Course Number: MEMB 321
Day and Date experiment performed
: 2000
Due Date: 2000
Lecturer : ****
Statement
of Purpose/ Objective:
The objective of the experiment is to
:-
·
investigate the kinematic motion of a
Crank and Slotted Lever Quick Return mechanism
·
to show that it is a quick return
mechanism
·
to evaluate the increase in efficiency
that this would offer if applied to a machine tool.
Data,
Observation and Results:
Crank Angle |
Theoretical Slider Position |
Experimental Slider Position (mm) |
Stroke |
% Error |
|
|
0 |
69 |
69 |
Cutting |
0 |
|
|
10 |
60.64455 |
60 |
Cutting |
1.062837 |
|
|
20 |
52.42229 |
51.5 |
Cutting |
1.759352 |
|
|
30 |
44.46838 |
43.5 |
Cutting |
2.177686 |
|
|
40 |
36.92207 |
36.5 |
Cutting |
1.143132 |
|
|
50 |
29.92906 |
29.5 |
Cutting |
1.433598 |
|
|
60 |
23.64426 |
24.9 |
Cutting |
-5.31096 |
|
|
70 |
18.23484 |
18.8 |
Cutting |
-3.09931 |
|
|
80 |
13.88352 |
14.7 |
Cutting |
-5.88091 |
|
|
90 |
10.79145 |
12 |
Cutting |
-11.1991 |
|
|
100 |
9.179517 |
10.1 |
- |
-10.0276 |
|
|
110 |
9.285631 |
10 |
- |
-7.69327 |
|
|
120 |
11.35386 |
12.1 |
Return |
-6.57164 |
|
|
130 |
15.60938 |
16.2 |
Return |
-3.78378 |
|
|
140 |
22.21236 |
22.5 |
Return |
-1.29494 |
|
|
150 |
31.18816 |
30.5 |
Return |
2.20649 |
|
|
160 |
42.34354 |
40.5 |
Return |
4.353774 |
|
|
170 |
55.20101 |
53.8 |
Return |
2.538007 |
|
|
180 |
69 |
62.1 |
Return |
10 |
|
|
190 |
82.79899 |
80.5 |
Return |
2.776597 |
|
|
200 |
95.65646 |
94 |
Return |
1.731674 |
|
|
210 |
106.8118 |
105 |
Return |
1.696288 |
|
|
220 |
115.7876 |
114 |
Return |
1.543893 |
|
|
230 |
122.3906 |
121 |
Return |
1.136218 |
|
|
240 |
126.6461 |
126 |
Return |
0.51019 |
|
|
250 |
128.7144 |
129 |
- |
-0.22191 |
|
|
260 |
128.8205 |
129 |
- |
-0.13935 |
|
|
270 |
127.2086 |
127 |
Cutting |
0.163943 |
|
|
280 |
124.1165 |
124 |
Cutting |
0.093845 |
|
|
290 |
119.7652 |
120 |
Cutting |
-0.19609 |
|
|
300 |
114.3557 |
114 |
Cutting |
0.311079 |
|
|
310 |
108.0709 |
108 |
Cutting |
0.06564 |
|
|
320 |
101.0779 |
101 |
Cutting |
0.077101 |
|
|
330 |
93.53162 |
93 |
Cutting |
0.568384 |
|
|
340 |
85.57771 |
86 |
Cutting |
-0.49346 |
|
|
350 |
77.35545 |
77 |
Cutting |
0.459499 |
|
|
360 |
69 |
69 |
Cutting |
2.06E-14 |
|
|
|
|
||||
Sample
calculation:
Calculation
of the theoretical value:
u = 100 , AC = 240 mm , OB = 40 mm
sin u =BE/40
tan u =BE/EO
BE =sin u*40
= 6.95 mm
So,
= 39.4 mm
EA = 160 + 39.4
= 199.4 mm
AB2 = (BE2+EA2)
AB=199.52 mm
Then, sin a = BE/AB
= y’/AC
= y’/240
so, y’ = 8.36 mm
Since we initiate the rotation of the
revolute part counterclockwise,
Thus, x = 69 – y’
=
60.64
mm
Calculation
of the percentage error:
%
error= ((Theoretical value- Experimental value)/Theoretical Value) *100
=
((60.64455- 60)/60.64455)*100
=
1.062837
Analysis
and Discussion:
Based on the data collected, the
experimental value error reached as high as 10 % of the theoretical value
calculated. This range of error will somewhat make the crank and slotted lever
quick return motion a suitable mechanism to be applied to a machine tool. The
accuracy of the slider position is essential especially if to be applied on
machine tools in order to obtain a fine machining process.
The experiment predicts that for an
infinite radius curvature of the revolute pair, the movement of the slider will
alter from an angular motion to a linear motion. This will require the error
analysis to be referred again to make it relevant in discussion. The error
ranges around 0.06564 to 10 percent of variation from the theoretical
value. It is acceptable to consider that the slider behaves as a linear motion
body.
From
the data collected, it can be understood that the cutting stroke is indicated by
a decrease in the slider position and return stroke is idicated by an increase
in the slider position. There are two set of angles where the angles does not
vary from a single degree which are at 10.1o-10o and 129o-129o.
This angles show the transition between the cutting and return stroke. Out of 36
slider positions measured, which is a complete revolution, there are 19 or 190o
cutting strokes and 13 or 130o return
strokes. Thus the machine efficiency out of 32 strokes that does not include the
transition stroke can be calculated as below.
Efficiency
= (Cutting stroke – Return Stroke) / 32
Conclusion:
As a conclusion, the kinematic motion
of the Crank and Slotted Lever is a mechanism which translates a rotational
movement to a linear motion. By applying the inversion technique, which is to
obtain a different mechanism by setting the various links in turn, the mechanism
can work to produce a linear motion with the least of error percentage.
The experiment also shows that the
Crank and Slotted Lever is indeed a quick return mechanism based on the degree
of cutting stroke it produced which is greater than that of return stroke. A
greater degree of stroke means that a longer time is taken and since the return
stroke only took 130o of the revolution compared to 190o
of cutting stroke, the return stroke took less time than cutting stroke.