CADquest Article Series

Featured in "Pro/E The Magazine", September 1998

Creating Datum Curves Using Parametric Equations

Datum curves are used in many Pro/ENGINEER designs. The curves are frequently sketched or projected. It also may be necessary to create curves in exact geometric shapes other than what the sketcher provides. This article presents a method to make elliptical, parabolic, sinusoidal, and helical datum curves using parametric equations.

The Procedure

To create datum curves defined by parametric equations, select #Feature; #Create; #Datum; #Curve; #From Equation. Next you will have to select (or create) a coordinate system. If you are creating the coordinate system, you will also have to specify the type of coordinate system to use. Be sure to use the correct type for the equations you will be using. The equations shown for elliptical, parabolic, and sinusoidal curves use a Cartesian (XYZ) coordinate system. Cylindrical and spherical coordinate systems may also be used. An example using each type of coordinate system is included.

Pro/ENGINEER will provide an editor with some instructions (see Figure 1). This is where you enter the equations to create the datum curve. The instructions include the equations to make a perfect circle. The equations have been altered the equations so you can create other mathematical shapes. After the equations are entered, save the file and quit the editor. Then select OK from the dialog box. Creation of the datum curve will then be completed.



Figure 1

The Equations

The equations use a pre-defined system parameter called "t", which must be used in at least one of the three equations. This parameter evaluates from zero to one in each equation where it is used, similar to the "trajpar" parameter used in the variable section sweep feature.

Example equations for an ellipse (see Figure 2) using the major and minor diameter follow:

x = 24 * cos (t * 360) / 2

(24 is the major diameter)

y = 8 * sin (t * 360) / 2
(eight is the minor diameter)

z = 0

You can switch the major and minor diameter values to control whether the major diameter falls in the X or Y plane. If you wish to use a radius value instead of a diameter value, simply remove the /2 at the end of the equations.



Figure 2

To create a datum curve in the shape of a sine function (see Figure 3), 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



Figure 3

To create a datum curve in the shape of a parabola (see Figure 4), 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



Figure 4

When using the cylindrical coordinate system, helical curves (see Figure 5) can be created. Try the following equations:

r = 4

(four is the radius)

theta = t * 360 * 5
(five is the number of turns)

z = 10 * t
(ten is the height of the helix)



Figure 5

When using the spherical coordinate system, the results can be amazing (see Figure 6). Try the following equations:

rho = 8 * t

theta = 360 * t * 4

phi = -360 * t * 8



Figure 6

Steven G. Smith, CADquest, Harrisburg, PA