A serial manipulator consists of a fixed base, a series of links connected by joints, and ending at a free end carrying the tool or the end-effector. In contrast to parallel manipulators, there are no closed loops. By actuating the joints, one can position and orient the end-effector in a plane or in three-dimensional (3D) space to perform desired tasks with the end-effector.

1. 1
DESIGN AND FABRICATION OF
SERIAL MANIPULATOR WITH HYBRID
CONTROL THEORY
MAJOR PROJECT REPORT
SUBMITTED TO THE
UNIVERSITY OF PETROLEUM AND ENERGY STUDIES
FOR THE DEGREE OF
BACHELOR OF TECHNOLOGY
IN
MECHATRONICS ENGINEERING
Submitted By
Abhishek Mittal 500047398
Ajinkya Deshmukh 500045814
Jatin Gupta 500047508
Ruturaj Gaikwad 500046520
UNDER THE GUIDANCE OF
Mr. Natraj Mishra
(Asst. Professor-SS)
DEPARTMENT OF MECHANICAL ENGINEERING
UNIVERSITY OF PETROLEUM AND ENERGY STUDIES
DEHRADUN-248007
MAY 2019

2. 2
CANDIDATE’S DECLARATION
I/We hereby certify that the project work entitled “Design and Fabrication of Serial
Manipulator with Hybrid Control Theory” in partial fulfillment of the requirements for the
award of the Degree of Bachelor of Technology in Mechatronics Engineering and submitted
to the Department of Mechanical Engineering at School of Engineering Studies, University of
Petroleum & Energy Studies, Dehradun, is an authentic record of my/ our work carried out
during a period from August, 2018 to May 2019 under the supervision of Mr. Natraj
Mishra.
The matter presented in this project has not been submitted by me/ us for the award of any
other degree of this or any other University.
(Abhishek, Ajinkya, Jatin, Ruturaj)
Roll No.04, 07, 30, 54
This is to certify that the above statement made by the candidate is correct to the best of
my knowledge.
Date:
Mr. Natraj Mishra
(Project Guide)
Dr. Ajay Srivastava
Head – Department of Mechatronics
School of Engineering Studies
University of Petroleum & Energy Studies

3. 3
UNIVERSITY OF PETROLEUM AND ENERGY STUDIES
Department of Mechanical Engineering
Dehradun
Certificate
This is to certify that the “Design and Fabrication of Serial Manipulator with Hybrid Control
Theory” has been successfully completed by Abhishek, Ajinkya, Ruturaj and Jatin with the
Enrollment number R880215004, 07, 54, 30 for the degree of B.tech in Mechatronics
Engineering. The work has been reviewed by Natraj Mishra and found satisfactory for the
completion of the project.
Dr. Ajay Srivastava Mr. Natraj Mishra
HOD – Mechatronics Engineering Project Guide

4. 4
ACKNOWLEDGEMENT
We give all honor and praise to the LORD who gave us wisdom and enabled us to
complete this project successfully.
The success and final outcome of this project required a lot of guidance and assistance
from many people and we are extremely privileged to have got this all along the
completion of my project. All that we have done is only due to such supervision and
assistance and we would not forget to thank them.
We respect and owe our deepest gratitude to our project mentor Mr. NATRAJ MISHRA,
for providing us an opportunity to do the project work and giving us all support and
guidance which made us complete the project duly. We are extremely thankful to him for
providing such a nice support and guidance.
We are thankful to and fortunate enough to get constant encouragement, support and
guidance from all teaching staffs of Department of Mechanical Engineering which helped
us in successfully completing our project work. Also, we would like to extend our sincere
esteems to all staff in laboratory for their timely support.
We are extremely grateful to our parents for their silent prayer.

