INVERSE
MODELING OF THE STEWART FOOT
Adriana
Comanescu
IFToMM, Romania
E-mail: adrianacomanescu@yahoo.com
Alexandra Rotaru
IFToMM, Romania
E-mail: alexandra.rotaru11@gmail.com
Liviu Marian
Ungureanu
IFToMM, Romania
E-mail: ungureanu.liviu.marian@gmail.com
Florian Ion
Tiberiu Petrescu
IFToMM, Romania
E-mail: fitpetrescu@gmail.com
Submission: 1/20/2021
Accept: 7/17/2021
ABSTRACT
The Stewart's leg is used today in the majority of parallel robotic systems, such as the Stewart platform, but also in many other types of mechanisms and kinematic chains, in order to operate them or to transmit motion. A special character in the study of robots is the study of inverse kinematics, with the help of which the map of the motor kinematic parameters necessary to obtain the trajectories imposed on the effector can be made. For this reason, in the proposed mechanism, we will present reverse kinematic modeling in this paper. The kinematic output parameters, ie the parameters of the foot and practically of the end effector, ie those of the point marked with T, will be determined for initiating the working algorithm with the help of logical functions, "If log(ical)", with the observation that here they play the role of input parameters; it is positioned as already specified in the inverse kinematics when the output is considered as input and the input as output. The logical functions used, as well as the entire calculation program used, were written in Math Cad.
Keywords: IFLOG; Math Cad;
Stewart platform; Stewart's leg; Robot; Kinematics; Inverse kinematics
1.
INTRODUCTION
The
parallel structure system that formed the basis of one of the most studied and
well-known parallel robots is the Gough platform from 1947. Described as a
mechanism with a mobile platform connected to a fixed base by six arms of
variable length, the Gough platform was used for testing tire wear in the most
varied operating conditions. Since 1965, this parallel configuration (in a
slightly modified form) has been proposed as a solution for the development of
flight simulators by Stewart.
Parallel
structures can be classified into completely parallel structures, whose final
effector is connected to the mobile platform by closed kinematic chains; and
hybrid or mixed structures consisting of a combination of serial and parallel
structures.
The
number of degrees of freedom (GDL) in a robot is the number of independent
movements that a robot-type mechanism can perform. The total number of degrees
of freedom of a body in space cannot exceed 6 (six). The degree of mobility of
a robot can be understood as the number of motors that drive it.
The
final effector (a gripping mechanism) is the device mounted on the end of a
manipulator that performs operations to hold the tool or the manipulated
object. The workspace is the volume of points in the space where the final
effector of a robot can be located.
By
the position of any object or point of the robot in question is meant the value
of the linear coordinates in the three-dimensional space of the object (or the
respective characteristic point).
Orientation
refers to the angular coordinates of an element (of the robot in question)
according to the axes of the fixed coordinate system.
Precision
(Accuracy) is the ability of the robot to position itself in a certain position
with a certain previously allowed limit error.
Repeatability
is the robot's ability to repeat its positioning when repetitive movements are
required.
Stability
refers to the robot's ability to operate with as few oscillations as possible.
A
good dynamics of a robot is obtained when it is statically and dynamically
balanced when it is positioned correctly and precisely, without oscillations,
without vibrations and high noises, with relatively high speeds, in imposed
repeatability conditions, and at the necessary work rhythm.
The
definition of a parallel robot is very broad: it can also include mechanisms
with more actuation systems than the number of degrees of mobility, including
the situation in which several robots work in cooperation.
Parallel
mechanisms have several main features: at least two kinematic chains support
the final effector, and each of them contains at least one actuating element;
the number of actuating elements is the same as the number of degrees of the
mobility of the final effector; the robot's mobility becomes zero when the
actuators are locked.
The
main advantages of parallel robots: they have very high stability even in
critical positions occupied even during high-speed movement, so that the
objects handled by them are always safe; positioning accuracy is extremely
high; at least two of the kinematic chains allow the distribution of the load
on them; the number of actuators is minimal; the number of sensors required for
closed-loop control of the machine is minimal; if the actuators are locked, the
parallel robot remains in the position reached the moment when it was locked,
i.e. it will become unbalanced, or fall, or drop the manipulated object, as can
happen with serial robots. For the most part, the balancing of these parallel
systems is done automatically, from the construction, giving them in this way
great stability and precision.
In
parallel robots, the motors are located on or near the frame, which makes the
moving masses much smaller than in the case of robots based on serial
structures. This makes it possible to reduce the masses to the constructive
execution of the components without the rigidity of the whole system being
harmed. This increases the dynamic capacity of the system and decreases the
weight of the system.
Because
the work platform is supported by several kinematic chains, the reaction forces
on the component chains are small, so that it is possible to obtain a
satisfactory ratio between the mass of the manipulated object and the mass of
the robot. Increasing the rigidity of the system can also be used for micro
robots for high positioning accuracy and very small dimensions. Due to the
stiffness and the small moving masses, the components of the parallel robots
can be executed more easily. This reduces the power requirement in the drive
system.
In
the case of parallel robots, drive systems with motors based on solid bodies (eg piezo-alloy motors with memory) can also be built. These
motors cannot be used in the case of serial structures due to their low driving
power. Passive torques of parallel structures contribute to the miniaturization
of the system.
Due
to the high rigidity of the parallel structures, the positioning accuracy, and
repeatability increase. In parallel robots, the errors in the components and in
the couplings do not accumulate as in the case of serial robots. Parallel
structures have rather compensatory characteristics that are advantageous in
micro-assembly and simplify the adjustment, command, and control system.
