kinematic mechanism (3).pdf

8/14/2019 kinematic mechanism (3).pdf

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KINEMATICS OF MECHANISMSKINEMATICS OF MECHANISMS(BDC4043)

Lecture Module 3: Analysis of Position and Displacement

Waluyo Adi SiswantoUniversiti Tun Hussein Onn Malaysia

This module is licensed under a Creative Commons Attribution 3.0 License.
http://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/


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Lecture Module 3 BDC4043 2

Topics

nderstandin! position and displacementDisplacement"position analysis #!raphical and analytical$Limit position #!raphical and analytical$Complete CyclePosition Dia!ramDisplacement dia!ram


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Position and displacementdefinition

PositionPositionrefers to the location of an ob%ect

Position of a point P

O

P

RP

RP RP={RPxRPy}

N

A

An!ular position of a point N(AN ,)


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Position and displacementdisplacement

Displacement (Shift)Displacement (Shift)is the end product of movement #motion$.&t is a vector that represents the distance bet'een the startin! and endin! positionof a point or lin(.

O

P

RP

N

A

Linear displacement

P '

RP

'

RP

RP=R

P'R

P


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Position and displacementdisplacement

Displacement (Shift)Displacement (Shift)is the end product of movement #motion$.&t is a vector that represents the distance bet'een the startin! and endin! positionof a point or lin(.

O

P

N

A '

an!ular displacement

= '


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Displacement analsisdegrees of freedom

De!"ees of f"eedomDe!"ees of f"eedom(mo#ilit)(mo#ilit)is the number of independent inputs re)uired to preciselyposition all lin(s of the mechanism 'ith respect to the !round.

D*+, the number of actuators needed to operate the mechanism.

-rueblers e)uation: F=3(n1)2 jpj h

, total number of lin(s includin! frames

, total number of primary %oints #pins or slidin! %oints$

, total number of hi!her/order %oints #cam or !ear %oints$

n

jp

jh


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Displacement analsisdegrees of freedom

F! Constrained mechanism

F" Loc(ed mechanism

F#! nconstrained mechanism

F=3(41)2(4)0

F=3(31)2(3)0

F=1

F=0

F=3(51)2(5)0

F=2


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E$ample %&'

&dentify the mobility #dof$ of follo'in! mechanisms:


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1

3 2

4

&dentify the lin(s : 4 lin(s


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1

3 2

4

&dentify the %oints : 4 pin %oints 5 slidin! %oint

A

6

C

D

7

+ , 3#4/$ 8 1#9$ ,

$ounted as % pin &oints

T'e mec'anism wor(sonly from ! actuator


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inematics dia!ram


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&dentify the lin(s : 2 lin(s

&dentify the %oints : 3 pin %oints 5 slider %oints

+ , 3#2/$ 8 1#2$ ,

T'e mec'anism wor(sonly from ! actuator


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Displacement analsisgrap'ical met'od

;tartin! from the driver #master$ 'here the actuator located2 at Df. The intersection #d$ and #e$ is point C. Dra' lin( 6C!. Dra' lin( CD

6

D

C


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A

6

D

C

30o


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A

6 D

C

60o


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6

D

C

90o

A


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A

6

DC

120o

Displacement analsis


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Displacement analsisanalytical met'od

020

30o

Determine #analytically$ the displacement of the clamp surface as thehandle rotates do'n'ard de!.

Do the same thin! by usin! a !raphical method.



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020

30o

A

6

C

020

30o

;implified model



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A

6

C30o

A6,0 6C,20

@ector e)uation AB+BC=AC

{AB cos30AB sin30}+{BCcosBCsin}={AC0 }

sin=AB sin30

BC =38.68o

AC=74.53

=hen the an!le de!

sin=AB sin15

BC =18.87o

AC '=86.15

The displacement of C : 86.1574.53=11.62

E l % %


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E$ample %&%

LL1

*

A

C

+ind the mathematical e)uations to calculate < and the distance *C#use vector analysis $. Plot the ma!nitude *C and the an!le for one cycle,L5L1 at *#b$ The intersection 'ith slider trac( is C1 #upper limit end$#c$ Dra' a circle >,L1 8L at *#d$ The intersection 'ith slider trac( is C #lo'er limit end$

R=ACOA

R=AC+OA

Trac( C

E$ample % ,


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A

D

E$ample %&,

Air spray

*1 cm

2 cm

. cm

2 cm

2 cmC

The movement of a 'ater sprayer is automatically controlled by rotatin!the lever *A. Dra' the upper and lo'er positions of the sprayer boom DCand find the s'ayin! an!le of the boom.