5. 5
TABLE OF CONTENTS
SR.NO TOPIC PAGE
NO.
1 CHAPTER 1
1.1 INTRODUCTION 5
1.2 PID CONTROL 5
1.3 HYBRID CONTROL THEORY 6
2 CHAPTER 2 – WORK PROGRESS
2.1 MECHANICAL DESIGN 7
2.2 MATHEMATICAL MODELLING 8
2.3 CAD MODELLING 12
2.4 ELECTRONICS DESIGN 15
3 CHAPTER 3 - CONCLUSION 16
4 CHAPTER 4- REFERENCES 17

6. 6
TABLE OF FIGURES
SR.NO FIGURE PAGE NO.
1 PID CONTROL 6
2 KINEMATICS 8
3 GRAPH – 1: JOINT ANGLE 10
4 GRAPH – 2: JOINT VELOCITY 10
5 GRAPH – 3: JOINT TORQUES 11
6 CAD MODEL – 1 13
7 CAD MODEL – 2 13
8 CAD MODEL – 3 14
9 CAD MODEL – 4 14
10 ENCODERS & FEEDBACK 15

7. 7
INTRODUCTION
1.1 Introduction
A serial manipulator consists of a fixed base, a series of links connected by joints, and ending
at a free end carrying the tool or the end-effector. In contrast to parallel manipulators, there
are no closed loops. By actuating the joints, one can position and orient the end-effector in a
plane or in three-dimensional (3D) space to perform desired tasks with the end-effector. An
automatically controlled, reprogrammable, [1] multipurpose manipulator programmable in
three or more axes, which may be either fixed in place or mobile for use in industrial
automation applications. In robotics, constant monitoring of positions and orientations of
manipulator links, tools, objects it handles, and other objects in the vicinity is essential.
Therefore, understanding control of robots is very important. Different approaches are
currently applied in the industry for the control of these serial manipulators. In the subject of
control theory, we find different control strategies which can be applied to control a robot.
Some of the very basic approaches are PID [2], PI [3], PD control which facilitate linear
control [4]. Some other more difficult approaches are computed torque control, hybrid
control, adaptive control, robust control, sliding mode controller and Fuzzy logic.
1.2 PID Control
Proportional Response:
The proportional component depends only on the difference between the set point and the
process variable. This difference is referred to as the Error term. The proportional
gain (Kc) determines the ratio of output response to the error signal. For instance, if the error
term has a magnitude of 10, a proportional gain of 5 would produce a proportional response
of 50. In general, increasing the proportional gain will increase the speed of the control
system response. However, if the proportional gain is too large, the process variable will
begin to oscillate. If Kc is increased further, the oscillations will become larger and the
system will become unstable and may even oscillate out of control.
Integral Response
The integral component sums the error term over time. The result is that even a small error
term will cause the integral component to increase slowly. The integral response will
continually increase over time unless the error is zero, so the effect is to drive the Steady-
State error to zero. Steady-State error is the final difference between the process variable and
set point. A phenomenon called integral windup results when integral action saturates a
controller without the controller driving the error signal toward zero.
Derivative Response
The derivative component causes the output to decrease if the process variable is increasing
rapidly. The derivative response is proportional to the rate of change of the process variable.
Increasing the derivative time (Td) parameter will cause the control system to react more
strongly to changes in the error term and will increase the speed of the overall control system
response. Most practical control systems use very small derivative time (Td), because the
Derivative Response is highly sensitive to noise in the process variable signal. If the sensor

8. 8
feedback signal is noisy or if the control loop rate is too slow, the derivative response can
make the control system unstable.
Figure 0.1: Hbrid Control
1.3 Hybrid control Theory
Discrete systems may have a set of rules and the behavior of a system will be determined by
those rules. As the system becomes more complex, more rules may be added and this kind
systems may be modelled as a hybrid system. Let's look at the case of a volume control of an
ordinary radio. [5] Assuming the volume change is decided by the logic, from one particular
volume level to next level, the current allowed to flow to the speaker may increase but there
should be no volume change in between. If we include sufficient logic for enough levels, it
will be just the same as a continuous system. The whole system become a hybrid, the top
layer you have decision logic and the bottom layer you have a system that behaves as a
continuous system. As a result, the performance of the system increases. Performance is
another important factor in control engineering. It has been well-developed over the last two
decades as a branch of control called optimal control.

