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| author | hardythe1 | 2015-06-03 15:27:17 +0530 |
|---|---|---|
| committer | hardythe1 | 2015-06-03 15:27:17 +0530 |
| commit | df60071cf1d1c18822d34f943ab8f412a8946b69 (patch) | |
| tree | ab059cf19bad4a1233a464ccf5d72cf8b3fb323c /_Theory_Of_Machines/Chapter4.ipynb | |
| parent | fba055ce5aa0955e22bac2413c33493b10ae6532 (diff) | |
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diff --git a/_Theory_Of_Machines/Chapter4.ipynb b/_Theory_Of_Machines/Chapter4.ipynb new file mode 100755 index 00000000..de08c088 --- /dev/null +++ b/_Theory_Of_Machines/Chapter4.ipynb @@ -0,0 +1,946 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:fdf50666cfa70019db7241b6e1fb1e819c70fb9987ea0caadb1e777e93e7d898"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter4-Gears and Gear Drivers"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex1-pg133"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##Chapter-4, Illustration 1, Page 133\n",
+ "##Title: Gears and Gear Drivers\n",
+ "##=============================================================================\n",
+ "import math\n",
+ "\n",
+ "##INPUT DATA\n",
+ "TA=48.;##Wheel A teeth\n",
+ "TB=30.;##Wheel B teeth\n",
+ "m=5.;##Module pitch in mm\n",
+ "phi=20.;##Pressure angle in degrees\n",
+ "add=m;##Addendum in mm\n",
+ "\n",
+ "##CALCULATIONS\n",
+ "R=(m*TA)/2.;##Pitch circle radius of wheel A in mm\n",
+ "RA=R+add;##Radius of addendum circle of wheel A in mm\n",
+ "r=(m*TB)/2.;##Pitch circle radius of wheel B in mm\n",
+ "rA=r+add;##Radius of addendum circle of wheel B in mm\n",
+ "lp=(math.sqrt((RA**2.)-((R**2.)*(math.cos(phi/57.3)**2.))))+(math.sqrt((rA**2.)-((r**2.)*(math.cos(phi/57.3)**2.))))-((R+r)*math.sin(phi/57.3));##Length of path of contact in mm\n",
+ "la=lp/math.cos(phi/57.3);##Length of arc of contact in mm\n",
+ "\n",
+ "##OUTPUT\n",
+ "print'%s %.1f %s'%('Length of arc of contact is ',la,' mm')\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "##================================END OF PROGRAM=============================================\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Length of arc of contact is 26.7 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex2-pg133"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##Chapter-4, Illustration 2, Page 133\n",
+ "##Title: Gears and Gear Drivers\n",
+ "##=============================================================================\n",
+ "import math\n",
+ "\n",
+ "##INPUT DATA\n",
+ "TA=40.;##Wheel A teeth\n",
+ "TB=TA;##Wheel B teeth\n",
+ "m=6.;##Module pitch in mm\n",
+ "phi=20.;##Pressure angle in degrees\n",
+ "pi=3.141\n",
+ "x=1.75;##Ratio of length of arc of contact to circular pitch\n",
+ "\n",
+ "##CALCULATIONS\n",
+ "Cp=m*pi;##Circular pitch in mm\n",
+ "R=(m*TA)/2.;##Pitch circle radius of wheel A in mm\n",
+ "r=R;##Pitch circle radius of wheel B in mm\n",
+ "la=x*Cp;##Length of arc of contact in mm\n",
+ "lp=la*math.cos(phi/57.3);##Length of path of contact in mm\n",
+ "RA=math.sqrt((((lp/2.)+(R*math.sin(phi/57.3)))**2.)+((R**2.)*(math.cos(phi/57.3))**2.));##Radius of addendum circle of each wheel in mm\n",
+ "add=RA-R;##Addendum in mm\n",
+ "\n",
+ "##OUTPUT\n",
