# Chapter 8 : Acceleration in Mechanisms¶

## Example 8.1 Page No : 177¶

In [1]:
import math

# Variables:
NBO = 300. 			#rpm
OB = 150./1000
BA = 600./1000 			#m

#Solution:
#Refer Fig. 8.4
#Calculating the angular velocity of BO
#Calculating the linear velocity of B with respect to O
vBO = omegaBO*OB 			#m/s
vB = vBO
#By measurement from the velocity diagram Fig. 8.4(b)
vAB = 3.4
vD = 4.1 			#m/s
#Calculating the radial component of the acceleration of B with respect of O
arBO = vBO**2/OB 			#m/s**2
aB = arBO
#Calculating the radisla component of the accaleration of A with respect to B
arAB = vAB**2/BA 			#m/s**2
#By measurement from the acceleration diagram Fig. 8.4(c)
#Calculating the angular velocity of the connecting rod
#Calculating the angular acceleration of the connecting rod

#Results:
print " The linear velocity of the midpoint of the connecting rod, vD  =  %.1f m/s."%(vD)
print " The linear acceleration of the midpoint of the connecting rod, aD  =  %d m/s**2."%(aD)
print " The angular velocity of the connecting rod, omegaAB  =  %.2f rad/s, anticlockwise about B."%(omegaAB)
print " The angular acceleration of the connecting rod, alphaAB  =  %.2f rad/s**2, clockwise about B."%(alphaAB)

 The linear velocity of the midpoint of the connecting rod, vD  =  4.1 m/s.
The linear acceleration of the midpoint of the connecting rod, aD  =  117 m/s**2.
The angular velocity of the connecting rod, omegaAB  =  5.67 rad/s, anticlockwise about B.
The angular acceleration of the connecting rod, alphaAB  =  171.67 rad/s**2, clockwise about B.


## Example 8.2 Page No : 180¶

In [2]:
import math

# Variables:
CB = 100/1000.              #m
BA = 300/1000.   			#m/

#Solution:
#Refer Fig. 8.5
#Calculating the linear velocity of B with respect to C
vBC = omegaBC*CB 			#m/s
#Calculating the math.tangential component of the acceleration of B with respect to C
alphatBC = alphaBC*CB 			#m/s**2
#By measurement from the velocity diagram Fig. 8.6(b)
vG = 6.8
vAB = 4 			#m/s
#Calculating the angular velocity of AB
#Calculating the radial component of the acceleration of B with respect to C
arBC = vBC**2/CB 			#m/s**2
#Calculating the radial component of the acceleration of A with respect to B
arAB = vAB**2/BA 			#m/s**2
#By measurement from the acceleration diagram Fig. 8.6(c)
arBC = 120.
arAB = 53.3
aG = 414.
atAB = 546. 			#m/s**2
#Calculating the angular acceleration of AB

#Results:
print " The velocity of G, vG  =  %.1f m/s."%(vG)
print " The angular velocity of AB, omegaAB  =  %.1f rad/s, clockwise."%(omegaAB)
print " The acceleration of G, aG  =  %d m/s**2."%(aG)
print " The angular accaleration of AB, alphaAB  =  %d rad/s**2."%(alphaAB)

 The velocity of G, vG  =  6.8 m/s.
The angular velocity of AB, omegaAB  =  13.3 rad/s, clockwise.
The acceleration of G, aG  =  414 m/s**2.
The angular accaleration of AB, alphaAB  =  1820 rad/s**2.


