ADDIS ABABA UNIVERSITY

ADDIS ABABA INSTITUTE OF TECHNOLOGY

SCHOOL OF MECHANICAL AND INDUSTRIAL ENGINEERING
POST-GRADUATE STUDY
MECHANICAL DESIGN STREAM

MACHINE DYNAMICS (MENG 6202)

MINI-PROJECT
Tittle: - Determination of the motion of board eraser device by modified
scotch yoke mechanism
By
Wondimu Dessalegn ID No - GSR/8629/11

Submitted To: - Mr. Mulugeta H.

Submitted Date: -Feb, 02/2019
Addis Ababa, Ethiopia
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Acknowledgements
First as usual I would like to thanks my lord who always help in any obstacles which happened on
me. And also, to make me powerful while I am working any external works, examinations, projects
like this etc. Next, I have to thank my Instructor Mr. Mulgata who have given to me this project in
order to develop and acquiring me based on the objective of the course who gave me and to know
the MATLAB software to become real mechanical engineer.

The last but not the least I would like to thanks my classmates for helping me by giving me hints
how to do this project as well as sharing documents and their software knowledge what they have
and what they know.

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Abstract
The manually operated blackboard eraser is a device that is generally used to clean board
automatically with the help of duster by using the rotation human hand not any power sources.
The design of this device is held to erase the writings on the board without the user rubbing of the
board with duster so it reduces much effort, prevent straining oneself, and be able to reduce the
time used.

The manually operated blackboard eraser’s intended application is to erase the writings on the
board which would consume less effort and time compared to manual erasing but it is not just only
save time but also use that time to do other thing while the machine is working. It is also healthful
for lecturers because when cleaning of board by hand, it may cause hygiene problem. The project
is done based on senior teachers from previous experiences of the effects of fragment of chalk and
the effort executed during cleaning. And also, its effect on the colleague’s health.

To simulate and to show how the device is works some mechanical software’s can be used like
solid works and MATLAB. Finally, the paper shows the results from the software’s according to
the real motion of component/link of the device according to the machine dynamics concept.

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Table of contents
Contents
Acknowledgements ......................................................................................................................... ii

Abstract .......................................................................................................................................... iii

Table of contents ............................................................................................................................ iv

List of figures ................................................................................................................................. vi

Chapter one ..................................................................................................................................... 1

1. Introduction ............................................................................................................................. 1

1.1. Statement of the Problem ................................................................................................. 2

1.2. Objectives ......................................................................................................................... 3

1.2.1. General objective ...................................................................................................... 3

1.2.2. Specific objective ...................................................................................................... 3

1.3. Limitations ....................................................................................................................... 3

1.4. Advantage of device ......................................................................................................... 4

1.5. Application Area .............................................................................................................. 4

Chapter two ..................................................................................................................................... 5

2. Literature review ..................................................................................................................... 5

2.1. Who first invent duster? ................................................................................................... 5

2.2. Real Time Automatic Blackboard Eraser using Embedded System ................................ 6

2.2.1. Limitations ................................................................................................................ 6

2.3. Automated Pneumatic Board Cleaning System (APBCS) ............................................... 7

2.3.1. Limitations of APBCS .............................................................................................. 7

2.4. Conclusions ...................................................................................................................... 7

Chapter Three.................................................................................................................................. 8

3. Working Principle and Modeling............................................................................................ 8

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3.1. Components...................................................................................................................... 8

3.1.1. Black board ............................................................................................................... 8

3.1.2. Scotch yoke mechanism ............................................................................................ 8

3.1.3. Handle ....................................................................................................................... 9

3.1.4. Frame ........................................................................................................................ 9

3.1.5. Eraser/duster ............................................................................................................. 9

3.2. Working principle .......................................................................................................... 10

Chapter 4 ....................................................................................................................................... 12

4. Mathematical formulation ..................................................................................................... 12

4.1. Specifications ................................................................................................................. 12

4.2. Kinematic representation of the system ......................................................................... 13

4.3. Position equation ............................................................................................................ 14

4.4. Velocity equation ........................................................................................................... 14

4.5. Acceleration equation ..................................................................................................... 15

4.6. Lagrange method formulation of equation of motion .................................................... 15

Chapter five ................................................................................................................................... 21

5. Results and discussion .......................................................................................................... 21

5.1. Result from MATLAB software .................................................................................... 21

5.1.1. Simulation code for board eraser device ................................................................. 21

5.1.2. Motion Analysis ...................................................................................................... 24

5.2. Discussion ...................................................................................................................... 26

References ..................................................................................................................................... 27

Appendix ....................................................................................................................................... 28

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List of figures
Figure 1. Early invented duster ...................................................................................................... 5
Figure 2. Embedded system of board eraser .................................................................................. 6
Figure 3. Scotch yoke mechanism ................................................................................................. 9
Figure 4. 3D modeling of the device ............................................................................................ 11
Figure 5. The free body diagram of the device at maximum position .......................................... 12
Figure 6. The free body diagram of a device at minimum position.............................................. 13
Figure 7. Position representation of the links ............................................................................... 13
Figure 8. MATLAB simulation result .......................................................................................... 21
Figure 9. Motion analysis for crank and yoke .............................................................................. 25

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Chapter one
1. Introduction
Education in Ethiopia is one of the focused areas for the development of the country in social,
economic and political issues. This sector has a vital role in literate the people in all aspects of
their livelihood. Traditional education in Ethiopia were started earlier [1]. Nowadays modern
education is expanded throughout the territory of the nation. Education in Ethiopia has been
dominated by the northern nations of the country for many centuries until secular education was
adopted in the early 1900s. Prior to 1974, Ethiopia had an estimated illiteracy rate well above 90%
and compared poorly with the rest of Africa in the provision of schools and universities [1]. After
the Ethiopian Revolution, emphasis was placed on increasing literacy in rural areas.

By 2015, the literacy rate had increased to 49.1%, though this is still poor compared to most of the
rest of Africa. Recently, there has been massive expansion throughout the educational system [1].

In Ethiopia, education has been in expansion year to year. These enrollment in education revealed
by the increment of students, schools and etc. for information there are 35,838 primary schools,
3,393 secondary schools and around 40 university in total in national level by including only the
governmental institution [1]. These all schools in higher as well as in lower level needs the
materials for teaching learning materials like chalk, textbooks, blackboards etc. as mandatory. And
these all infrastructures should be used wisely and not to have effect on the customers. So, the
focus area for the project is goes to the how could to minimize the time, power and health effect
losses during teaching learning activity? Solution for the question is mechanizing the way of using
infrastructures like blackboard as well any of. So, adopting as well as shaping of the existed type
of devices in the world is critical solution for such problems.

