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"source": [
"Chapter 4: Mechanisms with Lower Pairs"
]
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{
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"level": 2,
"metadata": {},
"source": [
"Example 1, Page 138"
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"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"rpm=1000\n",
"angle=20#degree\n",
"\n",
"#Calculations&Results\n",
"ang=(angle*math.pi)/180\n",
"w=2*math.pi*rpm/60\n",
"print \"The angular velocity of the driving shaft is %.1f rad/s\"%w\n",
"#maximum value of w1=w/cos(angle) and minimum value w2=w*cos(angle)\n",
"w1=w/math.cos(ang)\n",
"w2=w*math.cos(ang)\n",
"print \"\\nExtreme angular velocities :-\"\n",
"print \"maximum value of angular velocity w1=%.1f rad/s \\nminimum value of angular velocity w2=%.1f rad/s\"%(w1,w2)\n",
"#using equation 4.11, cos(2x)=(2*sin(angle)**2)/(2-sin(angle)**2)\n",
"x=math.acos((2*math.sin(ang)**2)/(2-math.sin(ang)**2))*180/(math.pi)\n",
"y=360-x#for cosine inverse, angle and 360-angle are same and must be considered\n",
"x1=x/2\n",
"y1=y/2\n",
"print \"The acceleration of driven shaft is a maximum when theta =%.2f or %.2f degrees\"%(x1,y1)\n",
"amax=(w**2*math.cos(ang)*(math.sin(ang)**2)*math.sin(x*math.pi/180))/((1-((math.cos(x1*math.pi/180)**2)*(math.sin(ang)**2)))**2)#maximum angular acceleration, numerically\n",
"print \"Maximum angular acceleration is %.f rad/s^2\"%amax\n"
],
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{
"output_type": "stream",
"stream": "stdout",
"text": [
"The angular velocity of the driving shaft is 104.7 rad/s\n",
"\n",
"Extreme angular velocities :-\n",
"maximum value of angular velocity w1=111.4 rad/s \n",
"minimum value of angular velocity w2=98.4 rad/s\n",
"The acceleration of driven shaft is a maximum when theta =41.43 or 138.57 degrees\n",
"Maximum angular acceleration is 1370 rad/s^2\n"
]
}
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|