## Example 8.3 Page No : 182¶

In [3]:
import math

# Variables:
vC = 1.
vCD = vC 			#m/s
aC = 2.5 			#m/s**2
AB = 3.             #m
BC = 1.5 			#m

#Solution:
#Refer Fig. 8.8
#By measurement from the velocity diagram Fig. 8.8(b)
vBA = 0.72
vBC = 0.72 			#m/s
#Calculating the radial component of acceleration of B with respect to C
arBC = vBC**2/BC 			#m/s**2
#Calculating the radial component of acceleration of B with respect to A
arBA = vBA**2/AB 			#m/s**2
#By measurement from the acceleration diagram Fig. 8.8(c)
aCD = 2.5
aC = aCD
arBC = 0.346
arBA = 0.173
atBA = 1.41
atBC = 1.94
vectorbb = 1.13
vectorab = 0.9 			#m/s**2
#Calculating the angular accaleration of AB
#Calculating the angular acceleration of BC

#Results:
print " The magnitude of vertical component of the acceleration of the point B is %.2f m/s**2."%(vectorbb)
print " The magnitude of horizontal component of the acceleration of the point B is %.1f m/s**2."%(vectorab)
print " The angular acceleration of the link AB, alphaAB  =  %.2f rad/s**2."%(alphaAB)
print " The angular acceleration of the link BC, alphaBC  =  %.1f rad/s**2."%(alphaBC)

 The magnitude of vertical component of the acceleration of the point B is 1.13 m/s**2.
The magnitude of horizontal component of the acceleration of the point B is 0.9 m/s**2.


## Example 8.4 Page No : 184¶

In [5]:
import math

# Variables:
PQ = 62.5/1000          #m
QR = 175./1000          #m
RS = 112.5/1000         #m
PS = 200./1000 			#m

#Solution:
#Refer Fig. 8.9
#Calculating the velocity of Q with respect to P
vQP = omegaQP*PQ 			#m/s
vQ = vQP
#By measurement from the velocity diagram Fig. 8.9(b)
vRQ = 0.333
vRS = 0.426
vR = vRS 			#m/s
#Calculating the angular velocity of link QR
#Calculating the angular velocity of link RS
#Calculating the radial component of the acceleration of Q with respect to P
arQP = vQP**2/PQ 			#m/s**2
aQP = arQP
aQ = aQP
#Calculating the radial component of the acceleration of R with respect to Q
arRQ = vRQ**2/QR 			#m/s**2
#Calculating the radial component of the acceleration of R with respect to S
arRS = vRS**2/RS 			#m/s**2
aRS = arRS
aR = aRS
#By measurement from the acceleration diagram Fig. 8.9(c)
atRQ = 4.1
atRS = 5.3 			#m/s**2
#Calculating the angular acceleration of link QR
#Calculating the angular acceleration of link RS

#Results:
print " The angular velocity of link QR, omegaQR  =  %.1f rad/s anticlockwise."%(omegaQR)
print " The angular velocity of link RS, omegaRS  =  %.2f rad/s clockwise."%(omegaRS)
print " The angular acceleration of link QR, alphaQR  =  %.2f rad/s**2 anticlockwise."%(alphaQR)
print " The angular acceleration of link RS, alphaRS  =  %.1f rad/s**2 anticlockwise."%(alphaRS)

 The angular velocity of link QR, omegaQR  =  1.9 rad/s anticlockwise.


## Example 8.5 Page No : 186¶

In [6]:
import math

# Variables:
P1A = 300./1000         #m
P2B = 360./1000         #m
AB = P2B 			#m

#Solution:
#Refer Fig. 8.10
#Calculating the velocity of A with respect to P1
vAP1 = omegaAP1/P1A 			#m/s
vA = vAP1
#By measurement from the velocity diagram Fig. 8.11(b)
vBP2 = 2.2
vBA = 2.05 			#m/s
#Calculating the angular velocity of P2B
#Calculating the angular velocity of AB
#Calculating the math.tangential component of the acceleration of A with respect to P1
atAP1 = alphaAP1*P1A 			#m/s**2
#Calculating the radial component of the acceleration of A with respect to P1
arAP1 = vAP1**2/P1A 			#m/s**2
#Calculating the radial component of the acceleration of B with respect to A
arBA = vBA**2/AB 			#m/s**2
#Calculating the radial component of B with respect to P2
arBP2 = vBP2**2/P2B 			#m/s**2
#By measurement from the acceleration diagram Fig. 8.11(c)
aBP2 = 29.6
aB = aBP2
atBA = 13.6
atBP2 = 26.6 			#m/s**2
#Calculating the angular acceleration of P2B
#Calculating the angular acceleration of AB

