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: 自动装配模型注塑模具外文文献和中文翻译(3):http://www.751com.cn/fanyi/lunwen_15952.html