xcad
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Joined: 24 June 2002
Location: Greece
Online Status: Offline
Posts: 468
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| Posted: 26 October 2002 at 7:24am | IP Logged
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Hello, proe user,
Pro/engineer uses this system variables :
• t (varies from 0 to1) t is used to generate varying values for theta and z. The start of the datum curve is t=0 and the end of datum curve is t=1
• Theta (angle from x axis of coordinate system) - cylindrical coordinate system.
• Theta (angle from y axis of coordinate system) - spherical coordinate system.
• Phi (angle from x axis of coordinate system) - spherical coordinate system only.
• z (distance in z from coordinate system) - cylindrical coordinate system and Cartesian coordinate system.
• x (distance along x-axis) - Cartesian coordinate system.
• y (distance along y-axis) - Cartesian coordinate system.
All other symbols are user defined e.g. IR- inner radius, OR- outer radius, XOR - overall size in X, YOR - overall size in Y. The purpose is to make it easier to change values by only having to edit the value in one place.
Below I describe to you a lot of curves that is given by equation. Use cut and paste to copy these equations into the equation editior.
1. ELLIPTICAL CURVE
Cartesian coordinate system
XOR = 'overall size in y'
YOR = 'overall size in x'
x = XOR / 2 * cos ( t * 360)
y = YOR / 2 * sin ( t * 360)
z = 0
2. SPIRAL CURVE
Cylindrical Coordinate system
IR='start radius'
OR='final radius'
TURNS='number of turns'
r= IR + t * (OR-IR)
theta=t * 360 * TURNS
z=0
Wavy Spiral
change z to z='size of wave'*sin(360*t*'no of waves')
3. Helical Curve
Cylindrical coordinate system
IR='start radius'
OR='final radius'
r=IR + t * (IR-OR)
theta=t * 360 * 'no of turns'
z='height' * t (or pitch * no of turns * t)
4. Helical Curve
Cartesian coordinate system
XOR='final radius'
YOR='final radius'
x = XOR * cos (t * 360 * 'no of turns')
y = YOR * sin (t * 360 * 'no of turns')
z = t * 'height'
TAPERED HELIX
change r to r= IR+t*(OR-IR)
WAVY HELIX
change z to z='height' * t + 'size of wave' * sin(360 * t * 'no of waves')
ELLIPTICAL HELIX
Cartesian coordinate system
XOR = 'overall size in y'
YOR = 'overall size in x'
x = XOR * cos ( t * 360 * 'no of turns')
y = YOR * sin ( t * 360 * 'no of turns')
z = 'height' * t
5. WAVY CIRCLE
Cylindrical Coordinate system
r='radius'
theta=t * 360 * TURNS
t='size of wave' * sin(360 * t * 'no of waves')
6. Weird Curve
Spherical Coordinate System
rho=360*8*t
theta=360*t*4
phi=-360*t*8
7. To create a datum curve in the shape of a sine function , use the following equations:
x = 5 * t
(five is the total width of the curve along the X axis)
y = sin (360 * t * 2)
(two is the number of cycles created)
z = 0
8. To create a datum curve in the shape of a parabola , use the following equations (mirror the curve about DTM1 after creating it to get a full parabola):
x = t
y = 2 * t^2
(equivalent of y=2x2)
z = 0
9. When using the spherical coordinate system, the results can be amazing. Try the following equation:
rho = 8 * t
theta = 360 * t * 4
phi = -360 * t * 8
regards
karavasilis Christos, Greece
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Topic: Sinusoidal curve through equation
