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DOI 10 1007 s00170 004 2374 2 ORIGINAL ARTICLE Int J Adv Manuf Technol 2006 28 370 378 C L Li K M Yu Y H Lee Automatic datum dimensioning for plastic injection mould design and manufacturing Received 7 May 2004 Accepted 10 August 2004 Published online 20 April 2005 Springer Verlag London Limited 2005 Abstract Datum dimensioning or ordinate dimensioning tech nique is very popular in plastic injection mould drawings where the location dimensions of a large number of hole features must be specified in the drawings of the mould plates Although com mercial CAD CAM systems provide semi automatic tools to as sist the designer in the dimensioning process it is still a very tedious process as the user has to specify the location of each di mension tag This paper reports a completely automatic method where optimal placements of the dimension tags can be deter mined The method employs dynamic programming technique to optimize the dimension process with respect to several criteria that can be selected by the user The method has been imple mented and incorporated into a commercial CAD CAM system and examples are given to illustrate the important features of the program Keywords Automatic dimensioning Datum dimensioning Dynamic programming Optimal dimensioning Ordinate dimensioning 1 Introduction CAD CAM systems are now widely used in the plastic injec tion mould making industry Many companies are using a solid modeling system to design the injection mould They use a CAD system to model not only the core and cavity inserts of the mould which are the most important components that form the im pression of the mould but also all other components in the C L Li a117 Y H L e e Department of Manufacturing Engineering and Engineering Management City University of Hong Kong Tat Chee Avenue Kowloon Hong Kong E mail meclli cityu edu hk Tel 8 52 27888432 Fax 8 52 27888423 K M Yu Department of Industrial and Systems Engineering The Hong Kong Polytechnic University entire mould assembly With the advance in Internet technology and the recent development of Internet enabled CAD the de sign information of the injection mould can be communicated electronically between the product engineer who designs the plastic part and the tooling engineer who designs the injection mould even though they may be located in different geographic regions of the world While flow of design information between product design and tooling design are communicated effectively through an electronic means the communication of manufac turing information to the shop floor is done by both electronic and traditional techniques Computer Numerical Control CNC machining toolpath or inspection instructions can be generated directly from the CAD CAM system and downloaded through a network to the CNC controller for the machining or inspection operations However set up instructions for a particular machin ing job may be specified in an engineering drawing Moreover not all machining tasks are done using CNC machine tools Some traditional machining processes such as drilling and grinding are done using conventional machine tools because of cost con sideration Conventional engineering drawings are thus still play ing an important role in communicating engineering information to the shop floor The orthographic projections in engineering drawings can be generated automatically from the CAD model of the parts Automatic tools for dimensioning of the parts are also provided by many commercial CAD systems However as pointed out by Chen et al 1 those automatic dimensioning tools are not able to generate dimensions according to the draw ing standards and engineering practices adopted in the shop floor In the specific application of injection mould design datum dimensioning or ordinate dimensioning of hole features are used extensively Figure 1 shows a typical detail drawing that can be found on the shop floor of a mould making company Shown in the figure are the hole features and datum dimensions which are used to specify the locations of the holes It can be seen that the dimensions are very crowded and it is a tedious task to manually adjust the placement of all the datum dimensions The quality of the final fully dimensioned drawing thus depends very much on the experience of the draftsman who produces the draw ing The purpose of this research is to develop a tool that can 371 Fig 1 Use of datum dimensioning in a drawing of a plastic injection mould part generate the datum dimensions automatically from a given part of the injection mould The resulting dimensions must satisfy two obvious requirements first that no two dimension tags may overlap 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 work While dimensioning and tolerancing are two closely related pro cesses 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 synthesis Tolerancing representation is concerned with the incorporation of tolerance information into a product modeling scheme Exam ples include the solid offset approach developed by Requicha 2 the feasibility space approach proposed by Turner 3 and the TTRS by Desrochers and Clement 4 More detailed review can be found in Roy et al 5 and Yu et al 6 Tolerance analy sis aims to determine the combined effect of part tolerances on the assembly tolerance It can be used to verify the functional ity of a design given known or assumed variations of individual part dimensions Examples of technique in tolerance analysis in clude Monte Carlo simulation 7 and the direct linearization method 8 The main objective of tolerance synthesis or tol erance allocation is to allocate part tolerances based on given functional requirements of the assembly Recently Islam 9 re ported a concurrent engineering approach to address this prob lem Based on a systemic analysis of the functional requirements from different customer requirements and the technical require ments from engineering considerations a methodology for ex tracting dimensional requirements is developed A software pro totype FDT 10 is also developed for supporting the implemen tation 