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    A mould base is the result of this standardisation.
    According to the feature-based and object-oriented assembly
    representation, the feature-based solid models for component
    parts of the mould base are first constructed; next, the assembly
    objects are defined by establishing relationships between
    components and encapsulating some functions in the component
    parts; then, using these assembly objects, a hierarchical subassembly
    object – a mould base – can be formed. This mould
    base object can be instantiated by a group of data from the
    catalogue database. Figure 4 shows the instantiation of the
    mould base object to generate the specified mould base. This
    specified mould base instance can be added automatically to
    the mould assembly. The structural relations between the mould
    base subassembly and top assembly can be expressed by Eqs.
    (8) and (9), where Mp and Mr are the unit matrices.
     
    5.2 Automatic Addition of Standard Parts
    A standard part is an assembly object. It can be defined
    according to Eq. (1) in Section 3.1. In the database, the spatial
    constraints are specified by mate, planeFalign and axisFalign,
    but unlike the mould base, the position and orientation matrices
    of a standard part are left unknown. During instantiation,
    the software then automatically infers the explicit structural
    relationships by using the simplified symbolic geometric
    approach described in Section 4.
    5.3 Pocketing for Assembly Objects
    One of the important issues for automatic assembly design is
    the automation of the pocketing process. Pocketing is an
    operation that makes an empty space in corresponding components
    to accommodate the inserted components. When an ejector
    is added to the assembly, an empty space is required on
    the EA plate to accommodate the ejector, as shown in Fig. 5.
     
    Since an object-oriented representation is adopted, each
    assembly object can be represented by two solids, the real
    object and the virtual object. The virtual object is modelled
    according to the space that a real object will occupy. Whenever
    an assembly object is added to an assembly, its virtual object
    is also added to the assembly. The operation function
    pocketFplate() in M of O will subtract the virtual object from
    the corresponding components (see Eq. (1) and Table 1).
    Moreover, because there are associativities between the virtual
    object and real object, the pockets on the corresponding components
    will change with the modification of the real object.
    This automatic pocketing function further demonstrates the
    advantage of an object-oriented representation.
         6. System Implementation
    Based on the Unigraphics system [13], the proposed featurebased
    and object-oriented assembly scheme and automation of
    assembly modelling have been implemented in the IMOLD
    system [14] developed at the National University of Singapore.
    The Unigraphics system provides a user-friendly application
    programming interface (API). Through this interface, the users
    can call Unigraphics internal functions such as adding parts to
    an assembly, modifying parameters, etc. Although Unigraphics
    provides functions for mating conditions, the proposed approach
    is still needed to infer the component configuration, because
    it is necessary to calculate the degrees of freedom, and check
    the validity of mating conditions before the component can be
    added to the assembly. The proposed synthesised constraints
    are compatible with Unigraphics constraints.
    Figure 6 shows an injection moulded product, and the
    designed injection mould assembly for this product is shown
    in Fig. 7(a). The corresponding parent–child relationships for
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