# Chapter1-Basic kinematics¶

## Ex1-pg15¶

In [1]:
##CHAPTER 1 ILLUSRTATION 1 PAGE NO 15
#calculate inclination of slotted bar with vertical
##TITLE:Basic kinematics
##Figure 1.14
import math
pi=3.141
AO=200.##                 distance between fixed centres in mm
OB1=100.##                length of driving crank in mm
AP=400.##                 length of slotter bar in mm
##====================================
OAB1=math.asin(OB1/AO)*57.3##              inclination of slotted bar with vertical in degrees
beeta=(90-OAB1)*2.##               angle through which crank turns inreturn stroke in degrees
A=(360.-beeta)/beeta##             ratio of time of cutting stroke to the time of return stroke
L=2.*AP*math.sin(90.-beeta/2.)/57.3##       length of the stroke in mm
print'%s %.2f %s %.3f %s'%('Inclination of slotted bar with vertical= ',OAB1,' degrees' 'Length of the stroke=',L,' mm')

Inclination of slotted bar with vertical=  30.00  degreesLength of the stroke= -13.790  mm


## Ex2-pg16¶

In [2]:
##CHAPTER 1 ILLUSRTATION 2 PAGE NO 16
#calculate ratio of time taken on the cutting to the return
##TITLE:Basic kinematics
##Figure 1.15
import math
OA=300.##               distance between the fixed centres in mm
OB=150.##                 length of driving crank in mm
##================================
OAB=math.asin(OB/OA)##              inclination of slotted bar with vertical in degrees
beeta=(90/57.3-OAB)*2.##               angle through which crank turns inreturn stroke in degrees
A=(360/57.3-beeta)/beeta##             ratio of time of cutting stroke to the time of return stroke
print'%s %.1f %s'%('Ratio of time taken on the cutting to the return stroke= ',A,'')

Ratio of time taken on the cutting to the return stroke=  2.0


## Ex3-pg16¶

In [3]:
##CHAPTER 1 ILLUSRTATION 3 PAGE NO 16
#calculate ratio of time taken on the cutting to the return stroke
##TITLE:Basic kinematics
##Figure 1.16
import math
OB=54.6/57.3##               distance between the fixed centres in mm
OA=85./57.3##                 length of driving crank in mm
OA2=OA
CA=160.##                length of slotted lever in mm
CD=144.##                length of connectin rod in mm
##================================
beeta=2.*(math.cos(OB/OA2))##        angle through which crank turns inreturn stroke in degrees
A=(360/57.3-beeta)/beeta##             ratio of time of cutting stroke to the time of return stroke
print'%s %.1f %s'%('Ratio of time taken on the cutting to the return stroke= ',A,'')

Ratio of time taken on the cutting to the return stroke=  2.9


## Ex4-pg 17¶

In [4]:
##CHAPTER 1 ILLUSRTATION 4 PAGE NO 17
#calculate velocity position and Angular velocity connection
##TITLE:Basic kinematics
##Figure 1.18,1.19
import math
pi=3.141
Nao=180.##     speed of the crank in rpm
wAO=2.*pi*Nao/60.##  angular speed of the crank in rad/s
AO=.5##          crank length in m
AE=.5
Vao=wAO*AO##      velocity of A in m/s
##================================
Vb1=8.15##    velocity of piston B in m/s by measurment from figure 1.19
Vba=6.8##    velocity of B with respect to A in m/s
AB=2##       length of connecting rod in m
wBA=Vba/AB##      angular velocity of the connecting rod BA in rad/s
ae=AE*Vba/AB##     velocity of point e on the connecting rod
oe=8.5##           by measurement velocity of point E
Do=.05##           diameter of crank shaft in m
Da=.06##           diameter of crank pin in m
Db=.03##           diameter of cross head pin B m
V1=wAO*Do/2.##            velocity of rubbing at the pin of the crankshaft in m/s
V2=wBA*Da/2.##            velocity of rubbing at the pin of the crank in m/s
Vb=(wAO+wBA)*Db/2.##      velocity of rubbing at the pin of cross head in m/s
ag=5.1##                by measurement
AG=AB*ag/Vba##      position and linear velocity of point G on the connecting rod in m
##===============================
print'%s %.3f %s %.3f %s %.3f %s %.3f %s %.3f %s %.3f %s %.3f %s'%('Velocity of piston B=',Vb1,' m/s''Angular velocity of connecting rod= ',wBA,' rad/s''velocity of point E=',oe,' m/s'' velocity of rubbing at the pin of the crankshaft=',V1,' m/s' 'velocity of rubbing at the pin of the crank =',V2,' m/s''velocity of rubbing at the pin of cross head =',Vb,' m/s''position and linear velocity of point G on the connecting rod=',AG,' m')


