{
"metadata": {
"name": "",
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 6 : Velocity in Mechanisms(Instantaneous Centre Method)"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.1 Page No : 126"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"# Variables:\n",
"NAB = 100. \t\t\t#rpm\n",
"AB = 300./1000\n",
"BC = 360./1000\n",
"CD = BC \t\t\t#m\n",
"\n",
"#Solution:\n",
"#Refer Fig. 6.9\n",
"#Calculating the angular speed of link AB\n",
"omegaAB = 2*math.pi*NAB/60 \t\t\t#rad/s\n",
"#Calculating the velocity of point B on link AB\n",
"vB = omegaAB*AB \t\t\t#m/s\n",
"#Calculating the angular velocity of link BC\n",
"#By measurement from instantaneous centre diagram Fig. 6.10\n",
"\n",
"I13B = 500./1000 \t\t\t#m\n",
"omegaBC = vB/I13B \t\t\t#rad/s\n",
"\n",
"#Results:\n",
"print \" The angular velocity of the link BC omegaBC = %.3f rad/s.\"%(omegaBC)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" The angular velocity of the link BC omegaBC = 6.283 rad/s.\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.2 Page No : 128"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"# Variables:\n",
"omegaOB = 10. \t\t\t#rad/s\n",
"OB = 100/1000. \t\t\t#m\n",
"\n",
"#Solution:\n",
"#Refer Fig. 6.12\n",
"#Calculating the velocity of the crank OB\n",
"vOB = omegaOB*OB \t\t\t#m/s\n",
"vB = vOB\n",
"#By measurement from the instantaneous cemtre diagram Fig. 6.13\n",
"\n",
"I13A = 460./1000\n",
"I13B = 560./1000 \t\t\t#m\n",
"#Calculating the velocity of slider A\n",
"vA = vB/I13B*I13A\n",
"#Calculating the angular velocity of the connecting rod AB\n",
"omegaAB = vB/I13B \t\t\t#rad/s\n",
"\n",
"#Results:\n",
"print \"The velocity of slider A vA = %.2f m/s.\"%(vA)\n",
"print \"The angular velocity of connecting rod AB omegaAB = %.2f rad/s.\"%(omegaAB)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The velocity of slider A vA = 0.82 m/s.\n",
"The angular velocity of connecting rod AB omegaAB = 1.79 rad/s.\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.3 Page No : 130"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"# Variables:\n",
"NOA = 120. \t\t\t#rpm\n",
"OA = 200./1000 \t\t\t#m/s\n",
"\n",
"#Results:\n",
"#Refer Fig. 6.15\n",
"#Calculating the angular velocity of the crank OA\n",
"omegaOA = 2*math.pi*NOA/60 \t\t\t#rad/s\n",
"#Calculating the velocity of crank OA\n",
"vOA = omegaOA*OA \t\t\t#m/s\n",
"vA = vOA\n",
"#By measurement from the instantaneous cemtre diagram Fig. 6.16\n",
"\n",
"I13A = 840./1000\n",
"I13B = 1070./1000\n",
"I14B = 400./1000\n",
"I14C = 200./1000\n",
"I15C = 740./1000\n",
"I15D = 500./1000 \t\t\t#m\n",
"\n",
"#Calculating the velocity of point B\n",
"vB = vA/I13A*I13B \t\t\t#m/s\n",
"#Calculating the velocity of point C\n",
"vC = vB/I14B*I14C \t\t\t#m/s\n",
"#Calculating the velocity of point B\n",
"vD = vC/I15C*I15D \t\t\t#m/s\n",
"#Calculating the angular velocity of the link AB\n",
"omegaAB = vA/I13A \t\t\t#rad/s\n",
"#Calculating the angular velocity of the link BC\n",
"omegaBC = vB/I14B \t\t\t#rad/s\n",
"#Calculating the angular velocity of the link CD\n",
"omegaCD = vC/I15C \t\t\t#rad/s\n",
"\n",
"#Results:\n",
"print \" The velocity of point B vB = %.1f m/s.\"%(vB)\n",
"print \" The velocity of point C vC = %.1f m/s.\"%(vC)\n",
"print \" The velocity of point D vD = %.2f m/s.\"%(vD)\n",
"print \" The angular velocity of the link AB omegaAB = %.2f rad/s.\"%(omegaAB)\n",
"print \" The angular velocity of the link BC omegaBC = %d rad/s.\"%(omegaBC)\n",
