Drawing Ellipses

In AutoCAD 2002, you can draw true ellipses and elliptical arcs, both of which are exact mathematical representations of ellipses. The default method of drawing an ellipse is to specify the endpoints of the first axis along with the distance, which is half the length of the second axis. The longer axis of an ellipse is called the major axis, and the shorter one is the minor axis. The order in which you define the axes does not matter.

Ellipses are somewhat complicated geometric figures, but if you have a basic understanding of the geometry of an ellipse, AutoCAD enables you to draw them easily. An ellipse has both a major axis and a minor axis, as shown in Figure 7.14. Although from a mathematical point of view an ellipse has two “centers” or foci, AutoCAD considers the geometric center to be the intersection of the two axes. The quadrants of an ellipse are the points of intersection between the axes and the ellipse. In AutoCAD, you can use both the quadrants and center of an ellipse as object snap points.

AutoCAD offers you several ways to specify the various parameters of an ellipse. Those methods are covered in the following section.

ELLIPSE Command Options

When you issue the ELLIPSE command, the following prompt appears:

							Specify axis endpoint of ellipse or [Arc/Center]:
						

To respond to this prompt, you can use one of the following methods:

• Axis endpoint. You specify an axis (major or minor) endpoint. The Specify other endpoint of axis: prompt will appear, at which you specify the second axis endpoint. The Specify distance to other axis: or [Rotation]: prompt then appears. If you specify the other axis distance, AutoCAD draws the ellipse. If you specify Rotation (by typing R and pressing Enter), AutoCAD prompts for an angle and then completes the ellipse.

• Center. If you choose the Center option (by typing C and pressing Enter), the Specify center of ellipse: prompt appears, at which you specify the center point. The Specify endpoint of axis: prompt appears next. Specify an endpoint. Then the Specify distance to other axis: or [Rotation]: prompt appears. If you specify the other axis distance, AutoCAD draws the ellipse. If you specify Rotation (by typing R and pressing Enter), AutoCAD prompts for an angle. The angle specifies the ratio of the major axis to the minor axis. An angle of 0 defines a circle. The maximum angle that’s acceptable is 89.4, which yields a “flat” ellipse.

• Arc. If you choose the arc option (by typing A and pressing Enter), the Specify axis endpoint of elliptical arc: or [Center]: prompt appears, which requests the same information as the prompt for a full ellipse. After you answer the prompt sequence for the full ellipse, the Specify start angle: or [Parameter]: prompt appears. Specify a point to define the start angle of the arc, and the Specify end angle: or [Parameter/Included angle]: prompt appears. Specify an end angle to draw the arc. Specifying I, for Included angle, enables you to specify an included angle for the arc, beginning with the start angle.

In the following exercises, you practice drawing ellipses in a three-view mechanical drawing. Throughout the exercises, you will use the object snap techniques you learned in Chapter 6, “Accuracy in Creating Drawings with AutoCAD 2002.”

In this exercise, you first use a full set of construction lines to draw an ellipse in one view, and then a reduced set of construction lines provides the information you need to draw an ellipse in another view.