Due
to the fact that the motors are positioned on the frame, they can be separated
from the working space of the parallel structure. In this way, the power
supply, power, and communication cables can be easily insulated. This improves
the ability of robotic systems to work in a clean or aseptic environment (Antonescu
& Petrescu, 1985; 1989; Antonescu
et al., 1985a; 1985b; 1986; 1987; 1988; 1994; 1997; 2000a; 2000b; 2001; Atefi et al., 2008; Avaei et al.,
2008; Aversa et al., 2017a; 2017b; 2017c; 2017d; 2017e; 2016a; 2016b;
2016c; 2016d; 2016e; 2016f; 2016g; 2016h; 2016i; 2016j; 2016k; 2016l; 2016m;
2016n; 2016o; Azaga & Othman, 2008; Cao et al.,
2013; Dong et al., 2013; El-Tous, 2008; Comanescu,
2010; Franklin, 1930; He et al., 2013; Jolgaf
et al., 2008; Kannappan et al., 2008; Lee, 2013; Lin et
al., 2013; Liu et al., 2013; Meena & Rittidech,
2008; Meena et al., 2008; Mirsayar et al.,
2017; Ng et al., 2008; Padula, Perdereau
& Pannirselvam, 2008; 2013; Perumaal
& Jawahar, 2013; Petrescu,
2011; 2015a; 2015b; Petrescu & Petrescu, 1995a; 1995b; 1997a; 1997b; 1997c; 2000a; 2000b;
2002a; 2002b; 2003; 2005a; 2005b; 2005c; 2005d; 2005e; 2011a; 2011b; 2012a;
2012b; 2013a; 2013b; 2016a; 2016b; 2016c; Petrescu et
al., 2009; 2016; 2017a; 2017b; 2017c; 2017d; 2017e; 2017f; 2017g; 2017h;
2017i; 2017j; 2017k; 2017l; 2017m; 2017n; 2017o; 2017p; 2017q; 2017r; 2017s;
2017t; 2017u; 2017v; 2017w; 2017x; 2017y; 2017z; 2017aa; 2017ab; 2017ac;
2017ad; 2017ae; 2018a; 2018b; 2018c; 2018d; 2018e; 2018f; 2018g; 2018h; 2018i;
2018j; 2018k; 2018l; 2018m; 2018n; Pourmahmoud, 2008;
Rajasekaran et al., 2008; Shojaeefard
et al., 2008; Taher et al., 2008; Tavallaei & Tousi, 2008; Theansuwan & Triratanasirichai,
2008; Zahedi et al., 2008; Zulkifli
et al., 2008).
The Stewart's
leg is used today in the majority of parallel robotic systems, such as the
Stewart platform, but also in many other types of mechanisms and kinematic
chains, in order to operate them or to transmit motion. A special character in
the study of robots is the study of inverse kinematics, with the help of which
the map of the motor kinematic parameters necessary to obtain the trajectories
imposed on the effector can be made. For this reason, in the proposed
mechanism, we will present reverse kinematic modeling in this paper.
The
kinematic output parameters, ie the parameters of the
foot and practically of the end effector, ie those of
the point marked with T, will be determined for initiating the working
algorithm with the help of logical functions, "If log(ical)",
with the observation that here they play the role of input parameters; it is
positioned as already specified in the inverse kinematics when the output is
considered as input and the input as output. The logical functions used, as
well as the entire calculation program used, were written in Math Cad 2000.
2.
METHODS AND MATERIALS
The paper briefly studies the
inverse kinematics of a foot mechanism (Figure 1), formed with the help of
Stewart's foot.
Figure 1: Kinematic scheme of the step mechanism
2.1.
Trajectory of the extreme point t
In order to determine the trajectory
necessary for the extreme point T, the end effector, which represents the point
of contact between the foot and the ground, the logical functions (1-2)
"If Log" are used, as follows, where k is the general variable
considered:
XTk: = if
(k <= 50, X0-c.k, X0- c.50) (1)
YTk: = if
[k <= 50, Y0, Y0 + c. (K- 50)] (2)
3.
RESULTS AND DISCUSSION
3.1.
First, within the program used, in Mathcad 2000, the initial constants
are established (3):
XD := 0 YD:= -0.4
TK := 0.7 DF:= 0.7 TE:= 0.8 DE:= 0.8 DC:= 0.3 (3)
Next is established the "TRACK OF THE EXTREME T POINT"
(relation 4, Figure 2), where c represents the step:
X0:= -0.3 Y0:= -0.5
k:= 0..100
c:= 0.005
XTk: = if (k <= 50, X0-c.k, X0- c.50)
YTk: = if [k <= 50, Y0, Y0 + c. (K- 50)]
(4)
Figure 2: The coordinates of
the point T, y as a function of x
3.2.
Following are the kinematic calculations on the modular group "Dyad
RRR (6,3)".
Write
the initial values (5):
F60: = 45
F30: = 120
(5)
Convert
to computer radians (6):
F6: =
F60.p / 180
F3: =
F30.p / 180
(6)
"Given,
Solve and Find" are used to solve (8) the following nonlinear system (7), Figure
3.
Given
XTk-XD+TE.cos(F6)-DE.cos(F3)=0 (7)
YTk-YD+TE.sin(F6)-DE.sin(F3)=0
solk:=Find(F6,F3)
(8)
Figure 3: The angle Fi60 and
Fi30 values as a function of k
Note:
The general input variable k is generally written as a lower index in
MathCad2000, while in MathCad 15 it is written as a
variable (k) in a function between two small parentheses.
The
assignment equal used so far consists of two signs ":" and
"=", and can be entered from the corresponding toolbar, while the
equal used in an equation is the Boolean “=”.
The
parameters of the K-coupling, of the C-coupling, and of the F-coupling can now
be determined directly by assignment ":=" (9-11):
(9)
(10)
(11)
3.3.
Following are the kinematic calculations on the modular group "Dyad
RTR (1,2)".
Write
the initial values (12), and the algorithm (13), with diagrams (Figure 4):
F10: = 210
F1: = F10.p / 180
AC:= 0.1
(12)
Given
0-XCk+AC.cos(F1)=0
0-YCk+AC.sin(F1)=0
solk:=Find(AC,F1)
(13)
Figure 4: The angle Fi10 and
AC values as a function of k
Repeat
the procedure for determining the dyad (4,5).
3.4.
Following are the kinematic calculations on the modular group "Dyad
RTR (4,5)".
Write
the initial values (14), and the algorithm (15), with diagrams (Figure 5):
F40: = 210
F4: = F40.p / 180
FK:= 0.1 (14)
Given
XFk - XKk
+ FK.cos(F4)=0
YFk - YKk
+ FK.sin(F4)=0
solk:=Find(FK,F4)
(15)
Figure 5: The angle Fi40 and
FK values as a function of k
4.
CONCLUSIONS
The parallel structure system that
formed the basis of one of the most studied and well-known parallel robots is
the Gough platform from 1947.
The main advantages of parallel
robots: they have very high stability even in critical positions occupied even
during high-speed movement, so that the objects handled by them are always
safe; positioning accuracy is extremely high; at least two of the kinematic
chains allow the distribution of the load on them; the number of actuators is
minimal; the number of sensors required for closed-loop control of the machine
is minimal; if the actuators are locked, the parallel robot remains in the
position reached the moment when it was locked, i.e. it will become unbalanced,
or fall, or drop the manipulated object, as can happen with serial robots.
