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

not occur at the extreme positions of the linkage

5

Fig. 4.1. Showing Transmission Angle.

Fig. 4.2. Double-Rocker Mechanism

Fig. 4.3 The Crank-Rocker Mechanism.

Fig. 4.4 Double-Crank Mechanism.

4.2. OPTIMUM TRANSMISSION ANGLE

The deviation of transmission angle from 90° is the measure of reduction in

effectiveness of force transmission. So the aim in linkage design is to proportion the links

so that these deviations are as small as possible, especially in the presence of appreciable

joint friction. If the range of operation is sufficiently small, it seems as if we could obtain

a linkage with optimum variation of transmission angle if it is set equal to 90° in the

designed position . Among the family of possible 4-bar linkages, there is one linkage that

has a minimum transmission angle, which is greater than the minimum transmission

angles of all the others. This is called optimum transmission angle and this particular

linkage has the best dimensions for most effective force transmission.

If the designer tries to optimize the linkage with respect to its force transmission

characteristics simultaneously with optimum transmission angle synthesis, it increases the

difficulty of problem extensively. Therefore combined force transmission and synthesis

studies have been restricted to relatively simple linkages. On the other hand, the problem

simplifies significantly if the transmission angle is restricted such that Δμ<δ where Δμ

=maximum deviation of transmission angle μ from optimum one and δ=a specific bound

on Δμ .

6

5 ENUMERATION OF THE GFBM

The mechanism studied in this work has a topology type A, which is simply a gear

pair combined with a four-bar mechanism. Different mechanisms can be obtained by

fixing links 1 to 5 respectively. These mechanisms can be summarized as in (Fig.5.1).

Moreover, by changing the input and output links, different input–output functions can be

achieved. Note that, instead of external gears internal gears can also be used in some of

these mechanisms. Type A3 is nothing but a four-bar driven by another gear, and type A5

is a four-bar with a floating gear pair.

The mechanism studied in this work is of topology type A1. One of the gears is

rigidly connected to the coupler and the other gear has a fixed axis of rotation. This forms

a planetary gear train with link 3 as the arm. The input torque is applied to link 2, and the

output is obtained at the arm (link 3). Thus, the input and the output displacements are

about the same rotation axis.

7

Fig.

5.1 Enumeration Of The GFBM.

6 MOTION ANALYSIS OF THE GFBM

In order to obtain the relationship between the input (θ12) and output (θ13), an

equation can be obtained from the loop closure equation of the four-bar mechanism

(Fig.6.1).

a3e iθ13 + a4e iθ14 − a1 = a5e iθ15 (1)

There is another equation which is the velocity ratio of the planetary gear arrangement

formed by links 2, 3 and 4:

−¿ r4

r2 =

ω12−ω13

ω14−ω13 = −¿R (2)

Integrating this equation:

θ14 = (R+1)

R θ13−¿

θ12

R + k (3)

Where, R = r4/r2 and k is a constant determined by the initial relative positions of links 2

and 4 with respect to link 3 (integration constant).

Eq. (3) can be used in Eq. (1) to eliminate θ14 and a new equation can be obtained.

Then, this obtained equation can be multiplied by its complex conjugate (eliminating θ15)

to obtain a relationship between θ12 and θ13. However, obtaining an explicit relationship

between the input and the output is very hard if not impossible by this method. Therefore,

a novel approach is used to determine the input–output relationship in two steps.

It is assumed that the input link of the mechanism is not link 2 but link 4. Hence,

according to this assumption, an explicit relationship between θ14 and θ13 can be

determined from the loop closure equation of the four-bar mechanism. Since, θ13 is

determined as a function of θ14, then by using Eq. (3) a relationship between θ12 and θ14

can be obtained. Hence, for a given θ14 corresponding θ13 and θ12 can be determined

explicitly. Therefore, a chart which gives the relationship between the input θ12 and output

θ13 can be determined. With this approach, an iterative numerical solution is eliminated.

For link 2 to have a complete rotation, the coupler link (link 4) must also have a

complete rotation, while links 3 and 5 will have oscillations only. The full cycle rotation

of link 3 imparts a full cycle rotation of the coupler link of the four-bar formed by links 1,

3, 4 and 5 (Fig. 3). This four-bar mechanism must then be of Grasshof type double-rocker

mechanism (the sum of the longest and shortest link lengths is less than the sum of the

two intermediate link lengths and the link opposite the shortest link is the frame).

