Nueva Vizcaya State University College of Engineering: Transport Mechanism For Variable Loads

Nueva Vizcaya State University
College of Engineering
TRANSPORT MECHANISM FOR VARIABLE LOADS
A thesis proposal presented to the

Faculty of the College of Engineering
NUEVA VIZCAYA STATE UNIVERSITY
Bambang, Nueva Vizcaya
In Partial Fulfillment
of the Requirements for the Degree
Bachelor of Science in Mechanical Engineering
Agustin, Jan Carlo V.

Benolirao, Noel Paul G.
Besa, John Michael F.
Binay-An, Katreena T.
Dela Cruz, Greg S.
Fernandez, Sunshine C.
Pacipas, King Janperson I
Sagyawan, Efrilyne C.
Serquiña, Glorilynn B.
Ubina, Ivy Joy A.
March 2019
DEDICATION
Every challenging work needs self-efforts as well as guidance of elders especially to

those who where very close to our hearts, our humble effort, this thesis is dedicated to:
Our Families, especially to our parents for financial support, understanding and
encouragement to pursue our project study;
Our friends who are always there to support and motivate;
Our Adviser who assisted us to make this project study possible;
The College of Engineering where we build our dreams and molding us to become what
we are today; and
Above all, our Almighty God for the blessings, guidance and wisdom which enabled us
to complete the work.
The Researchers
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ACKNOWLEDGEMENT
The proponent of this study would like to express their heartfelt gratitude and deepest
appreciation to those people who gave their full support for the completion of the study.
Andres Z. Taguiam, Ph.D., the university president for the vitality and novelty she has
rendered in the university;
Carlo F. Vadil, DPA., the campus administrator for her unending support to student
development.
Engr. Mary B. Pasion, Dean of College of Engineering, for the support, encouragement
and motivation he is imparting to us.
Engr. Simpher R, Guyong, our Chairman, Bachelor of Science in Mechanical
Engineering for the time, effort, improvement and monitoring of this research study.
Engr. Ranier Sam G. Mateo, the researcher’s adviser, for her guidance, concern,
patience and wisdom in the preparation and completion of this project to make it possible.
And to the faculty of the College of Engineering who are always there to lend a
helping hand.
To all our Family and Friends, who are always there to help Sus in many ways.
And above all, our Almighty God for guiding us and providing all our needs to complete
this project study.
The Researche
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APPROVAL SHEET
This thesis entitled “TRANSPORT MECHANISM FOR VARIABLE LOADS” has

been prepared and submitted by Jan Carlo V. Agustin, Noel Paul G. Benolirao, John Michael F.
Besa, Katreena T. Binay-an, Greg S. Dela Cruz, Sunshine C. Fernandez, King Janperson I.
Pacipas, Efrilyne C. Sagyawan, Glorilynn B. Serquiña, and Ivy Joy A. Ubina, in partial
fulfillment of the requirements for graduation with the degree of BACHELOR OF SCIENCE
IN MECHANICAL ENGINEERING.
RANIER SAM G. MATEO, RME

Adviser
APPROVED in partial fulfillment of the requirements for graduation with the DEGREE OF
BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING by the oral Examination
Committee
MARIA TERESA M. COSTALES, MA JANE P. AGBANLOG, BSCE

Member Member
VINCENT BRYAN L. REYES, RECE LARRY P. REMOLAZO, RME

Member Member
JEANELYN R. TOMINEZ, RME

Chair
ACCEPTED as a partial fulfillment of the requirements for graduation with the degree of
BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING.
MARY B PASION, RME, MSME SIMPHER R. GUYONG, RME

Dean, College of Engineering Chairman, ME Department
Recorded:
ROSALIA D. ALEMAN
Administrative Officer V, Acting Registrar
Date:
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TABLE OF CONTENTS
TITLE PAGE i
DEDICATION ii
ACKNOWLEDGEMENT iii
APPROVAL SHEET iv
TABLE OF CONTENT v
LIST OF TABLES vi
LIST OF FIGURES vii
Chapter 1: INTRODUCTION
The Problem and its Background 1
General and Specific Objective 2
Scope and Delimitation 2
Statement of the Problem 3
Significance of the Study 4
Conceptual Framework 5
Definition of terms 6
Chapter II: REVIEW OF RELATED LITERATURE AND STUDIES
Review of related literature 8
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LIST OF TABLES
Table Title Page

1 Design parameters of the rolling shear mechanism 30
2 The design result of the new rolling shear mechanism 31
3 Conventions to be followed to denote the linkages and the angle in 46
Phase – I and in phase – II
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LIST OF FIGURES
Figure Title Page
1 Conceptual Framework 5
2 Three-Bar Linkage 9
3 Four-Bar Linkage 11
4 Five -Bar Linkage 12
5 Klann Linkage 13
6 Sketch of a seven-bar rolling mechanism 14
7 Motion cycle of the rolling shear mechanism. 18