+ "print'%s %.1f %s'%('Addendum of wheel is ',add,' mm')\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "##================================END OF PROGRAM=============================================\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Addendum of wheel is 6.1 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex3-pg134"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##Chapter-4, Illustration 3, Page 134\n",
+ "##Title: Gears and Gear Drivers\n",
+ "##=============================================================================\n",
+ "import math\n",
+ "\n",
+ "##INPUT DATA\n",
+ "TA=48.;##Gear teeth\n",
+ "TB=24.;##Pinion teeth\n",
+ "m=6.;##Module in mm\n",
+ "phi=20.;##Pressure angle in degrees\n",
+ "\n",
+ "##CALCULATIONS\n",
+ "r=(m*TB)/2.;##Pitch circle radius of pinion in mm\n",
+ "R=(m*TA)/2.;##Pitch circle radius of gear in mm\n",
+ "RA=math.sqrt(((((r*math.sin(phi/57.3))/2.)+(R*math.sin(phi/57.3)))**2.)+((R**2)*(math.cos(phi/57.3))**2));##Radius of addendum circle of gear in mm\n",
+ "rA=math.sqrt(((((R*math.sin(phi/57.3))/2.)+(r*math.sin(phi/57.3)))**2.)+((r**2)*(math.cos(phi/57.3))**2));##Radius of addendum circle of pinion in mm\n",
+ "addp=rA-r;##Addendum for pinion in mm\n",
+ "addg=RA-R;##Addendum for gear in mm\n",
+ "lp=((R+r)*math.sin(phi/57.3))/2.;##Length of path of contact in mm\n",
+ "la=lp/math.cos(phi/57.3);##Length of arc of contact in mm\n",
+ "\n",
+ "##OUTPUT\n",
+ "print'%s %.1f %s %.1f %s %.1f %s '%('Addendum for pinion is',addp,' mm' ' Addendum for gear is ',addg,' mm' ' Length of arc of contact is ',la,' mm')\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "##================================END OF PROGRAM=============================================\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Addendum for pinion is 11.7 mm Addendum for gear is 4.7 mm Length of arc of contact is 39.3 mm \n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex4-pg135"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##Chapter-4, Illustration 4, Page 135\n",
+ "##Title: Gears and Gear Drivers\n",
+ "##=============================================================================\n",
+ "import math\n",
+ "\n",
+ "##INPUT DATA\n",
+ "x=3.5;##Ratio of teeth of wheels\n",
+ "C=1.2;##Centre distance between axes in m\n",
+ "DP=4.4;##Diametrical pitch in cm\n",
+ "\n",
+ "##CALCULATIONS\n",
+ "D=2*C*100.;##Sum of diameters of wheels in cm\n",
+ "T=D*DP;##Sum of teeth of wheels\n",
+ "TB1=T/(x+1);##Teeth of wheel B\n",
+ "TB=math.floor(TB1);##Teeth of whhel B\n",
+ "TA=x*TB;##Teeth of wheel A\n",
+ "DA=TA/DP;##Diametral pitch of gear A in cm\n",
+ "DB=TB/DP;##Diametral pitch of gear B in cm\n",
+ "Ce=(DA+DB)/2.;##Exact centre distance between shafts in cm\n",
+ "TB2=math.ceil(TB1);##Teeth of wheel B\n",
+ "TA2=T-TB2;##Teeth of wheel A\n",
+ "VR=TA2/TB2;##Velocity ratio\n",
+ "\n",
+ "##OUTPUT\n",
