1. Disc spring

circular cylindrical coordinates

Equation: r = 5

θ= t * 3600

z =(sin(3.5 *θ-90))+24 * t

2. Leaf line.

cartesian coordinate system

Equation: a= 10

x=3*a*t/( 1+(t^3))

y=3*a*(t^2)/( 1+(t^3))

3. Spiral curve

Cylindrical coordinates (cylindrical)

Equation: r=t

θ= 10+t *(20 * 360)

z=t*3

4. Butterfly curve

spherical coordinates

Equation: ρ= 8 * t

θ= 360 * t * 4

phi = -360 * t * 8

5. Progressive line

Using Cartesian coordinate system

Equation: r= 1

ang=360*t

s=2*pi*r*t

x0=s*cos(ang)

y0=s*sin(ang)

x=x0+s*sin(ang)

y=y0-s*cos(ang)

z=0

6. Spiral line.

Cartesian coordinates

Equation: x = 4 * cos (t *(5*360))

y = 4 * sin ( t *(5*360))

z = 10*t

7. Logarithmic curve

Cartesian coordinate system

Equation: z=0

x = 10*t

y = log( 10*t+0.000 1)

8. Spherical helix

Adopt spherical coordinate system

Equation: p = 4

θ= t * 180

φ= t * 360 * 20

9. Double arc epicycloid

Cartier coordinates

Equation: l=2.5

b=2.5

x=3*b*cos(t*360)+l*cos(3*t*360)

Y=3*b*sin(t*360)+l*sin(3*t*360)

Figure 9

10. Xinghang Line

Cartier coordinates

Equation: a=5

x=a*(cos(t*360))^3

y=a*(sin(t*360))^3

Figure 10

1 1. Health and emotional line

circular cylindrical coordinates

Equation: a= 10

r = a *( 1+cos(θ))

θ= t * 360

Figure 1 1

12. Spiral in the circle

Adopt cylindrical coordinate system

Equation: θ= t * 360

r = 10+ 10 * sin(6 * theta)

z = 2 * sin(6 *θ)

Figure 12

13. Sinusoidal curve

Cartesian coordinate system

Equation: x=50*t

y= 10*sin(t*360)

z=0

Figure 13

14. Solar line (this was originally made for other curves, but it turned out to be wrong, so it became like this).

15. Fermat curve (a bit like thread line)

Mathematical equation: r * r = a * a *

circular cylindrical coordinates

Equation 1:θ= 360 * t * 5.

a=4

r=a*sqrt(theta* 180/pi)

Equation 2:θ= 360 * t * 5

a=4

r=-a*sqrt(theta* 180/pi)

Because Pro/e can only make continuous curves, it can only be done twice.

16. Talbot curve

Cartier coordinates

Equation: θ= t * 360

a= 1. 1

b=0.666

c = sin(θ)

f= 1

x =(a * a+f * f * c * c)* cos(θ)/a

y =(a * a-2 * f+f * f * c * c)* sin(θ)/b

17.4 leaf line (made by equation, not copied)

18.Rhodonea curve

Using Cartesian coordinate system

Equation: θ= t * 360 * 4

x = 25+( 10-6)* cos(θ)+ 10 * cos(( 10/6- 1)*θ)

y = 25+( 10-6)* sin(θ)-6 * sin(( 10/6- 1)*θ)

19. parabola

Cartesian coordinates

Equation: x =(4 * t)

y =(3 * t) + (5 * t ^2)

z =0

20. Spiral line

circular cylindrical coordinates

Equation: r = 5

θ= t * 1800

z =(cos(θ-90))+24 * t

Figure 20

2 1. trilobal line

circular cylindrical coordinates

Equation: a= 1

θ= t * 380

b = sin(θ)

r = a * cos(θ)*(4 * b * b- 1)

Figure 2 1

22. Epicycloid

Duke coordinates

Equation: θ= t * 720 * 5.

b=8

a=5

x =(a+b)* cos(θ)-b * cos((a/b+ 1)*θ)

y =(a+b)* sin(θ)-b * sin((a/b+ 1)*θ)

z=0

23. Lissajous curve

θ= t * 360

a= 1

b= 1

c= 100

n=3

x = a * sin(n *θ+c)

y = b * sin(θ)

24. Long and short hypocycloids

Cartier coordinates

Equation: a=5

b=7

c=2.2

θ= 360 * t * 10

x =(a-b)* cos(θ)+c * cos((a/b- 1)*θ)

y =(a-b)* sin(θ)-c * sin((a/b- 1)*θ)

25. Long and short turnover lines

Cartier coordinates

Equation: θ= t * 360 * 10.

a=5

b=3

c=5

x =(a+b)* cos(θ)-c * cos((a/b+ 1)*θ)

y =(a+b)* sin(θ)-c * sin((a/b+ 1)*θ)

26. Tricuspid valve line

a= 10

x = a*(2*cos(t*360)+cos(2*t*360))

y = a*(2*sin(t*360)-sin(2*t*360))

27. Probability curve!

Equation:

Cartesian coordinates

x = t* 10-5

y = exp(0-x^2)

28. White tongue line

cartesian coordinate system

a = 1

x = -5 + t* 10

y = 8*a^3/(x^2+4*a^2)

Archimedes spiral.