9. 9
WORK PROGRESS
2.1 Mechanical Design
Degree of Freedom
It is the number of parameters that determine the state of a physical system and is important
to the analysis of systems of bodies. In our design of the articulated robotic arm we are
achieving 3 degrees of freedom.
The 3 degrees of freedom are achieved by-
1. Cylindrical joint at the base
2. Revolute joint between the base link and the mid arm
3. Revolute joint between the middle arm and the end arm
Links
Since the dimensions of an articulated robot is designed according to the requirement or the
workspace therefore, we have decided to design the robot according to the size of an average
human arm. There are going to be 3 links in this model and an end effector as a clamp. We
have decided to manufacture the links by using Aluminum Composite board since it is more
durable as compared to wood and less expansive and easy to fabricate when compared with
Acrylic. Cutting and shaping was done by cutting the board by use of cutters and then a
sudden jerk is applied to break it apart and the finishing is achieved by using sand paper
rubbing.
Aluminum Composite Board
An Aluminum composite board made of aluminum composite material (ACM), are flat
panels consisting of two thin coil-coated aluminum sheets bonded to a non-aluminum core.
ACPs are frequently used for external cladding or facades of buildings, insulation,
and signage. ACP is also widely used within the signage industry as an alternative to heavier,
more expensive substrates. ACP has been used as a light-weight but very sturdy material in
construction, particularly for transient structures like trade show booths and similar
temporary elements.
Mechanical properties:
The space between the supports can be up to 11 m (walls), depending on the type of panel
used. Normal applications have spaces between the supports that are approx. 3 m – 5 m.
The thickness of panels is from 40 mm up to more than 200 mm.
The density of sandwich panels range from 10 kg/m2
up to 35 kg/m2
, depending on the foam
and metal thickness, decreasing time and effort in: transportation, handling and installation.
All these geometric and material properties influence the global/local failure behavior of the
sandwich panels under different loading conditions such as indentation, impact, fatigue and
bending.

10. 10
Gripper
Grippers are difficult to be fabricated because they need much precision which is very much
difficult to be achieved via mechanical in house fabrication. So we have used a gripper
fabricated by mechatronics engineers private limited. Grippers are the end effectors used for
holding the parts or objects. Grippers are devices which can be used for holding or gripping
an object. Grippers should be designed so that it requires the minimum amount of
maneuvering in order to grip the work piece. The two-finger gripper is driven by a DC servo
motor and a gear-and-rack mechanism. 13cm is total length of the 3rd
link including gripper
because there is no joint between the link and the gripper that’s why there is no relative
movement, so no need consider gripper as another link.
Gear and Rack mechanism: movement of input due to gear motion which makes connecting
links to go in motion to make gripping action at the output link.
Technical Details
Material Type: Acrylic
Weight: 249 g
Package Dimensions: 18 x 12 x 5 cm
Item part number: 503/1
Figure 0.1: gripper
Joints
The links will be interconnected with each other with help of a free pin joints i.e. the axis of
rotation will be along the shaft used for pin joint. The material of the shaft will be cast iron or
steel, basically the one which is easily procurable.
Motor Mounting Technique and Torque Control Mechanisms

11. 11
The individual motors responsible for the motion of each arm will be mounted on the arm
with the help of ties and fixed with help of adhesives and silicon glue gun. To transfer the
motion from the motors to the links we are going to connect the shaft of motor and the link
with plastic couplings. They are already available or provided by the servo manufacturers.
These are just the couplings which are used to mount these motors.
Figure 0.2: motor mountings
Material Requirement
 Aluminium Composite Board– Links
 Steel - Shafts
 Bolts & Nuts – End effector working
 Silicon Gun and Adhesives – For fixing the links to a common base

12. 12
2.2 Mathematical Modelling
Denavit Hartenberg Parameters:
The architecture of industrial robots is usually represented by Denavit‐Hartenberg (DH)
parameters. It forms the basis for performing kinematic and dynamic analyses of robots. A set
of four DH parameters is used to represent the position and orientation of a robot‐link with
respect to its previous link.
Sr no. Link length
(a)m
Joint offset
(b)m
Joint angle
(theta) degree
Twist angle
(alpha) degree
1. 0 0.14 Variable 90
2. 0.95 0 Variable 0
3. 0.13 0 Variable 0
Direct Kinematics
If we state the end effector coordinates of manipulator based on the angles of the joints, it
means the forward kinematics. In other word, in forward kinematics, the measures of the joint
space are available and we want to determine the measures of coordinate space. In reality,
forward kinematics analyzing is a mapping from joint space to the coordinate space.
According to Figure 2 the forward kinematics of the 3DOF articulated manipulator has been
determined as shown below:
Figure 0.3: 3 DOF Serial manipulator
Px = (l2cosθ2 + l3cos(θ2+θ3) × sinθ1
(1)
Py = (l2cosθ2 + l3cos(θ2+θ3) × cosθ1
(2)
Pz = (l2cosθ2 + l3cos(θ2+θ3) + l1
(3)