8

With this consideration, the rotation of link 3 can be determined in terms of the rotation

of the coupler (link 4).

Multiplying the loop closure Eq. (1) by its complex conjugate, the output θ13 can

be determined as a function of θ14.

θ13 = 2arc tan (−B±√B2−4 AC2 A

) (4)

Where,

A = K1−K2 cos θ14 + K3−K4 cos θ14

B = 2K2 sin θ14

C = K1 + K2 cos θ14−K3−K4cosθ14

K1 = a21 + a23 + a24 −a25

K2 = 2a3a4

K3 = 2a1a3

K4 = 2a1a4.

Since θ13 is determined for a given θ14, corresponding θ12 can be determined from Eq. (3).

θ12 = (R + 1) θ13 - R θ14 + K (5)

Therefore, the input–output relationship can be determined at two steps by solving Eqs.

(4) and (5) respectively.

k is a constant determined by the initial relative positions of links 2 and 4 with

respect to link 3 (integration constant). It can be choosen arbitrarily. While obtaining

input–output curves, in order to start θ12 values from 0° (when θ14=0°, θ13initial is

calculated, so in order to obtain θ12=0°), k is chosen as: k = −(R + 1) θ13initial.

9

Fig. 6.1. The GFBM And The Corresponding Four-Bar Mechanism When The Gears Are Removed.

7 TRANSMISSION ANGLE OF THE GFBM

The transmission angle of a mechanism is defined as :

tan(μ) =

forcecomponent actingon the ouptput link tending¿ produceoutput rotation ¿forcecomponent tending¿

apply pressureon the drivenlink bearing ¿

Neglecting the mass of the links, the free-body diagrams of the links of the GFBM

will be as shown in Fig.7.1. Where, Ti is the input torque applied to link 2, To is the

output torque at link 3, and α is the pressure angle of the gears. The transmission angle of

the mechanism can be obtained as:

tan(μ) = F43t / F43n (6)

From the free-body diagrams of the links, F43t and F43n can be obtained, and from Eq. (6),

the transmission angle can be determined as:

tan(μ) =

−a4

r 4

sin (θ15−θ14 )−sin (θ15−θ13)

a4

r4

tan(α )sin (θ15−θ14 )+cos (θ15−θ13)

If the direction of rotation of the input link is changed, then the transmission angle of the

GFBM alters since the line of action of the force between links 2 and 4 changes (Fig.7.2).

In this case, the transmission angle will be given by:

tan(μ) =

−a4

r4

sin (θ15−θ14 )−sin (θ15−θ13)

a4

−r 4

tan(α )sin (θ15−θ14 )+cos (θ15−θ13)

Note that there is a minus sign in front of the term including α.

Unlike all other mechanisms known up to now, for this mechanism the force

transmission characteristics are also a function of rotation direction. A mechanism which

has proper transmission angle values in one rotation direction can even lock if the

direction of rotation of the input is reversed.

10

Fig. 7.1. The FBD Of The Links When Link 2 Is Rotating

Counterclockwise.

Fig. 7.2 The FBD Of Link 4 When Link 2 Is Rotating Clockwise.

8 SYNTHESIS OF THE GFBM

The problem is considered in two parts. The first part is the synthesis problem in

which one must determine a four-bar mechanism of Grashof type with double-rocker

proportions that have given swing angles ϕ and ψ for links 3 and 5 respectively. There is

an infinite set of solutions for this part of the problem. The second part of the problem is

concerned with the optimization. Out of the infinite possible set of solutions obtained in

the first part, one must determine a particular mechanism whose maximum transmission

angle deviation from 90° is a minimum.

The extended and folded positions of the mechanism are shown in Fig. 8.1. At the

extended position link 3 is at the forward position and at the folded position link 3 is at

the fully withdrawn position. θ is the angle of link 3 and ξ is the angle of link 5 at the

folded position.

