FEATURE RECOGNITION OF ROTATIONAL PARTS USING BIQUADRATIC BEZIER PATCHES

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1 roceedigs of the Iteratioal Coferece o Mechaical Egieerig 7 (ICME7) 9-31 December 7, Dhaka, Bagladesh ICME7- FEATURE RECOGNITION OF ROTATIONAL ARTS USING BIQUADRATIC BEZIER ATCHES J. Kumar 1 ad N. Roy 3 1 Departmet of Mechaical egieerig, B.B.S. College of Egieerig & Techology, haphamau Allahabad-1113 U Idia Departmet of Mechaical egieerig, M.N.N.I.T.Allahabad-114 U Idia jitedra5@rediffmail.com ABSTRACT For the automatio of the process plaig fuctio a complete represetatio of the part is very useful. Features recogitio is cosidered as the bridge betwee computer aided desig (CAD) ad computer aided process plaig (CA). The purpose of feature recogitio is to covert the geometric CAD data of a part ito a set of features suitable to support maufacturig activities such as i process plaig system. This paper proposes a method for features recogitio by usig biquadratic Bezier patch, which is similar to sytactic patter recogitio approach. I this paper a part is represeted by the some specific coordiates accordig to give table ad these coordiates are used oly for idetifies the differet faces of the part with the help of patter primitives. Now these coordiates are implemeted i biquadratic Bezier patch equatio for the purpose of feature recogitio of the rotatioal parts by matchig from predefied features. This method of feature recogitio is limited to the turig features such as all types of grooves, chamfer, cocave & covex surfaces, tapers, etc. Keywords: Form features; Feature recogitio; Surface represetatio; art represetatio Bezier patch 1. INTRODUCTION For maufacturig a part process plaig is ecessary which ivolves detailed descriptio of the part for the purpose of process plaig activity icludig selectio of processes, sequecig of the processes, selectio of machie tools ad cuttig tools, decisio about cuttig parameters, choice of jigs ad fixtures ad calculatio of machiig times ad costs. Computer aided process plaig has a very importat role for the itegratio of computer aided desig ad computer aided maufacturig, ad makes a purpose full relatio betwee CAD ad CAM. art descriptio of the CAD model i basic form of geometry ad topology that ca ot be used for directly for process plaig because it requires iformatio i the form of features ad ca be extracted from this CAD model. It is a problem for process plaig that how the feature ca be maufactured ad this iformatio ca be used i process plaig. I this paper a algorithm to recogize features by usig biquadratic Bezier patch which has got similarities with sytactic patter recogitio approach. The applicatio of this techique to recogize turig features is preseted. Turig features are selected i this study because they form the majority type of features i mechaical parts ad products. rocess plaig requires part form feature iformatio ot geometric iformatio. Hece extractig promisig approach to solve this problem [1]. the required iformatio from the CAD data is a problem that must be solved. Feature recogitio is the most Oral et al. [] defie computer aided optimum operatio ad tool sequeces that are to be used i Geerative rocess laig System developed for rotatioal parts. The recogitio of features such as U-groove, V-groove, slot, tapers, covex ad cocave form a importat subset of feature recogitio [3]. Kim et al. [1] deals with the developmet of a computer-aided process plaig system iterfaced with CAD for turig operatio. The method developed by Joshi ad Chag is a good example of a graph based approach to feature recogitio. I this the boudary represetatio of the part is traslated ito a graph where its odes represet faces ad its arcs represet edges [13]. Features are cosidered to be machied volumes ad are described i a hierarchical taxoomy that is desiged to be useful across a rage of machied compoets [6]. Feature recogitio is a sub-disciplie of solid modelig that focuses o the desig ad implemetatio of algorithms for detectig maufacturig iformatio from solid models produce by CAD system [4]. For the purposes of feature recogitio, segmetatio or shape aalysis it is ofte importat to compute curvature ICME7 1

