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A
Project Proposal
on
UNIVERSAL TESTING MACHINE WITH LOAD CAPACITY OF 0.3KN
for
Core project (CPP301)
Under
Dr.Dhiraj k.Mahajan
Assistant Professor
School of Mechanical, Materials & Energy Engineering (SMMEE)
Indian Institute of Technology Ropar
Rupnagar 140001
Punjab
Submitted by
Aashish Kholiya
2012meb1083
K.Raviteja
2012meb1103
Fast Track Proposal Scheme for Young Scientist
1. Broad subject area (Physical Sciences, Mathematical Sciences, Engineering
Sciences):
Engineering Science
2. Specialization : Mechanics of Material, Machine element design ,Control engineering
3. Title of the proposed project:
Universal Testing Machine for max load capacity 300 N.
4. Name and address of the Investigator:
Aashish Kumar Kholiya
Room Number 305, Wing-A, Mercury Hostel
School of Mechanical Material and Energy Engineering
Indian Institute of Technology, Ropar
Nangal Road, Rupnagar-140001, Punjab, India.
Phone:8968112819
Email: aashishkk@iitrpr.ac.in
Ravi Teja
Room Number 408,Wing-A ,Mercury Hostel
School of Mechanical Material and Energy Engineering
Indian Institute of Technology, Ropar
Nangal Road, Rupnagar-140001, Punjab, India.
Phone:8288909899
Email:kurichetir@iitrpr.ac.in
5. Details of the proposed project to be undertaken:
5.1 Origin of proposal
Now a days in many applications polymers are playing major role because of its advanced
properties like low cost, corrosion resistive and some other issues. For this importance of
polymers we need to find the mechanical properties
Universal testing machines (UTMs) that test mechanical properties such as tensile, flexural,
compressive and shear are among the most commonly used instruments plastics compounders.
Product development is among the key reasons compounders and resin makers test compounds
and resins with UTMs. Others include testing the material to determine its suitability for various
plastics processes and whether its properties will meet the particular end-use application, as well
as for quality control following development to ensure lot-to-lot consistency. However, increased
interest in improving quality control either of incoming material, or, more importantly, at the end
of the manufacturing process, as well as product and process development, has led many
processors to consider a UTM when outfitting or upgrading a lab.
5.2 Research work engaged in at present:
5.2.1 Design of ball screw and collar
For designing ball screw and collar we have taken pitch is equal to lead or single thread because
this is more efficient than double thread. Higher precision can obtained by taking pitch as minimum
as possible by considering manufacturing limitations. In our case we have decided our pitch 5mm.
And efficiency of ball screw is taken 90% by literature survey.
Maximum load in axial direction is 300 N, we calculated critical diameter by considering three
cases. These are (i) Buckling (ii) Tensile and Compressive (iii) Shear
(i) Buckling
It is necessary that it satisfy specific strength, and deflection and stability requirements.
If these member are long the loading may be large enough to deform member in lateral
direction.
π‘ƒπ‘π‘Ÿ =
𝑓𝑠. πœ‹2
. 𝐸. 𝐼
𝐿2
Pcr = Critical load on the column just before it begins to buckle.
E = Modulus of elasticity for the material
I = Least Moment of inertia for the column’s cross sectional area
L = Unsupported length of the column, whose ends are pinned
Fs =factor of safety
In our case Pcr = 300 N
𝐼 = πœ‹. (
𝑑
2
)
4
.
1
4
𝑑 = (
𝑓𝑠.𝑃 π‘π‘Ÿ.𝐿2
πœ‹3. 𝐸
)
1
4
(ii) Tensile and compression
To prevent with yielding of ball screw it is necessary to consider tensile and
compression
Strength of member.
𝜎 < 𝜎 𝑦𝑖𝑒𝑙𝑑
𝜎 =
πΏπ‘œπ‘Žπ‘‘
πΆπ‘Ÿπ‘œπ‘ π‘  π‘ π‘’π‘π‘‘π‘–π‘œπ‘› π‘Žπ‘Ÿπ‘’π‘Ž
𝑑 = (
4.πΏπ‘œπ‘Žπ‘‘
πœ‹.𝜎 𝑦𝑖𝑒𝑙𝑑
)
1
4
(ii) Tensile and shear stress
In dynamic condition there is moment associated with ball screw because of rotation
Of ball screw by stepper motor. Here we have consider max shear stress criteria.
