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{
"metadata": {
"name": "",
"signature": "sha256:0872fbc3ae91821d4330e3facbf2559c866bc6b64416332df388f5fee66480e0"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 9 : Mechanisms with Lower Pairs"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.1 Page No : 245"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"# Variables:\n",
"c = 1.2\n",
"b = 2.7 \t\t\t#m\n",
"\n",
"#Solution:\n",
"#Calculating the inclination of the track arm to the longitudinal axis\n",
"alpha = math.tan(c/(2*b))*180/math.pi \t\t\t#degrees\n",
"\n",
"#Results:\n",
"print \" Inclination of the track arm to the longitudinal axis, alpha = %.1f degrees.\"%(alpha)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" Inclination of the track arm to the longitudinal axis, alpha = 12.9 degrees.\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.2 Page No : 251\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"# variables\n",
"a = 180. - 160. # degrees\n",
"N = 1500. # r.p.m.; \n",
"m = 12. # kg ; \n",
"k = 0.1 # m\n",
"\n",
"# calculations\n",
"w = round(2*math.pi*N/60)\n",
"I = m*k**2\n",
"cos2theta = 2*math.sin(math.radians(a))**2/(2 - math.sin(math.radians(a))**2)\n",
"theta = math.degrees(math.acos(cos2theta))/2\n",
"dw1bydt = w**2*math.cos(math.radians(a)) * math.sin(math.radians(2*theta)) * math.sin(math.radians(a))**2 / ( 1 - math.cos(math.radians(theta))**2 * math.sin(math.radians(a))**2)**2\n",
"max_t = I * dw1bydt\n",
"\n",
"# results\n",
"print \"Maximum angular acceleration of the driven shaft : %.f rad/s**2\"%dw1bydt\n",
"print \"maximum torque required : %.f N-m\"%max_t\n",
"\n",
"\n",
"# answers are different because of rounding error. please check using calculator."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Maximum angular acceleration of the driven shaft : 3080 rad/s**2\n",
"maximum torque required : 370 N-m\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.3 Page No : 252"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"# Variables:\n",
"alpha = 18*math.pi/180 \t\t\t#radians\n",
"\n",
"#Solution:\n",
"#Maximum velocity is possible when\n",
"theta1 = 0.\n",
"theta2 = 180. \t\t\t#degrees\n",
"\n",
"#Calculating the angle turned by the driving shaft when the velocity ratio is unity\n",
"theta3 = math.cos(math.sqrt((1-math.cos(alpha))/(math.sin(alpha)**2)))*180/math.pi \t\t\t#degrees\n",
"theta4 = 180-theta3 \t\t\t#degrees\n",
"\n",
"#Results:\n",
"print \" Angle turned by the driving shaft when the velocity ratio is maximum, theta = %d degrees\\\n",
" or %d degrees.\"%(theta1,theta2)\n",
"print \" Angle turned by the driving shaft when the velocity ratio is unity, theta = %.1f degrees or\\\n",
" %.1f degrees.\"%(theta3,theta4)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" Angle turned by the driving shaft when the velocity ratio is maximum, theta = 0 degrees or 180 degrees.\n",
" Angle turned by the driving shaft when the velocity ratio is unity, theta = 43.2 degrees or 136.8 degrees.\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.4 Page No : 252"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"# Variables:\n",
"N = 500. \t\t\t#rpm\n",
"\n",
"#Solution:\n",
"#Calculating the angular velocity of the driving shaft\n",
"omega = 2*math.pi*N/60.0 \t\t\t#rad/s\n",
"#Calculating the total fluctuation of speed of the driven shaft\n",
"q = 12./100*omega \t\t\t#rad/s\n",
"#Calculating the greatest permissible angle between the centre lines of the shafts\n",
"#alpha = math.cos((-(q/omega)+math.sqrt(0.12**2+4))/2.0)*180/math.pi\t\t\t#degrees\n",
"cosalpha =((-(q/omega)+math.sqrt(0.12**2+4))/2.0)\t\t\t#degrees\n",
"alpha = math.degrees(math.acos(cosalpha))\n",
"\n",
"#Results:\n",
