KOMPAS-3D v23

Example 1

Plot a parabola determined by the law: y = x2), within the range from -10 to 10.

The parametric representation of a parabola in the rectangular coordinate system:

X = t,

y = t 2,

z = 0.

The following sequence of actions is recommended to plot the parabola.

1.Run the Spline by Law command.

By default, in the group Coordinate Type, the Rectangular X,Y,Z button is pressed . It means that the curve is plotted using rectangular coordinates.

2.Set the function for the X coordinate.

2.1. In the Law by X group, select the By expression function type.
On the Parameter Panel, the following controls will appear: the expression field to enter the function expression; the parameter and Spacing fields to enter the function parameter and variation interval. The fields contain the default data: name t and default variation interval [0;1].

2.2. In the Expression field, enter the expression of the t function.

2.3. Enter in the field Interval the range of parameter variation
t = [10;-10]. Press <Enter>.

3.Set the function for the Y coordinate.

3.1. In the Law by Y group, select the By expression function type.

3.2. In the Expression field, enter the expression of the t^2 function.
The variation interval of the t parameter is determined automatically: it will be the same as the previously specified interval for the X coordinate.

3.3. Press <Enter>.

4.Set the function for the Z coordinate.

4.1. In the Law by Z group, select the constant function type.

4.2. Enter 0 in the Value field.

5.Press the Create Object button on the Parameter Panel.

Example 2

For a calculation related to sagging of a rope or cable, you need to plot a catenary curve by law: y = a · ch (x / a) = a / 2 · (e x / a + e - x / a), in the range from -50 to 50 with a = 80.

Parametric representation of the curve in the rectangular coordinate system:

x = t,

y = a / 2 · (exp t / a + exp - t / a),

z = 0.

The following sequence of actions is recommended to plot a catenary curve.

1.Run the Curve by Law command.

By default, in the group Coordinate Type the Rectangular X,Y,Z button is pressed. It means that the curve is plotted using rectangular coordinates.

2.Set the function for the X coordinate.

2.1. In the Law by X group, select the Linear function type. Fields for entering start and final values of the X coordinate appear on the Parameter Toolbar.

2.2. Please enter in the field Initial value -50.

2.3. Enter 50 in the Final value field.

3.Set the function for the Y coordinate.

3.1. In the Law by Y group, select the By expression function type. On the Parameter Panel, the following controls will appear: the expression field to enter the function expression; the parameter and Spacing fields to enter the function parameter and variation interval. The fields contain the default data: name t and default variation interval [0;1].

3.2. Enter in the field the function expression function expression
a / 2 *(exp(t/a)+exp(-t/a)).

3.3. Press <Enter>. A table named Parameter Values will appear on the Parameter Panel table. The parameter a is entered into it.

3.4. Set the value of the non-interval parameter a. To do this, double-click the cell of the table Expression and enter 80. Press <Enter>.

3.5. Enter in the field Interval interval of parameter variation
t = [-50;50]. Press <Enter>.

4.Set the function for the Z coordinate.

4.1. In the Law by Z group, select the constant function type.

4.2. Enter 0 in the Value field.

5.Click the Create Object button on the Parameter Panel.

Example 3

When designing a gear transmission, you need to set the profile of a cog wheel. The profile of the tooth of the cog wheel is drawn using the involute of a circle.

Wheel parameters:

•wheel module m = 3,

•number of cog wheel teeth z = 20,

•The profile angle α = 20°.

Parametric representation of the involute in the rectangular coordinate system:

R = Db / cos(t) / 2 (pitch circle radius),

A = tg(t) - t (evolvent angle),

Z = 0,

where 0 < t < 0.4 (in radians).

The following sequence of actions is recommended to plot the involute.

1.Create the variables on the Variables panel (see the table).

Variables for plotting an involute

2.Run the Curve by Law command.

3.Click the button of the group Coordinate Type on the Parameters toolbar Cylindrical R, A, Z .

4.Set the function for the R coordinate.

4.1. In the Law by R group, select the By expression function type.
On the Parameter Panel, the following controls will appear: the expression field to enter the function expression; the parameter and Spacing fields to enter the function parameter and variation interval. The fields contain the default data: name t and default variation interval [0;1]

4.2. Type in the box Expression expression function Db / cos(t) / 2.

4.3. Press <Enter>. A table named Parameter Values will appear on the Parameter Panel. The table will be populated with the expression and the value of the Db variable from the Variables panel.

4.4. Enter in the field Interval interval change parameter
t = [0;0.4]. Press <Enter>.

5.Set the function for the A coordinate.

5.1. In the Law by A group, select the By expression function type.

5.2. In the Expression field, enter the expression of the tan(t)-t function.
The function parameter  t  variation interval is determined automatically: it will be the same as the previously specified interval for coordinate R.

5.3. Press <Enter>.

6.Set the function for the Z coordinate.

6.1. In the Law by Z group, select the constant function type.

6.2. Enter 0 in the Value field.

7.Press the Create Object button on the Parameter Panel.