Cotter & Knuckle Joint - 2 | Design of Machine Elements - Mechanical Engineering PDF Download

 Page 1


  Design of a cotter joint 
If the allowable stresses in tension, compression and shear for the socket, rod 
and cotter be 
t
s ,
c
s and t respectively, assuming that they are all made of the 
same material, we may write the following failure criteria: 
 
 
1. Tension failure of rod at diameter d  
 
           
2
t
dP
4
p
s=
  
 
  
      
   
4.2.2.1F- Tension failure of the rod (Ref.[6]). 
 
 
2. Tension failure of rod across slot 
 
2
11 t
ddt P
4
p??
-s=
??
??
 
 
 
 
 
         4.2.2.2F- Tension failure of rod across slot (Ref.[6]). 
 
 
 
 
 
 
t
Page 2


  Design of a cotter joint 
If the allowable stresses in tension, compression and shear for the socket, rod 
and cotter be 
t
s ,
c
s and t respectively, assuming that they are all made of the 
same material, we may write the following failure criteria: 
 
 
1. Tension failure of rod at diameter d  
 
           
2
t
dP
4
p
s=
  
 
  
      
   
4.2.2.1F- Tension failure of the rod (Ref.[6]). 
 
 
2. Tension failure of rod across slot 
 
2
11 t
ddt P
4
p??
-s=
??
??
 
 
 
 
 
         4.2.2.2F- Tension failure of rod across slot (Ref.[6]). 
 
 
 
 
 
 
t
3. Tensile failure of socket across slot 
22
21 2 1 t
(d d ) (d d )t P
4
p??
-- - s=
??
??
 
 
 
 
 
 
      
   4.2.2.3F- Tensile failure of socket across slot. 
 
4. Shear failure of cotter 
2bt P t= 
 
 
 
 
 
 
     4.2.2.4F- Shear failure of cotter. 
 
5. Shear failure of rod end 
11
2d P t= l 
 
 
 
 
     4.2.2.5F- Shear failure of rod end 
 
 
 
d
2
t
Page 3


  Design of a cotter joint 
If the allowable stresses in tension, compression and shear for the socket, rod 
and cotter be 
t
s ,
c
s and t respectively, assuming that they are all made of the 
same material, we may write the following failure criteria: 
 
 
1. Tension failure of rod at diameter d  
 
           
2
t
dP
4
p
s=
  
 
  
      
   
4.2.2.1F- Tension failure of the rod (Ref.[6]). 
 
 
2. Tension failure of rod across slot 
 
2
11 t
ddt P
4
p??
-s=
??
??
 
 
 
 
 
         4.2.2.2F- Tension failure of rod across slot (Ref.[6]). 
 
 
 
 
 
 
t
3. Tensile failure of socket across slot 
22
21 2 1 t
(d d ) (d d )t P
4
p??
-- - s=
??
??
 
 
 
 
 
 
      
   4.2.2.3F- Tensile failure of socket across slot. 
 
4. Shear failure of cotter 
2bt P t= 
 
 
 
 
 
 
     4.2.2.4F- Shear failure of cotter. 
 
5. Shear failure of rod end 
11
2d P t= l 
 
 
 
 
     4.2.2.5F- Shear failure of rod end 
 
 
 
d
2
t
6.  Shear failure of socket  end 
()
31
2d d P -t= l 
 
 
 
 
 
       
4.2.2.6F- Shear failure of socket end 
 
 
 
7. Crushing failure of rod or cotter 
1c
dt P s= 
 
 
 
 
    4.2.2.7F- Crushing failure of rod or cotter  
 
 
8. Crushing failure of socket or rod 
()
31 c
dd t P -s=
 
 
 
 
 
 
 
                      4.2.2.8F- Crushing failure of socket or rod 
d
Page 4


  Design of a cotter joint 
If the allowable stresses in tension, compression and shear for the socket, rod 
and cotter be 
t
s ,
c
s and t respectively, assuming that they are all made of the 
same material, we may write the following failure criteria: 
 
 
1. Tension failure of rod at diameter d  
 
           
2
t
dP
4
p
s=
  
 
  
      
   
4.2.2.1F- Tension failure of the rod (Ref.[6]). 
 
 
2. Tension failure of rod across slot 
 
2
11 t
ddt P
4
p??
-s=
??
??
 
 
 
 
 
         4.2.2.2F- Tension failure of rod across slot (Ref.[6]). 
 
 
 
 
 
 
t
3. Tensile failure of socket across slot 
22
21 2 1 t
(d d ) (d d )t P
4
p??
-- - s=
??
??
 
 
 
 
 
 
      
   4.2.2.3F- Tensile failure of socket across slot. 
 
4. Shear failure of cotter 
2bt P t= 
 
 
 
 
 
 
     4.2.2.4F- Shear failure of cotter. 
 