8 Fixed and moving centrodes of two rigid bodies. 19
9 Schematic diagram and Topological Structure of the mechanism 20
10 Kinematic model of the seven-bar linkage 21
11 Design parameters of the rolling shear mechanism 25
12 Centrodes and profiles of the shear blades 27
13 Motion simulation of rolling shear mechanism 31
14 Fixed centrode of upper shear blade and lower horizontal shear blade 32
15 Moving centrode of upper shear blade and are profile of upper shear 32
blade
16 Trajectory of arc middle point on the upper shear blade 33
17 Trajectory of the lowest moving point W on upper shear blade 34
18 Comparison of shear angle and stress before and after the design. 34
19 Free body diagram of linear pathway 36
20 Free body diagram of inclined pathway 37
21 A planar seven – bar slider mechanism 43
22 A planar seven – bar slider mechanism with variable topology at its 44
two dead – center positions, in phase-I
23 A planar seven – bar slider mechanism with variable topology at its 44
two dead – center positions, in phase-II
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Chapter I
THE PROBLEM AND ITS BACKGROUND
Rationale
Transportation is essential to our life that coordinate the movement of people, goods and
vehicles in order to utilize routes most efficiently. In order to maintain a functioning economy,
people must be able to circulate between the various points that are important to them and do so
with ease .Transportation is not just movement of people but movement of goods that is often
overlooked by transportation planners but it includes the shipment of raw materials, finished
products and even wastes. Raw materials such as minerals, energy, food and other resources are
obvious candidates for transportation as most occur in limited concentrations away from their
eventual points of consumption. Movement of finished goods from manufacturers to their
eventual end users also requires a well established transport network.
Peak Energy (in all of its forms) is the massive and fatal threat to the modern
transportation system. It disrupts the system insidiously at first before ultimately rendering it
useless. As energy becomes scarcer, it also increases in price. Over the past few years, those
increases have taken a toll on economic activity. In the future they will render whole sectors of
the economy unprofitable and ultimately not viable. As bad as that is, continued energy shortages
will eventually manifest themselves in the form of actual fuel shortages. When that occurs, hard
decisions will need to made on what to ship and when. In an orderly Powerdown scenario, those
exact choices would be made based on their relative importance to human life so that no one
starves or dies as a result of decreasing energy supplies. Unfortunately, the human track record in
dealing with crisis situations has been less than stellar. In all likelihood, government actions may
staunch the crisis for a few years, before the level of available energy decline begins undoing the
global transportation system altogether.
In many industrial manufacturing product different machines was made for transport
mechanism that are useful wherever items needed to be transported and fed from one place to
another, making the process easier, faster and more convenient because human labor is a lot less
efficient and not very cost-effective in the long run. A concept of conveyor is an example of
materials that would require manual efforts which involves hiring labor force and creates its own set
of human resource challenges used in variety of industries in food, pharmaceuticals, manufacturing
and transportation.
Many transport mechanisms are available in the market today have only a single function
and inefficient that is why the transport mechanism is hereby proposed and to provide a wide
range of uses and to increase the productivity output of the user. Manual lifting and carrying is a
tiring and sometimes dangerous process that can be easily avoided with the use of a transport
mechanism for variable loads. The researchers aim to produce a transport mechanism that
can increase efficiency in the workplace when compared to moving loads by hand, makes it
quick and easy to transport goods and materials from one place to another, saving time and
saving human energy in the process. The transport mechanism is not battery powered or run on
electric power, thus, it’s an eco-friendly mechanism which helps save money in the long run. The
mechanism is light, easy to store and incredibly portable. In this project, we apply the path of
generation synthesis and coupler synthesis and the study to fabricate our own model of transport
mechanism for a variable load.
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In day to day life, we may have to carry so many goods and objects of various quantities
through stairs especially in offices, schools, colleges, hotels, industries, apartments etc. where the
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lifts may not be available, may be crowded with people or may be under repair. It is highly
tiresome to carry various objects through stairs manually for higher floors for so many times.
The various applications may be carrying bundles of answer sheets in a school or a college,
carrying furniture in different buildings, different apparatus in colleges, in hospitals etc., carrying
electronic items in houses and offices. So, there should be a way to carry the objects through the
stairs in a more comfortable and tireless manner without forcing the user to apply more force.
(Jodie, D., 2019).
Objectives of the Study
The research paper aims to manipulate the box transport mechanism using the seven-bar
linkage mechanism to be able to produce an improved box transport mechanism which will have
better mobility and versatility than the conventional ones. The study specifically aims to
determine:
1. The different factors that may affect the mobility and versatility of the box transport
mechanism like speed, applied load, maximum load capacity of the mechanism, and other
loads that may be present and may affect the mechanism.
2. The environmental factors that may affect the performance of the mechanism like the
terrain and how to deal with it.
3. Other mechanisms that may help improve the present box transport mechanisms at
present.
Scope and Delimitation of the Study
This study focuses in designing and fabricating a portable transporting mechanism by
manipulating linkages for variable loads. The mechanism to be developed is simple yet can carry
loads and transport it even in elevated areas. This study aims in to create a transport mechanism
with high quality, easily operated and also save time. The system will be using linkages to
provide the ideal rotation, movement or slide.
The amount of load is only limited to a certain value depending on the material to be used
for the box transport mechanism. The proposed project will be utilized for transporting loads for
climbing up or downstairs, or be used conventionally. Calculations of forces that affect the whole
system were considered for the design of the study.
Statement of the problem
Technology saves time and money, producing a mechanism that consist a seven-bar linkage
that is affordable and portable is of great help as lifting heavy loads with just our body may cause
back injuries. Often lifting may affect our health thus, the transport mechanism may help lift
variable loads to higher points and/or can be used conventionally for easier transport of loads. Its
flexibility and versatility will be beneficial to various places of application.
Some specific problems were also considered:
1. How is the transport mechanism for variable loads designed?
2. What are the materials, supply and equipment needed to fabricate the research project?
3. What are the steps in the fabrication of the proposed transport mechanism?
4. What is the cost of the developed transport mechanism?
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Significance of the study
The researchers aim to produce a transport mechanism that can help improve productivity
in the workplace in terms of transport of goods making it easier to move objects from one place
to another saving time and energy in the process. The results of the study could be beneficial to
the following:
Storage Industry. Having this transport mechanism for variable loads specifically
benefits industries that require the transport of materials and goods. The transport
mechanism will help workers transfer a variety of materials with less effort.
Merchandising. The transport mechanism will help for faster and more efficient
transport of products for stores and shops. As new products are becoming
available online, the variety of these products may also become bigger in size and
soon will have shipping or delivery difficulties, the transport mechanism may
come in handy to these changes.
Future Academic Researchers. This study will help future researchers expand their
range of data and imagination, and will also serve as a guide for similar projects
involving the seven-bar linkage.
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Conceptual Framework
INPUT
 Supplies and Materials Design of Transport Mechanism
 Reference materials, internet, books Variable loads
 Gathered information and its application
 Ideas and information
PROCESS
DESIGNING FABRICATING TESTING
Planning Design Fabricated transport ADJUSTMENT

mechanism
Ideas information Materials needed Redesign
Design of transport
Blueprint Welding mechanism
Grinding
Cutting Human work
OUTPUT
Fabricated Transport Mechanism for Variable Loads
Figure 1. Conceptual Framework
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Figure 1 shows the input, throughput and output of the design and fabrication of a
transport mechanism for variable loads to be conducted at Nueva Vizcaya State University
Bambang Campus.
The input of the study includes the idea information that an idea is usually generated
with intent but can also be created unintentionally. Ideas often form during brainstorming session
or through discussions. Reference materials, internet and books are also included in order to
ascertain something. The design of transport mechanism for variable loads also included in
constructing the transport mechanism for variable loads. The throughput of the study shows the
procedures and processes for conducting study, designing, fabricating, testing and adjustment. In
designing, planning idea information and blueprint are included. The researcher thinking about
the activities required to achieved desired goals. It is the first and foremost activity to achieved
desired results. The design, materials needed, welding, grinding, and cutting are the process to
achieved a desired result in fabricating. The testing process includes the fabricated transport
mechanism, design transport mechanism and human work. If the testing process fails the
researchers need to adjust to achieved a desired fit, appearance, or result. The output of the study
is the fabricated transport mechanism.
Definition of Terms
Mechanism. A mechanism is a part of a machine or is a set of parts that work together.
The mechanism is the one to be manipulated in the study; specifically, the seven-
bar linkage mechanism.
Conveyor. It is a machine that transports something from one place to another.
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Specifically, a conveyor belt is a continuous moving strip or surface that is used
for transporting objects from one place to another. In the study, the conveyor
served for comparison for the box transport mechanism.
Variable load. The load refers to the amount to be carried, especially by a vehicle or a
structure. The word variable means the load may vary depending on the
application. The variable load will serve as a parameter for the study.
Seven-bar linkage. A mechanical linkage is an assembly of bodies connected to manage
forces and movement. The seven-bar linkage is a mechanism that is constructed
from seven links and eight joints. For the study, the seven-bar linkage will be used
or be utilized, or will be based upon for the final design of the study.
Mobility. It refers to the ability of something to move freely or be easily moved.
Mobility is used in the study as one performance factor of the mechanism.
Versatility. It refers to the ability of something to adapt or be adapted to many different
functions or activities. Versatility is used in the study as one performance factor of the
mechanism.
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Chapter II
REVIEW OF RELATED LITERATURE
I. Design of Linkage Mechanism
Linkage mechanism
A linkage mechanism is a mechanism composed of one or more lever that attached each
other together and its assembly of bodies connected to manage force and movement. the
movement of the body is to be designed to make two or more linked object to move at the same
time. Linkages may be constructed from open chains, closed chains, or a combination of open
and closed chains.
Linkage can be classified according to their primary functions: Function generation is the
relative motion between the links connected to the frame, Path generation is the path of the tracer
point, Motion generation is the motion of the coupler link. Coupler is a link that connects two
crank and connecting rod is a coupler that connects crank and slider.
Concept of Linkage
A linkage consists of a number of pairs of elements connected by links. Link may be
defined as a rigid piece or a non-elastic substance which serves to transmit force from one piece
to another or to cause or control motion. If the combination in such that relative motion of the
link is possible, and the motion of each piece relative to others is definite, the linkage becomes a
kinematic chain. If one of the links of a kinematic chain is fixed, then the chain becomes
mechanism. In order that a linkage may constitute a kinematic chain, the number of fixed points,
or points whose motion are determined by means outside the particular linkage in question, must
bear such relation to the total number of links that the linkage may form a four-bar linkage or a
combination of two or more four-bar linkages. (Doughtie & James, 2005)

