design report ii (1)

8/18/2019 Design Report II (1)

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DESIGN OF FOURBAR LINKAGE AND FINDING THE ANGLE OF TRANSMISSION

BY

Mechanical Engineering departent

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Ta%le $& '$ntent(

1.1 Problem !tatement....................................................................................................................."

1." #ake a bar chart showing proposed tasks and starting and finishing dates for these tasks......$

1.% &eep a log of work attempted and completed...........................................................................'

".1 Perform a feasibility study of the proposed work......................................................................(

"." )xplanations of design decisions...............................................................................................(

".% Problem solving methodology* methods of analysis* and synthesis..........................................(

".% )ngineering principles used in the design.................................................................................+

"., !election of failure theories.......................................................................................................+

".,.1 Design -riteria....................................................................................................................

".,." Design )/uations................................................................................................................

".,.% !ample -alculations..........................................................................................................10

".,.%.1 -ase 1........................................................................................................................10

".,.%." -ase "........................................................................................................................11

".,.%.% -ase %........................................................................................................................11

%.1 !afety aspects of the project....................................................................................................1"

%.1.1 Designer2s 3esponse to Potential !afety Problems..........................................................1"

%." -reative thinking4 decision making.........................................................................................1%

,.1 5ptimi6ation............................................................................................................................1%$.1 -omputer simulation...............................................................................................................1%

$.1.1 Position P1........................................................................................................................1%

$.1." Position P"........................................................................................................................1'

$.1.% Position P%........................................................................................................................1(

'.1 7dentification of group work and individual work...................................................................1+

(.1 Discussion and interpretation of results...................................................................................1+

3eferences......................................................................................................................................1

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Li(t $& Fig)re(

Figure ".1 Position 1 for the object 10

Figure "." Position " for the object 11

Figure ".% Position % for the object 1"Figure $." !tress analysis 1,

he results for stresses obtained were as follows. 1,

Figure $.% !train analysis 1$

Figure $., otal deformation analysis 1$

Figure $.$ !tress analysis 1'

Figure $.$ !tress analysis 1'

Figure $.' !tress analysis 1(

Figure $.( !train analysis 1(

Li(t $& Ta%le(

able 1.1 8og of work attempted was kept under the project leader9s custody and surely it was

completed on the time. '

able '.1 7dentification of group work and individual work 1(

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!"* Bar chart (h$+ing pr$p$(ed ta(,( and (tarting and &ini(hing date( &$r the(e ta(,("

10/8/2014

10/18/2014

10/28/2014

11/7/2014

11/17/2014

11/27/2014

12/7/2014

Start Date Finish Date

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!"- Keep a l$g $& +$r, attepted and c$pleted"

able 1.1 8og of work attempted was kept under the project leader9s custody and surely it was completed on the time.

N)%er Ta(, D)rati$n Start Date Fini(h Date Re($)rce '$(t '$pleted

1 3esearch ( days 11:01:"01, 11:0+:"01,7nterview

companies

Phone minutes*

hourly wage

and visits

;es

" 5nline research " days 11:0,:"01, 11:0':"01, s above ;es

'Discussing mechanism

to employees:companies" days 11:"+:"01, 11:%0:"01, >s above ;es

( 7mplementing designs 1 day 11:"+:"01, 11:":"01, 8abor ;es

)valuating the feedback 1 day 11:"+:"01, 11:":"01, Projectmanager

;es

11!etting of future

presentations" days 11:"(:"01, 11:":"01, #anagement ;es

1% esting $ days 11:"0:"01, 11:"$:"01, >ttendees ;es

1,Feedback from the future

attendees" days 11:"':"01, 11:"+:"01, >ttendees ;es

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*"! #er&$r a &ea(i%ilit. (t)d. $& the pr$p$(ed +$r,"

he four bar mechanism was designed for the specific operation. he links connected with the

mechanism were estimated for the specified path. heir dimensions and details were taken into

account.

>s it was re/uired that progress reports will be made* and it must contain the visual aids and

comments in order to improve the design. he design changes were incorporated because the

comments were valid.

he report made on the four bar linkage was comprised with )xplanations of design decisions

Problem solving methodology* methods of analysis* and synthesis* engineering principles use in

the design* selection of failure theories and design criteria* design e/uations and sample

calculations* safety aspects of the project and the designer2s response to potential safety

problems* creative thinking4 decision making* optimi6ation* computer simulation* identification

of group work and individual work and discussion and interpretation of results.

*"* E/planati$n( $& de(ign deci(i$n(

First of all the mechanism was designed to carry the object in Figure P1 considering the design

principles being used to design the four bar mechanisms. he design criteria were set according

to the application of the mechanism.

he links were designed with their proper length* width and thickness. 5ne of the four links was

fixed with the base. hough there were three positions shown in their numbered order without

regard for the fixed pivots shown. 5ne of the points on the object was taken as attachment point

and the transmission angle was found.