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 strat egy 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 5 Ngoi and Ong 11 and Hong and Chang 12 Several methods have been developed for generating dimen sions automatically from the CAD model of a part Yuen et al 13 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 cylin ders are extracted from the solid model The coordinates of the points are arranged in a tree structure to generate linear dimen sions 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 6 Recently Chen et al 1 14 reported a more in depth study of automatic dimensioning Their method analyzed di mension redundancy determined dimensioning schemes that are specific to feature patterns selected appropriate views for spec ifying the dimension and determined the appropriate location of the dimension using an expert system approach 15 The ex pert 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 cur rent dimensioning feature With the placement of one dimension a forbidden region is constructed so that all subsequent dimen sions will not be placed in this region This avoids overlap or intersection between two dimensions 372 A limitation in the existing approach for the placement of the dimension is due to the sequential nature of the method For example in Chen s 1 14 method the features to be dimen sioned 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 di mension may have an effect on the placement of another dimen sion that may be located far away from the current dimension This 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 pro gramming approach to optimization this new method overcomes the limitation of the sequential approach used in the existing method 3 Basic characteristic of datum dimensioning In datum dimensioning the location of a feature is specified by the horizontal and vertical distances from the reference lo cation of the feature and a reference datum The default form of datum dimension is shown in Fig 2a When the vertical dis tance between two features to be dimensioned is less than the dimension tag size i e the sum of the dimension text height and the minimum spacing between adjacent dimension texts Fig 2 Basic characteristics of datum dimensioning the alternative forms shown in Fig 2b are required 1 The di mension tags are shifted upward or downward from the default location to prevent overlap As shown in Fig 2c the shifting of the dimension tag is achieved by breaking the single exten sion line of the dimension into three segments two horizontal segments which are connected by one inclined segment The ex tent to which a dimension tag can be shifted is governed by three parameters i the dogleg angle which is the angle be tween the inclined segment and the horizontal segments of the dimension line ii the margin distance m between the dimen sion text and the part boundary and iii the location x f i y f i of the feature f i The two extreme positions i e the uppermost pos ition y max i and lowermost position y min i of the dimension tag are given by y max i y f i x f i m tan y min i y f i x f i m tan 1 4 Automatic datum dimension The objective of the automatic datum dimensioning system is to find an optimal position for each datum dimension The process consists of two phases of operation the preparation phase and the optimization phase In the preparation phase major param eters that facilitate the optimization process will be established Feasibility for placing the dimensions for all the features using the given dogleg angle margin offset and dimension tag size will also be tested In the optimization phase a dynamic pro gramming approach is used The dimension tag locations can be optimized with respect to different sets of criteria including the minimization of the shift of every dimension from their default locations or maximization of the use of the default form as much as possible 4 1 The preparation phase The features to be dimensioned are first grouped into one or more feature sets For each feature in a feature set there exist at least one other feature in the set such that the vertical dis tance between them is less than the dimension tag size In other words the features in a feature set cannot be dimensioned using the default form exclusively without overlap between adjacent dimension tags Instead at most one feature can use the de fault form while all others require the use of the alternative form The set of dimension tags associated with a feature set is called a dimension block The configuration of a dimension block refers to the forms and locations of each datum dimen sion within the dimension block For each position of a dimen sion block its configuration is uniquely defined Figure 3 shows two feature sets and their dimension blocks at two different configurations 1 To simplify the explanation of the technique only vertical dimensions placed on the left hand side of the part are discussed The method developed is general and can be applied to the other sides of the part 373 Fig 3 Feature sets and different con figurations of dimension blocks Definition 1 Validity of a configuration A configuration of a di mension block is valid if there is no overlap between any dimen sion tags in the dimension block and each dimension tag lies within its extreme positions The configurations of the dimension blocks shown in Fig 3b are valid Two examples of invalid configuration are shown in Fig 4 The configuration shown in Fig 4a is invalid because two of the dimension tags overlap For the configuration shown in Fig 4b the extension line of the dimension tag 14 00 is at its lowermost position while the required position for the dimen sion tag is beyond this lowermost position Fig 4 Invalid configurations of a dimension block Fig 5 Dimension block at extreme configurations Definition 2 Extreme configurations There are two extreme configurations the uppermost and lowermost configurations A dimension block is at its uppermost lowermost configuration if the dimension block is valid and is at a position such that any other higher lower position results in an invalid configuration The extreme configurations