Experimental Investigation on the Kinematics of an Underactuated
Mechanical Finger through Vision-Based Technology
C. COSENZA, R. BRANCATI , V. NIOLA*, S. SAVINO
Department of Industrial Engineering
University of Naples Federico II
Via Claudio 21 – 80125, Naples, Italy
ITALY
Abstract: Marker-less vision techniques represent a promising route in the development of experimental
methods to study the kinematic and the dynamic parameters of mechanical systems. The knowledge of a great
number of these parameters is a fundamental issue in the system behaviour analysis and represents an even
more crucial aspect for underactuated mechanical systems. In this paper, a technique is proposed to identify the
kinematics of the phalanges of an underactuated mechanical finger, starting from the acquisition of the finger
point cloud data by means of contactless vision system devices. The analytical model identified allows to
determine the underactuated finger configuration as function of the shaft rotation of the single motor of the
mechanical system.
Key-Words: underactuated mechanical systems, computer vision devices, robotic hand, kinematics, geometric
reconstruction algorithm
Received: April 21, 2021. Revised: January 1, 2022. Accepted: January 21, 2022. Published: February 9, 2022.
1 Introduction
In underactuated mechanisms, the main design
criterion is the lower number of actuators in respect
to the degrees of freedom. Underactuated
mechanical hands are able to perform several
grasping tasks due the shape adaptation ability to a
wide range of objects [1]–[3]. At the same time,
the complexity design reduction is associated to an
easier control by the user and, furthermore, cost,
weight and size decrease [4]. In previous papers, a
model of a highly underactuated robotic hand, based
on tendon driven fingers for prosthesis applications
[5], [6], has been proposed. The robotic hand is
composed of five fingers, each of which is made of
three phalanges hinged to each other by pins, which
represent the different articulations. A single
actuator drives the movement of each finger by
means of a differential system obtained with a self-
adaptive pulleys mechanism. Moreover, the
capabilities of this hand in grasping complex shape
objects through a combined approach of theory,
simulation and experiments have been already
demonstrated and the first prototypes have been
built [7], [8]. Underactuated mechanical systems
require appropriate and suitable experimental
methods to correctly monitor each component
dynamics. Indeed, it is not a feasible solution to deal
with multiple encoders assembled to each
component; the encoders could modify the system
behaviour due to the increase of weight. A possible
route in this field is to adopt vision techniques to
track the kinematics and the dynamics of these
mechanical systems. Hand tracking has become of
great interest due to several applications connected
with hand gesture and sign recognition for human-
computer interaction, especially in
virtual/augmented reality and game console control
[9]. Hand pose estimation is a very challenging task
since the hand is an articulated body with many
degrees of freedom and it is not easy to deal in
detail with its anatomical and physiological
constraints [10]. For human hand detection, tracking
and recognition, researchers have used visual
markers, coloured gloves, and electro-
mechanical/magnetic sensing devices, as well as
other specifically designed hardware, such as
wearable haptics [11], [12]. However, these sensors
may hinder the natural hand and finger motions.
Research groups in computer vision have also
focused their attention to the development of
markerless vision-based methods to detect, track
and recognize hand poses, employing RGB-D depth
sensors or Digital Image Correlation apparatus [13],
[14]. Low-cost sensors, like the Microsoft© Kinect
or Intel© RealSense, to measure the displacement of
mechanical systems have been adopted even for
control applications [15]–[26]. The output of a depth
sensor is a point cloud, containing the three-
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dimensional coordinates of a point set, expressed
within a certain coordinate system, representing the
external surface of an object. Optimization
algorithms or neural networks allow the hand
detection and tracking due to three-dimensional or
appearance models [27], [28]. A more complex
scenario is associated with approaches proposed to
deal with the detection and tracking of hand
grasping or interacting with objects or with
deformable object tracking [29]. As for the
experimental analysis of underactuated components,
researchers have already adopted vision methods
with the limitation of qualitative analysis. To
quantitatively assess the motion of mechanical
fingers (i.e. joint angle rotations) researchers have
also employed different methodologies: elastomeric
sensors that can directly be deposited on the fingers
of a prosthetic hand, flexible cables equipped with
potentiometers, magnetic rotary encoders embedded
between the proximal and medial phalanges [30]–
[33]. In this paper, an experimental marker-less
approach is proposed to quantitatively acquire the
motion an underactuated mechanical finger. This
approach exploits vision system acquisition
instruments to measure the joint angles (i.e. the
angles formed between the phalanges), at different
actuator rotations. In this perspective, the main issue
is to use a non-invasive methodology, able to not
influence the behaviour of each low-mass phalanx
(5-10 g) composing the finger. The use of sensors
could affect the original motion of the robotic
finger. A customized algorithm has been developed
to build a geometrical model of the fully articulated
robotic finger, starting from the output of a vision
system device. Finally, the results of the
methodology are used to write an analytical
expression to describe each phalanx rotation as a
function of the actuator rotation.
