An experimental mechatronic design and control
of a 5 DOF Robotic arm for identification and
sorting of different sized objects
Christos Tolis and George F. Fragulis
Laboratory of Robotics and Applied Control Systems
Dept. Of Electrical Engineering
Western Macedonia Univ. of Applied Sciences ,Kozani, Hellas
November 13, 2017
Abstract
The purpose of this paper is to present the construction and pro-
gramming of a five degrees of freedom robotic arm which interacts with
an infrared sensor for the identification and sorting of different sized ob-
jects. The main axis of the construction design will be up to the three
main branches of science that make up the Mechatronics: Mechanical En-
gineering, Electronic-Electrical Engineering and Computer Engineering.
The methods that have been used for the construction are presented as
well as the methods for the programming of the arm in cooperation with
the sensor. The aim is to present the manual and automatic control of
the arm for the recognition and the installation of the objects through a
simple (in operation) and low in cost sensor like the one that was used
by this paper. Furthermore, this paper presents the significance of this
robotic arm design and its further applications in contemporary industrial
forms of production.
Keywords: Robotic Arm, Infrared (IR) Sensor, Actuators, Effectors, Mi-
crocontroller, Joints, Links, Work Space, Degrees Of Freedom (DOF), Kine-
matic Analysis, Forward Kinematics, Inverse Kinematics, Torque, Velocity,
Servo Motor, PWM, Homogenous Transformations, Kinematic Chain, Denavit
– Hartenberg Parameters, Schematic, Datasheet, Consumptions, Java-C++-C,
Libraries, Arduino.
1
Introduction
The aim of this paper is to present the control and driving mechanism of robotic
arm, which aims to grab different sized objects which can find applications
within the industry or other working environments. The robotic arm must be
highly functional, light weight and provide ease of attachment and control. The
1
arXiv:1711.03808v1  [cs.RO]  10 Nov 2017
interdisciplinarity that characterizes Mechatronics between the notions of Me-
chanical Engineering, Electronic-Electrical Engineering and Computer Science
is used for the selection of materials and devices to construct the arm. Fur-
thermore it helped us to encounter any kinetic, power, torque, compatibility or
other problems that would have resulted from the completion of the project .
The major problem these robotic arms face is their cost ([16], [5], [14]). The
main factors for their expensiveness are use of advanced actuators, too com-
plex design and manufacturing techniques and finnaly specialized sensors for
user input and control.
To address the challenge we adopted a design that
uses infrared(IR) sensors providing the virtual vision and low cost commercially
available actuators.
2
Robot Arm and Infrared Sensor Description
The Robotic Arm is a modular arm consisting of five rotary joints plus the end
effector which is a grip. The five rotating joints consist of: 1 joint for base rota-
tion, 1 for shoulder rotation, 1 for elbow rotation, 1 for wrist rotation and 1 for
grip rotation. The mechanical parts of the project were selected by Lynxmotion
one by one to meet our needs and are of the AL5 type. The six servo motors by
Hitec are chosen based on their torque for proper operation. The Infrared Sen-
sor is by Sharp and is a distance sensor. The Sharp 2Y0A21 F46 composed of
an integrated combination of PSD (position sensitive detector), IRED (infrared
emitting diode) and signal processing circuit. The device outputs the voltage
corresponding to the detection distance.
Every rotational joint of the arm is being controlled by servo motors. These
motors are connected to a microcontroller (BotBoarduino) which is controlled
by a computer. The sensor is placed in front of the arm, above gripper, so can
‘’read” the distance between the gripper and the reflected surface.
3
Mechanical Engineering issues
We studied the torque of the servo motors which have been chosen, to avoid
any kinetic problems. Furthermore we analyze the Degrees Of Freedom and the
Work Space of the arm. To control the arm, the Forward Kinematics and Inverse
Kinematics has also been developed. After we measured all the materials of the
arm we made the CAD through the SolidWorks software
3.1
Torque Calculation
Torque (T) is defined ([17],[6]) as a turning or twisting force and is calculated
using the relation:
T = F ∗L
2
The force (F) acts at a length (L) from a pivot point. In a vertical plane
the force that causing an object to fall is the acceleration due to gravity (g)
multiplied by its mass (m):
F = g ∗m
The above relation is the object’s weight (W):
W = m ∗g
Figure 1:
In Figure 1 we can see the lengths (L) of the links as well as the weights
(W) of the links considered that the center of mass is located at roughly the