Column coordinates

a= 100

θ= t * 400

r = a *θ

3 1. vine line

cartesian coordinate system

a= 10

y=t* 100-50

solve

x^3 = y^2*(2*a-x)

For x

32. Tangent curve

cartesian coordinate system

x = t*8.5 -4.25

y = tan(x*20)

33. Hyperbolic cosine

x = 6*t-3

y = (exp(x)+exp(0-x))/2

Figure 33

34. hyperbolic sine

x = 6*t-3

y = (exp(x)-exp(0-x))/2

Figure 34

35. Hyperbolic tangent

x = 6*t-3

y =(exp(x)-exp(0-x))/(exp(x)+exp(0-x))

36. One peak and three stagnation curves

x = 3*t- 1.5

y=(x^2- 1)^3+ 1

37. Eight-character curve

x = 2 * cos ( t *(2* 180))

y = 2 * sin ( t *(5*360))

z = 0

38. spiral

r = t *( 10 * 180)+ 1

θ= 10+t *(20 * 180)

z=t

circle

x = cos ( t *(5* 180))

y = sin ( t *(5* 180))

z = 0

40. Closed spherical encircling curve

ρ= 2

θ= 360 * t

phi=t*360* 10

4 1. Cylindrical coordinate spiral curve

x = 100 * t * cos(t *(5 * 180))

y = 100 * t * sin(t *(5 * 180))

z = 0

42. Serpentine curve

x = 2 * cos((t+ 1)*(2 * 180))

y = 2 * sin ( t *(5*360))

z = t*(t+ 1)

43.8 curve

Column coordinates

θ= t * 360

r= 10+(8*sin(theta))^2

44. Elliptic curve

Cartesian coordinate system

a = 10

b = 20

θ= t * 360

x = a * cos(θ)

y = b * sin(θ)

45. plum blossom curve

Column coordinates

θ= t * 360

r= 10+(3*sin(theta*2.5))^2

46. Another flower curve

θ= t * 360

r= 10-(3*sin(theta*3))^2

z=4*sin(theta*3)^2

47. Change to a flower curve with a stronger sense of space; )

θ= t * 360

r= 10-(3*sin(theta*3))^2

z=(r*sin(theta*3))^2

48. Spiral rising elliptic line

a = 10

b = 20

θ= t * 360 * 3

x = a * cos(θ)

y = b * sin(θ)

z=t* 12

49. Even this spiral flower curve.

θ= t * 360 * 4

r= 10+(3*sin(theta*2.5))^2

z = t* 16

50 drum line

Cartesian equation

r=5+3.3*sin(t* 180)+t

θ= t * 360 * 10

z=t* 10

5 1 long life locking curve:

Cartesian equation

a= 1*t*359.5

b=q2*t*360

c=q3*t*360

rr 1=w 1

rr2=w2

rr3=w3

x = RR 1 * cos(a)+rr2 * cos(b)+rr3 * cos(c)

y = RR 1 * sin(a)+rr2 * sin(b)+rr3 * sin(c)

52 hairpins

spherical coordinates

Equation:

ρ= 200 * t

θ= 900 * t

phi=t*90* 10

53. Spiral rising curve

r=t^ 10

theta=t^3*360*6*3+t^3*360*3*3

z=t^3*(t+ 1)

54. Mushroom curve

rho=t^3+t*(t+ 1)

θ= t * 360

phi=t^2*360*20*20

55.8 word curve

a= 1

b= 1

x=3*b*cos(t*360)+a*cos(3*t*360)

Y=b*sin(t*360)+a*sin(3*t*360)

56. Plum blossom curve

θ= t * 360

r= 100+50*cos(5*theta)

z=2*cos(5*theta)

57. Peach Curve

rho=t^3+t*(t+ 1)

θ= t * 360

phi=t^2*360* 10* 10

58. Name: Disc Spring

Establishing environment: pro/e

Cylindrical seat

r = 5

θ= t * 3600

z =(sin(3.5 *θ-90))+24

59. Circular conic curve

Cartesian equation:

x=50*cos(t*360)

y=50*sin(t*360)

z= 10*cos(t*360*8)

60 butterfly line

Spherical coordinates:

rho=4*sin(t*360)+6*cos(t*360^2)

θ= t * 360

phi=log( 1+t*360)*t*360

6 1. sine coil spring

Descartes:

ang 1=t*360

ang2=t*360*20

x=ang 1*2*pi/360

y=sin(ang 1)*5+cos(ang2)

z=sin(ang2)