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*

D

C

A

6oom at upper position

R=ACOA

Trac( C


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D

*

C1

A1

6oom at upper position

R=AC+OA

Trac( C


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D

*

C1

C

47oMeasure this an!le

+imitin! position


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! panalytical met'od

*

A

x

y

C

sin= y

L2L1

tan=y

x x=

y

tan

=asin y

L2L1

+imitin! position


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! panalytical met'od

sin= y

L2+L1

tan=y

x x=

y

tan

=asin y

L2+L1

*

C1

A1

y

x

Complete ccle


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p position and displacement diagram

The movement of a mechanism can be seen clearly if it simulated ina complete cycle. Any point can be eamined the cycle pattern.

/ !raphical method/ analytical approach

E$ample %&-


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E$ample % -

A

6

C

D

9. cm

1. cm3. cm

2 cm9. cm

Dra' the initial settin!considerin! the correctdimensions

;imulate the movement

of the mechanism 'henA6 rotates CC=.The simulation must beat least cycle.#!raphical methodDra' every 30de!$

Plot the horiBontal andvertical positions ofpoint C #refer to D$


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A

6

D

C

A6 CD CDy0 /0. 3.?


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A

6

D

C

A6 CD CDy0 /0. 3.?

30 /1.1 3.2


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A

6 D

C

A6 CD CDy0 /0. 3.?

30 /1.1 3.2

40 /3. 1.0


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6

D

C

A

A6 CD CDy0 /0. 3.?

30 /1.1 3.2

40 /3. 1.0

?0 /3.? 0.2


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A

6

DC

A6 CD CDy0 /0. 3.?

30 /1.1 3.2

40 /3. 1.0

?0 /3.? 0.2

10 /3.? /0.4


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A

6

D

C

A6 CD CDy0 /0. 3.?

30 /1.1 3.2

40 /3. 1.0

?0 /3.? 0.2

10 /3.? /0.4

0 /2 /0.


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A

6

D

C

A6 CD CDy0 /0. 3.?

30 /1.1 3.2

40 /3. 1.0

?0 /3.? 0.2

10 /3.? /0.4

0 /2 /0.

E0 /3.? 0.9


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A

6

D

C

A6 CD CDy

0 /0. 3.?

30 /1.1 3.2

40 /3. 1.0

?0 /3.? 0.2

10 /3.? /0.4

0 /2 /0.

E0 /3.? 0.9

10 /3.4 .9


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A

6

D

C

A6 CD CDy

0 /0. 3.?

30 /1.1 3.2

40 /3. 1.0

?0 /3.? 0.2

10 /3.? /0.4

0 /2 /0.

E0 /3.? 0.9

10 /3.4 .9

120 /1.9 3


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A

6

D

C

A6 CD CDy

0 /0. 3.?

30 /1.1 3.2

40 /3. 1.0

?0 /3.? 0.2

10 /3.? /0.4

0 /2 /0.

E0 /3.? 0.9

10 /3.4 .9

120 /1.9 3

190 /0.1 3.?


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A

6

D

C

A6 CD CDy

0 /0. 3.?

30 /1.1 3.2

40 /3. 1.0

?0 /3.? 0.2

10 /3.? /0.4

0 /2 /0.

E0 /3.? 0.9

10 /3.4 .9

120 /1.9 3

190 /0.1 3.?

300 .9 3.4


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A

6D

C

A6 CD CDy

0 /0. 3.?

30 /1.1 3.2

40 /3. 1.0

?0 /3.? 0.2

10 /3.? /0.4

0 /2 /0.

E0 /3.? 0.9

10 /3.4 .9

120 /1.9 3

190 /0.1 3.?

300 .9 3.4

330 3.E


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A

6

D

C

A6 CD CDy

0 /0. 3.?

30 /1.1 3.2

40 /3. 1.0

?0 /3.? 0.2

10 /3.? /0.4

0 /2 /0.

E0 /3.? 0.9

10 /3.4 .9

120 /1.9 3

190 /0.1 3.?

300 .9 3.4

330 3.E

340 /0. 3.?


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A6 CD CDy

0 /0. 3.?

30 /1.1 3.2

40 /3. 1.0

?0 /3.? 0.2

10 /3.? /0.4

0 /2 /0.

E0 /3.? 0.9

10 /3.4 .9

120 /1.9 3

190 /0.1 3.?

300 .9 3.4

330 3.E

340 /0. 3.?

0 30 40 ?0 10 0 E0 10 120 190 300 330 340

/

/2

/3

/1

/

0

1

3PositionPoint C #/ais$ refer to D

rotation

PositionC#

/ais$

0 30 40 ?0 10 0 E0 10 120 190 300 330 340

/

0

1

3

2

PositionPoint C #y/ais$ refer to D

rotation

Position

C#

/ais$

E$ample %&.


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Do the simulation in 7ample 3/4 by usin! &MPACT

Fints: dra' line in -iD. This 'ill be considered as rod element.The lin( should be defined only a sin!le element.

E$ample %&/


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LL1

*

A

C

Plot the ma!nitude *C and the an!le for one cycle

kinematic mechanism (3).pdf

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