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attribute of O, associated with each attribute is a type,
t, and a value, v.
M is a set of tuples, (m, tc1, tc2, %, tcn, tc). Each
element of M is a function that uniquely identifies a
method. The symbol m represents a method name; and
methods define operations on objects. The symbol tci (i
R is a set of relationships among O and other assembly
objects. There are six types of basic relationships
between assembly objects, i.e. Part-of, SR, SC, DOF,
Lts, and Fit.
3.2 Assembly Relationships
There are six types of basic relationships between assembly
objects, Part-of, SR, SC, DOF, Lts, and Fit.
Part-of An assembly object belongs to its ancestor object.
SR Spatial relations: explicitly specify the positions
and orientations of assembly objects in an
assembly. For a component part, its spatial
relationship is derived from spatial constraints
(SC).
SC Spatial constraints: implicitly locate a component
part with respect to the other parts.
DOF Degrees of freedom: are allowable translational/
rotational directions of motion after assembly, with
or without limits.
Lts Motion limits: because of obstructions/interferences,
the DOF may have unilateral or bilateral limits.
Fit Size constraint: is applied to dimensions, in order
to maintain a given class of fit.
Among all the elements of an assembly object, the relationships
are most important for assembly design. The relationships
between assembly objects will not only determine the position
of objects in an assembly, but also maintain the associativities
between assembly objects. In the following sub-sections, we
will illustrate the relationships at the same assembly level with
the help of examples.
3.2.1 Relationships Between Form Features
Mould design, in essence, is a mental process; mould designers
most of the time think on the level of real-world objects such
as plates, screws, grooves, chamfers, and counter-bore holes.
Therefore, it is necessary to build the geometric models of all
product-independent parts from form features. The mould
designer can easily change the size and shape of a part,
because of the relations between form features maintained in
the part representation. Figure 3(a) shows a plate with a
counter-bore hole. This part is defined by two form features,
i.e. a block and a counter-bore hole. The counter-bore hole
(FF2) is placed with reference to the block feature FF1, using
their local coordinates F2 and F1, respectively. Equations (2)–
(5) show the spatial relationships between the counter-bore
hole (FF2) and the block feature (FF1). For form features,
there is no spatial constraint between them, so the spatial
relationships are specified directly by the designer. The detailed
assembly relationships between two form features are defined
as follows:
Equations (2)–(7) present the relationships between the form
feature FF1 and FF2. These relationships thus determine the
position and orientation of a form feature in the part. Taking
the part as an assembly, the form feature can be considered
as “components” of the assembly.
The choice of form features is based on the shape characteristics
of product-independent parts. Because the form features
provided by the Unigraphics CAD/CAM system [13] can meet
the shape requirements of parts for injection moulds and the
spatial relationships between form features are also maintained,
we choose them to build the required part models. In addition
to the spatial relationships, we must record LTs, Fits relationships
for form features, which are essential to check the
validity of form features before updating the models in the