The study is organized as follows: in Section 2, the
mechanical finger system has been presented; in
Section 3, the experimental setup and the algorithm
description; in Section 4, we have discussed the
results for both the adopted instruments; in section
5, the validation of the results in comparison to a
non-vision method instrumentation and the
analytical expression for phalanx rotations are
shown; in Section 7, the main conclusions are
pointed out.
2 The Underactuated Mechanical
Finger
The mechanical finger, object of this study, is
composed by three phalanges, the proximal, the
medial and the distal, connected to each other and to
the hand through three hinges. Inside the three
phalanges, the actuator and the antagonist tendons
slide allowing the finger closing and opening,
respectively. Both the tendons are connected on one
side to the distal phalanx and on the other side to the
same actuator; so, it is possible to guarantee the
correct closing sequence, which is necessary to
facilitate grasping tasks. An elastic element,
connected to the antagonist tendon, compensates for
the inevitable different displacements of the two
tendons, due to the different geometries of their
paths, Figure 1.
Fig. 1: Scheme of the underactuated finger.
By assembling several fingers, it is possible to
realize an underactuated gripper. Activating all the
fingers with a single actuator, it is possible to realize
a strongly underactuated system. In this
configuration, both the tendons of each finger are
actuated by one actuator; two differential systems
distribute the forces between the fingers in a fixed
manner, but at the same time leave the fingers free
to move to better wrap different shape objects.
Fig. 2: CAD model of two underactuated grasping
end-effectors: (a) the three-finger gripper; (b) the
five-finger hand.
In Figure 2, it is possible to observe two different
assemblies of the fingers to realize a three-finger
gripper and a five-finger hand. The correct
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behaviour of each finger is crucial in the efficiency
of the multi-finger gripper. For this reason, it is
important to be able to analyse the real behaviour of
the finger during the motion steps and avoid sensors
that can alter the system dynamics. Thus, the
approach that will be proposed in the following
paragraphs aims to be non-invasive for the
mechanical system.
3 Description of the Proposed
Approach
The goal of the proposed approach is to acquire the
finger phalanx rotations through vision devices and
compute the relative angles between the phalanges.
As a first step, it is necessary to acquire the 3D point
data of the finger through vision devices. Afterward,
the data must be purged of points not belonging to
the finger itself and divided in three different point
clouds representing the proximal, the medial and the
distal phalanges. The point clouds of the phalanges
are processed through an appropriately developed
algorithm (hereafter the finger reconstruction
algorithm), which aims to reconstruct the finger
geometrical model by means of three cylinders. In
this paper, we have acquired data with two different
vision systems to test the reliability of the algorithm.
3.1 Experimental Setup and Acquisition
Instruments
The experimental setup comprises of a mechanical
finger, a controller unit and a servomotor. Figure 3
shows the whole test rig employed in this study. The
finger is linked to a pulley by an inextensible wire
that represents the tendon system. An analog
servomotor sets the finger tendon displacement; the
servomotor is controlled by a National Instruments
myRIO Embedded Device controller. The
experimental setup is also equipped with an
incremental encoder, with 10000 pulses per
revolution, to measure the motor angular position.
Fig. 3: Test rig of the single finger prototype.
Through the controller, it is possible to set a given
motor shaft rotation. The motor shaft rotation
produces the movement of the actuator and the
antagonist tendons and consequently it determines a
given finger configuration associated to the rotation
of the three phalanges.
