Cad Guidebook: A Basic Manual for Understanding and Improving Computer-Aided Design (26 page)

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2-D CAD 107

come less expensive. A long trend toward lower cost per seat continued with the
advent of the personal computer. So, over these decades (and certainly by 1990),
CAD became the standard method of producing drawings.

5.3 “SMART PAPER”

Probably the best way to think of doing 2-D CAD design and drawings is to think
of the system as “smart paper.” Although the geometric entities (lines, arcs, etc.)
being created on the screen could also be manually drawn on a piece of paper, the
CAD system has the ability to provide important information and intelligence
about that geometry. The key to this intelligence is the simple mathematical
model that supports the entities.

If one works with a drawing as a piece of paper, and one wants to draw a
circle at a specific location on the paper with a specific radius to size the circle,
then there is no choice but to approximate the circle. The CAD system, however,
has the ability to idealize that circle and essentially make it perfect. The CAD
system can be “told” to make a circle that has a 10 mm radius and lies at a point
100 mm from the bottom and side edge of the paper. Although the CAD system
will eventually make a hardcopy that is (like the manual drawing) only an esti-
mation of the circle, internally the CAD system can remember the exact dimen-
sions that the CAD user had in mind. It can store the 10 mm and 100 mm values
as actual numbers. Although the CAD system also has a finite accuracy of per-
haps 8 significant digits, and the 10 mm ideal value may actually be stored as
9.999999 mm, this is well within the accuracy of virtually all manufacturing
processes.

There are a number of advantages that can be exploited from the “smart
paper” analogy or the idea that the CAD system stores a mathematical model of
the design. Table 5.1 lists a number of these advantages. It is important to note,
however, that these functions will not work properly if the CAD system is not
used accurately. For instance, whenever possible the actual numerical values for
the geometry (i.e., “object lines”) should be
entered to the
CAD system (as op-
posed to just guessing based on the appearance). If a circle is supposed to be
15/16 of an inch in diameter, then the value of 0.9375 should be typed into the
CAD system somehow. Even if the eventual dimension shown on the drawing
might be 0.93 (to reflect the tolerances associated with decimal places), it makes
the most sense to have the CAD system automatically round the number instead
of just making the circle only 0.93″
in diameter (which will degrade the mathe-
matical model).

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TABLE
5.1

Advantages of the “Smart Paper” Concept in 2-D CAD

“Smart Paper” Advantage Description

Dynamic measurement Although one can calculate distances, areas, angles,

etc. by manually writing out formulae and solving

them, basically all these values can be quickly and

easily calculated and displayed by the CAD system.

It can continue to provide these measurements

throughout the design process.

Projections If the CAD system tracks views, their scale, and their

viewing angle (Front, Top, Right, etc.), then it should

be able to create projections. This option allows the

user to create geometry in one view and have some

of it automatically created in other views with the

correct orientation. With the advent of 3-D models

however, this is a much less used capability.
Scaling Geometry that is created properly can be scaled to

larger and smaller sizes and create accurate new ge-

ometries based on existing ones. Some systems may

also allow the scaling to not be uniform in the X- and

Y-directions. For instance, a part could be stretched

to be longer in the X-direction, but not changed in

the Y-direction.

Accurate moves and rotations Geometry that is created properly can be reoriented in a

number of ways, for example, shifting or moving

what has been drawn by a specific amount (say move

all holes to the right by 10.523 mm). It can be much

more accurate than following methods that only look

right.

Automatic dimensions Geometry that is created properly can have the CAD

system determine the values of dimensions easily

and automatically (even if a variety of drawing view

scales are used in the drawing). In this case, after the

design is drawn, the user can just pick the lines,

edges, points, etc., and the system will figure out the

proper distance between them and create a dimen-

sion that shows the appropriate value.

2-D CAD 109

5.4 PAPER SPACE AND MODEL SPACE

Given the many advantages of the “smart paper” concept, it becomes necessary to
understand exactly how the CAD system is implementing the mathematical
model. The first part of this understanding is to figure out how the CAD system
uses paper space
and/or
model space. These “spaces” are like a grid or a field of
possible data or numbers associated with the drawing geometry (lines, arcs, etc.).
For example, a line is usually going to be defined by two sets of X and Y values
(one set for the beginning of the line; the second set for the end of the line). The
actual numbers used for these X and Y values are going to be dictated by the
“space” implemented by the CAD system.

5.4.1 Paper Space

A CAD system that uses a paper space approach essentially “knows” the size of
the drawing (refer to drawing sizes in the previous chapter). Furthermore, the
drawing size can indicate the unit system (inches, millimeters, etc.) and the scale
needed to enter the geometric data for the drawing. For example, if an E-size inch
drawing is being used, then the basic paper space is going to go from 0 to 44 in.
in the horizontal direction and from 0 to 34 in. in the vertical direction. So, the
paper space approach not only indicates the boundaries of the drawings, but it
also sets the units. If paper space is for an “inch size” (such as E-size just men-
tioned), then obviously the units are inches. If a millimeter size such as A0 is
used, then obviously the drawing is going to use millimeters.

