A Seminar II Report On “SYNTHESIS OF GEARED FOUR BAR MECHANISM” Submitted In Partial Fulfillment of the Requirement For The Award of Degree of Master of Engineering In Mechanical –Design Engineering of North Maharashtra University, Jalgaon Submitted By Patil Yogesh Balu Under The Guidance of Prof. R B Barjibhe Department of Mechanical Engineering Shri Sant Gadge Baba College of Engineering and Technology, Bhusawal
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SeminarII on Sysnthesis of Geared Four Bar Mechanism
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A
Seminar II
Report On
“SYNTHESIS OF GEARED FOUR BAR MECHANISM”
Submitted In Partial Fulfillment of the Requirement
For The Award of Degree of Master of Engineering
In Mechanical –Design Engineering of
North Maharashtra University, Jalgaon
Submitted By
Patil Yogesh Balu
Under The Guidance of
Prof. R B Barjibhe
Department of Mechanical Engineering
Shri Sant Gadge Baba
College of Engineering and Technology, Bhusawal
North Maharashtra University, Jalgaon
2011-2012
Shri Sant Gadge Baba
College of Engineering and Technology,
Bhusawal 425201
Certificate
This is to certify that Mr. Patil Yogesh Balu has successfully completed his
seminar II on “Synthesis of Geared Four Bar Mechanism” for the partial
fulfillment of the Masters Degree in the Mechanical- Design Engineering as prescribed by
the North Maharashtra University, Jalgaon during academic year 2011-12.
Prof. R. B. Barjibhe Prof. R. B. Barjibhe
[Guide] [P.G.Co-Ordinator]
Prof. A. V. Patil Prof. R. P. Singh
(H.O.D.) (Principal)
ABSTRACT This paper presents an analysis and synthesis method for a certain type of
geared four-bar mechanism (GFBM) for which the input and output shafts are collinear.
A novel analysis method is devised, expressions for the transmission angle are derived
and charts are prepared for the design of such mechanisms. It is observed that the GFBM
considered is inherently a quick-return mechanism. During the working stroke,
approximately constant angular velocity at the output link is observed. For the type of
GFBM analyzed, direction of rotation of the input link affects the force transmission
characteristics.
INDEX
Sr. No. Name of Topic Page No.
Abbreviations i
List Of Figures ii
List of Graphs iii
1 Introduction 1
2 Literature review 2
3 Synthesis of mechanism 3
3.1 Type synthesis 3
3.2 Number synthesis 3
3.3 Dimensional synthesis 3
3.3.1 Function generation 3
3.3.2 Path generation 4
3.3.3 Motion generation 4
4 Transmission angle 5
4.1 Maximum and Minimum transmissions angle 5
4.2 Optimum transmission angle 6
5 Enumeration of the GFBM 7
6 Motion analysis of the GFBM 8
7 Transmission angle of the GFBM 10
8 Synthesis of the GFBM 11
9 Transmission angle optimization 13
N Conclusion
ABBREVIATIONS
GFBM GEARED FOUR BAR MECHANISM
i/p INPUT
o/p OUTPUT
i
FIG. NO. TITLE OF FIGURE
1.1 TOPOLOGY TYPE A, AND TOPOLOGY TYPE B.
4.1 SHOWING TRANSMISSION ANGLE.
4.2 DOUBLE-ROCKER MECHANISM.
4.3 THE CRANK-ROCKER MECHANISM.
4.4 DOUBLE-ROCKER MECHANISM.
5.1 ENUMERATION OF THE GFBM.
6.1 THE GFBM AND THE CORRESPONDING FOUR-BAR MECHANISM
WHEN THE GEARS ARE REMOVED.
7.1 THE FBD OF THE LINKS WHEN LINK 2 IS ROTATING
COUNTERCLOCKWISE.