+ "print'%s %.1f %s %.1f %s %.1f %s%.1f %s%.1f %s'%('Number of teeth on wheel A is ',TA,'' 'Number of teeth on wheel B is ',TB,'' ' Exact centre distance is ',Ce,' cm ' 'If centre distance is ',C,' m' 'then Velocity ratio is',VR,'')\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "##================================END OF PROGRAM=============================================\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Number of teeth on wheel A is 819.0 Number of teeth on wheel B is 234.0 Exact centre distance is 119.7 cm If centre distance is 1.2 mthen Velocity ratio is3.5 \n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex5-pg136"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##Chapter-4, Illustration 5, Page 136\n",
+ "##Title: Gears and Gear Drivers\n",
+ "##=============================================================================\n",
+ "import math\n",
+ "\n",
+ "##INPUT DATA\n",
+ "C=600;##Distance between shafts in mm\n",
+ "Cp=30;##Circular pitch in mm\n",
+ "NA=200;##Speed of wheel A in rpm\n",
+ "NB=600;##Speed of wheel B in rpm\n",
+ "F=18;##Tangential pressure in kN\n",
+ "pi=3.141\n",
+ "\n",
+ "##CALCULATIONS\n",
+ "a=Cp/(pi*10.);##Ratio of pitch diameter of wheel A to teeth of wheel A in cm\n",
+ "b=Cp/(pi*10.);##Ratio of pitch diameter of wheel B to teeth of wheel B in cm\n",
+ "T=(2*C)/(a*10.);##Sum of teeth of wheels\n",
+ "r=NB/NA;##Ratio of teeth of wheels\n",
+ "TB=T/(r+1);##Teeth of wheel B\n",
+ "TB1=math.ceil(TB);##Teeth of wheel B\n",
+ "TA=TB1*r;##Teeth of wheel A\n",
+ "DA=a*TA;##Pitch diameter of wheel A in cm\n",
+ "DB=b*TB1;##Pitch diameter of wheel B in cm\n",
+ "CPA=(pi*DA)/TA;##Circular pitch of gear A in cm\n",
+ "CPB=(pi*DB)/TB1;##Circular pitch of gear B in cm\n",
+ "C1=(DA+DB)*10/2.;##Exact centre distance in mm\n",
+ "P=(F*1000.*pi*DA*NA)/(60.*1000.*100.);##Power transmitted in kW\n",
+ "\n",
+ "##OUTPUT\n",
+ "print'%s %.1f %s %.1f %s %.1f %s %.1f %s %.1f %s %.1f %s %.1f %s %.1f %s '%('Number of teeth on wheel A is ',TA,' '' Number of teeth on wheel B is ',TB1,' '' Pitch diameter of wheel A is ',DA,' cm'' Pitch diameter of wheel B is ',DB,' cm'' Circular pitch of wheel A is',CPA,'cm ' 'Circular pitch of wheel B is ',CPB,' cm '' Exact centre distance between shafts is ',C1,' mm'' Power transmitted is',P,' kW')\n",
+ "##================================END OF PROGRAM=============================================\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Number of teeth on wheel A is 96.0 Number of teeth on wheel B is 32.0 Pitch diameter of wheel A is 91.7 cm Pitch diameter of wheel B is 30.6 cm Circular pitch of wheel A is 3.0 cm Circular pitch of wheel B is 3.0 cm Exact centre distance between shafts is 611.3 mm Power transmitted is 172.8 kW \n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex6-pg137"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##Chapter-4, Illustration 6, Page 137\n",
+ "##Title: Gears and Gear Drivers\n",
+ "##=============================================================================\n",
+ "import math\n",
+ "\n",
+ "##INPUT DATA\n",
+ "r=16.;##Speed ratio\n",
+ "mA=4.;##Module of gear A in mm\n",
+ "mB=mA;##Module of gear B in mm\n",
+ "mC=2.5;##Mosule of gear C in mm\n",
+ "mD=mC;##Module of gear D in mm\n",
+ "C=150.;##Distance between shafts in mm\n",
+ "\n",
+ "##CALCULATIONS\n",
+ "t=math.sqrt(r);##Ratio of teeth\n",
+ "T1=(C*2.)/mA;##Sum of teeth of wheels A and B\n",
+ "T2=(C*2.)/mC;##Sum of teeth of wheels C and D\n",
+ "TA=T1/(t+1.);##Teeth of gear A\n",
