Question

For the linkage demonstrated in class (illustrated in the following figure, not to scale), NO APS HO ---- 02 1) Measure length of the four links. 2) Using Grashof condition to classify this linkage and predict its motion. 3) Measure the length of AP and the angle between PA and BA. 4) calculate and plot the angular displacement of links 3 and 4 and the path coordinates of point P with respect to the angle of the input crank 0,4 for one revolution Hint: You can use the MATLAB script on ecourses as a basis. Using the script (only the OPEN configuration, not the CROSSED), you should be able to find the angular displacement of links 3 and 4 (ez and B.) given the angle of the input crank 02A (0) Now if you use this script manually, you can have sth. like 3° 10° 360 Now you can plot 83 and @ with respect to ez Hint: It will be easier if you know how to turn the script into a function, and plot the results using MATLAB. (+1 bonus point if you do that) To find the position of point P, you need to use the equation that we talked about in class to find any point on the link in this case, coupler) AND make that part of the

Answer 1

2)

The values you gave are wrong.

I sketched the picture again.

13.95 17.60 25.83 19.74 8.55 30.649 18.64

Link 2 is the smallest link. s = 8.55

Link 4 is longest. l = 19.74

p = 17.6. q = 18.64.

Groshoff Condition.

(s +1 = 28.29) < (p +9= 36.24)

So, this is a crank-rocker mechanism.

The driving link can rotate completely and other links rock.

4)

Matlab Code: You may have to rearrange theta3 and theta4 after running the first section of the code to make them continuous.

Matlab Code:

%%
clear;clc;

syms q3 q4;
q2 = 0:2:360;
l1 = 18.64;l2 = 8.55;l3 = 17.60;l4 = 19.74;
Q3 = zeros(length(q2),2);
Q4 = zeros(length(q2),2);

for i = 1:length(q2)
%loop equations
Q2 = q2(i);
e1 = l1+l4*cosd(q4) - l3*cosd(q3) - l2*cosd(Q2);
e2 = l4*sind(q4) - l3*sind(q3) - l2*sind(Q2);
[Q3(i,:),Q4(i,:)] = solve(e1,e2);
  
end
%%

%%plotting theta3 and theta 4
figure(1)
plot(q2,Q3(:,1))
title('theta3 vs theta 2');
figure(2)
plot(q2,Q4(:,1))
title('theta4 vs theta 2');
%Calculating location of Point P
Px = l2*cosd(q2') + 25.83*cosd(Q3(:,1) - 30.64);
Py = l2*sind(q2') + 25.83*sind(Q3(:,1) - 30.64);
%plotting Point P
figure(3)
plot(Px,Py);
title('plot of path of point P');

Plots:

theta3 vs theta 2 0 50 100 150 200 250 300 350 400

theta4 vs theta 2 100 90 0 50 100 150 200 250 300 350 400

plot of path of point P 12 14 16 18 20 22 24 26 28 30 32

Hope you like the answer. Please rate positively if you can.
Q3 =
86.465 -86.465
84.744 -88.13
82.977 -89.729
81.176 -91.253
79.352 -92.695
77.515 -94.047
75.677 -95.304
73.846 -96.462
72.032 -97.518
70.244 -98.471
68.489 -99.319
66.773 -100.06
65.101 -100.71
63.477 -101.25
61.905 -101.7
60.387 -102.05
58.925 -102.31
57.519 -102.49
56.171 -102.58
54.88 -102.6
53.646 -102.54
52.467 -102.41
51.343 -102.21
50.273 -101.95
49.255 -101.63
48.287 -101.26
47.368 -100.84
46.497 -100.36
45.671 -99.847
44.889 -99.287
44.149 -98.688
43.451 -98.051
42.791 -97.381
42.169 -96.679
41.584 -95.947
41.033 -95.188
40.516 -94.404
40.032 -93.596
39.579 -92.766
39.156 -91.916
38.763 -91.048
38.397 -90.163
38.06 -89.263
37.748 -88.348
37.463 -87.421
37.202 -86.483
36.966 -85.534
36.753 -84.577
36.564 -83.611
36.397 -82.639
36.252 -81.661
36.129 -80.678
36.028 -79.691
35.947 -78.701
35.887 -77.709
35.847 -76.716
35.828 -75.722
35.828 -74.729
35.847 -73.737
35.887 -72.747
35.945 -71.759
36.023 -70.775
36.119 -69.796
36.235 -68.821
36.37 -67.851
36.523 -66.888
36.695 -65.932
36.886 -64.983
37.096 -64.042
37.324 -63.11
37.571 -62.187
37.837 -61.274
38.122 -60.372
38.426 -59.48
38.748 -58.6
39.089 -57.732
39.449 -56.876
39.827 -56.034
40.225 -55.205
40.641 -54.39
41.077 -53.589
41.531 -52.803
42.003 -52.032
42.495 -51.277
43.005 -50.538
43.534 -49.815
44.081 -49.108
44.647 -48.418
45.231 -47.746
45.833 -47.09
46.453 -46.453
47.09 -45.833
47.746 -45.231
48.418 -44.647
49.108 -44.081
49.815 -43.534
50.538 -43.005
51.277 -42.495
52.032 -42.003
52.803 -41.531
53.589 -41.077
54.39 -40.641
55.205 -40.225
56.034 -39.827
56.876 -39.449
57.732 -39.089
58.6 -38.748
59.48 -38.426
60.372 -38.122
61.274 -37.837
62.187 -37.571
63.11 -37.324
64.042 -37.096
64.983 -36.886
65.932 -36.695
66.888 -36.523
67.851 -36.37
68.821 -36.235
69.796 -36.119
70.775 -36.023
71.759 -35.945
72.747 -35.887
73.737 -35.847
74.729 -35.828
75.722 -35.828
76.716 -35.847
77.709 -35.887
78.701 -35.947
79.691 -36.028
80.678 -36.129
81.661 -36.252
82.639 -36.397
83.611 -36.564
84.577 -36.753
85.534 -36.966
86.483 -37.202
87.421 -37.463
88.348 -37.748
89.263 -38.06
90.163 -38.397
91.048 -38.763
91.916 -39.156
92.766 -39.579
93.596 -40.032
94.404 -40.516
95.188 -41.033
95.947 -41.584
96.679 -42.169
97.381 -42.791
98.051 -43.451
98.688 -44.149
99.287 -44.889
99.847 -45.671
100.36 -46.497
100.84 -47.368
101.26 -48.287
101.63 -49.255
101.95 -50.273
102.21 -51.343
102.41 -52.467
102.54 -53.646
102.6 -54.88
102.58 -56.171
102.49 -57.519
102.31 -58.925
102.05 -60.387
101.7 -61.905
101.25 -63.477
100.71 -65.101
100.06 -66.773
99.319 -68.489
98.471 -70.244
97.518 -72.032
96.462 -73.846
95.304 -75.677
94.047 -77.515
92.695 -79.352
91.253 -81.176
89.729 -82.977
88.13 -84.744
86.465 -86.465