"print \" Greatest permissible angle between the centre lines of the shafts, alpha = %.2f degrees.\"%(alpha)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" Greatest permissible angle between the centre lines of the shafts, alpha = 19.64 degrees.\n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.5 Page No : 252"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"# Variables:\n",
"N = 1200.\n",
"q = 100. \t\t\t#rpm\n",
"#Solution:\n",
"#Calculating the greatest permissible angle between the centre lines of the shafts\n",
"cosalpha = ((-(100./1200)+math.sqrt(0.083**2+4))/2)\n",
"alpha = math.degrees(math.acos(cosalpha)) #degrees\n",
"#Calculating the maximum speed of the driven shaft\n",
"N1max = N/cosalpha \t\t\t#rpm\n",
"#Calculating the minimum speed of the driven shaft\n",
"N1min = N*cosalpha\t\t\t#rpm\n",
"\n",
"#Results:\n",
"print \" Greatest permissible angle between the centre lines of the shafts, alpha = %.1f degrees.\"%(alpha)\n",
"print \" Maximum speed of the driven shaft, N1max = %d rpm.\"%(N1max)\n",
"print \" Minimum speed of the driven shaft, N1min = %d rpm.\"%(N1min)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" Greatest permissible angle between the centre lines of the shafts, alpha = 16.4 degrees.\n",
" Maximum speed of the driven shaft, N1max = 1251 rpm.\n",
" Minimum speed of the driven shaft, N1min = 1151 rpm.\n"
]
}
],
"prompt_number": 24
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.6 page no : 253"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"# variables\n",
"N = 240. # r.p.m \n",
"w = 2 * math.pi * 240./60 #rad/s \n",
"alpha = 20 \n",
"m = 55. # kg ;\n",
"k = .150 \n",
"mm = 0.15 #m ; \n",
"T1 = 200. #N-m ; \n",
"theta = 45. # \u00b0 ; \n",
"q = 24. # r.p.m.\n",
"\n",
"# calculations\n",
"I = round(m * k**2,2) \n",
"dw1bydt = round(-(w**2)*math.cos(math.radians(alpha))*math.sin(math.radians(2*theta))*math.sin(math.radians(alpha))**2 / (1- math.cos(math.radians(theta))**2 * math.sin(math.radians(alpha))**2)**2,2)\n",
"T2 = I * dw1bydt\n",
"T = T1 + T2\n",
"Tdash = T*math.cos(math.radians(alpha))/(1-math.cos(math.radians(theta))**2 * math.sin(math.radians(alpha))**2)\n",
"cosapha = (-0.1+math.sqrt((0.1**2)+4))/2\n",
"alpha = math.degrees(math.acos(cosapha))\n",
"\n",
"# result\n",
"print \"T' = %.1f N-m\"%Tdash\n",
"print \"Alpha a = %.1f degrees\"%alpha\n",
"\n",
"# rounding off error"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"T' = 102.7 N-m\n",
"Alpha a = 18.0 degrees\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.7 Page No : 254"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"# Variables:\n",
"alpha = 20. \t\t\t#degrees\n",
"NA = 500. \t\t\t#rpm\n",
"\n",
"#Solution:\n",
"#Calculating the maximum speed of the intermediate shaft\n",
"NBmax = NA/math.cos(math.radians(alpha)) \t\t\t#rpm\n",
"#Calculating the minimum speed of the intermediate shaft\n",
"NBmin = NA*math.cos(math.radians(alpha)) \t\t\t#rpm\n",
"#Calculating the maximum speed of the driven shaft\n",
"NCmax = NBmax/math.cos(math.radians(alpha)) \t\t\t#rpm\n",
"#Calculating the minimum speed of the driven shaft\n",
"NCmin = NBmin*math.cos(math.radians(alpha)) \t\t\t#rpm\n",
"\n",
"#Results:\n",
"print \" Maximum speed of the intermediate shaft( NBmax) = %.1f rad/s.\"%(NBmax)\n",
"print \" Minimum speed of the intermediate shaft( NBmin) = %.2f rad/s.\"%(NBmin)\n",
"print \" Maximum speed of the driven shaft( NCmax) = %.2f rad/s.\"%(NCmax)\n",
"print \" Minimum speed of the driven shaft( NCmin) = %.1f rad/s.\"%(NCmin)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" Maximum speed of the intermediate shaft( NBmax) = 532.1 rad/s.\n",
" Minimum speed of the intermediate shaft( NBmin) = 469.85 rad/s.\n",
" Maximum speed of the driven shaft( NCmax) = 566.24 rad/s.\n",
" Minimum speed of the driven shaft( NCmin) = 441.5 rad/s.\n"
]
}
],
"prompt_number": 27
}
],
"metadata": {}
}
]
}
|