2 iformatio. Razda ad Bae [7] preset a ovel method, which uses biquadratic Bezier patches as a surface fittig techique. Based o the CIM strategy, CA system allows the user to develop a itegrated structure that deals with the flow of iformatio betwee CAD, CA, MR ad CAM activities withi the compay [1]. Razda ad Bae [5] proposed a hybrid method, which takes advatage of both methods, ad create regios with complete feature loops. Satisfactory results have bee achieved for both CAD parts as well as other laser s caed objects such as boes ad ceramic.. ART RERESENTATION A object orieted part modular represets a part as a assembly of the form features. The part modular has the capability to represet ad store geometrical ad techological iformatio of each form feature. The form features class hierarchy classifyig the form features of a part as primary ad secodary features. The primary features give the overall shape to the part. The secodary features reside o the primary features ad add details to the part [11]. 3. SURFACE RERESENTATION Surfaces ca be described mathematically i 3D space by o-parametric or parametric equatios. There are several methods to fit o- parametric surfaces to a give set of data poits. The equatio of the surface or surface patch is give by = [x y z] T = [x y f(x, y)] T Where is the positio vector of a poit o the surface (figure 4.1). The atural form of the fuctio f (x, y) for a surface to pass through all the give data poits is a polyomial that is m i j Z = f( x, y) = y (1) i= j= ax ij Where the surface is described by a x y grid of size (m+1) * (+1) poits. The parametric represetatio of a surface meas a cotiuous vector valued fuctio (u, v) of two variables or parameters u ad v, where the variables are allowed to rage over some coected regio of the u v plae ad as they do so. (u, v) as sums every positio o the surface. The fuctio (u, v) at certai u ad v values is the poit o the surface at these values to described the parametric equatio of a 3D curved surface i space is (u, v) = [x y z] T = [x (u, v) y (u, v) z (u, v)] T () u mi u u max, v mi v v max This equatio gives the coordiates of a poit o the surface as the compoets of its positio vector. It uiquely maps the parametric space (E i u ad v values) to the Cartesia space (E 3 i x, y ad z) [8]. This equatio suggests that a geeral 3-d surface ca be modeled by dividig it ito a assembly of topological patches. The iterval is (, 1) for both u ad v. A patch is cosidered the basic mathematical elemet to model a composite surface. Some surfaces may cosist of oe patch oly while others may be a few patches. The topology of a patch may be rectagular or triagular. Triagular patches add more flexibility i surface modelig because they do ot require ordered rectagular array of data poits to create the surface as the rectagular patches do. 4. BEZIER CURVES AND SURFACES To obtai a more free form desig for aesthetic surfaces that satisfy some requiremets, the modelig techiques eed to provide more flexibility for chagig the shape. This ca be achieved by the use of Bezier curves amed after. Bezier, the desiger of the Frech car compay Reault, who iveted the procedure i the 196 s. Bezier curve uses the vertices as cotrol poits. The curve will pass through the first ad last poit with all other poits actig as cotrol poits. Figure 1 show the cotrol polygo ad the geerated smooth curve [9]. The flexibility of the process ca be see by chagig the positio of the idividual cotrol poits i space, thereby alterig the cotrol polygo. The flexibility of the curve becomes more with more cotrol poits. The process ca be exteded for the surfaces as well. Bezier select Berstei polyomials as the basis fuctios for the curves. They are specified as i Bi, ( u) = C(, i) u (1 u) Where i! Ci (, ) = i! i! ( ) Based o these basis fuctios, the equatio for the Bezier curve is give by ( u) bb ( u) = u (,1) i= For =3, we get i ( 1 u) 3 i, B,3 = B1,3 = 3(1 u u) B,3 = 3 u (1 u) 3 B3,3 = u ( u) = (1 u) b + 3 u(1 u) b + 3 u (1 u) b + u b The Bezier surface is the direct extesio of the Bezier curve. oits o a Bezier surface ca be specified as a extesio of the Bezier curve. m ( uv, ) bb ( ub ) ( v) uv, (,1) = i= j= ij i, m j, ICME7