Figure 2. Three-Bar Linkage
Linkages are capable of performing tasks such as describing straight lines or curves and
executing motions at differing speeds. Linkage is link has two or more joints, and the joints have
various degrees of freedom to allow motion between the links. It is called a mechanism if two or
more links are movable with respect to a fixed link. Mechanical linkages are usually designed to
take an input and produce a different output, altering the motion, velocity, acceleration, and
applying mechanical advantage.
Types of Linkages according to functionality
1. Four-bar linkage. A four-bar linkage also called a four-bar is the simplest movable
closed chain linkage. It consists of four bodies, called bars or links connected in a loop by
four joints. Generally, the joints are configured so the links move in parallel planes and
the assembly is called a planar four-bar linkage. If the linkage has four hinged joints with
axes angled to intersect in a single point, then the links move on concentric spheres and
the assembly is called a spherical four-bar linkage. Bennett's linkage is a spatial four-bar
linkage with hinged joints that have their axes angled in a particular way that makes the
system movable.
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This machine is basically working on the principle of Single Slider Crank
Mechanism which is the heart of this machine and it converts rotary motion into a
reciprocating machine to crush the Cans/Plastic bottles. In this, link 1 is fixed and link 2
which is a crank is rotating about fixed link 1 and converts this rotary motion into the
reciprocating motion of slider (corresponds to the link 4) by means of connecting rod
which corresponds to the link 3. This is the inversion of single slider crank which is
obtained by fixing link.
It is evident from Figure 3, that, while the crank arm rotates through 180°, the
piston moves from the position known as top-center (TC) to the other extreme, called
bottom-center (BC). During this period the piston travels a distance, S, called the stroke,
which is twice the length of the crank. For an angular velocity of the crank (ω) the crank
pin A has a tangential velocity component ω S/2. It is evident that, at TC and at BC, the
crank pin velocity component in the piston direction, and hence the piston velocity, is
zero. At these points, corresponding to crank angle = 0° and 180°, the piston reverses
direction. Thus, as varies from 0° to 180°, the piston velocity accelerates from 0 to a
maximum and then returns to 0. A similar behavior exists between 180° and 360°.The
connecting rod is a two-force member; hence it is evident that there are both axial and
lateral forces on the piston at crank angles other than 0° and 180°. These lateral forces
are, of course, opposed by the cylinder walls. The resulting lateral force component
normal to the cylinder wall gives rise to frictional forces between the piston’s rings and
cylinder. It is evident that the normal force, and thus the frictional force, alternates from
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one side of the piston to the other during each cycle. Thus, the piston motion presents a
challenging lubrication and reduction of both wear and energy loss.
The position of the piston with respect to the crank centreline problem for the
control is given by
x = (S/2) cos + Lcos Ø [ft | m] ……. (1)
where, yA = (S/2) sin = L sinØ can be used to eliminate Ø to obtain
X/L = (S/2L) cos + [1- (S/2L)si n ] ½
Thus, while the axial component of the motion of the crank pin is simple harmonic, XA=
(S/2) cos, the motion of the piston and piston pin is more complex.
Figure 3. Four-Bar Linkage
2. Five-Bar Linkage. A five-bar linkage mechanism has two degree of freedom and cannot
be connected in multi loop configurations as the only config possible is one loop. Since
two degrees of freedom is A bit bad design they tend to be avoided. Sometimes you see
these with a cam/Gear connection serving as link 5. It is easily mistaken as four-bar as
the fifth bar is of limited movement. These can be seen also in robotics setups where
corner connected four-bar would not fit.
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Figure 4. Five r-Bar Linkage
3. Six-bar linkage. A six-bar linkage is a one degree-of-freedom mechanism that is
constructed from six links and seven joints. An example is the Klann Linkage used to
drive the legs of a walking machine. In general, each joint of a linkage connects two
links, and a binary link supports two joints. If we consider a hexagon to be constructed
from six binary links with six of the seven joints forming its vertices, then, the seventh
joint can be added to connect two sides of the hexagon to forming a six-bar linkage with
two ternary links connected by one joint. This type of six-bar linkage is said to have the
Watt topology. A six-bar linkage can also be constructed by first assembling five binary
links into a pentagon, which uses five of the seven joints, and then completing the linkage
by adding a binary link that connects two sides of the pentagon. This again creates two
ternary links that are now separated by one or more binary links. This type of six-bar
linkage is said to have the Stephenson topology. The Klann linkage has the Stephenson
topology.
Klann Linkage. The Klann linkage is a planar mechanism designed to simulate the gait
of legged animal and function as a wheel replacement. The linkage consists of the frame,
a crank, two grounded rockers and two couplers all connected by pivot joints. It was
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developed by Joe Klann in 1994 as an expansion of Burmester curves which are used to
develop four-bar double-rocker linkages such as harbor crane booms. It is categorized as
a modified Stephenson type III kinematic chain.
The proportions of each of the links in the mechanism are defined to optimize the
linearity of the foot for one-half of the rotation of the crank. The remaining rotation of the
crank allows the foot to be raised to a predetermined height before returning to the
starting position and repeating the cycle. Two of these linkages coupled together at the
crank and one-half cycle out of phase with each other will allow the frame of a vehicle to
travel parallel to the ground.
The Klann linkage provides many of the benefits of more advanced walking
vehicles without some of their limitations. It can step over curbs, climb stairs, or travel
into areas that are currently not accessible with wheels but does not require
microprocessor control or multitudes of actuator mechanisms. It fits into the
technological space between these walking devices and axle-driven wheels.
Figure 5. Klann Linkage
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4. Seven-Bar Linkage.
i. Kinematic Design of a Seven-Bar Linkage with Optimized Centrodes for Pure-
Rolling Cutting
A seven-bar linkage has two degrees of freedom, which can be used in many machines
with variable trajectories. Of all associated machines, a typical example is the seven-bar pure-
rolling cutting mechanism, which generates pure-rolling motion between two contacting bodies.
Figure 6. Sketch of a seven-bar rolling mechanism
The design of pure-rolling mechanism is essentially a problem of trajectory synthesis of
linkages, for which many synthesized methods are available. The synthesis can be carried out
either for a set of given points or for a continuous trajectory. The synthesis results are either
exact or approximate. Normally exact synthesis is difficult to implement in practice and
approximate methods are used to approximate the given points or continuous trajectory as much
as possible. To evaluate the trajectory deviation of approximate synthesis, some trajectory
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deviation measurement functions are introduced, including deterministic error, Fourier deviation,
shape similarity, ambiguity function, and shape feature matching deviation.
Generally, there are two different ways to accomplish approximate synthesis, namely, direct and
indirect synthesis methods. The direct synthesis method generates a mechanism directly
according to the given points or continuous trajectory. Nelson Larsen used an atlas of coupler
curves to analyze the four-bar linkage, but the computation accuracy was unsatisfactory. Kramer
extended the selective precision synthesis method to generate four-bar motion mechanism with
prescribed input crank rotations, which used the Hooke-and-Jeeves search method to handle the
equality constraints during the synthesis process. Subbian and Flugrad implemented the
continuation method to deal with the sets of polynomial equations in the four-bar path generation
synthesis, which was proved to be more effective. Nevertheless, even with these numerical
methods, the nonlinear synthesis equations of high order are still difficult to solve. Cabrera et al.
used the genetic optimization algorithm to optimize the position error between the given target
points and the points reached by the resulting mechanism during the synthesis of four-bar planar
mechanisms. In order to obtain both effectiveness and high accuracy, many other optimization
algorithms are also adopted in the trajectory synthesis of the mechanism, such as simulated
annealing and stochastic method.
The indirect synthesis method is used to search for the matching trajectory from the predefined
trajectory atlas, instead of directly generating a mechanism scheme, which is done by analyzing
the expected trajectory and then exporting the corresponding mechanism types and sizes. If there
is a similar scheme, the minimum trajectory deviation will be obtained. The indirect synthesis
method mainly relies on the mass data-storage capacity and rapid retrieval ability of a computer.
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Although the rapid improvement of computers promotes the application and development of the
indirect synthesis, the difficulties of the establishment of a trajectory atlas, the mass data-storage
capacity of a computer, and the approach to effectively search for the best matching trajectory
are still challenging problems to be solved.
For the problem here, the design of seven-bar linkages for pure rolling needs to meet both the
trajectory and also other requirements for machining, that is, steel plates cutting. The shear
motion of a rolling shear mechanism is generally realized by means of the relative motion
between the upper shear blade and the lower shear blade. The expected shear motion should be a
pure-rolling motion without slipping. In this regard, Wang and Huang developed an optimized
model for rolling shear mechanism with single shaft and double eccentricity, choosing four
motion positions as access points to acquire the expected motions, while the phase difference
was set to be identical. Yang et al. used the constraints of equal radius of crank and equal length
of linkage to set up an optimization model of rolling shear mechanism with roll guide groove.
Sun et al. designed a rolling shear mechanism by optimizing the trajectory of the lowest moving
point of the upper shear blade, but the upper shear blade could not perform pure-rolling motion
relative to the lower blade due to the horizontal slide. Synthesis-optimized model was built to
design a rolling shear mechanism, using a guiding rod as an additional design variable, while
identical phase difference and identical length between the designed guide rod and the expected
guide rod are adopted for four positions. In order to improve shear quality, decrease blade wear,
and prolong blade life of the cutting machine, generally, the pure-rolling motion between the
shear blades can be transformed into a series of moving positions and phase angles of the seven-
bar linkages, with which an optimized method is adopted to obtain proper linkage sizes. In
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certain situations, the synthesis can only satisfy some key points; the motion accuracy of the
designed pure-rolling cutting mechanism is thus low. It is difficult to realize the pure-rolling
motion during the whole cutting process, due to the fact that the cutting performance was not
considered or embodied in the synthesis.
This paper proposes a method for the kinematic design of a seven-bar linkage to generate
pure-rolling motion by optimizing the centrodes. The introduced method is developed based
upon the interrelation between the centrodes and contacting lines of pure-rolling motion. A case
study of seven-bar rolling shear mechanism is included to demonstrate the method to accomplish
the pure-rolling motion. A genetic optimization algorithm is used to obtain mechanism sizes with
the metric function of minimum approximation error between mechanism centrodes and
expected trajectories of shear blade. The constraints of the formulated optimization problem for
the pure-rolling mechanism include the design requirements of the opening distance, the
maximum amount of overlap error, and peak value of shearing force. Moreover, the performance
of the newly designed rolling shear mechanism is investigated and compared with the original
one, which shows the advantages of the new method.
A new approach to design a seven-bar linkage for pure-rolling cutting by optimizing
centrodes is presented in this paper. Using the genetic optimization algorithm, the proposed
method allows the designer to obtain an optimum linkage which minimizes the error between the
centrodes of mechanisms and profiles of pure rolling. With the proposed method, a seven-bar
rolling shear mechanism is designed which has better performance compared to the original one
in the following aspects:(1)The horizontal slipping of the designed rolling shear mechanism has
been reduced by 78.0%, which increases the cutting efficiency and reduces the wear of the
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shearing blade.(2)The standard deviation of the lowest moving point on the upper shear blade
has been reduced by 80.1%, which indicates better quality of steel plates.(3)The peak value of
shear stress, which indicates the power performance of rolling shear mechanism, is decreased by
29% for long service life.
DESIGN MODEL
i. Design Issue and Problem Formulation
The seven-bar linkage has 2 degrees of freedom, corresponding to cranks AB and EF as
driving links, which rotate by the same angular velocity and with a constant phase difference,
sharing a power input. Link CDG, to which the upper blade is attached, outputs motion.
Generally, the lower shear blade is fixed on the frame, while the upper shear blade moves
relative to the lower shear blade to cut the steel plate between them, as shown in Figure 7
Figure 7. Motion cycle of the rolling shear mechanism.
The horizontal sliding of the upper shear blade should be as little as possible to reduce the
wear of the blade. Meanwhile, the cutting depth of the upper shear blade should be the same to
reduce the bending deformation of the steel plate, ensuring a stable cutting quality of the steel
plate. Thus, the ideal motion of the upper blade should be pure-rolling cutting relative to the steel
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plate during the shearing process, to make sure there is no horizontal sliding between the blade
and the steel plate at the cutting contact point.
One of the rigid bodies is usually chosen to be fixed and another moves relative to the
chosen one for convenience during the motion analysis of two rigid bodies, as shown in Figure 8.
Rigid body II is fixed in coordinate system Of −x f y f . Rigid body I, on which a moving
coordinate system Om−x m y mis built, moves in the fixed coordinate system Of −x f y f . A
point Om of body I has a velocity vOm and body I rotates about point Om with angular velocity
w Om . The motion state of body I at any moment is either (a) entire translation or (b) rotation
about a specific on body I, of which the velocity in the fixed coordinate system is zero. The
point P is called the instantaneous velocity center, and the entire translation can be regarded as
the point being at infinity. So, the motion of body I can be treated as a pure rotation about P at
any moment. As rigid body I moves, the instantaneous velocity center P traces a trajectory in
the fixed coordinate system Of −x f y f , which is called the fixed centrode T 1 , and a trajectory in
the moving coordinate system Om−x m y m, which is called the moving centrode T 2. The motion of
body I can be regarded as the pure-rolling motion of the moving centrode along with the fixed
centrode with no sliding.
19
Figure 8. Fixed and moving centrodes of two rigid bodies.
As the thickness of the steel plate is far less than the width of the steel plate and the
length of the blade, the contact line of the shear blade and steel plate is usually treated as a
contact point in practice. Thus, the ideal cutting motion can be regarded as the pure-rolling
motion between the upper shear blade and the lower shear blade with no sliding at the contact
point. The objective is to synthesize the linkage for pure-rolling shear motion, so that the
profiles of the upper and lower blades coincide with the moving and fixed centrodes of the
output link, respectively, during the shearing process.
ii. Kinematic Design Model
A seven-bar linkage is chosen to establish the kinematic design model, of which the
topological structure can be obtained, as shown in Figure 9.
20
Figure 9. Schematic diagram and Topological Structure of the mechanism

