path: root/The_Theory_of_Machines_by_T._Bevan/ch3.ipynb

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   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 3: Velocity and Acceleration"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3, Page 90"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "OC=6.#in\n",
      "CP=24#in\n",
      "N=240#rpm\n",
      "X=45#degrees\n",
      "XP=19#in\n",
      "XC=6#in\n",
      "YP=32#in\n",
      "YC=9#in\n",
      "#Scalling off lenghts from fig , we have\n",
      "CI=2.77#in\n",
      "PI=2.33#in\n",
      "XI=2.33#in\n",
      "YI=3.48#in\n",
      "\n",
      "#Calculations\n",
      "Vc=((math.pi*N)/30)*(OC/12)#changing OP into feets\n",
      "print \"\\nw=%.2f ft/s\"%Vc\n",
      "#w=Vc/CI=Vp/PI=Vx/XI=Vy/YI\n",
      "w=Vc/CI\n",
      "Vp=w*PI\n",
      "Vx=w*XI\n",
      "Vy=w*YI\n",
      "\n",
      "#Results\n",
      "print \"velocity of points P, X and Y are %.2f ft/s, %.2f ft/s and %.1f ft/s respectively\"%(Vp,Vx,Vy)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "w=12.57 ft/s\n",
        "velocity of points P, X and Y are 10.57 ft/s, 10.57 ft/s and 15.8 ft/s respectively\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4, Page 93"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "OC=9.#inches\n",
      "CP=36.#inches\n",
      "XC=12#inches\n",
      "X=40#degrees\n",
      "CM=6.98#from the scaled figure\n",
      "N1=240#rpm\n",
      "N2=240#rpm (instantaneous) with angular aceleration (ao) 100 rad/s^2\n",
      "ao=100 #rad/s^2\n",
      "\n",
      "#Calculations&Results\n",
      "w=(math.pi*N1/30)\n",
      "a=w**2*(OC/12)\n",
      "print \"Centripetal acceleration = %.f ft/s^2\"%a\n",
      "Wr=w*CM/CP#rad/s^2\n",
      "f1=Wr**2*(CP/12)#centripetal component of acceleration of p realtive to C\n",
      "#Solution a)\n",
      "#given from fig 58(a)\n",
      "tp=296 \n",
      "cp=306\n",
      "ox=422\n",
      "f2=tp #Tangential component of acceleration of p realtive to C\n",
      "f3=cp#acceleration of p realtive to C\n",
      "fx=ox#acce;eration of x\n",
      "ar=f2/(CP/12)#angular acceleration of rod\n",
      "print \"\\nCase a) \\nap= %.f ft/s^2,\\nax= %.f ft/s^2 and\\nar= %.1f rad/s^2\"%(f3,fx,ar)\n",
      "\n",
      "#Solution b)\n",
      "#given from fig 58(b)\n",
      "oc1=474\n",
      "oc=480\n",
      "pt=238.\n",
      "pc=246\n",
      "xo=452\n",
      "f4=pt#Tangential component of acceleration of p realtive to C\n",
      "f5=pc#acceleration of p realtive to C\n",
      "Ar=f4/(CP/12)#angular acceleration of rod\n",
      "f6=ao*(OC/12)#tangential component of acceleration realtive to C\n",
      "Fx=xo#acce;eration of x\n",
      "print \"\\nCase b) \\nap= %.f ft/s^2,\\nax= %.f ft/s^2 and\\nar= %.1f rad/s^2\"%(f4,Fx,Ar)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Centripetal acceleration = 474 ft/s^2\n",
        "\n",
        "Case a) \n",
        "ap= 306 ft/s^2,\n",
        "ax= 422 ft/s^2 and\n",
        "ar= 98.7 rad/s^2\n",
        "\n",
        "Case b) \n",
        "ap= 238 ft/s^2,\n",
        "ax= 452 ft/s^2 and\n",
        "ar= 79.3 rad/s^2\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5, Page 98"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "AB=2.5#inches\n",
      "BC=7.#inches\n",
      "CD=4.5#inches\n",
      "DA=8#inches\n",
      "N=100#rpm\n",
      "X=60#degrees\n",
      "\n",
      "#Calculations\n",
      "w=(math.pi*N)/30\n",
      "#From triangle ABM we have \n",
      "AM=0.14#feet\n",
      "BM=0.12#feet\n",
      "Vb=w*AB/12#ft/s\n",
      "Vc=w*AM#ft/s\n",
      "Vcb=w*BM#ft/s\n",
      "fb=w**2*(AB/12)#ft/s^2\n",
      "bt=Vcb**2/(BC/12)#ft/s^2\n",
      "os=Vc**2/(CD/12)#ft/s^2\n",
      "#By measurement from acceleration diagram\n",
      "sc=19.1#ft/s^2\n",
      "tq=14.4#ft/s^2\n",
      "Acd=sc/(CD/12)\n",
      "Abc=tq/(BC/12)\n",
      "\n",
      "#Results\n",
      "print \"Vb=%.2f ft/s \\nVc=%.2f ft/s\\nVcb=%.2f ft/s\\nfb=%.2f ft/s^2\\nbt=%.2f ft/s^2\\nos=%.2f ft/s^2\"%(Vb,Vc,Vcb,fb,bt,os)\n",
      "print \"Angular acceleration of CD(counter-clockwise)= %.1f rad/s^2\"%Acd\n",
      "print \"Angular acceleration of BC(counter-clockwise)= %.1f rad/s^2\"%Abc"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Vb=2.18 ft/s \n",
        "Vc=1.47 ft/s\n",
        "Vcb=1.26 ft/s\n",
        "fb=22.85 ft/s^2\n",