#Results:
print " The velocity of P2B, vBP2  =  %.1f m/s."%(vBP2)
print " The angular velocity of P2B, omegaP2B  =  %.1f rad/s, clockwise."%(omegaP2B)
print " The angular velocity of AB, omegaAB  =  %.1f rad/s, anticlockwise."%(omegaAB)
print " The acceleration of the joint B, aB  =  %.1f m/s**2."%(aB)
print " The angular acceleration of P2B, alphaP2B  =  %.1f rad/s**2, anticlockwise."%(alphaP2B)
print " The angular acceleration of AB, alphaAB  =  %.1f rad/s**2, anticlockwise."%(alphaAB)

 The velocity of P2B, vBP2  =  2.2 m/s.
The angular velocity of P2B, omegaP2B  =  6.1 rad/s, clockwise.
The angular velocity of AB, omegaAB  =  5.7 rad/s, anticlockwise.
The acceleration of the joint B, aB  =  29.6 m/s**2.
The angular acceleration of P2B, alphaP2B  =  73.9 rad/s**2, anticlockwise.
The angular acceleration of AB, alphaAB  =  37.8 rad/s**2, anticlockwise.


## Example 8.6 Page No : 188¶

In [7]:
import math

# Variables:
NAO = 20. 			#rpm
OA = 300./1000      #m
AB = 1200./1000     #m
BC = 450./1000      #m
CD = BC 			#m

#Solution:
#Refer Fig. 8.13
#Calculating the angular velocity of crank AO
#Calculating the linear velocity of A with respect to O
vAO = omegaAO*OA 			#m/s
vA = vAO
#By measurement from the velocity diagram Fig. 8.13(b)
vB = 0.4
vD = 0.24
vDC = 0.37
vBA = 0.54 			#m/s
#Calculating the angular velocity of CD
#Calculating the radial component of the acceleration of A with respect to O
arAO = vAO**2/OA 			#m/s**2
#Calculating the radial component of the acceleration of B with respect to A
arBA = vBA**2/AB 			#m/s**2
#Calculating the radial component of the acceleration of D with respect to C
arDC = vDC**2/CD 			#m/s**2
#By measurement from the acceleration diagram Fig. 8.13(c)
atDC = 1.28      			#m/s**2
#Calculating the angular acceleration of CD

#Results:
print " Velocity of sliding at B, vB  =  %.1f m/s."%(vB)
print " Velocity of sliding at D, vD  =  %.2f m/s."%(vD)
print " Angular velocity of CD, omegaCD  =  %.2f rad/s."%(omegaCD)
print " Angular acceleration of CD, alphaCD  =  %.2f rad/s**2, clockwise."%(alphaCD)

 Velocity of sliding at B, vB  =  0.4 m/s.
Velocity of sliding at D, vD  =  0.24 m/s.
Angular velocity of CD, omegaCD  =  0.82 rad/s.
Linear acceleration of D, aD  =  0.16 m/s**2.
Angular acceleration of CD, alphaCD  =  2.84 rad/s**2, clockwise.


## Example 8.7 Page No : 191¶

In [8]:
import math

# Variables:
NAO = 180. 			#rpm
OA = 150./1000      #m
AB = 450./1000      #m
PB = 240./1000      #m
CD = 660./1000 		#m

#solution:
#Refer Fig. 8.15
#Calculating the angular speed of crank AO
#Calculating the velocity of A with respect to O
vAO = omegaAO*OA 			#m/s
vA = vAO
#By measurement from the velocity diagram Fig. 8.15(b)
vD = 2.36
vDC = 1.2
vBA = 1.8
vBP = 1.5 			#m/s
#Calculating the radial component of the acceleration of B with respect to A
arAO = vBA**2/AB 			#m/s**2
#Calculating the radial component of the acceleration of B with respect to A
arBA = vBA**2/AB 			#m/s**2
#Calculating the radial component of the acceleration of B with respect to P
arBP = vBP**2/PB 			#m/s**2
#Calculating the radial component of D with respect to C
arDC = vDC**2/CD 			#m/s**2
#By measurement from the acceleration diagram Fig. 8.15(c)
atDC = 17.4 			#m/s**2
#Calculating the angular acceleration of CD

#Results:

 Acceleration of slider D, aD  =  69.6 m/s**2.