center of its length. The a1 in the image is the ‘’load” being held by the arm,
the a2, a3, a4, a5 and A6 are the actuators (servos). To calculate the required
torque (T6) of the A6 motor (HS −805BB servo) we use the relation:
T6 = (L1 + L2 + L3 + L4 + L5) ∗A1 + (0.5 ∗L1 + L2 + L3 + L4 + L5) ∗W1
+ (L2 + L3 + L4 + L5) ∗A2 + (0.5 ∗L2 + L3 + L4 + L5) ∗W2
(1)
+ (L3 + L4 + L5) ∗A3 + (0.5 ∗L3 + L4 + L5) ∗W3
+ (L4 + L5) ∗A4 + (0.5 ∗L4 + L5) ∗W4 + (L5) ∗A5 + (0.5 ∗L5) ∗W5
To calculate the required torque (T5) of the a5 motor (HS −755HB servo):
T5 = (L1 + L2 + L3 + L4) ∗A1 + (0.5 ∗L1 + L2 + L3 + L4) ∗W1
+ (L2 + L3 + L4) ∗A2 + (0.5 ∗L2 + L3 + L4) ∗W2
(2)
+ (L3 + L4) ∗A3 + (0.5 ∗L3 + L4) ∗W3 + (L4 + L5) ∗A4 + (0.5 ∗L4 + L5) ∗W4
The torque (T4) of the a4 (HS −645MG servo) is calculated:
3
T4 = (L1 + L2 + L3) ∗A1 + (0.5 ∗L1 + L2 + L3) ∗W1
(3)
+ (L2 + L3) ∗A2 + (0.5 ∗L2 + L3) ∗W2 + (L3) ∗A3 + (0.5 ∗L3) ∗W3
In a same manner the torque (T3) of the a3 (HS −225MG servo):
T3 = (L1 + L2) ∗A1 + (0.5 ∗L1 + L2) ∗W1 + (L2) ∗A2 + (0.5 ∗L2) ∗W2 (4)
and finally the torque (T2) of the a2 (HS −422 servo):
T2 = (L1) ∗A1 + (0.5 ∗L1) ∗W1
(5)
where: A2 = 45.5g(HS −422), A3 = 31g(HS −225MG), A4 = 55.2g(HS −
645MG)+7g(ASB−24) = 62.2g, A5 = 110g(HS−755HB)+13g(ASB−201) =
123g, A6 = 197g(HS −805BB) + 18g(ASB −204) = 215g .
The weights are
W1 = 15.7g (Grip), W2 = 10g (Sensor Bracket), W3 =
9g(Wrist Bracket), W4 = 10g (AT-04) +6g(ASB-06)+ 8g (HUB-08) =24g, W5 =
16g (ASB-205)+15g ( ASB-203) = 31g.
The lengths are : L1 = 2.8 cm, L2 = 2.8 cm, L3 = 2.85cm, L4 = 18.73 cm,
L5 = 14.6 cm. If we replace the above, to the relations (1) - (5) and the weight
of A1 (load) is zero, the torques of the motors are:
• T1 = 0.021 kg/cm
• T2 = 0.207 kg/cm
• T3 = 0.511 kg/cm
• T4 = 5.122 kg/m
• T5 = 12.25kg/cm
The nominal torques of the servo motors as given by the manufacturer are:
• HS −422(T1) = 4.1 kg/cm
• HS −225MG(T2) = 4.8 kg/cm
• HS −645MG(T3) = 9.6 kg/cm
• HS −755HB(T4) = 13.2 kg/cm
• HS −805BB(T5) = 24.7 kg/cm
From the above, we can say that the arm is capable to lift its own weight
because the nominal torques of the servos overlap the calculated torques with
zero load (A1 = 0). Now If the load A1 is set to be 100g the torques are:
4
• T1 = 0.3 kg/cm
• T2 = 0.767 kg/cm
• T3 = 1.356 kg/cm
• T4 = 7.84kg/cm
• T5 = 16.43 kg/cm
We notice, if the load is A1 = 100g, servos can cope. If we increase the
weight at A1 = 300g, then the calculated torques are:
• T1 = 0.86 kg/cm
• T2 = 1.887 kg/cm
• T3 = 3.04 kg/cm
• T4 = 13.27 kg/cm
• T5 = 24.79 kg/cm
Hence the maximum weight the arm can lift is approximately ˜300g because
the calculated torques reach the nominal torques of the servos.
3.2
DOF (Degrees Of Freedom)
The arm has six actuators, one of which is to open and close the gripper, thus
not being considered as a degree of freedom. The five rotational actuators have
a degree of freedom each, with a result that the hole system has a total of five
degrees of freedom.
If we see the DOF of the arm through a mathematical
point of view, the equation describing it is the Gruebler-Kutzbach equation and
is expressed by the relation:
M = 3 ∗(n −1) −2 ∗J1 −J2
where M is the DOF of the system, n is the number of links including the
base frame, J1 is the number of joints that have one DOF, J2 is the number of
joints that have more than one DOF
In figure 2 we can see the links (A, B, C, D, E and F) and the joints (1, 2,
3, 4 and 5) of the arm. The number of the J2 is zero because there is no joints
of two DOF in the system.
Therefore:
M = 3 ∗(n −1) −2 ∗J1 −J2 = 3 ∗5 −10 ⇒
(6)
M = 5 DOF
5
Figure 2:
3.3
Work Space
The work space of the arm is the space where the end effector can act. We
compiled a code using MatLab for the 3D representation of the arm’s work
space. In Figure 3 we can see the 3D presentation of the work space of the arm
using the Robotics toolboxTM(see [8], [?]. The top hemisphere (colored: yellow)
is the actual work space of the arm and the bottom hemisphere (colored: blue)
is a possible work space of the arm under certain circumstances. The diameter
of the work area of the arm is approximately 40 cm .
3.4
Forward Kinematic
Forward Kinematics ([20], [12])refers to the use of kinematics equations of a
robot to calculate the position of the end-effector from specified values for the
joint parameters.
The Denavit-Hartenberg parameters is the most common
method being used to determine the Forward Kinematics analyses. Using this
method we define the coordinate frames of the arm (Fig. 4), depending of the
joints of mechanisms and then the D-H parameters table (Table 1) has been
calculated
Coordinate Frames has been defined with respect to D-H methodology where:
ai is the length of the common perpendicular between points O1,2 and O4,
αi is the angle between axes zi and zi−1, di is the displacement distance of
points O0 −O1,2 and O4 −O5, θi is the angle between axis xi and xi−1.


