projek kdmprint

7/31/2019 PROJEK KDMprint

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INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA

KULLIYAH OF ENGINEERING

DEPARTMENT OF MECHANICAL ENGINEERING

MEC 3607

KINEMATICS AND DYNAMICS OF MACHINERY

SEMESTERII 09/10

KDM PROJECT: FOUR BAR MECHANISM (WIPER)

PREPARED BY:

MOHD HAFIZ BIN AZIZAN 0439701

MOHD REDZUAN BIN MOHD ZAIN 0439509

LECTURER:

FADLY JASHI DARSIVAN RIDHUAN SIRADJ

DUE DATE:

MARCH 22ND, 2010


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INTRODUCTION:

In study of mechanics of machines, engineers main concerns are on kinematic and kinetic

analysis on each member as well as joints. Kinematic analysis deals with members position,

velocity as well as acceleration. All these three parameters divided into two types, either in linear

or angular motion. On the other hand, kinetic analysis is a study of forces as well as moments

acting on or by the members of a particular mechanism.

Before producing any mechanism, engineer has to draw that mechanism first and

analytically analyze its kinematics and kinetics. This drawing and analyzing parts are exposed to

human and tool errors. After been analyzed, the mechanism will be assembled and tested for

accuracy of previous analysis during pre-producing period. If too many errors occur or purpose of

that mechanism is not achieved, then it has to be re-done, starting from review of drawing. This

kind of method wastes a lot of time and risky in term of cost (if the mechanism has to be re-done).

Thus, engineer comes out with new solution of pre-produced mechanism by using simulation

software, such as Working Model Program.


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APPLICATION OF THE MECHANISM

The four-bar linkage is a versatile planar mechanism, used extensively in articulated systems:

In wheel vehicles:

o For the Ackerman steering in all automobiles and trucks.

o For automotive and bicycle suspensions.

o For hydraulic tail lifts and scissor tippers on dump trucks.

In hydraulic machinery:o For tilting the bucket on hydraulic excavators and loaders.

o For the blade actuators of earth moving equipment.

o For the three-point hitch of agricultural tractors.

In industrial automation and material handling:

o For the needle mechanism on sewing machines.

o For scissor lifts and conveyor ancillary equipment.

o

For packaging machines. In doors and covers, instead of a simple hinge:

o For garage lifting doors.

o For engine hoods.

In hand tools:o For locking pliers.

o For bolt cutters.

o For manual clamps.


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Analytical Solution:

1 = 2 = 0 ;

3 = 20 ; 5 = 6 = 8 = 30 ;

3 = input = 5rad/s; 3 = 0;

r1 = 1.3m r2 = 2.9m r3= 0.5m r4 = 2.0m

Fig. 1

Two loop mechanism


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Fig. 2

Loop 1:

R3 + R4 - R1 - R5=0

Real i:

r3cos3 + r4cos4 r1cos1 r5cos5 = 0

r3cos3 + r4cos4 r1 r5cos5=0 (1)

Imaginary j:

r3sin3 + r4sin4 r1sin1 r5sin5 = 0 .. (2)


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Loop 2:

R6 + R7 R2 R8=0

Real i:

r6cos6 + r7cos7 r2cos2 r8cos8 = 0

7 = 0, 8 = 6, r8 = r6, r2 = r7;

Imaginary j:

r6sin6 + r7sin7 r2sin2 r8sin8 = 0

* independent 3(constant);

dependent rows: 4, 5,4, 5

For []

Loop 1:

- r33sin3 - r44sin4 + r55sin5 = 0 ..(3)

r33cos3 + r44cos4 - r55cos5 = 0 .(4)

Loop 2:

- r66sin6 + r88sin8 = 0

r66cos6 - r88cos8 = 0


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For []

Loop 1:

- r33sin3 - r332cos3 - r44sin4 - r44

2cos4

+ r55sin5 + r552cos5 = 0 .. (5)

