MIT2_007s09_sol_exam02

# MIT2_007s09_sol_exam02 - MIT OpenCourseWare...

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MIT OpenCourseWare http://ocw.mit.edu 2.007 Design and Manufacturing I Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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Page 1 of 9 NAME: ____ ”Solution” _______________________ 2.007 – Design and Manufacturing I Exam on Gears, Springs, Sensors, Programming, Drawing, etc. You have 1.5 hours to answer the following 11 questions. Please show your work and explain your resoning to the extent possible given the allotted time. Point allocations (out of 100 total) are listed for each question. 1. (5 points) Define the term “conjugate action.” Briefly (using one or two sentences) explain its significance for design of power transmission systems. “Conjugate action” is the property of a transmission that delivers constant rate of rotation of the output shaft if rate of rotation of the input shaft is also constant. It is important to note that this not not simply valuable in and of itself, but is also a requirement for smooth transmission of power. It reduces vibration, noise, and premature failure due to fatigue of the machine elements . 2. (10 points) You fill a one liter container with air at 60 psi gauge pressure and plan to use it as a source of power for a machine. The air in the bottle is at thermal equilibrium with the air in the room at 20 degrees Centigrade. Estimate (within ±10% is fine) the force applied if a valve is opened connecting the reservoir of air to a piston with a one inch internal diameter and a two inch stroke assuming the piston extends its full stroke in about 2 seconds. Dislacement of the piston 4 1 in ( ) 2 2 in 0.026L Since the piston is only 2% of the volume of the reservoir and we only need an estimate with 10%, it’s good enough to just multiply the original gauge pressure times the area of the face. 4 1 in ( ) 2 60 psi 209.618N 4 1 in ( ) 2 60 psi 47.124lbf
Page 2 of 9 3. (15 points) Sketch the mechanism in a position that places it in static equilibrium. Base your drawing on an estimate of the displacements to within ± 20%. Assume the joints have negligable friction and that the pulleys and links have negiligable weight. The 10 cm radius pulley is fixed with respect to the table and cannot rotate. You can assume the toothed belt will not slip. The extension springs are at their natural length. You may assume that the extension springs apply tension with the spring constant indicated but cannot apply any appreciable force in compression (they buckle). Briefly justify your solution with a couple equations, schematic diagrams, and/or a few sentences of explanation. Be sure to indicate clearly: Whether you think the 3cm pulley rotates clockwise or counterclockwise Whether you think the arm connecting the pulleys rotates clockwise or counterclockwise Whether you think the arm 1 kg mass is higher or lower at equilibrium than at the starting position Consider a modest clockwise rotation of the arm, say 0.1 radian (6 deg). To maintain the

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MIT2_007s09_sol_exam02 - MIT OpenCourseWare...

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