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    is possible, in a purely spatial relationship problem, that a
    mathematically valid, but physically unfeasible, solution can
    be obtained.
    Ambler and Popplestone [6] suggested a method of computing
    the required rotation and translation for each component
    to satisfy the spatial relationships between the components in
    an assembly. Six variables (three translations and three
    rotations) for each component are solved to be consistent with
    the spatial relationships. This method requires a vast amount
    of programming and computation to rewrite related equations
    in a solvable format. Also, it does not guarantee a solution
    every time, especially when the equation cannot be rewritten
    in solvable forms.
    Kramer [7] developed a symbolic geometric approach for
    determining the positions and orientations of rigid bodies that
    satisfy a set of geometric constraints. Reasoning about the
    geometric bodies is performed symbolically by generating a
    sequence of actions to satisfy each constraint incrementally,
    which results in the reduction of the object’s available degrees
    of freedom (DOF). The fundamental reference entity used by
    Kramer is called a “marker”, that is a point and two orthogonal
    axes. Seven constraints (coincident, in-line, in-plane, parallelFz,
    offsetFz, offsetFx and helical) between markers are defined.
    For a problem involving a single object and constraints between
    markers on that body, and markers which have invariant attributes,
    action analysis [7] is used to obtain a solution. Action
    analysis decides the final configuration of a geometric object,
    step by step. At each step in solving the object configuration,
    degrees of freedom analysis decides what action will satisfy
    one of the body’s as yet unsatisfied constraints, given the
    available degrees of freedom. It then calculates how that action
    further reduces the body’s degrees of freedom. At the end of
    each step, one appropriate action is added to the metaphorical
    assembly plan. According to Shah and Rogers [8], Kramer’s
    work represents the most significant development for assembly
    modelling. This symbolic geometric approach can locate all
    solutions to constraint conditions, and is computationally
    attractive compared to an iterative technique, but to implement
    this method, a large amount of programming is required.
    Although many researchers have been actively involved in
    assembly modelling, little literature has been reported on feature
    based assembly modelling for injection mould design.
    Kruth et al. [9] developed a design support system for an
    injection mould. Their system supported the assembly design
    for injection moulds through high-level functional mould
    objects (components and features). Because their system  was
    based on AutoCAD, it could only accommodate wire-frame
    and simple solid models.
         3. Representation of Injection Mould
         Assemblies
    The two key issues of automated assembly modelling for
    injection moulds are, representing a mould assembly in computers,
    and determining the position and orientation of a product-
    independent part in the assembly. In this section, we
    present an object-oriented and feature-based representation for
    assemblies of injection moulds.
    The representation of assemblies in a computer involves
    structural and spatial relationships between inpidual parts.
    Such a representation must support the construction of an
    assembly from all the given parts, changes in the relative
    positioning of parts, and manipulation of the assembly as a
    whole. Moreover, the representations of assemblies must meet
    the following requirements from designers:
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