In the case of parallel robots,
drive systems with motors based on solid bodies (eg
piezo-alloy motors with memory) can also be built. These motors cannot be used
in the case of serial structures due to their low driving power. Passive
torques of parallel structures contribute to the miniaturization of the system.
Due to the high rigidity of the
parallel structures, the positioning accuracy, and repeatability increase. In
parallel robots, the errors in the components and in the couplings do not
accumulate as in the case of serial robots. Parallel structures have rather
compensatory characteristics that are advantageous in micro-assembly and
simplify the adjustment, command, and control system.
Due to the fact that the motors are
positioned on the frame, they can be separated from the working space of the
parallel structure. In this way, the power supply, power, and communication
cables can be easily insulated.
In the paper is synthesized the
inverse kinematics of a robot leg, which uses in its mechanical structure the
Stewart leg mechanism.
Inverse kinematic modeling is
generally the most sought after, as the most important, but in most situations,
it is also the most difficult to determine. In the presented paper, the
MathCad2000 software was used in order to facilitate the calculations, because
the software automatically solves the linear and nonlinear systems through its
internal procedures that must be called within the program.
As an important function, the "IfLog" logic function was used twice in the program to
initiate the calculations, by determining the input variables in the inverse
kinematics.
5.
ACKNOWLEDGEMENT
This
text was acknowledged and appreciated by Dr. Veturia CHIROIU Honorific member of Technical Sciences
Academy of Romania (ASTR)
PhD supervisor in Mechanical Engineering.
6.
FUNDING INFORMATION
a) 1-Research contract: 1-Research contract: Contract number 36-5-4D/1986 from 24IV1985, beneficiary CNST
RO (Romanian National
Center for Science and Technology) Improving dynamic mechanisms.
b) 2-Contract research integration. 19-91-3 from 29.03.1991; Beneficiary:
MIS; TOPIC: Research on designing mechanisms with bars, cams
and gears, with application in industrial robots.
c) 3-Contract research. GR 69/10.05.2007: NURC in 2762; theme 8: Dynamic analysis of mechanisms and manipulators with bars and gears.
d) 4-Labor contract, no. 35/22.01.2013, the
UPB, "Stand for reading
performance parameters of kinematics and dynamic mechanisms, using inductive and
incremental encoders, to a
Mitsubishi Mechatronic System"
"PN-II-IN-CI-2012-1-0389".
e) All these
matters are copyrighted! Copyrights: 394-qodGnhhtej, from
17-02-2010 13:42:18; 463-vpstuCGsiy, from 20-03-2010
12:45:30; 631-sqfsgqvutm, from 24-05-2010 16:15:22;
933-CrDztEfqow, from 07-01-2011 13:37:52.
7.
ETHICS
Authors
should address any ethical issues
that may arise after the publication of this manuscript.
REFERENCES
Antonescu, P., & Petrescu, F. I. T. (1985). An analytical method of synthesis of
cam mechanism and flat stick. Proceedings of the 4th International Symposium on Theory
and Practice of Mechanisms, (TPM’ 89)., Bucharest.
Antonescu, P., & Petrescu, F. I. T. (1989). Contributions
to kinetoplast dynamic analysis of distribution mechanisms. SYROM’89,
Bucharest.
Antonescu, P., Oprean, M., & Petrescu, F. I. T. (1985a). Contributions
to the synthesis
of oscillating cam mechanism and oscillating flat stick. Proceedings of the 4th International Symposium on Theory and Practice
of Mechanisms, (TPM’
85)., Bucharest.
Antonescu, P., Oprean, M., & Petrescu, F. I. T. (1985b). At the
projection of the oscillate cams,
there are mechanisms and distribution variables. Proceedings of the 5th Conference of Engines,
Automobiles, Tractors and Agricultural Machines, (TAM’ 58)., I-Motors and Cars,
Brasov.
Antonescu, P., Oprean, M., & Petrescu, F. I. T. (1986). Projection
of the profile
of the rotating
camshaft acting on the oscillating
plate with disengagement. Proceedings of the 3rd National
Computer-aided Design Symposium in the field of Mechanisms
and Machine Parts, (MMP’ 86)., Brasov.
Antonescu, P., Oprean, M., & Petrescu, F. I. T. (1987). Dynamic analysis
of the cam
distribution mechanisms. Proceedings of the 7th National Symposium on Industrial Robots
and Space Mechanisms,
(RSM’ 87)., Bucharest.
Antonescu, P., Oprean, M., & Petrescu, F. I. T. (1988). Analytical synthesis of Kurz profile, rotating the flat cam. Mach, Build. Rev.
Antonescu, P., Petrescu, F. I. T., & Antonescu,
O. (1994). Contributions to the synthesis of
the rotating cam mechanism and the tip of
the balancing tip. Brasov.
Antonescu, P., Petrescu, F. I. T., & Antonescu,
O. (1997). Geometrical synthesis
of the rotary
cam and balance tappet mechanism. Bucharest(3), 23-23.
Antonescu, P., Petrescu, F. I. T., & Antonescu,
O. (2000ª). Contributions to
the synthesis of the rotary
disc-cam profile. Proceedings of the 8th International Conference on the Theory
of Machines and Mechanisms,
(TMM’ 00)., Liberec, Czech Republic),
51-56.
Antonescu, P., Petrescu, F. I. T., & Antonescu,
O. (2000b). Synthesis of the rotary cam
profile with balance follower. Proceedings of the 8th Symposium
on Mechanisms and Mechanical Transmissions,
(MMT’ 00)., Timişoara), 39-44.
Antonescu, P., Petrescu, F. I. T., & Antonescu,
O. (2001). Contributions to
the synthesis of mechanisms with
rotary disc-cam. Proceedings of the 8th IFToMM International Symposium on Theory
of Machines and Mechanisms,
(TMM’ 01)., Bucharest, ROMANIA), 31-36.
Atefi, G., Abdous, M. A., & Ganjehkaviri,
A. (2008). Analytical Solution
of Temperature Field in Hollow Cylinder under Time Dependent Boundary Condition Using Fourier series, Am.
J. Eng. Applied Sci.,
1(2), 141-148. DOI: 10.3844/ajeassp.2008.141.148
Avaei, A., Ghotbi, A. R., & Aryafar, M.