Velocity of piston B= 8.150  m/sAngular velocity of connecting rod=  3.400  rad/svelocity of point E= 8.500  m/s velocity of rubbing at the pin of the crankshaft= 0.471  m/svelocity of rubbing at the pin of the crank = 0.102  m/svelocity of rubbing at the pin of cross head = 0.334  m/sposition and linear velocity of point G on the connecting rod= 1.500  m


## Ex5-pg 19¶

In [13]:
##CHAPTER 1 ILLUSRTATION 5 PAGE NO 19
#calculate linear velocity at various point
##TITLE:Basic kinematics
##Figure 1.20,1.21
import math
pi=3.141
N=120.##      speed of crank in rpm
OA=10.##      length of crank in cm
BP=48.##      from figure 1.20 in cm
BA=40.##      from figure 1.20 in cm
##==============
w=2.*pi*N/60.##       angular velocity of the crank OA in rad/s
Vao=w*OA##          velocity of ao in cm/s
ba=4.5##            by measurement from 1.21 in cm
Bp=BP*ba/BA
op=6.8##           by measurement in cm from figure 1.21
s=20.##              scale of velocity diagram 1cm=20cm/s
Vp=op*s##           linear velocity of P in m/s
ob=5.1##            by measurement in cm from figure 1.21
Vb=ob*s##           linear velocity of slider B
print'%s %.2f %s %.2f %s'%('Linear velocity of slider B= ',Vb,' cm/s''Linear velocity of point P= ',Vp,' cm/s')

Linear velocity of slider B=  102.00  cm/sLinear velocity of point P=  136.00  cm/s


## Ex6-pg20¶

In [12]:
#calculate angular velocity at various points
##CHAPTER 1 ILLUSRTATION 6 PAGE NO 20
##TITLE:Basic kinematics
##Figure 1.22,1.23
import math
pi=3.141
AB=6.25##     length of link AB in cm
BC=17.5##     length of link BC in cm
CD=11.25##    length of link CD in cm
DA=20.##       length of link DA in cm
CE=10.
N=100.##       speed of crank in rpm
##========================
wAB=2.*pi*N/60.##      angular velocity of AB in rad/s
Vb=wAB*AB##          linear velocity of B with respect to A
s=15.##      scale for velocity diagram 1 cm= 15 cm/s
dc=3.##      by measurement in cm
Vcd=dc*s
wCD=Vcd/CD##       angular velocity of link CD in rad/s
bc=2.5##    by measurement in cm
Vbc=bc*s
wBC=Vbc/BC##     angular velocity of link BC in rad/s
ce=bc*CE/BC
ae=3.66##       by measurement in cm
Ve=ae*s##         velocity of point E 10 from c on the link BC
af=2.94##       by measurement in cm
Vf=af*s##       velocity of point F
print'%s %.3f %s %.3f %s %.3f %s %.3f %s'%('The angular velocity of link CD= ',wCD,' rad/s'' The angular velocity of link BC= ',wBC,'rad/s'' velocity of point E 10 from c on the link BC= ',Ve,' cm/s' ' velocity of point F= ',Vf,' cm/s')

The angular velocity of link CD=  4.000  rad/s The angular velocity of link BC=  2.143 rad/s velocity of point E 10 from c on the link BC=  54.900  cm/s velocity of point F=  44.100  cm/s