Links ABand EF are assigned as the driving links, while the ternary link CDG is assigned as
the output coupler, to which the upper shear blade is attached. Link AFH, which is also a ternary
link assigned number 7, is chosen as the frame. So, there are 6 movable links, corresponding to 6
angles { θi , i=1,2 , … ,6 }, as shown in Figure 5. Vector equations of closed-
loop HGDEFH and HGCBAH are listed as follows:
(1)
0
21
Figure 10. Kinematic model of the seven-bar linkage.
Usually, joints A and F are designed with the same height for convenience of structure design
and power transmission. For the convenience of the modeling, vectors HK and KF are introduced
to take the place of vectors HA and HF, as shown in Figure 10. The lengths of
vectors HK and KF represent the vertical and horizontal distances of joint F relative to joint H,
respectively.
So, can be obtained from the new closed-loop HGDEFKH and HGCBAFKH as
(2)
0
A fixed coordinate system H−xy and a moving coordinate system L−x m y m are established at
the hinged point H and the center of the driven link CD, respectively. Besides the basic length
parameters { Li ,i=1,2, … , 6 } , of the 6 movable links shown in Figure 10, L7, L8 and a are
introduced to determine the dimensions of link CDG, and L9, L10 , and L11 are introduced for
vectors AF, HK, and KF. Thus, the length parameters of the linkage are { Li ,i=1,2, … , 11 } .
Expanding (2) yields
(3)
0
The driving links AB and EF, have the same angular velocity with a constant phase difference,
sharing a power input. That means θ1−θ 2=θC . The differentiation with respect to time of (3)
yields.
22
(4)
0
whereω 1=ω2 , which are given quantities, denoting the angular velocity of links AB and EF.
Thus, θ5, θ6 , ω 5 and ω 6 can be obtained by solving (3) and (4)
The driven link CDF should generate pure-rolling cutting motion between the upper and lower
blades. During the cutting process, the instantaneous center P forms the moving centrode relative
to the driven link CDG and the fixed centrode relative to the fixed frame, represented by
curves Γ 1 and Γ 2, as displayed in Figure 10. In order to derive the kinematic equations of
centrodes, coordinate transformation matrix is used to transform the points from moving
coordinate system to fixed coordinate system, wch is related to rotation angle and translation
distance. Let the coordinates of instantaneous center P be ( x , y ) in the fixed coordinate
system H−xy and ( x m− y m ) in the moving coordinate system L−x m y m . An additional
coordinate system G−x G y G, which is established at hinged point G as shown in Figure 10, is
introduced to implement coordinate transform between the fixed and moving coordinate systems.
The two sets of coordinates ( x , y ) and ( x m− y m ) are related by
(5)
23
where matrix M HG is the homogeneous transformation matrix from the fixed coordinate system
H−xy to G−x P y P and M GL is the one from G−x P y P to the moving coordinate
system L−x m y m. They are given as
(6)
where θ1 and θ2 are orientation angles of links DG and GH , β 1 is the angle between
vectors GD and GL, and is the orientation angle of the x-axis of system L−x m y m in coordinate
system G−x G y G; LGL represents the length of GL. Substituting the above equation into (5) and
upon differentiation with respect to time, one has
(7)
where ẋ and ẏ are the velocities of instantaneous center P. ω 5 and ω 6 are the angular velocities
of links L5 and L6. As the velocity of instantaneous velocity center P at any moment in the fixed
coordinate system H−xy is zero, namely, ẋ = ẏ=0 , by arranging and rewriting the above
equation, the moving centrode of link system CDG is expressed as
(8)
Substituting (8) into (5), the fixed centrode is obtained as
24
(9)
So far, both the moving and the fixed centrodes have been obtained, upon which optimal sizes
and positions of the mechanism can be searched to ensure that the trajectories of moving and
fixed centrodes cooperate with each other in the way of pure rolling.
OPTIMIZATION DESIGN CASE