13. 13
Where l1, l2 and l3 are the length of the links, where q1, q2 and q3 are θ1, θ2, and θ3
respectively.
Inverse Kinematics
By inversing the forward kinematics definition, we have inverse kinematics definition. By
these equations we can find the appropriate angles for the desired end effector coordinates.
According to the two definitions of kinematics, it is clear that the inverse kinematics is more
sophisticated than the inverse kinematics. According to the Figure 2 we have:
θ1= a tan2(Py ,Py)
(4)
r = ± (Px
2
+ Py
2
)1/2
(5)
D = ±((Pz- l1)2
+ r2
)1/2
(6)
θ3 = a cos(D2
– l3
2
– l2
2
/ 2l2l3 )
(7)
θ2 = a tan2(r1,Pz – l1) – a tan2(l2 +l3cos θ3 , l3sinθ3)
(8)
Velocity kinematics
In order to design a controller to track a path we need to have relations between velocity of
the joints and velocity of the end effector that are named as velocity kinematics. In this case
we derive the differential equations of (1),(2),(3).
Xdot = (cosθ1*(l3cos(θ2+θ3) + l2cosθ2))*θ1dot – (sinθ1*(l3sin(θ2+θ3) + l2sin θ2))* θ2dot –
(l3sin(θ2+θ3)*sin θ1)*θ3dot
….(9)
Ydot = (-sinθ1*(l3cos(θ2+θ3) + l2cosθ2))* θ1dot - (cosθ1*(l3sin(θ2+θ3) + l2sin θ2))*θ2dot-
(l3sin(θ2+θ3)*cos θ1)*θ3dot
….(10)
Zdot = (l3cos(θ2+θ3)* l2cosθ2)*θ2dot + (l3cos(θ2+θ3))* θ3dot
….(11)
Thus, the Jacobian matrix can be determined from the above equations:
J =

14. 14
Where, S denotes sin and C denotes cos and J denotes the Jacobina matrix.
The determinant of the above matrix is given by the equation given below. The roots of the
equation given below are the singular points of the manipulator. Singular points of a
manipulator are those points where the manipulator cannot move in a certain direction.
Figure 0.4: RoboAnalyzer graph for joint angle
Figure 0.5: RoboAnalzer graph for joint velocity

15. 15
Trajectory Planning:
The trajectory planning is normally carried out in the joint space of the robot, after a
kinematic inversion of the given geometric path. The joint trajectories are then obtained by
means of interpolating functions which meet the imposed kinematic and dynamic constraints.
Planning a trajectory in the joint space rather than in the operating space has an advantage
that the control system acts on the robot's joints rather than on the end effector, so it would be
easier to adjust the trajectory according to the design requirements if working in the joint
space. Trajectory generation in the joint space would allow to avoid the problems arising with
kinematic singularities. The trajectory generation must fulfill the constraint set on the
maximum values of the generalized joint torques and must be such that no mechanical
resonance mode is excited. This can be achieved by smooth trajectories (continuity in
position, velocity, and acceleration). The joint variables as that of position, velocity,
acceleration, etc. must be continuous function of time and also smooth. In this we will use
quantic polynomial trajectory.
Quintic Trajectory Planning:
A cubic trajectory gives continuous positions and velocities at the start and finish points times
but discontinuities in the acceleration. The derivative of acceleration is called the jerk. A
discontinuity in acceleration leads to an impulsive jerk, which may excite vibrational modes
in the manipulator and reduce tracking accuracy. For this reason, one may wish to specify
constraints on the acceleration as well as on the position and velocity. In this case, we have
six constraints (one each for initial and final configurations, initial and final velocities, and
initial and final accelerations). Therefore, we require a fifth order polynomial

16. 16
Dynamic modelling:
The dynamical analysis of the robot investigates a relation between the joint torques/forces
applied by the actuators and the position, velocity and acceleration of the robot arm with
respect to the time. Dynamics of the robot manipulators is complex and nonlinear that might
make accurate control difficult. The dynamic equations of the robot manipulators are usually
represented by the following coupled non-linear differential equations which have been
derived from Langragians.
Q = M(q)q``+ C(q)q`+ G(q)
Where is M(q) the inertia matrix, is the C(q) Coriolis /centripetal matrix, is the G(q) gravity
vector, and Q is the control input torque. The joint variable q is an n-vector containing the
joint angles for revolute joints.
Figure 0.6: Joint torque comparison
Max value of torque generated:
Using 500 steps for 5 seconds in simulation, the max value of torque is obtained in the 236th
step. We get thus value of 2.1732Nm. Thus, incorporating a certain factor of safety, we
decide to use a motor with torque no less than 3Nm. When

17. 17
2.3 CAD Modelling:
Assembly of the 3d model is developed using Catia. This is done to get a better idea before
the fabrication of the model begins. This model is not to scale and the appropriate lengths
will be generated once the torque equations are generated.