Two different instruments were employed to acquire
the finger point clouds: a 3D laser scanner (ROMER
Absolute Arm with integrated scanner, Hexagon
Manufacturing Intelligence). The instrument
resolution is 0.001 mm on the point cloud
(Instrument 1); a white light scanner system
(AICON MoveInspect XR8, Hexagon
Manufacturing Intelligence) equipped with two
high-resolution 8-megapixel digital cameras. The
instrument resolution is 0.1 mm on the point cloud
(Instrument 2).
The acquisitions performed with instrument 1 were
made at a distance of a few centimetres from the
surface of the finger. The data collected with the
instrument 2 were obtained with acquisitions carried
out at a greater distance from the finger between 30
and 40 cm.
The finger point clouds were acquired in eleven
static poses of the finger, in the range 0 to 180
degree of motor shaft rotation with 18-degree step.
During the acquisition phase, the mechanical finger
is under no load. The data overlaps acquired through
both the instruments are shown in Figures 4 and 5.
Fig. 4: Point cloud data overlap for Instrument
1.
Fig. 5: Point cloud data overlap for Instrument
2.
In these two figures, the difference in the axis scale
is due the different reference systems of the two
instruments.
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The aim of this study is to estimate the finger
phalanx rotations, using measurements obtained
with non-contact equipment, independently of the
instrument and the position of the instrument.
3.2 Finger Reconstruction Algorithm: data
processing
The result of the acquisition is a point cloud of the
finger external surface, in three-dimensional
coordinates (x, y, z), in the reference system of the
instruments having the z-axis in the observation
direction.
As a preliminary process, it is necessary to remove
from the point cloud those points that do not belong
to the finger and to divide the point cloud in three
subsets corresponding to the proximal, the medial
and the distal phalanges. The 3D laser scanner, the
instrument 1, acquires the external surface of the
three phalanges in three separate point clouds.
Conversely, the instrument 2 acquires the external
surface of the finger in an overall point-cloud. Since
the acquisition gives also an image of the observed
area, it is possible to obtain three different point
clouds of the phalanges through image analysis with
morphology operations based on color
segmentation.
3.3 Finger Reconstruction Algorithm:
mathematical formulation
The finger reconstruction algorithm aims to build
the finger configuration as a simple 3D geometrical
model composed of three cylindrical elements. The
algorithm performs optimization procedures through
the linear regression models and geometrical
constraints.
At a given finger pose, the algorithm computes the
following steps:
Starting from the point cloud data of each phalanx,
consider the point
in the
instrument reference system and its
orthogonal projection,
, in the plane
, that is normal to the instrument
observation direction . For each phalanx, compute
the direction vector a that minimizes the maximum
distance of the points
from the straight line,
figure. 6.
The direction a is determined through the
parametric equation (1) representing the straight line
passing through the centroid
of the
points
.
(1)
(1)
In the equation (1), is the parameter, while and
are the vector a components. For each point
,
the equation (2) allows one to calculate the value of
parameter corresponding to the intersection point
between the straight line (1) and the perpendicular
line to (1) passing through the point
.
(2)
(2)
Thus, the distance from the point
to the straight
line (1) is obtained through the following
expression:
(3)
(3)
The maximum value of distances
, as a function
of and , is minimized. The minimization
outputs are the values and that allow to
evaluate the unit vector
(4)
(4)
in the plane.
Fig. 6: Direction vectors for each phalanx in the
xy-plane.
Consider the plane, containing the directions
and a, orthogonal to the plane , and
project the points
on this plane. The projected
points are defined as
Similarly, as in step 2, it is possible to find the data
direction vector v in the plane. The direction
v is computed considering the parametric equation
(5) of the straight line passing through the centroid
of the points
.
(5)
(5)
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In (5) is the parameter, while and are the
components of the vector v.
Even in this case, for each point
, by means of
equation (6) it is possible to calculate the value of
parameter
corresponding to the intersection point
between the straight line (5) and the perpendicular
line to (5) passing through the point
.
(6)
(6)
The distance from the point
to the straight line
(5) is defined as:
(7)
(7)
The maximum values of distances
, as function of
and m2, are minimized and it is possible to
calculate the unit vector
(8)
(8)
in the plane. The direction v is the
direction of the phalanx and its unit vector in the
instrument reference system is defined
as:
(9)
(9)
The unit vectors (9) associated to the three
phalanges are used as the initial values to compute
the cylinders.