3 Cotrol poits curve Cotrol polygoe features are those features that ca be created by machiig operatios o lathe or a turig machie. rismatic features ca be created by machiig operatios o a millig machie or a three-axis machiig ceter. With the special characteristics of the shapes ad operatios, rotatioal features are defied based o the D profile patter, ad the prismatic features are defied i terms of the 3D boudary faces Fig 1: Bezier curve ad the associated cotrol polygo Where b ij represet the rectagular array of cotrol poits (m+1) (+1) defiig the vertices of the characteristic polyhedro of the Bezier patch for a 4 4 poits. The matrix form of this equatio for a 4 4-cotrol poits is 3 (1 v) 3 3 3(1 v v) uv (, ) = (1 u) 3 u(1 u) 3 u(1 uu ) b 3 v (1 v) 3 v The matrix b cotais the poits that defie the characteristic polyhedro b b b b b b b b b = b1 b b3 b4 b b b b SYNTACTIC ATTERN-RECOGNITION AROACH The basic of the sytactic patter recogitio approach is the decompositio of patter ito sub patters or primitives such a decompositio of a chromosome structures i terms of primitives ad to detect ad ecode these primitives i the form of strig. Feature recogitio is a desig iterface for process plaig which is a automatic trasfer of part descriptio data from CAD system to process plaig system. Oral et al. [] have developed a sytactic patter recogitio techique for the extractio of maufacturig details from geometric models. I this system, a part is represeted as a sytactic patter made up of geometric primitives i D ad sixtee patter primitives were defied.. Turig surfaces ca be defied a elemets such as diameter, taper, face, arc, chamfer, ad groovig with the aim of patter primitives. 6. FEATURE DEFINITION A machiig feature ca be cosidered as a portio of part haveig a maufacturig attribute ad ca be created with certai machiig operatios. Rotatioal 7. FEATURE RECOGNITION ROCEDURE The part feature recogitio system that is developed has got similarities with sytactic patter recogitio approach. I sytactic patter recogitio approach 16 patter primitives are used to formalize the patter recogitio process. For example, a diameter ca be represeted by either the patter primitives A or C; a face ca be represeted by B or D. 7.1 atter rimitives The basic of this method is the decompositio of patters ito sub patters or primitives, that is the decompositio of complex patters ad sub patters is carried out util the simplest sub patters, kow as patter primitives, are obtaied. atter primitives will have simple descriptio ad ca easily be recogized. To desig part feature recogitio system, twety patter primitives have bee defied as show i figure. Each patter primitive is represeted by a specific coordiate ad this coordiate oly for idetifies the particular directio of primitive. These coordiates are show i table 1. It has differet shapes of lie ad arc segmets with a start poit, a termial poit, a ceter poit, ad a directio. A code i terms of coordiate is assiged to patter primitives to idetify them. With the help of patter primitives, turig surfaces such as diameter, taper, face, ad arc ca be defied specifically. 7. re- defied Features Each predefied feature cosists of three surfaces ad has a uique patter strig where patter strig is defied as a group of characters. Accordig to the directio some predefied features are show i table. The part feature recogitio system depeds o the umber of predefied features icluded ad the system is sophisticated whe it is used for a large umber of predefied features. I this method of feature recogitio a part is represeted by coordiates to formalize the patter recogitio process. I this all coordiates are varies from to 1 oly [u, v, (, 1)]. Bezier surface equatio is a parametric equatio of characteristic polyhedro ad the parameters are u ad v. oit o a Bezier surface are give by a simple expressio of geeral equatio for poits o a Bezier curve[9]. m ( uv, ) bb ( ub ) ( v) = i= j= ij i, m j, uv, (,1) (3) For features recogitio a biquadratic Bezier patch has bee used. The equatio of a biquadratic Bezier patch is ( uv, ) bb ( ub ) ( v) = i= o j= ij i, j, ICME7 3

4 uv, (,1) (4) Where b ij are Bezier cotrol poits, B i, (u) ad B j, (v) are Berstei basis fuctios i the u ad v parametric directio. i m i Bim, ( u) = C( m, i) u (1 u) m! Cmi (, ) = i! ( m i)! B, = (1 u) B1, = u(1 u) B, = u The equatio (4) ca be expaded to give (u, v) = B i, (u) [b i B, (v) + b i 1 B 1, (v) + b i B, (v)] i= = B, (u) [b B, (v) + b 1 B 1, (v) + b B, (v)] + B 1, (u) [b 1 B, (v) + b 1 1 B 1, (v) + b 1 B, (v)] + B, (u) [b B, (v) + b 1 B 1, (v) + b B, (v)] (6) 7.3 re-requisites of the model The followig assumptios are made for developmet of model: 1. Each patter primitive has give a uique code ad its coordiate accordig to give table.. Each pre-defied feature has a uique strig ad is a set of three coordiates. 3. The legth of patter primitive is ot cosidered. 4. The part feature recogitio system is applicable oly for two-dimesioal profile of ay rotatioal object. 5. Always read the strigs from left had sides. 