        "bt=2.71 ft/s^2\n",
        "os=5.73 ft/s^2\n",
        "Angular acceleration of CD(counter-clockwise)= 50.9 rad/s^2\n",
        "Angular acceleration of BC(counter-clockwise)= 24.7 rad/s^2\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6, Page 106"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Variable declaration\n",
      "OP=2#ft\n",
      "f=4#ft/s^2\n",
      "w=2 #rad/s (anticlockwise)\n",
      "a=5 #rad/s^2 (anticlockwise)\n",
      "Vpq=3 #ft/s\n",
      "\n",
      "#Calculations\n",
      "r=OP\n",
      "os=w**2*r#component 1\n",
      "sq=a*r#component 2\n",
      "qt=f#component 3\n",
      "tp=2*w*Vpq#component 4\n",
      "Aqo=(os**2+sq**2)**1./2#vector addition of component(a,b)\n",
      "Apq=(qt**2+tp**2)**1./2#vector addition of component(c,d)\n",
      "#Apo=Apq+Aqo (vector addition)\n",
      "Apo=((os-qt)**2+(sq+tp)**2)**(1./2)\n",
      "\n",
      "#Result\n",
      "print \"Acceleration of P realative to fixed point O is %.1f ft/s^2\"%Apo"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Acceleration of P realative to fixed point O is 22.4 ft/s^2\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7, Page 110"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "OC=8#inches\n",
      "CP=4#inches\n",
      "N=60#inches\n",
      "ON=15#inches\n",
      "RN=6.#inches\n",
      "X=120#degrees\n",
      "OP=10.6\n",
      "OQ=OP\n",
      "\n",
      "#Calculations\n",
      "#from fig 65(a)\n",
      "Vq=1.56#ft/s\n",
      "Vrn=0.74#ft/s\n",
      "#from fig 65(b)\n",
      "ftq=3.74#ft/s^2\n",
      "ftrn=2.03#ft/s^2\n",
      "w1=(math.pi*N)/30\n",
      "w=Vq/(OQ/12)\n",
      "wrn=Vrn/(RN/12)\n",
      "a=ftq/(OP/12)#Angular acceleration of ON\n",
      "a1=ftrn/(RN/12)#angular acceleration of RN\n",
      "\n",
      "#Results\n",
      "print \"W=%.2f rad/s\\nWrn=%.2f rad/s\"%(w,wrn)\n",
      "print \"Angular acceleration of ON= %.2f rad/s^2\\nAngular acceleration of RN=%.2f rad/s^2\"%(a,a1)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "W=1.77 rad/s\n",
        "Wrn=1.48 rad/s\n",
        "Angular acceleration of ON= 4.23 rad/s^2\n",
        "Angular acceleration of RN=4.06 rad/s^2\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8, Page 112"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "OC=3#inches\n",
      "CP=9.#inches\n",
      "N=1200 #rpm (clockwise)\n",
      "X=55 #degrees\n",
      "#from the figure 66\n",
      "OP=10.35#inches\n",
      "PM=10.74#inches\n",
      "OM=2.95#inches\n",
      "PC=12.84#inches\n",
      "PR=PC\n",
      "RV=2.49#inches\n",
      "UV=1.29#inches\n",
      "OU=5.90#inches\n",
      "PV=13.05#inches\n",
      "OV=6.06#inches\n",
      "OQ=OP\n",
      "\n",
      "#Calculations\n",
      "w=(math.pi*N)/30#the angular velocity of the cylinder line OP\n",
      "Vq=w*(OP/12)#the velocity of Q\n",
      "Vp=w*(PM/12)#The velocity of P\n",
      "w1=Vp/(CP/12)#The angular velocity of CP\n",
      "Vpq=w*(OM/12)#the velocity of sliding of the piston along the cylinder\n",
      "fq=w**2*(OQ/12)#the centripetal acceleration of Q\n",
      "Acp=w1**2*(PC/12)#The centripetal component of acceleration of P\n",
      "Atp=w**2*(RV/12)#The tangential component of acceleration of P\n",
      "acp=Atp/(CP/12)# The angular acceleration of the connecting rod CP\n",
      "f=w**2*(UV/12)#component c\n",
      "d=2*w*Vpq#component d\n",
      "Ap=w**2*PV#the resultant acceleration of P\n",
      "Apq=w**2*OV#the acceleration of P realative to Q\n",
      "\n",
      "#Results\n",
      "print \"The velocity and acceleration of the piston along the cylinder are %.1f ft/s and %.f ft/s^2 respectively\"\\\n",
      "      \"\\nThe angular velocity and angular acceleration of the connecting rod cp are %.1f rad/s and %.f rad/s^2 respectively\"\\\n",
      "      \"\\nAnd the coriolis component of the acceleration of P is %.f ft/s^2\"%(Vpq,f,w1,acp,d)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The velocity and acceleration of the piston along the cylinder are 30.9 ft/s and 1698 ft/s^2 respectively\n",
        "The angular velocity and angular acceleration of the connecting rod cp are 150.0 rad/s and 4369 rad/s^2 respectively\n",
        "And the coriolis component of the acceleration of P is 7764 ft/s^2\n"
       ]
      }
     ],
     "prompt_number": 9
    }
   ],
   "metadata": {}
  }
 ]
}