## Ex7-pg21¶

In [1]:
##CHAPTER 1 ILLUSRTATION 7 PAGE NO 21
##TITLE:Basic kinematics
#calculate Linear velocity slider and angular velocity of link
##Figure 1.24,1.25
import math
pi=3.141
Noa=600##      speed of the crank in rpm
OA=2.8##       length of link OA in cm
AB=4.4##       length of link AB in cm
BC=4.9##       length of link BC in cm
BD=4.6##       length of link BD in cm
##=================
wOA=2.*pi*Noa/60.##        angular velocity of crank in rad/s
Vao=wOA*OA##             The linear velocity of point A with respect to oin m/s
s=50.##                   scale of velocity diagram in cm
od=2.95##              by measurement in cm from figure
Vd=od*s/100.##             linear velocity slider in m/s
bd=3.2##              by measurement in cm from figure
Vbd=bd*s
wBD=Vbd/BD##     angular velocity of link BD
print'%s %.1f %s %.1f %s '%('linear velocity slider D= ',Vd,' m/s' 'angular velocity of link BD= ',wBD,' rad/s')

linear velocity slider D=  1.5  m/sangular velocity of link BD=  34.8  rad/s


## Ex8-pg22¶

In [10]:
##CHAPTER 1 ILLUSRTATION 8 PAGE NO 22
#calculate Angular velocity of link CD
##TITLE:Basic kinematics
import math
pi=3.141
Noa=60.##        speed of crank in rpm
OA=30.##     length of link OA in cm
AB=100.##       length of link AB in cm
CD=80.##         length of link CD in cm
##AC=CB
##================
wOA=2.*pi*Noa/60.##     angular velocity of crank in rad/s
Vao=wOA*OA/100.##      linear velocity of point A with respect to O
s=50.##          scale for velocity diagram 1 cm= 50 cm/s
ob=3.4##        by measurement in cm from figure 1.27
od=.9##         by measurement in cm from figure 1.27
Vcd=160.##       by measurement in cm/s from figure 1.27
wCD=Vcd/CD##    angular velocity of link in rad/s
print'%s %.d %s'%('Angular velocity of link CD= ',wCD,' rad/s')

Angular velocity of link CD=  2  rad/s


## Ex9-pg23¶

In [9]:
##CHAPTER 1 ILLUSRTATION 9 PAGE NO 23
#calculate velcity of Ram and anugular velocity of link and velocity of slidingof the block
##TITLE:Basic kinematics
##Figure 1.28,1.29
import math
pi=3.141
Nao=120.##            speed of the crank in rpm
OQ=10.##              length of link OQ in cm
OA=20.##              length of link OA in cm
QC=15.##              length of link QC in cm
CD=50.##              length oflink CD in cm
##=============
wOA=2.*pi*Nao/60.##      angular speed of crank in rad/s
Vad=wOA*OA/100.##         velocity of pin A in m/s
BQ=41.##               from figure 1.29
BC=26.##               from firure 1.29
bq=4.7##               from figure 1.29
bc=bq*BC/BQ##          from figure 1.29 in cm
s=50.##                 scale for velocity diagram in cm/s
od=1.525##             velocity vector od in cm from figure 1.29
Vd=od*s##              velocity of ram D in cm/s
dc=1.925##             velocity vector dc in cm from figure 1.29
Vdc=dc*s##             velocity of link CD in cm/s
wCD=Vdc/CD##           angular velocity of link CD in cm/s
ba=1.8##               velocity vector of sliding of the block in cm
Vab=ba*s##             velocity of sliding of the block in cm/s
print'%s %.3f %s %.2f %s %.1f %s '%('Velocity of RAM D= ',Vd,' cm/s''angular velocity of link CD= ',wCD,' rad/s'' velocity of sliding of the block= ',Vab,' cm/s')

Velocity of RAM D=  76.250  cm/sangular velocity of link CD=  1.93  rad/s velocity of sliding of the block=  90.0  cm/s