In this section, a design case of seven-bar rolling shear mechanism, as a kind of common
pure-rolling cutting mechanism, is considered. The ideal shear motion of a rolling shear
mechanism should be pure-rolling motion between the upper shear blade and the lower shear
blade. With the generated moving centrodes and fixed centrodes coinciding with the motion
contact lines of the upper shear blade and lower shear blade, respectively, the pure-rolling
motion can be obtained. Hence, the optimization objective function and the constraints could be
determined by pure-rolling motion and cutting performance requirements. A genetic
optimization method is employed to determine the proper linkage sizes of rolling shear
mechanism thanks to its effectiveness and convenience.
I. Design Parameters
The design parameters of a rolling shear mechanism are given by the cutting process.
These design parameters include the width of sheared plate B, the maximum shearing
thickness h max, the shearing overlap S, and the shearing angle α, as shown in Figure 6. The
width B determines the horizontal width of the lower shear blade, and the shearing
25
overlap S gives the overlapping amount between the upper and the lower shear blades in the
shearing process. The shear angle α refers to the contact point between the lower shear blade
and the tangent of arc upper shear blade.
Figure 11. Design parameters of the rolling shear mechanism.
II. Optimization Model
Based on the design parameters, the expected trajectories (or profiles) of upper and lower
shear blades can be obtained. The purpose of genetic optimization model is to seek a set of
optimal mechanism sizes to minimize the deviation between centrodes and expected trajectories
of upper and lower shear blades, subject to some specific design requirements. The detailed
optimization model is as follows.
Optimization Variables
The design variables of a rolling shear mechanism are generally the lengths of links and
pivoting joint positions. These design variables are defined as optimization variables,
expressed by a vector t:
(10)
26
in which each variable t i ( i=1,2 , … n ) represents the size parameter of a mechanism scheme,
such as the lengths of links { Li , i=1,2 , … 11 } and phase angles { θi , i=1,2, … 6 }. Each optimal
scheme can be expressed by vector t ¿, called optimal point.
Optimization Objective Function
The objective of the design optimization is to make the moving centrode approach the profile
of the upper shear blade and the fixed centrode approach the profile of the lower shear blade
as much as possible. Accordingly, the objective function of the optimization design can be
defined as the sum of approaching errors, including the approaching error for moving
centrode and upper shear blade, together with the approaching error for fixed centrode and
lower shear blade, which will be minimized as follows:
(11)
where U 1 ( t ) and U 2 (t) are the curve approximation errors between moving centrode and
upper shear blade and fixed centrode and lower shear blade, respectively. The errors should
be evaluated in the moving coordinate system Om−x m y m and the fixed coordinate system
O−xy on upper and lower shear blade, as shown in Figure 12
27
Figure 12. Centrodes and profiles of the shear blades.
The geometric equations of the moving centrode and profile of the upper shear blade in the
moving coordinate system Om−x m y m can be written as
(12)
Also, equations of the fixed centrode and profile of the lower shear blade in the fixed
coordinate system O−xy can be written as
(13)
where x n−x 1=B and C is a constant, describing the position of the sheared plate. The
errors U 1 (t) and U 2 (t) can be determined by
(14)
28
Hence, the objective function of optimization for the pure-rolling cutting mechanism design
can be expressed as
(15)
Constraints
The constraints of a rolling shear mechanism mainly include some motion parameters and
performance parameters, such as the opening distance, the shearing overlap error of the upper
and lower shear blade, and the peak value of shearing force.
(1) Opening Distance Constraint. In order to make the sheared plate get through smoothly
between the two shear blades, the clearance between the upper and lower shear blades after
shearing, also known as the opening distance (H), which is the function of design variable t,
should be greater than the designed value K associated with the thickness of sheared plate:
H (t) ≥ K
(2) Overlap Error Constraint. The overlap error in direction of plate width should be limited to a
given amount. The overlap amount is the distance from the lowest moving point of upper
shear blade to the lower shear blade. The coordinates of the lowest moving point W in the
fixed coordinate system can be obtained by a geometrical relationship as shown in Figure 11.
It can be written as
29
where R and β are the arc radius and the dip angle of upper shear blade, respectively,
and ( x v , y v ) is the coordinate of middle point V on upper shear blade in the fixed coordinate
system. Thus, the overlap error constraint is expressed as
(3) Peak Value of Shearing Force Constraint. Generally, the forces applied on upper shear blade
refer to both shear force and other forces, such as friction force. The peak value of shear
force constraint can be introduced by limiting the maximum shearing force that usually
appears in the initial shear stage. The shearing force of a rolling shear mechanism is
expressed as
where σ B and δ are the ultimate strength and percentage elongation of material for sheared
plate Z, represents the conversion coefficient, Y is the ratio of shear blade gap with the
thickness of steel plate, and X is the ratio of the distance between shear blade edge and steel
plate with the thickness of steel plate. The shearing force constraint may be limited by shear
angle α, because the peak value of shearing force can be highly correlated to the shear angle.
Therefore, it may be given by means of specified shear angle α 0, which is written as
α st ≥ α 0
where α st is the initial shear angle of upper shear blade. According to the above discussion
for determining the sizes of rolling shear mechanism, the final design vector, marked as t ¿,
30
where the mechanism sizes achieve pure-rolling motion of the upper shear blade, can be
obtained by means of the genetic optimization algorithm.
31
RESULTS AND ANALYSIS
According to the optimization functions and given shearing requirements, the seven-bar
mechanism for pure-rolling cutting will be synthesized and the kinematic performance will be
analyzed and compared to the original one.
Optimization Results
The seven-bar mechanism for pure-rolling cutting is shown in Figure 7. The actual design
parameters of sheared plate are used as the design parameters of rolling shear mechanism, as
shown in Table 1.
Table 1. Design parameters of the rolling shear mechanism
The length of each link and initial phase angles of two cranks are used as optimization variables.
Given that the constant C should be set as −400 mm, the constraint of initial shearing angle is
selected as follows a st ≥1.5 ° . Meanwhile, the optimization model of rolling shear mentioned
above can be established, together with the genetic optimization algorithm employed. Therefore,
the lengths of linkages, the coordinate of fixed hinge point F, and the initial phase angle of
crank AB of the new mechanism can be obtained, as shown in Table 2.
32
Table 2. The design result of the new rolling shear mechanism
Kinematic Performance Analysis
Figure 13. Motion simulation of rolling shear mechanism