Considering maximum shear stress
𝑇 =
π‘™π‘œπ‘Žπ‘‘ . π‘ƒπ‘–π‘‘π‘β„Ž
2πœ‹. πœ‚
𝜏 π‘€π‘Žπ‘₯ = √((
𝜎
2
)
2
+ 𝜏2)
5.2.2 Design of Base Plate
In experiment in universal testing machine we fix one end of ball screw on base plate an.
At the center of base plate where the grippers are connected, the tensile forces or pressure
force acting on area of gripper’s cross section. To prevent the yielding at the cross section
and base plate. We have to choose the thickness of base plate which has to overcome
that yielding.
By considering max load 300N we had obtained required thickness of the base plate by
using CAE software ( Abaqus).
Results obtained in abaqus: -
Thickness =2 cm
Pressure force on 20 mm circle at center of square.
Force 300 N
Thickness = 3cm
Thickness =3.5 cm
Thickness = 4 cm
5.2.3 Selection of Transducers
1. Linear Encoder
A linear encoder is a sensor, transducer paired with a scale that encodes
position. The sensor reads the scale in order to convert the encoded position into
an analog or digital signal, which can then be decoded into position by a digital
readout (DRO) or motion controller.
Linear encoders are two types
ο‚· Absolute linear encoders
This encoder says the position of the positioner at difference points but it is
not able to measure displacement from reference point
ο‚· Incremental linear encoders
Incremental Linear encoder will give high accurate results.it measures the
displacement of the positioner from the initial point .Here we are using
optical incremental linear encoder. Optical linear encoders dominate the
high resolution market and may employ shuttering, diffraction or holographic
principles. Optical encoders are the most accurate of the standard styles of
encoders, and the most commonly used in industrial automation applications.
When specifying an optical encoder, it’s important that the encoder has extra
protection built in to prevent contamination from dust, vibration and other
conditions common to industrial environments. Typical incremental scale
periods vary from hundreds down to sub-micrometer and following
Interpolation can provide resolutions as fine as a nanometer
Our specifications:
Travel distance - 300mm
Resolution - 1 Β΅m
Incremental linear encoder gives output in terms of pulses and resolution
also depends on PPR
For cross checking of displacement we have a formula
Amount of displacement = EDGE – COUNT
xN . PPI
N = number of pulses generated by the encoder per shaft revolution
x = encoding type
PPI= pulse per revolution
Edge and count values get from encoder
2. Load Cell
A load cell is a transducer that is used to create an electrical signal whose
Magnitude is directly proportional to the force being measured. Here we are
Going to use S-TYPE load cell because S-Type load cells are low-cost and
high performance side mounted load cells suitable for a number of weighing
and general force measurement applications
5.2.4 Selection of Stepper Motor
Accuracy and resolution is depend upon the motor. Stepper motor can give more
accuracy then servo.
Specifications:
Torque - A stepper motor has about the same torque as a comparably sized servo
Motor frame.
A servo motor offers an additional time-dependent peak toque rating, a more flexible
Speed curve, and higher performance but a properly sized stepper motor could help
You realize a better cost savings over a servo. If an application requires complete
Standstill stability, a stepper motor is the better choice
5.3 Objectives of the proposed project
Main objective of our project is universal testing machine with
1. Low cost
2. High accuracy and precision
5.4 Review of R&D in the proposed area (National & International Status, Importance,
patents etc.):
5.5 Work plan (including detailed methodology and time schedule)
5.5.1 Methodology
1. Design of ball screw
In universal testing machine we are using ball screw .Design of the ball screw is based
upon the following properties
ο‚· Buckling
ο‚· Shear
ο‚· Compression and tension
By doing all the above tests we finally decided the diameter of the ball screw is
30mm and pitch of the ball screw
2. Selection of Stepper Motor & Selection of Transducers
Stepper motor is chosen under the importance of accuracy and resolution of UTM.
Stepper gives more accurate results as compared with servo. Generally in motors,
accuracy is depend on no of degree of rotation for one revolution. Stepper give 1 degree
of rotation for one revolution of ball screw. Degree of rotation need to be as much as less
for accurate results.so we are going decrease that degree of rotation by arranging gears.