(2008). Investigation of
Pile-Soil Interaction Subjected to Lateral Loads in Layered Soils, Am. J. Eng. Applied Sci., 1(1), 76-81.
DOI: 10.3844/ajeassp.2008.76.81
Aversa, R., Petrescu, R. V. V., Apicella,
A., & Petrescu,
F. I. T. (2017a). Nano-diamond hybrid
materials for structural biomedical application. Am. J. Biochem. Biotechnol. (13),
34-41. DOI: 10.3844/ajbbsp.2017.34.41
Aversa, R., Petrescu, R. V. V., Akash, B., Bucinell, R. B., & Corchado, J. M. (2017b). Kinematics
and forces to a new model forging manipulator.
Am. J. Applied
Sci. (14), 60-80. DOI: 10.3844/ajassp.2017.60.80
Aversa, R., Petrescu, R. V. V., Apicella,
A., Petrescu,
F. I. T., & Calautit, J. k. (2017c). Something about the V engines
design. Am. J.
Applied Sci. (14),
34-52. DOI: 10.3844/ajassp.2017.34.52
Aversa, R., Parcesepe, D., Petrescu, R. V.
V., Berto, F., & Chen, G. (2017d). Process ability of bulk metallic
glasses. Am.
J. Applied Sci. (14),
294-301. DOI: 10.3844/ajassp.2017.294.301
Aversa, R., Petrescu, R. V.
V., Akash, B., Bucinell, R. B., & Corchado, J. M. (2017e). Something about the balancing of
thermal motors. Am. J. Eng. Applied
Sci. (10), 200-217. DOI: 10.3844/ajeassp.2017.200.217
Aversa, R., Petrescu, F. I. T., Petrescu, R.
V. V., & Apicella, A. (2016a). Biomimetic FEA bone modeling for customized
hybrid biological prostheses development. Am. J. Applied Sci. (13), 1060-1067. DOI: 10.3844/ajassp.2016.1060.1067
Aversa, R., Parcesepe, D., Petrescu, R. V.
V., G. Chen, G., & Petrescu, F. I. T. (2016b). Glassy amorphous metal injection molded induced morphological defects. Am. J. Applied Sci. (13), 1476-1482.
DOI: 10.3844/ajassp.2016.1476.1482
Aversa, R., Petrescu, R. V. V., Petrescu, F.
I. T., & Apicella, A. (2016c). Smart-factory: Optimization and process control of composite centrifuged pipes. Am.
J. Applied Sci. (13),
1330-1341. DOI: 10.3844/ajassp.2016.1330.1341
Aversa, R., Tamburrino, F., Petrescu, R. V. V., Petrescu, F. I. T., & Artur, M. (2016d). Biomechanically inspired shape memory effect machines driven by muscle
like acting NiTi alloys. Am. J. Applied Sci.
(13), 1264-1271. DOI: 10.3844/ajassp.2016.1264.1271
Aversa, R., Buzea, E. M., Petrescu, R. V. V.,
Apicella, A., & Neacsa,
M. (2016e). Present
a mechatronic system having able to
determine the concentration
of carotenoids. Am. J. Eng. Applied
Sci. (9), 1106-1111. DOI:
10.3844/ajeassp.2016.1106.1111
Aversa, R., Petrescu, R. V. V., Sorrentino, R., Petrescu,
F. I. T., & Apicella, A. (2016f). Hybrid ceramo-polymeric nanocomposite for biomimetic scaffolds design and preparation. Am. J. Eng. Applied
Sci. (9), 1096-1105. DOI:
10.3844/ajeassp.2016.1096.1105
Aversa, R., Perrotta, V., Petrescu, R. V. V.,
Misiano, C., & Petrescu,
F. I. T. (2016g). From structural
colors to super-hydrophobicity and achromatic
transparent protective coatings: Ion plating plasma assisted TiO2 and SiO2 nano-film deposition. Am. J.
Eng. Applied Sci. (9),
1037-1045. DOI: 10.3844/ajeassp.2016.1037.1045
Aversa, R., Petrescu, R. V. V., Petrescu, F. I. T., & Apicella,
A. (2016h). Biomimetic and evolutionary
design driven innovation in sustainable products development. Am. J. Eng. Applied
Sci. (9), 1027-1036. DOI: 10.3844/ajeassp.2016.1027.1036
Aversa, R., Petrescu, R. V. V., Apicella, A., & Petrescu, F.
I. T. (2016i). Mitochondria are naturally
micro robots - a review. Am. J. Eng. Applied Sci.,
9: 991-1002. DOI: 10.3844/ajeassp.2016.991.1002
Aversa, R., Petrescu, R. V. V., Apicella, A., & Petrescu, F. I. T. (2016j).
We are addicted to vitamins C and E-A review. Am. J. Eng. Applied Sci. (9), 1003-1018.
DOI: 10.3844/ajeassp.2016.1003.1018
Aversa, R., Petrescu, R. V. V., Apicella, A., & Petrescu, F. I. T. (2016k).
Physiologic human fluids
and swelling behavior of hydrophilic biocompatible hybrid ceramo-polymeric materials. Am. J.
Eng. Applied Sci. (9),
962-972. DOI: 10.3844/ajeassp.2016.962.972
Aversa, R., Petrescu, R. V. V., Apicella, A., & Petrescu, F. I. T. (2016l).
One can slow down the aging
through antioxidants. Am. J. Eng. Applied
Sci. (9), 1112-1126. DOI:
10.3844/ajeassp.2016.1112.1126
Aversa, R., Petrescu, R. V. V., Apicella, A., & Petrescu, F. I. T. (2016m).
About homeopathy or ≪Similia Similibus
Curentur≫. Am. J. Eng. Applied Sci. (9), 1164-1172.
DOI: 10.3844/ajeassp.2016.1164.1172
Aversa, R., Petrescu, R. V. V., Apicella, A., & Petrescu, F. I. T. (2016n). The basic elements of life's. Am. J. Eng. Applied Sci.
(9), 1189-1197. DOI: 10.3844/ajeassp.2016.1189.1197
Aversa, R., Petrescu, F. I. T., Petrescu, R.
V. V., & Apicella, A. (2016o). Flexible stem
trabecular prostheses. Am. J. Eng. Applied Sci.
(9), 1213-1221. DOI: 10.3844/ajeassp.2016.1213.122
Azaga, M., & Othman, M. (2008). Source Couple Logic (SCL).: Theory and Physical Design, Am. J. Eng. Applied Sci., 1(1), 24-32.