## Example 8.8 Page No : 193¶

In [9]:
# Variables:
NAO = 180. 			#rpm
OA = 180./1000
CB = 240./1000
AB = 360./1000
BD = 540./1000 			#m

#Solution:
#Refer Fig. 8.17
#Calculating the angular speed of crank AO
#Calculating the velcoity of A with respect to O
vAO = omegaAO*OA 			#m/s
vA = vAO
#By measurement from the velocity diagram Fig. 8.17(b)
vBA = 0.9
vBC = 2.4
vDB = 2.4
vD = 2.05 			#m/s

#Calculating the angular velocity of BD
#Calculating the tangential component of the acceleration of A with respect to O
atAO = alphaAO*OA 			#m/s**2
#Calculating the radial component of the acceleration of A with respect to O
arAO = vAO**2/OA 			#m/s**2
#Calculating the radial component of the acceleration of B with respect to A
arBA = vBA**2/AB 			#m/s**2
#Calculating the radial component of the acceleration of B with respect to C
arBC = vBC**2/AB 			#m/s**2
#Calculating the radial component of the acceleration of D with respect to B
arDB = vDB**2/BD 			#m/s**2
#By measurement from the acceleration diagram Fig. 8.17(c)
atDB = 38.5 			#m/s**2

#Calculating the angular acceleration of BD

#Results:
print " Velocity of slider D, vD  =  %.2f m/s."%(vD)
print " Angular velocity of BD, omegaBD  =  %.1f rad/s."%(omegaBD)
print " Angular acceleration of BD, alphaBD  =  %.1f rad/s**2, clockwise."%(alphaBD)

 Velocity of slider D, vD  =  2.05 m/s.
Angular velocity of BD, omegaBD  =  4.4 rad/s.
Acceleration of slider D, aD  =  13.3 m/s**2.
Angular acceleration of BD, alphaBD  =  71.3 rad/s**2, clockwise.


## Example 8.9 Page No : 196¶

In [2]:
import math

# Variables:
O1A = 100./1000             #m
AC = 700./1000              #m
BC = 200./1000              #m
BD = 150./1000              #m
O2D = 200./1000             #m
O2E = 400./1000             #m
O3C = 200./1000 			#m
m=0.0;
#Solution:
#Refer Fig. 8.19
#Calculating the linear velocity of A with respect to O1
vAO1 = omegaAO1/O1A 			#m/s
vA = vAO1
#By measurement from the velocity diagram Fig. 8.19(b)
vCA = 7.
vCO3 = 10.
vC = vCO3
vDB = 10.2
vDO2 = 2.8
vD = vDO2
vE = 5.8
vEO2 = vE 			#m/s
#Calculating the radial component of the acceleration of A with respect to O1
arAO1 = vAO1**2/O1A 			#m/s**2
aAO1 = arAO1
aA = aAO1
#Calculating the radial component of the acceleration of C with respect to A
arCA = vCA**2/AC 			#m/s**2
#Calculating the radial component of the acceleration of C with respect to O3
arCO3 = vCO3**2/O3C 			#m/s**2
#Calculating the radial component of the acceleration of D with respect to B
arDB = vDB**2/BD 			#m/s**2
#Calculating the radial component of the acceleration of D with respect to O2
arDO2 = vDO2**2/O2D 			#m/s**2
#Calculating the radial component of the acceleration of E with respect to O2
arEO2 = vEO2**2/O2E 			#m/s**2
#By measurement from the acceleration diagram Fig. 8.19(c)
aE = 1200.
atDO2 = 610. 			#m/s**2
aEO2 = aE
aB = 440. 			#Acceleration of point B
#m/s**2
#Calculating the angular acceleration of the bell crank lever
alpha = atDO2/O2D 			#The angular acceleration of the bell crank lever rad/s**2