+ "TB=T1-TA;##Teeth of gear B\n",
+ "TC=T2/(t+1.);##Teeth of gear C\n",
+ "TD=T2-TC;##Teeth of gear D\n",
+ "\n",
+ "##OUTPUT\n",
+ "print'%s %.1f %s %.1f %s %.1f %s %.1f %s '%('Number of teeth on gear A is ',TA,' '' Number of teeth on gear B is ',TB,'' 'Number of teeth on gear C is ',TC,'' ' Number of teeth on gear D is ',TD,'')\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "##================================END OF PROGRAM=============================================\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Number of teeth on gear A is 15.0 Number of teeth on gear B is 60.0 Number of teeth on gear C is 24.0 Number of teeth on gear D is 96.0 \n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7-pg138"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##Chapter-4, Illustration 7, Page 138\n",
+ "##Title: Gears and Gear Drivers\n",
+ "##=============================================================================\n",
+ "import math\n",
+ "\n",
+ "##INPUT DATA\n",
+ "N=4.5;##No. of turns\n",
+ "\n",
+ "##CALCULATIONS\n",
+ "Vh=N/2.;##Velocity ratio of main spring spindle to hour hand spindle\n",
+ "Vm=12.;##Velocity ratio of minute hand spindle to hour hand spindle\n",
+ "T1=8.## assumed no of teeth on gear 1\n",
+ "T2=32.## assumed no of teeth on gear 2\n",
+ "T3=(T1+T2)/4.## no of teeth on gear 3\n",
+ "T4=(T1+T2)-T3## no of teeth on gear 4\n",
+ "print'%s %.1f %s %.1f %s %.1f %s %.1f %s '%('no of teeth on gear 1=',T1,'' 'no of teeth on gear 2=',T2,' ''no of teeth on gear 3=',T3,' ''no of teeth on gear 4=',T4,'')\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "no of teeth on gear 1= 8.0 no of teeth on gear 2= 32.0 no of teeth on gear 3= 10.0 no of teeth on gear 4= 30.0 \n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex8-pg139"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##Chapter-4, Illustration 8, Page 139\n",
+ "##Title: Gears and Gear Drivers\n",
+ "##=============================================================================\n",
+ "import math\n",
+ "\n",
+ "##Input data\n",
+ "Tb=70.;##Teeth of wheel B\n",
+ "Tc=25.;##Teeth of wheel C\n",
+ "Td=80.;##Teeth of wheel D\n",
+ "Na=-100.;##Speed of arm A in clockwise in rpm\n",
+ "y=-100.##Arm A rotates at 100 rpm clockwise\n",
+ "\n",
+ "##Calculations\n",
+ "Te=(Tc+Td-Tb);##Teeth of wheel E\n",
+ "x=(y/0.5)\n",
+ "Nc=(y-(Td*x)/Tc);##Speed of wheel C in rpm\n",
+ "\n",
+ "##Output\n",
+ "print'%s %.1f %s'%('Speed of wheel C is ',Nc,' rpm ''Direction of wheel C is anti-clockwise')\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "##================================END OF PROGRAM=============================================\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Speed of wheel C is 540.0 rpm Direction of wheel C is anti-clockwise\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex9-pg140"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##Chapter-4, Illustration 9, Page 140\n",
+ "##Title: Gears and Gear Drivers\n",
+ "##=============================================================================\n",
+ "import math\n",
+ "\n",
+ "##Input data\n",
+ "Tb=25.;##Teeth of wheel B\n",
+ "Tc=40.;##Teeth of wheel C\n",
+ "Td=10.;##Teeth of wheel D\n",
