Cad Guidebook: A Basic Manual for Understanding and Improving Computer-Aided Design (44 page)

8.4.6 Types of Constraints

Table 8.4 lists a variety of constraints that may be explicitly created and/or inher-
ited. It is not possible to list all the degrees of freedom that can be removed by the
various constraints, but the documentation included with the CAD system may
provide this. The CAD system documentation should also indicate the various
symbols or icons that are shown for each of them.

8.4.7 Sketch Regeneration or Updating

When constraints are created or modified, the CAD system may or may not auto-
matically “solve” the constraint network. Whether it is done automatically and/or
immediately by the system, eventually all the constraints that are applied to a
sketch will have to be checked for consistency, and any pending changes imple-
mented. It is done this way so that many changes can be made individually, but
the sketch does not change until all the desired changes are made. Then, when all

208 Chapter 8

TABLE
8.4

Various Types of Constraints

Constraint Application Description

Parallel Applies to two straight lines in a
It forces the two lines to be

sketch.
parallel.

Perpendicular Applies to two straight lines in a
If forces the two lines to be

sketch.
perpendicular.

Coincident Applies to two points of various
If forces the two points (from

kinds. For instance, between
two separate geometric enti-

endpoints of lines, arcs,
ties) to share the same X, Y

splines, etc. It can also be ap-
location. This X, Y location

plied to centerpoints of circles
may move as the entities

and arcs.
move, but the two points stay

together.

Collinear Applies to two straight lines. If forces two lines (which are re-

ally line segments) to lie on

the same mathematical line

(which has infinite length).
Grounded,
Applies to lines and points of
For lines, it forces them to not
Fixed, or
various kinds.
move or rotate. For points, it
Rigidified
just forces the points to not

move at all.

Tangent Applies at least to lines and arcs,
If forces the 2 entities to just

arcs to other arcs, or perhaps
touch at a point; they each

to lines or arcs and splines.
share exactly one point, and

they seem to just graze each

other.

Dimensions Applies to points, lines, arcs, etc. It forces the various entities to be

separated by the amount

shown in the dimension value.

the dimensions or other constraints are as desired by the user, the user can then
regenerate or update the sketch.

In the regenerate or update process, some CAD systems may remove con-
straints in much the same way that they were inherited earlier. The system may
determine that some constraints are redundant or unnecessary based on other
constraints. It is important that the process complete successfully before the
sketch is used to create a new 3-D feature or the part. Indeed, some CAD systems
will force the user to resolve any problems with the sketch immediately. How-
ever, other systems will allow the user to continue to create the feature even
though there are unresolved, minor problems with the sketch.

Part Modeling 209

Although it is beyond the scope of this book, the regeneration or update
process does involve solving a system of equations. Each constraint (of all the
various types) represents an equation with a number of unknowns which usually
cannot be solved by itself. However, the process of regeneration or updating
solves all these equations together or simultaneously so that a solution for each
equation (representing where each line, arc, etc. belongs in the sketch) can be
found. This solving process can be complicated, and sometimes the system of
constraints can not be solved so that one single stable sketch is created. The next
few paragraphs explain some of these failure situations.

8.4.8 Overconstraining

One possible result from the attempt to regenerate the sketch is the identification
of redundant constraints. This problem can arise when geometric entities are
overconstrained. Referring back to Figure 8.13, it is clear that the hole is posi-
tioned by the dimensions that locate the center of the hole with respect to the
edges of the plate. Since a dimension is shown from the center of the hole and the
left edge of the plate, then there is no need to show a dimension from the right
edge of the plate. If this second horizontal dimension is placed on the sketch, then
the position of the hole is overconstrained. There is more constraint data than
necessary.

Different CAD systems may treat this situation differently. Some may sim-
ply fail to solve. Others may simply not allow the dimension to be created in the
first place. Yet other CAD systems may allow the dimension to be shown, but it
will automatically consider the extra dimension as a reference dimension. This
means that it is shown for reference only, and it is not really controlling the geo-
metric entities. A reference dimensional value of the constraint may be shown in
parentheses, or a “REF” may be shown at the end of the dimension value.

The case of the hole with a dimension to the left- and right-edge of the
plate is somewhat oversimplified. It is clear that the second dimension is redun-
dant. However, as a sketch becomes more complicated, it may be rather difficult
to actually identify such redundancies and overconstraints. Also, some CAD sys-
tems will simply not allow the new 3-D feature to be created for the part until the
redundancy and/or overconstraint it resolved. Sometimes, though, it is an advan-
tage to allow the extra dimensions to be shown on the sketch (as long as the extra
dimensions are clearly identified with REF or parentheses as not controlling the
sketch geometry). Perhaps the distance from that other edge was of interest to the
designer, so after a regeneration successfully completes, then this distance will be
automatically recalculated after the original, controlling dimension is modified.
In this case, the redundant constraint is just supplying interesting information,
and it really causes no problems.