Stepper motor is less expansive.so stepper is suitable for our application
Transducers also play important role in accuracy and resolution. We have chosen the
following transducers as per our requirements
ο‚· Linear encoder
Optical linear encoder is preferred for our universal testing machine. We had
referred many papers for finalizing the encoder. Generally these are the errors that
arise in encoders are follows
I. Positioning errors due to thermal behavior of the recirculating ball screw
II. Back lash
These errors are less in optical linear encoder.so it gives more accurate
results then other encoders. We finally decided the linear encoder with
travel distance 300mm and accuracy 1Β΅m
ο‚· Load cell
Load cell is used for finding force. Our load is static and mounting is inline, load
direction is axial to the ball screw (Z-axis).the load need to give high accurate
results and also it need to be less expensive .for above specification S-type load
cell suits better.so we had chosen S-type load cell
3. Simulation and Problem recognitions
Necessity of simulation in our project is only for finding dimensions of base plate. Base
plate has to bare the lode capacity of 30kg.we made the simulation in abacus with fixed
dimensions of 300mm length and 300mm breath with varying thickness. Thickness of
10mm, 15mm, 20mm, and 25mm.we had absorbed the deformation (u) at the point where
the gripper is going to fix, deformation is absorbed with varying thickness by doing
simulation in abacus. But many problems had been raised in that simulation process like
for cross checking the results we repeat the process but results had absorbed is different.
But finally we concluded that results by repeating the same process many times. Here the
dimensions of base plate
Length - 300mm
Breath - 300mm
Thickness - 30mm
4. Assembly of Components
Components:
I. Linear encoder
II. Stepper motor
III. Base plate
IV. Ball screw
V. Frame for attaching ball screw
VI. Controllers
VII. Cylindrical rods
VIII. Gears
The above components have been assembled according to the design
1. Cylindrical columns
2. Ball screw
3. Cross head
4. Load cell
5. Gripper
6. Base plate
7. Stepper motor
8. gears
5. Controller
Controllers is needed for every component. ARDUINO controllers is preferred because these
controllers are more accurate and less expansive.
6. Results
Finalized the dimensions and requirements or specifications of components
Stepper motor:
Considering ball screw parameter and max load capacity we get stepper motor torque.
Required torque - 265 mNm
Base plate
Dimensions of base plate
Length - 300mm
Breath - 300mm
Thickness - 30mm
Material - stainless steel
We did the simulation in abaqus with constant length and breath but thickness is different.
The results is shown below
Linear encoder
It measures the position of linear axis without any additional mechanical transfer elements
Optical linear encoder is preferred because the befits of this encoder is clearly explained
above
Travel distance - 300mm
Resolution - 1 Micrometer
Load cell
They are 5 types of load cell is available in market
Preferred load cell for our UTM - S-type
Load capacity - 300NM
Ball screw
Generally lead screw is used in universal testing machine but our case we are using ball
screw because ball screw give smooth movement without any errors
Stroke - 300mm
Pitch - 5mm
Length between both bearings - 500mm
5.5.2 Time Schedule
Table 2: Time Schedule of Work Plan
Months Aug. Sep. Oct. Nov. Jan. Feb. Mar. Apr.
Activities Week
1 & 2
Week
3 & 4
Week
1 & 2
Week
4
Week
1,2 &3
1.
2.
3.
4.
5.
6.