*"- #r$%le ($l0ing eth$d$l$g.1 eth$d( $& anal.(i(1 and (.nthe(i(

First of the understanding the correct positions of the links is necessary. hen it will be observed

that which parameter is given and which parameter is to sort out. >ccording to the given

parameters* only lengths of the links can be determined using simple trigonometric relations.

>fter knowing the lengths of the links* the angle of transmission will be known by using the

lengths of the links in designed mechanism and the angles of the mechanism whereas the

positions of the object has already been described. he cosine law will be used to know about the

angle of transmission. 7t is described as follows.

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cosθ34=

1

2a3a

4

[a4

2+a3

2−a1

2−a2

2+2a1a2cos θ

12]

?here

a1

a2, a

3, a

4 are the links

θ12 and

θ34 are the angles made by the corresponding links* whereas the angle

θ34 will be

named as the transmission angle. his angle will be evaluated by the above said e/uation.

*"- Engineering principle( )(ed in the de(ign

his four bar mechanism is a kinematic chain in which one of the links was fixed. Different

versions can be obtained by fixing any one of the links. he shapes of different mechanisms

which are obtained by fixing any one of the , links are called as @7nversionsA. ?hen the lengths

of the links are changed* then particular inversions are obtained by giving different mechanisms.

!o the engineering principle used in the design was inversion.


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system is used. 7f the failure is % dimensional then the maximum shear and maximum normal

stress theories are acceptable for the ductile material. σ 1*σ

"* andσ % are needed to be

known for this purpose. !tatic loading is very important in this regards.

*"2"! De(ign 'riteria

he linkage for the four bar mechanism* in order to move the object through the specific path is

needed to be designed. he design criterion for the linkage is to set the angle of transmission for

the object at specified locations. he lengths of the links must accommodate the position of the

object in a correct way. 5ne of the links must be fixed.

*"2"* De(ign E3)ati$n(

he design e/uations used in the four bar mechanism in order to move the object at given %

locations are as follows.he angle of transmission for the first position will be calculated by the following formula.

τ 1 (Transmissionangle )=Co s−1.

c2+d2−a2−b2−2abCos∅

2cd )/uation 1

he angle of transmission for the second position will be calculated by the following formula.

τ 2 (Transmissionangle )=Co s−1.

+d2−a2−b2−2abCos∅2cd )/uation "

he angle of transmission for the third position will be calculated by the following formula.

τ 3 (Transmissionangle )=Co s−1. +

d2−a2−b2−2abCos∅

2cd )/uation %

?hereas the width and thickness of the each link would be determine by the following formulae.

!o considering the final shape of )ular e/uation for 3ectangular column 1E

Pcr

A =

Cπ 2

EI

( Lk )2

)/uation ,

?here P is the critical force being applied at the links* 8 is the length of the link* ) is modulus of

elasticity* and 7 denotes moment of inertial for the link. ?here 8:k is called the slenderness ratio*

and k the radius of gyration*

E=30∗106 psi

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For the rectangular link* we specify a cross section for the link as h b with the restriction that

h G b. 7f the end conditions are pinned in both directions* then buckling may occur from center of

the link. How by applying the following -onditions in )ular e/uation 1E

I =bh

3

12 )/uation $

A=bh )/uation '

k 2= I / A=h2/12 )/uation (

Pcr=nd P CIere Force being applied is critical i.e. n J 1B

Putting all these values in above e/uation ,*

Pcr A

=Cπ

2

EI

( lk )2

)/uation +

?e can get the following e/uation

h

l2/(¿¿ 2/12)

Pcr

bh =

Cπ 2 E(

bh3

12)

¿

b=12 Pcr l

2

π 2CEh

3 )/uation

?here b is the width and h will be thickness of the link* and l denotes the length of the link.

*"2"- Saple 'alc)lati$n(

*"2"-"! 'a(e !4

>ccording to the first position* the angle of transmission can be calculated as follows %E.

τ 1 (Transmissionangle )=Co s−1. c

2+d2−a2−b2−2abCos∅2cd

τ 1 (Transmissionangle )=66.410

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Figure ".1 Position 1 for the object

*"2"-"* 'a(e *4

>ccording to the second position* the angle of transmission can be calculated as follows %E.

τ 2 (Transmissionangle )=Co s−1. c

2+d2−a2−b2−2abCos∅2cd

τ 1 (Transmissionangle )=300

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Figure "." Position " for the object

*"2"-"- 'a(e -4

>ccording to the third position* the angle of transmission can be calculated as follows %E.