18. 18
2.4 Electronics Design
Simultaneous work for developing a code to control motors and generate feedback with the
help of servo motors. DC motors with encoder control are used to generate feedback. This is
done to implement closed loop algorithm.
Closed loop algorithm with the help of encoder feedback will be implemented in the near
future.
DC motors

19. 19
Material Procurement:
o Arduino Uno
o Servo Motors
o Gripper Fitted with SG90 Servo
o Jumper wires
o Adapter(5V)
o Resistors
Arduino Uno:
The Uno is a microcontroller board based on the ATmega328P. It has 14 digital input/output
pins (of which 6 can be used as PWM outputs), 6 analog inputs, a 16 MHz quartz crystal, a
USB connection, a power jack, an ICSP header and a reset button. It contains everything
needed to support the microcontroller; simply connect it to a computer with a USB cable or
power it with a AC-to-DC adapter or battery to get started. Anyone can tinker with the UNO
without worrying too much about doing something wrong, worst case scenario you can
replace the chip for a few dollars and start over again. ”Uno” means one in Italian and was
chosen to mark the release of Arduino Software (IDE) 1.0. The Uno board and version 1.0 of
Arduino Software (IDE) were the reference versions of Arduino, now evolved to newer
releases. The Uno board is the first in a series of USB Arduino boards, and the reference
model for the Arduino platform; for an extensive list of current, past or outdated boards see
the Arduino index of boards. There is a USB connector for talking to the host computer and a
DC power jack for connecting an external 6-20 V power source, for example a 9 V battery,
when running a program while not connected to the host computer. Headers are provided for
interfacing to the I/O pins using 22 g solid wire or header connectors.
Figure 0.7: Arduino Uno
Servo Motors:
A servo motor is an electrical device which can push or rotate an object with great precision. To rotate
and object at some specific angles or distance, servo motor is used. It is just made up of simple motor
which run through servo mechanism. If motor is used is DC powered then it is called DC servo motor,
and if it is AC powered motor then it is called AC servo motor. We can get a very high torque servo
motor in a small and light weight packages. Doe to these features they are being used in many
applications like toy car, RC helicopters and planes, Robotics, CNC Machine etc. The position of a
servo motor is decided by electrical pulse and its circuitry is placed beside the motor. The servo used
is a MG996 motor. MG996 Metal Gear Servo Motor is a rapid standard servo can pivot around 180
degrees (60 toward every path).
Features:
Weight: 55g

20. 20
Dimension: 40.7 × 19.7 × 42.9 mm
Operating Speed (4.8V no load): 20sec / 60 deg
Operating Speed (6.0V no load): 16sec / 60 deg (no load)
Stall Torque (4.8V): 10kg/cm
Stall Torque (6.0V): 12kg/cm
Operation Voltage: 4.8 - 7.2Volts
Gear Type: All Metal Gears
Stable and shock proof double ball bearing design
Dead band width: 5 µs
Temperature range: 0 ºC – 55 ºC.
Control System: Analog
Operating Angle: 120degree
Required Pulse: 900us-2100us
Figure 0.8: MG996R servo motor
Circuit Diagram:
The below circuit diagram explains how the 4 motors take in how the motors are connected to
power and also take the pwm signals form the Arduino. This circuit diagram is made using
Proteus software.