Blackboards are used in the class rooms for teaching purpose. These blackboards form the basis
for an effective learning in the education sector. Chalk pieces are used to write on the blackboard.
The chalk powder obtained from the chalk pieces while erasing the blackboard, when inhaled by
human, cause problems to the respiratory organ. The Asthma patients and those who are allergic
to dust cannot sit near the blackboard due to explosion of fragment of chalk. Based on the problems
faced by the students as well as by teachers this design concept has been developed.

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A manually operated blackboard eraser is a device that is generally used to clean board
automatically with the help of duster. By the use of this blackboard duster we can save time and
energy [2]. It is an adopted technology that is generally used now a day but the world uses
automatically operated duster. A device for erasing a blackboard wherein a duster is mounted for
transverse/horizontal movement on the blackboard and has a crank mounted thereon that is
mechanically interconnected to a drive assembly for producing the movement of the duster in an
erasing operation. This appertains to new and useful improvements and more particularly to an
apparatus whereby blackboards can be cleaned in an easy and convenient manner. The principal
object of the present blackboard duster is to provide an attachment for blackboards in the form of
a manually-driven erasing apparatus which can be set in operation throw by handle, thus
eliminating the drudgery of manually cleaning blackboards by hand.

1.1. Statement of the Problem

As tradition in Ethiopia most institution workers as well as managers are not care about the safety,
health, and losses of their energy due to unwanted tradition devices of their colleagues. In fact, in
educational sector there is no research/data on the power losses of teachers and students in cleaning
of the blackboards. And the effect of fragment of chalk will drop on the human tongue. These will
have effect on the breathing system of any body. Due to this and other problems will initiate to
launch the project.

Mainly: -

❖ The time consumes in hand erasing is more.

❖ The problem of dust in hand erasing affect the human being.
❖ Hand erasing requires human power thus wastage of human energy

Are the most problems to hold the project.

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1.2. Objectives
The aim of this work is to keep the teacher or student away from the board while it is being erased,
in order to minimize the inhalation of chalk dust particles which are suspended in the air around
the black board while it is rubbed as well as reducing power during erasing blackboard by duster.

1.2.1. General objective

The primary envisioned goal of this mini project is to examine the motion as well as the governing
equation of motion for the manually operated blackboard eraser device using scotch yoke
mechanism and inspecting by MATLAB software.

1.2.2. Specific objective

➢ To show the equation of motion for the manually operated blackboard eraser by the
Lagrange and Newton-Euler method
➢ To check whether the equation of motion by using Lagrange method and Newton-Euler
method the same or not.
➢ To do the physical modeling of the device for the importance of obtaining the mathematical
model by using solid works 2013 software.
➢ Simulating the motion of device by using MATLAB programing software.
➢ To obtain numerical solution of motion for the manually operated blackboard device by
scotch yoke mechanism by using MATLAB software.
➢ To show displacement, velocity and acceleration graph for the motion of device by using
MATLAB software

1.3. Limitations
The device which can be induced in all of the schools including some universities throughout the
country including the rural and urban primary, elementary and secondary schools. So, to much
more reduce the human power during erasing manually by hand we need to automatic board eraser
using motors, generators, etc. but as the country statistics the coverage of the electric power
throughout the country especially in rural areas it is less. In fact, of these truths, the project is
limited to use human power but it reduces losses using torque reduction mechanism. Thus, the
project is going to designing board eraser device using manually operated by human labor force
of hand and it reduce energy, time as well as health effects on a body/hand.

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1.4. Advantage of device

Its construction is simple and requires less maintenance.
Low cost: - because it can be simply manufactured from surrounding materials
Portable in size and easily transportable: -The assembly and the components of the device
is small so it can be movable by easily disengaging the components
No external devices are used here to control it: - Due to operation of the device by manually
it is not depending on electricity any other.
Less manual work: - uses torque reduction mechanism
Time saving device

1.5. Application Area

Today there are different mechanisms/robots used for board eraser all over the world but in our
context of Ethiopia we need to use simple mechanism according to financial and infrastructural
constraint. And those mechanism application (robots and automatic mechanisms) are limited to a
specific area and environment. So manually operated device has to design to do specific activities
in specific area and environments to seek contextual satisfaction. Thus, the application area for the
device is where ever schools and/or teaching agents present because without board there will not
have learning.
It can be applicable for: -

Elementary schools
Primary schools
Secondary and preparatory schools
Colleges and universities
Where ever there is teaching boards
It can be also used for painting of wall as well.

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Chapter two
2. Literature review
2.1. Who first invent duster?
A chalkboard eraser (or blackboard duster) is a special type of eraser specifically used to erase
chalk markings on slating paint (used on chalkboards and slates) and blackboard. It is most
commonly made of felt/rubber strips attached to an ergonomically designed handle [3].

Chalkboard erasers were first invented around 1863 by John L. Hammett, who owned some stores
that sold and created school products in Rhode Island and then later in Boston [3]. Mostly slates
were sold there as well as chalk and so on. At the time, rags or old clothes were used to erase and
get rid of the chalk markings on slates in schools, offices, and for the most part, everywhere.

Hammett created the chalkboard before the invention of the chalkboard eraser by creating slating
paint. Hammett then, during a presentation on his chalkboard "discovered" that wool felt strips
wiped off the chalk writing better than rags. Following this discovery, he gathered a team to create
the custom eraser for sale. The erasers proved to be a success for Hammett and, later in the 19th
century, he created a company that also sold inexpensive supplies for teachers and schools, such
as paper, ink, etc. Hammett ultimately sold the company.

Figure 1. Early invented duster [3]

After John L. Hammett invents board eraser many researchers are going to invent whiteboards as
well as a better mechanization for cleaning the boards to reduce its hazardous due to fragments of
chalk as well as wastage of human energy.

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Only by considering the recent innovations there are a lot of works which are done using robotics
and automated mechanism.

2.2. Real Time Automatic Blackboard Eraser using Embedded System

’Real Time Automatic Blackboard Eraser using Embedded System’ has been designed by Rubhini
B. and Mrunalini T in 2014 which suggested to automatically erase the blackboard. It uses DC
motors of three different types are used for the movement of the instrument [2]. The instrument
moves forward and backward erasing the board and collecting the dust automatically from the
erasing material due to the rotation of the roller which can be automated using microcontroller.
Thus, the device avoids the dust flow in the environment and thereby providing good solution for
the problems faced by the student, faculty and other electronic equipment’s that are used inside
the class room in a cost effective and time efficient way.

