Title: Slider Crank

Objective;

To obtain the velocity and acceleration of the slider crank.

Apparatus;

Slider crank

Theory;

The slider crank chain is one of the two basic mechanisms which from the basic for many

more complicated motions. (The others are the four Bar Chain, Scoth Yoke or Chebyshev

linkage of which over 800 forms are known). It transforms linear motion to circular motion or

vice versa. r is radius of crank, l is length of connecting rod.

When ,

Therefore for any position

In order to find x, r and l need to be found.

r can be derived from the reading of q at

l can be derived from the reading of q at

Experiment Principle:

The output x varies with the input angle . In other word, x is a function of ; or

where constant (i)

is the gradient of the graph of against

(ii)

is the gradient of the graph of against

Hence the velocity and acceleration can be obtained just by plotting two graph. These values

of and can be compared to the theoretical values obtained from the equations shown

below.

Theoretical Principle

Using cosine rule:

With and are constants, differentiating with respect to time will yield:

where = 1 rad/s constant. (iii)

Differentiating again will yield:

(iv)

From (iii):

From (iv):

Experimental Procedure;

1. All of equipments for experiment of slider crank are set in good condition.

2. The angles of the circle and the piston are fixed at 00

3. The angle of the circle, is twisted at 300 and a resulting distance that the piston

moves, q is measured.

4. The position of sliding block/slider, x is calculated.

5. The procedures number 3 and number 4 are repeated with an increasing angle of 300

until the angle of circle reaches 360°.

6. The graph of the position of slider, againts angles of cirle, is plotted.

7. The slopes, from the graph are determined by using the computational method.

8. The graph of versus is plotted.

9. The results from both graphs are compared to the theoretical values.

Experimental Results;

and

When cm

Therefore for any position : [ x = ( r + l ) – q ]

( cm ) (cm) (cm) (cm) (cm)

0 0.000 0.000 0.000 0.000 27.450

30 1.490 1.362 1.362 1.404 26.046

60 5.272 5.090 5.090 5.151 22.299

90 9.636 9.636 9.544 9.605 17.845

120 13.218 13.162 13.144 13.175 14.275

150 15.254 15.254 15.254 15.254 12.196

180 15.908 15.890 15.890 15.896 11.554

210 15.244 15.254 15.254 15.251 12.199

240 13.144 13.218 13.236 13.199 14.251

270 9.618 9.690 9.708 9.672 17.778

300 5.126 5.290 5.290 5.235 22.215

330 1.362 1.490 1.508 1.453 25.997

360 0.000 0.000 0.000 0.000 27.450

Sample calculation;

a. Theoretical Calculations:

when the corresponding value of is 1.404 cm

then, cm

from the theoretical principles:

cm/s

cm/s²

b. Experimental Calculations: The graph of the position of slider versus the angle of the circle is plotted:

From above graph, the slop of every angle, is calculated by using the computational

method. The obtaining slops are included in the table below.

(cm) (cm) (cm)

0 0.000 27.450 -0.027

30 1.404 26.046 -0.089

60 5.151 22.299 -0.142

90 9.605 17.845 -0.131

120 13.175 14.275 -0.113

150 15.254 12.196 -0.013

180 15.896 11.554 0.00

210 15.251 12.199 0.053

240 13.199 14.251 0.136

270 9.672 17.778 0.141

300 5.235 22.215 0.138

330 1.453 25.997 0.087

360 0.000 27.450 0.032

0

5

10

15

20

25

30

0 50 100 150 200 250 300 350 400

The

po

siti

on

of

slid

er,

x(c

m)

Angle of the circle Ɵ (°)

The graph x (cm) versus θ(°)

Then the graph of versus is plotted

From above graph, the slop of every angle, is calculated by using the computational

method. The obtaining slops are included in the table below.