## Ex10-pg24¶

In [8]:
##CHAPTER 1 ILLUSRTATION 10 PAGE NO 24
##TITLE:Basic kinematics
#calculate linear velocity abd radial component of accerlation and anugular velocity of connecting rod and anugular accerlation of connecting rod
##Figure 1.30(a),1.30(b),1.30(c)
import math
pi=3.141
Nao=300.##         speed of crank in rpm
AO=.15##          length of crank in m
BA=.6##           length of connecting rod in m
##===================
wAO=2.*pi*Nao/60.##        angular velocity of link in rad/s
Vao=wAO*AO##             linear velocity of A with respect to 'o'
ab=3.4##        length of vector ab by measurement in m/s
Vba=ab
ob=4.##        length of vector ob by measurement in m/s
oc=4.1##         length of vector oc by measurement in m/s
fRao=Vao**2./AO##    radial component of acceleration of A with respect to O
fRba=Vba**2./BA##     radial component of acceleration of B with respect to A
wBA=Vba/BA##        angular velocity of connecting rod BA
fTba=103.##         by measurement in m/s**2
alphaBA=fTba/BA##    angular acceleration of connecting rod BA
print'%s %.1f %s %.1f %s %.1f %s %.1f %s %.1f %s  '%('linear velocity of A with respect to O= ',Vao,' m/s''radial component of acceleration of A with respect to O= ',fRao,' m/s**2'' radial component of acceleration of B with respect to A=',fRba,' m/s**2'' angular velocity of connecting rod B= ',wBA,' rad/s'' angular acceleration of connecting rod BA= ',alphaBA,' rad/s**2')

linear velocity of A with respect to O=  4.7  m/sradial component of acceleration of A with respect to O=  148.0  m/s**2 radial component of acceleration of B with respect to A= 19.3  m/s**2 angular velocity of connecting rod B=  5.7  rad/s angular acceleration of connecting rod BA=  171.7  rad/s**2


## Ex11-pg26¶

In [6]:
##CHAPTER 1 ILLUSRTATION 11 PAGE NO 26
#calcualte Angular accerlation at various point
##TITLE:Basic kinematics
##Figure 1.31(a),1.31(b),1.31(c)
import math
pi=3.141
wAP=10.##            angular velocity of crank in rad/s
P1A=30.##            length of link P1A in cm
P2B=36.##            length of link P2B in cm
AB=36.##             length of link AB in cm
P1P2=60.##           length of link P1P2 in cm
AP1P2=60.##          crank inclination in degrees
alphaP1A=30.##       angulare acceleration of crank P1A in rad/s**2
##=====================================
Vap1=wAP*P1A/100.##    linear velocity of A with respect to P1 in m/s
Vbp2=2.2##            velocity of B with respect to P2 in m/s(measured from figure )
Vba=2.06##            velocity of B with respect to A in m/s(measured from figure )
wBP2=Vbp2/(P2B*100.)##   angular velocity of P2B in rad/s
wAB=Vba/(AB*100.)##      angular velocity of AB in rad/s
fAB1=alphaP1A*P1A/100.##  tangential component of the acceleration of A with respect to P1 in m/s**2
frAB1=Vap1**2./(P1A/100.)##  radial component of the acceleration of A with respect to P1 in m/s**2
frBA=Vba**2./(AB/100.)##     radial component of the acceleration of B with respect to B in m/s**2
frBP2=Vbp2**2./(P2B/100.)##    radial component of the acceleration of B with respect to P2 in m/s**2
ftBA=13.62##             tangential component of B with respect to A in m/s**2(measured from figure)
ftBP2=26.62##            tangential component of B with respect to P2 in m/s**2(measured from figure)
alphaBP2=ftBP2/(P2B/100.)##   angular acceleration of P2B in m/s**2
alphaBA=ftBA/(AB/100.)##      angular acceleration of AB in m/s**2
##==========================
print'%s %.1f %s %.1f %s'%('Angular acceleration of P2B=',alphaBP2,' rad/s**2''angular acceleration of AB =',alphaBA,' rad/s**2')

