EQUATIONS TO GENERATE CURVES IN PRO/E
T.SHYAM,PGDTD
NTTF,COIMBATORE.
Email: [email protected]
Points to remember :-
1. In pro/e, we have to write the equations (for both curves and relations) in terms of "t", which value varies frm 0 to 1.
2. we write the angle in terms of "t". Example:- x=t*270
y=t*360*3
If u keep the angle as 360(degrees), full curve will generate.If the value is 180, half curve will generate.
3. Some of the symbols, which are used in pro/e are showned below.
Sine -----> sin()
Cosine -----> cos()
Exponential degree -----> exp()
Exponentation -----> ^ Ex:- x^2 ---> means, x square
Multiple -----> *
Divide -----> /
Note:- Expect 1st equation, all other equations are in cartesian form.
1.Spear: (Cylindrical equation) Look like a globe
rho=cos(t*90)
theta=90 * t
phi=t * 360 * 20
2.Spiral:
x = ((d/ 2 + P * r * t) * cos ((r* t) * 360))
y = ((d / 2 + p * r * t) * sin ((r * t) * 360))
z = 0
where, d ----> Inner dia
p ----> pitch
r----> No. of revolutions
If z=t*360, a curve look like a spring will come.
3.Butterfly curve
a=cos(t*360)
b=sin(t*360)
c=cos(4*t*360)
d=(sin((1/12)*t*360))^5
x=b*(exp(a)-2*c+d)
y=a*(exp(a)-2*c+d)
4.Fish curve
a=cos(t*360)
b=sin(t*360)
x=(C*a-20*((b)^2)/1.732)
y=C*a*b
here, " C " is variable like 1,2,3..........
5.Cappa curve: (look like number eight)
x=C*cos(t*360)*sin(t*360)
y=C*cos(t*360)
here, " C " is variable like 1,2,3..........
6.Ellipse/Astroid/diamond
x=a*(cos(t*360))^(2/r)
y=b*(sin(t*360))^(2/r)
Here,a,b are variables like 1,2,3..........
If, r=2/3 ----> astroid
If, r=2 ----> ellipse ,if a=b...its a circle
If, r=1 ----> diamond (some times diamond will not come)
7.Bicorn curve
a=cos(t*360)
b=sin(t*360)
x=c*a
y=C*(a^2)*(2+a)/(3+b^2)
here, " C " is variable
8.Talbots curve: ( make an expirement by changing the signs +,- in the below equations)
a=cos(t*360)
b=sin(t*360)
x=C*a*(1+exp(2)*(b^2))
y=C*b*(1+exp(2)*(b^2))
here, " C " is variable
9.Negative pedal curve
a=cos(t*360)
b=sin(t*360)
x=C*a*(1+exp(2)*(b^2))
y=C*b*(1-2*exp(2)+exp(2)*(b^2))
here, " C " is variable
10.pearl shaped curve
a=cos(t*360)
b=sin(t*360)
x=a
y=b*(sin(0.5*t*360))^C
here, " C " is variable, varies frm 0 to 7
If " C" is moer than 7 also, curve will come. but it not look like a pearl.
11.
a=cos(t*360)
b=sin(t*360)
x=C*(1+b)
y=C*a*(1+b)
here, " C " is variable, varies frm 0 to 7
12.Apple curve
a=cos(t*360)
b=sin(t*360)
x=C*a*(1-a)
y=C*b*(1-a)
here, " C " is variable
GENERAL EQUATIONS:-
1.Circle
x = C * cos ( t * 360 )
y = C * sin ( t * 360 ) , here, " C " is variable which gives the radius of the circle.
z = n, n is a variable which gives the distance frm the z-plane to the circle generated in z-axies.
if u give z=(x+y)*(x-y), some other curve will generate.like this u can experiment for some other
equatons also.
2.Parabola
x = C * cos ( t * 360 )
y=x^2
here, " C " is variable