7.2 THE FBD OF LINK 4 WHEN LINK 2 IS ROTATING CLOCKWISE.
8.1 THE DEAD-CENTER POSITIONS OF THE GFBM.
LIST OF FIGURES
ii
LIST OF GRAPHS
GRAPH
NO
TITLE OF GRAPH
8.1 Z1 AND Z2 CIRCLES FOR THE VALUES OF Φ=50° AND Ψ=10°.
9.1 THE DESIGN CHART FOR CW INPUT ROTATION AND R=1.
9.2 THE DESIGN CHART FOR CCW INPUT ROTATION AND R=1.
9.3 THE DESIGN CHART FOR CW INPUT ROTATION AND R=2.
9.4 THE DESIGN CHART FOR CW INPUT ROTATION AND R=4.
iii
1 INTRODUCTION
Geared linkages are useful mechanisms, which can be formed by combining
planar linkages with one or more pairs of gears. A geared five link mechanism in general
is a one degree of freedom planar mechanism with five revolute joints, one gear pair, and
five links. Two different topologies are possible as shown in (Fig.1.1). In type A, there is
a ternary joint between links 1, 2 and 3 whereas in type B all revolute joints are binary.
Type A contains a four-bar loop whereas type B has a five-bar loop when the gear pairs
are removed. The mechanism studied in this work has type A topology, which is named
as GFBM in the literature. Geared four-bar mechanisms are generally investigated to
obtain large swing angle, dwell motions and motion with approximately constant
transmission ratio ranges.
Mechanisms for non-uniform transmission of motion such as linkages are
characterized by continuously changing transmission ratios. Ideally a smooth motion
throughout the whole range of operation is expected. For designing such mechanisms it is
important to utilize fully all possibilities known from theory and practical experiences.
The criteria for the design of mechanism are low fluctuation of input torque, compact in
size and links proportion, good in force transmission, low periodic bearing loads, less
vibrations, less wear, optimum transmission angle and higher harmonics. The
transmission angle is an important criterion for the design of mechanism.
1
Fig. 1.1. Topology Type A, And Topology Type B.
2 LITERATURE REVIEW
Tuan-Jie Li , Wei-Qing Cao , in their paper , “ Kinematic analysis of geared
linkage mechanism”, present a general approach to the kinematic analysis of planar
geared linkage mechanisms (GLMs) is presented based on their structural topological
characteristics. Firstly, a systematic method for decomposing a GLM into a series of
sequential independent kinematic units, such as the simple links and the dyad link groups
is proposed. The criteria and process for the structural decomposition and for choosing
circuits using the theory of type transformation are established. Then the kinematic
equations and the analytic solutions for the kinematic units are derived, and the method
for the kinematic analysis of position, velocity and acceleration of GLMs is obtained in
an algorithmic fashion [2].
Shrinivas S Balli , Satish Chand , in their paper, “Transmission angle in
mechanisms (Triangle in mech)”, present that the transmission angle is an important
criterion for the design of mechanisms by means of which the quality of motion
transmission in a mechanism, at its design stage can be judged. It helps to decide the
“Best” among a family of possible mechanisms for most effective force transmission [3].
M. Khorshidi , M. Soheilypour, M. Peyro, A. Atai, M. Shariat Panahi, in their
paper, “Optimal design of four-bar mechanisms using a hybrid multi-objective GA with
adaptive local search”, present that a novel approach to the multi-objective optimal
design of four-bar linkages for path-generation purposes. Three, often conflicting criteria
including the mechanism's tracking error, deviation of its transmission angle from 90° and
its maximum angular velocity ratio are considered as objectives of the optimization
problem [4].
2
3 SYNTHESIS OF MECHANISM
The synthesis of mechanism is the design or creation of a mechanism to produce a
desired output motion for a given input motion. In other words, the synthesis of
mechanism deals with the determination of proportions of a mechanism for the given
input and output motion.
In the application of synthesis, to the design of a mechanism, the problem divides
itself into the following three parts.
1) Type synthesis
2) Number synthesis
3) Dimensional synthesis
3.1. TYPE SYNTHESIS:
Type synthesis refers to the kind of mechanism selected; it might be a linkage, a
geared system, belts and pulleys, or even a cam system.