#Results:
print " Velocity of the point E on the bell crank lever, vE  =  %.1f m/s."%(vE)
print " Acceleration of point B  =  %d m/s**2."%(aB)
print " Acceleration of point E, aE  =  %d m/s**2."%(aE)
print " Angular acceleration of the bell crank lever  =  %d rad/s**2, anticlockwise."%(alpha)

 Velocity of the point E on the bell crank lever, vE  =  5.8 m/s.
Acceleration of point B  =  440 m/s**2.
Acceleration of point E, aE  =  1200 m/s**2.
Angular acceleration of the bell crank lever  =  3050 rad/s**2, anticlockwise.


## Example 8.10 Page No : 199¶

In [11]:
import math

# Variables:
NAO = 100. 			#rpm
OA = 150./1000      #m
AB = 600./1000      #m
BC = 350./1000      #m
CD = 150./1000      #m
DE = 500./1000 		#m
dA = 50./1000
dB = dA
rA = dA/2
rB = dB/2 			#m
pF = 0.35 			#N/mm**2
DF = 250. 			#mm

#Solution:
#Refer Fig. 8.21
#Calculating the angular speed of the crank AO
#Calculating the velocity of A with respect to O
vAO = omegaAO*OA 			#m/s
vA = vAO
#By measurement from the velocity diagram Fig. 8.21(b)
vBA = 1.65
vBC = 0.93
vB = vBC
vED = 0.18
vEO = 0.36
vE = vEO
vF = vE 			#m/s

#Calculating the velocity of D with respect to C
vDC = vBC*CD/BC 			#m/s
#Calculating the angular velocity of B with respect to A
#Calculating the angular velocity of B with respect to C
#Calculating the rubbing velocity of pin at A
vrA = (omegaAO-omegaBA)*rA 			#The rubbing velocity of pin at A m/s
#Calculating the rubbing velocity of pin at B
vrB = (omegaBA+omegaBC)*rB 			#The rubbing velocity of pin at B m/s
#Calculating the force at the pump piston at F
FF = pF*math.pi/4*DF**2 			#N
#Calculating the force required at the crankshaft A
FA = FF*vF/vA 			#N
#Calculating the torque required at the crankshaft
TA = FA*OA 			#N-m
#Calculating the radial component of the acceleration of A with respect to O
arAO = vAO**2/OA 			#m/s**2
#Calculating the radial component of the acceleration of B with respect to A
arBA = vBA**2/AB 			#m/s**2
#Calculating the radial component of the acceleration of B with respect to C
arBC = vBC**2/BC 			#m/s**2
#Calculating the radial component of the acceleration of E with respect to D
arED = vED**2/DE 			#m/s**2
#By measurement from the acceleration diagram Fig. 8.21(c)
aBC = 9.2
aB = aBC
aBA = 9
aE = 3.8 			#m/s**2
#Calculating the acceleration of D

#Results:
print " The velocity of the cross-head E, vE  =  %.2f m/s."%(vE)
print " The rubbing velocity of pin at A  =  %.3f m/s."%(vrA)
print " The rubbing velocity of pin at B  =  %.3f m/s."%(vrB)
print " The torque required at the crankshaft, TA  =  %d N-m."%(TA)
print " The acceleration of the crosshead E, aE  =  %.1f m/s**2."%(aE)

 The velocity of the cross-head E, vE  =  0.36 m/s.
The rubbing velocity of pin at A  =  0.193 m/s.
The rubbing velocity of pin at B  =  0.135 m/s.
The torque required at the crankshaft, TA  =  590 N-m.
The acceleration of the crosshead E, aE  =  3.8 m/s**2.