Exercise 7.9 Drawing Ellipses in a Three-View Drawing

1.	Open the drawing 07DWG02.dwg on the accompanying CD-ROM. This drawing, shown in Figure 7.15, shows an unfinished three-view drawing of a mechanical mounting bracket. A shaded isometric view is included. The hole in the angled portion of the bracket has already been projected onto the Front view. You will use the Object Snap Tracking feature of AutoCAD 2002 (discussed in Chapter 6) to draw the ellipse and the elliptical arc representing the hole in the Top view. Figure 7.15. An incomplete three-view drawing of a mounting bracket.
2.	First, establish the settings you will need for Object Snap Tracking. Right-click on the OTRACK button on the mode status line at the bottom of the display and select Settings from the shortcut menu.
3.	In the Drafting Settings dialog box, on the Object Snap tab, choose Object Snap On and Object Snap Tracking On. Under Object Snap Modes, select Endpoint, Midpoint, Quadrant, and Intersection (see Figure 7.16). Click OK to close the dialog box. Figure 7.16. The settings for Object Snap Tracking.
4.	To zoom to a closer view, open the View menu and choose Named Views. In the View dialog box, select view AAA, select Set Current, and click OK to close the dialog box and establish the new view as shown in Figure 7.17. Figure 7.17. A close-up of the Top, Side, and Front views of the mounting bracket.
5.	Referring to Figure 7.17, you will use the intersections of the hidden lines with the surface of the bracket at and and the midpoint of the top edge at to establish Auto Tracking points to accurately position the ellipse in the Top view. From the Draw menu, choose Ellipse, and then select Axis, End.
6.	At the Specify axis endpoint of ellipse: or [Arc/Center]: prompt, move the cursor over in Figure 7.17 and hold it stationary until the Auto Track symbol appears (as shown in Figure 7.18 A). Figure 7.18. Auto Tracking points used to place the ellipse.
7.	Move the cursor up into the Top view and hold it over until the Midpoint Auto Track symbol appears. Then move the cursor back to the left until the tracking from appears. Auto Track will indicate the acquired point as Intersection <90, Midpoint <180, as shown in Figure 7.18 B. Pick this point as the axis endpoint of the ellipse.
8.	At the Specify other endpoint of axis: prompt, move the cursor over in Figure 7.17 and hold it stationary until the Auto Tracking symbol appears, as shown in Figure 7.18 C.
9.	Now drag the cursor up into the Top view again until the Auto Tracking point is acquired. Auto Tracking will report Endpoint 6.2889 < 90, as shown in Figure 7.18 D. Click on this point to establish the second axis endpoint. AutoCAD draws a tentative ellipse using the axis endpoints supplied thus far. Note that the ellipse center point is now established.
10.	At the Specify distance to other axis: or [Rotation]: prompt, type 1 and press Enter. AutoCAD completes the ellipse. This distance is referred to as the “ellipse center point,” and the dimension in the Side view gives the diameter of the hole as 2 units, or a radius of 1 unit. Your drawing should now resemble Figure 7.19. Figure 7.19. The completed Top view ellipse.
11.	Keep this drawing open for use in the next exercise.

In the following exercise, you use the Arc option of the ELLIPSE command to draw a partial ellipse, or an elliptical arc, to complete the ellipses in the Top view of the mounting bracket drawing.

Exercise 7.10 Drawing Elliptical Arcs

1.	Continue in the drawing of the mounting bracket from the preceding exercise. You will now place an elliptical arc “inside” the arc you drew in the last exercise, again using Auto Tracking to place the arc. Right now, the drawing should resemble Figure 7.19. When you have completed this exercise, the drawing will resemble Figure 7.22. You will use the same Auto Tracking settings you used in the last exercise. Figure 7.22. The completed baseplate fixture with ellipse and elliptical arc.
2.	From the Draw menu, choose Ellipse and then Arc. At the Specify axis endpoint of elliptical arc: or [Center]: prompt, rest the cursor over in Figure 7.20 until the tracking symbol appears. Figure 7.20. Auto Tracking points used to draw the elliptical arc.
3.	Move the cursor straight up into the Top view and then to the right to acquire the Midpoint of the bracket edge, as shown in Figure 7.20.
4.	Slowly move the cursor to the left until the Auto Track symbol appears, as shown in Figure 7.20. Select that point.
5.	At the Specify other endpoint of axis: prompt, move the cursor over in Figure 7.20 until you acquire the tracking point, as shown in Figure 7.20.
6.	Move the cursor back into the Top view to acquire the Midpoint again. Select this point as shown in Figure 7.20. AutoCAD draws a tentative ellipse based on the endpoints you’ve supplied thus far.
7.	At the Specify distance to other axis: or [Rotation]: prompt, type 1 and press Enter. AutoCAD draws the complete ellipse. At the Specify start angle: or [Parameter]: prompt, carefully place the crosshairs at in Figure 7.21 and pick. Then drag the crosshairs around the ellipse in a clockwise direction to and pick. This completes the elliptical arc. Figure 7.21. Specifying the included angle for the elliptical arc. The full ellipse and the elliptical arc should resemble those shown in Figure 7.22. This completes your work in this drawing.