DOI: 10.3844/ajeassp.2008.24.32
Cao, W., Ding, H., Bin, Z., & Ziming, C. (2013). New structural
representation and digital-analysis
platform for symmetrical parallel mechanisms. Int. J. Adv. Robotic Sys. DOI:
10.5772/56380
Comanescu,
A. (2010). Bazele Modelarii Mecanismelor. 1st Edn., E. Politeh, Press, Bucureşti, 274.
Dong, H., Giakoumidis, N., Figueroa, N., & Mavridis,
N. (2013). Approaching behaviour
monitor and vibration indication
in developing a General Moving
Object Alarm System (GMOAS).. Int. J. Adv. Robotic Sys. DOI:
10.5772/56586
Yousif El-Tous, (2008). Pitch
Angle Control of Variable Speed
Wind Turbine, Am.
J. Eng. Applied Sci.,
1(2), 118-120. DOI: 10.3844/ajeassp.2008.118.120
Franklin, D. J. (1930). Ingenious
Mechanisms for Designers and Inventors. 1st Edn., Industrial Press Publisher.
He, B., Wang, Z., Li,
Q., Xie, H., Shen, R. (2013). An
analytic method for the kinematics
and dynamics of a multiple-backbone continuum robot. IJARS. DOI: 10.5772/54051
Jolgaf, M., Sulaiman, S. B., M.K.A Ariffin,
M. K. A., & Faieza, A. A. (2008). Closed Die Forging Geometrical Parameters Optimization for Al-MMC, Am. J. Eng. Applied
Sci., 1(1), 1-6. DOI : 10.3844/ajeassp.2008.1.6
Kannappan, A. N., Kesavasamy, R., & Ponnuswamy,
V. (2008). Molecular Interaction Studies
of H-Bonded Complexes of Benzamide in 1,4-Dioxan with Alcohols From
Acoustic and Thermodynamic Parameters, Am. J.
Eng. Applied Sci.,
1(2), 95-99. DOI: 10.3844/ajeassp.2008.95.99
Lee, B. J. (2013). Geometrical
derivation of differential kinematics to calibrate model
parameters of flexible manipulator. Int. J. Adv. Robotic Sys. DOI:
10.5772/55592
Lin, W., Li, B., Yang,
X., & Zhang, D. (2013). Modelling and control of inverse dynamics for a 5-DOF parallel kinematic polishing machine. Int. J. Adv. Robotic
Sys. DOI: 10.5772/54966
Liu, H., Zhou, W., Lai, X., & Zhu, S. (2013). An
efficient inverse kinematic
algorithm for a
PUMA560-structured robot manipulator. IJARS. DOI: 10.5772/56403
Meena, P., & Rittidech, S. (2008). Comparisons
of Heat Transfer
Performance of a Closed-looped
Oscillating Heat Pipe and Closed-looped Oscillating Heat Pipe with Check Valves Heat
Exchangers, Am.
J. Eng. Applied Sci.,
1(1), 7-11. DOI: 10.3844/ajeassp.2008.7.11
Meena, P., Rittidech, S., & Tammasaeng,
P. (2008). Effect of Inner Diameter and Inclination Angles on Operation Limit of Closed-Loop Oscillating Heat-Pipes with Check Valves,
Am. J. Eng. Applied
Sci., 1(2), 100-103. DOI: 10.3844/ajeassp.2008.100.103
Mirsayar, M. M., Joneidi, A., Petrescu, R. V. V., Petrescu, F. I. T., & Berto,
F. (2017). Extended MTSN criterion for fracture analysis of soda lime glass. Eng. Fracture Mechan. (178), 50-59.
DOI: 10.1016/j.engfracmech.2017.04.018
Ng, K. C., Yusoff,M. Z., Munisamy, K., Hasini, H., & Shuaib, N. H. (2008). Time-Marching
Method for Computations of High-Speed Compressible Flow on Structured and Unstructured Grid, Am. J. Eng. Applied
Sci., 1(2), 89-94. DOI: 10.3844/ajeassp.2008.89.94
Padula, F., & Perdereau, V. (2013). An on-line path planner for
industrial manipulators. Int. J. Adv. Robotic Sys.
DOI: 10.5772/55063
Pannirselvam, N., Raghunath, N., & Suguna, K.
(2008). Neural Network for Performance of Glass Fibre
Reinforced Polymer Plated RC Beams, Am. J. Eng. Applied
Sci., 1(1), 82-88. DOI:
10.3844/ajeassp.2008.82.88
Perumaal, S., & Jawahar, N. (2013). Automated trajectory planner of industrial robot for
pick-and-place task. IJARS. DOI: 10.5772/53940
Petrescu, F. I. T., & Petrescu, R. V. V. (1995a). Contributions to optimization of the polynomial motion laws of
the stick from the internal
combustion engine distribution mechanism. Bucharest (1), 249-256.
Petrescu, F. I. T., & Petrescu, R. V. V. (1995b). Contributions to the synthesis of
internal combustion engine distribution mechanisms. Bucharest (1),
257-264.
Petrescu, F. I. T., & Petrescu, R. V. V. (1997a). Dynamics of cam mechanisms (exemplified on the classic
distribution mechanism).
Bucharest (3), 353-358.
Petrescu, F. I. T., & Petrescu, R. V. V. (1997b). Contributions to the synthesis of
the distribution mechanisms of internal
combustion engines with a Cartesian coordinate method. Bucharest (3), 359-364.
Petrescu, F. I. T., & Petrescu, R. V. V. (1997c). Contributions to maximizing polynomial laws for the
active stroke of the distribution mechanism from internal combustion engines. Bucharest (3),
365-370.
Petrescu, F. I. T., & Petrescu, R. V. V. (2000a).
Synthesis of distribution mechanisms by the rectangular (Cartesian). coordinate method. Proceedings of the 8th National
Conference on International
Participation, (CIP' 00)., Craiova, Romania,
297-302.
Petrescu, F. I. T., & Petrescu, R. V. V. (2000b). The design (synthesis). of cams using
the polar coordinate method (triangle method).. Proceedings of the 8th National
Conference on International
Participation, (CIP' 00)., Craiova, Romania,
291-296.
Petrescu, F. I. T., & Petrescu, R. V. V. (2002a). Motion
laws for cams. Proceedings of the International Computer Assisted Design, National Symposium Participation,
(SNP' 02)., Braşov, p 321-326.