Angular acceleration of P2B= 73.9  rad/s**2angular acceleration of AB = 37.8  rad/s**2


## Ex12-pg28¶

In [5]:
##CHAPTER 1 ILLUSRTATION 12 PAGE NO 28
#calculate velocities at various point
##TITLE:Basic kinematics
##Figure 1.32(a),1.32(b),1.32(c)
import math
PI=3.141
AB=12.##    length of link AB in cm
BC=48.##    length of link BC in cm
CD=18.##    length of link CD in cm
DE=36.##    length of link DE in cm
EF=12.##    length of link EF in cm
FP=36.##    length of link FP in cm
Nba=200.##   roating speed of link BA IN rpm
wBA=2*PI*200./60.##    Angular velocity of BA in rad/s
Vba=wBA*AB/100.##    linear velocity of B with respect to A in m/s
Vc=2.428##   velocity of c in m/s from diagram 1.32(b)
Vd=2.36##     velocity of D in m/s from diagram 1.32(b)
Ve=1##    velocity of e in m/s from diagram 1.32(b)
Vf=1.42##    velocity of f in m/s from diagram 1.32(b)
Vcb=1.3##    velocity of c with respect to b in m/s from figure
fBA=Vba**2.*100./AB##   radial component of acceleration of B with respect to A in m/s**2
fCB=Vcb**2*100./BC##   radial component of acceleration of C with respect to B in m/s**2
fcb=3.52##          radial component of acceleration of C with respect to B in m/s**2 from figure
fC=19.##              acceleration of slider in m/s**2 from figure
print'%s %.1f %s %.1f %s %.1f %s %.2f %s %.2f %s'%('velocity of c=',Vc,' m/s''velocity of d=',Vd,' m/s''velocity of e=',Ve,' m/s'' velocity of f=',Vf,' m/s''Acceleration of slider=',Vc,' m/s**2')

velocity of c= 2.4  m/svelocity of d= 2.4  m/svelocity of e= 1.0  m/s velocity of f= 1.42  m/sAcceleration of slider= 2.43  m/s**2


## Ex13-pg30¶

In [4]:
##CHAPTER 1 ILLUSRTATION 13 PAGE NO 30
#caculate angular acceleration at varoius points
##TITLE:Basic kinematics
##Figure 1.33(a),1.33(b),1.33(c)
import math
PI=3.141
N=120.##        speed of the crank OC in rpm
OC=5.##         length of link OC in cm
cp=20.##        length of link CP in cm
qa=10.##        length of link QA in cm
pa=5.##         length of link PA in cm
CP=46.9##        velocity of link CP in cm/s
QA=58.3##        velocity of link QA in cm/s
Pa=18.3##        velocity of link PA in cm/s
Vc=2.*PI*N*OC/60.##    velocity of C in m/s
Cco=Vc**2./OC##        centripetal acceleration of C relative to O in cm/s**2
Cpc=CP**2./cp##         centripetal acceleration of P relative to C in cm/s**2
Caq=QA**2./qa##          centripetal acceleration of A relative to Q in cm/s**2
Cap=Pa**2./pa##           centripetal acceleration of A relative to P in cm/s**2
pp1=530.
a1a=323.
a2a=207.5
ACP=pp1/cp##        angular acceleration of link CP in rad/s**2
APA=a1a/qa##        angular acceleration of link PA in rad/s**2
AAQ=a2a/pa##        angular acceleration of link AQ in rad/s**2
print'%s %.3f %s  %.3f %s  %.3f %s'%('angular acceleration of link CP =',ACP,' rad/s**2'' angular acceleration of link CP=',APA,' rad/s**2''angular acceleration of link CP=',AAQ,' rad/s**2')

angular acceleration of link CP = 26.500  rad/s**2 angular acceleration of link CP=  32.300  rad/s**2angular acceleration of link CP=  41.500  rad/s**2