A major kinematic performance concerned for this design is a pure-rolling motion
between two blades and is described by deviations between fixed and moving centrodes and
contacting lines, which is intuitively exhibited through the trajectory of the lowest moving point
and arc middle point of upper shear blade. The cutting performance is illustrated by the
comparison of the shear angle and shear stress between the original design and the new design in
this paper.
33
Simulation and performance analysis of the rolling shear mechanism based on Pro/E and
MATLAB software were conducted. Figure 13 shows the motion simulation model of the rolling
shear mechanism.
Figure 14. Fixed centrode of upper shear blade and lower horizontal shear blade.
The comparison of the fixed centrode of the upper shear blade and the lower shear blade
between the original and optimal results is shown in Figure 14. The designed fixed centrode has
better straightness in the segment, which can approximate the horizontal contact line in a better
way and is in accordance with the objective function. Notice that the axes are not isometric for
clear demonstration.
Figure 15. Moving centrode of upper shear blade and are profile of upper shear blade
34
Figure 15 shows that the designed moving centrode approximates the symmetrical arc
perfectly, which means that it approximates the moving contact arc perfectly, which is in
accordance with the objective function. Notice that the axes are not isometric for clear
demonstration.
Figure 16. Trajectory of arc middle point on the upper shear blade
Figure 16 shows the trajectory of arc middle point on the upper shear blade, which
presents the cutting process part. Notice that the axes are not isometric for clear demonstration.
The results demonstrate that the horizontal slipping of the designed upper shear blade is
confirmed as 0.97 mm, compared to the original result of 4.88 mm, reduced by 80.1%, which
illustrates that the designed upper shear blade profile is better in the realization of pure-rolling
motion and also indirectly proves the validity of the method of designing rolling shear
mechanism sizes.
35
Figure 17. Trajectory of the lowest moving point W on upper shear blade
Figure 17 shows that the trajectory of the lowest moving point of upper shear blade is
approximately a straight line, and its straightness reflects overlapping evenness of upper and
lower shear blade. Notice that the axes are not isometric for clear demonstration. The standard
deviation of optimal result in trajectory sets of upper arc lowest moving point during shearing
process is confirmed as 0.415 mm, compared to the original result of 1.890 mm, being reduced
by 78.0%, indicating more uniform overlap between upper and lower shear blade.
36
Figure 18. Comparison of shear angle and stress before and after the design.
The changes of shear angle and stress before and after the design are shown in Figure19,
which indicates that the initial angle of the designed rolling shear mechanism at the beginning of
the cutting process is roughly 1.5°, while the original initial angle is 0.9°. This improvement will
be of great interest to improving the initial peak value of shear force. The shear angle increases
to about 2.2° when the shearing process comes to the stable rolling stage, no matter in the
original design or in the new design. The peak value of shear stress of the designed rolling shear
mechanism is roughly 1.2 x 107 , decreasing by 29% in comparison with the original shear stress
peak of 1.7 x 107 . Moreover, the above figures, along with shear angle changing curve, show that
the shear stress and shear angle change oppositely. Therefore, it is beneficial to improve the
initial shear angle in order to reduce the initial shear stress.
VARIABLE LOADS
A. General principles of the use of safety factors in design and assessment
Any structure or component can be made to fail if it is subjected to loadings in excess of

its strength. Structural integrity is achieved by ensuring that there is an adequate safety margin or
reserve factor between strength and loading effects. The basic principles of ‘allowable stress’ and
‘limit state’ design methods to avoid failure in structural components. The use of risk as a means
of defining adequate safety is introduced where risk is defined as the product of probability of
failure multiplied by consequences of failure. The need to consider the effects of uncertainties in
loading information, calculation of stresses, input data and material properties is emphasized.
The way in which the effect of different levels of uncertainty can be dealt with by use of partial
safety factors in limit state design is explained. The need to consider all potential modes of
failure, including the unexpected, is emphasized and an outline given of safety factor treatments
for crack
tip dependent and time dependent modes. The relationship between safety factors appropriate for
the design stage and for assessment of structural integrity at a later stage is considered. The
effects of redundancy and system behavior on appropriate levels of safety factors are discussed.
37
B. The simplest definition of Factor of Safety (FOS) is FOS = Strength of Component
Material / Load applied on component
Structures or components can fail, collapse, rupture or break if the components or
structures is subjected to loading that over the material strength. Thus, there is a need to ensure
there is proper safety margin and the basic principles used is the allowable stress and limit state
design method. These methods basically divide the material strength with appropriate yield by
the safety factor of 1.5 or ultimate strength by the safety factor of 2.5-3.0. Thus, FOS is
important to avoid the structures and components fail.
Factor of safety greatly affect the design of a structures and components as when the
design exhibits the stresses that over the limit of the material strength, the structure or component
will fail and break. However, when the FOS is too high, it will be over-design and the design
most probably will be too bulky, less aesthetic values and eventually increase the costing from
excessive material usage.
Linear pathway
a.) Linear Pathway b.) Free body diagram

Figure 19. Free body diagram of linear pathway
Legend:
W= Variable loads
F= Exerted force by the 7-bar linkage
38
Fg= Gravitational force