1. Vacuum Cleaner
2. Wiper Motor
3. Chain as a Conveyor
4. Pre-Wheel
5. Eraser Apparatus
6. Roller Wound with Eraser
7. DC Gear Motor
8. Motor Base
9. Frame
10. Blackboard
11. Wheel Attached to Motor Base
12. Vacuum Pipe

Figure 2. Embedded system of board eraser [4]

2.2.1. Limitations

▪ It is sophisticated to use in manual areas

▪ It is only applicable where electric power exists
▪ It is costive due usage of Nano-technologies

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2.3. Automated Pneumatic Board Cleaning System (APBCS)

Automated Pneumatic Board Cleaning System were invented/developed by Lakshminarayana K.,
S, Sagar Venkatesh Halenaik, Karthik.R., Pranav.N.D. and N.Tejas kumar in 2017 GC which is
used for both for whiteboard and blackboard. This system was developed by using the concepts of
both mechanical and electronics concepts have been utilized. This cleaning system utilizes the
compressed air and cleans the black board and white boards automatically with the help of
pneumatic cylinders.
2.3.1. Limitations of APBCS

Due to the system uses air for cleaning purpose so its efficiency is less due less viscosity
of air it leaks easily.
It is limited where electric power exists.
Costive because the system uses pneumatic cylinders, motors. Etc.
Needs professional skill to run the system

2.4. Conclusions
Beside to the above-mentioned eraser devices there are also several innovations, but these
invented devices are the development of the above mechanisms. In general, the manually operated
board cleaning device will compensate all the limitation of the existed mechanism with condition
of the life standard of the country and the capacity of the government to install those sophisticated
devices in schools. Finally, I conclude that manually operated board eraser is appropriate and an
be easily installed and financially feasible for the private as well as governmental organizations.

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Chapter Three
3. Working Principle and Modeling
The manually operated board cleaning mechanism has different components to accomplish the
objective to erase any written things on board, it would be cleaned as a form of fragments of
chalk.

3.1. Components
The device has different components to do its task including either directly connected to the
working principle of the device or the parts which the mechanisms are applied.

3.1.1. Black board

A blackboard or chalkboard is a reusable writing surface on which text or drawings are made
with sticks of calcium sulphate or calcium carbonate, known, as chalk. Blackboards originally
made of smooth, thin sheets of black or dark grey slate stone. Modern versions are often green
because the color is considered easier on the eyes. A blackboard can simply be a piece of board
painted with matte dark paint (usually black or dark green). It has no directly distress on the
mechanism but the primary goal for the project is going to erase board.

3.1.2. Scotch yoke mechanism

The Scotch yoke (also known as slotted link mechanism) is a reciprocating motion mechanism,
converting the linear motion of a slider into rotational motion, or vice versa [5]. The primary
function of scotch yoke mechanism is used to actuate internal combustion engines due to
efficient compression stroke with double end acting piston. But, in black board erasing purpose
scotch yoke mechanism is used for forward and backward traction of the eraser which is sliding
along the length of the board.

This mechanism includes sub components like: -

i. Yoke: - which is sliding on the guide way to convert the rotation of the crank
in to back and forth motion of the eraser holding rod.
ii. Crank: - used to converts rotational motion driven by human hand to the
reciprocating motion of guide ways by yoke attached by the rod.
iii. Guideways: - used for sliding the yoke up and down.

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iv. Rods: - translates the rotation of crank in to reciprocating motion

2 5

1
1. Crank
2. Yoke
3. Connecting rode
4. Yoke
5. Rode

3 4

Figure 3. Scotch yoke mechanism [3]

3.1.3. Handle

handle is a part of, or attachment to, an object that can be moved or used by hand. The design of
each type of handle involves substantial ergonomic issues, even where these are dealt with
intuitively or by following tradition. Handles for tools are an important part of their function,
enabling the user to exploit the tools to maximum effect. Handle is used for reducing the wastage
of human energy. And it is the part of the mechanism to source of power from human hand.

3.1.4. Frame

frame is a supporting part used to support the mechanisms and translates loads due to weight of
each components to the ground or fixed attachments like wall.

3.1.5. Eraser/duster

duster is plastic material used for removing writing materials/chalks from black board which is
attached at the end of the longitudinal rod.

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3.2. Working principle

As per the reviews of literature above I conclude that the manually operated board eraser machine
gives satisfactory rubbing effect by converting rotary motion of crank by handle in to reciprocating
motion of duster rode. This eraser runs by human & will make it easier for teachers everywhere to
clean their blackboard. This project consists of a scotch yoke mechanism.

The scotch yoke mechanism enables the movability of any other components. This scotch yoke
mechanism run by human driving force due to the rotation of the crank. Load is directly applied
on the handle. After that the crank initiated for rotation. The crank and connecting rode are
connected directly by pin which is hinged at the crank edge end. The rotation of the crank is
inverted to longitudinal/ reciprocating motion due to traverse sliding of yoke on the guideways.

Due to this the rode in which eraser/duster attached moving forward and backward the cleaning of
blackboard is accomplished throughout the rotation of crank. The eraser is made same with
existing cleaning material but its size differ i.e. the height of the boards and the width of the duster
should the same. In this advanced world the competition is increasing day by day, thus the time of
every person is most precious. As blackboard duster clean the board in less time and saves the time
of student which is too important.

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slot
crank pin Connecting
rod
yoke

handle
pin Fixed support

shaft

Erase/duster

board

Figure 4. 3D modeling of the device

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Chapter 4
4. Mathematical formulation
4.1. Specifications
The Length of the board is considered according to the perimeter/circumference of the crank
due to this: -
radius of the crank, 𝑟 = 320 𝑚𝑚
diameter , 𝑑 = 640 𝑚𝑚
The length of the board , 𝐿 = 2π𝑟/2 = π𝑟 ≅ 1010𝑚𝑚
The width of board considered as , 𝑤 = 800𝑚𝑚
The total length from the center of the crank to the end edge of the board at maximum
extension of the duster link specified as 𝐿𝑡𝑜𝑡 = 2580 𝑚𝑚 as shown below.
Length of the slot should equal to the length of the board i.e. half of circumference of crank.
𝐿𝑠 = 1010 𝑚𝑚.
Length of duster link should be greater than the length of the board unless it would not
enable to erase the whole board so 𝐿𝑑 > 𝐿𝑏𝑜𝑎𝑟𝑑 = 1200𝑚𝑚

Eraser/
duster
support

Figure 5. The free body diagram of the device at maximum position

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Figure 6. The free body diagram of a device at minimum position

The above two free body diagram representation is used to represent how the motion would looks
like as human hand starts to operate the device. The total length of the device including the
equipment’s like board is same but the linkages are varying as manner of rotation.

