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(IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 2, February 2011 Rapid Prototyping Model Coordinate Estimation Using Radial Basis Function. 1 Anantmurty S. Shastry and 2S.Purushothaman 1 Anantmurty S. Shastry 2 Research Scholar, Dr.S.Purushothaman, Principal , Department of Mechanical Engineering Sun College of Engineering and Technology, Vinayaka Missions University, Sun Nagar, Erachakulum, Salem, Tamilnadu, India Kanyakumari district-629902,India E-Mail: email@example.com E-Mail: firstname.lastname@example.org ABSTRACT: This paper discusses the methods for making this decision, the designers and RP getting proper geometric coordinates of a sample machine operators should consider a number of object that has to be rapid prototyped. The different processes and specific constraints. This coordinates of the objects is obtained by using may be a difficult and time consuming task. Radial Basis Function (RBF). The training is done with many sample objects. It is expected to have The RP material flows through an minimum distance traveled by the Rapid orifice and comes out in the form of drops. The prototyping machine when the software follows the size of the drop is depending upon the speed of geometric coordinates produced by the RBF. the wire comes out and solidification of material. For example, 1 mm size of drop is placed in 1 Key words: Rapid Prototyping, Artificial mm size cube cavity to get the same size of cube Neural Network, Radial Basis Function. after solidification in fraction of seconds. The sides of the cube should be flat in all respects. To achieve this focus has been made on a method which can inform that how to make the above things with critical path method (CPM). Some 1. INTRODUCTION products have been chosen with their applications, particularly in medical area. By considering all the parameters in developing any Rapid prototyping (RP) refers to a variety of kind of object is being able to produce in shorter specialized equipment, software and materials time without any difficulty. capable of using 3D computer aided design (CAD) data input to directly fabricate 2. MATERIALS AND METHODS geometrically complex objects. RP technologies have emerged as a key element of time with their ability to shorten the product design and 2.1 Materials development process. This highly innovative and cost efficient technology has found A schematic flow of the proposed work is applications in automotive, aerospace and presented in Figure 1. medical equipment manufacturing, replacing the Rapid Model: It is the end product that has to commonly used slower and less accurate manual be rapid prototyped. methods of fabricating prototypes. With advances in established technologies, materials Coordinates: There are various Coordinates and the introduction of new methods, selecting measured from the RP model either through the right RP machine has become much more CMM/Reverse Engineering/existing drawing difficult and is one of the most important details. decisions to be made when employing any RP technology. This is vital in minimizing built time, cost and achieving optimal accuracy. When 199 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 2, February 2011 Sizes: The length, width /thickness, where breadth/height and other profiles are calculated from the coordinates. c is a vector containing the coefficients of the RBF, RBF: Coordinates and sizes of sample RP models are used as data for training the RBF R is a vector containing the neural network to obtain final weights that will centres of the RBF, and be used for testing. φ is the basis function or Obtain format to meet RP M/c: The outputs activation function of the network. of RBF are used as inputs for RP M/c converter Implementation where RP model will be developed. Step 1: Apply Radial Basis Function. Rp Model Co‐ordinates No. of Input = 15 No. of Patterns = 6 No. of Centre = 6 Calculate RBF as Input to RBF Define sizes RBF = exp (-X) Calculate Matrix as G = RBF A = GT * G Obtain format to Calculate meet RP M/c B = A-1 Calculate Fig.1 Schematic flow E = B * GT Step 2: Calculate the Final Weight. 2.2 Methods F=E*D Step 3: Store the Final Weights in a File. The concept of distance measure is 3. EXPERIMENT SET UP used to associate the input and output pattern values. Radial Basis Functions is capable of Six RP models have been considered as producing approximations to an unknown examples for testing the RBF network. Each RP function ‘f’ from a set of input data abscissa. The model has been labeled with Cartesian approximation is produced by passing an input coordinates. The models have been developed point through a set of basis functions, each of using CAD software. The models are defined which contains one of the RBF centres, with definite number of points. The distance multiplying the result of each function by a between points are calculated