Chapter 6 : Velocity in Mechanisms(Instantaneous Centre Method)

Example 6.1 Page No : 126

In [2]:
import math 

# Variables:
NAB = 100. 			#rpm
AB = 300./1000
BC = 360./1000
CD = BC 			#m

#Solution:
#Refer Fig. 6.9
#Calculating the angular speed of link AB
omegaAB = 2*math.pi*NAB/60 			#rad/s
#Calculating the velocity of point B on link AB
vB = omegaAB*AB 			#m/s
#Calculating the angular velocity of link BC
#By measurement from instantaneous centre diagram  Fig. 6.10

I13B = 500./1000 			#m
omegaBC = vB/I13B 			#rad/s

#Results:
print " The angular velocity of the link BC omegaBC  =  %.3f rad/s."%(omegaBC)

 The angular velocity of the link BC omegaBC  =  6.283 rad/s.

Example 6.2 Page No : 128

In [4]:
import math 

# Variables:
omegaOB = 10. 			#rad/s
OB = 100/1000. 			#m

#Solution:
#Refer Fig. 6.12
#Calculating the velocity of the crank OB
vOB = omegaOB*OB 			#m/s
vB = vOB
#By measurement from the instantaneous cemtre diagram  Fig. 6.13

I13A = 460./1000
I13B = 560./1000 			#m
#Calculating the velocity of slider A
vA = vB/I13B*I13A
#Calculating the angular velocity of the connecting rod AB
omegaAB = vB/I13B 			#rad/s

#Results:
print "The velocity of slider A vA  =  %.2f m/s."%(vA)
print "The angular velocity of connecting rod AB omegaAB  =  %.2f rad/s."%(omegaAB)

The velocity of slider A vA  =  0.82 m/s.
The angular velocity of connecting rod AB omegaAB  =  1.79 rad/s.

Example 6.3 Page No : 130

In [5]:
import math 

# Variables:
NOA = 120. 			#rpm
OA = 200./1000 			#m/s

#Results:
#Refer Fig. 6.15
#Calculating the angular velocity of the crank OA
omegaOA = 2*math.pi*NOA/60 			#rad/s
#Calculating the velocity of crank OA
vOA = omegaOA*OA 			#m/s
vA = vOA
#By measurement from the instantaneous cemtre diagram Fig. 6.16

I13A = 840./1000
I13B = 1070./1000
I14B = 400./1000
I14C = 200./1000
I15C = 740./1000
I15D = 500./1000 			#m

#Calculating the velocity of point B
vB = vA/I13A*I13B 			#m/s
#Calculating the velocity of point C
vC = vB/I14B*I14C 			#m/s
#Calculating the velocity of point B
vD = vC/I15C*I15D 			#m/s
#Calculating the angular velocity of the link AB
omegaAB = vA/I13A 			#rad/s
#Calculating the angular velocity of the link BC
omegaBC = vB/I14B 			#rad/s
#Calculating the angular velocity of the link CD
omegaCD = vC/I15C 			#rad/s

#Results:
print " The velocity of point B vB  =  %.1f m/s."%(vB)
print " The velocity of point C vC  =  %.1f m/s."%(vC)
print " The velocity of point D vD  =  %.2f m/s."%(vD)
print " The angular velocity of the link AB omegaAB  =  %.2f rad/s."%(omegaAB)
print " The angular velocity of the link BC omegaBC  =  %d rad/s."%(omegaBC)
print " The angular velocity of the link CD omegaCD  =  %.2f rad/s."%(omegaCD)

 The velocity of point B vB  =  3.2 m/s.
 The velocity of point C vC  =  1.6 m/s.
 The velocity of point D vD  =  1.08 m/s.
 The angular velocity of the link AB omegaAB  =  2.99 rad/s.
 The angular velocity of the link BC omegaBC  =  8 rad/s.
 The angular velocity of the link CD omegaCD  =  2.16 rad/s.

Example 6.4 Page No : 133

In [6]:
import math 

# Variables:
omegaO1A = 100. 			#rad/s
O1A = 100/1000. 			#m

#Solution:
#Refer Fig. 6.18
#Calculating the linear velocity of crank O1A
vO1A = omegaO1A*O1A 			#m/s
vA = vO1A
#By measurement from the instantaneous cemtre diagram Fig. 6.19
I13A = 910./1000
I13B = 820./1000
I15B = 130./1000
I15D = 50./1000
I16D = 200./1000
I16E = 400./1000 			#m
#Calculating the velocity of point B
vB = vA/I13A*I13B 			#m/s
#Calculating the velocity of point D
vD = vB/I15B*I15D 			#m/s
#Calculating the velocity of point E
vE = vD/I16D*I16E 			#m/s

#Results:
print " The velocity of point B vB  =  %.2f m/s."%(vB)
print " The velocity of point D vD  =  %.2f m/s."%(vD)
print " The velocity of point E vE  =  %.2f m/s."%(vE)

 The velocity of point B vB  =  9.01 m/s.
 The velocity of point D vD  =  3.47 m/s.
 The velocity of point E vE  =  6.93 m/s.

Example 6.5 Page No : 135

In [7]:
import math 

# Variables:
NO1A = 400. 			#rpm
O1A = 16./1000 			#m

#Solution:
#Refer Fig. 6.21
#Calculating the angular velocity of the crank O1A
omegaO1A = 2*math.pi*NO1A/60 			#rad/s
#Calculating the linear velocity of the crank O1A
vO1A = omegaO1A*O1A 			#m/s
vA = vO1A
#By measurement from the instantaneous cemtre diagram Fig. 6.22
I13A = 41./1000
I13B = 50./1000
I14B = 23./1000
I14C = 28./1000
I15C = 65./1000
I15D = 62./1000 			#m
#Calculating the velocity of point B
vB = vA/I13A*I13B 			#m/s
#Calculating the velocity of point C
vC = vB/I14B*I14C 			#m/s
#Calculating the velocity of of the needle at D
vD = vC/I15C*I15D 			#m/s

#Results:
print "The velocity of the needle at D vD  =  %.2f m/s."%(vD)

The velocity of the needle at D vD  =  0.95 m/s.

Example 6.6 Page No : 137

In [1]:
import math 

# Variables:
NOA = 120. 			#rpm
#Solution:
#Refer Fig. 6.24
#Calculating the angular speed of crank OA
omegaOA = 2*math.pi*NOA/60 			#rad/s
#By measurement from the instantaneous cemtre diagram Fig. 6.25
I12I26 = 65./1000 			#m
#Calculating the velocity of the ram
vD = omegaOA*I12I26 			#m/s

#Results:
print " The velocity of ram, vD  =  %.3f m/s."%(vD)

 The velocity of ram, vD  =  0.817 m/s.