## Example 8.11 Page No : 203¶

In [12]:
import math

# Variables:
NAO = 150. 			#rpm
OA = 150./1000      #m
AB = 550./1000      #m
AC = 450./1000      #m
DC = 500./1000      #m
BE = 350./1000 		#m

#Solution:
#Refer Fig. 8.23
#Calculating the angular speed of the crank AO
#Calculating the linear velocity of A with respect to O
vAO = omegaAO*OA 			#m/s
vA = vAO
#By measurement from the velocity diagram Fig. 8.23(b)
vCA = 0.53
vCD = 1.7
vC = vCD
vEB = 1.93
vE = 1.05 			#m/s
#Calculating the radial component of the acceleration of A with respect to O
arAO = vAO**2/OA 			#m/s**2
aA = arAO
#Calculating the radial component of the acceleration of C with respect to A
arCA = vCA**2/AC 			#m/s**2
#Calculating the radial component of the acceleration of C with respect to D
arCD = vCD**2/DC 			#m/s**2
#Calculating the radial component of the acceleration of E with respect to B
arEB = vEB**2/BE 			#m/s**2
#By measurement from the acceleration diagram Fig. 8.23(c)
aE = 3.1 			#m/s**2

#Results:
print " Velocity of the ram E, vE  =  %.2f m/s."%(vE)
print " Acceleration of the ram E, aE  =  %.1f m/s**2."%(aE)

 Velocity of the ram E, vE  =  1.05 m/s.
Acceleration of the ram E, aE  =  3.1 m/s**2.


## Example 8.12 Page No : 205¶

In [13]:
import math

# Variables:
NDC = 1140. 			#rpm
AB = 80./1000           #m
CD = 40./1000           #m
BE = 150./1000          #m
DE = BE                 #m
EP = 200./1000 			#m

#Solution:
#Refer Fig. 8.25
#Calculating the angular speed of the link CD
#Calculating the velocity of D with respect to C
vD = vDC
#Calculating the angular speed of the larger wheel
#Calculating the velocity of B with respect to A
vBA = omegaBA*AB 			#m/s
vB = vBA
#By measurement from the velocity diagram Fig. 8.25(b)
vEB = 8.1
vED = 0.15
vPE = 4.7
vP = 0.35 			#m/s
#Calculating the radial component of the acceleration of B with respect to A
arBA = vBA**2/AB 			#m/s**2
#Calculating the radial component of the acceleration of D with respect to C
arDC = vDC**2/CD 			#m/s**2
#Calculating the radial component of the acceleration of E with respect to B
arEB = vEB**2/BE 			#m/s**2
#Calculating the radial component of the acceleration of E with respect to D
arED = vED**2/DE 			#m/s**2
#Calculating the radial component of the acceleration of P with respect to E
arPE = vPE**2/EP 			#m/s**2
#By measurement from the acceleration diagram Fig. 8.25(c)
aP = 655. 			#m/s**2

#Results:
print " Velocity of P, vP  =  %.2f m/s."%(vP)
print " Acceleration of the piston P, aP  =  %d m/s**2."%(aP)

 Velocity of P, vP  =  0.35 m/s.
Acceleration of the piston P, aP  =  655 m/s**2.


## Example 8.13 Page No : 211¶

In [14]:
import math

# Variables:
NBA = 120. 			#rpm
AB = 150./1000      #m
OC = 700./1000      #m
CD = 200./1000 		#m

#Solution:
#Refer Fig. 8.29
#Calculating the angular speed of the crank AB
#Calculating the velocity of B with respect to A
vBA = omegaBA*AB 			#m/s
#By measurement from the velocity diagram Fig. 8.29(b)
vD = 2.15
vBBdash = 1.05
vDC = 0.45
vBdashO = 1.55
vCO = 2.15 			#m/s
BdashO = 0.52 			#m
#Calculating the angular velocity of the link OC or OB'
#Calculating the radial component of the acceleration of B with respect to A
arBA = omegaAB**2/AB 			#m/s**2
#Calculating the coriolis component of the acceleration of slider B with respect to the coincident point B'
acBBdash = 2*omegaCO*vBBdash 			#m/s**2
#Calculating the radial component of the acceleration of D with respect to C
arDC = vDC**2/CD 			#m/s**2
#Calculating the radial component of the acceleration of B' with respect to O
arBdashO = vBdashO**2/BdashO 			#m/s**2
#By measurement fro the acceleration diagram Fig. 8.29(c)
atBdashO = 6.4 			#m/s**2
#Calculating the angular acceleration of the slotted lever
alpha = atBdashO/BdashO 			#The angular acceleration of the slotted lever rad/s**2