The three cylinders, that approximate the
phalanges, are calculated solving a non-linear curve
fitting problem in least squares sense.
An optimization function describes the
geometrical constraints of the finger configuration.
The cylinders must assume the radii of the
phalanges and the lengths corresponding to the
distances between two consecutive hinges. Both the
coplanarity errors of the cylinder axes and the fitting
errors of each phalanx points from the respective
cylinder surface are considered. A least squares
minimization of such errors allows one to identify
the unit vectors that represent the axes of the three
cylinders. In this way, it is possible to reconstruct
the finger configuration. The finger configuration
reconstruction allows one to evaluate the relative
rotations between the phalanges by calculating the
relative rotations between the cylinder axes.
4 Results of the Finger
Reconstruction Algorithm
The instrument 1 acquires the complete external
surface of the finger. Fig. 7 shows the results of the
phalanges reconstruction algorithm by means of an
overlap between the point clouds acquired with
instruments 1 and the surfaces of the reconstructed
cylinders. Fig 7 shows three finger configurations,
corresponding to three motor positions: 0, 72 and
144 degrees.
Fig. 7: 3D model reconstruction for each phalanx
starting from the point cloud for three different
motor shaft angle rotations: (A) 0 deg., (B) 72 deg.
and (C) 144 deg. The point cloud is the output of the
Instrument 1.
Figure 8 shows the output of the elaboration for data
acquired with the instrument 2 for the same finger
configurations.
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Fig. 8: 3D model reconstruction for each phalanx
starting from the point cloud for three different
motor shaft angle rotations: A) 0 deg., B) 72 deg.
and C) 144 deg. The point cloud is the output of the
Instrument 2.
It is possible to observe that the finger
reconstruction algorithm is able to reproduce the
finger configurations through the cylinders, even
with the lower resolution data of instrument 2, in
which only a part of the phalanx surface has been
acquired. For the eleven static poses, in the motor
shaft rotation range [0-180] degrees, acquired
through the two different vision instruments, the
finger reconstruction algorithm allows to compute
the rotations of the three phalanges.
5 Validation of Results
To verify the goodness of the obtained results, a
comparison between the above results and those
obtained with another no vision-based instrument,
has been performed.
Thus, the angles of each phalanx have been
also acquired by means of an inclinometer sensor
(Dytran mod. 7546A1) equipped as showed in
Figure 9.
Inclinometer measurements were performed in
static finger poses and they were compared with the
results obtained with the vision system data and the
finger reconstruction algorithm.
Fig. 9: Experimental setup for the inclinometer
measurements for the distal phalanx.
The deployed inclinometer contains a variable
capacitance MEMS device that allows measuring
vibration data, including static inclination. The
experimental test rig has been posed in plane and
the inclinometer has been linked to each phalanx to
acquire the absolute inclination, at the same motor
shaft rotations actuated during the previous point
cloud acquisitions. In this way, the rotation angles
of the three phalanges, in the same static
configurations above analyzed, have been measured.
Figure 10 shows the measurements obtained from
the inclinometer sensor in comparison with the
rotations computed through the two vision
instruments. The measured behavior of the
phalanges is comparable for the three employed
instruments.
Fig. 10: Phalanx rotation angles as a function of the
motor shaft rotation. Comparison between data
acquired with the 3D laser scan (Instrument 1), the
white light scanner system (Instrument 2) and the
inclinometer sensor.
The standard deviation of the measurements
obtained by the three instruments has been analysed.
Figure 11 shows the standard deviations between
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the measurements for the three phalanges as a
function of the motor shaft rotation.
Fig. 11: Standard deviation of the measurements
obtained by the three instruments.
The mean values of the standard deviations, in
the motor shaft rotation range [0-180] degrees, are
less than 3 degrees for all three phalanges, with a
peak of about 5.5 degrees for the medial phalanx
and a peak of about 5 degrees for distal phalanx.
Since the medial phalanx is the central element of
the underactuated finger system, it is affected by a
greater error in the repeatability of the movements.
This condition contributes to raising the standard
deviation of the measurements of this phalanx.
The small values of the measurement
deviations, performed with different instruments,
indicate that the rotations evaluated by the finger
reconstruction algorithm can be considered reliable,
confirming the effectiveness of the proposed
approach.
