DESIGN OF MACHINERY
!
SOLUTION MANUAL 6-13-1
PROBLEM 6-13
Statement:
Find all of the instant centers of the linkages shown in Figure P6-6.
Solution:
See Figure P6-6 and Mathcad file P0613.
a.
This is a fourbar inverted slider-crank with n
1.
Determine the number of instant centers for this mechanism using equation 6.8a.
C
n .( n
1)
C=6
2
2.
4.
Draw the linkage to scale and identify those ICs that can be found by inspection.
2,3
2
3
3,4 at infinity
1
1,2
4
1
1,4
3.
Use Kennedy's Rule and a linear graph to find the remaining 2 ICs, I1,3 and I2,4
I1,3: I1,2-I2,3 and I1,4-I3,4
I2,4: I1,2-I1,4 and I2,3-I3,4
3,4 at infinity
2,3
2,4
2
1
4
3
2
3,4 at infinity
1
3
1,2
4
1
1,4
1,3
b.
This is a sixbar with slider, n
1.
Determine the number of instant centers for this mechanism using equation 6.8a.
C
n .( n
2
2.
1)
6.
C = 15
Draw the linkage to scale and identify those ICs that can be found by inspection.
2nd Edition, 1999
DESIGN OF MACHINERY
SOLUTION MANUAL 6-13-2
5,6
6
2,3
1,6 at infinity
2
3
1
5
3,4; 3,5; 4,5
1
4
1,2
1,4
1
3.
Use Kennedy's Rule and a linear graph to find the remaining 7 ICs.
I1,3: I1,2-I2,3 and I1,4-I3,4
I2,4: I1,2-I1,4 and I2,3-I3,4
I1,5: I1,6-I5,6 and I1,4-I4,5
I4,6: I1,6-I1,4 and I4,5-I5,6
I2,5: I1,2-I1,5 and I2,4-I4,5
I2,6: I1,2-I1,6 and I2,5-I5,6
I3,6: I1,6-I1,3 and I3,4-I4,6
3,6
1,3
1,6 at infinity
2,5
to 2,4
5,6
6
to 2,4
1,5
2,3
1
1,6 at infinity
2
3
6
2
1
5
5
1,6 at infinity
3
4
3,4; 3,5; and 4,5
1
4
1,2
1,4
2,6
4,6
1,6 at infinity
1
c.
This is a sixbar with slider and roller with n
1.
Determine the number of instant centers for this mechanism using equation 6.8a.
C
n .( n
1)
C = 15
2
2.
6.
Draw the linkage to scale and identify those ICs that can be found by inspection.
2,5
5,6
6
1,2
5
2,3
2
1
1
1,6
3
4
3,4
2nd Edition, 1999
1
1,4 at infinity
DESIGN OF MACHINERY
3.
SOLUTION MANUAL 6-13-3
Use Kennedy's Rule and a linear graph to find the remaining 8 ICs.
I1,3: I1,2-I2,3 and I1,4-I3,4
I2,6: I1,2-I1,6 and I2,5-I5,6
I1,5: I1,6-I5,6 and I1,2-I2,5
I2,4: I1,2-I1,4 and I2,5-I2,4
I4,5: I1,4-I1,5 and I2,4-I2,5
I3,5: I3,4-I4,5 and I2,5-I2,3
I3,6: I3,6-I5,6 and I2,3-I2,6
I4,6: I4,5-I5,6 and I3,4-I3,6
3,5
2,5
1,5
4,5
1,4 at infinity
5,6
1,2
5
1
1
2,3
2
6
2,6
6
2,4
2
1,4 at infinity
5
1
1,6
3
4,6
3,6
3,4
1,3
1,4 at infinity
4
1
d.
This is a sixbar with slider and roller with n
1.
Determine the number of instant centers for this mechanism using equation 6.8a.
C
n .( n
1)
6.
C = 15
2
2.
Draw the linkage to scale and identify those ICs that can be found by inspection.
3,4
4
1
1,4
3
5,6
5
1,2
2
1
6
2,3; 2,5; and 3,5
1
1,6 at infinit
3.
Use Kennedy's Rule and a linear graph to find the remaining 7 ICs.
I1,3: I1,2-I2,3 and I1,4-I3,4
I3,6: I1,6-I1,3 and I3,5-I5,6
I2,6: I1,2-I1,6 and I2,5-I5,6
I1,5: I1,6-I5,6 and I1,2-I2,5
I4,5 : I1,4-I1,5 and I3,5-I3,4
I2,4: I1,2-I1,4 and I2,3-I3,4
I4,6: I1,6-I1,4 and I4,5-I5,6
(See next page)
2nd Edition, 1999
3
4
DESIGN OF MACHINERY
SOLUTION MANUAL 6-13-4
2,4
4,6
3,4
4,5
4
1,3
1
1
1,4
6
3
1,5
1,6 at infinity
2
5
3
4
2,6
5,6
5
1,2
2
1
6
2,3; 2,5; and 3,5
3,6
1
1,6 at infinity
1,6 at infinity
2nd Edition, 1999