#Results:
print " Velocity of the ram D, vD  =  %.2f m/s."%(vD)
print " Angular acceleration of the slotted lever  =  %.1f rad/s**2, anticlockwise."%(alpha)

 Velocity of the ram D, vD  =  2.15 m/s.
Acceleration of the ram D, aD  =  8.4 m/s**2.
Angular acceleration of the slotted lever  =  12.3 rad/s**2, anticlockwise.


## Example 8.14 Page No : 214¶

In [15]:
import math

# Variables:
NBA = 200. 			#rpm
AB = 75./1000       #m
PQ = 375./1000      #m
QR = 500./1000 		#m

#Solution:
#Refer Fig. 8.31
#Calculating the angular velocity of the crank AB
#Calculating the velocity of B with respect to A
vBA = omegaBA*AB 			#m/s
#By measurement from the velocity diagram Fig. 8.31(b)
vR = 1.6
vBdashB = 1.06
vBdashP = 1.13
vRQ = 0.4
vQP = 1.7 			#m/s
PBdash = 248./1000 			#m
#Calculating the angular velocity of the link PQ
#Calculating the radial component of the acceleration of B with respect to A
arBA = omegaBA**2*AB 			#m/s**2
#Calculating the coriolis component of the acceleration of B with respect to coincident point B'
acBBdash = 2*omegaPQ*vBdashB 			#m/s**2
#Calculating the radial component of the acceleration of R with respect to Q
arRQ = vRQ**2/QR 			#m/s**2
#Calculating the radial component of the acceleration of B' with respect to P
arBdashP = vBdashP**2/PBdash 			#m/s**2
#By measurement from the acceleration diagram Fig. 8.31(d)
aR = 22.
aBBdash = 18. 			#m/s**2

#Results:
print " Velocity of the tool-box R, vR  =  %.1f m/s."%(vR)
print " Acceleration of the tool-box R, aR  =  %d m/s**2."%(aR)
print " The acceleration of sliding of the block B along the slotted lever PQ, aBBdash  =  %d m/s**2."%(aBBdash)

 Velocity of the tool-box R, vR  =  1.6 m/s.
Acceleration of the tool-box R, aR  =  22 m/s**2.
The acceleration of sliding of the block B along the slotted lever PQ, aBBdash  =  18 m/s**2.


## Example 8.15 Page No : 218¶

In [16]:
import math

# Variables:
NAO = 30. 			#rpm
OA = 150./1000      #m
OC = 100./1000      #m
CD = 125./1000      #m
DR = 500./1000 		#m

#Solution:
#Refer Fig. 8.33
#Calculating the angular speed of the crank OA
#Calculating the velocity of A with respect to O
vAO = omegaAO*OA 			#m/s
vA = vAO
#By measurement from the velocity diagram Fig. 8.33(b)
vBC = 0.46
vAB = 0.15
vRD = 0.12 			#m/s
CB = 240./1000 			#m
#Calculating the angular velocity of the link BC
#Calculating the radial component of the acceleration of A with respect to O
arAO = vAO**2/OA 			#m/s**2
#Calculating the coriolis component of the acceleration of A with respect to coincident point B
acAB = 2*omegaBC*vAB 			#m/s**2
#Calculating the radial component of the acceleration of B with respect to C
arBC = vBC**2/CB 			#m/s**2
#Calculating the radial component of the acceleration of R with respect to D
arRD = vRD**2/DR 			#m/s**2
#By measurement from the acceleration diagram Fig. 8.33(c)
aR = 0.18
atBC = 0.14 			#m/s**2
#Calculating the angular acceleration of the slotted lever CA
alphaBC = alphaCA