21. 21
Figure 0.9: Circuit diagram for position control of motors

22. 22
A NEW APPROACH
3.1: Position Control Mechanism:
The position control theory is achieved by the use of Servo motors.
A servo motor is a closed-loop system that uses position feedback to control its motion and
final position. In industrial type servo motors the position feedback sensor is usually a high
precision encoder, while in the hobby servos the position sensor is usually a simple
potentiometer. The actual position captured by these devices is fed back to the error detector
where it is compared to the target position. Then according to the error the controller corrects
the actual position of the motor to match with the target position. Inside a hobby servo there
are four main components a DC motor, a gearbox, a potentiometer and a control circuit. The
DC motor is high speed and low torque but the gearbox reduces the speed to around 60 RPM
and at the same time increases the torque. The potentiometer is attached on the final gear or
the output shaft, so as the motor rotates the potentiometer rotates as well, thus producing a
voltage that is related to the absolute angle of the output shaft. In the control circuit, this
potentiometer voltage is compared to the voltage coming from the signal line. If needed, the
controller activates an integrated H-Bridge which enables the motor to rotate in either
direction until the two signals reach a difference of zero.
A servo motor is controlled by sending a series of pulses through the signal line. The
frequency of the control signal should be 50Hz or a pulse should occur every 20ms. The
width of pulse determines angular position of the servo and these type of servos can usually
rotate 180 degrees (they have a physical limits of travel).
Generally, pulses with 1ms duration correspond to 0 degrees position, 1.5ms duration to 90
degrees and 2ms to 180 degrees. Though the minimum and maximum duration of the pulses
can sometimes vary with different brands and they can be 0.5ms for 0 degrees and 2.5ms for
180 degrees position.
Figure 0.1 internal Servo mechanism

23. 23
3.2 Force Control Mechanism:
Generally, the most used and easiest way of applying a force control mechanism in a serial
manipulator is by placing a sensor in the actuating element and generating a closed loop
mechanism such that it can control the torque and motion accordingly.
We have used a new approach which uses a force sensor which detects the force or weight of
a body and then accordingly the motor will be controlled.
Force sensor - The most basic force sensor is a simple force sensitive resistor. These are
mechanical pressure sensors. Force sensing resistor can be defined as a special type of
resistor whose resistance can be varied by varying the force or pressure applied to it. The
FSR sensors are made of conductive polymer which has a property of changing its resistance
based on the force applied to its surface. If force is applied to a surface of sensing film, then
the particles touches the conducting electrodes and thus resistance of the film changes.
Simply speaking the control electronics adjust shaft position by controlling DC motor. This
data regarding position of shaft is sent through the signal pin. The position data to the control
should be sent in the form of PWM signal through the signal pin of servo motor. The
frequency of PWM (Pulse Width Modulated) signal can vary based on type of servo motor.
The important thing here is the duty ratio of the PWM signal. Based on this duty ratio the
control electronics adjust the shaft. When the weight is applied on top of force sensor, the
resistance is changed drastically. The resistance of a pure conductor is given by:
Where,
P= Resistivity of conductor
l= Length of conductor
A= Area of conductor.
Now consider a conductor with resistance “R”, if some pressure is applied on top of
conductor, the area on conductor decreases and the length of conductor increases as a result
of pressure. So by formula the resistance of conductor should increase, as the resistance R is
inversely proportional to area and also directly proportional to length l. So with this for a
conductor under pressure or weight the resistance of conductor increases. But this change is
small compared to overall resistance. For a considerable change many conductors are
stacked together.
This change in resistance can do no good unless we can read them. The controller at hand can
only read the chances in voltage and nothing less, for this we are going to use voltage divider
circuit, with that we can derive the resistance change as voltage change. Voltage divider is a
resistive circuit . In this resistive network we have one constant resistance and other variable
resistance. As shown in figure, R1 here is a constant resistance and R2 is FORCE sensor
which acts as a resistance. The midpoint of branch is taken to measurement. With R2 change,
we have change at Vout. So with this we have a voltage which changes with weight. Now
when the force is applied on the force sensor, the voltage at divider end changes this pin as
connected to ADC channel of UNO, we will get a different digital value from ADC of UNO,
whenever force on sensor changes. This ADC digital value is matched to the duty ratio of
PWM signal, so we have the servo position control in relation to force applied on sensor.
Below circuit diagram shows pressure sensor

24. 24
Figure 0.2: Circuit diagram for pressure sensors

25. 25
CONCLUSION
We have completed the dynamic analysis of the serial manipulator. We have selected the
motors with the required torques. The robot joint mechanism is completed with linkages.
Electronics of the robot is under study. Fabrication of robot links is also completed and we
can now use the robot to perform small pick and place operations.

26. 26
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