# Theory of Machines

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```					Theory of Machines

Lecture 7
Bell Crank
OA+AB=OO’+O’B
B                        O’C=O’D+DC
3                                                                                   
1  L2 cos 2  L3 cos 3  d  L4 cos( 4   )  0
 2  L2 sin  2  L3 sin  3  L4 sin( 4   )  0
A                                                   3  L4 ' cos 4  e  L5 cos 5  0
4                          4  L4 ' sin  4  S  L5 sin  5  0
C                  5   2   20  20t  1  2t 2  0
2                                                                       2

O           d       O’                   5                                                      
1   L2 2 sin  2  L3 3 sin  3  L4 4 sin( 4   )  0
                         
e                                                                       
 2  L2 2 cos 2  L3 3 cos 3  L4 4 cos( 4   )  0

             
   L ' sin   L  sin   0
3
S      4  L4 ' 4 cos 4  S  L5 5 cos 5  0

4 4

4

5 5

5


 4   2  20   2t  0

D
1
q=[2, 3, 4, 5,S]T
Cam
OA+AB=OD+DB

x : e cos  2  r  S1
y : e sin  2  S 2
d :2    
2
A                 3
r   B
S1           S2
O
D

1
Position of a point
A
3

B
2

4

C
e
O

d
OB=OC+CB                       q=[2,3,4]T

 x  d  L4 cos 4 
OB   B   
 yB   e  L4 sin  4 

B=[d+L4*cos(qq(:,3)),e+L4*sin(qq(:,3))];
Loop Closure
• Minimum equations
• Quick solution for position, velocity and
acceleration
• convert generalised coordinate to desired
coordinate

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