6. At ay coditio remaiig patter strig will be p p 6 p [(.5,.5)(1, )(.6, -.6)(, )], which show shape of the raw material. p o p (, + ) ( ++, ) (, ) ( +, ) p 3 (u, v) = [ b B, (u) B, (v) + b 1 B, (u) B 1, (v) + b B, (u) B, (v) + b 1 B 1, (u) B, (v) + b 1 1 B 1, (u) B 1, (v) + b 1 B 1, (u) B, (v + b B, (u) B, (v) + b 1 B, (u) B 1, (v) + b B, (u) B, (v)] (7) p 7 p 5 The equatio ca be writte i a matrix form as b b1 b b1 uv (, ) = B,( ub ),( v) B, ( ub ) 1, ( v) B,( ub ),( v) b11 b1 b b1 b Now settig all the above values i matrix form accordig to equatio AB=, where A is computed from the Berstei basis fuctio cotributio of each poit, B is sigle colum matrix of Bezier cotrol poits b i j (figure 3) ad is the sigle colum matrix of poits to be fitted (p ) for the part [7]. B, ( u) B,( v ) B,( u ) B, ( v ) b b 1 1 b b1 3 b 11 = 4 b1 5 b 6 b1 7 B,( u) B, ( v) B,( u) B,( v) b p 8 p p Fig : atter rimitives 3 5 ICME7 4

5 Table 1: Sr. No. atter rimitive Coordiate 1 p o (, ) (,.5) 3 p (.5,.5) 4 p 3 (1,.5) 5 (1, ) 6 p 5 (1, -.3) 7 p 6 (.6 -.6) 8 p 7 (, -.3) 9 p 8 (1,.4) 1 p 9 (.4, 1) 11 (1,.7) 1 1 (.7, 1) 13 (1,.8) 14 3 (.8, 1) 15 4 (1,.6) 16 5 (.6, 1) 17 6 (.3,.5) 18 7 (.5,.3) 19 8 (.,.4) 9 (.4,.) 7.4 Model Developmet The model is follows a fixed procedural step. It has bee developed i C eviromet. The specific steps of procedure for recogizig features from the two-dimesioal profile of ay rotatioal object are described i the successive paragraphs of this paper. The algorithm is divided i six phases. The first phase cosiders the umber of turig features ad turig surfaces preset i -D profile of a rotatioal object. I the secod phase, a part is represeted by -D profile iformatio is expressed as a patter strig with the help of primitives ad its coordiates. I the third phase, a iput file is opeed for patter strig ad takig the prit out of the iput file makes subsequetly a maual checkig. The file ca be subsequetly modified i case if there is ay error I the fourth phase, the iput file created i phase three is utilized to calculatig Berstei basis fuctio for each surface ad used i biquadratic Bezier patch equatio, ad gettig the results i the form of sigle colum matrix of coordiates. I the fifth phase, the results are utilized to match the coordiates with the coordiate set of pre-defied feature. I the sixth phase, a output file is opeed to tore the umber of turig surface preset ad feature strigs that are matched with pre-defied features. The remaiig patter strig shows the shape of raw material. 7.5 Algorithm Ste: a. Create the profile view of the part. b. Assig a uique idetificatio umber correspodig to each turig surfaces. Specific rules are outlied for the idetificatio of turig surfaces: (i) The first surface is left ed of the part. (ii) Labelig will begi at surface 1 ad proceed i a clockwise maer. Step : Represet the part as a patter strig by usig patter primitives ad its correspodig coordiates. All coordiates are varies from to 1 [ uv, (,1)]. Step 3: Calculatig Berstei basis fuctio for each surface ad settig these i matrix form equatio of sigle colum matrix of a biquadratic Bezier patch. Ste: Examie the result of sigle colum matrix of coordiates if: a. A match is foud, extract the feature ad fill the void. Go to step 6. b. No match is foud. Go to step 5. Step 5: Create a ew feature, if possible ad store i the table of pre-defied feature. Step 6: Retrieve the features i chroological order. Stop. Fig 3: arametric space (Source: Ref. 9 Fi 3 t i 8. ILLUSTRATIVE EXAMLE A rotatioal part is cosidered ad figure 4 shows a biquadratic Bezier patch fitted to surface of the rotatioal part. Fig 4: A biquadratic Bezier atch fitted to surface of the rotatioal part rotatioal part ICME7 5

6 p Ste The part cosidered i the figure 5, creatig a two dimesioal profile of rotatioal part havig two grooves oe rectagular ad other is v-groove. art is desiged by revolvig the two-dimesioal profile about x-axis. I this figure total umber of turig surfaces are 13 p 6 p p 5 p 5 p 3 umber of extracted features are three (figure 6). Remaiig patter strigs give the shape of the blak. For example p p 6 p [(.5,.5) (1, ) (.6, -.6) (, )]. (.6, -.6) (.5,.5) (1, ) (1, ) (1, -.3) (1, ) p 6 p o Fig 5.: Two-dimesioal profile view of the part represet by patter primitives Step figure 5 represets the part as a patter strigs ad its coordiates by usig patter primitives accordig to table 1. All coordiates are varies from to 1 [u, v,(,1)]. atter Strig: p (.5,.5) (1, ) p 