#Results:
print " Acceleration of the sliding block R, aR  =  %.2f m/s**2."%(aR)
print " Angular acceleration of the slotted lever CA, alphaCA  =  %.3f rad/s**2, anticlockwise."%(alphaCA)

 Acceleration of the sliding block R, aR  =  0.18 m/s**2.
Angular acceleration of the slotted lever CA, alphaCA  =  0.583 rad/s**2, anticlockwise.


## Example 8.16 Page No : 221¶

In [17]:
import math

# Variables:
AB = 125./1000 			#m
NCO = 300. 			#rpm

#Solution:
#Refer Fig. 8.35
#By measurement from the space diagram Fig. 8.35(a)
OC = 85./1000 			#m
#Calculating the angular velocity of the link CO
#Calculating the velocity of C with respect to O
vCO = omegaCO*OC 			#m/s
vC = vCO
#By measurement from the velocity diagram Fig. 8.35(b)
vBC = 0.85
vBA = 2.85
vB = vBA 			#m/s
#Calculating the radial component of of the acceleration of C with respect to O
arCO = vCO**2/OC 			#m/s**2
#Calculating the coriolis component of of acceleration of the piston B with respect to the cylinder or the coincident point C
acBC = 2*omegaCO*vBC 			#m/s**2
#Calculating the radial component of of the acceleration of B with respect to A
arBA = vBA**2/AB 			#m/s**2
#By measurement from the acceleration diagram Fig. 8.35(d)
aBC = 73.2
atBA = 37.6 			#m/s**2
#Calculating the angular acceleration of the connecting rod AB

#Results:
print " Acceleration of the piston inside the cylinder, aBC  =  %.1f m/s**2."%(aBC)
print " Angular acceleration of the connecting rod AB, alphaAB  =  %d rad/s**2, clockwise."%(alphaAB)

 Acceleration of the piston inside the cylinder, aBC  =  73.2 m/s**2.
Angular acceleration of the connecting rod AB, alphaAB  =  300 rad/s**2, clockwise.


## Example 8.17 Page No : 223¶

In [18]:
import math

# Variables:
NAO = 100. 			#rpm
OA = 50./1000       #m
AB = 350./1000      #m
DE = 250./1000      #m
EF = DE             #m
CB = 125./1000 		#m

#Solution:
#Refer Fig. 8.37
#Calculating the angular velocity of the crank AO
#Calculating the velocity of A with respect to O
vAO = omegaAO*OA 			#m/s
vA = vAO
#By measurement from the velocity diagram Fig. 8.37(b)
vBA = 0.4
vBC = 0.485
vB = vBC
vSD = 0.265
vQS = 0.4
vED = 0.73
vFE = 0.6
vF = 0.27 			#m/s
DS = 85./1000 			#m
#Calculating the angular velocity of the link DE
#Calculating the velocity of sliding of the link DE in the swivel block
vS = vQS 			#m/s
#Calculating the radial component of the acceleration of A with respect to O
arAO = vAO**2/OA 			#m/s**2
#Calculating the radial component of the acceleration of B with respect to A
arBA = vBA**2/AB 			#m/s**2
#Calculating the radial component of the acceleration of B with respect to C
arBC = vBC**2/CB 			#m/s**2
#Calculating the radial component of the acceleration of S with respect to D
arSD = vSD**2/DS 			#m/s**2
#Calculating the coriolis component of the acceleration of Q with respect to S
#Calculating the radial component of the acceleration of F with respect to E
arFE = vFE**2/EF 			#m/s**2
#By measurement from the acceleration diagram Fig. 8.37(d)
arQS = 1.55 			#m/s**2

#Results:
print " Velocity of the slider block F, vF  =  %.2f m/s."%(vF)

 Velocity of the slider block F, vF  =  0.27 m/s.