4.2. Kinematic representation of the system

Figure 7. Position representation of the links

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4.3. Position equation

Let specify the device represent in 2D cartesian coordinate system with (X, Y). Point P
represents the pin connection between the connecting rode and the crank at radial position of r.
Point Q represents the motion of yoke relative to slot as well as rotation due to connecting rode.
The linear motion of duster connecting rode represented by x coordinate as shown above.

Thus 𝑟𝑃 = 𝑋𝑃 𝑖 + 𝑌𝑃 𝑗 − − − − − − − − − − − − − − − − − − − − − − − − − − − [1]

where 𝑋𝑃 = 𝑟 cos 𝜃

𝑌𝑃 = 𝑟 sin 𝜃

𝑟𝑃 = 𝑟 cos 𝜃 𝑖 + 𝑟 sin 𝜃 𝑗 − − − − − − − − − − − − − − − − − − − − − − − − − − − [2]

𝑟𝑄 = 𝑋𝑄 𝑖 + 𝑌𝑄 𝑗 − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − [3]

where 𝑋𝑄 = 𝑟 cos 𝜃 + 𝐿 cos 𝛽

𝑌𝑄 = 𝑟 sin 𝜃 + 𝐿 sin 𝛽

𝑟𝑄 =( 𝑟 cos 𝜃 + 𝐿 cos 𝛽) 𝑖 + (𝑟 sin 𝜃 + 𝐿 sin 𝛽)𝑗 − − − − − − − − − − − − − − − − − [4]

𝑋 = 𝑥𝑖

where 𝑥 = 𝑟(1 − cos 𝜃) − − − − − − − − − − − − − − − − − − − − − − − − − −[5]

4.4. Velocity equation

The velocity of a certain body or particle related with position is the time derivative of its
position.

𝑑𝑟
𝑉= [6]using this relationship, we can determine velocities of the rigid bodies.
𝑑𝑡

Velocity of link crank at point P from equation [2] can be determine as

𝑑𝑟𝑃
𝑉𝑃 = = −𝑟𝜃̇ sin 𝜃 𝑖 + 𝑟𝜃̇ cos 𝜃 𝑗 − − − − − − − − − − − − − − − − − − − − − − − [6]
𝑑𝑡

The velocity of yoke is also determined from the equation of position equation [4]; -

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𝑑𝑟𝑄
𝑉𝑄 = = (−𝑟𝜃̇ sin 𝜃 − 𝐿𝛽̇ sin 𝛽)𝑖 + (𝑟𝜃̇ cos 𝜃 + 𝐿𝛽̇ cos 𝛽)𝑗 − − − − − − − − − − − −[7]
𝑑𝑡

The linear velocity of the duster connecting rode from equation [5] is also obtained by derivation
of position with respect to time.

𝑑𝑥
𝑉𝐷 = = 𝑟𝜃̇ sin 𝜃 𝑖 − − − − − − − − − − − − − − − − − − − − − − − − − − − − − [8]
𝑑𝑡

4.5. Acceleration equation

Likewise, velocity the acceleration of a certain body or particle related with velocity is the time
𝑑𝑉
derivative of its velocity. 𝑎 = using this relationship [6], we can determine acceleration of the
𝑑𝑡

rigid bodies.

Acceleration of P is obtaining from equation [6] by derivation with respect to time

𝑑𝑣𝑃
𝑎𝑃 = = −(𝑟𝜃̈ sin 𝜃 + 𝑟𝜃̇ 2 cos 𝜃)𝑖 + (𝑟𝜃̈ cos 𝜃 − 𝑟𝜃̇ 2 sin 𝜃)𝑗 − − − − − − − − − − − [9]
𝑑𝑡

The acceleration of yoke or connecting rod is also determined from equation [7]

𝑑𝑣𝑄
𝑎𝑄 = = (−𝑟𝜃̈ sin 𝜃 − 𝑟𝜃̇ 2 cos 𝜃 − 𝐿𝛽̈ sin 𝛽 − 𝐿𝛽̇ 2 cos 𝛽)𝑖 + (𝑟𝜃̈ sin 𝜃 − 𝑟𝜃̇ 2 sin 𝜃 +
𝑑𝑡

𝐿𝛽̈ cos 𝛽 − 𝐿𝛽̇ 2 sin 𝛽)𝑗 − − − − − − − − − − − − − − − − − − − − − − − − − − − −[10]

The acceleration of duster connecting link obtained by derivation of its velocity

𝑑𝑣𝐷
𝑎𝐷 = = (𝑟𝜃̈ sin 𝜃 + 𝑟𝜃̇ 2 cos 𝜃)𝑖 − − − − − − − − − − − − − − − − − − − − − −[11]
𝑑𝑡

4.6. Lagrange method formulation of equation of motion

To apply the Lagrange equation of motion first describe the number of constrained equations,
number of dependent coordinates to specify its position and then the total number of degrees of
freedom of the system is determined.

As shown in the figure above, there are 5 coordinates to determine the movability of the system
that is 𝑋𝑃 , 𝑌𝑃 , 𝑋𝑄 , 𝑌𝑃 𝑎𝑛𝑑 𝑋 coordinates so 𝑛 = 3.

The constrained equations are: -

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𝑋𝑃 2 + 𝑌𝑃 2 = 𝑟 2
(𝑋𝑄 − 𝑋𝑃 )2 + (𝑌𝑄 − 𝑌𝑃 )2 = 𝐿2 } 𝑐𝑜𝑠𝑟𝑎𝑖𝑛𝑡 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛𝑠 𝑠𝑜
2𝜋𝑟 = 𝐿𝑆 𝑡ℎ𝑒 𝑐𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑟𝑎𝑛𝑘 = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑠𝑙𝑜𝑡

𝑚 = 3 − − − − − − − − − − − − − − − − − − − − − [12]

And this all constraints are holonomic constraints they are not dependent on time [8].

The degree of freedom of the system is 𝐷𝑂𝐹 = 𝑛 − 𝑚 = 5 − 3 = 2 − − − − − − − − − −[13]

So, the generalized coordinates are 2 which are them as dictated above 𝜃 𝑎𝑛𝑑 𝛽.