of a dimension block d i are denoted by Y max i and Y min i Figure 5a shows a dimension block at its uppermost config uration It cannot move further upward because the dimension tag 29 5 is at its highest position Figure 5b shows a dimen sion block at its lowermost configuration It cannot move fur 374 ther downward because the dimension tag 14 00 is at its lowest position The extreme configurations of a dimension block are the two important parameters that will be used by the optimization pro cess They are also useful in testing whether it is feasible to dimension all the features without any overlap between the di mension tags It is observed that two properties are useful in developing a method to determine the extreme configurations Property 1 For a dimension block at its uppermost lowermost configuration at least one of its dimension tags is at its upper most lowermost position Property 2 A dimension block has a valid configuration if and only if it has extreme configurations Property 1 can be proved by contradiction Assume that a di mension block is at its uppermost lowermost configuration and none of its dimension tags are at their uppermost lowermost positions Since all the dimension tags are not at their uppermost lowermost positions they can all be moved upwards down wards simultaneously by the same amount until any one of them reaches its uppermost lowermost position As all dimension tags are moved simultaneously by the same amount the dimen sion tags do not overlap and thus the resulting configuration is still valid and at a higher lower position than its original configuration This violates the assumption that the original con figuration is the uppermost lowermost configuration Property 2 can be verified directly Given a valid configura tion the dimension block is moved upward downward until one or more of its dimension tags reach its uppermost lowermost position Since all the dimension tags are moved simultaneously by the same amount overlap does not occur Moreover the di mension block cannot be moved upwards downwards any fur ther without invalidating the configuration because at least one of its dimension tags is at its uppermost lowermost position According to Definition 2 the resulting configuration is thus the uppermost lowermost configuration On the other hand it is ob vious that if a dimension block has extreme configurations then it has a valid configuration because the extreme configurations are by definition valid Property 1 indicates that the extreme configurations of a di mension block can be obtained by investigating the extreme pos itions of the dimension tags in the block The configuration of a dimension block can be specified by y i i 1 2 n where y i is the location of the dimension tag of the ith feature in the feature set f i Thisassumesthat f i are arranged in ascend ing order by their vertical positions i e y f i y f j if i j Then to avoid overlap between dimension tags the location of the ith dimension tag is given by y i i 1 SIZE y 1 n i 2 2 where SIZE is the dimension tag size and y 1 is the location of the dimension tag for the first feature f 1 oftheset y 1 is also used as the reference location of the dimension block For a configuration to be valid all dimension tags must lie below its own uppermost position given by Eq 1 That is y max i y i and thus y max i i 1 SIZE y 1 The above relationship must be satisfied by all i Therefore the highest allowable value for y 1 is given by Min i y max i i 1 SIZE 3 with the y 1 value given by Eq 2 and one or more y i equal to y max i All other y i are less than its y max i Since no other larger value of y 1 results in a configuration that satisfies y max i y i the resulting configuration if valid is the uppermost configuration However it is possible that at this configuration some of the y i given by Eq 2 is less than y min i Therefore a check is performed for each y i Ify i y min i for all i then the uppermost configura tion is found If y i i Y max j SIZE n i YF min i Max Y min i Max i j 1 Y min j SIZE n j where n i and n j are the number of dimension tags in dimension blocks d i and d j respectively Using this definition of the feas ible range those configurations that always cause overlap with adjacent dimension blocks are excluded from the feasible range A fixed resolution say 0 5 mm is specified and the number of states for a given stage is obtained by dividing the feasible range by the given resolution 4 4 Cost functions The overall cost of a stage and the cost function C i t i j t i 1 k are vector and vector valued functions respectively A cost vec tor consists of five components c i i 1 5arrangedinde scending order of importance That is c i is considered more important than c j if i p vextendsingle vextendsingle YF max i YF min i vextendsingle vextendsingle and is set to zero otherwise When two adjacent dimension blocks at their default loca tions overlap for a certain amount a the overlap can be removed by shifting d i upwards by a i and shifting d i 1 downwards by a i 1 such that a i a i 1 a It may be desirable that a i a i 1 That is the required total shift is being shared equally between two dimension blocks The sub cost function D V t i j is not able to achieve this purpose because it only measures the total shift amount and not the distribution of the amount between adjacent dimension blocks D E t i j is devised to equalize the amount of shift between adjacent dimension blocks It is set to the differ ence between the extent of deviations of the adjacent dimension blocks D E t i j t i 1 k D V t i j D V t i 1 k The four optional sub cost functions are freely selected and assigned to the second to fifth cost components by the user to achieve different objectives In the next section examples are given to illustrate the different results obtained by choosing dif ferent optional sub cost functions 5 Illustrative examples The 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 sub cost functions consider the example illustrated in Fig 6 There are five dimension blocks in the figure All the dimension blocks are at their default configuration