Link i
ai
αi
di
θi
1
0
0
d1
θ1
2
0
90o
0
θ2
3
a3
0
0
θ3
4
a4
0
0
θ4(90o)
5
0
−90o
d5
θ5


(7)
6
Figure 3:
Figure 4:
Using the D-H parameter table, homogeneous transformations matrixes are
7
resulted
H1
0 =


cos θ1
−sin θ1
0
0
sin θ1
cos θ1
0
0
0
1
0
d1
0
0
0
1

,
H2
1 =


cos θ2
−sin θ2
0
0
0
0
−1
0
sin θ2
cos θ2
0
0
0
0
0
1


,
(8)
H3
2 =


cos θ3
−sin θ3
0
α3
sin θ3
cos θ3
0
0
0
1
0
0
0
0
0
1


H4
3 =


cos θ4
−sin θ4
0
α4
sin θ1
cos θ1
0
0
0
1
0
0
0
0
0
1

,
H5
4 =


cos θ5
−sin θ5
0
0
0
0
1
0
sin θ5
cos θ5
0
0
0
0
0
1


The multiplication of the matrixes (7)-(8) gives the table of the total homo-
geneous transformation, which is expressed:
H5
0 = H1
0 ∗H2
1 ∗H3
2 ∗H4
3 ∗H5
4