Petrescu, F. I. T., & Petrescu, R. V. V. (2002b). Camshaft
dynamics elements. Proceedings of the International Computer Assisted Design, National Participation Symposium, (SNP' 02)., Braşov, 327-332.
Petrescu, F. I. T., & Petrescu, R. V. V. (2003). Some elements regarding the improvement of the engine
design. Proceedings of the National
Symposium, Descriptive Geometry,
Technical Graphics and Design, (GTD' 03)., Braşov, 353-358.
Petrescu, F. I. T., & Petrescu, R. V. V. (2005a). The cam design for
a better efficiency. Proceedings of the International Conference on Engineering Graphics and Design, (EGD’
05)., Bucharest, 245-248.
Petrescu, F. I. T., & Petrescu, R. V. V. (2005b). Contributions
at the dynamics of cams. Proceedings of the 9th IFToMM International Symposium on Theory of
Machines and Mechanisms, (TMM’ 05)., Bucharest, Romania, 123-128.
Petrescu, F. I. T., & Petrescu, R. V. V. (2005c). Determining
the dynamic efficiency of cams.
Proceedings of the 9th IFToMM International Symposium on Theory
of Machines and Mechanisms,
(TMM’ 05)., Bucharest, Romania, 129-134.
Petrescu, F. I. T., & Petrescu, R. V. V. (2005d). An
original internal combustion
engine. Proceedings of the 9th IFToMM
International Symposium on Theory of Machines and Mechanisms, (TMM’ 05)., Bucharest,
Romania, 135-140.
Petrescu, F. I. T., & Petrescu, R. V. V. (2005e). Determining
the mechanical efficiency of Otto engine’s mechanism. Proceedings of the 9th IFToMM International Symposium on Theory
of Machines and Mechanisms,
(TMM 05)., Bucharest, Romania, 141-146.
Petrescu, F. I. T., & Petrescu, R. V. V. (2011a). Mechanical
Systems, Serial and Parallel
(Romanian).. 1st Edn., LULU Publisher, London, UK, 124.
Petrescu, F. I. T., & Petrescu, R. V. V. (2011b). Trenuri
Planetare. Createspace Independent Pub., 104 pages,
ISBN-13: 978-1468030419.
Petrescu, F. I. T., & Petrescu, R. V. V. (2012a). Kinematics
of the planar quadrilateral mechanism. ENGEVISTA (14), 345-348.
Petrescu, F. I. T., & Petrescu, R. V. V. (2012b). Mecatronica-Sisteme
Seriale si Paralele. 1st Edn.,
Create Space Publisher,
USA, 128.
Petrescu, F. I. T., & Petrescu, R. V. V. (2013a). Cinematics
of the 3R dyad. ENGEVISTA (15),
118-124.
Petrescu, F. I. T., & Petrescu, R. V. V. (2013b). Forces
and efficiency of cams. Int. Rev. Mechanical Eng.
Petrescu, F. I. T., & Petrescu, R. V. V. (2016a). Parallel
moving mechanical systems kinematics. ENGEVISTA (18), 455-491.
Petrescu, F. I. T., & Petrescu, R. V. V. (2016b). Direct and inverse kinematics to the
anthropomorphic robots. ENGEVISTA (18), 109-124.
Petrescu, F. I. T., & Petrescu, R. V. V. (2016c). Dynamic cinematic
to a structure 2R. Revista Geintec-Gestao
Inovacao E Tecnol. (6),
3143-3154.
Petrescu, F. I. T., Grecu, B., Comanescu, A., & Petrescu, R. V. V. (2009).
Some mechanical design elements. Proceeding of the International Conference on Computational Mechanics and Virtual Engineering,
(MVE’ 09)., Braşov, 520-525.
Petrescu,
F. I. T. (2011).
Teoria Mecanismelor si a Masinilor: Curs Si Aplicatii. 1st Edn., CreateSpace Independent
Publishing Platform. ISBN-10: 1468015826. P. 432.
Petrescu,
F. I. T.
(2015a). Geometrical synthesis
of the distribution
mechanisms. Am.
J. Eng. Applied Sci. (8),
63-81. DOI: 10.3844/ajeassp.2015.63.81
Petrescu,
F. I. T.
2015b. Machine motion equations
at the internal combustion heat engines. Am. J. Eng.
Applied Sci., (8)
127-137. DOI: 10.3844/ajeassp.2015.127.137
Petrescu, R. V. V., Aversa, R., Apicella, A., & Petrescu, F.
I. T. (2016). Future medicine services robotics. Am. J.
Eng. Applied Sci. (9),
1062-1087. DOI: 10.3844/ajeassp.2016.1062.1087
Petrescu, R. V. V., Aversa, R., Akash, B., Bucinell, R., & Corchado, J. (2017a). Yield at thermal engines internal combustion. Am. J. Eng. Applied
Sci. (10), 243-251. DOI:
10.3844/ajeassp.2017.243.251
Petrescu, R. V. V., Aversa, R., Akash,
B., Ronald, B., & Corchado, j. ( 2017b).
Velocities and accelerations
at the 3R mechatronic systems. Am. J. Eng.
Applied Sci. (10),
252-263. DOI: 10.3844/ajeassp.2017.252.263
Petrescu, R. V. V., Aversa, R., Akash, B., Bucinell, R., & Corchado, J. (2017c). Anthropomorphic solid structures n-r kinematics. Am. J. Eng. Applied
Sci. (10), 279-291. DOI: 10.3844/ajeassp.2017.279.291
Petrescu, R. V. V., Aversa, R., Akash, B., Bucinell, R., & Corchado, J. (2017d). Inverse kinematics at the anthropomorphic robots, by a trigonometric method. Am. J. Eng. Applied
Sci. (10), 394-411. DOI: 10.3844/ajeassp.2017.394.411
Petrescu, R. V. V., Aversa, R., Akash, B., Bucinell, R., & Corchado, J. (2017e). Forces at internal combustion engines. Am. J. Eng. Applied
Sci. (10), 382-393. DOI:
10.3844/ajeassp.2017.382.393
Petrescu, R. V. V., Aversa, R., Akash, B., Bucinell, R., & Corchado, J. (2017f). Gears-Part I. Am. J. Eng. Applied
Sci. (10), 457-472. DOI:
10.3844/ajeassp.2017.457.472
Petrescu, R. V. V., Aversa, R., Akash, B., Bucinell, R., & Corchado, J. (2017g). Gears-part II. Am. J. Eng. Applied
Sci. (10), 473-483. DOI:
10.3844/ajeassp.2017.473.483
Petrescu, R. V. V., Aversa, R., Akash, B., Bucinell, R., & Corchado, J. (2017h).. Cam-gears forces, velocities, powers and efficiency. Am. J. Eng. Applied
Sci. (10), 491-505. DOI:
10.3844/ajeassp.2017.491.505
Petrescu, R. V. V., Aversa, R., Akash, B., Bucinell, R., & Corchado, J. (2017i). Dynamics of mechanisms with cams illustrated in the classical distribution.