internally by the coefficient and then summing them linearly. program. During training RBF, only the point For each function ‘t’, the coordinates are input in the input layer. The approximation to this function is essentially number of centers used is 6. The targets used is stored in the coefficients and centres of the RBF. 15. These parameters are in no way unique, since for each function ‘t’ being approximated, many Table 1 presents 6 sample RP models under combinations of parameter values exist. RBFs consideration. Table 2 presents number of points have the following mathematical representation: considered in this analysis for each RP model. N −1 Table 3a-c presents actual coordinates in mm for F(x) = c o + ∑ c i Φ(|| x − R i ||) each point. The total number of points (1) considered is 15 in each object. i =0 200 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 2, February 2011 Table 1 Sample RP models Table 2 Number of points in the RP model RP Number of points 1 8 2 10 3 12 4 15 5 4 6 5 Table 3a Cartesian coordinate P1 P2 P3 P4 P5 x y z x y z x y z x y z x y z 1 0 0 0 50 0 0 50 50 0 0 50 50 0 0 50 2 9.08 0 0 38.47 0 0 47.55 27.95 0 23.77 45.22 0 0 27.95 0 3 12.5 0 0 37.5 0 0 50 21.65 0 37.5 43.30 0 12.5 43.30 0 4 13.52 0 0 32.66 0 0 46.19 13.52 0 46.19 32.66 0 32.66 46.19 0 5 0 0 0 25 0 0 12.5 21.65 0 12.5 7.22 50 x x x 6 0 0 0 25 0 0 25 25 0 0 25 0 12.5 7.22 50 4 RESULTS AND DISCUSSION the actual implementation, the RP model The coordinates of the RP models are learnt coordinates are given as inputs to the RBF to by RBF. Table 4 presents the outputs of RBF for obtain the actual coordinates that helps in RP all the 6 RP models for the points p1, p2. Similar modeling. close outputs are obtained for points p3, p4, p5, p6, p7, p8, p9, p10, p11, p12, p13, p14, p15 Conclusion: This work has made an attempt to train RBF with RP model coordinates. During 201 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 2, February 2011 Table 3b Cartesian coordinate P6 P7 P8 P9 P10 x y z x y z x y z x y z x y z 1 50 0 50 50 50 50 0 50 50 x x x x x x 2 9.08 0 50 38.47 0 50 47.55 27.95 50 23.77 45.22 50 0 27.95 50 3 0 21.65 0 12.5 0 50 37.5 0 50 50 21.65 50 37.5 43.30 50 4 13.52 46.19 0 0 32.66 0 0 13.52 0 13.52 0 50 32.66 0 50 5 x x x x x x x x x x x x x x x 6 x x x x x x x x x x x x x x x Table 3c Cartesian coordinate P11 P12 P13 P14 P15 x y z x y z x y z x y z x y z 1 x x x x x x x x x x x x x x x 2 x x x x x x x x x x x x x x x 3 12.5 43.30 50 0 21.65 50 x x x x x x x x x 4 46.19 13.52 50 46.19 32.66 50 32.66 46.19 50 13.52 46.19 50 0 32.66 50 5 x x x x x x x x x x x x x x x 6 x x x x x x x x x x x x x x x X represents no coordinates REFERENCES  Pham, D.T., and Pham, P.T. N. Computational  Rao, P.N., Lerner, Y. and Kouznetsov, V. Rapid Intelligence for Manufacturing. Computational Prototyping Applications in Metal Intelligence in Manufacturing Handbook, CRC Casting.Institution of Engineers Journal, Press, New York, 2000. Malaysia. Vol. 64, No.3, 2003, pp.1-7.  Fadel, G.M. and Kirschman, C. “ Accuracy Issues  Pham, D.T. and Dimov, S.S. Rapid in CAD to RP Translations”, Invited paper to the Manufacturing: The Technologies & Applications first Internet conference on Rapid Prototyping, of Rapid Prototyping & Rapid Tooling. Springer- Forwarded to Rapid Prototyping Journal, 1995 Verlag, London, 2001.Proceedings of The 2006  Wodziak, J. R., Fadel, G. M. and Kirschman, C. IJME - INTERTECH Conference F., “A Genetic Algorithm for Optimizing multiple  Fadel, G.M., and Ganti, R. ”Parametric Based part placement to reduce build time”, Paper Controller For Rapid Prototyping Applications” presented at the Fifth International Rapid Presented at the 1998 Solid Freeform Fabrication Prototyping Conference, Dayton OH, 1994, Conference, Austin, TX, 1998 published in the conference proceedings. 202 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 2, February 2011 Table 4 RBF outputs X -coordinate of P1 Y -coordinate of P1 14 1 Target Target RBF output 0.8 RBF output 12 Estimated and target coordinate outputs Estimated and target coordinate outputs 0.6 10 0.4 0.2 8 0 6 -0.2 4 -0.4 -0.6 2 -0.8 0 -1 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 RP model RP model Z -coordinate of P1 X -coordinate of P2 1 55 Target Target 0.8 RBF output RBF output 50 Estimated and target coordinate outputs Estimated and target coordinate outputs 0.6 0.4 45 0.2 40 0 35 -0.2 -0.4 30 -0.6 25 -0.8 -1 20 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 RP model RP model Y -coordinate of P2 Z -coordinate of P2 1 1 Target Target 0.8 RBF output 0.8 RBF output Estimated and target coordinate outputs Estimated and target coordinate outputs 0.6 0.6 0.4 0.4 0.2 0.2 0 0 -0.2 -0.2 -0.4 -0.4 -0.6 -0.6 -0.8 -0.8 -1 -1 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 RP model RP model 203 http://sites.google.com/site/ijcsis/ ISSN 1947-5500
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