+ r33cos3 - r332sin3 + r44cos4 - r44

2sin4

- r55cos5 + r552sin5 = 0 ..(6)

For []

Loop 2:

- r66sin6 r662cos6 + r88sin8 + r88

2cos8 = 0

r66cos6 r662sin6 - r88cos8 + r88

2sin8 = 0

From Loop 1:

(1): r4cos4 = r1 + r5cos5 - r3cos3

(2): r4sin4 = r5sin5 - r3sin3

(1)2+(2) 2

r42 = (r1 + r5cos5 - r3cos3)

2 + (r5sin5 - r3sin3)2

yielding


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r42 = r1

2+ r5

2 + r32 - 2r3r5cos(3-5) + 2r1r5cos5 - 2r1r3cos3

r52 + r5[-2r3r5cos(3-5) + 2r1cos5]+[r1

2+ r3

2 -r42 - 2r1r3cos3] = 0

Quadratic equation solve for r5 , then substitute to (2)& solve for 4;

r5 = 1.2856 m, 4 = 13.64

[]: solution

3: (3) x cos5:

- r33sin3cos5 - r44sin4cos5 + r55sin5cos5 = 0

4: (4) x sin5:

r33cos3sin5 + r44cos4sin5 - r55cos5sin5 = 0

3+4:

r33(cos3sin5 - sin3cos5) + r44(cos4sin5 - sin4cos5)= 0

r33sin(5 - 3) + r44sin(5 4)= 0

4 = [- r33sin(5 - 3)]/[ r4sin(5 4)]

Substitute 4 to (3) & solve for 4

4 = - 0.77 rad/s, 5 = 0.77 rad/s


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[]: solution

5: (5) x cos5:

6: (6) x cos6:

4 = [- r332cos(3-5)- r33sin(3-5)- r44

2cos(4- 5)

+ r552]/ [r4sin(4- 5)]

5 = [- r332cos(3-5)- r33sin(3-4)- r44

2

+ r552cos(4- 5)]/ [r5sin(4- 5)]

4 = 22.52 rad/s2, 5 = 35.56 rad/s

2

Fig. 3: Drawing


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Fig. 4: Simulation

Table 1 (comparison between analytical and simulation)

ParametersMethods 4 (rad/s) 5 (rad/s) 4 (rad/s

2) 5 (rad/s2)

Analytical -0.77 0.77 22.52 35.56

Simulation -0.866 0.616 24.972 39.774

Percentage error for angular velocity:


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4 % diff =

5 % diff =

Percentage error for angular acceleration:

4 % diff =

5 % diff =

Discussion and Conclusion:


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This mechanism has two loops to be considered on the left and right-hand sides

respectively (see figure 2). Loop 1 has to be evaluated to find r5, 4, 4, 5, 4 and 5. By using loop

closure equations, we can determine all these unknowns which represent length (r), angle (),

angular velocity () and angular acceleration (). Loop 2 is also known as parallelogram four-bar

mechanism, thus we can easily know that r6 || r8 and r2 || r7 and the lengths are equal respectively.

From parallelogram four-bar mechanism evaluation, we can conclude that 6 = 8 and 2 = 7, so as

the angular velocity and acceleration.

In this project, we are determining the kinematics of links/bars at the position shown in

figure 1. The input motor at joint (1,3) is set to be 5 rad/s and other dimensions are given. When

comparing between analytical and simulation methods of determining kinematic properties of the

mechanism, we found out that the analytical results are close to the simulation results (see results

section). Thus, the calculation of analytical method is considered as correct.

As a conclusion, in comparison between analytical and simulation methods for this project,

the analytical is more accurate, due the fact that it uses exact geometry of the mechanism.

Simulation should be the real case, but it is difficult to set the evaluation of simulation kinematics

at exact position. Nevertheless, engineer just needs to use the simulation to complete the job as it

reduces time consumption efficiently and such an easy method.

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