Once the user is forced to work within the given set of values based on the
paper size in the paper space system, a CAD system of this type is probably also
going to offer the option of working with viewports. As shown in Figure 5.1,
viewports are a common computer graphics technique for segregating and manip-
ulating different parts of the computer monitor. Viewports have distinct bound-
aries, and the graphics programming usually does not plot anything beyond the
boundaries (this is known as “clipping”). Most importantly viewports have their
own mathematically defined space with a minimum X- and Y-value and a maxi-
mum X- and Y-value. It turns out the concept of computer graphics viewports
corresponds very well with the 2-D drawing concept of views (such as Front
View, Right View, etc. presented in the previous chapter). So viewports are easily
applied to become drawing views.

Once the paper space–type of CAD drawing has the viewports equated to
drawing views, then the viewports can easily have a mathematical scale factor
that corresponds to drawing view scale as well as its own origin. Now each of the
views can have its own value of scale, and any size design can be worked on
within the context of the size drawing selected. The user can be released from
being to forced into just the paper’s boundaries (such as the limits of 44 in. and
34 in. mentioned above for E-size). For example, if the object being designed is

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Viewports (solid border) and paper space (dashed border).

5.1

IGURE

F

2-D CAD 111

very large, then view scales such as 1/32 can be used and as the user enters the
length of line as 320 inches to the CAD system, the CAD system can automati-
cally apply the 1/32 scale factor and put a line 10 inches long onto the CAD
drawing. Furthermore, if the user measures the length of the line in the CAD
drawing, the CAD system can automatically “undo” the effects of the view scale
(thus indicating the length of the line just mentioned as the product design’s
“real” 320 inches), even though a hardcopy of the drawing would only have the
line 10 inches long on the paper.

The main concept to keep in mind, then, for the paper space approach is
that there is a predetermined relationship between the actual, physical object and
the object’s appearance on an actual size of drawing.

5.4.2 Model Space

Some CAD systems do not use the paper space approach. Instead, they use an
approach that can be called model space. In the model space approach, the cre-
ation of geometry is not concerned with the drawing sizes while the drawing is
being created. The CAD system simply considers all of the information to be
drawn in an unbounded two-dimensional field or plane.

This type of CAD system needs to indicate the origin or the center of the
model space (this is where the X- and Y-values are zero). Since there is no math-
ematical consideration for the drawing size, the coordinates of the geometric en-
tities can stretch to any values, and without concern for the units being used
(inches, millimeters, etc). For instance, the edge of the physical object may be
250 mm long. The CAD user can then create a line in model space that is 250
units long (regardless of inches or millimeters). At this point, there is no neces-
sity to add a scale factor, since the drawing does not need to be shrunk to fit on
the printed drawing. One can consider this approach as at “full scale” or “1 to 1.”
When the drawing is completed, and all the pertinent geometry has been shown
in the model space, “analyzing” or measuring distances and other geometric
properties is rather simple. It can all be done with respect to the single mathemat-
ical field.

Of course, the drawing also needs to be plotted. Now the model space must
be converted to fit some paper space. This is easily done by overlaying or map-
ping the drawing size to the geometric entities in the drawing. This can involve
scaling (shrinking or expanding) either drawing size or the geometric entities.
Once the geometric entities fit into the border of the selected drawing size, then
the drawing can be printed. Often the user has a drawing size in mind while creat-
ing the drawing (instead of waiting until the hardcopy is needed) so that it is not
overly difficult to fit the information into the drawing size. To prevent difficulties
with this, it is often possible to show the overlay of the drawing size border or
format while the drawing is being created.

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FIGURE
5.2

Drawing with views at different scale.

It is also possible to work with a scale in the model space approach. For
some CAD systems, however, there will be just a single scale applied to the
model space (as opposed to a different scale for each view shown on the draw-
ing). Figure 5.2 shows a drawing where a Detail View B is showing a “close up”
of a part of the object in the drawing. This Detail View B is at a different scale
than the “main” view. This can be a problem for CAD systems using the model
space approach without viewports. This is why many drawing “translations”
from one CAD system to another shows parts of the drawing blown up or shrunk.
One CAD system is probably using viewports and the paper space approach with
a mixture of view scales, but the other CAD system can not handle this.

5.5 DIMENSIONS

Considering the concept of using a 2-D CAD system as “smart paper,” where the
CAD system is used to create an accurate but limited mathematical model of the
object, the methods for creating dimensions becomes extremely important. It is
the dimensions that bridge the mathematical model and useful information that
needs to be shown to the eventual reader or customer of the drawing. Also, if the
geometric entities in the drawing are created accurately enough, then the dimen-