The loop closure equations for the folded and extended positions of the

mechanism can be written as:

a3eiθ = a1 + (a5−a4) eiξ (7)

a3ei(θ + ϕ) = a1 + ( a5 + a4) ei(ξ + ψ) (8)

One can define Z1, Z2 and λ as:

Z1 = a3eiθ (9)

Z2 = a5eiξ (10)

λ = a4

a5

(11)

Without a loss of generality the fixed link can be chosen as unity; a1=1.

Then, Eqs. (7) and (8) can be written in normalized form as:

Z1−Z2 (1−λ) = 1 (12)

Z1eiϕ−Z2eiψ (1 + λ) = 1 (13)

These complex equations are linear in terms of the unknowns Z1 and Z2. Then, Z1 and Z2

can be solved in terms of λ, ϕ, and ψ as:

Z1 = (1−λ)– (1+ λ)ei ψ

(1− λ)ei ϕ – (1+λ)ei ψ (14)

Z2 = 1−e iψ

(1− λ)ei ϕ – (1+λ)ei ψ (15)

As λ changes from −∞ to +∞, Z1 and Z2 describe a curve which is the loci of the

tip of the vectors AoAf and BoBf. These loci are two circles for any given value of ϕ and ψ.

In (Graph 8.1), these two circles are shown for the values of ϕ=50° and ψ=10°.

11

A line can be drawn from (0, 0), which is Ao, at an angle θ with respect to AoBo.

Af is the intersection point of this line and the Z1 circle. Another line can be drawn from

Bo at angle ξ with respect to AoBo which intersects the circles at Af and Bf, respectively.

This corresponds to the folded position of the mechanism, where the link lengths are,

AoA = a3, AfBf = a4, BoBf=a5 and AoBo=a1

Analytically, link lengths can be determined as:

The link lengths are functions of the free parameter λ, and swing angles ϕ, and ψ.

For a given ϕ and ψ, there is a set of solutions with respect to the free parameter λ.

A necessary but not sufficient condition for double-rocker proportions is:

0< ⃓ λ ⃓<1.

In order to obtain double-rocker proportions there are limits on swing angles as:

0<ϕ<180.

ϕ2

−¿900 ¿ ψ¿ ϕ2+¿ 900

12

Fig. 8.1. The Dead-Center Positions Of The GFBM.

Graph 8.1. Z1 And Z2 Circles For The Values Of Φ=50° And Ψ=10°.

9 TRANSMISSION ANGLE OPTIMIZATION

Among the set of solutions for a given ϕ and ψ, the one for which the maximum

deviation of the transmission angle from 90° is a minimum must be selected (λopt will be

determined). The design charts are obtained for a given output swing angle ϕ and the

corresponding input link rotation β. Therefore, the optimum mechanism in terms of the

transmission angle can be determined, for a given output swing angle ϕ and a time ratio,

from the design charts. Using Eq. (5) at the folded and extended positions, β can be

obtained for a gear ratio R, and according to the input direction of rotation (− sign for cw

input) as:

β = (R + 1) ϕ∓Rπ – Rψ

A parametric optimization routine is developed and design charts for optimum

GFBM are prepared by using MATLAB. According to the direction of rotation of the

input, the transmission angle of the GFBM changes. That condition leads to two different

optimum mechanisms which have the same output swing angle ϕ and corresponding input

rotation β. Therefore, transmission angle optimization is performed for both of the input

directions of rotation and two sets of design charts are prepared. The affect of gear ratio

(R) is very clear, it affects the transmission angle; if R is increased, then the transmission

angle improves. Therefore, transmission angle optimization is performed for several gear

ratios and the corresponding design charts are also prepared. Some of those design charts

are displayed in (Graph 9.1-9.4). The Y-axis represents the output swing angle ϕ, and the

X-axis represents the corresponding input link rotation β. The full lines represent the

optimum λ parameter, and the dotted lines represent the maximum deviation of the

transmission angle from 90° (δμmax) for the corresponding mechanism. Since, ϕ and β

are the given parameters, a value for ϕ and another value for β is chosen from Y and X

axes respectively. Then, these values are intersected and the value of optimum λ

parameter, and for that mechanism, the value of maximum deviation of the transmission

angle from 90° can be obtained. If the obtained δμmax is not preferred, then ϕ or β is

changed, and another optimum solution can be obtained. Therefore, by the aid of these

design charts, by specifying ϕ and β, the corresponding optimum mechanism and δμmax

for that mechanism can be determined easily.

