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The International Journal of Computer Science and Information Security (IJCSIS Vol. 9 No. 2) is a reputable venue for publishing novel ideas, state-of-the-art research results and fundamental advances in all aspects of computer science and information & communication security. IJCSIS is a peer reviewed international journal with a key objective to provide the academic and industrial community a medium for presenting original research and applications related to Computer Science and Information Security. . The core vision of IJCSIS is to disseminate new knowledge and technology for the benefit of everyone ranging from the academic and professional research communities to industry practitioners in a range of topics in computer science & engineering in general and information & communication security, mobile & wireless networking, and wireless communication systems. It also provides a venue for high-calibre researchers, PhD students and professionals to submit on-going research and developments in these areas. . IJCSIS invites authors to submit their original and unpublished work that communicates current research on information assurance and security regarding both the theoretical and methodological aspects, as well as various applications in solving real world information security problems.
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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: ansshastry@yahoo.co.in E-Mail: dr.s.purushothaman@gmail.com
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[1]. 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)[6]. 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[3].
capable of using 3D computer aided design
(CAD)[5] 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[2]. 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[4]. 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
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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 [4] Pham, D.T., and Pham, P.T. N. Computational
[1] 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. [5] Fadel, G.M. and Kirschman, C. “ Accuracy Issues
[2] 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 [6] Wodziak, J. R., Fadel, G. M. and Kirschman, C.
IJME - INTERTECH Conference F., “A Genetic Algorithm for Optimizing multiple
[3] 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.
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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
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