Ff= Frictional force
L= Length of the transport mechanism
Inclined pathway
An inclined plane is one of the six types of simple machines. It is exactly what it sounds
like - it is a plane (a flat surface) that is inclined, or slanted at an acute angle. Inclined planes
connect a lower level to a higher level, they make work easier. In science, 'work' is when you
apply force (a push or a pull) and it moves an object.
a.) Inclined pathway b.) Free body diagram

Figure 20. Free body diagram of Inclined pathway
LEGEND:
W= Variable loads
F= Exerted force by the 7-bar linkage
Fg= Gravitational force
Ff= Frictional force
L= Length of the stair
h= Height of the stair
θ= Angle of Elevation
SELECTION OF MATERIALS AND OTHER FACTORS
39
According to the studies of S. Balli et al, (2003) metal forming is one of the oldest
production processes and yet, it is one the most commonly used manufacturing technologies
even today. In order to achieve the desirable punch motion, today many mechanical presses use
multiple links. The metal forming operations like shearing, bending and deep drawing require
different variable motions of the punch, like shearing requires very short stroke of the ram and
deep drawing requires a slow and long stroke of the punch. The common materials used in
constructing the linkage mechanism are cast iron, alloy steel, plastic, and aluminum alloy.
However, in selecting the materials there are factors to be considered like cost, availability and
its mechanical properties,
Manufacturing Processes
A linkage is a mechanism formed by connecting two or more levers together. Linkages
can be designed to change the direction of a force or make two or more objects move at the same
time. Many different fasteners are used to connect linkages together yet allow them to move
freely such as pins, end-threaded bolts with nuts, and loosely fitted rivets. A linkage is a
mechanism formed by connecting two or more levers together. Linkages can be designed to
change the direction of a force or make two or more objects move at the same time. Many
different fasteners are used to connect linkages together yet allow them to move freely such as
pins, end-threaded bolts with nuts, and loosely fitted rivets. There are two general classes of
linkages: simple planar linkages and more complex specialized linkages; both are capable of
performing tasks such as describing straight lines or curves and executing motions at differing
speeds. The names of the linkage mechanisms given here are widely but not universally accepted
in all textbooks and references. Linkages can be classified according to their primary functions
40
Function generation: the relative motion between the links connected to the frame Path
generation: the path of a tracer point. Motion generation: the motion of the coupler Eight link.
Different simple planar linkages are identified by function: (Norton, 2004).
According the research studies of Shindel et al, (2018) a system has the advantage that
the system has a time delay between moving packages and this delay can be used to introduce
any alterations in the package or move the package for any other purpose and likewise. Unlike a
conveyor system whose actions can’t be performed unless programmable module is used to
produce stopping of the belt occurring at irregular intervals this is costly. A transport mechanism
transfers and includes shifting of boxes by using simple and basic mechanical principle. Upon
their experimentation, they have encountered some problems in constructing the transport
mechanism here are some of the problems they have encountered and how they solved it;
a.) “At first we made a simple planar four bar chain out of MS plates by using nut and
screw as fasteners. We set it up with a motor of very high speed. On running the mechanism, the
links were wobbling and it was very unstable.”
b.) A bushing for smoother rotation of the links. It reduced the noise. But still did not
solve the wobbling problem. We then tried changing the motor to a lower speed wiper motor of
35 & 50rpm. As wiper motors come with different speed settings, we had two speeds in one
motor. The motor worked well. The wobbling was reduced to a certain extent but not up to
satisfactory levels. Then we figured the problem was the mechanism. It worked but not quite
right. It wasn’t able to produce a continuous motion as during the return stroke it got stuck at the
box. So, we decided to try out a crank-rocker mechanism. We disassembled the mechanism from
the frame and connected the upper links at a distance equal to the lower link which remains
41
parallel to the frame. After doing the above we were finally able to get our mechanism up and
running smoothly and produce a continuous transfer of boxes with required time delay.
Application
It is useful in transferring any material from one location to another, more often in the
application of bulky and heavy materials where human effort is not enough to carry such
materials or load. This can also be efficient for quick material handling in transporting wide
variety of products in the industries like in medical production fields, packaging industries, bottle
filling and drink production. Other applications can be in automotive and even in
pharmaceutical.
Advantages
Replacing human operators in tedious tasks, and a huge enhancement over using human
labor to perform the activity. Replacing humans in tasks that should be done in dangerous
environments, examples involves fire, space, volcanoes, nuclear facilities, underwater, etc.
Making tasks that are beyond the human capabilities such as handling too heavy loads, too large
objects, too hot or too cold substances or the requirement to make things too fast or too slow.
Aside from reducing human effort, using mechanically operated conveyor also reduces
electricity consumption but it adds financial savings instead. In accordance to economy
improvement, sometimes, some kinds of automation imply improves in economy of enterprises,
society or most of humankind. For example, when an enterprise that has invested in automation
technology recovers its investment; when a state or country increases its income due to
automation like Germany or Japan in the 20th Century or when the humankind can use the
internet which in turn use satellites and other automated engines.
42
B. Disadvantages
There is still some disadvantage of using manual conveyor. First are the technology limits,
where current technology is unable to automate all the desired tasks. Second is the unpredictable
development costs. The research and development cost of automating a process is difficult to
predict accurately beforehand. This cost can have a large impact on profitability, it's possible to
finish automating a process only to. Initial costs are relatively high. The automation of a new
product required a huge initial investment in comparison with the unit cost of the product,
although the cost of automation is spread in many product batches. The automation of a plant
required a great initial investment too, although this cost is spread in the products to be produced.
Factors to consider in designing
1. Space. When faced with a shortlist of mechanisms, the one that will produce the required
operations while consuming the least amount of space is the best way to go. This is
especially true for products that have space requirements as a factor, such as with
products that are meant to be operated with one hand.
2. Efficiency. If the primary purpose of the desired mechanism is to do work for the user,
the mechanism with the highest mechanical advantage will take precedence. That means
that the mechanism that does the most work with the smallest input will rank higher than
the mechanism that does not have as high an output versus input ratio.
3. Materials. Some mechanisms simply won’t work if you use certain materials or if you
are limited as to what materials you have available. Gear mechanisms, for example,
require a certain amount of rigidity before they can work and so, for gear mechanisms,
43
rubber-like materials would not be a feasible option. In other cases, such as with
compliant mechanisms, rigid materials will not work at all.
4. Power. Just like in material constraints, some mechanisms lend themselves more to
operations with high torque or high forces. If you have requirements for high input or
output forces, some mechanisms will be more suitable than others. Cams are generally a
precision-based mechanism and not one for delivering or withstanding high amounts of
forces. Gears, on the other hand, combine precision and the ability to work with high
torque.
5. Aesthetics. In today’s market, sometimes beauty is as important as function. When the
design team is conceptualizing a design concept, they usually start from how they want
the finished product to look before they work back to what will be under the hood and
how they are going to make it work. We believe there is no such thing as an ugly
mechanism, but there are certainly extremely beautiful, mesmerizing, ingenious ones. A
proud designer may be tempted to use a transparent body so that the user can fully view
the product’s inner mechanisms in action.
6. Ease of production. A very easy consideration to miss is the ease with which a
mechanism can be mass produced. Product manufacturers are in the business of making
money and the best mechanism is not necessarily the most cost-effective mechanism.
You will want to choose the mechanism that will not significantly impact lead time and
will not be so costly as to price out the majority of the product’s consumers. A balance
must be sought to make sure the product is affordable for the buyers and yet profitable for
the manufacturers.
44
7. Complexity. The most elegant designs are the simplest ones. When all other
considerations have been decided upon, the least complicated design should be adopted
because that will reduce the risk of failure. A less complicated mechanism generally
means fewer things can go wrong or fail.
TEST PROCEDURES AND PARAMETERS
Seven bar slider linkage mechanism with variable topology
In the studies of Joshi et al, (1998) any mechanism with five or more links and with two or more
degrees of freedom could be made to act as variable topology mechanism operating in two or
more phases.
II.1Phase-I
Figure 21. A planar seven – bar slider mechanism
In Phase-I, the link OcC is temporarily fixed and the resulting mechanism is a six-bar
slider mechanism of single degree of freedom. It is a combination of five-bar slider and four-bar
mechanism in series. OaA1 is the input link. B is the possible path tracer point. Suffix 1 and 2 of
alphabets in Fig. 2 represent the two finitely separated positions of the six-bar slider portion of
the seven-bar slider variable topology mechanism in Phase-I. C is a temporarily fixed pivot. Oa
and Oc are the permanently fixed pivots.
45
Figure 22. A planar seven – bar slider mechanism with variable topology at its two dead – center
positions, in phase-I
ii.2. Phase-II
Figure 23. A planar seven – bar slider mechanism with variable topology at its two dead – center
positions, in phase-II
ii.3. Once the above six-bar slider portion of seven-bar slider mechanism with variable
topology reaches the position 2 , the link OcC is released to move and the link OaA is
fixed temporarily, thus switching on to the Phase-II. Again the resulting mechanism is
six-bar slider of single degree of freedom. Here link OcC is input link, B is the tracer
point. Suffix 2 and 3 of alphabets in Fig.3 represent the two finitely separated positions
of the six-bar slider portion of the seven-bar slider variable topology mechanism in
46
Phase-II. Also, it is to be noted that C is no more a fixed pivot where as A2 is a
temporarily fixed pivot. Oc and Oa are the permanently fixed pivots.
III. SYNTHESIS
3.1 Solution steps. The solution to the problem consists of the following steps:
(i) Identification of the links to be fixed temporarily in each phase so that in both the phases one
can get six-bar slider portion of seven-bar slider variable topology mechanism.
(ii) Recognition of the type of mechanism in each phase.
(iii) Writing of the standard dyad equations for the motion between position 1 and position 2 of
Phase-I and also between position 2 and position 3 of Phase-II.
(iv) Identification of the values to be prescribed, values to be chosen freely and the unknowns
based on the task to be performed.
(v) Solving of the equations of motion in each phase for the link lengths. (vi) Retaining of link
parameters determined in Phase-I while solving other link lengths in Phase-II.
(vii) Finding of the total number of solutions that are possible in all phases by the method. When
it is required to synthesize a planar seven-bar slider mechanism (shown in Fig.1) with variable
topology, one can have three options as follows:
(i) One end link is fixed temporarily,
(ii) Another end link is fixed temporarily,
(iii) Middle link, the slider is fixed temporarily.
The options (i) and (ii) are considered for the present paper. It is assumed that the mechanism
moves from dead center position 1 to the dead center position 2 in Phase-I and from the dead
center position 2 to the dead center position 3 in Phase-II. In the present case, as soon as the
47
mechanism moves from one dead-center position to the other, it stops and then switches on to the
Phase-II. So there is no question of overcoming the dead lock and hence, no auxiliary drive is
needed. Moreover, the dead lock positions can overcome by inertia forces of the cranks.
Table 3. Conventions to be followed to denote the linkages and the angle in Phase – I and in phase – II
The conventions to be followed in Phase-I and Phase-II are given in Table 1. The input motion in
Phase-I is φ12, the displacement vector B1B2 is given by δ12. Writing the dyad equations [1, 17]
for Phase-I (refer Fig.2),
3.2 Motion generation. In motion generation mechanisms, the body to be guided usually is a part
a floating link. Hence, the location of tracer point on the coupler and the coupler orientation are
the part of design specifications as the entire motion of the coupler link is to take place. It
requires that an entire body be guided through a prescribed motion order. 3.2.1 Phase-I synthesis
In the standard dyad Eqs.(1)-(4), in motion generation, the coupler point motions (γ12, β12) and
48
the displacement vector δ12 are prescribed. φ12 , 12 X , θ12 and 2 Z are the free choices.
Hence, there will be ∞ 6 numbers of solutions. Then the unknowns 3 Z , 4 Z , 5 Z , 7 Z and 1 Z
are determined as follows;
Where α1 is the angle made by 7 Z with the vertical line passing through Oa in CW. 3.2.2 Phase-
II synthesis Input motion in Phase-II is ψ23 the displacement vector B1B2 is given by δ23.
Writing the dyad equations for Phase-II (refer Fig. 3)
49