+ "Te=25.;##Teeth of wheel E\n",
+ "Tf=30.;##Teeth of wheel F\n",
+ "y=-120.;##Speed of arm A in clockwise in rpm\n",
+ "\n",
+ "##Calculations\n",
+ "x=(-y/4.)\n",
+ "Nb=x+y;##Speed of wheel B in rpm\n",
+ "Nf=(-10/3.)*x+y;##Speed of wheel F in rpm\n",
+ "\n",
+ "##Output\n",
+ "print'%s %.1f %s %.1f %s'%('Speed of wheel B is',Nb,' rpm Direction of wheel B is clockwise' ' Speed of wheel F is ',Nf,' rpm Direction of wheel F is clockwise')\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "##================================END OF PROGRAM=============================================\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Speed of wheel B is -90.0 rpm Direction of wheel B is clockwise Speed of wheel F is -220.0 rpm Direction of wheel F is clockwise\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex10-pg141"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##Chapter-4, Illustration 10, Page 141\n",
+ "##Title: Gears and Gear Drivers\n",
+ "##=============================================================================\n",
+ "import math\n",
+ "\n",
+ "##Input data\n",
+ "Ta=96.;##Teeth of wheel A\n",
+ "Tc=48.;##Teeth of wheel C\n",
+ "y=-20.;##Speed of arm C in rpm in clockwise\n",
+ "\n",
+ "##Calculations\n",
+ "x=(y*Ta)/Tc\n",
+ "Tb=(Ta-Tc)/2.;##Teeth of wheel B\n",
+ "Nb=(-Tc/Tb)*x+y;##Speed of wheel B in rpm\n",
+ "Nc=x+y;##Speed of wheel C in rpm\n",
+ "\n",
+ "##Output\n",
+ "print'%s %.1f %s %.1f %s'%('Speed of wheel B is ',Nb,' rpm' 'Speed of wheel C is ',Nc,' rpm')\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "##================================END OF PROGRAM=============================================\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Speed of wheel B is 60.0 rpmSpeed of wheel C is -60.0 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex11-pg142"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##Chapter-4, Illustration 11, Page 142\n",
+ "##Title: Gears and Gear Drivers\n",
+ "##=============================================================================\n",
+ "import math\n",
+ "import numpy\n",
+ "from numpy.linalg import inv\n",
+ "##Input data\n",
+ "Ta=40.## no of teeth on gear A\n",
+ "Td=90.## no of teeth on gear D\n",
+ "\n",
+ "##Calculations\n",
+ "Tb=(Td-Ta)/2.## no of teeth on gear B\n",
+ "Tc=Tb## no of teeth on gear C\n",
+ "##\n",
+ "##x+y=-1\n",
+ "##-40x+90y=45\n",
+ "\n",
+ "A=([[1, 1],[-Ta, Td]])##Coefficient matrix\n",
+ "\n",
+ "B=([[-1],[Td/2]])##Constant matrix\n",
+ " \n",
+ "X=numpy.dot(inv(A) ,B)##Variable matrix\n",
+ "##\n",
+ "##x+y=-1\n",
+ "##-40x+90y=0\n",
+ "A1=([[1, 1],[-Ta, Td]])##Coefficient matrix\n",
+ "B1=([[-1],[0]])##Constant matrix\n",
+ "X1=numpy.dot(inv(A1) ,B1)##Variable matrix\n",
+ "b=X1[1] \n",
+ "print(X[1]) \n",
+ "print'%s %.4f %s'%('speed of the arm =',b,' revolution clockwise')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "[ 0.03846154]\n",
+ "speed of the arm = -0.3077 revolution clockwise\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex12-pg144"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##Chapter-4, Illustration 12, Page 144\n",
+ "##Title: Gears and Gear Drivers\n",
+ "##=============================================================================\n",
