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there are usually around one hundred product-independent parts
in a mould set, and these parts are associated with each other
with different kinds of constraints. It is time-consuming for
the designer to orient and position the components in an
assembly. Secondly, while mould designers, most of the time,
think on the level of real-world objects, such as screws, plates,
and pins, the CAD system uses a totally different level of
geometrical objects. As a result, high-level object-oriented ideas
have to be translated to low-level CAD entities such as lines,
surfaces, or solids. Therefore, it is necessary to develop an
automatic assembly modelling system for injection moulds to
solve these two problems. In this paper, we address the following
two key issues for automatic assembly modelling: representing
a product-independent part and a mould assembly in
a computer; and determining the position and orientation of a
component part in an assembly.
This paper gives a brief review of related research in
assembly modelling, and presents an integrated representation
for the injection mould assembly. A simplified geometric symbolic
method is proposed to determine the position and orientation
of a part in the mould assembly. An example of automatic
assembly modelling of an injection mould is illustrated.
2. Related Research
Assembly modelling has been the subject of research in perse
fields, such as, kinematics, AI, and geometric modelling. Libardi
et al. [3] compiled a research review of assembly modelling.
They reported that many researchers had used graph
structures to model assembly topology. In this graph scheme,
the components are represented by nodes, and transformation
matrices are attached to arcs. However, the transformation
matrices are not coupled together, which seriously affects the
transformation procedure, i.e. if a subassembly is moved, all
its constituent parts do not move correspondingly. Lee and
Gossard [4] developed a system that supported a hierarchical
assembly data structure containing more basic information
about assemblies such as “mating feature” between the components.
The transformation matrices are derived automatically
from the associations of virtual links, but this hierarchical
topology model represents only “part-of” relations effectively.
Automatically inferring the configuration of components in
an assembly means that designers can avoid specifying the
transformation matrices directly. Moreover, the position of a
component will change whenever the size and position of its
reference component are modified. There exist three techniques
to infer the position and orientation of a component in the
assembly: iterative numerical technique, symbolic algebraic
technique, and symbolic geometric technique. Lee and Gossard
[5] proposed an iterative numerical technique to compute the
location and orientation of each component from the spatial
relationships. Their method consists of three steps: generation
of the constraint equations, reducing the number of equations,
and solving the equations. There are 16 equations for “against”
condition, 18 equations for “fit” condition, 6 property equations
for each matrix, and 2 additional equations for a rotational
part. Usually the number of equations exceeds the number of
variables, so a method must be devised to remove the redundant
equations. The Newton–Raphson iteration algorithm is used to
solve the equations. This technique has two disadvantages:
first, the solution is heavily dependent on the initial solution;
secondly, the iterative numerical technique cannot distinguish
between different roots in the solution space. Therefore, it