= =

0 -0.027 -0.00175

30 -0.089 -0.00300

60 -0.142 0.0000

90 -0.131 0.0010

120 -0.113 -0.0070

150 -0.013 0.0019

180 0.00 0.0011

210 0.053 0.0025

240 0.136 0.0017

270 0.141 0.0000

300 0.138 -0.0009

330 0.087 -0.0018

360 0.032 -0.0019

is equal to according to equation (i) since = 1 rad/s constant.

is equal to according to equation (ii) since = 1 rad/s constant.

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0 50 100 150 200 250 300 350 400

dx/dθ versus θ

θ

To compare from theoretical values for all angles of , the table is prepared below.

(cm) (cm) Experimental Theoretical

(cm/s) (cm/s²) (cm/s) (cm/s²)

0 0.000 27.450 -0.027 -0.00175 0.000 -11.91

30 1.404 26.046 -0.089 -0.00300 -5.403 -8.641

60 5.151 22.299 -0.142 0.0000 -8.378 -2.372

90 9.605 17.845 -0.131 0.0010 -7.950 3.542

120 13.175 14.275 -0.113 -0.0070 -5.385 5.583

150 15.254 12.196 -0.013 0.0019 -2.541 5.121

180 15.896 11.554 0.00 0.0011 0.000 4.710

210 15.251 12.199 0.053 0.0025 2.541 5.118

240 13.199 14.251 0.136 0.0017 5.383 5.585

270 9.672 17.778 0.141 0.0000 7.950 3.555

300 5.235 22.215 0.138 -0.0009 8.385 -5.910

330 1.453 25.997 0.087 -0.0018 5.407 -8.646

360 0.000 27.450 0.032 -0.0019 0.000 -11.19

Discussion;

Both results of velocities and accelerations in respectives angles from experiment differed

greatly with the theoretical calculations. So the percentage of average error (Appendix) was

very large.

This was happen because the instruments could not measure precisely, the sample was not

pure or was contaminated, or calculated values from theoretical results did not take account of

friction.

This was also because the angular velocity taken during experiment was not exactly measued

in 1 rad/s. Thus it would produce very significant results.

Conclusion;

In conclusion, when the positions of slider, are plotted against the angles of the

circle, on the graph, the sinusoidal form will be obtained. will decrease until reaches

180° then it will turn to increasing values until reaches 360°. From the similar graph, the

slopes in every point of are equal to the velocities of or slider. The velocity starts from

negative value and decrease uniformly until reaches 60 .Then it increase steadily and turn

positive values when reaches 180. It continues to increase until reaches 300 then turn to

decreasing values until the position of slider are complete in cycle.

The accelerations can be concluded from the graph of vesus where the

accelerations are equal to the slope of every point of the angle, . The acceleration decreases

and increases harmoniously along the axis of angle, .

References:

1. Engineering Mechanics Dynamics, R.C. Hibbeler, Prantice Hall, 2007

2. http://www.ecf.toronto.edu/~writing/handbook-lab.html#Discussion

3. http://en.wikipedia.org/wiki/Crank_%28mechanism%29

4. http://en.wikipedia.org/wiki/Scotch_yoke

5. http://en.wikipedia.org/wiki/Chebyshev_linkage

Appendix:

Experimental Theoretical Percentage of error(%)

(cm/s) (cm/s²) (cm/s) (cm/s²)

-0.027 -0.00175 0.000 -11.91 100 100

-0.089 -0.00300 -5.403 -8.641 98.35 99.97

-0.142 0.0000 -8.378 -2.372 98.31 100

-0.131 0.0010 -7.950 3.542 98.35 99.97

-0.113 0.0070 -5.385 5.583 97.90 99.87

-0.013 0.0019 -2.541 5.121 98.49 99.96

0.00 0.0011 0.000 4.710 100 99.98

0.053 0.0025 2.541 5.118 97.91 99.95

0.136 0.0017 5.383 5.585 97.47 99.97

0.141 0.0000 7.950 3.555 98.23 100

0.138 -0.0009 8.385 -5.910 98.35 99.98

0.087 -0.0018 5.407 -8.646 98.39 99.97

0.032 -0.0019 0.000 -11.19 100 99.98

Percentage of average error 98.60 99.97