Nueva Vizcaya State University College of Engineering: Transport Mechanism For Variable Loads

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Nueva Vizcaya State University

TRANSPORT MECHANISM FOR VARIABLE LOADS

A thesis proposal presented to the

Agustin, Jan Carlo V.

Every challenging work needs self-efforts as well as guidance of elders especially to

rendered in the university;

and motivation he is imparting to us.

Engr. Simpher R, Guyong, our Chairman, Bachelor of Science in Mechanical

this project study.

This thesis entitled “TRANSPORT MECHANISM FOR VARIABLE LOADS” has

RANIER SAM G. MATEO, RME

MARIA TERESA M. COSTALES, MA JANE P. AGBANLOG, BSCE

VINCENT BRYAN L. REYES, RECE LARRY P. REMOLAZO, RME

JEANELYN R. TOMINEZ, RME

MARY B PASION, RME, MSME SIMPHER R. GUYONG, RME

Table Title Page

Phase – I and in phase – II

7 Motion cycle of the rolling shear mechanism. 18

THE PROBLEM AND ITS BACKGROUND

eventual points of consumption. Movement of finished goods from manufacturers to their

eventual end users also requires a well established transport network.

global transportation system altogether.

of human resource challenges used in variety of industries in food, pharmaceuticals, manufacturing

mechanism for a variable load.

(Jodie, D., 2019).

Objectives of the Study

loads that may be present and may affect the mechanism.

terrain and how to deal with it.

Scope and Delimitation of the Study

This study focuses in designing and fabricating a portable transporting mechanism by

provide the ideal rotation, movement or slide.

system were considered for the design of the study.

Statement of the problem

flexibility and versatility will be beneficial to various places of application.

Some specific problems were also considered:

1. How is the transport mechanism for variable loads designed?

4. What is the cost of the developed transport mechanism?

Significance of the study

come in handy to these changes.

involving the seven-bar linkage.

 Reference materials, internet, books Variable loads

 Gathered information and its application

 Ideas and information

DESIGNING FABRICATING TESTING

Planning Design Fabricated transport ADJUSTMENT

Fabricated Transport Mechanism for Variable Loads

Figure 1. Conceptual Framework

is the fabricated transport mechanism.

Mechanism. A mechanism is a part of a machine or is a set of parts that work together.

bar linkage mechanism.

Conveyor. It is a machine that transports something from one place to another.

Specifically, a conveyor belt is a continuous moving strip or surface that is used

served for comparison for the box transport mechanism.

Seven-bar linkage. A mechanical linkage is an assembly of bodies connected to manage

forces and movement. The seven-bar linkage is a mechanism that is constructed

Mobility. It refers to the ability of something to move freely or be easily moved.

Mobility is used in the study as one performance factor of the mechanism.

Versatility. It refers to the ability of something to adapt or be adapted to many different

REVIEW OF RELATED LITERATURE