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other mould components are built into the mould insert, a
mould component O1 is found to interfere with channel C1.
As C1 cannot be moved to a nearby location due to the possible
interference with other components, it is shortened. As a result,
C2 is moved and C3 is elongated accordingly to maintain the
connectivity, as shown in Fig. 2(b). Owing to its new length,
C3 is found to interfere with another mould component, O2,
and further modification is needed, which results in the final
design shown in Fig. 2(c). Given that a typical injection mould
may have more than ten cooling channels, with each channelpotentially interfering with a few other mould components,
finding an optimal layout design manually is very tedious.
This paper reports a new technique that supports the
automation of the layout design process. In this new technique,
a configuration space (C-space) method is used to provide a
concise representation of all of the feasible layout designs. The
C-space representation is constructed by an efficient method
that exploits the special characteristics of the layout design
problem. Instead of using heuristic rules to generate layout
designs, as in the automatic layout design system developed
previously by the authors [13,14], this new C-space method
enables an automatic layout design system to conduct a more
systematic search among all of the feasible layout designs.
2. The configuration space method
In general, the C-space of a system is the space that
results when each degree of freedom of that system is treated
as a dimension of the space. Regions in the configuration
space are labeled as blocked region or free region. Points
in the free regions correspond to valid configurations of the
system where there is no interference between the components
of the system. Points in the blocked regions correspond to
invalid configurations where the components of the system
interfere with one another. C-space was initially formalized
by Lozano-Perez [15] to solve robot path planning problems
and a survey in this area of research has been reported by
Wise and Bowyer [16]. The C-space method has also been
used to solve problems in qualitative reasoning (e.g., [17,18]) and the analysis and design automation of kinematic devices
(e.g., [19–21]). The author investigated a C-space method in the
automatic design synthesis of multiple-state mechanisms [22,
23] in previous research.
2.1. C-space of a cooling system
A high-dimensional C-space can be used to represent all of
the feasible layout designs of a given preliminary design of
a cooling system. Fig. 3 gives an example. The preliminary
design of this cooling system consists of four cooling channels.
To generate a layout design from the preliminary design, the
centers and lengths of the channels are adjusted. As shown in
Fig. 3, the center of channel C1 can be moved along the X1
and X2 directions, and its length can be adjusted along the X3
direction. Similarly, the length of C2 can be adjusted along the
X4 direction, while its center adjustment is described by X1
and X3 and thus must be the same as the adjustment of C1 to
maintain the connectivity. By applying similar arguments to the
other channels, it can be seen that the cooling system has 5 degrees of freedom, and they are denoted as Xi , i = 1, 2, . . . , 5.
In principle, the C-space is a five-dimensional space and any
point in the free region of this space gives a set of coordinate
values on the Xi axes that can be used to define the geometry of
the channels without causing interference with the other mould
components. To determine the free region in a high-dimensional
C-space of a cooling system, the first step is to construct the free