6. Name and address of the institution where the proposal will be/likely to be executed:
Indian Institute of Technology Ropar, Distt. - Rupnagar, Punjab-140001
1.1.1.1.1.1Detailed Biodata
Applicant No. 1
1. Name of the Applicant : kuricheti ravi teja
2. Mailing Address : kurichetir@iitrpr.ac.in
3. Date of Birth : December 25, 1994
4. Educational Qualifications (Starting from Graduation onwards): undergraduate
S.No. Degree University Year Subjects Percentage
1. B.Tech IIT Ropar 2012-
2016*
ME
1.1.2 Place & date: Signature of the applicant
Applicant No. 2
1. Name of the Applicant : Aashish kholiya
2. Mailing Address : aashishkk@iitrpr.ac.in
3. Date of Birth : January 28, 1995
4. Educational Qualifications (Starting from Graduation onwards):
S.No. Degree University Year Subjects Percentage
1. B.Tech IIT Ropar 2012-
2016*
ME
1.1.3 Place & date: Signature of the applicant
Reference
[1] V.B.BHANDARI,Design of machine elements,3rd
edition
[2] RUSSELL C.HIBBELER ,Mechanics of materials,9th
edition
[3] ROBERT NORTON, An introduction to the synthesis and analysis of mechanisms,2nd
edition

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Universal Testing Machine

  • 1. A Project Proposal on UNIVERSAL TESTING MACHINE WITH LOAD CAPACITY OF 0.3KN for Core project (CPP301) Under Dr.Dhiraj k.Mahajan Assistant Professor School of Mechanical, Materials & Energy Engineering (SMMEE) Indian Institute of Technology Ropar Rupnagar 140001 Punjab Submitted by Aashish Kholiya 2012meb1083 K.Raviteja 2012meb1103
  • 2. Fast Track Proposal Scheme for Young Scientist 1. Broad subject area (Physical Sciences, Mathematical Sciences, Engineering Sciences): Engineering Science 2. Specialization : Mechanics of Material, Machine element design ,Control engineering 3. Title of the proposed project: Universal Testing Machine for max load capacity 300 N. 4. Name and address of the Investigator: Aashish Kumar Kholiya Room Number 305, Wing-A, Mercury Hostel School of Mechanical Material and Energy Engineering Indian Institute of Technology, Ropar Nangal Road, Rupnagar-140001, Punjab, India. Phone:8968112819 Email: aashishkk@iitrpr.ac.in Ravi Teja Room Number 408,Wing-A ,Mercury Hostel School of Mechanical Material and Energy Engineering Indian Institute of Technology, Ropar Nangal Road, Rupnagar-140001, Punjab, India. Phone:8288909899 Email:kurichetir@iitrpr.ac.in
  • 3. 5. Details of the proposed project to be undertaken: 5.1 Origin of proposal Now a days in many applications polymers are playing major role because of its advanced properties like low cost, corrosion resistive and some other issues. For this importance of polymers we need to find the mechanical properties Universal testing machines (UTMs) that test mechanical properties such as tensile, flexural, compressive and shear are among the most commonly used instruments plastics compounders. Product development is among the key reasons compounders and resin makers test compounds and resins with UTMs. Others include testing the material to determine its suitability for various plastics processes and whether its properties will meet the particular end-use application, as well as for quality control following development to ensure lot-to-lot consistency. However, increased interest in improving quality control either of incoming material, or, more importantly, at the end of the manufacturing process, as well as product and process development, has led many processors to consider a UTM when outfitting or upgrading a lab. 5.2 Research work engaged in at present: 5.2.1 Design of ball screw and collar For designing ball screw and collar we have taken pitch is equal to lead or single thread because this is more efficient than double thread. Higher precision can obtained by taking pitch as minimum as possible by considering manufacturing limitations. In our case we have decided our pitch 5mm. And efficiency of ball screw is taken 90% by literature survey. Maximum load in axial direction is 300 N, we calculated critical diameter by considering three cases. These are (i) Buckling (ii) Tensile and Compressive (iii) Shear (i) Buckling It is necessary that it satisfy specific strength, and deflection and stability requirements. If these member are long the loading may be large enough to deform member in lateral direction. π‘ƒπ‘π‘Ÿ = 𝑓𝑠. πœ‹2 . 𝐸. 𝐼 𝐿2 Pcr = Critical load on the column just before it begins to buckle. E = Modulus of elasticity for the material I = Least Moment of inertia for the column’s cross sectional area L = Unsupported length of the column, whose ends are pinned Fs =factor of safety In our case Pcr = 300 N