3.2. NUMBER SYNTHESIS:
Number synthesis deals with the number of links and the number of joints or pairs
that are required to obtain certain mobility. Number synthesis is the second step in design
following type synthesis.
3.3. DIMENSIONAL SYNTHESIS:
The third step in design, determining the dimensions of the individual links, is
called dimensional synthesis.
Following are various problems occurring in dimensional synthesis.
3.3.1. Function generation
A frequent requirement in design is that of causing an output member to rotate,
oscillate, or reciprocate according to a specified function of time or function of the input
motion. This is called function generation. That is correlation of an input motion with an
output motion in a linkage.
A simple example is that of synthesizing a four-bar linkage to generate the
function the function y=f(x). In this case, x would represent the motion (crank angle) of
the input crank, and the linkage would be designed so that the motion (angle) of the
output rocker would approximate the function y.
3
Other examples of function generation are as follows:
In a conveyor line the output member of a mechanism must move at the constant
velocity of the conveyor while performing some operation for example, bottle capping,
return, pick up the cap, and repeat the operation. The output member must pause or stop
during its motion cycle to provide time for another event. The second event might be a
sealing, stapling, or fastening operation of some kind. The output member must rotate at a
specified no uniform velocity function because it is geared to another mechanism that
requires such a rotating motion.
3.3.2. Path generation
A second type of synthesis problem is called path generation. This refers to a
problem in which a coupler point is to generate a path having a prescribed shape that is
controlling a point in a plane such that it follows some prescribed path. Common
requirements are that a portion of the path be a circular arc, elliptical, or a straight line.
Sometimes it is required that the path cross over itself. For this minimum 4-bar linkage
are needed. It is commonly to arrive a point at a particular location along the path
without/with prescribed times.
3.3.3. Motion generation
The third general class of synthesis problem is called body guidance. Here we are
interested in moving an object from one position to another. The problem may call for a
simple translation or a combination of translation and rotation. In the construction
industry, for example, heavy parts such as a scoops and bulldozer blades must be moved
through a series of prescribed positions.
4
4 TRANSMISSION ANGLE
The transmission angle is an important criterion for the design of mechanisms by
means of which the quality of motion transmission in a mechanism, at its design stage can
be judged. It helps to decide the “Best” among a family of possible mechanisms for most
effective force transmission.
Transmission angle is a smaller angle between the direction of velocity difference
vector VBA of driving link and the direction of absolute velocity vector VB of output link
both taken at the point of connection (Fig 4.1). It is the angle between the follower link
and coupler of a 4-bar linkage. The definitions are related to a joint variable and depend
on the choice of driver and driven links. It appears to be an acute angle μ and an obtuse
angle (180°−μ). It varies throughout the range of operation and is most favorable when it
is 90°. The recommended transmission angle is 90°±50°. In mechanism having a reversal
of motion, i.e. if roles of i/p and o/p links are reversed during the cycle, transmission
angle must be investigated for both directions of motion transmission.
Transmission of motion is impossible when transmission angle is 0° or 180°. If
transmission angle is zero, no torque can be realized on output link, i.e. mechanism is at
its dead center position. A large transmission angle does not necessarily guarantee the low
fluctuation of torque. Very small or very large transmission angle results in large error of
motion, high sensitivity to manufacturing error, noisy and unacceptable mechanism. It is
not the absolute value of transmission angle but its deviation from 90° that is significant.
Different limits for transmission angle suggested are 35–145°; 40–140°; 45–135°.
4.1. MAXIMUM AND MINIMUM TRANSMISSION ANGLES
The transmission angles at the extreme positions of a double rocker linkage will
also be the minimum and maximum values of transmission angle for the entire motion of
mechanism (Fig. 4.2).
In case of crank-rocker and drag mechanisms, the transmission angle will be
minimum when input crank angle is zero and maximum when input crank angle is 180°
(Fig.4.3 and Fig.4.4).These occur twice in each revolution of the driving crank. They do