Q4
Q4 =
117.14 -117.14
115.45 -118.84
113.78 -120.53
112.13 -122.21
110.53 -123.87
108.96 -125.5
107.46 -127.09
106.02 -128.63
104.65 -130.13
103.35 -131.58
102.14 -132.97
101.01 -134.31
99.974 -135.58
99.023 -136.8
98.161 -137.95
97.389 -139.05
96.705 -140.09
96.108 -141.08
95.595 -142
95.166 -142.88
94.816 -143.71
94.544 -144.48
94.346 -145.21
94.218 -145.9
94.159 -146.54
94.164 -147.14
94.23 -147.7
94.354 -148.22
94.534 -148.71
94.766 -149.16
95.047 -149.59
95.375 -149.98
95.746 -150.34
96.159 -150.67
96.611 -150.97
97.099 -151.25
97.621 -151.51
98.176 -151.74
98.76 -151.95
99.373 -152.13
100.01 -152.3
100.67 -152.44
101.36 -152.56
102.07 -152.67
102.79 -152.75
103.54 -152.82
104.3 -152.87
105.08 -152.9
105.87 -152.92
106.67 -152.91
107.49 -152.9
108.31 -152.86
109.15 -152.81
109.99 -152.74
110.84 -152.66
111.7 -152.57
112.56 -152.45
113.43 -152.33
114.3 -152.18
115.17 -152.03
116.04 -151.86
116.92 -151.67
117.79 -151.47
118.67 -151.25
119.54 -151.02
120.41 -150.78
121.28 -150.51
122.14 -150.24
123 -149.95
123.86 -149.64
124.71 -149.32
125.55 -148.99
126.39 -148.64
127.22 -148.27
128.04 -147.89
128.86 -147.5
129.66 -147.09
130.45 -146.66
131.24 -146.22
132.02 -145.76
132.78 -145.29
133.53 -144.8
134.27 -144.3
135 -143.78
135.72 -143.25
136.42 -142.7
137.11 -142.14
137.79 -141.56
138.46 -140.97
139.11 -140.36
139.74 -139.74
140.36 -139.11
140.97 -138.46
141.56 -137.79
142.14 -137.11
142.7 -136.42
143.25 -135.72
143.78 -135
144.3 -134.27
144.8 -133.53
145.29 -132.78
145.76 -132.02
146.22 -131.24
146.66 -130.45
147.09 -129.66
147.5 -128.5
147.89 -128.04
148.27 -127.22
148.64 -126.39
148.99 -125.55
149.32 -124.71
149.64 -123.86
149.95 -123
150.24 -122.14
150.51 -121.28
150.78 -120.41
151.02 -119.54
151.25 -118.67
151.47 -117.79
151.67 -116.92
151.86 -116.04
152.03 -115.17
152.18 -114.3
152.33 -113.43
152.45 -112.56
152.57 -111.7
152.66 -110.84
152.74 -109.99
152.81 -109.15
152.86 -108.31
152.9 -107.49
152.91 -106.67
152.92 -105.87
152.9 -105.08
152.87 -104.3
152.82 -103.54
152.75 -102.79
152.67 -102.07
152.56 -101.36
152.44 -100.67
152.3 -100.01
152.13 -99.373
151.95 -98.76
151.74 -98.176
151.51 -97.621
151.25 -97.099
150.97 -96.611
150.67 -96.159
150.34 -95.746
149.98 -95.375
149.59 -95.047
149.16 -94.766
148.71 -94.534
148.22 -94.354
147.7 -94.23
147.14 -94.164
146.54 -94.159
145.9 -94.218
145.21 -94.346
144.48 -94.544
143.71 -94.816
142.88 -95.166
142 -95.595
141.08 -96.108
140.09 -96.705
139.05 -97.389
137.95 -98.161
136.8 -99.023
135.58 -99.974
134.31 -101.01
132.97 -102.14
131.58 -103.35
130.13 -104.65
128.63 -106.02
127.09 -107.46
125.5 -108.96
123.87 -110.53
122.21 -112.13
120.53 -113.78
118.84 -115.45
117.14 -117.14