【正文】 verlap。 and second, that a dimension tag be placed as close as possible to the feature being dimensioned. The key issue in this research is to develop a method that can optimize the placement of the datum dimensions.2 Related workWhile dimensioning and tolerancing are two closely related processes in specifying the size and location information of the features in a mechanical part or an assembly, most of the past research work has focused on tolerancing. The major research issues in tolerancing are representation, analysis and representation is concerned with the incorporation of tolerance information into a product modeling scheme. Examples include the solid offset approach developed by Requicha,the feasibility space approach proposed by Turner, and the TTRS by Desrochers and Clement. More detailed review can be found in Roy et al. and Yu et al. Tolerance analysis aims to determine the bined effect of part tolerances on the assembly tolerance. It can be used to verify the functionality of a design given known or assumed variations of individual part dimensions. Examples of technique in tolerance analysis include Monte Carlo simulation and the direct linearization method. The main objective of tolerance synthesis or tolerance allocation is to allocate part tolerances based on given functional requirements of the assembly. Recently, Islam reported a concurrent engineering approach to address this on a systemic analysis of the functional requirements from different customer requirements and the technical requirements from engineering considerations, a methodology for extracting dimensional requirements is developed. A software prototype FDT is also developed for supporting the implementation of the methodology. FDT provides tools for representing the functional requirements, dimensions, tolerances and process capability into a functional requirement/ dimensions matrix. The functional equations captured in the matrix are then separated into groups, and each group is then solved using a solution strategy specific to the functional requirement and the tolerancing problem involved. More detailed review in tolerance analysis and synthesis can be found in Roy et al, Ngoi and Ong and Hong and Chang.Several methods have been developed for generating dimensions automatically from the CAD model of a part. Yuen et al. Reported an early attempt in automatic dimensioning of parts represented in Constructive Solid Geometry (CSG) solid modeling technique. Points from planar faces and axes of cylinders are extracted from the solid model. The coordinates of the points are arranged in a tree structure to generate linear dimensions in the three principal directions. A simple technique for diametric and radial dimensions was also reported. Other early works in automatic dimensioning have been summarized by Yu et al. Recently, Chen et al. reported a more indepth study of automatic dimensioning. Their method analyzed dimension redundancy, determined dimensioning schemes that are specific to feature patterns, selected appropriate views for specifying the dimension, and determined the appropriate location of the dimension using an expert system approach. The expert system analyses the geometry and topology of the feature to be dimensioned, and determined a position for placing the dimension based on a set of rules that is relevant to the current dimensioning the placement of one dimension,a forbidden region is constructed so that all subsequent dimensions will not be placed in this region. This avoids overlap or intersection between two dimensions.A limitation in the existing approach for the placement of the dimension is due to the sequential nature of the example, in Chen’s method the features to be dimensioned are prioritized, and the positions of the dimensions are determined one after another. The approach is not appropriate for determining the placement of datum dimensions, especially when the dimensions are very crowded, as in the case of injection mould plates. This is because the placement of one datum dimension may have an effect on the placement of another dimension that may be located far away from the current paper reports our work in solving the placement problem in datum dimensioning. The major contribution of our work is the development of a new method that determines the optimal placement of each datum dimension. Using the dynamic programming approach to optimization, this new method overes the limitation of the sequential approach used in the existing method.3 Illustrative examplesThe proposed optimization method has been implemented using C++ and incorporated into the Unigraphics II CAD/CAM system through its Application Program Interface (API). To illustrate the effects of the subcost functions, consider the example illustrated in Fig. 6. There are five dimension blocks in the figure. All the dimension blocks are at their default configurations and overlap occurs between d1 and d2, and between d4 and d5. These dimensions are generated automatically by the optimization program, with the cost function contributed only by the subcost function DV . As a result, the dynamic programming procedure selects a set of states where the lowest cost corresponds to the minimum deviation from the default location of each dimension block.Fig. 6. Dimension blocks at their default configurationFig. 7. Minimizing the amount of shift and the number of dimension blocksto be shifted to remove overlaps between dimension blocksFig. 8. Comparison of the effects obtained from DN and DEFig. 9. Execution of the optimization program to generate datum dimensions for an example partFigure 8 shows another example which pares the effect of DN and DE. Figure 8a shows the result obtained by using DV and DN. The lower block is shifted while the upper block remains at its default configuration. Figure 8b shows the result obtained by using DV and DE. Both dimension blocks are shifted by a small