*10kms开思网kms开思网kms开思网图57kms开思网kms开思网58.名稱:碟形弹簧 kms开思网建立環境
26、:pro/e kms开思网圓柱坐 kms开思网r = 5 kms开思网theta = t*3600 kms开思网z =(sin(3.5*theta-90)+24kms开思网kms开思网kms开思网图58kms开思网kms开思网59.环形二次曲线kms开思网笛卡儿方程：kms开思网x=50*cos(t*360)kms开思网y=50*sin(t*360)kms开思网z=10*cos(t*360*8)kms开思网kms开思网kms开思网图59kms开思网kms开思网60 蝶线kms开思网球坐标：kms开思网rho=4*sin(t*360)+6*cos(t*3602)kms开思网theta=t*360
27、kms开思网phi=log(1+t*360)*t*360kms开思网球坐标：kms开思网rho=t*202kms开思网theta=t*log(30)*60kms开思网phi=t*7200kms开思网kms开思网kms开思网图66kms开思网kms开思网67. 手把曲线kms开思网thta0=t*360kms开思网thta1=t*360*6kms开思网r0=400kms开思网r1=40kms开思网r=r0+r1*cos(thta1)kms开思网x=r*cos(thta0)kms开思网y=r1*sin(thta1)kms开思网z=0kms开思网kms开思网kms开思网图67kms开思网kms开思网
28、68.篮子 kms开思网圆柱坐标 kms开思网r=5+0.3*sin(t*180)+t kms开思网theta=t*360*30 kms开思网z=t*5kms开思网kms开思网kms开思网图68kms开思网kms开思网69. 圆柱齿轮齿廓的渐开线方程：kms开思网afa=60*tkms开思网x=10*cos(afa)+pi*10*afa/180*sin(afa)kms开思网x=10*sin(afa)-pi*10*afa/180*cos(afa)kms开思网z=0kms开思网注：afa为压力角，取值范围是0到60，10为基圆半径。kms开思网kms开思网kms开思网图69kms开思网kms开思网
29、70.对数螺旋曲线kms开思网柱坐标：kms开思网r=sqrt(theta)kms开思网theta=t*360*30kms开思网z=0kms开思网71. 罩形线kms开思网球坐标:kms开思网rho=4kms开思网theta=t*60kms开思网phi=t*360*10kms开思网kms开思网kms开思网图71kms开思网kms开思网72. 向日葵线kms开思网theta=t*360kms开思网r=30+10*sin(theta*30)kms开思网z=0kms开思网kms开思网kms开思网图72kms开思网kms开思网73. 太阳线kms开思网r=1.5*cos(50*theta)+1kms开思网theta=t*360kms开思网z=0kms开思网kms开思网kms开思网图73kms开思网kms开思网74 塔形螺旋线kms开思网r=t*80+50kms开思网theta=t*360*10kms开思网z=t*80kms开思网kms开思网kms开思网图74kms开思网kms开思网75 花瓣线kms开思网球坐标：kms开思网rho=t*20kms开思网theta=t*360*90kms开思网phi=t*360*10kms开思网