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8.4.9 Underconstraining

Another result from the attempt to regenerate the sketch is that it may be found to
be underconstrained. In this case, there are not enough constraints. This would be
the case for the hole in Figure 8.13 where one of the dimensions for the hole is
missing, for instance, if the horizontal dimension was present but there was no
vertical dimension for the center of the hole. In this case, there would be no way
to be certain that the CAD system could always locate the hole vertically.

The problem that arises in this case is that the CAD system may or may not
demand that the vertical dimension be present. As the system solves the simulta-
neous equations, the solution will not yield a single reliable answer for the verti-
cal location of this hole. Therefore, the hole may actually move up and down
unexpectedly during regeneration. Of course, the CAD system may simply exam-
ine where the hole has been placed on the sketch and assume that there is a di-
mensional constraint there, even though the user did not explicitly create one. In
this case, the CAD system will be able to work with the hole as already shown
and allow the creation of the new feature. However, other CAD systems are writ-
ten so that the user is forced to indicate the dimensional constraint; this type of
system forces the designer to fully constrain.

In reality, allowing underconstrained sketches entails some risk, but some-
times it can be valuable. One example is that when a company manufactures a
specific product, they often don’t design everything within that product. Instead,
a fair amount of the design would be components purchased from suppliers. If
the company uses 3-D design methods for the product, then the company will
need 3-D models for parts that they do not actually design and manufacture. It
could be quite a waste of resources to use a CAD system that forces them to use
the fully constrained approach for these parts. Creating a model based on just
sketching something reasonably close and not bothering with constraints could
save valuable design time.

Another argument for not fully constraining would be creating legacy 3-D
models for parts that are not new enough to warrant a fully constrained approach.
These parts may be quite unlikely to be revised any more. And, again, it could be
quite a waste of time to be forced to do the fully constrained approach for these
types of parts.

8.4.10 “Multiple Solutions”

Another issue from attempting to solve the constraint equations may be the dis-
covery of multiple, yet potentially equally valid solutions. In this case, there are
enough degrees of freedom removed, but there is some ambiguity in how a con-
straint is interpreted.

Figure 8.16 shows an example of this. The two lines through the center of
the sketch shown are fully constrained; they can not move. They are drawn, how-

Part Modeling 211

FIGURE
8.16

A potentially ambiguous constraint system.

ever, just to help set the position of the circle. The circle, in turn, is constrained
by being tangent with the two lines, and it has been located in the upper right
quadrant formed by the lines. One can imagine that the circle cannot move; it
seems fully constrained. Although the circle can not actually move into any arbi-
trary location, it actually would be equally valid to show that circle in the same
position in any of the other three quadrants (lower right, for instance). It would
still be tangent to those two lines in the same way. Therefore, in this case, there
are four equally valid solutions to the constraints (even though the degrees of
freedom were seemingly removed). Different CAD systems may handle this situ-
ation differently, but in the end, the user simply needs to think through the prob-
lem and deal with it accordingly.

8.4.11 Inconsistent Constraints

Finally, a result from attempting to solve the constraint system or network may be
an inconsistency. In this case, there are constraints that conflict in such a way that
no stable solution is possible. Unlike the underconstraining, overconstraining,
and multiple solutions scenarios, inconsistencies must be corrected to have a to-
tally valid model. The inconsistency situation can lead to erroneous designs.

As an example, Figure 8.17 shows a dimension which tries to fix the loca-
tion of the circle example from Figure 8.16. This can be a valid dimension since

212 Chapter 8

FIGURE
8.17

A dimension that may cause inconsistency.

it removes the ambiguity of which quadrant to place the circle. Therefore, the
CAD system should allow this constraint system to regenerate or update.

But, what if the designer changes this dimension to some other value be-
sides the four valid values (for the four quadrants)? This constraint system could
not be solved. The dimension cannot be too low and still maintain the tangency to
both lines. If a “too low” dimension value is placed on the sketch, the system of
constraints is considered inconsistent. And, whatever the CAD system shows af-
ter an attempt to solve the constraints may be totally invalid. The CAD system
may keep trying to find a solution and then give up, at that point leaving the ge-
ometry in the last position it tried. Situations like this need to be corrected by the
designer.

8.4.12 Parametrics

A natural extension of the constraining capability in 3-D CAD systems is apply-
ing mathematical relationships (such as equations or formulae) between dimen-
sional constraints. This can be referred to as creating parametric models. It can
also be referred to as storing design intent, using varying geometry, using family
tables, or using driving dimensions. In any case, this is a very powerful capabil-
ity. It allows the designer to create a complicated sketch that can be changed in
significant but predictable ways by only changing one or a few vital dimensions.
This can save a large amount of time in a design project.