nx
ox
αx
dx
ny
oy
αy
dy
nz
oz
αz
dz
0
0
0
1


(9)
where:
• n = (nx, ny, nz)T is the vector representing the direction of the axis
(O1, x1) in the coordinate system (O0, x0, y0, z0)
• o = (ox, oy, oz)T is the vector representing the direction of the axis (O1, y1)
in the coordinate system (O0, x0, y0, z0)
• α = (αx, αy, αz)T is the vector representing the direction of the axis
(O1, z1) in the coordinate system (O0, x0, y0, z0)
• d = (dx, dy, dz)T is the vector representing the direction of the axis (O1, x1)
is the vector representing the joint’s position
where:
nx= ((c1c2c3 −c1s2s3)c4 + (−c1c2s3 −c1s2c3)s4)c5 + s1s5
ny = ((s1c2c3 −s1s2s3)c4 + (−s1c2s3 −s1s2c3)s4)c5 −c1s5
nz= ((s2c3 + c2s3)c4 + (−s2s3 + c2c3)s4)c5
ox = −((c1c2c3 −c1s2s3)c4 + (−c1c2s3 −c1s2c3)s4)s5 −s1c5
oy = −((s1c2c3 −s1s2s3)c4 + (−s1c2s3 −s1s2c3)s4)s5 −c1c5
oz= (c2c3 −s2s3)s4 −((−s2c3 −c2s3)c4
αx = −(c1c2c3 −c1s2s3)s4 + (−c1c2s3 −c1s2c3)c4
8
αy = −(s1c2c3 −s1s2s3)s4 + (−s1c2s3 −s1s2c3)c4
αz = (c2c3 −s2s3)c4 −(s2c3 + c2s3)s4
dx = (−(c1c2c3 −c1s2s3)s4 +(−c1c2s3 −c1s2c3)c4)d5 +(c1c2c3 −c1s2s3)a4 +
c1c2a3
dy = (−(s1c2c3 −s1s2s3)s4 +(−s1c2s3 −s1s2c3)c4)d5 +(s1c2c3 −s1s2s3)a4 +
s1c2a3
dz = (−(s2c3 + c2s3)s4 + (−s2s3 + c2c3)c4)d5 + (s2c3 −c2s3)a4 + s2a3 + d1
[6]
and ci = cos θi , si = sin θi .
3.5
Inverse Kinematic Analysis
In the Inverse kinematic ([20], [12])analysis we use the kinematics equations to
find the desired position of the end-effector. In other words, forward kinematics
uses the joint parameters to compute the configuration of a kinematic chain, and
inverse kinematics reverses this calculation to determine the joint parameters
that achieves a desired configuration.
Calculation of the inverse kinematics
problem is much more complex than forward kinematics, since there is no unique
solution. In this project a geometric approach been used for solving the inverse
kinematics problem. The complexity of the inverse kinematic problem increases
with the number of nonzero link parameters and the geometric approach that
used to solve the problem is simplest and more natural. The general idea of the
geometric approach is to project the manipulator onto the x0-y0 plane (Figure
5) and solve a simple trigonometry problem to find θ1
Figure 5:
From the projection we can see that
θ1 = atan
y
x

(10)
9
The distance from the base to the edge of the grip is r, therefore
r =
p
x2c + y2c
(11)
where
xc = r ∗cos(θ1) and yc = r ∗sin(θ1)
(12)
A second projection of the manipulator is shown in Figure 6. From this
projection we can see that the A1 is :
A1 = atan
y
x