From Lagrange equation

𝑑 𝜕𝐿 𝜕𝐿
( ) − 𝜕𝑞 = 0 [8]− − − − − − − − − − − − − − − − − − − − − − − − − − − − [14]
𝑑𝑡 𝜕𝑞̇

Assumptions

❖ No external applied force on the system

❖ Frictions along slot and along support is small so it would be negligible
❖ Force due to weight is not considered as considered
❖ The system is conservative system

Based on the above assumptions we can drive equation of motion for the system.

1
𝐿 = 𝑇 − 𝑉 𝑤ℎ𝑒𝑟𝑒 𝑇 = ∑𝑛𝑖=1 2 𝑚𝑖 𝑣𝑖 2 [8]− − − − − − − − − − − − − − − − − − −[15]

𝑓𝑟𝑜𝑚 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 [6] 𝑉𝑃 = −𝑟𝜃̇ sin 𝜃 𝑖 + 𝑟𝜃̇ cos 𝜃 𝑗

To write the velocity in the form of Lagrange equation we need to square each velocity

2
𝑉𝑃 2 = (−𝑟𝜃̇ sin 𝜃 𝑖 + 𝑟𝜃̇ cos 𝜃 𝑗) = 𝑟 2 𝜃̇ 2 𝑠𝑖𝑛2 𝜃 + 𝑟 2 𝜃̇ 2 𝑐𝑜𝑠 2 𝜃 = 𝑟 2 𝜃̇ 2 − − − − − −[16]

The velocity of yoke from equation [10] is

𝑉𝑄 = (−𝑟𝜃̇ sin 𝜃 − 𝐿𝛽̇ sin 𝛽)𝑖 + (𝑟𝜃̇ cos 𝜃 + 𝐿𝛽̇ cos 𝛽)𝑗

2
𝑉𝑄 2 = [(−𝑟𝜃̇ sin 𝜃 − 𝐿𝛽̇ sin 𝛽) + (𝑟𝜃̇ cos 𝜃 + 𝐿𝛽̇ cos 𝛽)𝑗] − − − − − − − − − − − [17]

2 2
= (−𝑟𝜃̇ sin 𝜃 − 𝐿𝛽̇ sin 𝛽) + (𝑟𝜃̇ cos 𝜃 + 𝐿𝛽̇ cos 𝛽)

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=𝑟 2 𝜃̇ 2 (𝑠𝑖𝑛2 𝜃 + 𝑐𝑜𝑠 2 𝜃) + 𝐿2 𝛽̇ 2 (𝑠𝑖𝑛2 𝛽 + 𝑐𝑜𝑠 2 𝛽) + 2𝐿𝑟𝜃̇𝛽̇ (sin 𝜃 sin 𝛽 + cos 𝜃 cos 𝛽)

𝑉𝑄 2 = 𝑟 2 𝜃̇ 2 + 𝐿2 𝛽̇ 2 + 2𝐿𝑟𝜃̇𝛽̇ cos(𝜃 − 𝛽) − − − − − − − − − − − − − − − − − − − [18]

The velocity of duster link at point D is also determined in equation [11] is square can be written

𝑉𝐷 2 = 𝑟 2 𝜃̇ 2 𝑠𝑖𝑛2 𝜃 − − − − − − − − − − − − − − − − − − − − − − − − − − − − − −[19]

The kinetic energy

1 1 1
T= 𝑚𝑃 𝑣𝑃 2 + 𝑚𝑄 𝑣𝑄 2 + 𝑚𝐷 𝑣𝐷 2 − − − − − − − − − − − − − − − − − −[20]
2 2 2

1 2 1 2 2 1 2
T= 𝑚𝑃 𝑟2 𝜃̇ + 𝑚𝑄 [𝑟2 𝜃̇ + 𝐿2 𝛽̇ + 2𝐿𝑟𝜃̇ 𝛽̇ cos(𝜃 − 𝛽)]+ 𝑚𝐷 𝑟2 𝜃̇ 𝑠𝑖𝑛2 𝜃 − − − − − [21]
2 2 2

The potential energy V; 𝑉 = 𝑉𝑄 + 𝑉𝑃 + 𝑉𝐷 − − − − − − − − − − − − − − − − − − − −[22]

Where 𝑉𝑃 𝑖𝑠 𝑡ℎ𝑒 𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝑒𝑛𝑒𝑟𝑔𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑟𝑎𝑛𝑘 𝑎𝑡 𝑝𝑜𝑖𝑛𝑡 𝑝

𝑉𝑄 𝑖𝑠 𝑡ℎ𝑒 𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝑒𝑛𝑒𝑟𝑔𝑦 𝑜𝑓 𝑦𝑜𝑘𝑒

VD is the potential energy of daster connecting link but is zero becouse no change in

Y direction from the reference of its motion because its motion is only sliding along

Its support horizontally.

As shown in the above free body diagrams

𝑉𝑃 = −𝑚𝑝 g𝑌𝑝 = −𝑚𝑝 𝑔𝑟 sin 𝜃 − − − − − − − − − − − − − − − − − − − − − − − − − [23]

𝑉𝑄 = −𝑚𝑄 𝑔(𝑌𝑝 + 𝐿 sin 𝛽) = −𝑚𝑄 𝑔(𝑟 sin 𝜃 + 𝐿 sin 𝛽) − − − − − − − − − − − − − −[24]

𝑉 = 𝑉𝑄 + 𝑉𝑃 + 𝑉𝐷

𝑉 = −𝑚𝑄 𝑔(𝑟 sin 𝜃 + 𝐿 sin 𝛽) − 𝑚𝑝 𝑔𝑟 sin 𝜃 + 0

The total potential energy of the system can be hesitated as follow

𝑉 = −𝑚𝑄 𝑔(𝑟 sin 𝜃 + 𝐿 sin 𝛽) − 𝑚𝑝 𝑔𝑟 sin 𝜃 − − − − − − − − − − − − − − − − − − − [25]

Lagrange, 𝑳 = 𝑇 − 𝑉 [8]− − − − − − − − − − − − − − − − − − − − − − − − − − −[26]

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1 1
𝑳= 𝑚𝑃 𝑟 2 𝜃̇ 2 + 𝑚𝑄 [𝑟 2 𝜃̇ 2 + 𝐿2 𝛽̇2 + 2𝐿𝑟𝜃̇𝛽̇ cos(𝜃 − 𝛽)]
2 2
1 2
+ 𝑚𝐷 𝑟2 𝜃̇ 𝑠𝑖𝑛2 𝜃 + 𝑚𝑝 𝑔𝑟 sin 𝜃 + 𝑚𝑄 𝑔(𝑟 sin 𝜃 + 𝐿 sin 𝛽)
2

1 1 1 1
𝑳= 𝑚𝑃 𝑟 2 𝜃̇ 2 + 𝑚𝑄 𝑟 2 𝜃̇ 2 + 𝑚𝑄 𝐿2 𝛽̇ 2 + 𝑚𝑄 𝐿𝑟𝜃̇𝛽̇ cos(𝜃 − 𝛽) + 𝑚𝐷 𝑟 2 𝜃̇ 2 𝑠𝑖𝑛2 𝜃
2 2 2 2
+ (𝑚𝑝 + 𝑚𝑄 )𝑔𝑟 sin 𝜃 + 𝑚𝑄 𝑔𝐿 sin 𝛽 − − − − − − − − − − − − − − − −[27]

For 𝜽 equation

From equation [14] q indicates the generalized coordinate which is independent and the equation
of motion can be describe as follow according to the Lagrange formulation.