+ "\n",
+ "\n",
+ "##Input data\n",
+ "Te=30.;##Teeth of wheel E\n",
+ "Tb=24.;##Teeth of wheel B\n",
+ "Tc=22.;##Teeth of wheel C\n",
+ "Td=70.;##Teeth of wheel D\n",
+ "Th=15.;##Teeth of wheel H\n",
+ "Nv=100.;##Speed of shaft V in rpm\n",
+ "Nx=300.;##Speed of spindle X in rpm\n",
+ "\n",
+ "##Calculations\n",
+ "Nh=Nv;##Speed of wheel H in rpm\n",
+ "Ne=(-Th/Te)*Nv;##Speed of wheel E in rpm\n",
+ "Ta=(Tc+Td-Tb);##Teeth of wheel A\n",
+ "##x+y=-50\n",
+ "##y=300\n",
+ "x=(Ne-Nx)\n",
+ "Nz=(187/210.)*x+Nx;##;##Speed of wheel Z in rpm\n",
+ "\n",
+ "##Output\n",
+ "print'%s %.1f %s'%('Speed of wheel Z is ',Nz,' rpm Direction of wheel Z is opposite to that of X')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Speed of wheel Z is -11.7 rpm Direction of wheel Z is opposite to that of X\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex13-pg145"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##Chapter-4, Illustration 13, Page 145\n",
+ "##Title: Gears and Gear Drivers\n",
+ "##=============================================================================\n",
+ "\n",
+ "\n",
+ "##Input data\n",
+ "Tp=20.;##Teeth of wheel P\n",
+ "Tq=30.;##Teeth of wheel Q\n",
+ "Tr=10.;##Teeth of wheel R\n",
+ "Nx=50.;##Speed of shaft X in rpm\n",
+ "Na=100.;##Speed of arm A in rpm\n",
+ "\n",
+ "##Calculations\n",
+ "##x+y=-50\n",
+ "##y=100\n",
+ "x=(-Nx-Na)\n",
+ "y=(-2.*x+Na);##Speed of Y in rpm\n",
+ "\n",
+ "##Output\n",
+ "print'%s %.1f %s'%('Speed of driven shaft Y is ',y,' rpm Direction of driven shaft Y is anti-clockwise')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Speed of driven shaft Y is 400.0 rpm Direction of driven shaft Y is anti-clockwise\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex4-pg146"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##Chapter-4, Illustration 14, Page 146\n",
+ "##Title: Gears and Gear Drivers\n",
+ "##=============================================================================\n",
+ "import math\n",
+ "\n",
+ "##Input data\n",
+ "d=216.;##Ring diameter in mm\n",
+ "m=4.;##Module in mm\n",
+ "\n",
+ "##Calculations\n",
+ "Td=(d/m);##Teeth of wheel D\n",
+ "Tb=Td/4.;##Teeth of wheel B\n",
+ "Tb1=math.ceil(Tb);##Teeth of wheel B\n",
+ "Td1=4.*Tb1;##Teeth of wheel D\n",
+ "Tc1=(Td1-Tb1)/2.;##Teeth of wheel C\n",
+ "d1=m*Td1;##Pitch circle diameter in mm\n",
+ "\n",
+ "##Output\n",
+ "print'%s %.1f %s %.1f %s %.1f %s%.1f %s '%('Teeth of wheel B is ',Tb1,' ' 'Teeth of wheel C is ',Tc1,' ' 'Teeth of wheel D is ',Td1,' '' Exact pitch circle diameter is ',d1,' mm')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Teeth of wheel B is 14.0 Teeth of wheel C is 21.0 Teeth of wheel D is 56.0 Exact pitch circle diameter is 224.0 mm \n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex15-pg147"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##Chapter-4, Illustration 15, Page 147\n",
+ "##Title: Gears and Gear Drivers\n",
+ "##=============================================================================\n",
+ "import math\n",
+ "\n",
+ "##Input data\n",
+ "Ta=100.## no of teeth on gear A\n",
+ "Tc=101.## no of teeth on gear C\n",
+ "Td=99.## no of teeth on gear D\n",
