path: root/Theory_Of_Machines_by__B._K._Sarkar/Chapter4.ipynb

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  {
   "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": {}
  }
 ]
}