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    actuated collapsible core design is proposed in industry (Wong 1997). Tor et al.
    (2000a, 2000b) have established geometrical features for such a core with the motiv-
    ation towards the automation of the design process (Chung 1999). This moulding
    tool is designed for UPVC pipe fittings of size from Ø100 mm to Ø350 mm. For the
    groove of the 87.58 elbow with a diameter of Ø50 mm, however, such a two-stage
    design is not workable because the diameter of the moulded part is too small to
    provide enough space for segments to collapse in two stages. In light of this, we
    propose a modified design; that is, an additional stage is added to the original two-
    stage system. In this modified design, two different patterns of segments are designed
    in different lengths.
    The operating sequence of this three-stage collapsible core is illustrated in
    figure 13. At the starting position, the two different patterns of segments are placed
    one after another. This is the moulding position of the core. A bush is used to
    support segments and keep them in position during the injection process. When
    the injection process is over and the moulded part has solidified, the bush starts to withdraw (step 1). A spring force causes the set of small segments to collapse at the
    moment the bush leaves the inner surface of the segments. This is the first stage of
    collapse (step 2). Coinciding with the collapse of small segments, the spring force
    on the large segments starts to collapse as well. Due to the small diameter of the
    groove undercut, there is no enough space for the set of large segment to collapse
    and clear the undercut. To solve this, we use a method that lets both the set of
    small segments and the bush withdraw further (step 3). This clears more space for
    the set of large segments to retract inwards and thus to clear the undercut for demould-
    ing (step 4). This is the additional movement added to the original two-stage mechan-
    ism. Reverse procedures take place when the bush is return to the original position for
    the next moulding cycle.
    4.5. Interference check
    The interference for the segments of the collapsible core was checked using Pro/
    Engineer software. Within the software environment, all parts are modelled together
    with assembly relations among them. A trial and error method is used to find out all
    related dimensions and the interference. The software enables interactive changing of
    the input values of variables until there is no interference between related parts. For
    example, the angle at the interface between two segments is found interactively
    through a few runs of trial and error until the retraction of the segments can be satisfac-
    tory. Using the commands available in the software (e.g. the ‘Model Analysis’ function),
    the interference between segments and the moulded part during retraction can also
    be checked interactively. The segments are modelled and assembled together in the
    assembly mode. Then the segments of the core are interrelated using relations and set
    parameters for user input. This helps simplify the whole trial and error process.
    Figure 14 shows the interference result calculated by the software, in which all
    intersecting parts are listed. The volume of each intersection is also shown. Three- 4.6. Housing and moving mechanism
    Plates and holders for mounting the spring and the pivot of the segments need to be
    designed at this stage. Accordingly, the actuating mechanism used for creating the
    operating sequence of the collapsible core can be detailed. A cut-away section of
    the holder in three-dimensional views is shown in figure 15. The small segments of
    the collapsible core are pivoted by a pin and secured in their respective holders.
    Slots enable the mounting of springs to retract the segments. The large segments
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