"print \" The angular velocity of the link CD omegaCD = %.2f rad/s.\"%(omegaCD)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" The velocity of point B vB = 3.2 m/s.\n",
" The velocity of point C vC = 1.6 m/s.\n",
" The velocity of point D vD = 1.08 m/s.\n",
" The angular velocity of the link AB omegaAB = 2.99 rad/s.\n",
" The angular velocity of the link BC omegaBC = 8 rad/s.\n",
" The angular velocity of the link CD omegaCD = 2.16 rad/s.\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.4 Page No : 133"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"# Variables:\n",
"omegaO1A = 100. \t\t\t#rad/s\n",
"O1A = 100/1000. \t\t\t#m\n",
"\n",
"#Solution:\n",
"#Refer Fig. 6.18\n",
"#Calculating the linear velocity of crank O1A\n",
"vO1A = omegaO1A*O1A \t\t\t#m/s\n",
"vA = vO1A\n",
"#By measurement from the instantaneous cemtre diagram Fig. 6.19\n",
"I13A = 910./1000\n",
"I13B = 820./1000\n",
"I15B = 130./1000\n",
"I15D = 50./1000\n",
"I16D = 200./1000\n",
"I16E = 400./1000 \t\t\t#m\n",
"#Calculating the velocity of point B\n",
"vB = vA/I13A*I13B \t\t\t#m/s\n",
"#Calculating the velocity of point D\n",
"vD = vB/I15B*I15D \t\t\t#m/s\n",
"#Calculating the velocity of point E\n",
"vE = vD/I16D*I16E \t\t\t#m/s\n",
"\n",
"#Results:\n",
"print \" The velocity of point B vB = %.2f m/s.\"%(vB)\n",
"print \" The velocity of point D vD = %.2f m/s.\"%(vD)\n",
"print \" The velocity of point E vE = %.2f m/s.\"%(vE)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" The velocity of point B vB = 9.01 m/s.\n",
" The velocity of point D vD = 3.47 m/s.\n",
" The velocity of point E vE = 6.93 m/s.\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.5 Page No : 135"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"# Variables:\n",
"NO1A = 400. \t\t\t#rpm\n",
"O1A = 16./1000 \t\t\t#m\n",
"\n",
"#Solution:\n",
"#Refer Fig. 6.21\n",
"#Calculating the angular velocity of the crank O1A\n",
"omegaO1A = 2*math.pi*NO1A/60 \t\t\t#rad/s\n",
"#Calculating the linear velocity of the crank O1A\n",
"vO1A = omegaO1A*O1A \t\t\t#m/s\n",
"vA = vO1A\n",
"#By measurement from the instantaneous cemtre diagram Fig. 6.22\n",
"I13A = 41./1000\n",
"I13B = 50./1000\n",
"I14B = 23./1000\n",
"I14C = 28./1000\n",
"I15C = 65./1000\n",
"I15D = 62./1000 \t\t\t#m\n",
"#Calculating the velocity of point B\n",
"vB = vA/I13A*I13B \t\t\t#m/s\n",
"#Calculating the velocity of point C\n",
"vC = vB/I14B*I14C \t\t\t#m/s\n",
"#Calculating the velocity of of the needle at D\n",
"vD = vC/I15C*I15D \t\t\t#m/s\n",
"\n",
"#Results:\n",
"print \"The velocity of the needle at D vD = %.2f m/s.\"%(vD)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The velocity of the needle at D vD = 0.95 m/s.\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.6 Page No : 137"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"# Variables:\n",
"NOA = 120. \t\t\t#rpm\n",
"#Solution:\n",
"#Refer Fig. 6.24\n",
"#Calculating the angular speed of crank OA\n",
"omegaOA = 2*math.pi*NOA/60 \t\t\t#rad/s\n",
"#By measurement from the instantaneous cemtre diagram Fig. 6.25\n",
"I12I26 = 65./1000 \t\t\t#m\n",
"#Calculating the velocity of the ram\n",
"vD = omegaOA*I12I26 \t\t\t#m/s\n",
"\n",
"#Results:\n",
"print \" The velocity of ram, vD = %.3f m/s.\"%(vD)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" The velocity of ram, vD = 0.817 m/s.\n"
]
}
],
"prompt_number": 1
}
],
"metadata": {}
}
]
}