6 Analytical Expression of Phalanx
Rotations
To verify the goodness of the obtained results, a
comparison between the above results and those
obtained with another no vision-based instrument,
has been performed.
The values of phalanx rotations have been used
to find an analytical expression which allows to
compute the rotation of the three phalanges as a
function of the motor shaft rotation and
consequently of the actuator tendon displacement.
The experimental data reported in Figure 10
show that the trend of each phalanx as a function of
motor shaft rotation could be described by a
discontinuous function with three rectilinear
sections and with six coefficients.
For the sake of simplicity, a sigmoid function,
having a characteristic S-shaped curve or sigmoid
curve, represents the best choice to describe the
diagram of Figure 10.
A special case of the sigmoid curve is the
logistic function whose general expression is:
(10)
(10)
where a, b, c and d are the four function
coefficients.
In this way, the data can be expressed through a
continuous function and with a reduced number of
coefficients.
Assume θ as the motor shaft rotation, it is
possible to define three functions, p(θ), m(θ), d(θ),
that are respectively the expressions of the
behaviour of the proximal, medial and distal
phalanges as function of θ.
In the figures 12, 13 and 14, it is possible to
observe the results of the fitting for the three
functions. The expression (10) well describes the
behaviour of all the three phalanges. The fitting
coefficient of determination (R-squared) assumes
values 0.9926, 0.9945 and 0.9863 respectively for
the three phalanges proximal, medial and distal, as
reported in Table 1.
Fig. 12: Comparison between the experimental data
and the fitting function p(θ) for the proximal
phalanx.
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Fig. 13: Comparison between the experimental data
and the fitting function m(θ) for the medial phalanx.
Fig. 14: Comparison between the experimental data
and the fitting function d(θ) for the distal phalanx.
Table 1 reports the coefficient values of the
equation (8) for the functions associated to the three
phalanx rotations.
The motor shaft rotation θ is related to the
tendon displacement, therefore also the analytical
functions p(θ), m(θ) and d(θ) can be related to the
actuator tendon displacements.
It is worth to notice that the trend of these
analytical functions, obtained through the proposed
methodology, include most of the phenomena that
characterize the real behaviour of the mechanical
system.
The analysis of the rotation laws shows a
different behaviour for the three phalanges. In figure
15, the derivatives of the phalanx rotations with
respect to the motor shaft rotation have been
reported: they assume the highest value for the distal
phalanx, while the lowest one for the proximal
phalanx.
Table 1. Analytical expression coefficients of the
phalanx rotations
Phalanx
function
Logistic function coefficients
R-
squared
a
b
c
d
p(θ)
63
15
0.08064
-4.109
0.9926
m(θ)
75.48
5393
0.1011
14.12
0.9945
d(θ)
84.5
1.095e+06
0.097
13.76
0.9863
In the motor shaft rotation range [0, 180]
degrees, five ranges can be identified; they
correspond to finger configurations that are
associated to different combinations of the three
phalanx rotations, figure.15.
In particular:
1. 0-30 degrees proximal rotation
2. 30-90 degrees proximal and medial
rotations
3. 90-100 degrees proximal, medial and distal
rotations
4. 100-140 degrees medial and distal
rotations
5. 140-180 degrees distal rotation
Fig. 15: Derivatives of the phalanx rotations with
respect to the motor shaft rotation.
The analytical expressions p(θ), m(θ) and d(θ),
represent the first step in defining a mathematical
expression of the whole configuration of the
underactuated mechanical finger and, therefore, of
the underactuated mechanical hand as a function of
the actuator tendon displacement. Such a
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mathematical expression can be a tool to improve
the control of this mechanical system.
The kinematic finger model, with the reference
systems placed in the hinges of each phalanx, [Xi,
Yi, Zi], [Xp, Yp, Zp], [Xm, Ym, Zm], and in the
finger-tip of the distal phalanx, [Xd, Yd, Zd], is
showed in figure 16.
Fig. 16: Reference systems of kinematic finger
model:(A) distal, (B) medial.
The coordinates of the ending point of the
distal phalanx, (x,y,z), coincide with the origin of
the reference system [Xd, Yd, Zd], and in the
reference system [Xi, Yi, Zi] are:
(11)
(11)
Where lp, lm, ld are proximal, medial and distal
phalanx lengths (as above described, these lengths
are the distances between two consecutive hinges);
θp, θm, θd are the phalanx rotation angles.