5. Shear failure of rod end 
11
2d P t= l 
 
 
 
 
     4.2.2.5F- Shear failure of rod end 
 
 
 
d
2
t
6.  Shear failure of socket  end 
()
31
2d d P -t= l 
 
 
 
 
 
       
4.2.2.6F- Shear failure of socket end 
 
 
 
7. Crushing failure of rod or cotter 
1c
dt P s= 
 
 
 
 
    4.2.2.7F- Crushing failure of rod or cotter  
 
 
8. Crushing failure of socket or rod 
()
31 c
dd t P -s=
 
 
 
 
 
 
 
                      4.2.2.8F- Crushing failure of socket or rod 
d
 
9. Crushing failure of collar 
22
41 c
(d d ) P
4
p??
-s=
??
??
 
 
 
 
 
 
  
     4.2.2.9F- Crushing failure of collar. 
 
10. Shear failure of collar  
11
dt P pt=
 
 
 
 
 
 
 
     4.2.2.10F- Shear failure of collar.   
 
Cotters may bend when driven into position. When this occurs, the bending 
moment cannot be correctly estimated since the pressure distribution is not 
known. However, if we assume a triangular pressure distribution over the rod, as 
shown in figure-4.2.2.11 (a), we may approximate the loading as shown in figure-
4.2.2.11 (b) 
 
 
 
 
 
Page 5


  Design of a cotter joint 
If the allowable stresses in tension, compression and shear for the socket, rod 
and cotter be 
t
s ,
c
s and t respectively, assuming that they are all made of the 
same material, we may write the following failure criteria: 
 
 
1. Tension failure of rod at diameter d  
 
           
2
t
dP
4
p
s=
  
 
  
      
   
4.2.2.1F- Tension failure of the rod (Ref.[6]). 
 
 
2. Tension failure of rod across slot 
 
2
11 t
ddt P
4
p??
-s=
??
??
 
 
 
 
 
         4.2.2.2F- Tension failure of rod across slot (Ref.[6]). 
 
 
 
 
 
 
t
3. Tensile failure of socket across slot 
22
21 2 1 t
(d d ) (d d )t P
4
p??
-- - s=
??
??
 
 
 
 
 
 
      
   4.2.2.3F- Tensile failure of socket across slot. 
 
4. Shear failure of cotter 
2bt P t= 
 
 
 
 
 
 
     4.2.2.4F- Shear failure of cotter. 
 
5. Shear failure of rod end 
11
2d P t= l 
 
 
 
 
     4.2.2.5F- Shear failure of rod end 
 
 
 
d
2
t
6.  Shear failure of socket  end 
()
31
2d d P -t= l 
 
 
 
 
 
       
4.2.2.6F- Shear failure of socket end 
 
 
 
7. Crushing failure of rod or cotter 
1c
dt P s= 
 
 
 
 
    4.2.2.7F- Crushing failure of rod or cotter  
 
 
8. Crushing failure of socket or rod 
()
31 c
dd t P -s=
 
 
 
 
 
 
 
                      4.2.2.8F- Crushing failure of socket or rod 
d
 
9. Crushing failure of collar 
22
41 c
(d d ) P
4
p??
-s=
??
??
 
 
 
 
 
 
  
     4.2.2.9F- Crushing failure of collar. 
 
10. Shear failure of collar  
11
dt P pt=
 
 
 
 
 
 
 
     4.2.2.10F- Shear failure of collar.   
 
Cotters may bend when driven into position. When this occurs, the bending 
moment cannot be correctly estimated since the pressure distribution is not 
known. However, if we assume a triangular pressure distribution over the rod, as 
shown in figure-4.2.2.11 (a), we may approximate the loading as shown in figure-
4.2.2.11 (b) 
 
 
 
 
 
 
 
 
 
 
 
 
   
  (a)        (b) 
         4.2.2.11F- Bending of the cotter 
 
This gives maximum bending moment = 
31 1
dd d P
26 4
-??
+
??
??
 and 
 
The bending stress, 
31 31 11
b 3 2
dd dd dd Pb
3P
26 42 6 4
tb tb
12
-- ?? ? ?
++
?? ? ?
?? ? ?
s= = 
 
Tightening of cotter introduces initial stresses which are again difficult to 
estimate. Sometimes therefore it is necessary to use empirical proportions to 
design the joint. Some typical proportions are given below: 
1
d 1.21.d = 
2
d 1.75.d = 
d
3
 = 2.4 d 
4
d1.5.d = 
t0.31d = 
b 1.6d = 
1
l l 0.75d == 
1
t0.45d = 
s= clearance 
d
3
b
d
1
P/2
P/2
P/2
P/2
-
+
31 1
dd d
64
31 1
dd d
64
-
+
1
d
4
1
4
d