Cad Guidebook: A Basic Manual for Understanding and Improving Computer-Aided Design (29 page)

Beyond just recognizing the geometric relationships for particular points in
the model or paper space, some CAD systems may also permit the relationships
to be utilized in the creation of new entities. For instance, after allowing a spe-
cific point on a line to be selected for the starting point, the CAD system may
then recognize a relationship such as perpendicular or parallel or tangent to that
original line or other surrounding geometric entities. Figure 5.6 shows a case

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FIGURE
5.6

An example of recognition of a geometric relationship.

where the previewed direction of a line about to be drawn is at a perpendicular
relationship to another line. Notice that when this condition is recognized the
CAD system needs to let the user know that this has happened (such as showing
the perpendicularity symbol in Figure 5.6). This allows the user to judge whether
this is an intended condition.

5.9.3 Odometer

Another feature of some CAD systems is a dynamic indicator of the current posi-
tion of the mouse (or other pointing device) with respect to the model space or
viewport coordinates. This is often called an odometer since it shows how far the
mouse has moved from the origin. As the mouse moves, the numbers in the
odometer part of the screen are constantly changing. This is helpful for deciding
where to draw the geometry (particularly in terms of positive or negative coordi-
nates); however, this technique probably should not be relied upon to get precise
geometry. If a point needs to be located at a specific X, Y coordinate, then these
numbers should be entered directly from keyboard (using whatever input data
method is used by the particular CAD system). Refer to Figure 5.7.

5.9.4 Points

Points are probably the simplest geometric entity to create in the CAD system.
All that is required are the X- and Y-positions of the point. Of course, points are

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FIGURE
5.7

An example of an odometer.

of little use in creating geometry for the object of the drawing (which really only
arise from the edges and surfaces of the object or part). Points are typically used
to assist with the overall design and drawing procedure.

For example, if a designer is designing a device such as a motor casing, the
center of rotation of the motor’s rotating assembly is of vital importance. How-
ever, this imaginary location is not actually part of the casing; the point is in the
middle of the air for the physical object. In order to help with the design, then, the
CAD user may create a point in the drawing to represent this location. It may
then be easier to measure from or analyze the motor casing. If nothing else, it will
help as a visual reference to the location. Refer to Table 5.2.

5.9.5 Lines

Lines are probably the most prevalent and important geometric entity in the CAD
system. They are used for many functions. Of course, they are used for the object
of the drawing. These object or “geometry” lines will be for straight edges of the

TABLE
5.2

Point Creation Information

Geometric entity Point

Geometry defined by
Possible methods for creation
in the CAD system

1 X, Y coordinate in paper space or model space
Enter the X and Y values directly

Snap to existing geometry with recognition of: inter-
sections, midpoints, centerpoints, etc.

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TABLE
5.3

Line Segment (i.e. a “line” in the drawing) Creation Information

Geometric entity Line segment

Geometry defined by

Possible methods for creation
in the CAD system

2 X,Y coordinates (start and end)

1 X,Y coordinate with a direction angle, heading, or
“slope” and length

Y = mX + B (m = slope, B is Y-intercept; infinite line)
Enter the X and Y values directly for start and end
points.

Snap to existing geometry for the points with recogni-
tion of: intersections, midpoints, centerpoints, etc.
Snap to or enter X and Y for the start point, then enter
an angle or slope value or indicate a direction for the
line with recognition of parallelism or perpendicu-
larity from existing geometry.

Polyline: snap the X and Y for the start point of a line
segment and then continuously snap or enter X and
Y values for a “chain” of line segments (each new
segment begins where the previous one ends).

part, and for locations where a curved surface meets a flat surface (“seams”).
Lines are also going to be used for centerlines (the imaginary central axis for cy-
lindrical features such as holes), and in layout drawings, they will be used to cre-
ate “construction” geometry that helps the design process.

Generally in the context of a CAD system, a line is straight, and it is actu-
ally a line segment. In geometric terminology, a line is infinitely long, and what
one sees is just a segment of that infinite span. This infinite character is the result
of the mathematics that describe lines. In the context of 2-D CAD, it can be as-
sumed that these lines are going to just lie in a plane (such as the paper space
mentioned earlier). Refer to Table 5.3.

5.9.6 Circular Entities

The next geometric entity is circular features. This would include circles for
holes, shafts, etc. It would also include arcs (parts of a circle) and the special arcs
called fillets.