This kinematic model allows to evaluate the
fingertip position as function of the three phalanx
rotations, but by means of the functions p(θ), m(θ)
and d(θ), the fingertip position can be related to the
only variable θ, the motor shaft rotation, and
therefore also to the actuator tendon displacement.
The kinematic model of the fingertip position
in the reference system [Xi, Yi, Zi] is described by
the equations (12) as a function of the motor shaft
rotation θ.
(12)
(12)
The fingertip displacements in the coordinate
refence system [Xi, Yi, Zi] are showed in Fig. 17a),
the fingertip trajectory, for a motor shaft rotation
range of [0,180] degrees, is showed in Fig 17b).
Fig. 17: (A) Coordinates of the fingertip in the
reference system [Xi, Yi, Zi] as a function of the
motor shaft rotation; (B) Fingertip trajectory for a
motor shaft rotation range of [0,180] degrees.
7 Conclusions
Experimental methods designed to monitor the
kinematics and dynamics of underactuated systems
are still lacking. Our study aims to propose an
experimental technique to evaluate the
configurations of an underactuated mechanical
finger corresponding to different actuator rotations.
An algorithm has been developed to reconstruct the
three-dimensional shape of an underactuated
mechanical finger, starting from the output of vision
acquisition instruments. Two high-resolution
instruments have been employed, namely a 3D laser
scan and a white light scanner. For both the
instruments, the algorithm reconstructs the three-
dimensional configuration of the finger in a very
accurate manner.
The results of the finger reconstruction algorithm
have also been validated by means of an
inclinometer sensor that measures the inclinations of
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each phalanx. The standard deviations of the
measurements performed with three different
instruments confirm the effectiveness of the
proposed methodology.
The main outcome of the activity is to obtain a
kinematic model of an underactuated system like the
finger of “Federica hand”, starting from
experimental data acquired without producing any
interference on the behaviour of the system itself.
The methodology results have been used to evaluate
an analytical expression describing the behaviour of
each phalanx as a function of the motor shaft
rotation. Such analytical expression could be a
powerful tool in the finger behaviour analysis in its
possible tasks. It should be noted that this technique
of acquisition of the finger configuration, is non-
invasive and could be used even for the human
fingers.
The methodology can be applied even to other kind
of fingers, but it is necessary to acquire their point
clouds during a closing sequence. For mechanical
fingers with a different design, it is possible that the
analytical functions describing the phalanx rotations
could be different; but if only the geometrical
parameters (phalanx radii and lengths) change, the
above functions could be the same with different
values of the coefficients. These aspects could be
addressed in a subsequent study in which the
procedure can be performed on different fingers in
order to build an experimental database and try to
obtain a generic mathematical expression.
This study represents a first step to develop a
quantitative approach to study the kinematics and
the dynamics of underactuated mechanical systems
adopting marker-less vision techniques. Future
developments will concern the extension of this
methodology to the data acquired during the finger
motion to measure its dynamics. Indeed, the
analytical expression of the phalanx rotation
obtained with the finger in static poses, is not able to
describe the whole dynamic behaviour of the finger,
i.e. the dissipative phenomena cannot be observed in
static configuration.
Acknowledgments:
During this research, a valuable help was provided
by Luca Sanseverino who was working for the
bachelor’s degree thesis, and the company
HEXAGON Manufacturing Intelligence Italy. The
authors thank Gennaro Stingo and Giuseppe Iovino
(Department of Industrial Engineering), Mario
Minocchi and Davide Marcone (IT Laboratory) for
their technical support during the tuning stages of
the test rig.
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
All the authors participated in the:
conceptualization, investigation, writing, and
revision phases. V.N. and C.C. took particular care
of the experimental setup development and
laboratory tests, R.B. developed the numerical
models, and S.S. took care the results analysis.
Sources of Funding for Research Presented
in a Scientific Article or Scientific Article
Itself
“This research received no external funding”.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
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WSEAS TRANSACTIONS on ENVIRONMENT and DEVELOPMENT
DOI: 10.37394/232015.2022.18.32
C. Cosenza, R. Brancati, V. Niola, S. Savino
E-ISSN: 2224-3496
332
Volume 18, 2022