  • 4. 𝐼 = πœ‹. ( 𝑑 2 ) 4 . 1 4 𝑑 = ( 𝑓𝑠.𝑃 π‘π‘Ÿ.𝐿2 πœ‹3. 𝐸 ) 1 4 (ii) Tensile and compression To prevent with yielding of ball screw it is necessary to consider tensile and compression Strength of member. 𝜎 < 𝜎 𝑦𝑖𝑒𝑙𝑑 𝜎 = πΏπ‘œπ‘Žπ‘‘ πΆπ‘Ÿπ‘œπ‘ π‘  π‘ π‘’π‘π‘‘π‘–π‘œπ‘› π‘Žπ‘Ÿπ‘’π‘Ž 𝑑 = ( 4.πΏπ‘œπ‘Žπ‘‘ πœ‹.𝜎 𝑦𝑖𝑒𝑙𝑑 ) 1 4 (ii) Tensile and shear stress In dynamic condition there is moment associated with ball screw because of rotation Of ball screw by stepper motor. Here we have consider max shear stress criteria. Considering maximum shear stress 𝑇 = π‘™π‘œπ‘Žπ‘‘ . π‘ƒπ‘–π‘‘π‘β„Ž 2πœ‹. πœ‚ 𝜏 π‘€π‘Žπ‘₯ = √(( 𝜎 2 ) 2 + 𝜏2)
  • 5. 5.2.2 Design of Base Plate In experiment in universal testing machine we fix one end of ball screw on base plate an. At the center of base plate where the grippers are connected, the tensile forces or pressure force acting on area of gripper’s cross section. To prevent the yielding at the cross section and base plate. We have to choose the thickness of base plate which has to overcome that yielding. By considering max load 300N we had obtained required thickness of the base plate by using CAE software ( Abaqus). Results obtained in abaqus: - Thickness =2 cm Pressure force on 20 mm circle at center of square. Force 300 N
  • 7. Thickness = 4 cm 5.2.3 Selection of Transducers 1. Linear Encoder A linear encoder is a sensor, transducer paired with a scale that encodes position. The sensor reads the scale in order to convert the encoded position into an analog or digital signal, which can then be decoded into position by a digital readout (DRO) or motion controller. Linear encoders are two types ο‚· Absolute linear encoders This encoder says the position of the positioner at difference points but it is not able to measure displacement from reference point ο‚· Incremental linear encoders Incremental Linear encoder will give high accurate results.it measures the displacement of the positioner from the initial point .Here we are using optical incremental linear encoder. Optical linear encoders dominate the high resolution market and may employ shuttering, diffraction or holographic principles. Optical encoders are the most accurate of the standard styles of encoders, and the most commonly used in industrial automation applications. When specifying an optical encoder, it’s important that the encoder has extra protection built in to prevent contamination from dust, vibration and other conditions common to industrial environments. Typical incremental scale periods vary from hundreds down to sub-micrometer and following Interpolation can provide resolutions as fine as a nanometer Our specifications: Travel distance - 300mm Resolution - 1 Β΅m
  • 8. Incremental linear encoder gives output in terms of pulses and resolution also depends on PPR For cross checking of displacement we have a formula Amount of displacement = EDGE – COUNT xN . PPI N = number of pulses generated by the encoder per shaft revolution x = encoding type PPI= pulse per revolution Edge and count values get from encoder 2. Load Cell A load cell is a transducer that is used to create an electrical signal whose Magnitude is directly proportional to the force being measured. Here we are Going to use S-TYPE load cell because S-Type load cells are low-cost and high performance side mounted load cells suitable for a number of weighing and general force measurement applications 5.2.4 Selection of Stepper Motor Accuracy and resolution is depend upon the motor. Stepper motor can give more accuracy then servo. Specifications: Torque - A stepper motor has about the same torque as a comparably sized servo Motor frame. A servo motor offers an additional time-dependent peak toque rating, a more flexible Speed curve, and higher performance but a properly sized stepper motor could help You realize a better cost savings over a servo. If an application requires complete Standstill stability, a stepper motor is the better choice 5.3 Objectives of the proposed project Main objective of our project is universal testing machine with 1. Low cost 2. High accuracy and precision
  • 9. 5.4 Review of R&D in the proposed area (National & International Status, Importance, patents etc.): 5.5 Work plan (including detailed methodology and time schedule) 5.5.1 Methodology 1. Design of ball screw In universal testing machine we are using ball screw .Design of the ball screw is based upon the following properties ο‚· Buckling ο‚· Shear ο‚· Compression and tension By doing all the above tests we finally decided the diameter of the ball screw is 30mm and pitch of the ball screw 2. Selection of Stepper Motor & Selection of Transducers Stepper motor is chosen under the importance of accuracy and resolution of UTM. Stepper gives more accurate results as compared with servo. Generally in motors, accuracy is depend on no of degree of rotation for one revolution. Stepper give 1 degree of rotation for one revolution of ball screw. Degree of rotation need to be as much as less for accurate