(13)
The A2 is :
A2 = acos(a2
3 −a2
4 + r2)
a2
3 ∗r
(14)
Therefore, the angle of the shoulder joint θ2 is :
θ2 = A1 + A2
(15)
The second solution of the angle θ2 is written:
θ2 = A1 ± A2
(16)
The elbow joint corresponds to the angle θ3 which equals to :
θ2 = acos(a2
3 + a2
4 + r2)
a2
3 ∗a4
(17)
The relation between the angle ψ (grip rotation) and the angles θ1, θ2, θ3 is
written:
θ4 = ψ −θ2 −θ3
(18)
From the geometric approach that analyzed above, the user will have com-
plete control of the manipulator, controlling all six arm servos. When the user
changes the angles θ2 and θ3, the angle θ4 will not change, thus not changing
the point of the grip and its orientation. This is a consequence of the geometric
approach (Figure 6). In other words, the three thrust mechanisms θ4 (rotation
of the wrist), θ5 (grip rotation), θ6 (opening and closing of the grip) are not
affected by the movement of angular movement mechanisms θ1 (base rotation),
θ2(shoulder rotation) , θ3(elbow rotation), and the inverse . [6]
3.6
SolidWorks CAD-CAE
All the parts comprising the project have been measured and designed with
usage of SolidWorks c
⃝software. It’s a solid modeling computer-aided design
(CAD) and computer-aided engineering (CAE) computer program. Users can
see the full dimensionality (2D or 3D) of every part comprising the arm, as
well as the material of every part. Additionally SolidWorks provides users with
“countless” capabilities like measuring
parts, mass properties, motion study,
collision check etc. In Figure 7, we can see the final 3D rendering of the arm.
10
Figure 6:
Figure 7:
4
Electrical-Electronic wiring
Communication compatibility between devices and the proper powering of these
devices is important for the right operation of the project [11].
Once the
correct devices have been selected based on their mechanical analysis, their
electrical behavior should be analyzed in order to avoid encounter any com-
munication or powering problems. In Figure 8 we can see the electrical dia-
gram of the project. A current source (220V AC/50Hz socket) feeds the com-
11
puter’s power supply adapter (18.5V DC/6.5A) and another source feeds the
BotBoarduino’s power supply adapter (6V DC/2.25A). All servos are powered
by the
BotBoarduino’s adapter, the IR sensor is powered by the computer’s
USB cable (5V DC/0.5A),through the BotBoarduino’s regulator (5V DC/1.5A).
The red (+ positive) and black (-negative) cables of the servos and IR sensor
are for powering the devices, the yellow cable is for the communication with
microcontroller ATMEGA328 and the computer through the USB cable (see
[1],[3],[4],[9],[2],[13]).
Figure 8:
4.1
Microcontroller Description
There are a lot of microcontroller boards in the market today with different func-
tions, depending on the needs. The microcontroller board that was selected for
this project is the BotBoarduino board because can give us the desired currents
for the devices (servos and IR sensor) and can also split two sources of power
for different powering needs. For example, in our project, servos are powered
with 6VDC by bridging the jumper to the VS input and IR sensor is powered
with 5VDC by bridging the jumper to the VL input. BotBoarduino is based
on the ATMEGA328 microcontroller, it has a USB mini port that connects to
a computer for programming the microcontroller. The LD29150DT50R regula-
tor that BotBoarduino has onboard can power up to 1.5A current through the
VL input. An external source of power (VS input) can also be connected onto
the board, like the adapter (6V/2.25A) we use, for powering devices that need
grater volts and amps, than the 5V/1.5A of VL input (see [3],[15],[9]).
4.2
Servomotors and IR Sensor
The angle of each servo controlled by the Pulse Width Modulation (PWM)
value which is defined during programming. Each of the servo have an IC inside
that can check the emitted PWM of the BotBoarduino and drive the servo to
12
the desired position. Servos are powered by 6V DC by the adaptor through the
BotBoarduino. The distance of IR sensor is measured by the Position Sensitive
Detector (PSD) which then ‘’translate” the measured distance, through the IC
of the sensor, to an output voltage. The greater the output voltage, the greater
the distance. In the Figure 9 we can see the curve of the measured distance
in relation with the output voltage. We can observe that the best accuracy
region of the sensor is between the values of 10cm and 15cm. According to this,
the distance between the sensor and the sorting objects must be between these
values, for best accuracy (see [18],[3],[4]).
Figure 9:
4.3
Power Consumptions
The power consumption of the devices of the arm, is one of the most important
topics in this study. The current consumed by the servos appears below:
• HS-485HB = 180mA
• HS-805BB = 830mA
• HS-755HB = 285mA
• HS-645MG = 450mA
• HS-225MG = 340mA
13
• HS-422 = 180mA
The sum of the consumption current of the servos is 2.265mA. The adap-
tor we selected for powering the servos gives us 2.250mA. The problem that
occurs can be solved by moving one servo at a time. We achieve that in the
programming. The communication current of each servo shown below:
• HS-485HB = 40mA
• HS-805BB = 40mA
• HS-755HB = 40mA
• HS-645MG = 40mA