There are a few special considerations to keep in mind for the circular enti-
ties when using a CAD system. First, there is likely to be quite a variety of com-
mands or methods for creating these types of entities. Naturally, a circle can be
created by selecting the center of the circle and then specifying the radius. But it
can also be created by selecting the center and one point on the edge of the circle,

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TABLE
5.4

Circular Feature Creation Information

Geometric entity Circular

Geometry defined by

Possible methods for creation
in the CAD system

X,Y coordinate for center (Xc, Yc) and a radius (R)

(X – Xc)2
+ (Y – Y

c)2

= R

2

Enter the X and Y values directly for the center and a
radius (or diameter)

Snap to existing geometry for the center point with rec-
ognition of: intersections, midpoints, etc. and also
snap to a point on the edge of the circle.

Snap to existing geometry for 3 points on the edge of
the circle.

Create fillet geometry by selecting 2 existing lines (not
necessarily perpendicular to each other), entering a
radius, and then selecting from among ambiguous
choices.

Select 3 existing lines that have tangency with the de-
sired circle.

specifying 3 points on the edge of the circle, specifying 2 points on the edge and
then a radius, etc. Secondly, some circular feature methods have redundant
choices for the geometry. Although the 2 points on the edge and a radius specifies
a size of circle, there are actually two possible circles in two different locations
(see Figure 5.8) for this method. When this situation arises, the CAD system
should indicate this redundancy and permit the user to make a selection of the
desired circle. Refer to Table 5.4.

Finally, there are issues that arise with respect to tangency. The CAD sys-
tem will generally offer the capability to create circular entities that are tangent to
lines (a circle’s edge is tangent with a line when the circle and the line “just
touch” and have a single point or X,Y value that is part of both entities). Creating
the circular feature with tangency is especially important for fillets. Fillets repre-
sent a blending of two surfaces of the object or part shown in the drawing. Since
the fillet blends with two different surfaces, it is supposed to be tangent to two
lines simultaneously. Fortunately, the CAD system can quickly calculate the fillet
to meet this geometric constraint; however, as mentioned earlier, there may be
redundancies. Indeed, two lines (mathematically) have 4 possible fillets, but usu-
ally only one is what is desired. Refer to Figure 5.8.

5.9.7 Ellipses

Another fairly common geometric entity is the ellipse. The ellipse is basically
oval-shaped. It is usually described by a major axis and a minor axis. As the

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FIGURE
5.8

Examples of redundant geometry creation, tangency, and fillets.

names imply, the major axis is the longer or stretched distance, and the minor
axis is the shorter or compressed distance. Refer to Table 5.5.

Ellipses are most often created in CAD drawings for cases where circular
features of the object or part are seen at an angle in a given view. Commonly
these would include shafts, holes, fittings, etc. Manufacturing a section of a part
to be elliptical might be rather unusual, but the CAD system will handle this quite

TABLE
5.5

Elliptical Feature Creation Information

Geometric entity Elliptical

Geometry defined by

Possible methods for creation
in the CAD system

X,Y coordinate for center (Xc, Yc), direction and length
(a) of X-axis direction of ellipse, and length (b) of
Y-axis direction of ellipse

(X – Xc)2/a2
+ (Y – Y

c)2/b2

= 1

Enter the X- and Y-values directly for the center and
axis lengths.

Snap to existing geometry for the center point with rec-
ognition of: intersections, midpoints, etc. and select
a length for the major and minor axis.

Snap to existing geometry for points that lie at the cor-
ner of a rectangle that would bound or contain the
ellipse.

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easily. The center and major and minor axes can be entered, and the CAD system
will create the geometry.

The ellipse is a conic section. That is, the mathematics of the shape is de-
rived from intersecting a cone with a plane at a specific range of angles. Some
CAD systems contain commands for creating other conic sections such as a pa-
rabola’s and a hyperbola’s. These may be useful geometric entities in some cases.

5.9.8 Splines

The last geometric entity presented here for a typical CAD system is the spline.
The spline is modeled after a bendable strip of plastic material that was weighted
down at specific points on a table. Then a free-form curve was drawn along the
strip. The spline is able to meander through an arbitrary set of points and create a
smooth curve between them. Splines would be used for creating geometry in the
drawing for such things as hoses, pipes, wires, or free-form surface items such as
body panels. Splines are also interesting because they can crossover themselves.
Refer to Figure 5.9 for examples.

The spline is usually created in the CAD system by having the user click on
or select specific points that lie on the spline that needs to be created. For in-
stance, the user would select clamping locations where a hose must pass through.
Then the CAD system would create the actual spline curve that passes through all
those points. However, the spline’s mathematical formulation is actually based on
something known as a Bezier Curve, and this curve uses control points. These are
points that actually lie some distance off the final spline between the start and end

FIGURE
5.9

Examples of splines in a CAD drawing.

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TABLE
5.6

Spline Creation Information