results.so we are going decrease that degree of rotation by arranging gears. Stepper motor is less expansive.so stepper is suitable for our application Transducers also play important role in accuracy and resolution. We have chosen the following transducers as per our requirements ο‚· Linear encoder Optical linear encoder is preferred for our universal testing machine. We had referred many papers for finalizing the encoder. Generally these are the errors that arise in encoders are follows I. Positioning errors due to thermal behavior of the recirculating ball screw II. Back lash These errors are less in optical linear encoder.so it gives more accurate results then other encoders. We finally decided the linear encoder with travel distance 300mm and accuracy 1Β΅m ο‚· Load cell Load cell is used for finding force. Our load is static and mounting is inline, load direction is axial to the ball screw (Z-axis).the load need to give high accurate results and also it need to be less expensive .for above specification S-type load cell suits better.so we had chosen S-type load cell
  • 10. 3. Simulation and Problem recognitions Necessity of simulation in our project is only for finding dimensions of base plate. Base plate has to bare the lode capacity of 30kg.we made the simulation in abacus with fixed dimensions of 300mm length and 300mm breath with varying thickness. Thickness of 10mm, 15mm, 20mm, and 25mm.we had absorbed the deformation (u) at the point where the gripper is going to fix, deformation is absorbed with varying thickness by doing simulation in abacus. But many problems had been raised in that simulation process like for cross checking the results we repeat the process but results had absorbed is different. But finally we concluded that results by repeating the same process many times. Here the dimensions of base plate Length - 300mm Breath - 300mm Thickness - 30mm 4. Assembly of Components Components: I. Linear encoder II. Stepper motor III. Base plate IV. Ball screw V. Frame for attaching ball screw VI. Controllers VII. Cylindrical rods VIII. Gears The above components have been assembled according to the design
  • 11. 1. Cylindrical columns 2. Ball screw 3. Cross head 4. Load cell 5. Gripper 6. Base plate 7. Stepper motor 8. gears 5. Controller Controllers is needed for every component. ARDUINO controllers is preferred because these controllers are more accurate and less expansive. 6. Results Finalized the dimensions and requirements or specifications of components Stepper motor: Considering ball screw parameter and max load capacity we get stepper motor torque.
  • 12. Required torque - 265 mNm Base plate Dimensions of base plate Length - 300mm Breath - 300mm Thickness - 30mm Material - stainless steel We did the simulation in abaqus with constant length and breath but thickness is different. The results is shown below
  • 13. Linear encoder It measures the position of linear axis without any additional mechanical transfer elements Optical linear encoder is preferred because the befits of this encoder is clearly explained above Travel distance - 300mm Resolution - 1 Micrometer
  • 14. Load cell They are 5 types of load cell is available in market Preferred load cell for our UTM - S-type Load capacity - 300NM
  • 15. Ball screw Generally lead screw is used in universal testing machine but our case we are using ball screw because ball screw give smooth movement without any errors Stroke - 300mm Pitch - 5mm Length between both bearings - 500mm 5.5.2 Time Schedule Table 2: Time Schedule of Work Plan Months Aug. Sep. Oct. Nov. Jan. Feb. Mar. Apr. Activities Week 1 & 2 Week 3 & 4 Week 1 & 2 Week 4 Week 1,2 &3 1. 2. 3. 4. 5. 6. 6. Name and address of the institution where the proposal will be/likely to be executed: Indian Institute of Technology Ropar, Distt. - Rupnagar, Punjab-140001
  • 16. 1.1.1.1.1.1Detailed Biodata Applicant No. 1 1. Name of the Applicant : kuricheti ravi teja 2. Mailing Address : kurichetir@iitrpr.ac.in 3. Date of Birth : December 25, 1994 4. Educational Qualifications (Starting from Graduation onwards): undergraduate S.No. Degree University Year Subjects Percentage 1. B.Tech IIT Ropar 2012- 2016* ME 1.1.2 Place & date: Signature of the applicant
  • 17. Applicant No. 2 1. Name of the Applicant : Aashish kholiya 2. Mailing Address : aashishkk@iitrpr.ac.in 3. Date of Birth : January 28, 1995 4. Educational Qualifications (Starting from Graduation onwards): S.No. Degree University Year Subjects Percentage 1. B.Tech IIT Ropar 2012- 2016* ME 1.1.3 Place & date: Signature of the applicant
  • 18. Reference [1] V.B.BHANDARI,Design of machine elements,3rd edition [2] RUSSELL C.HIBBELER ,Mechanics of materials,9th edition [3] ROBERT NORTON, An introduction to the synthesis and analysis of mechanisms,2nd edition