• HS-225MG = 40mA
• HS-422 = 40mA
The powering current of IR sensor is 30mA and the communication current
is 40mA. The sum of the communication currents of the servos plus the powering
and communication currents of the sensor is 310mA. These currents powered
by the USB cable (5V-0.5A) of the computer through the ‘’LD29150DT50R
current regulator IC (5V-1.5A)” of the microcontroller. The regulator gives us
a maximum of 1.5A current, which means that we can overlap the needs of
310mA (see [1],[13],[15], [9]).
5
Programming the Robotic Arm
In this section we provide the programming of the robotic arm. The software
that have been used is the Arduino IDE (Integrated Development Environ-
ment). The programming language that he software supports are C and C + +
(see [19],[10]). Arduino IDE supplies programmers with software libraries which
provides them with many input or output procedures. A library, for example,
can be loaded into the program by writing #include <math.h> to the com-
mand line of Arduino IDE, this library is for the identification of the mathe-
matical equations during programming. After the analysis of previous studies
(Mechanical/Electrical-Electronic Engineering) we came up with four programs
that show us the cooperation of the arm-sensor and its further applications
within contemporary industrial forms of production.
14
5.1
Control cases
5.1.1
Autonomous Operation No.1
During the first autonomous operation, the arm takes the initial start position
of the program, shown in Figure 10, then the arm takes the measuring position,
according to the study that we have performed for the IR sensor (Fig. 11). As
the arm reaches the measuring position, the IR sensor starts to collect distance
measurements between the ‘’eye” of the sensor and the sorting area, as shown
in the red circle in Figure 11. The distance between the sensor and the empty
sorting area is set to 13.8 cm approximately. If the measurement is lower than
13.8 cm the sensor is set to recognize that an object is placed to the sorting area
and the arm picks it up and puts it into the bucket
Figure 10:
The video for the first autonomous operation can be seen in this URL:
www.youtube.com/watch?v=srE3x6y4jqU&feature=youtu.be
5.1.2
Autonomous Operation No.2
The initial start position and the measurement position is the same as the
autonomous operation No.1.
If the sensor measures between <13.8cm and
>=10cm, recognizes that the object is ‘’short” (predefined measurements given).
If the measurement is >greater than 10cm then the sensor recognizes that the
object is ‘’tall”. The arm, then picks the object and places it to a predefined
positioned bucket (Left for ‘’short” and Right for ‘’tall”).
The video for the second autonomous operation can be seen in this URL:
www.youtube.com/watch?v=e8vaBb9g2A&feature=youtu.be
15
5.1.3
Autonomous Operation No.3
Third autonomous operation is almost the same as the autonomous operation
No.2. It differs in the placement of said objects. ‘’Short” object is placed to the
predefined area, shown in Figure 12 and ‘’tall” object is placed to the predefined
area, shown in Figure 13
The video for the third autonomous operation can be seen in this URL:
www.youtube.com/watch?v=rFqdlcLnQ08
5.1.4
Manual Operation
The fourth program is the manual operation of the arm performed by a user
with the keyboard of a computer loaded with said program. Users have full
control of the arm manipulating each servo independently. Additionally users
can see measurements of the sensor at the display of Arduino IDE.
The video for the manual operation can be seen in this URL:
www.youtube.com/watch?v=oFLjFvMqPjs&feature=youtu.be ([18],[19],[20])
6
Conclusions
A robot arm has been designed to cooperate with an infrared sensor for the
identification of different sized objects and sorting them to predefined positions.
Also the manual operation of the arm through computer’s keyboard is presented.
The study is based on the three main axes that Mechatronics consist:
• Mechanical Engineering
Figure 11:
16
Figure 12:
Figure 13:
• Electrical-Electronic Engineering
• Computer Science
In the case of mechanical engineering, we analyze the torque of servos, de-
grees of freedom and work space of the arm, mathematical modeling of forward
and inverse kinematics and the CAD of the arm. Analysis of electrical-electronic
engineering was important for the required powering of the devices (BotBoard-
uino, Servos, IR Sensor), for communication between devices and for the max-
imum efficiency of devices. Three promising experiments have been conducted
concerning the use of autonomous operations and the manual operation of the
arm , that can be applied to the industry, as well as to other working environ-
ments. The IR sensor can identify a variety of objects based on their height
and to validate position and orientation information of the grasped object. The
designed robotic arm might be an educational one, but the procedure and the
methodology followed is similar for an industrial type of robotic arm. The next
steps comprises, kinematic update to the arm, object reorientation routine, Dy-
namics and kinematics of the object to improve stable grasping.
17
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19