𝑑 𝜕𝐿 𝜕𝐿
( )− = 0 − − − − − − − − − − − − − − − − − − − − − − − − − − − − − −[28]
𝑑𝑡 𝜕𝛳̇ 𝜕𝛳

𝜕𝐿
= 𝑚𝑃 𝑟 2 𝛳̇ + 𝑚𝑄 𝑟 2 𝛳̇ + 𝑚𝑄 𝐿𝑟𝛽̇ cos(𝜃 − 𝛽) + 𝑚𝐷 𝑟 2 𝛳̇𝑠𝑖𝑛2 𝜃 − − − − − − − − − −[29]
𝜕𝛳̇

𝑑 𝜕𝐿
( ) = 𝑚𝑃 𝑟 2 𝜃̈ + 𝑚𝑄 𝑟 2 𝜃̈ + 𝑚𝑄 𝐿𝑟(𝛽̈ cos(𝜃 − 𝛽) − 𝛽̇ (𝛳̇ − 𝛽̇ ) sin(𝜃 − 𝛽))
𝑑𝑡 𝜕𝛳̇
+ 𝑚𝐷 𝑟 2 𝜃̈𝑠𝑖𝑛2 𝜃 + 2𝑚𝐷 𝑟 2 𝛳̇2 sin 𝜃 cos 𝜃 − − − − − − − − − − − − − −[30]

𝜕𝐿
= −𝑚𝑄 𝐿𝑟𝜃̇𝛽̇ sin(𝜃 − 𝛽) + 𝑚𝐷 𝑟 2 𝜃̇ 2 sin 𝜃 cos 𝜃 + (𝑚𝑝 + 𝑚𝑄 )𝑔𝑟 cos 𝜃 − − − − − −[31]
𝜕𝛳

By substituting equation [30] and [31] in to equation [28] and after simplification we finally get

𝑑 𝜕𝐿 𝜕𝐿
( )− = 𝑚𝑃 𝑟 2 𝜃̈ + 𝑚𝑄 𝑟 2 𝜃̈ + 𝑚𝑄 𝐿𝑟(𝛽̈ cos(𝜃 − 𝛽) − 𝛽̇ 𝛳̇ sin(𝜃 − 𝛽)
𝑑𝑡 𝜕𝛳̇ 𝜕𝛳
+ 𝛽̇ 2 sin(𝜃 − 𝛽)) + 𝑚𝐷 𝑟 2 𝜃̈𝑠𝑖𝑛2 𝜃 + 2𝑚𝐷 𝑟 2 𝛳̇2 sin 𝜃 cos 𝜃
+ 𝑚𝑄 𝐿𝑟𝜃̇𝛽̇ sin(𝜃 − 𝛽) − 𝑚𝐷 𝑟 2 𝜃̇ 2 sin 𝜃 cos 𝜃 − (𝑚𝑝 + 𝑚𝑄 )𝑔𝑟 cos 𝜃 = 0

For small angles the black arrows become zero and sin(𝜃 − 𝛽) = 𝜃 − 𝛽

The equation of motion for 𝜃 𝑓𝑖𝑛𝑎𝑙𝑙𝑦 𝑐𝑎𝑛 𝑏𝑒

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(𝑚𝑃 + 𝑚𝑄 )𝑟 2 𝜃̈ + 𝑚𝑄 𝐿𝑟(𝜃 − 𝛽) = 0 − − − − − − − − − − − − − − − − − − − − − −[32]

For 𝛽 equation

From equation [14] q represents the generalized coordinate 𝜃 and 𝛽 coordinates sofrom lagrange
equation the equation of 𝛽 expressed as: -

𝑑 𝜕𝐿 𝜕𝐿
( )− = 0 − − − − − − − − − − − − − − − − − − − − − − − − − − − − − −[33]
𝑑𝑡 𝜕𝛽̇ 𝜕𝛽

From equation [27] expression of Lagrange the beta equations with time derivation and only
displacement differentiation is calculated as; -

𝜕𝐿
= 𝑚𝑄 𝐿2 𝛽̇ + 𝑚𝑄 𝐿𝑟𝛳̇ cos(𝜃 − 𝛽) − − − − − − − − − − − − − − − − − − − − − −[34]
𝜕𝛽̇

𝑑 𝜕𝐿
( ) = 𝑚𝑄 𝐿2 𝛽̈ + 𝑚𝑄 𝐿𝑟𝜃̈ cos(𝜃 − 𝛽) − 𝑚𝑄 𝐿𝑟𝛳̇(𝛳̇ − 𝛽̇ ) sin(𝜃 − 𝛽) − − − − − −[35]
𝑑𝑡 𝜕𝛽̇

𝜕𝐿
= 𝑚𝑄 𝐿𝑟𝜃̇𝛽̇ sin(𝜃 − 𝛽) + 𝑚𝑄 𝑔𝐿 cos 𝛽 − − − − − − − − − − − − − − − − − − − [36]
𝜕𝛽

𝑑 𝜕𝐿 𝜕𝐿
( )− = 𝑚𝑄 𝐿2 𝛽̈ + 𝑚𝑄 𝐿𝑟𝜃̈ cos(𝜃 − 𝛽) − 𝑚𝑄 𝐿𝑟𝛳̇2 sin(𝜃 − 𝛽)
𝑑𝑡 𝜕𝛽̇ 𝜕𝛽
+ 𝑚𝑄 𝐿𝑟𝛳̇ 𝛽̇ sin(𝜃 − 𝛽) − 𝑚𝑄 𝐿𝑟𝜃̇𝛽̇ sin(𝜃 − 𝛽) − 𝑚𝑄 𝑔𝐿 cos 𝛽 = 0 − −[37]

For small angles

The red arrows are cancelled to each other the black arrows are zero for small angles.