62. Annular spiral

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. Internal spring

x = 2 * cos(t * 360 * 10)+cos(t * 180 * 10)

y = 2 * sin(t * 360 * 10)+sin(t * 180 * 10)

z=t*6

64. Variable internal spring

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*8

65. Cylindrical sine wave line

Column coordinates:

equation

r=30

θ= t * 360

z = 5 * sin(5 *θ-90)

66. UFO (vortex line)

Spherical coordinates:

rho=t*20^2

θ= t * log(30)* 60

phi=t*7200

67. Handle curve

thta0=t*360

thta 1=t*360*6

r0=400

r 1=40

r=r0+r 1*cos(thta 1)

x=r*cos(thta0)

y=r 1*sin(thta 1)

z=0

basket

circular cylindrical coordinates

r=5+0.3*sin(t* 180)+t

θ= t * 360 * 30

z=t*5

69. Involute equation of cylindrical gear tooth profile;

afa=60*t

x = 10 * cos(AFA)+pi * 10 * AFA/ 180 * sin(AFA)

x = 10 * sin(AFA)-pi * 10 * AFA/ 180 * cos(AFA)

z=0

Note: afa is the pressure angle, ranging from 0 to 60, and 10 is the base circle radius.

70. Logarithmic spiral curve

Column coordinates:

r = sqrt(θ)

θ= t * 360 * 30

z=0

7 1. coverage line

Spherical coordinates:

ρ= 4

θ= t * 60

phi=t*360* 10

72. Sunflower Line

θ= t * 360

r = 30+ 10 * sin(θ* 30)

z=0

73. Sunline

r = 1.5 * cos(50 *θ)+ 1

θ= t * 360

z=0

74-tower spiral

r=t*80+50

θ= t * 360 * 10

z=t*80

75 petal line

Spherical coordinates:

ρ= t * 20

θ= t * 360 * 90

phi=t*360* 10

76 twin spindle production line

r=sin(t*360* 10)+30

θ= sin(t * 360 * 15)

z=sin(t*3)

Archimedean spiral's transformation (I want it)

I wonder if there is: what?

In cylindrical coordinates:

θ= 360 * 2 *(t-0.5)

r = 10 *θ

z=0

78 modified involute equation

r=20

ang = t*360

x=r*cos(ang)+2*pi*r*t*sin(ang)

y=r*sin(ang)-2*pi*r*t*cos(ang)

z=0

79 Pisces curve

spherical coordinates

rho = 30+ 10 * sin(t * 360 * 10)

θ= t * 180 * cos(t * 360 * 10)

φ= t * 360 * 30

80 arcuate curve

x=200*t*sin(t*3600)

y=250*t*cos(t*3600)

z=300*t*sin(t* 1800)

8 1 "two-sided" curve

spherical coordinates

ρ= 30

θ= t * 360 * cos(t * 360 * 20)

φ= t * 360 * 20

82 bees

Cartesian coordinate system:

x=cos(t*360)+cos(3*t*360)

Y=sin(t*360)+sin(5*t*360)

Meniscus 83

x=cos(t*360)+cos(2*t*360)

Y=sin(t*360)*2+sin(t*360)*2

84 tropical fish

a=5

x=(a*(cos(t*360*3))^4)*t

y=(a*(sin(t*360*3))^4)*t

85 dovetail shears

x=3*cos(t*360*4)

y=3*sin(t*360*3)

z=t

86 days silk

θ= t * 3600

r =(cos(360 * t * 20)* . 5 * t+ 1)* t

87 electrocardiogram

Cylindrical coordinate system:

r=sin(t*360*2)+.2

θ= 10+t *(6 * 360)

z=t*3

88 variable star line

Duke coordinate system

θ= t * 360

x= 10*cos(theta)^3

y= 10*sin(theta)^3

z = cos(θ)

89 rabbit

θ= t * 360-90

r=cos(360*(t/( 1+t^(6.5)))*6*t)*3.5+5

Hello, everybody!

θ= t * 360+ 180

r=cos(360*t^3*6)*2+5

9 1 serpentine

Cartesian coordinate system:

x=2*cos(t*360*3)*t

y=2*sin(t*360*3)*t

z=(sqrt(sqrt(sqrt(t))))^3*5

92 wuhuan

Column coordinates:

θ= t * 360 * 4

r=cos(t*360*5)+ 1

93 spider web

Column coordinates:

θ= t * 360 * 5

r=t*sin(t*360*25)*5+8

94 times sound wave

Descartes:

x=t*5

y=t*cos(t*360*8)

95 crossed involute

Column coordinates:

θ= t * 360 * 4

r =(cos(t * 360 * 16)* 0.5 * t+ 1)* t

96 inner five rings

Descartes

θ= t * 360 * 4

x = 2+( 10-5)* cos(θ)+6 * cos(( 10/6- 1)*θ)

y = 2+( 10-5)* sin(θ)-6 * sin(( 10/6- 1)*θ)

97 worm track

Column coordinates;

θ= t * 360 * 2

r=cos(t*360*30)*t*0.5+t*2