【正文】
world objects, such as screws, plates,and pins, the CAD system uses a totally different level ofgeometrical objects. As a result, highlevel objectoriented ideashave to be translated to lowlevel CAD entities such as lines,surfaces, or solids. Therefore, it is necessary to develop anautomatic assembly modelling system for injection moulds tosolve these two problems. In this paper, we address the followingtwo key issues for automatic assembly modelling: representinga productindependent part and a mould assembly ina puter。 secondly, the iterative numerical technique cannot distinguish between different roots in the solution space. Therefore, it 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 puting the required rotation and translation for each ponent to satisfy the spatial relationships between the ponents in an assembly. Six variables (three translations and three rotations) for each ponent are solved to be consistent with the spatial relationships. This method requires a vast amount of programming and putation 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, inline, inplane, 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 putationally attractive pared 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 highlevel functional mould objects (ponents and features). Because their system was based on AutoCAD, it could only acmodate wireframe 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 puters, and determining the position and orientation of a product independent part in the assembly. In this section, we present an objectoriented and featurebased representation for assemblies of injection moulds. The representation of assemblies in a puter involves structural and spatial relationships between indivi