Chapter 5 : Simple Mechanisms¶

Example 5.1 Page No : 110¶

In [1]:
import math

# Variables:
AC = 300.
CB1 = 120. 			#mm

#Solution:
#Refer Fig. 5.28
#Calculating the sine of inclination of the slotted bar with the vertical
sineCAB1 = CB1/AC
#Calculating the inclination of the slotted bar with the vertical
angleCAB1 = math.sin(sineCAB1)*180/math.pi 			#degrees
#Calculating the angle alpha
alpha = 2*(90-angleCAB1) 			#degrees
#Calculating the ratio of time of cutting stroke to time of return stroke
r = (360-alpha)/alpha 			#Ratio of time of cutting stroke to time of return stroke

#Results:
print " The ratio of the time of cutting stroke to the time of return stroke is %.1f"%(r)

# rounding off error

 The ratio of the time of cutting stroke to the time of return stroke is 1.7


Example 5.2 Page No : 110¶

In [5]:
import math

# Variables:
AC = 240.
CB1 = 120.
AP1 = 450. 			#mm

#Solution:
#Refer Fig. 5.29
#Calculating the math.sine of inclination of the slotted bar with the vertical
sineCAB1 = CB1/AC
#Calculating the inclination of the slotted bar with the vertical
angleCAB1 = math.sin(sineCAB1)*180/math.pi 			#degrees
#Calculating the angle alpha
alpha = 2*(90-angleCAB1) 			#degrees
#Calculating the time ratio of cutting stroke to the return stroke
r = (360-alpha)/alpha 			#Time ratio of cutting stroke to the return stroke
#Calculating the length of the stroke
R1R2 = 2*AP1*round(math.sin(math.pi/2-alpha/2*math.pi/180),1) 			#mm

#Results:
print " The time ratio of cutting stroke to the return stroke is %.f."%(r)
print " The length of the stroke R1R2  =  P1P2  =  %d mm."%(R1R2)

 The time ratio of cutting stroke to the return stroke is 2.
The length of the stroke R1R2  =  P1P2  =  450 mm.


Example 5.3 Page No : 112¶

In [9]:
import math

# Variables:
#Refer Fig. 5.30 and Fig. 5.31
BC = 30.
R1R2 = 120. 			#mm
r = 1.7 			#Time ratio of working stroke to the return stroke

#Solution:
#Calculating the angle alpha
alpha = 360/(1.7+1) 			#degrees
#Calculating the length of the link AC
B1C = BC
#Calculating the length of the link AP
AP = AP1

#Results:
print " The length of AC  =  %.1f mm."%(AC)
print " The length of AP  =  %.2f mm."%(AP)

 The length of AC  =  75.7 mm.
The length of AP  =  151.48 mm.


Example 5.4 Page No : 112¶

In [5]:
import math

# Variables:
CD = 50.  #mm
CA = 75.  #mm
PA = 150. #mm
PR = 135. #mm

#Solution:
#Refer Fig. 5.32 and Fig. 5.33
#Calculating the cosine of angle beta
CA2 = CA
cosbeta = CD/CA2
#Calculating the angle beta
beta = 2*math.degrees(math.acos(cosbeta)) 			#degrees
#Calculating the ratio of time of cutting stroke to time of return stroke
r = (360-beta)/beta            			#Ratio of time of cutting stroke to time of return stroke
#Calculating the length of effective stroke
R1R2 = 87.5 			#mm

#Results:
print " The ratio of time of cutting stroke to time of return stroke is %.3f."%(r)
print " The length of effective stroke R1R2  =  %.1f mm."%(R1R2)

 The ratio of time of cutting stroke to time of return stroke is 2.735.
The length of effective stroke R1R2  =  87.5 mm.