6 (.6, -.6) (1, ) p (.5,.5) (1, ) p 5 (1, -.3) (1, ) p 5 (1, -.3) p 3 (1,.5) (1, ) p 6 (.6, -.6) p (, ) Step 3 Now calculatig Berstei basis fuctio for each surface accordig to equatio (5) ad settig the results i matrix form accordig to equatio (9). We get the followig result i the form of sigle colum matrix of coordiates. For p (.5,.5) B,( u) B,( v) =.65 B,( u) B1, ( v) =.15 B,( u) B,( v) =.65 B1, ( u) B, ( v) =.15 B1, ( u) B1, ( v) =.5 B1, ( u) B, ( v) =.15 B,( u) B,( v) =.65 B,( u) B1, ( v) =.15 B ( u) B ( v) =.65,, Ste Read three coordiates at a time start from upper side ad match with predefied features from table. For example read coordiates (.5,.5)(1, )(.6, -.6) [p p 6 ] ad matched with pre-defied features. We ca see that this strig is ot matched with pre-defied features; skip the first coordiate ad read ext three coordiate set. Repeat the procedure, till the lowermost coordiate is evaluated ad update the patter strig. We get the followig results i the form of features. I this part total (1, ) (1, -.3) (1,.5) Fig 6:. Extracted features 9. RESULT AND DISCUSSION This method of feature recogitio by biquadratic Bezier patch performs better tha others ad has some similarities from sytactic patter recogitio approach. From above example we ca see that every part is requirig coordiates which are easily selected from the table: 1. Feature recogitio by this method is easy ad simple from earlier methods of feature recogitio. The methodology developed i this thesis has bee used for two-dimesioal profile view of differet rotatioal parts coverig various types of features. Subsequetly, a few examples are used to illustrate the validatio of the methodology. We ca see that the methodology developed here ca give approximately same result as compared to sytactic patter recogitio approach. 1. CONCLUSION The importat advatages of recogizig features usig coordiates iformatio of the rotatioal parts are its ability to easily recogize turig features. Further research is required to be coducted for compoud features. The feature iformatio ca be used to determie tool approach directios for machiig ad developmet of machiig sequeces. It has bee observed that ew features ca be idetified ad added to pre defied feature table. The outcome of the aalysis will result i creatig the blak, represeted by a set of primitives. The remaiig patter strig represets the shape of the raw material. The procedure developed by the author are based o certai assumptios such as every turig face is represeted by a specific coordiate. ICME7 6

7 = 6 6 = Table : Sr. No. redefied Features Strig Coordiates 1 p p (1, )(.5,.5)(, ) p 6 p (.6, -.6)(1, )(.5,.5) 3 p 5 p 3 (1, )(1, -.3)(1,.5) 4 p p p 6 (.5,.5)(, )(.6, -.6) 5 p 5 (1, )(1, -.3)(1, ) ICME7 7

8 11. REFERENCES 1. Liu, S., Feature extractio ad classificatio for rotatioal parts takig 3D data files as iput. Joural of the Chiese Istitute of Idustrial Egieers (5) Oral, A., ad Cemal Cakir, M., Automated cuttig tool selectio ad cuttig tool sequece optimizatio for rotatioal parts. Robotics ad Computer-Itegrated Maufacturig Ismail, N., Abu Baker, N., ad. Juri, A. H., Recogitio of cylidrical ad coical features usig edge boudary classificatio. Iteratioal Joural of Machie Tools & Maufacture Ha, J., ratt, M., ad Regli, W. C., Maufacturig Feature recogitio from solid models: A status report. IEEE Trasactios o Robotics ad Automatio (6).. 5. Razda, A., ad Bae, M., A hybrid approach to feature segmetatio of triagle meshes. Computer-Aided Desig Case, K., ad Haru, W. A. W., Feature-based represetatio for maufacturig plaig. Iteratioal Joural of roductio Research (17).. 7. Razda, A., ad Bae, M., Curvature estimatio scheme for triagle meshes usig biquadratic Bezier patches. Computer-Aided Desig Zeid, I., CAD/CAM Theory ad ractice. (New York: McGraw-Hill). pp Morteso, M. E., Geometric Modelig. (Washigto: Joh Wiley & Sos). pp Ciuraa, J., Garcia-Romeu, M. L., Castro, R., ad Alberti, M., A system based o machied volumes to reduce the umber of route sheets i process plaig. Computers i Idustry Shumugam, M. S., Mahesh,., ad Bhaskara Reddy, S. V., A method of prelimiary plaig for rotatioal compoets with C-axis features usig geetic algorithm. Computers i Idustry Kim, I., ad Cho, K., A itegratio of feature recogitio ad process plaig fuctios for turig operatio. Computers ad Idustrial Egieerig (1-4) Joshi, S., ad Chag, T. C., Graph-based heuristics for recogitio of machied features from a 3D solid model. Computer-Aided Desig ICME7 8