The equation of motion for 𝛽 is

2
𝑚𝑄 𝐿2 𝛽̈ − 𝑚𝑄 𝐿𝑟𝛳̇ (𝜃 − 𝛽) = 0 by simplification

The equation of motion for 𝛽 is

𝐿2 𝛽̈ − 𝐿𝑟𝛳̇2 (𝜃 − 𝛽) = 0 − − − − − − − − − − − − − − − − − − − − − − − − − − − [38]

Where: -

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𝑚𝑄 = 𝑡ℎ𝑒 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑦𝑜𝑘𝑒 𝑎𝑛𝑑 𝑡ℎ𝑒 𝑖𝑛𝑒𝑟𝑡𝑖𝑎𝑙 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑙𝑖𝑛𝑘 𝑠𝑙𝑜𝑡
𝑚𝑃 = 𝑡ℎ𝑒 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑟𝑎𝑛𝑘 𝑤ℎ𝑖𝑐ℎ 𝑖𝑛𝑐𝑙𝑢𝑑𝑒𝑠 𝑖𝑡𝑠 𝑚𝑜𝑚𝑒𝑛𝑡 𝑜𝑓 𝑖𝑛𝑒𝑟𝑡𝑖𝑎
𝑚𝐷 = 𝑡ℎ𝑒 𝑐𝑒𝑛𝑡𝑒𝑟 𝑜𝑓 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑡ℎ 𝑑𝑢𝑠𝑡𝑒𝑟 𝑙𝑖𝑛𝑘

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Chapter five
5. Results and discussion
5.1. Result from MATLAB software
5.1.1. Simulation code for board eraser device

The final results by using the MATLAB software has two outputs one is the overall simulation of
the system and the next result is the position, velocity and acceleration of selected points.

MATLAB simulation code: -

1000

H
500 B E

0 D G
A

F
-500 J

-1000
-1000 -500 0 500 1000 1500 2000 2500 3000

Figure 8. MATLAB simulation result

Where A, B, C, D, E, F, G, J and H are selected points which leads the system to rotate and
translate to plot linkages.

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MATLAB code which simulates the motion of device: -

%%% Machine Dynamics mini project
%%% TITTLE: - manually operated board eraser device by using scotch
yoke
%%% mechanism
%%% Name WONDIMU DESSALEGN ID NO GSR/8629/11
% simulation of manually operated board duster device run by hand
rotation
% all dimension given below are in millimeter(mm)
r=320; % the radius of crank its dimension is by mm
lc=600; % the length of connecting link
ld=1200; % the length of duster holding link
ls=1010; % the length of slot in which the yoke slides through it
lb=1010; % the length of board
hb=800; % the height of board
lt=2580; % the total length of the device from crank center to end of
board
A=[0 0];% the position of point A or the origin crank
for teta=0:0.3:20.5*pi % the rotation of crank with 0.3 value gap to
20.5*pi
XB=r*cos(teta); % x coordinate of point B
YB=r*sin(teta); % Y coordinate of point B
B=[r*cos(teta) r*sin(teta)]; % x-y coordinate of point B
% the relation between the connecting rode to the crank by angle beta
beta=asin(r*sin(teta)/lc);
% the distance from the end of duster to the minimum reciprocating
distance
P=lt-(r*cos(teta)+lc*cos(beta));
R=r*sin(teta)-lc*sin(beta);
X=[A(1) XB];
Y=[A(2) YB];
% ploting the line of crank by making the size of line 3 with color of
black including points
plot(X,Y,'-ko','LineWidth',3,'MarkerEdgeColor','k','MarkerSize',2)
% waiting till to plot any other lines or not to cancel the plot
before
hold on
% the line of the crank in which it rotates
B_traj=viscircles([0 0],r,'linestyle','--');
XC=r*cos(teta)+lc*cos(beta); % x coordinate of point C
YC=(lc-r)*sin(teta-beta); % y coordinate of point C
X=[XB XC];
Y=[YB YC];
% ploting the line of connecting rode by making the size of line 3
plot(X,Y,'-bs','LineWidth',3,'MarkerEdgeColor','g',
'MarkerSize',5)
XE=lt-P;
YE=ls/3;
XF=lt-P;
YF=-ls/3;
X=[XE XF];

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Y=[YE YF];
% ploting the line of slot link in which the yoke slides by making the
size of line 3
plot(X,Y,'-ms','LineWidth',3,'MarkerEdgeColor','b',
'MarkerSize',2)
XD=lt-P;
YD=0;
XG=lt+ld-P;
YG=0;
X=[XD XG];
Y=[YD YG];
% ploting the line of duster hold rode by making the size of line 3
plot(X,Y,'-bo','LineWidth',3,'MarkerEdgeColor','y',
'MarkerSize',2)
H=[lt+ld-P hb/2];
J=[lt+ld-P -hb/2];
X=[H(1) J(1)];
Y=[H(2) J(2)];
% plotting the line of duster rode by making the size of line 3
plot(X,Y,'-ks','LineWidth',3,'MarkerEdgeColor','r',
'MarkerSize',2)
X=[lt-1400 lt-1200];
Y=[30 30];
plot(X,Y)
X=[lt-1400 lt-1200];
Y=[-30 -30];
plot(X,Y,'LineWidth',1,'MarkerEdgeColor','k')
X=[lt-1100 lt-450];
Y=[hb/2 hb/2];
X1=[lt-1100 lt-450];
Y1=[-hb/2 -hb/2];
X2=[lt-1100 lt-1100];
Y2=[hb/2 -hb/2];
X3=[lt-450 lt-450];
Y3=[hb/2 -hb/2];
% ploting the the dimension of the board by making the size of line 2
plot(X,Y,X1,Y1,X2,Y2,X3,Y3,'-k','LineWidth',2)
axis(gca,'equal');
% the dimension of the window in which the simulation plot
axis([-1000 3000 -1000 1000])
grid on
hold off
pause(0.005)
end

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5.1.2. Motion Analysis

As entitled in the above code all links and also points on the system has their motion due to the
cause from the external rotation exerted by hand. So, the rotation of the crank will be transferred
to the system. So, every point has position, velocity and acceleration relative to the fixed frame of
reference. The following MATLAB code shows the motion analysis for selected points.