τ 3 (Transmissionangle)=Cos−1. c

2

+d2

−a2

−b2

−2abCos∅

2cd

τ 1 (Transmissionangle )=300

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Figure ".% Position % for the object

-"! Sa&et. a(pect( $& the pr$5ect

7t is extremely important to focus the point of extreme stresses* or joints. !afety aspects must be

paramount before initiali6ing the mechanism. he joints must be checked in such a way that they

are firmly connected with each other. 7n the sense of design of the links* safety factor or factor of

safety is the Ultimate structural strength or stress divided by the minimum structural strength or

stress re/uired. !mall links often have large safety factors because of the weak linkage. he four

bar mechanism links* because of the tighter tolerances and safe value of stresses re/uired* are

often chosen in such a way that they are thicker and wider than re/uired. =enerally* the greater

safety factor causes safe designing* handling and testing the structure4 but* this is a unclear

relationship which is not modeled in such mechanism elements. 7t will be calculated by the

following formulae.

Factor of !afety J #aximum stress : Design stress C&hurmi "00B )/uation 10

-"!"! De(igner6( Re(p$n(e t$ #$tential Sa&et. #r$%le(

>ll of the parameters regarding links and pins must be kept a little larger than the designed

values regardless of the factor of safety. he life of the component is increased and it may lower

the rate of ha6ardous accidents.

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-"* 'reati0e thin,ing7 deci(i$n a,ing

he design must be scientific in such a way that the extra material should be removed. 7f there is

the re/uirement to move the object of $0 kg* then the linkage must be designed according to the

weight being displaced. he lengths* widths* and thicknesses for the links must accommodate the

weight of the object in a correct way.

7t was decided to design the linkage for three positions shown* in the statement* and it was clear

that the object must be fixed at the one point and must point towards the base. !o the relation of

the object with the base was made by fixing an angle with the corresponding link as shown in

figure.

2"! Optii8ati$n

>ccording to the design* the most suitable values were taken for the length* width and

thicknesses for the links of four bar mechanism. he optimi6ation was necessary for such

mechanism because the point of connections might be weak due to improper selection of the

design parameters of the links. !o it was decided to put the suitable values for the lengths* width*

and thickness. >fter the selection of these parameters* it was decided to check the relation for

angle of transmission. he positions which were described i.e. 00* '$0* K110 were correlated with

the design in order to find the angle of transmission. !o the results were reasonable.

9"! '$p)ter (i)lati$n

he design was prepared on the solidworks software "01, version. 7t was checked by doing the

simulation on it. he simulation was also done by solidwork "01,. he results obtained by the

simulation were as follows.

9"!"! #$(iti$n #!

he force being applied by the object on the link was assumed as $00 H because the man can put

the force of average $00 H.

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Figure $.1 Force being applied for simulation

he results for stresses obtained were as follows.

Figure $." !tress analysis

he results obtained due to strain were as follows

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Figure $.% !train analysis

otal deformation observed on the links was as follows.

Figure $., otal deformation analysis

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9"!"* #$(iti$n #*

Figure $.$ !tress analysis

Figure $.$ !tress analysis

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9"!"- #$(iti$n #-

!tress results for the links at which the maximum stresses will be induced.

Figure $.' !tress analysis

!train results for the links at which the maximum stresses will be induced.

Figure $.( !train analysis

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:"! Identi&icati$n $& gr$)p +$r, and indi0id)al +$r,

N)%er Ta(,

Indi0id)a

l +$r, Gr$)p +$r,

1 3esearch

" 5nline research

% =athering of all information

, -ompiling of all information

$ -reating rough draft of failures

'Discussing mechanism

to employees:companies ( 7mplementing design

)valuate feedback

1% esting

1, Feedback from the future attendees able '.1 7dentification of group work and individual work

;"! Di(c)((i$n and interpretati$n $& re()lt(

he design made on four bar linkage to place the object from one position to other position was

accomplished and results obtained from the calculations synchroni6ed with the design. he

transmission angle received from the calculations was checked by the !olid ?orks design* and it

was found that if the lengths* of the links would be same as were calculated to found the angle of

transmission* then same angle of transmission was observed in solid works too. he values for

the width and thickness of the links were kept a little higher than the values of the design

parameters due to safety aspect. >s much as the width and thickness of the link would be greater*

the links would be stronger.

7n order to observe the failure in the design* the simulation was done on it and it was found that

point junction or connection where the pins were mounted was with more excessive stresses.

7t also was observed that when the load was too much then the links were observed* if they

buckle or not. he main thing was to notice the correct positions and the angle of transmission.

!o all were synchroni6ed with the design and finally were selected for the final simulation.

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Re&erence(

1. 3ichard =.

design report ii (1)

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