13

It can be observed that transmission characteristics of the mechanisms deteriorate

as the input rotation β approaches to R×180° (R=1,2,3,4). Therefore, for an acceptable

transmission angle, centric mechanisms can be obtained for small output swing angles

only. Hence, it can be concluded that this type of GFBM is useful for quick-return

motions. This condition is explained as below.

If a mechanism is to be designed from graph 8.1, which has an output swing angle

ϕ=50° and a large time ratio of 2 (β=120°), from the intersection point of these values it is

seen that the value of λ≈0.7, and for that mechanism the maximum deviation of the

transmission angle from 90° is ≈42°. If a smaller time ratio is desired, for example

210/150 (still ϕ=50°) β is chosen as 150°. Then, from the intersection point of these

values it is determined that λ≈0.67 and δμmax ≈ 62° which lead to a mechanism with

poor transmission characteristics. So, it can be observed that as the time ratio approaches

to 1 (β approaches to 180°) for a fixed value of ϕ, the maximum deviation of the

transmission angle from 90° (δμmax) of the corresponding mechanism increases (also

note that in graph 9.3, since R=2, as time ratio approaches to 1, β approaches to 360°).

The gear ratio R significantly affects the transmission angle of the GFBM. As R

increases, the transmission angle improves and mechanisms with larger output swing

angles can be obtained (Graph 9.3 and 9.4). Conversely, if R is decreased, transmission

characteristics deteriorate. Therefore, transmission angle optimization is performed for

several gear ratios and the corresponding design charts are also prepared.

14

Graph 9.1.The Design Chart For CW Input Rotation And R=1.

Graph 9.2. The Design Chart For CCW Input Rotation And R=1.

Graph 9.3. The Design Chart For CW Input Rotation And R=2.

Graph 9.4.The Design Chart For CW Input Rotation And R=4.

CONCLUSION

In this work a new type of geared four-bar mechanism for which the input and

output shafts are collinear has been investigated. A novel analysis method is devised,

expressions for the transmission angle are derived and charts are prepared for the

optimum design of such mechanisms. By the aid of these design charts, by specifying the

output swing angle and the time ratio, the corresponding mechanism which has the best

transmission characteristics can be determined easily. It is observed that, the gear ratio

significantly affects the transmission angle; as the gear ratio (R) increases, the

transmission angle improves. According to the direction of rotation of the input, there are

two different optimum mechanisms which have the same output swing angle and

corresponding input rotation. During the working stroke, approximately constant angular

velocity at the output link is observed. This type of GFBM is suitable as a quick-return

mechanism. Large time ratios can be obtained with acceptable force transmission

characteristics.

ACKNOWLEDGEMENT

First of all I thank the almighty for providing me with the strength and courage to

present the seminar.

I would to like to express my sincere thanks to Prof. A. V. Patil Head of

Department of Mechanical engineering for all his assistance.

I wish to express my deep sense of gratitude to Prof. R. B. Barjibhe, Department

of Mechanical Engineering who guided me throughout the seminar. His overall direction

and guidance has been responsible for the successful completion of the seminar.

I am also indebted to all the teaching and non-teaching staff of the Department of

Mechanical Engineering for their cooperation and suggestions, which is the spirit behind

this report. Last but not the least, I express my sincere gratitude from the depth of my

heart to my parents, friends and all well wishers for their kind support and encouragement

in the successful completion of my report work.

Y. B. Patil

REFERENCES

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four-bar mechanism”, Mechanism and Machine Theory, Volume 45, Issue 8,

August 2010, Pages 1142-1152

2) Tuan-Jie Li, Wei-Qing Cao “Kinematic analysis of geared linkage mechanisms”,

Mechanism and Machine Theory, Volume 40, Issue 12, December 2005, Pages

1394-1413.

3) Shrinivas S Balli, Satish Chand Edmund H.M. Cheung, “Transmission angle in

mechanisms (Triangle in mech)” , Mechanism and Machine Theory, Volume 37,

Issue 2, February 2002, Pages 175-195

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design of four-bar mechanisms using a hybrid multi-objective GA with adaptive

local search”, Mechanism and Machine Theory, Volume 46, Issue 10, October

2011, Pages 1453-1465

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