% The program intended to show the position, velocity and acceleration of the
crank and yoke
% All dimensions are in mm
r=320;
lc=600;
ld=1200;
ls=1010;
lb=1010;
hb=800;
lt=2580;
teta=linspace(0,2*pi,50)
t=0:0.03:10;
teta=2*pi*t/3;
beta=asin(r*sin(teta)/lc);
omega=2*pi/3;
ang_teta=omega./t;
gamma=(r*omega*sin(teta))./(lc*sin(beta));
ang_beta=(r/lc.*(ang_teta.*cos(teta)-
omega.^2.*sin(teta))+gamma.^2.*sin(beta))./cos(beta);
% coordinates of B which is only under rotation
XB=r*cos(teta);
YB=r*sin(teta);
r_B=sqrt(XB.^2+YB.^2);
% coordinates of C which is under translation and rotation
XC=r*cos(teta)+lc*cos(beta);
YC=lc*sin(teta-beta);
r_C=sqrt(XC.^2+YC.^2);
% The resultant velocity equation for B
VB_x=-r*omega.*sin(teta);
VB_y=r*omega.*cos(teta);
velo=sqrt(VB_x.^2+VB_y.^2);
VB=sqrt((-r*omega.*sin(teta)).^2+(r*omega.*cos(teta)).^2);
%The resultant velocity equation for C
VC_x=-r*omega.*sin(teta);
VC_y=(lc-r)*(omega-gamma).*cos(teta-beta);
velo2=sqrt(VC_x.^2+VC_y.^2);
VC=sqrt((-r*omega.*sin(teta)).^2+((lc-r)*(omega-gamma).*cos(teta-beta)).^2);
%%%% The resultant acceleratioin equation for B
aB_x=-r.*ang_teta.*sin(teta)-r.*omega.^2.*cos(teta);
aB_y=r.*ang_teta.*cos(teta)-r.*omega.^2.*sin(teta);
acc=sqrt(aB_x.^2+aB_y.^2);
aB=sqrt((-r.*ang_teta.*sin(teta)-
r.*omega.^2.*cos(teta)).^2+(r.*ang_teta.*cos(teta)-
r.*omega.^2.*sin(teta)).^2);
% the resultant acceleration equation for C
aC_x=-r.*(ang_teta.*sin(teta)+omega.^2.*cos(teta));

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MANUALLY OPERATED BOARD ERASER DEVICE

aC_y=(lc-r).*(ang_teta-ang_beta).*cos(teta-beta)-(lc-r).*(omega-
gamma).^2.*sin(teta-beta);
acc2=sqrt(aC_x.^2+aC_y.^2);
aC=sqrt((-r.*(ang_teta.*sin(teta)+omega.^2.*cos(teta))).^2+((lc-
r).*(ang_teta-ang_beta).*cos(teta-beta)-(lc-r).*(omega-gamma).^2.*sin(teta-
beta)).^2);
plot(t,r_B,t,r_C,t,VB,t,VC,t,aB,t,aC)
title('motion for yoke and crank','FontSize',12)
legend('position of B','position of C','velocity of B','velocity of
C','acceleration of B','acceleration of C')
xlabel('time(s)')
ylabel('motion in (mm,mm/s,mm/s^2)')
xlim([0 10])
ylim([-1 2500])

motion for yoke and crank

2500
position of B
position of C
velocity of B
2000
velocity of C
motion in (mm,mm/s,mm/s 2)

acceleration of B
acceleration of C
1500

1000

500

0
0 1 2 3 4 5 6 7 8 9 10
time(s)

Figure 9. Motion analysis for crank and yoke

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MANUALLY OPERATED BOARD ERASER DEVICE

5.2. Discussion
The device has around five linkages, this all linkages have their own motion relative to the
corresponding meeting linkages. The MATLAB software shows the motions of all points which
represents the output results from the devices. And the MATLAB simulation is also held by the
software with the corresponding result of position, velocity and acceleration of the crank pin in
which the connecting rode assembled, the rotational and translational motion of yoke, and the
translational motion of the duster link. And this all results are much with manual expected results
from the motion of each point on linkages.

The results as depicted in the above picture are cyclic as well as consistence throughout the rotation
of the system and it much with the real calculations manually for instance the position of crank
and the point B is constant what if the rotation of the crank. And also, its velocity is cyclic which
repeats itself after one revolution rotation. Generally, the motions in the system are consistent and
become same with any rotations.

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MANUALLY OPERATED BOARD ERASER DEVICE

References

[1] FDRE Ministry of Education, "Education Statistics Annual Abstract," Addis Ababa,
Ethiopia, 2009.

[2] N. T. Neeraj Saraswat, "Development of New Design of Automatic Blackboard," vol. Six,
2017.

[3] "https://en.wikipedia.org/w/index.php?title=Special:ElectronPdf&page=Scotch+yoke&acti
on=show-download-screen," [Online].

[4] S. P. A. a. V. V. B. Pankaj D. Vatare, "Design and Fabrication of Automatic Board Eraser,"

vol. Volume: 2, no. Issue: 5 , May 2015.

[5] D. H. Myszka, MACHINES AND MECHANISMS, 2nd edition ed., New Jersey: Prentice
Hall, 2012.

[6] R. Hibbeler, Engineering Mechanics, Dynamics, vol. Tweleve Edition, Upper Saddle River,
New Jersey: Pearson Prentice Hall, 2010.

[7] J.L. Meriam and L.G. Kraige, Engineering Mechanics, Dynamics, Sixth Edition ed.

[8] D. T. Greenwood, Principle of Dynamics, Cambridge, New York: Cambridge University

Press, 2003.

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MANUALLY OPERATED BOARD ERASER DEVICE

Appendix
The assemblages of the device with wall and board by solid work 2013 software.

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 Item No Name
1 crank
2 key way
3 shaft
4 handle
5 connecting rode
6 duster link
7 7 yoke
8 duster
9 pin 1
10 pin 2
11 blackboard/wall
3

11
6

UNLESS OTHERWISE SPECIFIED: FINISH: DEBUR AND

DO NOT SCALE DRAWING REVISION
DIMENSIONS ARE IN MILLIMETERS BREAK SHARP
SURFACE FINISH: EDGES
TOLERANCES:
LINEAR:
ANGULAR:

NAME SIGNATURE DATE

TITLE: Assembly Drawing
DRAWN Wondimu Desssalegn 30/02/2019

CHK'D Mr. Mulugeta H.

APPV'D Mr. Mulugeta H.

MFG
MATERIAL:
assembly of the device
Q.A DWG NO.
A4

WEIGHT: SCALE:1:100 SHEET 1 OF 1