Am. J. Eng. Applied
Sci. (10), 551-567. DOI:
10.3844/ajeassp.2017.551.567
Petrescu, R. V. V., Aversa, R., Akash, B., Bucinell, R., & Corchado, J. (2017j). Testing by non-destructive control. Am. J. Eng. Applied Sci.
(10), 568-583. DOI: 10.3844/ajeassp.2017.568.583
Petrescu, R. V. V., Aversa, R., Apicella,
A., & Petrescu, F. I. T. (2017k). Transportation engineering. Am. J.
Eng. Applied Sci. (10),
685-702. DOI: 10.3844/ajeassp.2017.685.702
Petrescu, R. V. V., Aversa, R., Kozaitis, S., Apicella, A., &
Petrescu, F. I. T. (2017l).
The quality of transport and environmental protection, part I. Am. J. Eng. Applied Sci. (10), 738-755.
DOI: 10.3844/ajeassp.2017.738.755
Petrescu, R. V. V., Aversa, R., Akash, B., R. Bucinell, R., &
Corchado, J. (2017m). Modern propulsions for aerospace-a review. J. Aircraft Spacecraft Technol. (1), 1-8.
DOI: 10.3844/jastsp.2017.1.8
Petrescu, R. V. V., Aversa, R., Akash, B., Bucinell, R., &
Corchado, J. (2017n). Modern propulsions for aerospace-part II. J. Aircraft Spacecraft Technol. (1),
9-17. DOI: 10.3844/jastsp.2017.9.17
Petrescu, R. V. V., Aversa, R., Akash, B., Bucinell, R., &
Corchado, J. (2017o). History of
aviation-a short review. J. Aircraft Spacecraft Technol. (1),
30-49. DOI: 10.3844/jastsp.2017.30.49
Petrescu, R. V. V., Aversa, R., Akash, B., Bucinell, R., &
Corchado, J. (2017p). Lockheed martin-a short review. J. Aircraft Spacecraft Technol. (1), 50-68. DOI: 10.3844/jastsp.2017.50.68
Petrescu, R. V. V., Aversa, R., Akash, B., Bucinell, R., &
Corchado, J. (2017q). Our
universe. J. Aircraft
Spacecraft Technol. (1),
69-79. DOI: 10.3844/jastsp.2017.69.79
Petrescu, R. V. V., Aversa, R., Akash, B., Corchado, J., & Berto,
F. (2017r). What is a UFO? J. Aircraft Spacecraft Technol. (1),
80-90. DOI: 10.3844/jastsp.2017.80.90
Petrescu, R. V. V., Aversa, R., Akash, B., Corchado, J., & Berto,
F. (2017s). About bell helicopter FCX-001 concept aircraft-a short review. J. Aircraft Spacecraft Technol. (1),
91-96. DOI: 10.3844/jastsp.2017.91.96
Petrescu, R. V. V., Aversa, R., Akash, B., Corchado, J., & Berto,
F. (2017t). Home at airbus. J. Aircraft Spacecraft
Technol. (1), 97-118. DOI:
10.3844/jastsp.2017.97.118
Petrescu, R. V. V., Aversa, R., Akash, B., Corchado, J., & Berto,
F. (2017u). Airlander.
J. Aircraft Spacecraft Technol. (1),
119-148. DOI: 10.3844/jastsp.2017.119.148
Petrescu, R. V. V., Ersa, R., Akash, B., Corchado, J.,
& Berto, F. (2017v). When
boeing is dreaming-a review. J. Aircraft Spacecraft Technol. (1),
149-161. DOI: 10.3844/jastsp.2017.149.161
Petrescu, R. V. V., Aversa, R., Akash, B., Corchado, J., & Berto,
F. ( 2017w). About
Northrop Grumman. J. Aircraft Spacecraft
Technol. (1), 162-185. DOI:
10.3844/jastsp.2017.162.185
Petrescu, R. V. V., Aversa, R., Akash, B., Corchado, J., & Berto,
F. (2017x). Some
special aircraft. J. Aircraft Spacecraft Technol. (1),
186-203. DOI: 10.3844/jastsp.2017.186.203
Petrescu, R. V. V., Aversa, R., Akash, B., Corchado, J., & Berto,
F. (2017y). About helicopters.
J. Aircraft Spacecraft Technol. (1),
204-223. DOI: 10.3844/jastsp.2017.204.223
Petrescu, R. V. V., Aversa, R., Akash, B., Berto, F., & Apicella, A. (2017z).
The modern flight. J. Aircraft Spacecraft Technol. (1), 224-233. DOI: 10.3844/jastsp.2017.224.233
Petrescu, R. V. V., Aversa, R., Akash, B., Berto, F., & Apicella, A. (2017aa).
Sustainable energy for aerospace vessels.
J. Aircraft Spacecraft Technol. (1),
234-240. DOI: 10.3844/jastsp.2017.234.240
Petrescu, R. V. V., Aversa, R., Akash, B., Berto, F., & Apicella, A. (2017ab).
Unmanned helicopters. J. Aircraft Spacecraft Technol. (1),
241-248. DOI: 10.3844/jastsp.2017.241.248
Petrescu, R. V. V., Aversa, R., Akash, B., Berto, F., & Apicella, A. (2017ac).
Project HARP. J. Aircraft
Spacecraft Technol. (1),
249-257. DOI: 10.3844/jastsp.2017.249.257
Petrescu, R. V. V., Aversa, R., Akash, B., Berto, F., & Apicella, A. (2017ad). Presentation of Romanian engineers
who contributed to the development
of global aeronautics-part
I. J. Aircraft
Spacecraft Technol. (1),
258-271. DOI: 10.3844/jastsp.2017.258.271
Petrescu, R. V. V., Aversa, R., Akash, B., Berto, F., & Apicella, A. (2017ae).