+ "Tp=20.## no of teeth on planet gear\n",
+ "y=1.## from table 4.9(arm B makes one revolution)\n",
+ "x=-y## as gear is fixed\n",
+ "\n",
+ "##Calculations\n",
+ "Nc=(Ta*x)/Tc+y## Revolution of gear C \n",
+ "Nd=(Ta*x)/Td+y## Revolution of gear D\n",
+ "\n",
+ "##Output\n",
+ "print'%s %.4f %s %.4f %s '%('Revolution of gear C =',Nc,'' ' Revolution of gear D = ',Nd,'')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Revolution of gear C = 0.0099 Revolution of gear D = -0.0101 \n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex16-pg148"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##Chapter-4, Illustration 16, Page 148\n",
+ "##Title: Gears and Gear Drivers\n",
+ "##=============================================================================\n",
+ "import math\n",
+ "\n",
+ "##Input data\n",
+ "Ta=12.## no of teeth on gear A\n",
+ "Tb=60.## no of teeth on gear B\n",
+ "N=1000.## speed of propeller shaft in rpm\n",
+ "Nc=210.## speed of gear C in rpm\n",
+ "\n",
+ "##Calculations\n",
+ "Nb=(Ta*N)/Tb## speed of gear B in rpm\n",
+ "x=(Nb-Nc)\n",
+ "Nd=Nb+x## speed of road wheel driven by D\n",
+ "\n",
+ "##Output\n",
+ "print'%s %.1f %s'%('speed of road wheel driven by D= ',Nd,' rpm')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "speed of road wheel driven by D= 190.0 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex17-pg148"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##Chapter-4, Illustration 17, Page 148\n",
+ "##Title: Gears and Gear Drivers\n",
+ "##=============================================================================\n",
+ "import math\n",
+ "import numpy\n",
+ "from numpy.linalg import inv\n",
+ "##Input data\n",
+ "Ta=20.## no of teeth on pinion A\n",
+ "Tb=25.## no of teeth on wheel B\n",
+ "Tc=50.## no of teeth on gear C\n",
+ "Td=60.## no of teeth on gear D\n",
+ "Te=60.## no of teeth on gear E\n",
+ "Na=200.## SPEED of the gear A\n",
+ "Nd=100.## speed of the gear D\n",
+ "\n",
+ "##calculations\n",
+ "##(i)\n",
+ "##(5/6)x+y=0\n",
+ "##(5/4)x+y=200\n",
+ "A1=([[Tc/Td, 1],[Tb/Ta, 1]])##Coefficient matrix\n",
+ "B1=([[0],[Na]]) ##Constant matrix\n",
+ "X1=numpy.dot(inv(A1),B1)##Variable matrix\n",
+ "Ne1=X1[1]-(Tc/Td)*X1[0]## \n",
+ "T1=(-Ne1/Na)## ratio of torques when D is fixed\n",
+ "##(ii)\n",
+ "##(5/4)x+y=200\n",
+ "##(5/6)x+y=100\n",
+ "A2=([[Tc/Td, 1],[Tb/Ta, 1]])##Coefficient matrix\n",
+ "B2=([[Nd],[Na]])##Constant matrix\n",
+ "X2=numpy.dot(inv(A2),B2)##Variable matrix\n",
+ "Ne2=X2[1]-(Tc/Td)*X2[0]\n",
+ "T2=(-Ne2/Na)## ratio of torques when D ratates at 100 rpm\n",
+ "\n",
+ "##Output\n",
+ "print'%s %.2f %s %.2f %s %.2f %s %.2f %s'%('speed of E= ',Ne1,' rpm in clockwise direction' and 'speed of E in 2nd case(when D rotates at 100 rpm)= ',Ne2,' rpm in clockwise direction' and 'ratio of torques when D is fixed= ',T1,' ' 'ratio of torques when D ratates at 100 rpm= ',T2,'')\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "speed of E= -800.00 speed of E in 2nd case(when D rotates at 100 rpm)= -300.00 ratio of torques when D is fixed= 4.00 ratio of torques when D ratates at 100 rpm= 1.50 \n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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