A first-class ticket to the planet mars,
please. J. Aircraft Spacecraft Technol. (1), 272-281. DOI: 10.3844/jastsp.2017.272.281
Petrescu, R. V. V., Aversa, R., Apicella, A., Mirsayar, M. M.,
& Kozaitis, S. (2018a). NASA started
a propeller set on board voyager 1 after 37 years of break. Am. J. Eng. Applied
Sci. (11), 66-77. DOI: 10.3844/ajeassp.2018.66.77
Petrescu, R. V. V., Aversa, R., Apicella, A., Mirsayar, M. M.,
& Kozaitis, S. (2018b).
There is life on mars?
Am. J. Eng. Applied
Sci. (11), 78-91. DOI: 10.3844/ajeassp.2018.78.91
Petrescu, R. V. V., Aversa, R., Apicella, A., & Petrescu, F.
I. T. (2018c). Friendly environmental transport. Am. J.
Eng. Applied Sci. (11),
154-165. DOI: 10.3844/ajeassp.2018.154.165
Petrescu, R. V. V., Aversa, R., Akash, B., Abu-Lebdeh, T. M., T.
M., & Apicella, A. (2018d). Buses running on gas. Am. J. Eng. Applied
Sci. (11), 186-201. DOI:
10.3844/ajeassp.2018.186.201
Petrescu, R. V. V., Aversa, R., Akash, B., Abu-Lebdeh, T. M., T.
M., & Apicella, A. (2018e). Some aspects
of the structure
of planar mechanisms. Am. J. Eng. Applied
Sci. (11), 245-259. DOI:
10.3844/ajeassp.2018.245.259
Petrescu, R. V. V., Aversa, R.,
Abu-Lebdeh, T. M., Apicella,
A., & Petrescu, F. I. T. (2018f). The forces
of a simple carrier manipulator. Am. J.
Eng. Applied Sci. (11),
260-272. DOI: 10.3844/ajeassp.2018.260.272
Petrescu, R. V. V., Aversa, R.,
Abu-Lebdeh, T. M., Apicella,
A., & Petrescu, F. I. T. (2018g). The dynamics
of the otto engine. Am. J. Eng. Applied Sci. (11), 273-287.
DOI: 10.3844/ajeassp.2018.273.287
Petrescu, R. V. V., Aversa, R.,
Abu-Lebdeh, T. M., Apicella,
A., & Petrescu, F. I. T. (2018h). NASA satellites help us to
quickly detect forest fires. Am. J. Eng. Applied
Sci. (11), 288-296. DOI:
10.3844/ajeassp.2018.288.296
Petrescu, R. V. V., Aversa, R.,
Abu-Lebdeh, T. M., Apicella,
A., & Petrescu, F. I. T. (2018i). Kinematics of a mechanism with a triad. Am. J.
Eng. Applied Sci. (11),
297-308. DOI: 10.3844/ajeassp.2018.297.308
Petrescu, R. V. V., Aversa, R., Apicella, A., & Petrescu, F.
I. T. (2018j). Romanian engineering "on the wings
of the wind".
J. Aircraft Spacecraft Technol. (2),
1-18. DOI: 10.3844/jastsp.2018.1.18
Petrescu, R. V. V., Aversa, R., Apicella, A., & Petrescu, F.
I. T. (2018k). NASA Data used to discover
eighth planet circling distant star. J. Aircraft Spacecraft Technol. (2), 19-30. DOI: 10.3844/jastsp.2018.19.30
Petrescu, R. V. V., Aversa, R., Apicella, A., & Petrescu, F.
I. T. (2018l). NASA has found the most
distant black hole. J. Aircraft Spacecraft Technol. (2), 31-39. DOI: 10.3844/jastsp.2018.31.39
Petrescu, R. V. V., Aversa, R., Apicella, A., & Petrescu, F.
I. T. (2018m). Nasa selects concepts for a new mission to titan, the moon
of saturn. J. Aircraft Spacecraft Technol., 2:
40-52. DOI: 10.3844/jastsp.2018.40.52
Petrescu, R. V. V., Aversa, R., Apicella, A., & Petrescu, F.
I. T. (2018n). NASA sees first
in 2018 the direct proof of ozone hole recovery. J. Aircraft Spacecraft Technol. (2),
53-64. DOI: 10.3844/jastsp.2018.53.64
Pourmahmoud, N. (2008). Rarefied Gas Flow Modeling inside Rotating Circular Cylinder, Am. J.
Eng. Applied Sci.,
1(1), 62-65. DOI: 10.3844/ajeassp.2008.62.65
Rajasekaran, A., Raghunath, N., & Suguna, K.
(2008). Effect of Confinement on the Axial Performance of Fibre Reinforced Polymer Wrapped RC Column, Am. J. Eng. Applied Sci., 1(2), 110-117.
DOI: 10.3844/ajeassp.2008.110.117
Shojaeefard, M. H., Goudarzi, K., Noorpoor, A. R.,
& Fazelpour, M. (2008). A Study
of Thermal Contact using Nonlinear
System Identification Models, Am. J. Eng. Applied Sci., 1(1), 16-23.
DOI: 10.3844/ajeassp.2008.16.23
Taher, S. A., Hematti, R., & Nemati, M.
(2008). Comparison of Different Control Strategies in
GA-Based Optimized UPFC Controller in Electric Power Systems, Am. J. Eng.
Applied Sci., 1(1),
45-52. DOI: 10.3844/ajeassp.2008.45.52
Tavallaei, M. A., & Tousi, B. (2008). Closed Form Solution to
an Optimal Control Problem by Orthogonal
Polynomial Expansion, Am. J. Eng. Applied
Sci., 1(2), 104-109. DOI:
10.3844/ajeassp.2008.104.109
Theansuwan, W., & Triratanasirichai, K. (2008). Air Blast
Freezing of Lime Juice: Effect of Processing Parameters, Am. J.
Eng. Applied Sci.,
1(1), 33-39. DOI: 10.3844/ajeassp.2008.33.39
Zahedi, S. A., Vaezi, M., & Tolou, N. (2008). Nonlinear Whitham-Broer-Kaup Wave Equation
in an Analytical Solution, Am. J.
Eng. Applied Sci.,
1(2), 161-167. DOI: 10.3844/ajeassp.2008.161.167
Zulkifli, R., Sopian, K., Abdullah, S., & Takriff,
M. S. (2008). Effect of Pulsating Circular Hot Air Jet Frequencies
on Local and Average Nusselt Number, Am. J. Eng. Applied
Sci., 1(1), 57-61. DOI:
10.3844/ajeassp.2008.57.61